Oxygen-related defects in Carbon-rich Solar Silicon studied by Fourier Transform Infrared

UNIVERSITY OF OSLODepartment of physics

Master’s Thesis

Oxygen-related defects in Carbon-rich SolarSilicon studied by Fourier Transform Infrared

Spectroscopy

Mette Fjelltveit Rye-Larsen

A thesis submitted in partial fulfilment of the requirementsfor the degree of MSc

in

Materials, Energy and Nanotechnology

May, 2016

Abstract

The study of point defect complexes and thermal double donors (TDDs) in Silicon, has beenof great interest in the field of semiconductor physics for several decades. However, due to agrowing environmental awareness and increasing demand for high-efficiency and low-cost solarcells, the research activity in this field is once again flourishing. In this work, n-type Cz-Siliconwith high and low carbon concentrations have been sequentially annealed in the temperaturerange of 450-550°C, and investigated using FTIR spectroscopy. MeV electron irradiation hasfacilitated a detailed study of vacancy-oxygen (VOn) and carbon-related complexes. Theirformation and evolution during thermal treatments have been studied, and their relation toTDD formation has been addressed.

TDDs were found to form at 450 and 500°C, while being unstable at 550°C. FPP resistivitymeasurements provided an estimate for TDD concentrations after thermal treatments. Thepresence of high carbon concentrations were found to strongly inhibit TDD generation. Cz-Siwith carbon concentrations of 2.5×1017cm−3 were found to reduce the final TDD concentrationby factors of 7 and 30 when annealing at 450 and 500°C, respectively, relative to carbon-leansamples. The obtained results suggest that carbon specifically impedes the formation ofTDD3. Formation kinetics confirmed a sequential formation of the larger CsO3i complexes byprolonged annealing of the carbon-rich samples at the highest temperatures, while the smallerCsOi centres became unstable. The direct involvement of VOn centres in TDD formation wasruled out. The presence of both VOn and CsOn defects were found to consume oxygen and actas traps for migrating oxygen atoms during annealing, effectively reducing TDD formation.PL measurements have been correlated with IR measurements in terms of carbon-complexesand formation of TDDs. Zero-phonon and phonon replica luminescence lines of TDDs andirradiation induced carbon-complexes have been identified.

i

Acknowledgements

I would like to express my utmost gratitude to my supervisor Prof. Bengt Gunnar Svenssonfor introducing me to the exciting field of semiconductor physics. Thank you for sharing yourendless knowledge and expertise in this field of science through fruitful discussions, invaluableadvice, and revision that made this thesis possible.

I would like to thank Frank Herklortz for introducing me to FTIR spectroscopy, AlexanderHupfer for helping me with analysis in Python, Thomas Sky for a helping hand when MatLabwouldn’t cooperate and for proof-reading my thesis. Dr. Augustinas Galackas, thank youfor carrying out the PL measurements, and for all your patient help and advice. A specialthanks to Vegard Skiftestad Olsen for revising my thesis repeatedly, and for being a greatfriend through these years at LENS. A big thanks goes to Micke and Victor for always helpingme with practical issues at MiNaLab, and for your wonderful humour. Micke, thank you fornot giving up after endless hours of repairing the FTIR lifting-table with me.

To everyone at LENS, thank you for making these years a rewarding and fulfilling period ofmy life. I have highly appreciated the environment between us master students, where sharingand discussions of each others work has been encouraged amongst everyone.

Mom and dad, thank you for being the most supportive parents one could ever ask for, I wouldnot have finished this degree without you. Mamma, thank you for always wholeheartedly car-rying all of my frustrations. And to Eric, thank you for motivating me when inspiration waslow, always being there for me, and for tolerating long working hours during this year.

Mette Fjelltveit Rye-Larsen, Oslo, May 2016

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Contents

1 Introduction 1

2 Background 32.1 Crystal structure and defects . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.2 Fundamentals of semiconductors . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.2.1 Electronic energy bands . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.2.2 Charge carrier generation . . . . . . . . . . . . . . . . . . . . . . . . . . 82.2.3 Charge carrier density . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.3 Theory of vibrational spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . 122.3.1 Molecular vibrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.3.2 Infrared absorption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.3.3 Vibrational modes in crystals . . . . . . . . . . . . . . . . . . . . . . . . 142.3.4 Localized vibrational modes . . . . . . . . . . . . . . . . . . . . . . . . . 152.3.5 Electronic transitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.3.6 Free carrier absorption . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.3.7 Infrared transmission measurements . . . . . . . . . . . . . . . . . . . . 16

3 Silicon; growth, main impurities and defects 183.1 Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183.2 Crystal growth and impurity incorporation . . . . . . . . . . . . . . . . . . . . . 193.3 Point defects and their complexes . . . . . . . . . . . . . . . . . . . . . . . . . 20

3.3.1 Oxygen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213.3.2 Carbon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213.3.3 Vacancy-oxygen complexes . . . . . . . . . . . . . . . . . . . . . . . . . 213.3.4 Carbon-related complexes . . . . . . . . . . . . . . . . . . . . . . . . . . 22

3.4 Thermal donors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223.4.1 Formation kinetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233.4.2 Structural models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243.4.3 The effect of carbon on donor formation . . . . . . . . . . . . . . . . . . 26

3.5 Light induced degradation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

4 Experimental techniques and procedure 284.1 Fourier Transform Infrared (FTIR) Spectroscopy . . . . . . . . . . . . . . . . . 28

4.1.1 The Michelson interferometer . . . . . . . . . . . . . . . . . . . . . . . . 284.1.2 Generation of the interferogram . . . . . . . . . . . . . . . . . . . . . . . 294.1.3 Spectral treatment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

iii

4.1.3.1 Interference fringes . . . . . . . . . . . . . . . . . . . . . . . . . 324.1.3.2 Spectral subtraction . . . . . . . . . . . . . . . . . . . . . . . . 324.1.3.3 Baseline correction . . . . . . . . . . . . . . . . . . . . . . . . . 33

4.1.4 Advantages and limitations of FTIR spectroscopy . . . . . . . . . . . . . 334.1.5 FTIR instrumentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

4.2 Four-point probe (FPP) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364.3 Photoluminescence (PL) Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . 374.4 Experimental Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

5 Results and discussion 405.1 FTIR measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

5.1.1 Issues with MCT detector . . . . . . . . . . . . . . . . . . . . . . . . . 405.2 Impact of electron irradiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

5.2.1 Simulation of VO development with irradiation . . . . . . . . . . . . . . 445.3 Isothermal annealing studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

5.3.1 Irradiation induced complexes of low thermal stability . . . . . . . . . . 455.3.2 Interstitial oxygen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 465.3.3 Substitutional carbon . . . . . . . . . . . . . . . . . . . . . . . . . . . . 495.3.4 Vacancy-oxygen complexes . . . . . . . . . . . . . . . . . . . . . . . . . 515.3.5 Carbon-related complexes . . . . . . . . . . . . . . . . . . . . . . . . . . 565.3.6 Thermal Double Donors . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

5.4 FPP resistivity measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . 685.5 Photo Luminescence measurements . . . . . . . . . . . . . . . . . . . . . . . . . 75

5.5.1 Carbon lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 755.5.2 TDD lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

6 Summary 796.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 796.2 Suggestions for further work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

Appendices 82

A Overview of IR absorption bands 83

B Overview of FPP measurements 87

C VO simulation 89

iv

Chapter 1

Introduction

While the global demand for energy increases rapidly, a strong reduction in the exploitation offossil fuels is required to reduce the environmental consequences of electrical power generation.The International Energy Association (IEA) predicts a growth in energy demand by nearlyone third between 2013 and 2040, in which the global electricity demand is predicted toincrease by a staggering 70% [1]. At the same time, the Intergovernmental Panel on ClimateChange (IPPC) reports that the human influence on the climate system is clear, and recentanthropogenic emission of green-house gases is the highest in history [2].

A growing awareness for the need to secure sources of electricity, alternative to fossil fuels, hasexpanded the interest in harvesting solar energy by the use of Photovoltaics (PV). Since 2010,the world has added more solar PV capacity than the previous four decades, and the totalglobal capacity overtook 150 GW in early 2014 [3]. The IEAs technological roadmap envisionsPVs share of global electricity to reach 16% by 2050, corresponding to a total of 4600 GW ofinstalled PV capacity. If this roadmap is reached, the emission of up to 4 Giga-tonnes (Gt)of CO2 would be avoided annually [3].

Despite the promising development in installed PV capacity, most European consumers arestill depending on government incentives to achieve grid parity, in terms of electricity cost [4].This calls for further development of the technologies in terms of reduced production cost andhigher module efficiency. Silicon (Si) is the "work horse" of the PV industry, and constitutesthe greater majority of all commercial solar cells. A vast abundance of the precursor materialquartz, and a relatively low production cost are essential reasons for this predominance. Whilethe theoretical efficiency limit for a single-crystal, homo-junction Si solar cell is approximately30%, the commercial solar cells today are normally limited to only 16-18%. Therefore, tomake PVs a competitive source of electricity, further progress must be made in both processingtechnology and material quality. Point defects and point defect complexes which form duringcrystal growth and subsequent thermal processing, are decisive for the materials structuraland electrical quality.

The present work reports on a study of various oxygen and carbon related defects which de-velop in Czochralski (Cz) grown Si during thermal treatment. Oxygen together with carbonare the two most abundant, unintentionally introduced impurities in Cz-Si. When oxygenand carbon atoms are present in their usual interstitial and substitutional positions in the

1

CHAPTER 1. INTRODUCTION

Si lattice, respectively, they are rather stable, immobile and electrically inactive. However,heating of Cz-Si to temperatures typical for solar cell processing steps, leads to the formationof electrically active, detrimental defect complexes in the material. In this work, the develop-ment of defect complexes in Cz-Si after sequential isothermal heat treatments (annealings) inthe temperature range of 450-550°C has been investigated using Fourier Transform Infrared(FTIR) Spectroscopy. A particular focus has been devoted to the development of Thermaldouble donors (TDDs), a series of electrically active defect species caused by the agglomer-ation of oxygen atoms into specific structural formations. Furthermore, the effect of a highcarbon concentration on the development of these species has been investigated.

To facilitate the investigation of different reaction paths for the oxygen and carbon atoms in thematerial, defects have been intentionally generated by MeV electron irradiation. An objectiveof the present work has been to determine if a direct involvement of VOn (n≤6) centres ortheir dissociation to form fast diffusing oxygen species, contributes to TDD formation. Fourpoint probe (FPP) resistivity measurements have been used to estimate the concentration ofdonor species. Photoluminescence (PL) spectroscopy has been utilized in correlation with IRbands to study the development of carbon related species.

The contents of this thesis are divided into five chapters, excluding the current introduc-tory one. Chapter 2 presents fundamental theory on semiconductor physics and vibrationalspectroscopy. In chapter 3, theory on Silicon; growth, main impurities and defects will bepresented to lay a foundation for the experimental work performed in this thesis. Chapter4 outlines the experimental methods utilized, with a particular focus on the main technique,Fourier Transform Infrared Spectroscopy. In chapter 5 the obtained results are presented anddiscussed consecutively. A summary and conclusion on the established results are then givenin chapter 6.

2

Chapter 2

Background

In this chapter some fundamental concepts of crystals and electronic properties of semicon-ductors will be given. Further, relevant theory of vibrational motion in molecules and solidsare presented. This is applied to explain the main principles of infrared (IR) spectroscopy,with a particular focus on the absorption mechanisms in silicon.

2.1 Crystal structure and defects

This section is based on the references by Tilley [5] and Campbell [6].A solid can be classified with respect to the periodicity of the atoms constituting the material.Crystalline solids consist of one single crystal, polycrystalline solids are composed of severalsmall crystallites and amorphous solids have no long range order. In a crystalline solid theatoms or ions are joined together in a periodical network in three dimensions. The periodicity isdefined in terms of a symmetric array of points in space, having the same spatial surroundings,called the lattice. At each lattice point an arrangement of one or more atoms, termed the basis,is added, making up the crystal. The lattice is therefore a mathematical concept, and can bedefined by three translational vectors a, b and c. If an arbitrary lattice point is chosen as theorigin, the position P of any other lattice point is defined by,

P(uvw) = ua + vb + wc, (2.1)

where u,v and w are positive or negative integers. The parallelepiped formed by the threetranslational vectors defines the unit cell. The lattice will for all crystals contain a smallestvolume, or cell, that represents the entire lattice and is regularly repeated throughout thecrystal. Thus, when a, b and c represent the smallest distance between two lattice points,|a|=a0, |b|=b0 and |c|=c0, they are defined as primitive vectors, and the cell they span is calledthe primitive cell. A perfect crystal can therefore be constructed by an infinite repetition ofthe basis, attached to the lattice, illustrated in figure 2.1.

A perfect crystal is an idealization, and is only theoretically possible at absolute zero tem-perature (0 K). At finite temperatures (T>0 K) defects are inevitable as disorder increasesthe entropy of the system. Deviations from a perfect crystal structure may exist as a singlepoint defect or extend in one-, two- or three dimensions. A point defect disturbs the crystal

3

CHAPTER 2. BACKGROUND

(a) Lattice points (b) Basis (c) Crystal structure

a

b

Figure 2.1: At each lattice point (a) a basis (b) of one or more atoms is added to obtain thetotal crystal structure (c). The translational vectors a and b are illustrated.

pattern at an isolated site and the simplest type is a vacancy, in which an atom is absent froma normally occupied site, as can be seen from the illustration in figure 2.2. A closely relatedpoint defect is an atom residing in the space between lattice positions, and is referred to asan interstitial atom. If the atom that resides on an interstitial site is of the same element asthe atoms in the lattice, it is termed a self-interstitial. Both vacancies and self-interstitials areintrinsic defects. Another type of one dimensional defect is an extrinsic point defect, whichoccurs when an impurity atom substitutes a lattice site or occupies an interstitial site. In theformer case it is referred to as a substitutional impurity. Furthermore, an accumulation ofpoint defects extending in only one dimension would result in a line defect, where the mostcommon example is a dislocation. Defects extending in two dimensions are termed area de-fects, in which the most obvious type is a grain boundary. Controlling grain boundaries isimportant for polycrystalline materials, as they tend to decrease the electrical and thermalconductivity. Furthermore, if the concentration of a defect exceeds its solubility upon cooling,it tends to precipitate from the crystal, leading to three-dimensional precipitation defect com-plexes. Subsequent heat treatments of a material may also lead to the formation of precipitatedefects.

In this thesis the main focus will be on the development of point defect complexes. Thenomenclature commonly used for describing a point defect is:

Xqp . (2.2)

Here, X corresponds to the defect species, which may be a host atom or impurity atom/-molecule or a vacancy (V). p indicates the lattice site in which the species occupy. This canbe at an interstitial position (i) or at a substitutional position (s). q denotes the electroniccharge of the species relative to the site it occupies. Defects in semiconductors may havemore than one possible charge state, so the charge is not always specified. In the case of anelemental crystal (e.g. Si), self-interstitials are commonly denoted I.

4


I

X

V

s

Xi

Figure 2.2: Two-dimensional illustration of point defects in a crystal structure. A vacancy (V),a self-interstitial (I), and an impurity element X occupying substitutional (Xs) and interstitial(Xi) lattice sites.

2.2 Fundamentals of semiconductors

This section is based on the references by Streetman [7], Nelson [8], Kittel [9] and Hemmer [10].Semiconductor materials have characteristic electrical properties, with conductivities rangingbetween those of metals and insulators. The conductivity of semiconductors can further bevaried as a function of temperature, optical excitation or by doping. These materials can hencebe tailored to meet the specific needs of a desired application. The electronic characteristicsof solids are understood by examining the band structure and associated electronic occupancyof the respective materials.

2.2.1 Electronic energy bands

The electrons in an isolated atom are restricted to discrete energy levels. The allowed energylevels, the eigenvalues, are found by solving the Schrödinger equation for the atom’s valenceelectrons1. In a solid material the number of atoms, and thus electrons, is very large and asimplification of this many-body problem is necessary. An approximation of the electronicnature of electrons in solids is found by the nearly free electron model. Here the valenceelectrons are modelled as a free electron gas distributed over the material, only perturbed bya positive potential set up by the fixed ion cores at the lattice points. The periodic potentialhas the same periodicity as the lattice, i.e., U(r)=U(r+R), where R is a translational vector.The time-independent Schrödinger equation for an electron in such a potential is,

Hψ(r) =

[− ~2

2m∇2 + U(r)

]ψ(r) = Eψ(r), (2.3)

where H is the Hamiltonian operator, ψ(r) is the wave function of the electron, ~ = h/2πis the reduced Planck’s constant, m the electron mass and E the energy eigenvalue for the

1The valence electrons of an atom is the outermost electrons that can participate in forming bonds.

5


given potential. Felix Bloch proved in 1928 that the wave functions, ψ(r), for such a periodicpotential must be on the form of a Bloch function [11], that is,

ψ(r) = eikruk(r) (2.4)

where k is an arbitrary wave vector, eikr is a plane wave and uk(r) inherits the same periodicityas the potential:

uk(r + R) = uk(r). (2.5)

The energy eigenvalue in eq.(2.3) depends on the wave vector, k, and gives the energy statesthat an electron is allowed to occupy. For a given k several discrete levels En(k) exists, wherethe band index, n, can take positive integer values. The energy eigenvalues will further varywith k, as illustrated in figure 2.3. The range that the function En(k) sweeps over when kvaries is termed an energy band. Two consecutive bands can overlap or be separated by gaps offorbidden states, called band gaps (Eg). These forbidden regions are a result of the interactionsbetween the valence electrons and the ion cores of the crystal. Electrons will further seek tominimize their energy, and in the ground state electrons will occupy the lowest possible energyconfiguration. The highest occupied band at absolute zero temperature (0 K) is called thevalence band (VB), while the lowest unoccupied band is termed the conduction band (CB).The energy of the corresponding bands edges are termed Ev and Ec, respectively.

E

k

E (k)3

E (k)1

E (k)2

E

E

E

c

v

g

Figure 2.3: An arbitrary (E, k) relationship. The energy ranges that the electron eigenvaluesspan correspond to energy bands. Here band 2 and 3 overlap, while an area of forbidden states,i.e. the band gap, exists between band 1 and 2. The figure is adapted from Hemmer [10].

An analogous approach for deriving the band gaps in solids, is to consider the crystal as a linearcombination of atomic orbitals (LCAO). This is done by envisioning a stepwise combinationof atoms to form the solid. If two atomic orbitals (AOs) (with one electron each) are joinedtogether to form a molecular orbital (MO) the discrete energy levels will split into a bonding(symmetric) and antibonding (antisymmetric) level, slightly lower and higher in energy thanthe initial energy levels, respectively. The number of MOs is thus equivalent to the initialAOs. When a larger number of atoms are joined together the discrete energy levels multiplyas more and more atoms are added to the crystal. Eventually, the energy levels will be soclosely spaced that they can be considered as continuous bands of energy that the electronscan occupy, separated by ranges of no MOs.

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Depending on the energy landscape and the occupancy of the bands, a material can be cate-gorized as a metal, semiconductor or insulator. For conduction of current to occur, electronsmust be able to experience acceleration in an applied electric field, which implies that allowedenergy states, not already occupied, must be available. If the VB is not completely filled, oroverlaps with the CB, electrons will be free to move and can easily conduct current. Sucha material is a metal. At 0K a semiconductor and an insulator inherit essentially the samestructure, a filled VB separated from an empty CB by a band gap. What distinguishes a semi-conductor from an insulator is the magnitude of this gap. The relatively small band gap (Eg .3-5 eV [8]) of semiconductors allows for excitation across the gap at reasonable2 amounts ofenergy. An insulator will in contrast have a negligible number of excitations for the sameconditions. The important difference between an insulator and semiconductor is thus thatthe number of electrons available for conduction can be increased vastly in semiconductors byoptical or thermal excitation. The described characteristics are illustrated in figure 2.4.

Filled states

Insulator

Filled states

Semiconductor

Filled states

Partially filled states

Overlap

Metal

Eg

Empty states

Empty states

Eg

Ec

Ev

Ec

Ev

Ec

Ev

Ec

Ev

Figure 2.4: Energy diagram for an insulator, a semiconductor and a metal at 0K. In metals,free states are always available for electrons, and the material conducts current. In an insulatorthe band gap is of such magnitude that negligible amounts of charge carriers will be generatedby thermal or optical excitation. For semiconductors the band gap is small and charge carrierscan be generated. Figure adapted from Streetman [7].

Semiconductors can further be divided into two categories, depending on the position of theVB maximum with respect to the CB minimum, as illustrated in figure 2.5. In a direct bandgap semiconductor the extreme band values occur at the same wavevector, k. In this case anelectron can be excited directly across the band gap by the absorption of a photon with energycorresponding to the band gap (Eg). If the extremes exist at different k, the smallest possibletransition from VB to CB requires a change in the electron momentum, p=~k. As photonscarry virtually no momentum, the transition must be assisted by the absorption of a latticevibration, a phonon, of the correct energy. In the latter case the material is consequentlytermed an indirect band gap semiconductor.

2Reasonable amounts is referring to thermal energy in the room temperature range or photon energiescorresponding to the wavelengths of visible light.

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E E

Eg Eg

Ec Ec

Ev Ev Direct

Indirect

Photon Photon

Phonon assisted

k k

Figure 2.5: A simple illustration of a direct and indirect band gap. In a direct band gap semicon-ductor an electron can be excited from the VB maximum to the CB minimum by the absorptionof a photon of energy Eg. The indirect transition requres a change in momentum (p=~k),generally supplied by the absorption of a phonon.

