\begin{thebibliography}{100} - TU Berlin · Web viewWith these techniques it was soon established that the GaAs(001) surface is As terminated under MBE growth conditions [77,27,]

$Page 1: \begin{thebibliography}{100} - TU Berlin · Web viewWith these techniques it was soon established that the GaAs(001) surface is As terminated under MBE growth conditions [77,27,]$
Published in: Prog. Crystal Growth and Charact. Vol. 35, pp. 27-98, 1997

CHARACTERIZATION OF EPITAXIAL SEMICONDUCTOR GROWTH

BY REFLECTANCE ANISOTROPY SPECTROSCOPY AND ELLIPSOMETRY

J.-T. Zettler

Technische Universität Berlin, Institut für Festkörperphysik, Hardenbergstr. 36, 10623 Berlin, Germany

KEYWORDSsemiconductor growth, optical in-situ spectroscopy, real-time monitoring

ABSTRACT

The recent developments in optical real time analysis of epitaxial growth are reviewed. Emphasis is placed on reflectance anisotropy spectroscopy (RAS) and spectroscopic ellipsometry (SE) which by their accuracy and sensitivity are presently the most promising tools for analysis of the main epitaxial methods: metal organic vapor phase epitaxy (MOVPE), molecular beam epitaxy (MBE) and their hybrid techniques gas source MBE (GSMBE), metal-organic MBE (MOMBE) and chemical beam epitaxy (CBE).

After discussing the basic principles of the spectroscopic techniques a review is given on the contributions of real-time spectroscopy to the surface science of growth surfaces both in UHV and gas phase environments. Finally it is shown that, irrespective of the specific growth technique, RAS and SE can be used for a wide field of real-time monitoring and control tasks.

J.-T. Zettler

1 INTRODUCTION.........................................................................................................

2 SOME OPTICS............................................................................................................

2.1 Ellipsometric and RAS principles......................................................................2.2 Multilayer structures and virtual substrate approach.........................................2.3 Morphology contributions to the Ellipsometry and RAS spectra.......................2.4 Ellipsometry and RAS: hardware, systematic and random errors.....................2.5 Kramers-Kronig relations...................................................................................2.6 Coupling of the in-situ optics to the growth chamber........................................

3 ON THE MICROSCOPIC ORIGIN OF THE SPECTROSCOPIC FEATURES...........

3.1 The dielectric function of the isotropic semiconductor bulk...............................3.2 The surface dielectric anisotropy.......................................................................3.3 Field effects to the reflectance anisotropy spectra............................................

4 STUDYING BASIC EPITAXIAL GROWTH PROCESSES BY MEANS OF OPTICAL TECHNIQUES............................................................................................

4.1 Static surfaces...................................................................................................4.2 Surfaces during growth.....................................................................................

5 EXAMPLES OF GROWTH MONITORING AND GROWTH CONTROL....................

5.1 Surface preparation before growth....................................................................5.2 Measurement of surface temperature and pre-growth

surface reconstruction......................................................................................5.3 Growth rate measurement.................................................................................5.4 In-situ measurement of the composition of compound semiconductors............5.5 Optimization of switching sequences................................................................5.6 In-situ measured dopand concentrations..........................................................5.7 In-situ monitoring of epitaxial growth of quantum sized structures....................5.8 Ordering effects in ternary III-V semiconductors...............................................

6 MODELLING THE DIELECTRIC FUNCTION OF SEMICONDUCTORS...................

7 SUMMARY AND OUTLOOK......................................................................................

2

Characterization of epitaxial semiconductor growth

1 INTRODUCTION

The purpose of this article is to review recent developments in real-time epitaxial growth characterization by means of reflectance anisotropy spectroscopy (RAS, which is also termed reflectance difference spectroscopy (RDS)) [1,2,3] and spectroscopic ellipsometry (SE) [4,5,6,Error: Reference source not found,7,8].