2.2.2 Charge carrier generation

A perfect semiconductor crystal, free of defects and impurities, is called intrinsic. At 0 K anintrinsic semiconductor will have a completely filled VB separated from an empty CB and nocharge carriers exists. When an electron is thermally or optically excited from the VB to theCB, an accompanying hole remains in the VB, and an electron-hole-pair (EHP) is created.Both electrons and holes conduct current, where the hole can be considered as a positivecharge carrier, moving in the opposite direction as electrons in an applied electric field. Inintrinsic semiconductors EHPs are the only charge carriers and the concentration of electrons(n) in the CB and holes (p) in the VB must be equal. The concentration is called the intrinsiccarrier concentration ni,

p = n = ni. (2.6)

A semiconductors ability to conduct current depends primarily on the number of availablecharge carriers. By introducing impurity elements by a process called doping, the number ofcharge carriers and therefore the conductivity can be increased. When impurities or latticedefects are incorporated into the crystal, additional levels are created in the energy bandstructure. Generally, heterovalent atoms containing more valence electrons than the hostmaterial will generate an energy level close below the CB edge. This level is filled withelectrons at 0 K, meaning that the valence electrons of the impurity element are bound totheir ion core. At relatively low thermal energies these electrons will ionize, and be donated tothe CB. The dopant is termed donor and the energy level is accordingly termed donor level.Similarly, impurities with fewer electrons than the host atom generate energy levels close abovethe VB. At 0 K this band is empty, i.e. filled with holes. An increase in temperature leads toelectrons being accepted from the VB to this level. The dopants thus contribute holes to theVB by accepting electrons. Such a dopant is termed acceptor and its energy level is an acceptor

8


level. When a material is doped with a significant number of donor atoms, the equilibriumconcentration of electrons, n0, greatly exceeds the equilibrium concentration of both holesp0 and intrinsic carriers ni, n0 p0,ni, and the material is called n-type. The material istermed p-type when the same is true for acceptors, p0 n0,ni. Donors and acceptors withthe characteristics described above are termed shallow impurities, referring to the position ofthe impurity level with respect to the CB and VB edges. Shallow impurities are easily ionizedand thus contribute with free charge carriers to the semiconductor. The positioning of shallowdonor- and acceptor energy levels are illustrated in figure 2.6. Impurities may also producedeep energy levels, positioned further from the band edges, these are termed deep impurities.Deep impurities are less likely to ionize, due to a higher requirement of thermal energy andmay instead act as traps and/or recombination centres, where charge carriers can be trappedand/or annihilate. When a crystal is doped such that the equilibrium carrier concentrationsn0 and p0 are different from the intrinsic carrier concentration ni the material is said to beextrinsic.

Figure 2.6: Illustration of N-type and P-type semiconductors, at low temperature. Shown is afilled donor level (ED), acceptor level (EA) and Fermi level (EF ) for the respective materials.

The effect of doping is easily understood by the covalent binding model. For instance, Sihas four valence electrons that all participate in covalent bonding with four neighbouring Siatoms, as illustrated in figure 2.7. If a Phosphorous (P) atom is introduced to the crystal,substituting Si, four of the P valence electrons will participate in bonding, while the fifth willbe held by Coulomb interactions to the ion core. Only a small amount of energy is requiredto excite this electron and it will thus be available to conduct current. P is therefore a donor,with a donor level just below the CB of Si. Similarly, if a Boron (B) atom, containing onlythree valence electrons is introduced, an electron is missing to complete the covalent bondingto all four Si neighbours. B is an acceptor, and by accepting a valence electron from Si itcontributes conducting holes to the VB.

2.2.3 Charge carrier density

To understand the electronic properties of semiconductors, the distribution of carriers overavailable energy states must be evaluated. The electrons and holes in solids obey Fermi-Dirac3 statistics. The Fermi-Dirac distribution function, f(E), gives the probability of finding

3Fermi-Dirac statistics describes a distribution of particles (fermions) over energy states in systems consist-ing of many identical particles that obey the Pauli exclusion principle.

9


h+

e-

B

P

Si

-

+

Figure 2.7: When a phosphorous (P) atom substitutes a silicon (Si) atom it donates an electronto the lattice. When boron (B) is the substituent, a hole is created. These processes are knownas donor- and acceptor doping, respectively.

an electron at an available energy state, E, at an absolute temperature, T :

f(E) =1

1 + e(E−EF )/kBT, (2.7)

where kB is the Boltzmann constant and EF is known as the Fermi level. EF represents anenergy state at which the probability of occupancy is exactly 1/2. At T=0 K all allowed statesbelow EF will be filled and all above will be empty. Hence, for an intrinsic semiconductorat absolute zero temperature where the VB is completely filled and CB is empty, the Fermilevel lies approximately in the middle of the band gap. When the temperature is increased,there exists a finite probability of finding electrons above and holes below the Fermi level,however the Fermi function is symmetrical about EF for all temperatures, making it a naturalreference point for calculations. The probability of finding a hole in an available energy state isequivalent to the probability of not finding an electron, hence the function [1−f(E)] representsthe probability of finding a hole.

By combining the probability distribution of carriers, f(E), with the density of states in therelevant energy range, N(E)dE, the equilibrium concentration of electrons, n0, and holes, p0,in the CB and VB, respectively, can be found:

n0 =

∫ ∞EC

f(E)N(E)dE, (2.8)

p0 =

∫ Ev

−∞[1− f(E)]N(E)dE. (2.9)

The product f(E)N(E) decreases rapidly above Ec, as f(E) in eq.(2.7) becomes extremelysmall for large energies. For that reason, very few electrons occupy energy states far abovethe CB edge. Similarly, few holes are found far below the VB edge, as [1− f(E)] accordinglydecreases rapidly below the VB edge. The distributed electron states in the CB can furtherbe represented by an effective density of states Nc, located at the Ec:

Nc = 2

(2πm∗nkT

h2

)3/2

(2.10)

10


and for holes in the VB at Ev:

Nv = 2

(2πm∗pkT

h2

)3/2

(2.11)

Here m∗n and m∗p represent the effective mass of electrons and holes, respectively. As describedin section 2.2.1, the electrons and holes are not completely free to move since they interactwith the periodic potential of the lattice. The influence from the potential is contained in thecurvature of the energy bands, d2E

dk2 . This modification of charge carrier mass allows for theuse of electrodynamic equations. The representations of effective density of states in eq.(2.10)and (2.11) gives the same results as obtained by performing the integration over the statesin eq.(2.8) and (2.9). If the Fermi level is assumed to lie at least several kT from the bandedges, f(E) can be approximated by the Maxwell Boltzmann function. This approximationsimplifies the electron and hole concentration to:

n0 = Ncf(Ec) (2.12)

p0 = Nv[1− f(Ev)], (2.13)

where the aforementioned distribution function for electrons and holes are approximatedto:

f(Ec) = [1 + e(Ec−EF )/kT ]−1 ' e−(Ec−EF )/kT (2.14)

1− f(Ev) = 1− [1 + e(Ev−EF )/kT ]−1 ' e−(EF−Ev)/kT . (2.15)

Hence, the electron and hole concentrations in the CB and VB, respectively, can now beexpressed as:

n0 = Nce−(Ec−EF )/kT (2.16)

p0 = Nve−(EF−Ev)/kT . (2.17)

For an intrinsic semiconductor, the Fermi level lies at some intrinsic level, Ei, near the middleof the band gap. By combining eq.(2.16) and the corresponding equation for the intrinsiccharge carrier concentration, ni in which EF = Ei, the electron concentration can be givenby:

n0 = nie(−(Ec−EF )+(Ec−Ei))/kT = nie

(EF−Ei)/kT . (2.18)

By applying the same approach for holes in eq.2.17, and realizing that ni=pi, since intrinsiccarriers are generated in pairs:

p0 = nie(−(EF−Ev)+(Ei−Ev))/kT = nie

(Ei−EF )/kT . (2.19)

The charge carrier concentration in an intrinsic semiconductor depends only on temperatureand the inherent properties of the material. The only charge carriers in such material areEHPs. For an extrinsic material, donors or acceptors are added to increase the charge carrierdensity. By evaluating eq.(2.16) and (2.17) it is evident that the Fermi level will move closer tothe CB edge as the number of electrons is increased by the addition of donor species. The sameis true for holes, where the Fermi level is positioned closer to the VB as the number of acceptorsare increased. When a semiconductor is doped with a significant number of donor atoms,i.e. the number of donors is several orders of magnitude larger than the number of intrinsiccarriers, the charge carrier concentrations can be approximated by the doping concentration.

11


If a semiconductor is doped with Nd single donor species4 the electron concentration is simplyequal to the donor concentration. The hole concentration can be calculated utilizing the lawof mass action (np = n2i ):

n0 ≈ Nd (2.20)

p0 ≈n2iNd

. (2.21)

Similarly, for a p-type semiconductor the hole concentration is equal to the acceptor dopingconcentration, Na, and the electron concentration is found:

p0 ≈ Na (2.22)

n0 ≈n2iNa

. (2.23)

When a semiconductor contains both donors and acceptors, one can not expect a concentrationof holes in the VB corresponding to the number of acceptors, or a concentration of electronsin the CB equal to the number of donors. The excess carriers provided by the dopants mayinstead compensate each other by recombining. The relationship between electron, hole, donorand acceptor concentrations can be found by considering the requirement for space chargeneutrality :

p0 +N+d = n0 +N−a (2.24)

2.3 Theory of vibrational spectroscopy

This section is based the on references by Griffiths [12], Kittel [9] and Schroder [13].Vibrational spectroscopy is the study of the interaction between electromagnetic radiationand matter, where the particular interaction depends on the radiation wavelength. When amaterial is exposed to electromagnetic radiation in form of infrared (IR) light the chemicalbonds in the material may absorb this radiation at specific frequencies, characteristic of theirnature and chemical environment. The IR region corresponds approximately to wavelengthsspanning from 700 nm to 1 mm, or an energy in the range 1.24 meV - 1.7 eV. This is in therange of energies separating the quantum states of molecular vibrations, which makes IR spec-troscopy an efficient method for investigating the chemical composition of semi-transparentsolid-state materials.

In silicon there are four main origins of radiation absorption: lattice vibrations (phonons),localized vibrations (due to defects perturbing the lattice symmetry), electronic transitions inimpurities and free charge carriers. To understand the principles of vibrational spectroscopy,some knowledge of the vibrational motion of atoms is necessary, before proceeding to thefundamentals of specific absorption mechanisms.

4Single donor species contribute one electron each to the CB when ionized.

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2.3.1 Molecular vibrations

In the simple case of a diatomic molecule, vibrational motion can be described using Newtonianmechanics, where the atoms are modelled as masses connected by a massless spring. A simpleharmonic oscillator is a system that when displaced from its equilibrium position, experiencesa restoring force F proportional to the displacement x. A diatomic molecule can be modelledas such a system, where the displacement represents the change in bond length from itsequilibrium value. The motion is governed by Hooke’s law :

F = −kx = µd2x

dt2, (2.25)

where k is the force constant in units N/m, µ = m1m2/(m1 + m2) is the reduced mass of aheteronuclear molecule, and Newton’s second law is applied. The solution to this differentialequation is a simple harmonic motion describing the vibration x(t):

x(t) = Asin(ωt), (2.26)

where A is the amplitude, t is the time and ω is the angular frequency of oscillation, givenby:

ω =

√k

µ=

√m1 +m2

m1m2k. (2.27)

This simple classical model gives an accurate description of the vibration in a molecule, vir-tually any oscillatory motion is approximately simple harmonic as long as the amplitude issmall [14]. However, when describing the interaction with electromagnetic radiation, a quan-tum mechanical approach is required.

The spring force in eq.(2.25) gives rise to the one-dimensional potential:

U(x) =1

2µω2x2, (2.28)

where the spring constant is eliminated in favour of the classical frequency in eq.(2.27). Thequantum mechanical equivalent of the derivation in the previous section is to solve the time-independent Schrödinger equation for a molecule moving in such a potential, i.e.:(

− ~2m

d2

dx2+

1

2mω2x2

)ψ(x) = Eψ(x). (2.29)

By solving the differential equation the vibrational energies in a quantum mechanical harmonicoscillator is found to be:

En = ~ω(n+

1

2

). (2.30)

The quantum number n in eq.(2.30) characterizes the different eigenstates of the harmonicoscillator, and can take non-negative integer values (n=0,1,2,..). The equation shows thatthe energies of vibrational motion is quantized, and the only transitions allowed are from oneeigenstate to another. Under certain conditions molecules may participate in allowed energytransitions, and this can be observed in IR spectroscopy.

13


2.3.2 Infrared absorption

In order for IR radiation to be absorbed by matter, two conditions must be fulfilled. First, theresonance condition requires that the oscillating frequency of the incoming photon matchesthe natural frequency of a particular vibrational mode. Second, in order for energy to betransferred from the incoming photon to the molecule, the vibration must cause a change inthe molecules dipole moment5. The reason for this is that the absorption of a photon followsfrom the interaction between a mode and the time-varying electrical field of the incominglight. These requirements are the selection rules governing IR spectroscopy [15]. In vibrationalspectroscopy it is common to use wavenumber, v, rather than frequency to describe vibrationalmodes. The wavenumber is the spatial frequency of a wave in cycles per unit distance:

v =1

λ=

ω

2πc, (2.31)

where λ is the wavelength and c is the speed of light. Transitions between the ground state(n=0) and first excited state (n=1), in eq.(2.30), of most vibrational modes has an energy dif-ference corresponding to the frequency of electromagnetic radiation in the mid IR spectrum6.This makes IR spectroscopy a powerful tool for investigating the structure of a wide varietyof substances.

The requirement for a change in dipole moment as described above, means that not all vibra-tions will be detectable by IR spectroscopy. One example is that of the heteroatomic moleculeN2, that do not hold a time-varying dipole moment. However, in the absence of a changingdipole moment, a change in polarizability7 will make a vibration visible in a complementarytechnique called Raman spectroscopy, which is based on the detection of inelastic scatteringof monochromatic light. Raman-active vibrations are thus governed by different selectionrules than IR absorbing vibrations and will provide complementary information. Only IRspectroscopy will be considered in the following.

2.3.3 Vibrational modes in crystals

Like molecules, crystals can also vibrate as a whole. In a crystal, a large number of atoms (orions) are bonded together in a three-dimensional periodic array, as described in section 2.1.In this system, each atom will experience forces from all surrounding atoms, such that everyatom is held near its equilibrium position. A potential energy function characterizes the forceacting between a pair of atoms, depending on the distance between such a pair. The potentialenergy of the entire lattice, Vlattice, is thus the sum of all pairwise potential energies:

Vlattice =∑i 6=j

V (ri − rj), (2.32)

where ri is the position of the ith atom, and V is the potential energy between two atoms.However, the number of atoms in a crystal is extremely large, on the order of Avogadro’s

5The electric dipole moment is a measure of net molecular polarity, which is the magnitude of the chargeat either side of the molecular dipole times the distance between the charges.

6The mid IR spectrum spans from 400 to 4000 cm−1 or a wavelength of 2,5 to 25 µm.7The ease with which the charge distribution in a molecule can be distorted by an external electric field is

called its polarizability.

14


number (∼ 1023), and such calculations would be extremely complex. Two important ap-proximations are therefore applied; only nearest neighbour interactions are considered andharmonic potentials are assumed. In analogy to the harmonic oscillator described in the pre-vious sections, the lattice can now be modelled as a grid of N masses connected with springs,giving a total of 3N independent harmonic oscillators. Thus, the energy of a lattice vibrationis also quantized and the quantum of energy is called a phonon. Phonons are quasi particlesthat carry the lattice vibrations through the crystal.

The atoms in a solid can vibrate normal to- or in the same direction as the propagating wave,representing transversally- and longitudinally polarized phonons, respectively. For crystalswith more than one atom in their primitive unit cell, there are two types of phonons, opticaland acoustic. Acoustic phonons carry vibrations like sound waves, where neighbouring atomsvibrate coherently. When the neighbouring atoms vibrate out of phase, i.e with alternatingopposite velocities, the phonons are termed optical. In compound crystals like Zinc Oxide,where the two types of atoms carry different charges, the optical phonons create a time-varying dipole moment and can therefore interact with IR light. For elemental crystals,neighbouring atoms are the same and there is no first-order dipole moment, hence no one-phonon absorption is observed. Pure Si is therefore said to be transparent in the infraredrange. However, multi-phonon coupling, where a photon couples with more than one phonon,can lead to an asymmetry in the electronic charge distribution and a varying dipole moment.Hence, the lattice itself will absorb some IR radiation. When studying defects in silicon theintrinsic contribution from the lattice is usually undesirable. To circumvent this, a semi-intrinsic reference spectrum is measured, and the ratio of the two spectra is free from theintrinsic contribution.

2.3.4 Localized vibrational modes

The vibrational properties of crystals are significantly altered by the presence of defects andimpurities. Phonons in a perfect lattice have well-defined frequencies. When an impurityis introduced the translational symmetry is broken and one or more vibrational modes mayappear. If an impurity atom replaces a heavier host atom, its vibrational frequency will lieabove the phonon frequency range [16]. Conversely to a phonon, the vibrational mode of thedefect is localized in real space and frequency space, and is referred to as a localized vibra-tional mode (LVM). The LVMs of impurities are affected by the symmetry of the surroundingenvironment and gives rise to sharp peaks in IR absorption spectra.

2.3.5 Electronic transitions

When a semiconductor is intentionally doped or has energy states in the band gap due todefects, IR radiation can be absorbed by these defects under certain conditions. Shallowdonor or acceptor states in silicon are located meVs below the CB edge and above the VBedge, respectively. At room temperature these states are ionized and will thus not be availablefor absorption. However, at cryogenic temperatures donor states are filled with electrons andacceptor states are empty, i.e., filled with holes. In the case of an n-type semiconductor atlow temperature, electrons will be "frozen" at the donors, and the free carrier density in theconduction band (Ec) is low. In this condition the electrons are mainly located at the lowest

15


energy level or donor ground state (ED). With incident photons of energy hν≤ (Ec - ED), twooptical absorption processes can occur. The excitation of electrons from the ground state (ED)to the conduction band (Ec) leads to a broad absorption continuum. However, electrons canalso be excited from the ground state to one of several excited (donor level) states. The latterproduces sharp absorption lines in a transmission spectrum, characteristic of the shallow-levelimpurities [13]. Thermal donors are an example of shallow-level impurities in Si which giverise to such characteristic electronic transition bands. Thus, when the thermal donor levels arefilled, these can readily be observed in low temperature (LT) measurements. The detectionlimit for electronic transitions in impurities are lower than for the LVM’s, discussed in theprevious section, but are in contrast dependent on the Fermi level position and therefore morechallenging to quantify.

2.3.6 Free carrier absorption

At high temperatures, donors and acceptors are ionized and therefore contributing to a highcarrier concentration in the CB and VB, respectively (see section 2.2.2). Free carrier absorptionoccurs when the material absorbs a photon due to the excitation of a charge carrier from analready excited state to another unoccupied state in the same band. Electrons in the CB canthus absorb incoming photons and be excited to a higher, unoccupied state in the CB. Thelowest energy state for holes is at the top of the VB. Thus, when free holes absorb radiation theyare excited to a lower, unoccupied state in the VB. Free carriers in the semiconductor VB orCB, arising from electrically active defects and impurities in the crystal, may give a significantcontribution to the IR absorption by the sample. In the intrinsic regime, absorption by freecarriers can generally be neglected, but it can become significant in heavier doped materials,having high carrier concentrations. Free carrier absorption does not generally result in anyuseful photo-response in IR spectroscopy measurements and is often regarded as a performancedegrading mechanism [17]. In crystals with high carrier concentration, and thus low resistivity,the free carrier absorption can eventually limit the transmission to an extent that the methodis no longer useful [18].

2.3.7 Infrared transmission measurements

Infrared spectroscopy measurements of solid state samples are performed by measuring thetransmitted beam after interaction with the sample. A spectrum is then obtained by plot-ting the intensity (absorbance or transmittance) versus the wavenumber. The transmittedintensity, I(v), will decrease exponentially with sample thickness (penetration depth):

I(v) = I0(v)e−α(v)d. (2.33)

Here I0(v) is the intensity of the incident beam and I(v) of the transmitted beam as a functionof wavenumber, α(v) is the linear absorption coefficient in units of cm−1 and d is the samplethickness. This equation is known as the Bouguer-Lambert-Beer law, usually simplified toBeer’s Law, and it is the fundamental law of quantitative spectroscopy. Eq.(2.33) neglectslosses in intensity due to reflectance of the beam from the sample surfaces. The fraction ofthe incident radiation which is reflected from a surface is called the reflectance R, and is given

16


by [13]:

Rv =(nv − 1)2 + k2v(nv + 1)2 + k2v

. (2.34)

Here kv is the extinction coefficient and nv is the refractive index of the material. For a solidsample the beam may be reflected from both the front and rear surface, which can give riseto multiple internal reflections. The transmittance of a sample is defined as the ratio betweenthe transmitted and incident beam, and by including reflectance this gives:

T (v) =I(v)

I0(v)=

(1−R)2e−α(v)d

1−R2e−2α(v)d(2.35)

The refractive index of Si is approximately nv ≈ 3.42 for infrared radiation [19]. The extinctioncoefficient kv which is related to the absorption coefficient by the relation α = 4πk/λ is smallcompared to unity for the wavenumber region spanned by the mid infrared range [13]. By usingthese values in eq.(2.34), a constant reflectance of R≈0.3 is found for Si. The denominator ineq.(2.35) can therefore be taken as 1 without introducing any significant error. The absorptioncoefficient can further be divided into two parts, α = α1 + α2, where the first correspondsto absorption from the lattice and free electrons, while the second corresponds to absorptionfrom defects.

T =I

I0= (1−R)2e−(α1(v)+α2(v))d) ≡ C(v)e−α2(v)d. (2.36)

The factor C(v) = (1−R2e−α1(v)d) in this expression varies only slowly with the wavenumberv, while the impurity absorption from α2 can be detected as sharp peaks.

The absorbance, A(v), of the sample is defined as the negative natural logarithm of thetransmittance:

A(v) = −ln(T (v)) = −ln(I

I0) = α(v)d. (2.37)

Furthermore, the absorbance of any component i is proportional to its concentration in thesample. The concentration of a defect species, [N] (where square brackets denotes concentra-tion) can therefore be determined as the product of the absorption coefficient αi(v), i.e., theamplitude of the absorption peak, and a calibration factor a,

[N ] = a× αi(v) = a× Ai(v)

d(2.38)

Since IR absorption is a relative measurement, absolute methods are required to establishthe calibration factor that relates the absorption to the impurity content [18]. Calibrationfactors can for example be established by a micro-sectioning technique as Secondary Ion MassSpectrometry (SIMS). When calibration factors are established, the total concentration canbe deducted from integrated peak area or peak amplitudes of the associated absorption bands,depending on which the calibration factors are developed for.

17

Chapter 3

Silicon; growth, main impurities anddefects

Oxygen (O) and carbon (C) strongly contribute to, and influence major defects in Si duringcrystallization and temperature processing. Thermal double donors (TDDs), O precipitatesand defects causing light induced degradation (LID) are all related to O and affect the per-formance of photovoltaic cells. C is found to inhibit the formation of TDDs [20], however,the mechanisms involved in the suppression is still not clear. In the first two sections, brieftheory on the Si structure and impurity incorporation during crystal growth will be given.Further, the characteristics of important defects in Si will be discussed with a focus on O-and C-related complexes in n-type Czochralski (Cz) grown Si. The subsequent sections willpresent established results regarding the generation and electrical activity of TDDs in Si. Inmore recent years, two structural models of TDDs have been proposed.

3.1 Fundamentals

Si is a group IV element, and like C and Germanium (Ge), it crystallizes in the diamondcrystal structure, where each Si atom is bound to four neighbouring Si atoms [7]. The diamondstructure, illustrated in figure 3.1, consists of two inter-penetrating face-centred cubic (fcc)sublattices, or alternatively a fcc lattice with an extra atom placed at a/4 + b/4 + c/4 fromeach of the fcc atoms. The structure belongs to the Fd3m space-group. In Si, the latticeparameters are given by a = b = c = 543.09 pm [7]. The presence of defects may howeveraffect this value, by causing strain in the lattice, as will be discussed later.

Si is an indirect band gap semiconductor with a band gap of Eg=1.11 eV at 300 K [7]. Asmentioned in section 2.2.1, the excitation of an electron from the VB to the CB must beaccompanied by a momentum conserving phonon. This means that Si, due to the indirectband gap, would not be the optimal choice as a single PV cell, when considering only theefficiency. However, due to its great abundance, band gap fit for the visible spectrum and lowproduction cost, Si is the dominant PV material today.

18

CHAPTER 3. SILICON; GROWTH, MAIN IMPURITIES AND DEFECTS

Figure 3.1: Si crystallizes in the diamond structure, in which each Si atom is bound to fourneighbouring Si atoms. Figure adapted from [21].

3.2 Crystal growth and impurity incorporation

Most of the mono-crystalline Si used in the integrated circuit (IC) and PV industry, is pro-duced by the Cz pulling method. The technique was first invented and named by the Polishmetallurgist Jan Czochralski in 1918 [22], while the method used in today’s ingot productionwas developed by Teal and Little in the 1950s [23].

Several refining procedures, beyond the scope of this text, are performed to produce extremelypure, electronic grade polycrystalline Si from raw material, i.e. quartz. After refining, theSi does not become more purified, but subsequent processing is required to produce mono-crystals. In the Cz method, polycrystalline Si is melted in a crucible in an inert gas ambianceat reduced pressure, at approximately 1500°C. A chemically etched crystal seed is then loweredinto the melt and pulled at controlled rates to produce a mono-crystalline Si ingot. The crystalseed serves as a template for the crystal growth, and must therefore be oriented carefully. Priorto the crystal growth, a short necking procedure is performed, to ensure a dislocation freecrystal structure. During the growth process dissolution of and reactions with the environmentwill lead to the incorporation of significant amounts of impurities in the crystal structure,including O and C.

The crucible containing the molten silicon is made of amorphous silica (SiO2), during thecrystallization process it partly dissolves and enriches the Si melt with O, according to thereaction:

SiO2 + Si→ 2SiO. (3.1)

Over 95% of the dissolved O escapes from the surface of the melt as volatile silicon monoxide(SiO) [24], however, a small fraction will be incorporated into the Si crystal through the crystal-melt interface. During growth, the O is constantly replenished, while the surface area of themelt that is in contact with the crucible decreases as the melt solidifies. The O concentrationis therefore expected to be higher in the seed (top) part of the ingot compared to the tail(bottom). The solid solubility of oxygen can be found from Cs = 4.0×1023e−2×104/T (K)cm−3

[25], which corresponds to a value of 2.8×1018cm−3 at the melting point of Si (1412°C). AnO concentration, [Oi], of approximately 1018 cm−3 is common in Cz-Si [18]. These O atomscan have an adverse effect on the electrical, chemical and physical properties of the crystal.

19


However, the incorporation of oxygen is also beneficial, as it increases the crystals mechanicalstrength.

The source of C impurities is from the graphite material making up the hot zone of thegrower system, in addition to the C impurities which may have been present in the startingpolycrystalline material. The SiO, originating from the dissolving crucible described above,may interact with the hot graphite components and reduce to carbon monoxide (CO), beforere-entering the melt:

SiO + 2C → SiC + CO. (3.2)

C is expected to follow normal solidification behaviour, expressed by [6]:

Ns(x) = N0k(1− x)k−1 (3.3)

where Ns, k and x are the crystal impurity concentration, the impurity segregation coefficientand the fraction of melt solidified, respectively. Since the constant N0 represents the initialimpurity concentration in the melt, the equation will not reflect the system precisely. However,it gives an indication of the C distribution in the growing crystal. Since the C is constantlyreplenished (N0 constant or increasing) and the dopant segregation coefficient k0 is small(k0 = 0.07 [18]), the concentration of C in the grown crystal will increase towards the tail ofthe ingot. C concentrations of 1016 cm−3 is commonly observed in Cz grown crystals [18].

3.3 Point defects and their complexes

Point defects are present in all crystalline solids and affect many fundamental as well astechnologically important phenomena. Intrinsic elementary point defects (i.e., interstitialsand vacancies) formed during crystal growth and processing interact strongly with commonresidual impurities such as O, C, and various transition metals, as well as intentional dopants.Many of the point defect complexes are electrically active, with deep states in the band gap.In addition, they may act as vehicles for diffusion. Moreover, they can be strongly harmfulfor semiconductor devices by acting as nucleation sites for extended crystalline defects, suchas clusters, stacking faults or dislocations. In Si, point defect complexes manifest themselvesby affecting the electrical, optical, structural and mechanical properties of the material [26].Understanding and controlling point defect complexes are thus of decisive importance for thepresent and future use of Si in electronics and photovoltaics.

IR spectroscopy enables the identification and quantification of defect species, and is a highlysuited method to study the evolution of defects after sequential thermal treatments. However,IR absorption spectroscopy is a technique of relatively low sensitivity and the concentrationof a species must, at least, be on the order of ∼ 1014cm−3 to be detectable with this method.The concentration of point defect complexes in current, as-grown, mono-crystalline Si wafersis typically below 1013cm−3, except for the more abundant impurities such as interstitial Oand substitutional C [26]. Therefore, in order to study point defects with IR spectroscopythe number of defects must be increased, as compared to the amounts generated during crys-tal growth. This can be achieved by irradiating the Si crystal with high energy particles(e.g. electrons, neutrons or protons) in order to produce vacancies and self-interstitials whichsubsequently may interact with other defects, producing defect complexes in detectable con-centrations.

20


3.3.1 Oxygen

In its usual configuration O occupies an interstitial site, Oi, in Si. This was determined on thebasis of IR measurements [27], where O was found to occupy a position midway between twoneighbouring Si atoms, along the four equivalent <111> bond directions. In this configurationthe two neighbouring Si atoms give up their covalent bond and engage with the O atom instead,making the O impurity electrically inactive [18]. The interstitial oxygen concentration canbe determined by measuring the absorption band at 1107 cm−1 (RT), which is due to theasymmetric stretching vibration of the Si-O-Si bond [27].

The disadvantages or complications of O in Si will be elaborated in the following. However,the incorporation of O also has several important advantages, which partially is the reasonwhy Cz-Si is used to such an extent. O impurities improve the mechanical strength of Siwafers, which increase the wafers resistance to warpage and generation of dislocations duringthermal cycling in device production processing [18]. This advantage, in addition to the lowerproduction cost compared to other crystallization techniques (e.g. Float zone growth), makesCz wafers the most used in both electronics and PV industry [26].

3.3.2 Carbon

C is an isovalent impurity in Si and predominantly occupies a substitutional site, denoted Cs,in the crystal structure, where it is electrically inactive. In Si, Cs gives rise to absorption ina LVM at 605 cm−1 at RT [28] and 607 cm−1 at low temperature1 (LT) [29], in which theRT peak is commonly used for quantitative determination. The amount of C in a Si crystal isassumed to be limited by the lattice shrinking due to the small atomic radius of C comparedto Si. However, in Cz-grown crystals, large C solubilities can be achieved as C compensatesthe lattice expansion due to the presence of the relatively large O atoms [28].

3.3.3 Vacancy-oxygen complexes

Mono-vacancies generated during crystal growth and irradiation are highly mobile defects, witha diffusivity of DV ≈10−9cm2s−1 at RT [30]. Oi acts as a dominant trap for the migratingmono-vacancies, forming the vacancy-oxygen (VO) centre. The VO-centre is the primaryoxygen-related defect in irradiation damaged Cz-Si. The neutral VO-centre gives rise to an IR-absorption band at 835 cm−1 at LT and 830 cm−1 at RT [26]. In VO complexes the O residesslightly off-centre from the substitutional site and binds preferentially to two neighbouring Siatoms, while the other two Si neighbours form a bond [16]. The VO complex is electricallyactive, with a deep acceptor level Ec - 0.17 eV [26]. The complex is stable up to temperaturesin excess of approximately 300°C. Annealing at higher temperatures can lead to the formationof VO2 complexes via the reaction,

V O +Oi → V O2. (3.4)1In this text low temperature (LT) referrers to 18 K. This is the measurement temperature used for cold

IR measurements.

21


The oxygen LVM frequency in VO2 complexes is 895 cm−1 at LT and 889 cm−1 at RT. VO2

is electrically inactive in its low-energy configuration [26], and annealing of VO2 at around450°C leads to the formation of VO3 complexes,

V O2 +Oi → V O3. (3.5)

The VO3 complex gives rise to a series of IR-absorption peaks and can further develop to VO4.In general the reaction for the formation of higher index VOn species takes the form,

V On +Oi → V On+1. (3.6)

3.3.4 Carbon-related complexes

Self-interstitial Si atoms, I, are known to be highly mobile at RT, DI ≈10−4cm2s−1 [30], andinteract readily with other defects and impurities. Besides the interaction and annihilationwith V, one of the most prominent interactions are with substitutional carbon atoms, Cs, inwhich the C atom becomes interstitially positioned by the Watkins replacement mechanism[31],

Cs + I → Ci. (3.7)

Ci is a mobile defect, DCi = 1.0 × 10−15cm2s−1 at RT [32] and can readily be trapped byother defects. A major defect in irradiated Cz-Si is the CiOi centre. CiOi is electrically activewith a donor level at Ev + 0.36 eV [26]. CiOi gives rise to absorption bands at 742, 865 and1116 cm−3 at LT [33], and a zero-phonon Photoluminescence (PL) line termed the C-line at789 meV [34]. CiOi is thermally unstable above 300°C and in addition to loss by dissociation,interaction with the A-centre can form the complex,

CiOi + V O → CsO2i. (3.8)

The ICiOi defect is produced by the capture of an additional I. This complex is electricallyinactive, but can readily transform into CiOi, being a deep and detrimental recombinationcentre. In addition, since the formation of ICiOi requires two interstitials, this defect becomesincreasingly important at high irradiation or implantation doses. This complex is stable below300°C [26]. By diffusion of Oi and capturing by Cs, CsOi complexes form, giving rise to aseries of IR absorption lines termed X, Y, Z and A [34]. This can further take up an additionalOi atom forming CsO2i, giving rise to the PL P-line at 767 meV [34]. Moreover, the mobileCi atom may also be trapped by an immobile Cs atom, forming the CiCs complex. This pairis a prominent irradiation-induced defect in C-rich materials. The defect can be electricallyactive, with a donor level at Ev+0.09 eV and an acceptor level at Ec-0.17 eV [26]. The defectcentre gives rise to a zero-phonon PL line at 969 meV, termed the G-line [34].

3.4 Thermal donors

Over 60 years ago, Fuller et al. [35] discovered that electrically active centres formed in oxygen-rich Si subjected to heat treatment in the temperature range of 350-500°C. Kaiser et al.

22


[36, 37] recognized these centres as donors, and established the involvement of oxygen bydemonstrating a correlation between the oxygen concentration and donor formation. Theinitial formation rate and maximum concentration of these donors were shown to have a powerdependence on the interstitial oxygen concentration of third and fourth order, respectively.Due to the donor action and the fact that they were created during thermal treatment, thecentres were named thermal donors (TDs).

Bean and Newman [20] suggested that the TDs acted as double donors, which following wasconfirmed by Wruck and Gaworzewski [38] and supplemented with the discovery of severaldifferent TD species on the basis of Hall effect and IR measurements. With Hall effect mea-surements, they observed two donor ionization energies. Isothermal heat treatments of the Sisamples revealed a decrease in these levels, which was used to prove that the donor ionizationenergies decreased with increasing annealing time. Spectra obtained with IR spectroscopyexhibited two groups of absorption lines. These groups were found to have approximatelythe energy separation of hydrogenic and helium-like donors in Si. The IR measurements wereperformed at both liquid-nitrogen (∼80 K) and liquid-helium (∼8 K) temperatures. At 80 Kboth groups of absorption lines were detected, while at 8 K the high energy series vanished.This difference was attributed to the position of the Fermi level at the respective measure-ment conditions. At the lowest temperature both donor levels were completely filled, andhence only transitions from the shallow level were detectable. The characteristic temperaturedependence of the two groups of absorption lines lead to the conclusion that the TDs were infact double donors. The hydrogenic and helium-like levels they were referring to were indeedthe transitions occurring in the neutral and singly ionized species, respectively.

Wagner et al. [39] eventually relabelled the donors to thermal double donors (TDDs), andindexed them TDDi ; The index i here represents both the temporal position in the formationsequence and order of decreasing ionization energy. The absorption spectra associated withthe neutral TDDi0 have been reported up to i=16 [39, 40], with ionization energies rangingfrom 69.3 to 41.9 meV (558 to 338 cm−1) and those associated with the singly-ionized TDDi+

up to i=9, with ionization energies ranging from 156.3 to 116 meV. In addition to absorptionin electronic transitions, TDDs can be identified by absorption in LVMs, when present inconcentrations above ∼1015cm−3 [41].

The discussed TDDs have a limited stability domain and become unstable when the annealingtemperature is increased above 550°C. At this temperature the TDDs annihilate, and show anexponential decay [42, 43]. At temperatures between 650-850°C, a second electrically activecentre forms in Si. These centres are also associated with the presence of O, and have beentermed New Donors (NDs) [44]. The formation of NDs are, in contrast to TDDs, promotedby a high C concentration ([C] > 2 × 1016cm−3) [18]. This work is focused on the thermaldonors forming in the 450°C range, and NDs will not be considered in the following.

3.4.1 Formation kinetics

It is widely accepted in the literature that TDDs share a common core structure, and thatthe development of higher index species is achieved by the introduction of O atoms [41, 42,45–47]. The formation kinetics of TDDs, however, present a significant problem for the directinvolvement of oxygen. The diffusivity of interstitial O in Si, DOi , in the temperature range

23


of TDD formation is given by [48],

DOi = 0.17× e−2.54eV/kBT cm2s−1. (3.9)

This corresponds to a diffusivity of 3.4×10−19cm2s−1 at 450°C, which is far too slow comparedto the diffusivity extracted from the TDD formation rate, which is 2×10−16cm2s−1 [37]. Ingeneral, the oxygen diffusion is 2-3 orders of magnitude slower than what is expected from TDDformation kinetics. Different models have been developed to account for the high formationrate. One model includes the existence of a fast diffusing oxygen species. Gösele and Tan[49] proposed the oxygen dimer (O2) as this fast diffuser. Another model was based on thedecoration of O clusters with fast diffusing I’s, or a combination of a fast diffusing dimer withI [46]. Moreover, enhanced Oi migration may also occur via a vacancy-assisted mechanism,where formation and dissociation of the vacancy-oxygen complex leads to a net movement ofthe Oi atoms through the Si lattice [50].

In traditional studies, the formation of TDDs have been correlated with the electronic transi-tion bands observed by IR spectroscopy. Important progress was achieved by the assignmentof LVMs to the first forming TDD species by Lindström et al [41]. The presence of LVM ab-sorption bands enabled the study of the formation kinetics in detail, without any interferenceof Fermi-level shift. As a result, a quantitative and detailed comparison could be made be-tween experiments and computer simulations of the TDD formation kinetics [45]. Absorptionbands at 975, 988 and 999 cm−1 were assigned to TDD1-TDD3, respectively. In addition,two bands at 1005 and 1013 cm−1 were correlated with the TDD growth. By studying thedevelopment of the assigned LVMs, Åberg et al. [45] proposed the direct transformation model.In this model the oxygen dimer accounts for the fast diffusion, and TDD1 is formed by theassociation of two dimers. Further, TDD2 was found not to involve additional O atoms, butrather a reconfiguration of TDD1 by a local jump of an Oi atom. The band at 1013 cm−1 wasassigned to a reactive form of the O dimer, and showed a decrease with annealing time. Theproduction of higher index species was assumed to involve the successive addition of dimers.The high initial formation rate was thus found to be dependent on the non-equilibrium con-centration of dimers established during crystal growth. Decrease of the dimer-LVM indicatedthat as the dimers were consumed, a new equilibrium concentration was reached given by theinflow from the Oi pairing, thus accounting for the slower formation rate with time.

3.4.2 Structural models

Since the pioneering work by Fuller et al. the TDDs have been assumed to consist of O atoms.However, structural models including vacancies and interstitials have been proposed to accountfor the characteristic formation kinetics, remarked in the previous section. The involvementof an IO2 unit in the core was proposed by Deak et al. [46]. This was however ruled outby Chadi [51] on the basis of total energy calculations. Persola et al. [52] also found that allstructures containing interstitials or vacancies have significantly higher formation energies thanoxygen-only structures. Moreover, among the oxygen-only structures, the electrically active R-and di-Y-lid-type O-chains have been found to have the lowest formation energies [47].

Magnetic resonance measurements have been used extensively to investigate the symmetryand local environment of the TDDs [18]. Electron paramagnetic resonance (EPR) measure-ments have revealed a centre called NL8, which directly correlates to the singly positive charge

24


state of TDDs [53]. The centre has C2v symmetry, with possible small deviations. Electronnuclear double resonance (ENDOR) spectroscopy can further distinguish between differentTDD species [54], and detects the hyperfine interactions between the paramagnetic electronand the nuclei surrounding the defect. Five different TDDs with decreasing hyperfine inter-actions, reflecting a de-localization of the defect wave function, were identified from ENDORmeasurements of NL8 [18]. With these methods it has been shown that the O atoms of TDDsoccur in the <110> plane [53,54]. Further, ENDOR indicates that the defects only can have Sion the C2 axis, this is however somewhat uncertain, as will be discussed. If the C2v symmetryis to be preserved during the growth of TDDs, the O atoms should be added symmetricallyin pairs, as in the kinetic simulations by Åberg et al. [45]. However, it has also been arguedthat a more natural assumption would be the addition of one by one atom, in which case theC2v and C1h symmetries would occur alternately [47].

The R model

The R-model TDD structure consists of adjacent four-member rings (R’s) and flanking in-terstitial oxygen atoms (Oi’s), illustrated in figure 3.2. The R unit consists of two threefoldcoordinated O atoms (Or’s) bonded to two common Si atoms. The O chains obtained forTDD0, TDD1 and TDDn are Oi-O2r, O2i-O2r, and Oi-Onr-Oi (n>1) respectively [52]. TheTDD species with an odd number of R rings (n = odd), or alternatively an even number ofO atoms, have C2v symmetry, while the species with an even number of rings have essentiallya C2v core, but the overall symmetry is C1h. However, the deviation from the C2v symmetryof the core, decreases with increasing even number of R-rings, n [47]. High-field EPR mea-surements have further indicated that some TDD members have a lower C1h symmetry [47].The Oi-Onr-Oi complexes are found to become increasingly de-localized and anisotropic withincreasing n, in agreement with ENDOR experiments. The model, however, includes theexistence of a single O atom on the C2 symmetry axis, in disagreement with ENDOR experi-ments [54].

Figure 3.2: Illustration of TDD3 in the R-model. Oi-O3r-O++i (TDD3) in the (110) plane. Red

and blue spheres denote oxygen and silicon atoms, respectively [52].

The di-Y-lid model

In the di-Y-lid model, the di-Y-lid core, shown in figure 3.3, consists of two O atoms (OY ),each bonded to three near-Si atoms in a Y-shaped fashion. The corresponding Oki-O2Y -Oli

chains (k,l≥1) with an even number of O atoms (k=l) fulfil the symmetry requirements, witha C2v symmetry, no O atoms on the C2 axis and with the O atoms placed in the (110) plane.

25


For the chains with an odd number of O atoms (k 6= l) the symmetry is lowered to C1h, incorrelation with the R-ring model.

Figure 3.3: O4i-O2Y -O++4i in the (110) plane. Two threefold oxygen atoms make up the core.

Red and blue spheres denote oxygen and silicon atoms respectively [52].

Comparison of the models

On the basis of density functional theory (DFT) calculations for the formation energies ofthe different TDD species, Persola et al. [52] argued that the R-model was energetically mostfavourable up to TDD8, and thereafter the di-Y-lid model became competitive. They ascribedthe difference between the models as following: The R-core can gain energy fast by formingnew adjacent R’s. The formation of the di-Y-lid core originally requires more energy, buthas a better ability to deform and release the strain caused by aggregating Oi’s. Althoughthe calculated atomic structures of both models grow longer along the <110> chain axis withincreasing n, the spin densities of only the R-type O-chains become longer along the chain axis.The R-type O-chains have been suggested as a consistent model for the TDDs. The modelhas lower formation energies, both increasingly de-localized spin densities of double-donorstates and increasing structural anisotropy, in agreement with experiments [47]. Furthermore,the LVMs ascribed to the first TDDs by Åberg et al. [45], have later been correlated to theasymmetric stretching vibrations of the flanking Oi’s of the O-chains in the R model [55],providing further support for the model.

3.4.3 The effect of carbon on donor formation

It has been well established that the presence of high concentrations of C strongly suppressthe formation of TDDs in Si [20, 56, 57]. The mechanism governing the suppression has beententatively described on the basis of many different points of consideration. However, as theprecise atomic structure of TDDs is not yet fully understood, no unanimous explanation hasbeen reached. Below, some proposed theories are given, in which several may account for theobserved effect.

One approach ascribes the suppression to a competing process of the interaction of O and Catoms to form C-O complexes [57], in which O atoms migrate preferentially to these defects.Simply, the trapping of mobile Oi and O2i by Cs is assumed to reduce TDD formation. IRspectroscopy studies have shown that for each Cs atom, two Oi atoms are removed from thesolution, d[Oi]/dt ∼ 2d[Cs]/dt, and CsO2i complexes are formed [58]. Further, as discussedin the previous sections, some models for TDD formation involve Si self-interstitials, I’s [46].As C is a particularly effective trap for fast migrating I’s, the reduced concentration has beenproposed to lead to a reduction of the TDD formation. Lastly, as Si atoms are larger than C,the presence of C on lattice sites leads to tensile strain in the crystal structure. The small Catoms tend to compensate the compressive strains which is due to the presence of O atoms at

26


interstitial sites. The impact of O agglomeration is thus assumed to be weakened, leading toa reduction in TDD formation [49].