Modern semiconductor devices in general consist of many layers (planar or non-planar) and many different materials. Epitaxial growth of such structures requires continuous control of a number of highly sensitive parameters: variation of materials or composition in ternary or quaternary compounds, variation of doping, of temperature or growth rate. The most stringent demands on precision arise for low dimensional structures. There, the large area preparation of a well defined number of completely filled monolayers is essential for reaching the targeted transition energies and peak widths. The successful operation of a device depends on each single technological step and thus tight control throughout the whole growth procedure is necessary. In practice, presently the majority of epitaxial processes is still performed by blind operation with equipment settings fixed by previous empirical studies. The situation is most favorable in molecular beam epitaxy (MBE) or its hybrid derivatives (metal-organic-MBE (MOMBE), chemical beam epitaxy (CBE), gas source-MBE (GSMBE)) where reflection high-energy electron diffraction (RHEED) is usually available as a standard analytical tool [9,10,11]. The diffraction pattern observed can be used for a number of monitoring purposes, e.g., the deoxidization of the substrate surface, the temperature calibration, or thickness control via monolayer oscillations in two-dimensional island growth mode [12]. Thus, as far as the growth of complex structures is concerned, MBE has always been ahead of its gas phase counter parts (vapor phase epitaxy (VPE), metal-organic-VPE (MOVPE), chemical vapor phase deposition (CVD)) because in the latter techniques RHEED cannot be applied and control is therefore only exercised very indirectly on the gas phase parameters via flow meters and controllers. However, highly surface sensitive optical in-situ techniques such as reflectance anisotropy spectroscopy (RAS) [Error: Referencesource not found,Error: Reference source not found,Error: Reference source notfound] and surface photo absorption (SPA) [13,14] recently have been developed which are of course not restricted to ultra-high vacuum (UHV) conditions. Additionally, enormous improvements have been reached both in instrumentation and analysis methods for the 'good old' spectroscopic ellipsometry [15,16,17]. Aspnes and coworkers introduced the concept of virtual interfaces and applied it to the closed-loop controlled growth of a parabolic AlGaAs/GaAs quantum well in MOMBE [18]. Consequently, there is a tremendous chance to supply also the gas-phase based epitaxial processes with standard analytical tools allowing for at least a similar level of real-time control as RHEED does in MBE. Moreover, additional information gained by optical in-situ monitoring is expected to stimulate also further progress in MBE. This concerns for example the real time analysis of surface stoichiometry [19], surface temperature [20] or layer thickness [Error: Reference source not found].

3

J.-T. Zettler

The undoubted advantage of the optical techniques is that they are applicable to practically all the main growth techniques. Thus comparative studies became possible concerning not only the 'classical' optical measurements such as temperature, composition and layer thickness sensing. Due to the surface sensitivity of RAS even the atomic dimer configuration at growth surfaces in very different environments can be studied. On the other hand, ellipsometry has enormous advantages when the bread-and-butter task of real-time characterization has to be solved: measurement of layer thickness and of compound semiconductor's composition. While the intrinsically highly surface sensitive techniques (RHEED, RAS) can sense the growth rate via monolayer oscillations only during the growth of the first tenth of atomic layers, ellipsometry is capable of measuring layer thicknesses ranging from sub-monolayers up to some microns. Additionally, spectroscopic ellipsometry (SE) is known to be sensitive enough to respond also to changing surface conditions [21,22,Error: Reference source not found]. However, similar to SPA, while being very surface sensitive, SE has the disadvantage that the surface has to be modified in order to generate a signal, i.e., it is not possible to characterize the state of a surface. There are efforts to overcome these shortcomings. In SE this can be done, as recently shown by Wassermeier et al. [23], by using two samples oriented with perpendicular surface eigenvectors to each other in order to subtract the bulk optical response. But this technique is, while being useful for basic growth studies, too sophisticated for growth monitoring.

Reflectance anisotropy spectroscopy exploits the anisotropic optical response of surfaces which originates from their anisotropic geometrical structure [Error:Reference source not found]. Moreover, in materials where the bulk is optically isotropic, RAS becomes extremely surface sensitive because only the surface can produce an anisotropic signal. According to our present knowledge most III-V semiconductors qualify for surface studies by RAS. Because of their cubic crystal structure they behave optically isotropic in the bulk but exhibit in general anisotropic surface structures highly sensitive to the growth conditions applied.

Generally, epitaxial requirements on the optical real-time techniques are: operation at high temperatures, sufficiently high signal to noise ratio for time resolved studies, adaptability to growth equipment, low light intensities in order to avoid light stimulated changes of the growth process, and last but not least low costs. Considering all these criteria spectroscopic in-situ ellipsometry and reflectance anisotropy spectroscopy turned out to be the most promising candidates for monitoring and possibly also controlling epitaxial growth.

The outline of this article is as follows: section 2 starts with an overview over recent developments in instrumentation and experimental techniques. For specific ellipsometric configurations excellent recent review articles are available [Error:Reference source not found,Error: Reference source not found,Error: Referencesource not found,Error: Reference source not found,Error: Reference source notfound]. Here we will concentrate on a comparative discussion of the main optical systems including an error analysis that should assist the reader to decide whether or not a specific growth task can be supported by real-time optical techniques. In section 3 I will briefly discuss the microscopic origins of those spectroscopic features used in the following for monitoring the status of growth (For a more detailed and extended

4


discussion of this subject I refer to del Sole's recent and profound review article [24] and to the respective chapters in the just published book of Yu and Cardona [25] which I expect to become a standard reference also for the semiconductor growth community.). Section 4 will be focused on contributions of the in-situ optical techniques to basic growth studies. Section 5 gives a number of examples of how ellipsometry and RAS already have been used to characterize and control the different stages of device growth. Finally, in section 6 some aspects are discussed regarding the high-temperature dielectric function data that still have to be gained and to be made accessible for a broad application of the spectroscopic techniques for epitaxial growth characterization and control.