3.5 Light induced degradation

When discussing O in Si, it would be inadequate not to mention the highly detrimental effectof light induced degradation (LID) occurring in boron (B) doped, p-type Cz-Si. Despite thename light-induced degradation, photons are not directly involved in the effect. In fact, thedegradation is caused by the injection of excess minority carriers, i.e., electrons, by a carrier-induced recombination mechanism. Hence, LID can be seen as a degradation of the solar cellefficiency by prolonged exposure to above band gap light or by forward biasing the cell inthe dark. The degradation process occurring under these conditions is directly linked to theformation of a recombination active boron-oxygen complex. While BO-LID will be discussedin the following, it should be noted that LID also may occur due to a recombination enhanceddissociation of iron-boron pairs, FeiBs [59].

The LID effect occurs by a two-step reduction in the charge carrier lifetime: (i) a fast andmoderate reduction followed by (ii) a slow and stronger reduction [60]. The active centresproduced in the two steps are termed fast recombination centres (FRC) and slow recombinationcentres (SRC), respectively.

Although LID has been studied extensively for the past four decades, the exact compositionof the recombination-active defects remain yet to be identified [61]. In earlier models itwas believed that the recombination centres were BsO2i, produced due to a carrier-enhanceddiffusion of O dimers (O2) trapped by immobile Bs. This was however ruled out on the basisof measurements on samples of low dimer-concentration, as these showed no reduction indegradation [62]. The effect has later been attributed to a carrier-induced reconfiguration ofsome already present, latent defects of low recombination activity into another recombinationactive state. FRC is assumed to start from latent BsO2 complexes and SRC from latentBiBsO. BiBsO is believed to reconfigure into SRC during carrier injection, changing chargestate from 0 to -1 [61].

The effect of LID can be completely removed by a short anneal at 200°C [61]. Nevertheless,as the efficiency is reduced by only a short exposure to light (on the order of minutes), LIDhighly complicates the use of B doped Cz-Si in solar cells. Traditionally, LID is mitigated byminimizing the concentration of B and O in the Si bulk. By replacing B as dopant with gallium(Ga) the effect of LID is strongly reduced. However, Ga has a low segregation coefficient, k,(see equation 3.3), which makes the growth of uniform-resistivity ingots challenging [61]. Instead, by reorienting the traditional pn-junction of the solar cell, making the substrate n-typeLID is excluded, as no degradation has been measured in clean P doped Cz-Si. Normally thesubstrate is doped p-type and the emitter is formed by subsequently doping a small part ofthe cell n-type. Despite of this, the use of n-type wafer substrates, with p-doped emitter hasnot been the standard, which is primarily due to a higher cost of n-type material. It may,however, be argued that the higher cost of n-type Si wafers is due to production history, ratherthan an actual difference in cost [63].

27

Chapter 4

Experimental techniques andprocedure

The main characterization techniques utilized in this work are Fourier Transform InfraredSpectroscopy, Four Point Probe resistivity measurements and Photoluminescence Spectroscopy.An introduction to these techniques, together with experimental procedure details will be givenin the following sections.

4.1 Fourier Transform Infrared (FTIR) Spectroscopy

This section is based on the references Griffiths and De Haseth [12] and Smith [64].Fourier transform infrared (FTIR) spectroscopy is a non-destructive, optical technique whichcan provide the qualitative identification and quantitative determination of impurities anddefects in a sample of interest. In FTIR spectroscopy, absorption spectra are generated bycollecting an interferogram of a sample signal, by using an interferometer. This is followedby a Fourier Transformation (FT) to obtain the desired spectrum. Unlike traditional disper-sive instruments the FTIR spectrometer possesses the advantage of measuring over a widerange of wavelengths quasi-simultaneously. To better understand the advantages of the FTIRspectrometer, knowledge of the interferometer is necessary.

4.1.1 The Michelson interferometer

The main component of the FTIR spectrometer is the interferometer. Most interferometersused today are based on the original two-beam interferometer, designed by Albert Michelsonin 1891 [65]. Despite its central role in IR spectroscopy, it was originally designed for researchon the luminiferous aether theory, where it provided the first strong evidence against themedium. Modern interferometers are further developed and differ from the one designed byMichelson. However, the fundamentals are similar, and therefore the Michelson interferometeris used to portray how modern interferometers are utilized in the recording of transmissionspectra.

28

CHAPTER 4. EXPERIMENTAL TECHNIQUES AND PROCEDURE

The purpose of the interferometer is to split an incoming beam of light into two componentsand generate a varying path difference between them. The primary constituents are twoperpendicular plane mirrors, one of which can travel in a direction perpendicular to the plane,and the beamsplitter, a semi-reflecting film that bisects the planes of these mirrors, illustratedin figure 4.1. Radiation emerging from an external source is directed towards the beamsplitter,where half of the radiation is reflected to the fixed mirror, while the other half is transmittedto the moving mirror. The reflected light will travel a distance of 2L before returning to thebeamsplitter. The moving mirror can be displaced a distance x from its initial position L andthe transmitted beam thus travels a distance of 2(x+L) before returning. Hence, an opticalpath difference of 2x is generated between the beams, commonly termed the retardation,δ.

Figure 4.1: Schematic overview of the Michelson Interferometer. The beam reflected to the fixedmirror will travel a distance of (2L) before returning to the beamsplitter. The beam transmit-ted to the movable mirror travels a distance of 2(x+L). When recombined, the beams interferedepending on the displacement x.

4.1.2 Generation of the interferogram

By considering the simple case of a monochromatic, coherent light source, the two beams willbe completely in phase and interfere constructively if δ is an integer multiple of the wavelengthλ,

29


δ = nλ. n = 0, 1, 2, ... (4.1)

Similarly, the beams will be completely out of phase and interfere destructively 1 if δ is anodd multiple of λ/2,

δ = (2n+ 1)λ

2. (4.2)

The intensity measured at the detector, ID, will therefore vary sinusoidally, with a maximumeach time the retardation δ is an integer multiple of λ:

ID(δ) =S(v)

2

(1 + cos

(2πδ

λ

)), (4.3)

where S(v) is the intensity of the monochromatic beam emitted from the source. The firstterm of ID(δ) represents a constant component, while the second term is the modulated part ofthe signal. The constant component, S(v)/2, does not contain any spectroscopic informationand is generally omitted. The modulated component is referred to as the interferogram, I(δ).Substituting to wavenumber, v = 1/λ, gives;

I(δ) = 0.5S(v) cos(2πvδ). (4.4)

When radiation with a distribution of wavelengths is emitted from the source, the measuredinterferogram is the resultant of the interferograms corresponding to each wavelength. Thus,when the source is no longer monochromatic, but a continuum of wavelengths, the interfero-gram is represented by the integral,

I(δ) =

∫ +∞

−∞S(v) cos(2πvδ)dv, (4.5)

where S(v) now is the spectral power density of the source. When δ = 0, all the wavenumbers will interfere constructively, resulting in a large intensity burst in the interferogram,termed the centre burst. When δ increases, the light of different frequencies will interact.An interferogram is therefore characterized by a centre burst with a complex patter of wavessymmetrically dispersed about it, as can be seen in figure 4.2.

The spectrum is obtained by recognizing eq.(4.5) as the cosine FT of S(v), and carrying outthe inverse FT:

S(v) =

∫ +∞

−∞B(δ) cos(2πvδ)dδ. (4.6)

1No photons are destroyed, though named destructive interference. Photons are a form of energy and hencecan not be created, nor destroyed. The photons simply travel in a different direction than towards the detector,they travel back towards the source in the Michelson interferometer, therefore giving no signal at the detector.

30


The resolution of a spectrum measured interferometrically depends on the maximum retar-dation of the mirror scan. According to eq.(4.6), the entire spectrum can be measured atan infinitely high resolution by scanning the movable mirror an infinitely long distance. Aninfinitely long mirror displacement has no practical meaning, and the maximum retardationδ must be limited to a finite value ∆. By restricting the mirror displacement to ∆, theinterferogram is effectively multiplied by a truncation function, D(δ), given by:

D(δ) =

1 if −∆ ≤ δ ≤ ∆,

0 otherwise.(4.7)

D(δ) is a simple boxar function, and its FT has the shape of the sine cardinal function sin(x)/x.Because of this limitation, the spectrum of a monochromatic source will not be an infinitelynarrow line. The line shape of a spectral line will instead be a broadened peak with a seriesof side lobes of diminishing amplitudes. These side lobes complicate the quantification of thespectral intensity. To circumvent this and to reduce the amount of side lobes in the resultinginstrumental line shape, more suitable truncation functions can be used prior to the Fouriertransform. This process is called apodization, and several apodization functions have beendeveloped. In this thesis a Blackman-Harris 3-term function is used, given by:

A(δ) =

C1 + C2 cos

(πδ

d

)+ C3 cos

(2πδ

d

)if 0 ≤ δ ≤ d

0 otherwise.(4.8)

In which d is the maximummirror displacement, and C1=0.42323, C2=0.49755 and C3=0.07922[66]. The obtained resolution in a FTIR spectrum depends on the maximum optical path dif-ference and the apodization function that is applied. The resolution ∆v scales approximatelyas the inverse of the maximum mirror displacement:

∆v =1

d(4.9)

An increase in the displacement will give a greater spectral resolution. However, measurementnoise also increases linearly with d. Therefore, the optimum choice of d will vary, dependingon the instrument and the measured sample. Signal to noise ratio (SNR) of the spectrum isproportional to the resolution [64],

SNR ∝ ∆v. (4.10)

4.1.3 Spectral treatment

A variety of treatments may be performed on the measurement data to facilitate presenta-tion and interpretation. Important techniques includes manipulation of interference fringes,spectral subtraction and baseline correction. These will be considered in the following sec-tions.

31


4.1.3.1 Interference fringes

When a sample is subjected to IR radiation, the propagating light may be directly transmittedand/or reflected from the front or rear sample surfaces. The light reflected from the rearsurface may further cause multiple internal reflections, which can interfere with the directlytransmitted light. This can be seen as a sinusoidal pattern over the entire spectrum, knownas interference fringes. To eliminate this undesired noise, it is customary to manipulate theinterferogram prior to taking the FT. Since the FT of a narrow peak is a sinusoidal wave, theinterference fringes will appear as a spike, alternatively called a secondary burst or signature,in the interferogram. For the samples used in this work, the interference spikes occur in arange with low amplitude of the interferogram, and may therefore simply be replaced by astraight line. The effect of replacing the spikes in the intefreogram by generating a straightline is illustrated in figure 4.2.

(a) Interferrogram. (b) Transmission spectrum

Figure 4.2: (a) Correction of interference fringes by replacing the secondary burst with a straightline. (b) Transmission spectrum before and after interferogram manipulation.

4.1.3.2 Spectral subtraction

When studying defects and impurities with IR spectroscopy the use of a reference sampleis advantageous. In addition to impurities or defects, the sample may also present intrinsiclattice absorption in the spectral region of interest. The total absorption coefficient at agiven energy is thus initially the sum of an intrinsic and extrinsic part. To circumvent theeffect of the Si lattice itself, e.g., multi-phonon absorption, the absorption spectrum of areference sample, is subtracted from the spectrum obtained for the sample of interest. Thereference used when investigating defects in Cz-Si, is commonly a Float-zone (Fz) grownSi material. Fz-Si contains concentrations of oxygen and carbon that usually are below thedetection limit of FTIR spectrometers, and therefore represents only the intrinsic contributionof the absorption.

32


4.1.3.3 Baseline correction

In an ideal IR spectrum the baseline is flat, at either 100% in a transmission- or at zero inan absorbance spectrum. However, when a sample is measured, the baseline may deviatefrom the ideal due to effects of scattering, reflection, temperature, concentration or instru-ment anomalies. Reflection from the sample surface and broad absorption features, i.e., fromfree carriers, will lead to the transmitted intensity of the sample being lower than for thebackground spectrum over the whole range. Thus, when calculating the absorbance spectrumfrom eq.(2.37), the baseline will be above zero at all wavenumbers. This offset is the sim-plest form of deviation from a flat baseline. To facilitate more convenient interpretation andpresentation of the spectra, the baseline should be set to zero in absorbance spectra. If thebaseline is simply shifted upwards by an offset, a constant (typically the minimum value) canbe subtracted from all spectral points. However, if the baseline is nonlinear, a polynomialcan be fitted to the baseline of the original spectrum. Polynomials are fit to operator selectedspectral data points, where the sample is considered to have minimal absorption. In thisthesis, polynomial functions of third to fifth degree has been applied and subtracted from thedata points, except for the principal oxygen absorption band, where the baseline was simplydrawn as a straight line between two data points. Peak absorbance could then be read directlyfrom the spectra.

4.1.4 Advantages and limitations of FTIR spectroscopy

Compared to traditional dispersive spectrometers, the FTIR spectrometry technique holdsseveral advantages. As mentioned, one of the most important reasons for the FTIR spec-trometers superiority is the possibility of measuring over a whole range of frequencies quasi-simultaneously. In grating spectrometers, the spectrum, S(v), is measured by recording theintensity of successive, narrow wavelength ranges. In FTIR spectrometers a set of wavelengthsfrom the IR source impinge simultaneously on the sample, and the whole range is measuredwith a single scan of the mirror. This is called the multiplex or Fellgett advantage. Further,a FTIR spectrometer has a substantially higher throughput than dispersive spectrometers.This so called Jacquinot advantage arises from the fact that the circular apertures used inFTIR spectrometers have a larger area than the linear slits used in grating spectrometers, thusenabling higher throughput of radiation. The combination of the Fellgett and Jaquinot advan-tages means that the signal-to-noise ratio (SNR) is considerably higher and the measurementtime is substantially shorter in an FTIR spectrometer, compared to dispersive spectrometers.Finally, all modern FTIR instruments have a highly precise internal system for wavenumbercalibration. The sampling intervals of the interferogram, δx, is the distance between two zero-crossings of a HeNe laser interferogram, and is therefore precisely determined by the laserswavelength. Since the point spacing in the resulting spectrum, δv, is inversely proportionalto δx, FTIR spectrometers have an intrinsic, highly precise wavenumber scale. This is calledthe Connes advantage.

There are some disadvantages with (FT)IR spectroscopy. IR spectroscopy in general requiresthat a vibration has a time-varying electric dipole moment. However, in the absence of achanging dipole moment, a change in polarizability can be measured in the complementarytechnique Raman spectroscopy, as mentioned in section 2.3.2. IR spectroscopy also requires

33


that the sample is sufficiently transparent in the IR spectral region. This is not an issue forpure, low-conducting materials, but highly doped samples can be difficult to measure dueto a high free carrier absorption. Furthermore, the quantitative determination of absorbingspecies requires predetermined calibration coefficients, which must be determined by othertechniques and calibrated for different measurement temperatures and resolutions. Moreover,FTIR spectroscopy is a single beam instrument, which means that the sample, reference andbackground spectra can not be recorded simultaneously. Fluctuations in sample environment,adjustment of beam, temperature etc, can play a minor role when calculating ratios for ab-sorbance spectra. Lastly, IR spectroscopy presents generally a low detection limit of absorbingspecies, of approximately ∼1015 cm−3.

4.1.5 FTIR instrumentation

A Bruker IFS 125 HR FTIR spectrometer, situated at UiO MiNaLab, was used for the mea-surements presented in this thesis. The Genzel type interferometer includes retroflectingmirrors, and uses a stabilized HeNe laser to determine optical path difference. The opticalpath of the spectrometer is illustrated in figure 4.3. A CTI-Cryogenics 8200 compressor coldfinger cryostat was used to cool the sample down to ∼ 18 K in vacuum for LT measurements.The temperature was recorded with a LakeShore 331 temperature controller. The samples ofeach series were mounted in a sample holder, while one aperture was kept empty to recorda background spectrum at the same measurement conditions. The RT measurements wererecorded by averaging over 4000 scans, while the LT measurements were performed by aver-aging over 2000 scans. The measurement data was treated using the included software fromBruker, Opus version 7.0. Polynomials were fitted around the individual absorption lines tosubtract the baselines and calculate absorption amplitudes with Python 3.0. Table 4.1 liststhe performance and optical configuration of the spectrometer.

Two different detectors have been utilized in this work, these can be distinguished in theway they convert infrared radiation to an electrical signal. The deuterated tri-glycine sulfate(DTGS) detector belongs to the class of thermal detectors. DTGS is a ferroelectric crystalwith a high temperature dependence of its spontaneous polarization. When infrared radiationis incident on the detector the increased temperature causes displacement of the atoms in thecrystal, which induces a change in the materials dielectric constant. This produces a capaci-tance change in an electric circuit, which provides the detector signal. The DTGS detector hasa response down to a wavenumber of approximately 370 cm−1 and is thus preferable for mea-surements of TDDs, as the ionization energies of the neutral TDDs occurs in the wavenumberrange of 338 to 558 cm−1, given in section 3.4. The main drawback of thermal detectors istheir slow response time. The photo-conductive mercuric cadmium telluride (MCT) detectoris a semiconductor pn-junction compound. When IR photons with energies greater than theband gap are absorbed in the material, electrons are exited into the detectors CB. The in-creased charge carrier concentration changes the materials resistivity. A bias current detectsthis change and transforms it into signal. This detector has a significant advantage over theDTGS detector regarding signal-to-noise ratio, and is hence significantly more sensitive. Thisdetector is thus preferable for kinetic studies. However, the MCT detector has a more limitedresponse, and is efficient down to approximately 600 cm−1. In addition, MCT detectors areconsiderably more prone to non-linear artefacts, which will be discussed in section 5.1.1.

34


Figure 4.3: Optical path in the Bruker IFS 125HR. In the figure detector and sample com-partment is marked. Scanner with movable retroflecting mirror (A), beam splitter (B), fixedretroflecting mirror (D), folding mirror (D), input aperture (E), sources (F), spherical mirror(G), collimating parabolic mirror (H), focusing parabolic mirror (I), toroidal mirror (J), colli-mating parabolic mirror (K), focusing parabolic mirror (L). Figure obtained from the instrumentmanual.

Instrumental configuration

Parameter Specification Spectral range (cm−1)

Resolution 0.5 cm−1 (LT)

Performance 1.0 cm−1 (RT)

Scanner velocity 10 Hz (DTGS), 40 Hz (MCT)

IR-source SiC Globar 100 - 6000

Optics Beamsplitter KBr 450 - 4,800

Detectors DTGS 370 - 12,000

LN2 cooled MCT 600 - 12,000

Table 4.1: Instrumental configuration of the FTIR instrument at UiO MiNaLab. Values areobtained from the instrument manual.

35


4.2 Four-point probe (FPP)

This section is based on the references by Smith [67] and Valdes [68].The four point probe (FPP) method is an electrical impedance technique that utilizes separatepairs of current-carrying and voltage-sensing electrodes to measure the electrical resistivity ofa sample. The set-up which consists of four co-linear, equidistant Tungsten wire probes isbrought in contact with the substrate to be measured, as shown schematically in figure 4.4.A current, I, is passed between the two outer probes while the potential difference, V, thatarises due to this current, is measured across the two inner probes. The resistivity, ρ, of thesample can then be calculated from the relation,

ρ = 2πsKV

I, (4.11)

where s is the probe spacing and K is a geometrical correction factor dependent on thegeometry of the sample. A selection of correction factors are published by various authors,e.g., Valdes [68], covering the modifications to be made according to the specimen size andshape being measured. If the carrier mobility, µ, of the sample is known, the carrier densitymay be calculated from the resistivity. For an n-type material the following relation gives thecharge carrier concentration,

n =1

ρqµ, (4.12)

where q is the elementary charge.

V

A

s s s

Figure 4.4: Schematic illustration of the setup used for resistivity measurements

In this work a Jandel RM3-AR Wafer probing FPP system has been used for resistivitymeasurements. To obtain a high statistical accuracy, the resistivity was calculated from theaverage of at least two values by applying different currents over the outermost probes. Acorrection factor of K=0.77225 has been applied for all samples.

36


4.3 Photoluminescence (PL) Spectroscopy

This section is based on the references by Pelant [69] and Gilliland [70].Photoluminescence (PL) is the optical radiation emitted from a material, following excitationto a non-equilibrium state, caused by the absorption of energetic photons. When an electronis exited across the band gap in a semiconductor by the absorption of photons, electron-hole-pairs are generated. The excited electrons will quickly thermalize to the band edge, beforeit recombines through one of a variety of recombination processes. At low temperatures, theexcited electrons and holes may, prior to recombination, bind together via Coulomb inter-actions to form free excitons (FEs). An exciton is a quasi-particle representing the lowestelectronic excitation in a semiconductor. In the presence of defects or impurities the excitonscan become localized at the defect, forming bound excitons (BEs). These bound excitons areimportant when characterizing donors and acceptors in semiconductors. The non-equilibriumdensity of electrons and holes, exitons or any other number of quasi-particles generated byexcitation will then recombine. If the recombination proceeds with the emission of a photonit is termed radiative recombination. When the energy of the excited electron is emitted asphonons instead of photons, it is accordingly termed non-radiative. In an indirect band gapsemiconductor like silicon the recombination must in general be accompanied by emission ofa momentum conserving phonon. However, in doped silicon, it is possible to see no-phononas well as phonon-assisted transitions. The spatial localization of an exciton to an impuritysite in real space leads to a greater delocalization of the electron and hole wave function ink-space. An overlap of wave functions permits electron-hole transitions which conserve k-vector without a participating phonon emission. The presence of acceptors and donors in thesemiconductor will lead to emission at distinct energies. PL spectroscopy thus provides a nondestructive technique for the determination of certain impurities in semiconductors.

In PL spectroscopy a monochromatic laser is utilized to excite electrons across the band gapof the semiconductor sample which is often cooled to cryogenic temperatures. Lasers areused for excitation to allow localized spatial resolution, well-defined penetration depth, anda mono-energetic initial distribution of electrons and holes. The sample is cooled to utilizethe formation of excitons. The resulting PL is then collected from the sample surface. Aspectrometer disperses the emitted PL and a photomultiplier tube detects the signal. Byregistering the photons which are emitted by the sample, the position of defect energy levelsin the band gap and their concentrations can be deducted.

The photoluminesence measurements have in this thesis been performed by employing 808nm excitation of a solid-state laser (DL808), Action Spectra Pro-275 monochromator andthermo-electrically cooled, Hamamatsu H103330 NIR-PMT detector, coupled to lock-in tech-nique. The excitation power of 250 mW (5 Wcm−2) was maintained constant throughout themeasurements in order to enable comparison of the PL intensities of the different samples. Aclosed cycle He refrigerator cryo-unit (Oxford OptistatAC) was used for the low temperaturePL measurements at 4K.

37


4.4 Experimental Procedure

The samples studied in this work were provided by the Norwegian solar energy company,NorSun, within the framework of the Norwegian centre for solar cell technology (FME-SOL).The sample notations that will be used are listen in table 4.2. Samples "A" were measured withFTIR spectroscopy and samples "B" with PL spectroscopy. The notation thereafter includesthe temperature at which the sample series have been isothermally annealed (450, 500 or 550°C). "C" denotes carbon-rich samples, cut from the tail end of the ingot. Samples marked "O"have a carbon concentration below the detection limit of the FTIR method and a high oxygenconcentration. These have been cut from the seed end of the ingot. Samples marked "(i)"have been irradiated with 2 MeV electrons to a dose of 1×1018 electrons/cm2. The irradiationwas performed by the Japanese Atomic Energy Agency (JAEA) in Tsukuba, Japan. Whendiscussing the results, the samples marked "C" are frequently referred to as carbon-rich, whilethe samples marked "O" are referred to as carbon-lean. The samples have been polished to anoptical surface on two sides. The dimension of all samples are approximately 5× 5× 1.5 mm3

and they have been phosphorous doped to a resistivity of ∼2 and ∼10 Ωcm for the carbon-rich(C) and carbon-lean (O) samples, respectively.

FTIR 450°C FTIR 500°C FTIR 550°C PL 450°C

A450C(i) A500C(i) A550C(i) B450C(i)A450C A500C A550C B450C

A450O(i) A500O(i) A550O(i) B450O(i)A450O A500O A550O B450O

Table 4.2: Sample notation.

Figure 4.5 shows the sequential sample treatments and characterization steps conducted in thiswork. Prior to any treatment all samples were cleaned with a three step RCA2 procedure, toeliminate contaminants. Before any thermal processing the samples of series A were measuredwith the FPP method and FTIR spectroscopy. Prior to each annealing step the samples werecleaned with acetone, ethanol and de-ionized water. The annealing was performed in a tubefurnace with a nitrogen gas ambient, to ensure an inert atmosphere. The sample cooling wassimply done by pulling the samples directly out of the furnace when the annealing durationwas completed, and then left to cool at RT. After thermal treatment the samples were dippedin a 50:1 de-ionized water and hydrofluoric (HF) acid solution for approximately 10 seconds toremove a potential SiO2 layer. The resistivity measurements were conducted straight after theoxide layer had been eliminated. FTIR measurements utilizing the MCT detector at RT wereperformed after every annealing step for all the samples. LT measurements with the DTGSdetector were performed at all steps for series A450, while for series A500 and A550 everyother annealing step was measured, starting from the untreated sample. Series A450 was alsomeasured at LT with the MCT detector for durations up to 128 hours, but was terminatedthereafter, as it did not provide any additional information.

2The RCA procedure is a standard set of wafer cleaning steps to remove contaminants. Step 1 removesorganic contaminants: 5:1:1 solution of deionized water, NH4OH and H2O2. Step 2 removes native SiO2 layer:50:1 deionized water and HF. Step 3 removes ionic contamination: 5:1:1 deionized water, HCl and H2O2.

38


Figure 4.5: Sample flow chart. *The listed annealing times are given by total time of thermaltreatment. **For series A500 and A550 every other annealing step was measured with the DTGSdetector at LT, starting from untreated samples (0 h) and including the last annealing step. Allsteps were measured with the MCT detector at RT.

39

Chapter 5

Results and discussion

In this chapter the results of the experimental procedure outlined in section 4.4 will be pre-sented and discussed. The results will be conferred first with regards to FTIR measurements,secondly to FPP measurements and lastly to the PL measurements.

5.1 FTIR measurements

To minimize confusion various aspects of the IR spectroscopy results are presented and dis-cussed in separate sections. In section 5.2 the preparation for the annealing series in termsof electron irradiation, and the effect of this, will be discussed. In section 5.3 the annealingstudies are presented. For a full overview of all the IR measurements and amplitudes of thevarious peaks, see appendix A. In order for the reader to easily observe the development andappearance of absorption bands after the thermal treatments, the obtained spectra of eachsample have generally been plotted together. In all figures presenting more than one spectrum,i.e. annealing duration, the sequential spectra have been shifted upwards along the y-axis tofacilitate the presentation. Hence, the absorption coefficient should not be read directly, butfrom the baseline of the respective spectrum. Furthermore, the processing of all presentedIR spectra has been performed in Origin Lab, in which a baseline was generated from userdefined points. The spectra presented in the following figures may therefore deviate slightlyfrom the quantitative calculations, in which the baseline of each peak has been separatelyfitted to a polynomial of 3rd to 5th degree and amplitude found thereafter. The deviationbetween presented spectra and calculations are within 10%.

5.1.1 Issues with MCT detector

Unfortunately, the MCT detector utilized for RT measurements turned out to be prone tonon-linear artefacts, typical for this class of detectors. The non-linear response could be seenin the spectra as a non-zero value at wavenumbers below the detector cut-off, i.e. outside thespectral range, given in table 4.1. In addition to the obvious deviation from a non-zero valueoutside the spectral range, the offset extended into the single-beam spectrum. The effect ofsuch non-linear response is to reduce the accuracy at which strongly absorbing bands can be

40

CHAPTER 5. RESULTS AND DISCUSSION

measured [71]. In particular, the carbon line at 605 cm−1 was initially greatly underestimated,compared to expected values. To circumvent this issue, a non-linearity correction factor wasapplied on the interferogram, prior to taking the Fourier transform. A cut-off value of 600 cm−1

and a modulation efficiency of 0.8 have been applied. Furthermore, the non-linear artefact wasnot realized until late in this work, hence quantitative calculations have not been correlated tovalues obtained by utilizing a DTGS detector, which is not affected by non-linear artefacts, atRT. For future use of the broad band MCT detector such a control would be beneficial.

5.2 Impact of electron irradiation

In this study, measurements and annealing series have been performed in parallel for cor-responding as-grown and irradiated samples. In this section the impact of irradiating thesamples with high energy electrons will be presented, with a particular focus on the effectof carbon on the formation of the VO-centre. The VO-centre further acted as precursor forhigher index VOn complexes when the samples were thermally treated.

In figure 5.1 the IR spectra of the as-grown and irradiated samples in series A500 are presented.It can be seen that several absorption lines of defect-complexes appeared after irradiation, asintroduced in section 3.3. In the carbon-lean sample, figure 5.1a, the absorption line of inter-stitial oxygen at 1107 cm−1 was found to decrease, while the absorption band of the VO-centreappeared at 830 cm−1. In the carbon-rich sample, figure 5.1b, both the interstitial oxygenand the substitutional carbon line at 605 cm−1 decreased, while several carbon-containingcomplexes formed in addition to the VO-centre. Absorption lines of the complexes CiOi (862cm−1), ICiOi (936 and 1020 cm−1) and CsCi (550 cm−1 (obtained at LT, not shown)) wereall found to form as a consequence of the electron irradiation. Comparing the amplitude ofthe VO band in figure 5.1a and 5.1b, it is evident that the VO concentration is significantlyhigher in the carbon-rich material.

(a) A500O/A500O(i) (b) A500C/A500C(i)

Figure 5.1: Spectra comparing samples in as-grown state and after irradiation. Illustrated bythe samples in series A500.

41


Table 5.1 lists the change in concentration of interstitial oxygen, substitutional carbon andVO-pairs from the as-grown to irradiated state. In the carbon-rich samples a seemingly higherconcentration of oxygen was taken up in VO-complexes, than the amount of interstitial oxygenwhich was lost from solution. The standard approach for quantifying the interstitial oxygencontent in Si samples is to measure the intensity of the principal 1107 cm−1 band in roomtemperature (RT) spectra [18]. However, if other defects exhibit absorption lines in the samewavenumber range, the strength of the Oi absorption line may be affected. Figure 5.2 showsthe IR spectra of the as-grown and irradiated sample, measured at both RT and LT. By con-sidering the spectra at LT, it can be seen that two absorption lines at 1104 and 1116 cm−1,due to the CsOi and CiOi pairs, respectively, appear in close proximity to the Oi line at RT.The CiOi pair also exhibits an absorption line at 865 cm−1 at LT, which shifts to 862 cm−1

when measuring at RT. This indicates that the position of carbon-oxygen lines does not shiftsignificantly when comparing RT and LT measurements. Further, since the 1107 cm−1 line atRT has a full width at half maximum (FWHM) of ∼30cm−1, it is likely that this peak "con-sumes" the appointed C-O lines at RT by overlapping. A further indication of overlapping isthat no absorption lines, which correspond to the 1104 and 1116 cm−1 at LT, were found atRT. It can also be seen that the shape of the oxygen line in the RT spectrum changed to amore "pointed peak" after irradiation. This development was not observed for the carbon-leanCz-Si samples, supporting the assumption of overlapping bands. Since the greatest change inamplitude after irradiation occurred for the CiOi line, the deviation in oxygen quantificationmay be assumed to mainly be due to this complex. Concluding that the Oi line at RT afterirradiation, included a significant contribution from the CiOi line, the total calculated [Oi]loss (square brackets denote concentration) in table 5.1 is underestimated. The CiOi complexhas further been found to be thermally unstable at the temperatures studied in this work, andhence will not affect the Oi quantification after the first thermal treatment. However, as willbe presented later, the total concentration of the CsOi complex changes, depending on an-nealing duration and temperature. Hence, when the concentration of this complex increases,the interstitial oxygen concentration will again be overestimated. It is therefore argued thatthe standard method for quantifying oxygen concentration in Si samples is not adequate whenmeasuring samples of high carbon concentration. Especially when the samples are irradiationdamaged. Since there is no known method for removing the contribution of these absorptionlines at RT, the standard method has been applied throughout this thesis. It is however notedthat the measured interstitial oxygen concentration is affected by the presence of C-O com-plexes.

42


Sample ∆[Oi] (cm−3) ∆[Cs] (cm−3) ∆[VO] (cm−3)

A450C(i) - 8.09×1016 - 1.51×1017 1.45×1017

A500C(i) - 6.89×1016 - 1.29×1017 1.39×1017

A550C(i) - 8.94×1016 - 1.43×1017 1.33×1017

A450O(i) - 9.76×1016 BL 4.59×1016

A500O(i) - 9.78×1016 BL 4.56×1016

A550O(i) - 1.05×1017 BL 4.15×1016

Table 5.1: Change in concentration of defects after irradiation. ’BL’ denotes a concentrationbelow the detection limit. The difference in interstitial oxygen, Oi, and substitutional carbon, Cs,are found by subtracting the values from the corresponding as-grown samples, e.g. [Oi]A450C(i)-[Oi]A450C .

Figure 5.2: Comparison of as-grown and irradiated carbon-rich sample, measured at LT andRT. The lines of carbon complexes at 1104 and 1116 cm−1 in the LT spectrum are likely hiddenby the Oi line at RT. At LT the interstitial oxygen line splits into several components due toisotope shifts of both the silicon and oxygen isotopes.

For the carbon-lean-samples in table 5.1, it can be seen that a higher concentration of in-terstitial oxygen was lost, than the amount taken up in VO-complexes, and no other newabsorption lines were detected. However, the remaining oxygen may be trapped in other de-fect complexes. Previously, the formation of IOi complexes has been suggested [30]. If thisreaction is participating, the remaining oxygen loss could be attributed to this formation. Theinvolvement of such pairs is discussed in the following section.

43


5.2.1 Simulation of VO development with irradiation

When Si is irradiated with MeV electrons, vacancies and interstitials are generated. Thesedefects are highly mobile and may therefore diffuse and agglomerate with other defects in thematerial to form large complexes. The experimental results listed in table 5.1, show that theconcentration of VO-centres, after irradiation, is a factor of three higher in the carbon-richsamples, compared to the carbon-lean. Carbon is a particularly effective trap for migratingSi self-interstitials (Cs + I → Ci). By this trapping, carbon prohibits the interstitials fromannihilating by recombining with vacancies. Hence, in the carbon-rich material, a higherconcentration of vacancies will be available to complex with oxygen, compared to the carbon-lean sample.

To describe the evolution of the VO-centre and its concentration during irradiation, a modelhas been applied in which the theory of diffusion-limited reactions is utilized. Such a reac-tion occurs between two species when they migrate and approach each other within a captureradius R. Within this range the diffusing specie(s) will be trapped and a complex is formed.The reaction rate is given by 4πR(DA+DB)[A][B], where DA and DB represent the diffusionconstants, and [A] and [B] are the concentrations of the two species A and B, respectively. Thediffusion constants are described by the relation D = D0e

−Ea/kT , where D0 is a pre-factor, Eais the activation energy, k is the Boltzmann constant and T is the absolute temperature. Thediffusion constants D of the mobile defects V, I and Ci at RT were taken as 4.15×10−9cm2s−1,3.16×10−4cm2s−1 [30] and 1.0×10−15cm2s−1 [32], respectively. Initial concentration of all de-fects are set to zero, except for oxygen and carbon, which were calculated from an average ofthe experimental values of the samples. In the carbon-lean sample, where the concentrationis below the FTIR detection limit, the carbon concentration was set to 5×1015cm−3. The fol-lowing reactions were included in the simulation, in which the associated differential equationsare listed in appendix C:

I + V → ∅ (5.1)I + Cs → Ci (5.2)V +Oi → V O (5.3)Ci +Oi → CiOi (5.4)Ci + Cs → CiCs (5.5)CiOi + I → ICiOi (5.6)V O + I → Oi (5.7)

(5.8)

Figure 5.3 presents the simulated development of [VO] with irradiation dose, in the carbon-rich (red line) and carbon-lean (blue line) samples, compared to the obtained experimentalvalues (red cross and blue circle, respectively). Since the VO concentration in the carbon-richsample is slightly overestimated, while the carbon-lean is underestimated, it is likely that aparticipating reaction is missing from the simulation. The involvement of the suggested IOi

defect would manifest itself by increasing the simulated [VO] concentration in both samples.However, by including this reaction in the model, both values were extremely overestimated,indicating that no such complex is involved. The interstitials diffuse much faster than any otherdefect in the material at RT, and the involvement of the IOi defect would be highly dominant.

44


Absorption lines at 944 and 956 cm−1 have previously been ascribed to the IOi defect, forsamples irradiated at 70 K [33]. However, the complex was reported to anneal out between200-250 K, and is therefore highly unlikely to be involved in the process when irradiatingat RT (300 K). Furthermore, if the carbon concentration determined experimentally fromIR measurements is overestimated, the simulation will overestimate the concentration of VO,since this value served as starting point for the simulation. However, the presented simulationemphasises the promotion of VO formation by the presence of a high carbon concentration. Itis further evident that when irradiating silicon at RT the interstitial is a dominating diffusingspecie, and VO is the most prominent irradiation induced complex.

Figure 5.3: Development of [VO] with total irradiation dose in the carbon-rich (red line) andcarbon-lean (blue line) samples. The red cross and blue circle represents the experimental valuesfor the carbon-rich and -lean materials, respectively.

5.3 Isothermal annealing studies

5.3.1 Irradiation induced complexes of low thermal stability

Several of the reported carbon-related complexes, generated by electron irradiation, were foundto have a low thermal stability in the temperature range (450-550°C) studied in this work,meaning that the absorption lines were completely absent after the first thermal treatment.Hence, the detailed temperature dependence of these complexes could not be investigated.The dissociation and formation of higher index species by these centres, however, affect thedevelopment of other complexes studied. The CiOi (862 cm−1) and ICiOi (940 and 1020cm−1) complexes are prominent irradiation induced defects, and were both found to formin the carbon-rich samples. The absorption line positions given in brackets were found inthe RT spectra. However, these defects also exhibited strong absorption lines at LT. At LT,absorption lines were found at 742, 865, and 1116 cm−1 for the CiOi pair, and 939 and 1024cm−1 for the ICiOi complex. Furthermore, an absorption line at ∼550 cm−1 was found in theLT measurements, ascribed to the CiCs pairs. No absorption line of this centre was foundin the RT measurements due to a more limited spectral range of the MCT detector, givenin section 4.1.5. It can be argued that no centres involving interstitial carbon are thermally

45


stable at higher temperatures, as carbon preferentially occupies substitutional sites in thesilicon lattice. Table 5.2 lists the relative intensities of the carbon complexes of low thermalstability. The presented values are extracted from LT measurements for the CiOi, CiOi, andCsCi peaks at 865, 939, and 550 cm−1, respectively.

Sample CiOi ICiOi CsCi

A450C(i) 1.458 cm−1 0.232 cm−1 0.402 cm−1

A500C(i) 1.327 cm−1 0.222 cm−1 0.356 cm−1

A550C(i) 1.283 cm−1 0.238 cm−1 0.357 cm−1

Table 5.2: Complexes of low thermal stability generated by electron irradiation. Given valuesare absorption peak amplitudes, deducted from LT measurements.

As can be seen from the table, small variations (∼10%) occur in the content of the variousdefects, among the three samples, ascribed to small variations in O and C concentrations andlikely also irradiation dose. However, the samples were assumed to account for comparablestarting points for the annealing studies.

5.3.2 Interstitial oxygen

The interstitial oxygen content in the various Si samples has been monitored in order to relatethe concentration to donor formation and interaction with other defects in the crystal. Theconcentration, [Oi], has been determined from the amplitude of the principal absorption bandat 1107 cm−1 in RT spectra, employing a calibration factor of 3.14×1017cm−2 [72]. Thebaseline was drawn as a straight line from 1050 to 1150 cm−1. When measuring at LT, theinterstitial oxygen line splits into several components, as seen in figure 5.2. This splittingis ascribed to isotope shifts of the oxygen (16O, 17O, and 18O) and silicon (28Si, 29Si, and30Si) isotopes, see eq.(2.27), and therefore complicates the quantification of oxygen from LTmeasurements.

In figure 5.5 the interstitial oxygen concentrations, after sequential annealing at 450, 500,and 550°C are presented and figure 5.4 summarizes the total [Oi] reduction after completedannealing durations. In the series annealed at 450°C, figure 5.5a, the largest [Oi] loss wasfound in the carbon-lean samples, in which the non-irradiated sample, A450O, showed thelargest decrease. This reduction is due to a large agglomeration of oxygen atoms into TDDs,as will be presented later. Furthermore, a substantial loss is seen for both of the carbon-leansamples between 256 and 400 hours of annealing. This development is quite abrupt and theresults need to be reproduced for a conclusive discussion. In the carbon-rich samples, theconcentration was found to remain close to constant throughout the whole annealing durationat 450°C, but also here a decrease occurred during the last treatment. As discussed in section5.2, the presence of C-O complexes is assumed to affect the quantification of the Oi content,and [Oi] will therefore be overestimated when the concentration of these are high. This is inparticular true for sample A450C(i), in which the CsOi defect was found to reach a steadystate concentration at 450°C, as will be presented in section 5.3.5.

46


When the samples were annealed at 500°C, figure 5.5b, the oxygen concentration was found todecrease in all samples. However, the largest loss was here found to occur in the carbon-richmaterials, indicating a generation of carbon-oxygen complexes or oxygen clustering. Since thetotal TDD formation was found to be substantially smaller in the carbon-rich samples, as willbe presented in the following, the higher [Oi] loss in these samples is therefore most likelydue to the formation of some carbon-oxygen involving defects, suppressing the formation ofTDDs. Furthermore, in compliance with results obtained at 450°C, the [Oi] concentrationdecreased more in sample A500O than in A500O(i), despite the presence of oxygen trappingVOn centres in the irradiated sample. This illuminates the high oxygen consumption by TDDformation in the non-irradiated material.

In the carbon-lean samples annealed at 550°C, seen in figure 5.4 and 5.5c, the evolution inoxygen concentration reversed, and [Oi] increased with annealing time. In sample A550Oa small reduction can be seen after 1 hour, while the concentration increased by prolongedannealing. In this sample, a small formation of TDDs were detected after 1 hour, but thesewere found to annihilate by prolonged annealing. No TDDs were detected in any other sampletreated at 550°C. The high thermal energy is thus assumed to prohibit the agglomeration andformation of the oxygen structures, making up the electrically active TDDs at 550°C. In thecarbon-rich samples the oxygen content decreased, indicating agglomeration of oxygen aroundcarbon atoms, since no TDDs were detected in either one.

Figure 5.4: Total calculated oxygen loss in all studied samples after completed annealing dura-tions. Negative values indicate an increased [Oi] relative to the initial concentration.

47


(a) A450

(b) A500

(c) A550

Figure 5.5: Development of interstitial oxygen concentration, [Oi], in sample series isothermallyannealed at 450, 500, and 550 °C. Shown with linear fit. In (a), the last two points of the carbon-lean samples are separately fitted for illustrative purposes.

48


5.3.3 Substitutional carbon

The substitutional carbon concentration, [Cs], has been determined from the amplitude ofthe absorption line at 605 cm−1 in the RT spectra, by utilising a calibration factor of 1.0 ×1017cm−2 [73]. The absorption band of Cs is partially masked by the rather strong two-phononabsorption of the Si lattice. By subtracting the spectrum of a carbon-lean, Fz-Si sample, mostof this was removed. Nevertheless, the baseline was somewhat difficult to determine as theintrinsic contribution could not be completely eliminated. However, the same baseline has beenapplied for all spectra, in which a polynomial of 5th degree was fitted around the absorptionpeak, and the development is therefore assumed to be unaffected by the coupling. An absoluteaccuracy of [Cs] ± 2.5×1016 was estimated.

The Cs concentration in the as-grown and irradiated samples are shown in figure 5.6, aftereach annealing step at 450, 500, and 550°C. By comparing the carbon concentration in theas-grown and irradiated samples, it is observed that a substantial amount was removed fromsolution after irradiation. The [Cs] prior to irradiation was ∼2.5×1017, and decreased to∼1.0×1017cm−3, a reduction of approximately 60%. As previously discussed, carbon is aparticularly effective trap for silicon self-interstitials, Is, forming interstitial carbon, Ci. Themobile Ci atoms are then trapped by oxygen and carbon, generating the defect centres CiOi,ICiOi, and CsCi, presented in section 5.3.1.

The concentrations in the as-grown and irradiated samples were found to follow a general trend,for all studied temperatures. In the non-irradiated samples, the Cs concentration decreasedthroughout the entire annealing duration. This development indicates that the carbon atomswere initially substitutional positioned. When the samples were annealed, some of these atomstrapped either interstitials or migrating oxygen atoms, eventually forming C-O complexes. Therate loss of substitutional carbon from solution was further found to increase with increasingannealing temperature. At higher temperatures the oxygen diffusivity increases, and thetrapping of Oi by Cs proceeds at a higher rate. For the irradiated samples, however, [Cs]increased with annealing time, with an increasing growth rate for higher temperatures. Themajor irradiation induced centres, CiOi, CiCs, and ICiOi, were found to be thermally unstablefrom 450°C, as discussed in section 5.3.1. Within the first thermal treatment, some of thesecomplexes associate with other defects and forms the more stable CsOni complexes, whilea considerable amount dissociate, releasing Cs. A substantial amount of the increase in Csconcentration thus occurs within the first annealing step. The gradual release of Cs atomsseen at 500-550°C, is due to the dissociation of smaller C-O complexes at higher temperatures.The evolution and thermal stability of the CsOi and CsO2i complexes are presented in section5.3.5. By prolonged thermal treatment, both of these complexes were found to decrease inconcentration after the initial formation. It is therefore argued that when interstitial oxygenis lost from solution, they agglomerate and form higher index CsOn complexes, rather thanforming new diatomic defect centres, which would require the removal of free-standing Cs fromsolution.

49


(a) A450

(b) A500

(c) A550

Figure 5.6: Development of substitutional carbon concentration, [Cs], in sample series isother-mally annealed at 450, 500, and 550 °C. Shown with linear fit.

50


5.3.4 Vacancy-oxygen complexes

Vacancy-oxygen complexes have been induced by electron irradiation, in order to comparethe development of these with the formation of TDDs at different annealing temperatures.An objective has been to determine if the dissociation of VOn centres contribute to TDDformation, by generating fast diffusion oxygen species, or if a direct involvement of thesedefects contribute to TDD formation. The obtained results indicate that different processesgovern the formation and dissociation of VOn at the various annealing temperatures. The VOn

concentrations were deducted from the peak amplitudes of the associated LVM absorptionbands: for VO (830 cm−1), VO2 (889 cm−1), VO3 (905, 969 cm−1), and VO4 (985 cm−1)calibration factors of 8.5×1016, 4.25×1016, 8.5×1016, and 4.25×1016cm−2 have been applied,respectively [72]. The VO3 and VO4 defects also exhibit absorption lines at ∼1001 and 1009cm−1, respectively, but these were omitted in the quantitative determination, in accordancewith the method used in [72]. A total concentration of VOn complexes up to n=4, [V], hasbeen estimated by [V]=[VO]+[VO2]+[VO3]+[VO4].

Isothermal annealing of VOn defects at 450°C

Figure 5.7 shows the absorption spectra of the irradiated samples sequentially annealed at450°C, for durations up to a total of 400 hours. A high concentration of vacancies weregenerated by electron irradiation. These vacancies were, to a large extent, trapped by Oi

atoms, forming the VO-centre. When these samples were annealed, larger species like VO2

and VO3, were formed by association with interstitial oxygen atoms, and new associatedabsorption bands evolved in the IR spectra.

(a) Sample A450C(i) (b) Sample A450O(i)

Figure 5.7: Section of absorption spectra measured at room temperature after RT irradiationand sequential isothermal annealing at 450°C.

In figure 5.8, the concentrations of the various VOn species (n≤4), presented in the IR spectra,are plotted against the annealing duration. One of the most prominent differences between

51


the carbon-rich and carbon-lean sample is the difference in concentration of the VO centre,as previously discussed. Thermal treatment led to the formation of VO2 by association withinterstitial oxygen. If this was the only reaction path for VO, the concentration of VO2 shouldbe much higher in sample A450C(i) compared to A450O(i). This is not seen, in contrast, asmaller concentration of VO2 was found in the carbon-rich sample. This expresses the com-petition for oxygen atoms in the sample containing a substantially higher amount of carbon.Moreover, the presence of a large number of irradiation induced centres, like CiOi, ICiOi, andCsCi, in the carbon-rich sample effectively increases the competition for VO during the firstthermal treatment. It is further observed that [VO] and [VO2] were not comparable in eitherof the samples, indicating that the dissociation of VO also is an important process. It canfurther be seen that the decay of [VO2] closely follows the growth of [VO3] for both samplesat the present temperature, demonstrating that the VO2 centre is less likely to dissociateand/or is less mobile than VO. VO3 thus forms by association with an interstitial oxygenatom, VO2 + Oi → VO3. In the carbon-rich sample, the concentration of VO3 after 400 hourswas approximately 30% lower than for the carbon-lean and no VO4 was found to form. Hence,at 450°C, carbon likely suppresses the formation of higher index VOn species. A concludingremark for the samples treated at 450°C is that no indication for the dissociation of VOn

(2≤n≤4) was found, rather the interaction with other defects formed higher index species. Inboth samples [V] increased with total annealing time, after the first initial decrease causedby the dissociation of VO-pairs. It is therefore argued that neither the dissociation of VOn

species, to form dimers (O2) or trimers (O3), precursors of TDDs, nor a direct involvement ofthese species, contribute to TDD formation at 450°C.

(a) A450C(i) (b) A450O(i)

Figure 5.8: Change in concentration of VOn (n≤4) complexes with annealing time for samplesannealed at 450°C.

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Figure 5.9 presents the absorption spectra of the irradiated samples sequentially annealed at500°C, for durations up to a total of 81 hours. The anticipated unstable defect VO, and for thecarbon-rich sample, both VO and CiOi, were present in considerable concentrations after 1hour of annealing. This is somewhat surprising, as these centres were expected to be unstableat 500°C, especially when considering the rapid loss of these species in the samples treatedat 450°C. It can further be seen that higher index VOn species formed faster at 500°C, thanat 450°C, presumably due to the higher diffusion rates, especially of Oi. Furthermore, thespectra obtained for each of the samples at 81 hours deviate significantly from the foregoingannealing step, and exhibit several new absorption lines in the range between 975-1051 cm−1.Previously, lines at 965, 1004, 1034, and 1048 cm−1, have been attributed to VOn (n=5,6)defects [74], but have also been suggested to originate from other VmOn complexes, by thesame authors. The absorption lines found at 1004, 1034, and 1051, cm−1 in both samples, arehere assigned to VOn (n=5,6) defects.


Figure 5.9: Section of absorption spectra measured at room temperature after RT irradiationand sequential isothermal annealing at 500°C.

It should be noted that all of the absorption lines that are present after 81 hours of annealing,are considerably more prominent in the carbon-rich sample, indicating a larger formation ofhigher index VOn defects at 500°C, when carbon is present. Figure 5.10 presents a section ofthe spectra obtained after 81 hours of annealing, and displays the different absorption linesascribed to the VO5/6 complexes. The absorption line at 1025 cm−1, emerging after 81 hoursin the carbon-rich sample, is tentatively ascribed to the CsO3i complex, and will be discussedin more detail later.

53


Figure 5.10: IR absorption lines of the VO5/6 defects after 81 hours of annealing at 500°C.

In figure 5.11 the concentrations of the various VOn species (n≤4) are plotted against anneal-ing duration. Considering first the carbon-rich sample, it can be seen that the VO2 defectdominated up until 27 hours, before it started to decrease and then [VO3] and [VO4] increased.The presence of strong VO5/6 absorption lines, as shown in figure 5.9a and 5.10, indicates thatthe reaction VOn + Oi → VOn+1 proceeds quite unaffected by prolonged thermal treatmentat 500°C. An equal development was not found for the carbon-lean sample, A500O(i), wherethe total concentration of VOn (n≤3) defects approached zero between 27 and 81 hours. After81 hours only a small concentration of the VO4 and VO5/6 defects were present in this sample.The rapid loss of especially VO3 may indicate that the VOn defects dissociate by prolongedannealing at 500°C, and possibly forms fast diffusing oxygen species, like dimers (O3) andtrimers (O3). The direct involvement of VOn centres in TDD formation will be discussedlater.

Some additional uncertainty has to be taken into consideration when discussing the presenttemperature series. When the samples were supposed to be annealed for 18 hours, to achievea total of 27 hours of thermal treatment, they were accidentally left in the oven for 18 hoursand 40 minutes, and thereafter not removed while the oven was cooling down. Hence, thesamples were cooled very slowly. The temperature dropped from 500°C to RT over 2 hoursand 20 minutes, corresponding to a cooling rate of ∼3.4°C/min. The effect of a slow coolis to annihilate more defects, when the temperature decreases eventually only interstitialsand vacancies will be mobile. After 27 hours the resistivity decreased significantly for theirradiated samples, as will be discussed in section 5.4.

54


(a) A500C(i) (b) A500O(i)



Figure 5.12 shows the absorption spectra of the irradiated samples sequentially annealed at550°C, for durations up to a total of 5 hours. For both samples, the VO3 and VO4 bandsappeared after only 30 minutes of annealing, while the VO2 band was completely absent in thecarbon-lean sample, and only weakly present in the carbon-rich sample. Furthermore, absorp-tion lines of the VO5/6 defects were found to form at around 2 hours in both materials.


Figure 5.12: Section of absorption spectra measured at room temperature after RT irradiationand sequential isothermal annealing at 550°C. Several new absorption lines can be seen.

55


The concentrations of the various VOn species (n≤4) after each annealing step are presentedin figure 5.13. Initially VO3 was the dominating complex and nearly accounted for the entire[V] after 30 minutes of annealing. Furthermore, [V] started to decrease after only 30 minutesin both samples. For the carbon-rich sample the transition from VO3 to VO4 resembles thecorrelated evolution of VO2 to VO3 in the sample annealed at 450°, while in the carbon-leansample, the evolution of VO4 progressed more slowly. The IR spectra of both samples in figure5.12 shows a presence of VO5/6 defects. In addition to the VO5/6 lines at 1004, 1034, and1051 cm−1, presented in the previous section, an additional line at 965 cm−1 ascribed to thesame defect(s) was detected in the carbon-rich material, A550C(i).

In contrast to the results obtained for the samples annealed at 450°C, the concentrations ofthe various VOn (n≤6) complexes were considerably higher in the carbon-rich, than in thecarbon-lean sample, after every annealing step at 550°C. The maximum concentration of VO3

was approximately 15% higher in sample A550C(i), compared to A550O(i). Hence, at thepresent temperature the formation of VOn defects is promoted in the sample with high [Cs].The larger concentration of VOn defects observed in the carbon-rich sample, is argued topartly be due to the increased oxygen diffusivity at 550°C, making the migrating Oi atoms astronger competitor for the capture of VO-centres within the first thermal treatment. More-over, an increased dissociation rate of the irradiation induced carbon-complexes at 550°C, willlikely increase the formation of VOn, relative to for example CsO2i, as the reaction VO +CiOi may be reduced.

(a) A550C(i) (b) A550O(i)


5.3.5 Carbon-related complexes

In section 5.3.1 the carbon-related complexes of low thermal stability were discussed. TheCiOi, ICiOi, and CsCi absorption lines were in general all removed after the first thermal

56


treatment. In this section the development of the more stable CsOi and CsO2i complexesat the various annealing conditions will be presented. The evolution of these centres weremonitored in terms of absorption coefficients at both RT and LT. The CsOi defect exhibiteda series of absorption lines, termed the X, Y, Z, and A line [34], positioned at 587, 640, 690,and 1104 cm−1, respectively, when measuring at 18 K. In RT spectra, the Y and Z line werefound at 637 and 684 cm−1, respectively. The X line was not found at RT due to the limitedspectral range of the MCT detector, while the A line is most likely consumed by the principalOi line at 1107 cm−1, as discussed in section 5.2.

Isothermal annealing of CsOn centres at 450°C

In figure 5.14, the absorption strength of the CsOi and CsO2i defects are plotted againstannealing time, obtained from RT (a) and LT (b) measurements, respectively. Apart fromsome minor deviations, all the CsOi lines followed the same development, as expected sincethey originate from the same complex. The large increase in concentration observed withinthe first thermal treatment, indicates that a substantial amount of the CsOi centres formedby the reaction CiOi + V → CsOi, resulting from the dissociation of the unstable VO centre,in addition to Ci + VO. The CsOi pair further reached its maximum concentration after128 hours of annealing, and thereafter remained approximately constant. This indicates thatthe centres exist in a steady state at 450°C, in which the formation and dissociation likelyproceeds at equal rates. The amount of the CsO2i complex was found to reach its maximumvalue after the first annealing step. It is therefore suggested that the CiOi defect competeswith interstitial oxygen atoms to trap the irradiation induced VO-centres, by the reactionCiOi + VO → CsO2i. Furthermore, the concentration of the CsO2i defect was found toslowly decrease, with an approximately halved concentration after 400 hours. An explanationfor this could be the formation of higher index species, by the trapping of an additional oxygenatom (CsO2i + Oi → CsO3i). Thus, at 450°C, the smaller CsOi complexes exist in a steadystate, while the larger CsO2i defects were likely consumed to form the higher index CsO3i

complexes.

57


(a) RT (b) LT

Figure 5.14: Development of absorption coefficients of C-O complexes in sample A450C(i),obtained from RT and LT measurements.


Figure 5.15 shows the development of CsOi and CsO2i in sample A500C(i), after sequentialannealing steps at 500°C. The maximum concentration of CsOi was found after 27 hours,while the CsO2i centre formed during the first two annealing steps, and thereafter startedto decrease. (Remember that VO and CiOi were surprisingly still present in considerableconcentrations after the first thermal treatment, as shown in figure 5.9a). Since both centresdecreased in concentration, while an increased [Oi] loss occurred by prolonged annealing, seefig 5.5b, it may be argued that the oxygen loss can be attributed to the agglomeration ofoxygen around these defects, forming e.g. CsO3i and higher index CsOni defects. In addition,since the decrease of the CsOi line did not correlate with an increase of CsO2i, the formercentre is possibly thermally unstable, and may dissociate at 500°C, rather than forming higherindex species by the trapping of Oi. In figure 5.16, the IR spectra obtained at LT for sampleA500C(i) are shown. The measured spectrum, after 81 hours of thermal treatment, exhibited aseries of new absorption lines in the 980-1110 cm−1 range, in which several of these are ascribedto VO5/6 defects, as discussed in the foregoing sections. However, a new absorption line wasdetected at 1026 cm−1. This line has previously been attributed to the CsO3i complex [33],supporting the assumption of sequential agglomeration of Oi by CsO2i.

58


(a) RT (b) LT

Figure 5.15: Development of absorption coefficients of C-O complexes in sample A500C(i),obtained from RT and LT measurements.

Figure 5.16: IR spectra obtained at LT for sample A500C(i) after sequential annealing steps at500°C.

59



The development of the CsOi and CsO2i complexes in sample A550C(i), after sequentialannealing steps at 550°C, are presented in figure 5.15. The divergence observed for the Yand Z line of CsOi, extracted from RT spectra, is due to minor difficulties when measuringthe absorption lines after the last annealing step, and is therefore ascribed to practical errors,rather than an actual development. In the LT measurements, the lines correlate. Furthermore,this evolution resembles the results found for the sample annealed at 500°C, but proceeds ata higher rate. The CsOi defect formed during the first 30-60 minutes of annealing, andthereafter decreased. In compliance with the two previous temperatures, the CsO2i complexreached its maximum concentration within the first annealing step, and then decreased, as ittrapped migrating interstitial oxygen atoms. The CsO3i line was detected after approximately2 hours, see figure 5.12a.

(a) RT (b) LT

Figure 5.17: Development of absorption coefficient of carbon complexes in sample A500C(i),obtained from RT and LT measurements.

Thermal stability of C-O complexes

In the previous sections, it was argued that the observed decrease of CsO2i is due to thereaction CsO2i + Oi → CsO3i, in which the immobile carbon complex traps a migratingoxygen atom. The reaction rate is therefore assumed to be determined by the diffusion ofinterstitial oxygen atoms. To support this assumption, the theoretical reaction rate constant,k1, must be on the same order of magnitude as the experimental reaction rate constant, k2,determined from the slopes of the CsO2i plots in figure 5.14a, 5.15a, and 5.17a.

The process can be described by a diffusion-limited reaction [75]:

d[CsO2i]

dt= −4πRDOi[Oi][CsO2i], (5.9)

60


where DOi is the diffusion constant for interstitial oxygen and R is the capture radius, set to5Å (geometrical value). The reaction rate constant can then be expressed by:

k1 = 4πRDOi[Oi]. (5.10)

Here [Oi] is set to the initial measured concentrations for the three samples (shown in figure5.5), and DOi is calculated from eq.(3.9). Further, by assuming that the reaction follows firstorder kinetics ([Oi] [CsO2i]), the development with time will be proportional to the reactionrate constant k2:

d[CsO2i]

dt= −k2[CsO2i], (5.11)

which when rearranged and integrated gives:

ln[CsO2i] = −k2t+ ln[CsO2i]t=0. (5.12)

By plotting the natural logarithm of the absorption coefficients of CsO2i where the complexwas found to decrease in figure 5.14a, 5.15a, and 5.17a, versus the annealing time, presented infigure 5.18, the reaction rate constant k2 could be read directly from the slopes. In the sampletreated at 550°C, the amplitude of the absorption lines decreased quickly, making the calcula-tions for this sample somewhat uncertain. The deducted values for k1 and k2 are listed in table5.3. They are indeed at the same order of magnitude, hence supporting the assumed reactionpath of CsO2i. The same argument may further be used to support the suggested reactionpath for CsOi. It was argued that the CsOi centre exists in a steady state at 450°C, while athigher temperatures becomes unstable and dissociates. If the CsOi centre were to form CsO2i

by the trapping of migrating Oi atoms, the reaction rate would have been determined by thediffusion of oxygen and therefore match the reaction rate extracted for CsO2i. The apparentdifferences in the slopes of CsOi and CsO2i at the various temperatures therefore supportsthe argument that CsOi dissociates at higher temperatures, rather than forming CsO2i by thetrapping of Oi.

Temperature (°C) k1 (s−1) (theory) k2 (s−1) (experiment)

450 1.94×10−7 5.43×10−7

500 2.79×10−6 3.25×10−6

550 2.74×10−5 1.58×10−4

Table 5.3: Deducted reaction rate constants for the formation of CsO3i.

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(a) A450C(i)

(b) A500C(i)

(c) A500C(i)

Figure 5.18: Extraction of experimental reaction rate constants, k2, by plotting the naturallogarithm of the absorption coefficients of CsO2i versus annealing duration.

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5.3.6 Thermal Double Donors

The development of TDDs has been followed by monitoring the IR absorption lines of electronictransitions for the various donor species. For a full overview of absorption lines related toTDDs, the reader is referred to "Oxygen in Silicon" by Shimura [18]. Furthermore, TDDs alsoexhibit absorption in LVMs [41], but the detection of these requires a species-concentration onthe order of ∼1015cm−3. No such absorption bands have been detected for any of the samplesstudied in this work. Further, since the absorption in electronic transitions is dependent onfilled electronic states, i.e. the position of the Fermi level, the absence of absorption linesmay not be directly considered as evidence for the absence of TDD species. To conclude onTDD development, the results have been correlated with resistivity measurements, presentedin section 5.4. Series A450 has in this work been measured at LT after every successiveannealing step, and is therefore used to portray the evolution of TDDs in detail. The samplestreated at 500 and 550°C will be presented at the end of this section.

TDDs in carbon-lean samples, annealed at 450°C

Figure 5.19 presents a section of the IR spectra obtained at LT for sample A450O, aftersequential annealing at 450°C. The presented wavenumber range corresponds to the energiesof neutral TDD transitions (TDD0). Absorption lines of TDDs appeared in the IR spectrumafter 8 hours of annealing. At this stage only TDD1-TDD3 were present, in which TDD2was the dominating species. After 128 hours, absorption lines of TDD2-TDD5 were detected,while the lines of TDD1 were completely absent. This indicates that TDD2 formed directlyfrom TDD1 by a local reconfiguration, in accordance with previous studies [45]. After 256hours of annealing, strong absorption lines of species up to TDD7 can be seen in the presentedspectrum. In addition, weaker absorption lines were found outside the presented wavenumberrange, likely due to TDD8 (388 cm−1) and TDD9 (376 cm−1). Due to a low signal-to-noiseratio below 390 cm−1, this area was omitted from the presentation.

When sample A450O was treated for an additional 144 hours (400 hours total), it was nolonger possible to distinguish between the different TDD species. Figure 5.20 compares theIR spectra of sample A450O at the two last annealing steps. After 400 hours, the free carrierabsorption was so dominant, that almost no IR radiation in the wavenumber range of neutralTDD transitions was transmitted, hence making the interpretation of the separate absorptionlines impossible. The increase in concentration of TDDs in this annealing period has, however,been estimated by resistivity measurements, to be presented in section 5.4, and indeed showeda large increase in donor concentration.

63


Figure 5.19: Spectra of the neutral thermal donors, TDD0, in sample A450O after successiveannealing steps up to a total of 256 hours. TDD8 (388 cm−1) and TDD9 (376 cm−1) appearoutside presented range.

Figure 5.20: IR spectra of sample A450O, after 256 and 400 hours of annealing at 450°C. After400 hours, free carrier absorption dominated strongly in the wavenumber range of neutral TDDtransitions, and it was therefore impossible to distinguish between different absorbing species.

64


Figure 5.21 presents the spectra obtained at LT for the irradiated, carbon-lean sample,A450O(i), after 256 and 400 hours of thermal treatment. No absorption lines of TDDs weredetected up to 256 hours of annealing at 450°C, while after 400 hours, absorption lines of boththe neutral (TDD0) and singly ionized (TDD+) TDD transitions were readily detected. Aspreviously discussed, for absorption in electronic transitions to occur, the donor levels must befilled with electrons. The damage caused by irradiating the sample with high energy electrons,generated compensating acceptor energy levels, thereby effectively keeping any potential TDDlevels empty. Between the last two annealing steps, the Fermi level shifted towards the CB,by the annihilation of acceptor defects and growth of TDDs, such that the TDD levels becamefilled with electrons, allowing for detection of electronic transitions. Furthermore, A450O(i)was the only sample exhibiting absorption in both the neutral and singly ionized TDD species.In the non-irradiated samples, the Fermi level was positioned above the neutral TDD level at18 K, not allowing for singly ionized transitions.

(a) Absorption in neutral TDD species (b) Absorption in singly ionized TDD species

Figure 5.21: Electronic transitions in neutral (a) and singly ionized (b) TDDs in sampleA450O(i) after 400 hours. No TDDs were present at 256 hours, presumably due to a highconcentration of compensating defects.

TDDs in carbon-rich samples, annealed at 450°C

Figure 5.22 gives an overview of the evolution of TDDs in sample A450C, after sequentialannealing at 450°C. Weak absorption lines of TDD2 are seen after 8 hours, while TDD1and TDD2 were both found at 32 hours. The strength of TDD1 is almost always negligiblecompared to TDD2. When higher index species began to develop, no absorption lines ofTDD1 remained. Furthermore, it should be noted that TDD3 did not appear in the spectrumuntil 256 hours of annealing was completed, in contrast to the carbon-lean material (fig 5.19),where TDD3 appeared at the same time as TDD2, after only 8 hours. This indicates that theformation of TDD3 is suppressed in the carbon-rich material. After 400 hours, species up toTDD5 were detected. The corresponding irradiated sample, A450C(i), showed no developmentof thermal donors during the entire annealing duration of 400 hours.

65


Figure 5.22: Spectra of the neutral thermal donors, TDD0, in sample A450C after successiveannealing steps up to 400 hours.

TDDs in samples treated at 500°C

Figure 5.23 compares the IR spectra obtained for the carbon-lean samples annealed at 500°Cfor 81 hours. In the irradiated sample, A500O(i), rather weak absorption lines of TDD2-TDD5can be seen. No TDDs were detected at earlier stages for this sample. For the non-irradiatedsample, weak absorption lines of TDD2 were present after 27 hours of annealing, while strongabsorption lines of up to TDD7 can be seen at 81 hours. This indicates that the presence of ahigh concentration of VOn defects suppresses formation of TDDs by consuming oxygen atomsand acting as traps during annealing. VOn centres are therefore argued to not be directlyinvolved in the TDD formation. In sample A500C, weak absorption lines of TDD2 at 442and 488 cm−1 were found after 27 hours, while after 81 hours no TDD lines were detected.However, even though the electron concentration increased between the last two steps for thissample, as will be presented in section 5.4, the final estimated TDD concentration was on theborderline of what can be detected with IR spectroscopy. Thus, if some of the TDD2 speciestrapped oxygen and formed TDD3 etc., the concentration of each species is argued to be belowthe detection limit. As for the sample treated at 450°C, no absorption lines of TDDs weredetected in sample A500C(i). Again, the absence of TDDs is assumed to be a combination ofthe consumption of oxygen atoms by the various VOn defects, in addition to the suppressionby the presence of carbon and carbon-complexes.

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Figure 5.23: IR spectra of TDDs in sample A500O and A500O(i), after 81 hours of annealingat 500°C.

TDDs in samples treated at 550°C

A contrasting development was seen when annealing the samples at 550°C. Figure 5.24 presentsthe IR spectra of sample A550O, obtained for the as-grown state, and after 1 and 3 hours ofthermal treatment, respectively. A number of absorption lines of TDD2-TDD3 had formedafter 1 hour, where as by the fourth thermal treatment (3 hours total), these lines were com-pletely absent. Moreover, no new lines were detected after the final annealing step, indicatingthat the TDDs present after 1 hour where annihilated by prolonged thermal treatment at550°C. It is therefore suggested that the fast, but small formation of TDDs was largely due tothe agglomeration of an already present, initial concentration of oxygen dimers. These dimerslikely formed during crystal growth and cooling. By annealing the sample for a short periodthese initial dimers probably agglomerated, forming the first TDD species. By prolonged an-nealing however, these structures dissociated due to the high thermal energy. Furthermore,no absorption lines of TDDs were detected in either of the irradiated samples A550C(i) andA550O(i), nor in A550C, at any stage at 550°C.

67


Figure 5.24: IR spectra of TDDs in sample A550O. The prolonged annealing at 550°C presum-ably led to the annihilation of TDDs.

5.4 FPP resistivity measurements

The IR absorption lines of electronic transitions in the various TDD species are not suitablefor quantitative determination. By monitoring the change in resistivity after the sequentialthermal treatments, an estimate of the total TDD concentration has been made. In thissection the four point probe resistivity measurements are presented separately for the threestudied annealing temperatures, and discussed consecutively. The measured resistivities of allsamples, after each annealing step, are given with standard deviations in appendix B.

Resistivity change after sequential annealing at 450°C

In figure 5.25 the measured resistivities of the as-grown (a) and irradiated (b) samples, aftersequential thermal treatments at 450°C are shown. The resistivity of all samples was foundto decrease, which for the non-irradiated samples directly indicates a formation of donors.Annealing of the irradiation damaged samples resulted in a resistivity reduction, as defectswere annihilated, and possibly also due to the formation of donors.

The resistivity of the carbon-rich, non-irradiates sample, A450C, was found to be close toconstant at ∼2 Ωcm up to 256 hours of annealing. After 400 hours the resistivity decreasedto ∼1.25 Ωcm, indicating a small formation of donor species. This development is in strongaccordance with the results obtained by IR spectroscopy, presented in figure 5.22, where

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the spectra exhibited lines of TDD2 and TDD3 at 256 hours, while substantially strongerabsorption lines of up to TDD6 could be seen at 400 hours. In the carbon-lean sample, A450O,the resistivity decreased from 10.8 to 0.4 Ωcm, indicating a strong formation of donors. Inthe IR spectra in figure 5.23 and 5.20, species up to (at least) TDD9 were detected. Thetotal resistivity reduction is therefore found to be approximately 96% and 40% in samplesA450O and A450C, respectively, illuminating the strong suppression on TDD formation, bythe presence of a high carbon concentration. It should also be noted that the entire reductionin resistivity in sample A450C occurred between 256 and 400 hours.

The defects generated by high energy electron irradiation, caused an increase in the resistivityby several orders of magnitude, for samples A450C(i) and A450O(i). For the carbon-rich sam-ple, the resistivity was found to be 1.3×105 Ωcm prior to any thermal treatment, but rapidlydecreased as the material was annealed. This reduction is largely due to the annihilation ofdefects. By prolonged thermal treatment the resistivity of sample A450C(i) approached thevalue of the as-grown sample, but ended at 14 Ωcm, ∼12 Ωcm higher than the as-grown ma-terial. No absorption lines of TDDs were found in this sample. For the carbon-lean sample,A450O(i), the resistivity after irradiation was found to be 1.3×104 Ωcm. In the first 64 hoursof annealing the resistivity increased, likely due to the formation of deep acceptor species.However, after 64 hours the resistivity decreased, and after 400 hours the value was as low as0.77 Ωcm, almost 10 Ωcm below the value measured for the corresponding as-grown material,indicating a strong formation of donor species. Absorption lines of electronic transitions inboth the neutral and singly ionized TDDs up to TDD7 were found, as presented in figure5.21.

(a) Non-irradiated samples (b) Irradiated samples

Figure 5.25: Change in resistivity with annealing time for sample series A450. Dotted lines in(b) indicate the as-grown resistivity for the corresponding samples.

By assuming a room temperature electron mobility of µn = 1350 cm2Vs [7], the electronconcentration, n, has been estimated from eq.(4.12). The extracted electron concentrationsafter sequential annealing steps are shown in figure 5.26. It can be seen that both carbon-lean samples experienced a strong increase in charge carrier concentration between 256 and

69


400 hours. The strong increase observed for the irradiated sample, A450O(i), explains thesudden detection of several TDD species after 400 hours, while none could be seen after 256hours, as presented in figure 5.21. The total electron concentration in this sample went from1.15×1012cm−3 to 5.69×1015cm−3 between the two last annealing steps. By utilizing eq.(2.18)an approximation has been made for the position of the Fermi level at the two respectiveannealing durations. Rearranging eq.(2.18) gives:

EF = kT × ln(n0ni

)+ Ei. (5.13)

Where the intrinsic Fermi level, Ei, was approximated to lie in the middle of the band gap,Eg/2 = 555 meV, and the intrinsic carrier concentration at RT is ni = 1.5×1010cm−3 [7]. At256 hours, the Fermi level was, by this estimate, positioned at ∼667 eV, i.e. 443 eV belowthe CB. Whereas at 400 hours EF was found at ∼888 eV, only 222 eV below the CB. Hence,by imagining the band gap divided into four equal parts, the Fermi level was positioned inthe quantile directly above the middle of the band gap at 256 hours, while after 400 hours ofannealing, the Fermi level was positioned in the uppermost quantile. The presence of a highconcentration of acceptor defects thus prevented the detection of TDDs with IR spectroscopyat 256 hours of annealing. It is argued, however, that TDDs most likely had formed at 256hours, since species up to TDD7 had evolved after 400 hours.

Figure 5.26: Development of charge carrier concentration, n, in series A450.

From the extracted charge carrier concentration, n, an estimate of the total TDD concentra-tion, [TDD]tot, has been made. Since the TDDs are double donors, each species donates twoelectrons to the CB at RT. Hence, [TDD]tot may be estimated by calculating the difference incharge carrier concentration prior to, n1, and after, n2, annealing and dividing by two:

[TDD]tot =n2 − n1

2(5.14)

This estimate is only valid for the non-irradiated samples, as we can assume that no donorspecies, except for the Phosphorous doping, existed in the material prior to any thermaltreatment. However, the donor formation in the irradiated samples may be estimated by

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approximating n1 to the value of the corresponding non-irradiated sample. The results forsample series A450 are listed in table 5.4. The formation of TDDs is found to be a factor of 7higher in the non-irradiated carbon-lean sample, compared to the carbon-rich. However, themaximum concentration of TDDs is very sensitive to the oxygen content in the Si sample, andthe slight difference in [Oi] between the carbon-lean and carbon-rich sample should thereforebe taken into consideration. The maximum TDD concentration has been shown to have apower dependency on the interstitial oxygen concentration of fourth order [37], i.e. [TDD]max∝ [Oi]4. The interstitial oxygen concentration in the as-grown materials, shown in figure5.5a, was found to be 1.10×1018cm−3 and 9.84×1017cm−3, in sample A450O and A450C,respectively. By extracting the ratio of maximum TDD concentration in the two materials,a factor of approximately 1.6 higher concentration was expected in the carbon-lean material.The factor of 7 extracted experimentally therefore further illuminates the suppression on TDDformation by carbon. Furthermore, the non-irradiated sample A450O had developed a factorof 2 higher TDD concentration compared to the corresponding irradiated sample, A450O(i),after 400 hours of annealing at 450°C. It is therefore concluded that VOn defects are notdirectly involved in TDD formation, but rather act as traps for migrating oxygen atomsduring annealing, reducing the TDD formation.

Sample R1 (Ωcm) n1 (cm−3) R2 (Ωcm) n2 (cm−3) [TDDtot] (cm−3)

A450C 2.09 2.22×1015 1.25 3.69×1015 7.38×1014

A450O 10.84 4.27×1014 0.41 1.12 ×1016 5.41×1015

A450O(i) 10.84* 4.27×1014* 0.81 5.69 ×1015 2.63×1015

Table 5.4: Estimate of total TDD concentration after 400 hours of annealing at 450°C.*Value obtained from corresponding non-irradiated sample.


Figure 5.27 presents the resistivities of the samples thermally treated at 500°C. In compliancewith the results obtained at 450°C, the resistivity of the non-irradiated, carbon-rich sample,A500C, remained almost constant throughout the whole thermal treatment, with only a mod-est reduction from 2.16 to 1.99 Ωcm after 81 hours of annealing. As presented in section 5.3.6,weak absorption lines of TDD2 were detected at 27 hours, while no lines were found after 81hours. This was argued to likely be due to a partial evolution from TDD2 to TDD3, leadingto a concentration of both species below the detection limit. If the absence of absorption lineshad been due to annihilation of the TDDs, the resistivity should have increased, rather thanthe observed decrease. In contrast, the carbon-lean sample experienced an immense reductionfrom 11.32 to 0.81 Ωcm, which mainly occurred between 27 and 81 hours. In figure 5.23,strong IR absorption lines of donor species up to TDD7 were presented. The total resistiv-ity reduction was thus found to be approximately 93% and 8% in the carbon-lean and -richmaterials, respectively.

As described previously, the annihilation of defects caused a strong resistivity reduction in theirradiated materials. Furthermore, the resistivity of sample A500C(i) closely approached theas-grown material, with a final value of 2.24 Ωcm after 81 hours at 500°C. However, no TDDs

71


were detected with IR spectroscopy for this material. It is thus argued that the absence ofTDD absorption lines in the IR measurements were due to an actual absence of TDD speciesin the material, and not an effect of the Fermi level position, as the low resistivity of thissample should allow for electronic transitions. For sample A500O(i) the final resistivity wasfound to be 5.65 Ωcm, approximately 5.7 Ωcm below the as-grown material. Rather weakabsorption lines of up to TDD5 were detected in the material, as presented in figure 5.23.The extracted electron concentrations after each annealing step at 500°C, for all samples, arepresented in figure 5.28.




By the same approach as in the previous section, the total concentration of TDDs, [TDD]tot, inthe various samples, have been estimated and the results are listed in table 5.5. Here, an even

72


larger difference is seen between the carbon-lean and carbon-rich material, in which sampleA500O had developed a factor of 30 higher TDD concentration than sample A500C. The in-terstitial oxygen concentration in sample A500O and A500C were found to be 1.12×1018cm−3and 1.00×1018cm−3, respectively, again giving an expected factor of ∼1.6. Hence, after 81hours of annealing at 500°C, carbon has an even more prominent effect on TDD suppression.Comparing sample A500O and A500O(i), the total TDD concentration is found to be a fac-tor ∼13 higher in the non-irradiated material, supporting the exclusion of VOn as directlyinvolved in TDD formation. Furthermore, the absolute values of [TDD]tot were higher, for allsamples, after 400 hours at 450°C, than after 81 hours at 500°C. This is in accordance withprevious studies which showed a maximum saturation concentration of TDDs at 450°C [18].

Sample R1 (Ωcm) n1 (cm−3) R2 (Ωcm) n2 (cm−3) [TDDtot] (cm−3)

A500C 2.16 2.14×1015 1.99 2.32×1015 8.79×1013

A500O 11.32 4.08×1014 0.81 5.70×1015 2.65×1015

A500O(i) 11.32* 4.08×1014* 5.65 8.18×1014 2.05×1014

Table 5.5: Estimate of total TDD concentration in non-irradiated A500 samples after 81 hoursof annealing at 500°C. *Value obtained from corresponding, non-irradiated sample.


Figure 5.29 presents the development in resistivity for the samples treated at 550°C. In partialcompliance with the non-irradiated carbon-rich samples treated at 450 and 500°C, the resis-tivity of A550C was found to remain constant at ∼2.1 Ωcm, throughout the whole annealingduration at 550°C. At 450 and 500 °C, figure 5.25a and 5.27a, respectively, the resistivities ofthe non-irradiated, carbon-lean samples were shown to strongly decrease with annealing time,attributed to the large formation of TDDs in the materials. At 550°C, however, the resistivityof sample A550O decreased up to 1 hour, but thereafter regained its initial value. This is instrong accordance with the results obtained with IR spectroscopy, presented in figure 5.24,where the spectrum exhibited absorption lines of TDD2 and TDD3 after 1 hour, while thesewere completely absent in the next measurement. The regained as-grown resistivity indicatesthat the few TDDs which had formed initially, were unstable and annihilated by prolongedannealing. By evaluating the extracted electron concentration, presented in figure 5.30, itwas found that a total TDD concentration of [TDD]tot = 7.95×1013cm−3 had formed after 1hour, after which 98% had annihilated within the next hour of thermal treatment. Hence at550°C, the TDDs were found to be unstable. This is in agreement with previous studies onthe annihilation of TDDs, which showed an exponential decay at temperatures between 540and 565°C [42].

The large drop in resistivity observed for sample A550O(i) and A550C(i), indicates a rapidannihilation of defects at 550°C. In the irradiated carbon-lean material, a large resistivitydrop is observed within the first annealing, followed by a slower reduction until completedannealing duration. The final resistivity was measured to approximately 12.7 Ωcm, ∼1.7 Ωcmabove the as-grown material. In the carbon-rich sample, A550C(i), the initial development

73


was similar, but the resistivity did not decrease any further after the first drop, remainingapproximately 1.2 Ωcm above the as-grown material. This indicates that some deep acceptordefects possibly form in the material at 550°C, prohibiting the resistivity from reaching theas-grown value.




It could be argued that the samples were not annealed for a long enough time period at 550°C,to be comparable with the series treated at 450 and 500°C, with regards to TDD formation.However, by evaluating the oxygen diffusivity, given in eq.(3.9), at the various temperatures,a comparison could be made for the formation rates expected. Thus, by extracting the oxygendiffusivity at the three temperatures and calculating the ratio between them, it was found thatthe oxygen diffusion proceeds approximately 14 times faster at 500°C than at 450°C. While

74


the diffusivity is over 141 times faster at 550°C than at 450°C. Comparing 500 and 550°Cgives a ratio of 10. Therefore, since a large TDD formation was found to occur between 27and 81 hours at 500°C, and 5 hours is estimated to correspond to 5×10=50 hours at 550°Cin terms of oxygen diffusion, it is argued that it is not the short annealing time that accountsfor the absence of TDDs at 550°C. Rather, the high thermal energy hinders the agglomerationof oxygen into the specific structures of TDDs at the highest temperature, i.e. the TDDs arenot stable at 550°C. This reasoning is further supported by the observed annihilation of TDDspecies in sample A550O, shown in figure 5.24.

5.5 Photo Luminescence measurements

PL measurements have been performed in an attempt to relate the obtained results to theIR measurements, specifically with regards to carbon-related complexes and TDDs. In thissection, the most prominent luminescence lines will be discussed.

5.5.1 Carbon lines

In analogy with the irradiation induced carbon-complexes studied with IR spectroscopy, ir-radiation damage generates photoluminescence centres in Si. Several of the carbon-relatedcomplexes generated by electron irradiation forms deep defect states in the band gap of Si,and exhibit a series of luminescence lines in the 0.7-0.9 eV range [76]. Previously, a numberof PL lines have been reported and related to various carbon-related defects. The two lines,termed the C-line at 789 meV and G-line at 969 meV, have been shown to be induced byelectron irradiation. The P-line at 767 meV has been reported to form by annealing C- andO-rich Si. [76].

In figure 5.31, the mid band-gap emissions of sample B450C(i) after irradiation and sequentialannealing, are displayed. The obtained PL spectra of the irradiation damaged carbon-rich Sisample can be described as a broad luminescence band, with sharp lines superimposed on thebroad feature. In accordance with the previously reported lines, two particularly sharp andnarrow lines are observed after irradiation. The zero-phonon G-line at 969 meV has previouslybeen ascribed to the CiCs complex [77]. In compliance with the FTIR results, where the CiCscomplex was found to be thermally unstable, the G-line is completely absent after the firstthermal treatment. The C-line has previously been correlated to the CiOi complex [78], andis strongly present in the spectrum after electron irradiation. Neither the C- or the G-linewere detected in the irradiated carbon-lean sample, nor in the as-grown materials.

In figure 5.32 a selected section of the PL spectra are presented, displaying the developmentof the C- and P-line after sequential thermal treatments. The almost completely maintainedintensity of the C-line after both 2 and 4 hours of annealing is unexpected, and contradictsthe FTIR results, which showed that the CiOi complex was unstable at 450°C. However, after64 hours, the C-line is completely absent. It may therefore be argued that the C-line, afterannealing for 2-4 hours, contains a contribution from another defect, as the CiOi complexis highly unlikely to withstand several hours of annealing at 450°C. The P-line, ascribed tothe CsO2i complex [79], emerged after the first thermal treatment, and exhibited a seeminglyincreased intensity after 64 hours of annealing. The intensity of the IR absorption band of

75


CsO2i, presented in figure 5.14, revealed a slight decrease in concentration after 64 hours.PL spectroscopy is however considered as a qualitative, rather than a quantitative method.Especially when compared to IR measurements, where the absorption strength of a species isdirectly proportional to its concentration in the material.

Figure 5.31: PL spectra of the carbon-rich sample B450C(i) after irradiation and sequentialannealing at 450°C. The sample notation N2T3C in the figure corresponds to B450C(i).

Figure 5.32: PL spectra of carbon-related defects emitting zero-phonon lines at 767 meV (P-line)and 789 meV (C-line). The sample notation N2T3C in the figure corresponds to B450C(i).

76


5.5.2 TDD lines

Three luminescence lines at 1.143, 1.124, and 1.085 eV have previously been assigned toTDDs, in which the 1.143 line has been identified as a zero-phonon line, and the other two asphonon replicas [80]. Figure 5.33 presents the PL spectra in the range of TDD luminescencelines for the non-irradiated, carbon-lean sample B450O. This material corresponds to sampleA450O, which by IR spectroscopy and FPP resistivity measurements was determined to formthe absolute highest concentration of TDDs among the studied samples. Considering thespectrum obtained after 64 hours of annealing at 450°C, it is observed that the phonon-replicalines, TD-TO and TD-TA, have increased. The zero-phonon TD line likely overlaps with thefree exciton line at ∼1.37 eV, and it is therefore difficult to determine the development withoutfurther data processing. By considering the evolution of TDDs in the corresponding samplestudied with IR spectroscopy, presented in figure 5.19, it is evident that further annealingwould have been beneficial. In sample A450O, absorption lines of up to TDD3 had formedafter 64 hours. Therefore, in order to achieve a more thorough comparison between FTIRand PL measurements, more prolonged annealing of sample series B450 should be carriedout.

Figure 5.33: PL spectra presenting the zero-phonon, and phonon-replica TDD lines (indicatedby blue vertical lines). The sample notation N3S11d in the figure corresponds to B450O.

Figure 5.34 presents the intensity of the P-line in the various studied samples, after 64 hours ofannealing at 450°C. The presence of a strong P-line in the carbon-rich materials is expected,while the strong line seen in the carbon-lean, non-irradiated material is more surprising.However, this gives an indication that the P-line is either not due to the CsO2i defect centre, orthat the line contains a significant contribution from another defect. The P-line has previouslybeen suggested to have a correlation with TDDs [81]. The sample containing the highestconcentration of TDDs is B450O. Some authors have suggested that a transition from thedonor level Ec - 0.07 eV of TDDs to a deep centre at Ev + 0.35 eV would accomplish within afew meV from the experimental value of the transition associated with the P-line. In this case,

77


the PL emission at 767 meV would present both the carbon isotope shift, which was used toascribe the line to CsO2i, and its time evolution would closely follow that of TDDs [82].

Figure 5.34: Section of PL spectra presenting the P-line after 64 hours of annealing at 450°C. Inthe sample notation in the figure N2T3C corresponds to B450C(i), N2T11d to B450C, N3S3Cto B450O(i) and N3S11d to B450O.

78

Chapter 6

Summary

6.1 Conclusion

Cz-grown, n-type silicon samples with high and low carbon concentrations have been isother-mally annealed in the temperature range of 450-550°C, and investigated using FTIR spec-troscopy, FPP resistivity and PL spectroscopy measurements. The annealing series have beenperformed in parallel for as-grown and MeV electron irradiated samples. The evolution ofirradiation and annealing induced VOn (n≤4) and CsOni complexes have been studied andtheir relation to the formation of TDDs has been addressed.

Isothermal annealing at 450 and 500°C resulted in a sequential development of TDDs inall studied samples, excluding the irradiated carbon-rich ones, in which no TDD formationoccurred. Increasingly strong absorption lines of electronic transitions in the various TDDspecies were detected with IR spectroscopy. After annealing for 1 hour at 550°C, absorptionlines of TDD2-TDD3 were observed in the carbon-lean sample, while subsequent annealinglead to the annihilation of these, and no further TDD formation occurred. The first formingspecies were therefore suggested to be due to the agglomeration of some initially present, fastdiffusing oxygen dimers. Hence, at 550°C the TDDs were found to be unstable. Carbon hasproved to strongly suppress the formation of TDDs. 400 hours of annealing at 450°C resultedin estimated TDD concentrations of 5.4×1015cm−3 and 7.4×1014cm−3, in the carbon-leanand carbon-rich samples, respectively. After 81 hours at 500°C, the corresponding valueswere 2.7×1015cm−3 and 8.8×1013cm−3. Therefore, by including a carbon concentration of∼2.5×1017cm−3 in the crystals, the final TDD concentrations were reduced by factors of 7 at450°C, and 30 at 500°C. By taking the small differences in oxygen content into consideration,a factor of 1.6 higher saturated TDD concentration was expected in the carbon-lean samples.The highly apparent amplifications of this value arguably illuminates carbon’s role as TDDsuppressant. Furthermore, TDD3 was found to exhibit a strongly delayed appearance in thecarbon-rich sample, and it was suggested that this species might act a limiting factor regardingTDD formation, when a high concentration of carbon is present. This was not observed forTDD1 and TDD2.

The VO centre was found to be the most prominent defect generated by the electron irradi-ation, with a factor of approximately 3 higher concentration in the carbon-rich samples. The

79

CHAPTER 6. SUMMARY

formation of VO as a function of irradiation dose has been simulated, based on the theoryof diffusion-limited reactions, and illuminated carbon’s role as trap for silicon self-interstitialsduring irradiation. Annealing lead to the formation of higher index VOn defects, in which theassociation with oxygen and formation of larger VOn centres proceeded with higher rates atincreasing temperatures. The evolution in concentration of VOn (n≤4) was studied in detail,and in addition, a series of new absorption lines forming at 500-550°C, were ascribed to VOn

(n=5/6) complexes. At 450°C, species up to VO4 were detected, with a considerably higherconcentration in the carbon-lean material, compared to the carbon-rich. At 550°C the highestconcentration of VOn up to n=5/6 was found in the carbon-rich material. At higher temper-atures it was argued that a larger portion of the initial VO-centres were captured by oxygen,partly due to the increased oxygen diffusivity, but also since the competing carbon-relatedtraps have a lower thermal stability at higher temperatures.

The irradiation induced carbon-complexes, CiOi, ICiOi and CsCi were found to be thermallyunstable in the studied temperature range. Annealing lead to the formation of the more stableCsOi and CsO2i centres and the development of these were investigated. Coinciding theoreticaland experimental reaction rate constants confirmed a sequential formation of CsO3i complexes,as CsO2i captures additional oxygen atoms during annealing, with a formation rate determinedby the diffusivity of interstitial oxygen. CsOi was shown to exhibit a different behaviour, anddid not form CsO2i by sequential trapping of oxygen. The diatomic complex was argued toexist in a steady state at 450°C, while dissociating at higher temperatures. The observeddevelopments indicates that oxygen agglomerates around already present carbon-complexesand forms larger C-O complexes at higher temperatures and by prolonged annealing.

Irradiating silicon with high energy electrons thus facilitated a detailed study of the evolutionof VOn and C-O complexes, but proved to suppress the formation of TDDs. The final TDDconcentration was determined to be a factor of 2 lower in the irradiated, carbon-lean materialwhen annealed at 450°C, and a factor 13 lower at 500°C, compared to the corresponding non-irradiated samples. The direct involvement of VOn centres in TDD formation was thereforeruled out. In stead, the VOn centres consume Oi atoms, and act as traps for oxygen duringthermal treatment. The initial TDD formation rate is arguably further slowed down in theirradiated materials, as any initial concentration of oxygen dimers, precursors of TDDs, likelybecome trapped by VOn centres during the early stages of thermal treatment. The irradiatedcarbon-rich samples were found to not develop any TDDs during this study, ascribed to thelarge concentration of traps for oxygen and likely strain caused by the presence of carbonand carbon-complexes. Resistivity measurements excluded Fermi level pinning as a reason forabsence of TDD absorption lines.

The presence of a high carbon concentration has thus proved to strongly suppress the for-mation of TDDs in oxygen-rich Si samples, providing a promising result for further use ofCz-Silicon in photovoltaic cells. By reversing the conventional Si pn-homojunction, makingthe substrate n-type and doping the emitter p-type, the effect of BO-LID can be nearly com-pletely excluded. Further, the results of this study indicates that both the total concentration,and also the formation rate of TDDs is strongly reduced by employing Cz-Silicon of a highcarbon concentration. The concentration of TDDs can therefore likely be kept to a min-imum by using carbon-rich silicon, and limiting the duration of thermal treatments. WhenTDD3 was found to develop the TDD formation seemingly accelerated, and TDD3 is thereforeemphasized as a potential limiting key in carbon-rich materials.

80

CHAPTER 6. SUMMARY

6.2 Suggestions for further work

Some of the results obtained in this thesis needs to be reproduced in order to establish a con-clusive discussion. The sample series annealed at 450°C exhibited a quite abrupt developmentbetween 256 and 400 hours of thermal treatment. In particular did the carbon-lean samplesexhibit a strong reduction in interstitial oxygen concentration during the last annealing, aspresented in figure 5.5. If the nitrogen flow, which was used to ensure an inert annealing at-mosphere, was limited during the last thermal treatment, annealing in air might have causedan increased oxygen diffusivity. In order to exclude such discrepancies in treatment conditionsas reason for this result, reproduction is necessary. If the same result can be reproduced, aspecific mechanism may cause the rapid loss occurring at long annealing durations (t≥256h).

The relation between carbon and TDD3 calls for further work. Obtained results indicatesthat carbon specifically affect the formation of TDD3. An extended study involving samplesof various carbon concentrations could reveal a more detailed image on the suppression ofTDD3 formation. Smaller annealing steps around the formation of this defect could givemore information whether TDD formation could be almost completely eliminated if thermalprocessing is kept within a certain time frame. Moreover, by also including samples irradiatedat elevated temperatures, the initial concentration of fast diffusing oxygen dimers could bestrongly increased, and larger TDD formation stimulated. This could give a further indicationof how carbon act on TDD3 formation.

The PL measurements performed in this work could only be partially correlated to the FTIRresults. By extending the annealing durations, further comparisons can be made. In order toobtain a more precise study, the same samples should be investigated with both techniques,rather than using corresponding sets. Both PL and FTIR spectroscopy are non-destructivetechniques, making it unproblematic to employ both techniques on the same sample set.

81

Appendices

82

Appendix A

Overview of IR absorption bands

In this work, the concentration of various defects and defect complexes have been deductedfrom their associated absorption line amplitudes. Table A.1 lists the reported values forthe non-irradiated samples, deducted from RT measurements. Tables A.2 and A.4 lists allreported values obtained at RT for the irradiated carbon-rich and carbon-lean samples, re-spectively. Table A.3 lists all reported carbon-related values, in the irradiated, carbon-richsamples, obtained at LT.

Carbon-rich (C) Carbon-lean (O)

Defect amplitude & position (cm−1) Defect amplitude & position (cm−1)

Annealing conditions Oi Cs Oi

Temperature (°C) Time (h) 1107 cm−1 605 cm−1 1107 cm−1

450

0 3,1325 2,5207 3,4977

2 3,1597 2,4464 3,5454

4 3,1232 2,4293 3,5111

8 3,1711 2,4677 3,5842

16 3,2195 2,4450 3,5582

32 3,2266 2,4919 3,5815

64 3,1485 2,6333 3,5197

128 3,1866 2,4645 3,5031

256 3,2040 2,4746 3,4880

400 3,1006 2,3765 2,9192

500

0 3,1857 2,5207 3,5683

1 3,1553 2,5315 3,5405

3 3,1956 2,513 3,5514

9 3,2108 2,5609 3,5715

27 3,2138 2,5259 3,5591

81 2,7098 1,9565 3,2699

550

0 3,1653 2,4808 3,4629

0.5 3,1516 2,4174 3,4662

1 3,1163 2,3926 3,4099

2 3,1456 2,3333 3,5102

3 3,125 2,2196 3,4786

5 3,0957 2,2414 3,4755

Table A.1: List of reported IR peak amplitudes of defects in the non-irradiated carbon-rich(A450C, A500C and A550C) and carbon-lean (A450O, A500O and A550O) samples. Obtainedfrom room temperature measurements.

83

APPENDIX A. OVERVIEW OF IR ABSORPTION BANDS

Am

plitu

de

ofox

yge

ndef

ect/

com

ple

x(c

m−

1)

&pos

itio

n(c

m−

1)

Am

plitu

de

ofca

rbon

def

ect/

com

ple

x&

line

(cm

−1)

&pos

itio

n(c

m−

1)

Annea

ling

condit

ions

Oi

VO

VO

2V

O3

VO

3V

O3

VO

4C

sC

iO

iIC

iO

iIC

iO

iC

sO

i(Y

)C

sO

i(Z

)C

sO

2i

T(°

C)

Tim

e(h

)11

0783

088

996

910

0090

598

560

586

293

610

2063

768

410

48

450

02,

8748

1,70

1-

--

--

0,88

060,

656

0,09

060,

1474

--

-

22,

9232

-0,

2879

--

--

1,06

85-

--

0,16

460,

1613

0,06

86

42,

9040

-0,

2929

--

--

1,07

66-

--

0,17

540,

1357

0,06

50

82,

9345

-0,

2860

--

--

1,05

93-

--

0,18

570,

1632

0,05

44

162,

9930

-0,

3029

0,03

040,

0055

--

1,07

75-

--

0,21

450,

1579

0,05

95

323,

0179

-0,

3075

0,03

040,

0093

--

1,15

38-

--

0,22

430,

1346

0,06

43

642,

9144

-0,

3099

0,03

090,

0084

--

1,17

84-

--

0,20

740,

1505

0,05

84

128

2,93

51-

0,26

500,

0570

0,01

920,

0252

-1,

0995

--

-0,

2641

0,15

430,

0386

256

2,97

66-

0,27

340,

0556

0,02

160,

0291

-1,

1930

--

-0,

2621

0,14

620,

0378

400

2,91

67-

0,14

920,

1273

0,03

970,

0790

-1,

0948

--

-0,

2644

0,12

570,

0302

500

02,

9662

1,63

42-

--

--

0,95

080,

6393

40,

0929

0,15

62-

--

12,

9767

0,84

590,

1651

--

--

1,02

540,

4830

4-

0,05

880,

1651

10,

0841

0,05

16

32,

9196

-0,

3254

-0,

0141

--

1,02

25-

--

0,27

420,

1350

0,06

15

92,

9307

-0,

3428

0,04

550,

0184

0,01

18-

1,09

77-

--

0,25

810,

1351

0,05

25

272,

9060

-0,

3218

0,06

980,

0254

0,03

84-

1,09

41-

--

0,27

469

0,12

820,

0384

812,

4872

--

0,08

85-

0,04

820,

1422

1,27

21-

--

0,11

141

0,02

88-

550

02,

8804

1,57

06-

--

--

0,86

530,

6098

0,09

920,

1615

0,07

580,

0495

-

0.5

2,91

26-

0,01

240,

1052

0,03

770,

088

0,03

421,

2130

-(0

,016

0-

0,17

820,

0878

0,02

72

12,

8394

-0,

0170

0,09

930,

0347

0,08

310,

0396

1,24

39-

(0,0

217)

-0,

1739

0,09

680,

0204

22,

9091

--

0,08

360,

0210

0,06

770,

0686

1,36

87-

--

0,09

850,

0393

-

32,

8954

--

0,06

980,

0083

0,05

770,

0870

1,37

20-

--

0,06

800,

0316

-

52,

7974

--

0,04

93-

0,03

100,

0954

1,41

73-

--

0,06

99-

-

Table

A.2:Listof

reported

IRpeak

amplitud

esof

defectsan

ddefect-com

plexes

intheirradiated,carbon

-richsamples

(A450C

(i),

A500C

(i)

andA550C

(i)).Obtainedfrom

room

temperature

measurements."-"deno

tesno

observable

peak.

84


Am

plitu

de

ofC

-rel

ated

com

ple

xes

(cm

−1)

&pea

kpos

itio

n(c

m−

1)

Annea

ling

condit

ions

CiO

iC

iO

iIC

iO

iIC

iO

iC

iC

sC

sO

i(A

)C

sO

i(Y

)C

sO

i(X

)C

sO

i(Z

)C

sO

2i

T(°

C)

Tim

e(h

)86

5cm

-111

16cm

-193

9cm

-110

24cm

-155

0cm

-111

04cm

-164

0cm

-158

7cm

-169

0cm

-110

52cm

-1

450

01,

4585

0,71

020,

2325

0,21

650,

4019

0,23

06-

--

-

2-

--

--

1,43

030,

5798

0,47

160,

2999

0,16

34

4-

--

--

1,43

980,

5998

0,49

370,

2797

0,15

84

8-

--

--

1,39

790,

5592

0,47

600,

2702

0,13

87

16-

--

--

1,48

330,

5960

0,50

160,

3045

0,15

64

32-

--

--

1,43

460,

5883

0,46

450,

3145

0,15

76

64-

--

--

1,44

970,

5870

0,50

400,

3019

0,16

19

128

--

--

-1,

5906

0,61

100,

5261

0,32

190,

1172

256

--

--

-1,

5265

0,58

040,

5369

0,31

250,

0992

400

--

--

-1,

4491

0,62

450,

5283

0,31

840,

0763

500

01,

3267

0,72

900,

2222

0,21

340,

3558

0,18

090,

1197

0,14

690,

0901

0,02

98

3-

--

--

1,38

540,

5627

0,39

880,

2924

0,17

03

27-

--

--

1,42

890,

6120

0,47

670,

2899

0,10

40

81-

--

--

0,25

210,

1644

0,15

310,

0637

0,06

16

550

01,

2829

0,68

660,

2376

0,20

990,

3567

0,19

410,

1193

0,14

570,

0766

-

1-

--

--

0,73

560,

3511

0,33

460,

1564

0,05

20

3-

--

--

0,27

890,

1574

0,16

790,

0828

0,04

75

5-

--

--

0,20

600,

1213

0,14

720,

0648

0,02

37

Table

A.3:Listof

reported

IRpeak

amplitud

esof

carbon

-related

complexes


-richsamples

(A450C

(i),

A500C

(i)an

dA550C

(i)).Obtainedfrom

lowtemperature


tesno

observable

peak.

85


Am

plitu

de

ofdef

ect/

com

ple

x(c

m−

1)

&pos

itio

n(c

m−

1)

Annea

ling

condit

ions

Oi

VO

VO

2V

O3

VO

3V

O3

VO

4

Tem

per

ature

(°C

)A

nnea

ling

tim

e(h

)11

07cm

−1

830

cm−

188

9cm

−1

969

cm−

190

5cm

−1

1000

cm−

198

5cm

−1

450

03,

1870

0,54

--

--

-

23,

2331

-0,

3824

0,01

163

0,00

984

0,01

116

-

43,

1835

-0,

3938

0,01

397

0,01

046

0,01

387

-

83,

2991

-0,

3763

0,02

562

0,01

956

0,02

232

-

163,

3264

-0,

3802

0,02

624

0,02

179

0,01

931

-

323,

3218

-0,

3906

0,03

029

0,02

075

0,01

509

-

643,

2568

-0,

4028

0,02

814

0,01

804

0,01

384

-

128

3,25

91-

0,33

990,

0505

00,

0367

80,

0290

2-

256

3,30

78-

0,35

770,

0462

70,

0373

50,

0233

2-

400

2,95

78-

-0,

1626

40,

1313

80,

0846

00,

0567

8

500

03,

2568

0,53

65-

--

--

13,

2046

0,44

150,

0519

--

--

33,

2851

-0,

3851

0,01

153

0,00

895

0,01

481

-

93,

2985

-0,

4029

0,01

372

0,01

172

0,01

205

-

273,

2324

-0,

2941

0,11

515

0,09

287

0,04

932

-

813,

0703

--

--

-0,

0299

550

03,

1265

0,48

80-

--

--

0,5

3,16

22-

-0,

0745

0,06

531

0,02

712

0,04

363

13,

1155

--

0,07

509

0,06

486

0,02

262

0,03

796

23,

1948

--

0,05

603

0,04

479

0,01

347

0,04

687

33,

1760

--

0,03

985

0,03

051

-0,

0424

2

53,

1760

--

0,02

664

0,01

647

-0,

0476

5

Table

A.4:Listof

reported

IRpeak

amplitud

esof

defectsan

ddefect-com

plexes


-lean

samples

(A450O

(i),

A500O

(i)

andA550O

(i)).Obtainedfrom

room

temperature


tesno

observable

peak.

86

Appendix B

Overview of FPP measurements

Table B.1 lists the resistivities of all samples studied with IR spectroscopy, obtained by theFPP method, presented in section 5.4. Given are the resistivities (ρ) of the as-grown andirradiated samples prior to thermal treatment, and after every successive annealing step, withstandard deviations (σ). Listed is also the total electron concentration at every step, calculatedfrom eq.(4.12) by assuming an electron mobility of µ=1350 cm2Vs.

87

APPENDIX B. OVERVIEW OF FPP MEASUREMENTS

C(i

)C

O(i

)O

Tem

per

ature

(°C

)T

ime

(h)

ρ(Ω

cm)

σ(Ω

cm)

n(c

m−

3)

ρ(Ω

cm)

σ(Ω

cm)

n(c

m−

3)

ρ(Ω

cm)

σ(Ω

cm)

n(c

m−

3)

ρ(Ω

cm)

σ(Ω

cm)

n(c

m−

3)

450

013

1162

243,

52E10

2,08

71,

41E-2

2,22

E15

1297

819

3,56

E11

10,8

42,

4E-2

4,27

E14

160

767

145

7,61

E10

2,04

92,

28E-2

2,26

E15

3454

049

51,

34E11

12,7

82,

7E-2

3,62

E14

269

026

160

6,70

E10

2,12

92,

74E-2

2,17

E15

3500

592

11,

32E11

12,0

50,

313,

84E14

461

218

1372

7,55

E10

2,08

22,

06E-2

2,22

E15

3414

258

1,35

E11

12,2

60,

193,

77E14

847

387

8366

9,76

E10

2,06

52,

11E-2

2,24

E15

3526

066

21,

31E11

8,76

94,

85E-4

5,27

E14

1642

183

310

1,10

E11

2,07

61,

79E-2

2,23

E15

4008

333

321,

15E11

9,30

85,

82E-3

4,97

E15

3231

026

4585

1,49

E11

2,17

11,

48E-2

2,13

E15

4579

627

791,

01E11

8,28

61,

87E-1

5,58

E14

6440

713

160

1,14

E11

2,07

11,

09E-2

2,23

E15

4576

949

441,

01E11

8,41

98,

73E-2

5,49

E14

128

9385

144,

93E11

2,03

81,

77E-2

2,27

E15

4235

6,5

1,09

E12

2,33

81,

82E-2

1,99

E15

256

2412

51,

92E12

2,05

36,

79E-3

2,25

E15

4022

401,

15E12

1,51

21,

21E-3

3,06

E15

400

14,0

60,

773,

29E14

1,25

31,

50E-2

3,69

E15

0,81

31,

02E-3

5,69

E15

0,41

11,

07E-3

1,12

E16

500

014

6219

339

3,16

E10

2,16

01,

60E-2

2,14

E15

1443

016

73,

20E11

11,3

21,

21E-2

4,08

E14

115

9095

364

2,91

E10

2,16

31,

26E-2

2,14

E15

1268

6929

874

3,64

E10

11,2

91,

45E-2

4,09

E14

356

805

742

8,14

E10

2,16

61,

50E-2

2,13

E15

4744

716

79,

74E10

11,1

81,

70E-2

4,13

E14

928

051

2648

1,65

E11

2,21

71,

28E-2

2,09

E15

4362

858

1,06

E11

11,4

06,

06E-2

4,05

E14

2754

2359

8,53

E11

2,15

32,

11E-2

2,15

E15

24,5

30,

439

1,88

E14

10,7

90,

1552

4,29

E14

812,

245

1,67

E-2

2,06

E15

1,99

61,

60E-2

2,32

E15

5,65

01,

89E-2

8,18

E14

0,81

11,

55E-2

5,70

E15

550

015

1893

485

3,04

E10

2,14

61,

77E-2

2,15

E15

1215

117

3,80

E11

11,0

40,

133

4,19

E14

0,5

3,25

42,

23E-2

1,42

E15

2,08

31,

33E-2

2,22

E15

24,7

30,

145

1,87

E14

10,8

01,

9E-2

4,28

E14

13,

313

1,60

E-2

1,39

E15

2,13

51,

21E-2

2,16

E15

23,8

90,

145

1,93

E14

8,00

6E-3

5,78

E14

23,

151

1,94

E-2

1,47

E15

2,13

51,

48E-2

2,17

E15

17,5

10,

183

2,64

E14

11,1

11,

70E-2

4,16

E14

33,

349

1,79

E-2

1,38

E15

2,13

81,

58E-2

2,16

E15

15,5

93,

64E-2

2,96

E15

11,4

10

4,05

E14

53,

250

1,89

E-2

1,42

E15

2,11

71,

48E-2

2,18

E15

12,7

32,

67E-2

3,63

E14

10,5

80,

162

4,37

E14

Table

B.1:Fu

lloverview

ofcalculated

resistivities(ρ)withstan

dard

deviations

(σ)an

dtotalelectron

concentration(n)forthesamples

stud

iedwithIR

spectroscopy

(seriesA).

The

electron

concentrationis

foun

dfrom

eq.(4.12).

88

Appendix C

VO simulation

The differential equations included in the VO-simulation are given below.

d[I]

dt= gI − 4πR (Dv +DI)[V ][I] +DI [I][Cs] +DI [I][CiOi] +DI [I][V O] (C.1)

d[V ]

dt= gV − 4πR (DI +Dv)[V ][I] +DV [V ][Oi] (C.2)

d[Cs]

dt= −4πR DI [I][Cs] +DCi [Ci][Cs] (C.3)

d[Oi]

dt= −4πR Dv[V ][Oi] +DCi [Ci][Oi]−DI [V O][I] (C.4)

d[Ci]

dt= −4πR DCi [Oi][Ci] +DCi [Ci][Cs]−DI [I][Cs] (C.5)

d[V O]

dt= 4πR (DV [V ][Oi]−DI [V O][I] (C.6)

d[CiCs]

dt= 4πR DCi [Ci][Cs] (C.7)

d[CiOi]

dt= 4πR DCi [Ci][Oi]−DI [CiOi][I] (C.8)

d[ICiOi]

dt= 4πR DI [CiOi][I] (C.9)

89

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