2 SOME OPTICS

2.1 Ellipsometric and RAS principles

Both optical techniques, RAS and SE, sense the change in state of polarization due to the reflection from the sample. Both normalize to the light intensity thus being insensitive to light source fluctuations or a changing transmittance of the optical ports at the growth chamber and, finally, they are both gaining a complex parameter as the result of a single measurement thus yielding two real parameters per measurement point. The main difference between SE and RAS is caused by the different angles of incidence. While ellipsometry operates under oblique conditions near the Brewster angle the reflectance anisotropy is measured at near normal incidence. Therefore, RAS gives a zero signal from an isotropic sample while SE does not because at oblique incidence the reflection coefficients for light polarized parallel and perpendicular to the plane of incidence, respectively, are different.

The ellipsometric analysis is based on the complex reflectance ratio

r

rrr

e ep

s

p

s

i r r ip s psarg arg

(1)

where r

rp

s and arg( ) ps are the parameters directly measured1.

Most of the group IV semiconductors and III-V semiconductor compounds are optically isotropic in the bulk due to their cubic lattice structure. Therefore their bulk

1 Besides the reflectance ratio there is for historic reasons a sometimes confusing large number of parameters that can describe the result of an ellipsometric measurement (Y, ; tanY, cos; complex optical density D, etc.). This is because the spectroscopists like to use those parameters coming straight out of their specific type of ellipsometer (nulling ellipsometers, rotating analyzer ellipsometers, phase modulating ellipsometers, respectively). Not enough, in solid-state physics (where it is preferred to think in terms of the dielectric function e because it is directly linked to the electronic band structure) the so called effective, or apparent dielectric function e is used alternatively. For this purpose Eq. (2), which is valid only for a bare substrate's surface, is applied to all kinds of samples and the respective result is named e .

5

J.-T. Zettler

Fig. 1. Schematic diagram for an anisotropic sample to be characterized by optical in-situ techniques. eb and eo are

the dielectric functions of the bulk and the anisotropic overlayer of thickness d, respectively. The angle of incidence f and the azimuth of sample orientation are defined with respect to a fixed sample coordinate system x, y, z.

optical properties are completely given by a complex but isotropic dielectric function eb. Modern semiconductor epitaxy is capable of creating optically ideal surfaces which are atomically smooth and planar. If additionally the uppermost layer is much thicker than the respective penetration depth of light, its bulk dielectric function eb can be directly derived from the ellipsometrically measured reflectance ratio [26]:

e f f f b

sin sin tan2 2 221

1 (2)

with f being the angle of incidence. This can be utilized for establishing a database ofthe bulk optical properties at growth-relevant temperatures of the most important semiconductors (see, e.g., section 6).

While the semiconductor bulk is isotropic, the clean surface under UHV and MOVPE conditions, in most cases, gives an anisotropic response to a normal incidence reflectance measurement (f=0 in Fig. 1):

rr

r rr r

rr

i rr

x y

x y

2 Re Im (3)

6


Fig. 2: Optical spectra of a (2x4) reconstructed GaAs(001) surface under As flow in MBE at 500°C.a) bulk dielectric function as measured by ellipsometry; b) real and imaginary part of the RAS spectrum and c) surface dielectric function anisotropy as derived from the RAS spectrum and the GaAs bulk dielectric function.

This is because the symmetry at the surface is reduced with respect to the bulk. At reconstructed surfaces dimer bonds are usually formed which minimize the total energy of the surface region. This microscopic behavior, which has been investigated in detail by a large number of LEED, RHEED and STM studies [27,28,29,30,31], must be translated into a quasi-macroscopic optical model: The anisotropic geometry of surface atoms is accompanied by an anisotropic probability for optical transitions involving surface electronic states and by an anisotropic interaction with electrons in extended bulk states. For the interpretation of optical experiments therefore an anisotropic surface layer was introduced in [32] by defining a surface dielectric function

e e e e e e eo o

o b a o x o y

2 2 2, ,

(4)

that is basically an isotropic average over bulk and ambient dielectric properties eb

and ea, respectively, plus a small anisotropic contribution eo due to the specific character of the surface. In Fig. 1 the anisotropic eigenvectors of the surface are specified by x and y. In the diamond and zinc-blende type semiconductors they are given by [ 110] and [110 ], respectively, on a (001)-surface. The reflectance anisotropy, sensed in a normal

7

J.-T. Zettler

incidence RAS measurement and defined in Eq. (3), is correlated to this reconstruction-related surface dielectric anisotropy by [33]

rr

i do

b

4

1

ee (5)

with i and being the imaginary unit and the wavelength of light, respectively. In Eq. (5) the thickness d of the optically anisotropic overlayer has to be d<<. Fig. 2 gives for a (2x4) reconstructed GaAs (001) surface the measured ellipsometry and RAS spectra and the resulting surface dielectric anisotropy eo d as calculated with Eq. (5). Next it will be demonstrated how closely related both techniques, RAS and SE, are. In an ellipsometric configuration with the plane of incidence (defined by the incoming and reflected light beam) oriented perpendicular to one of the eigenvectors (y in Fig. 1, i.e., =0), the transition from oblique to normal incidence (f®0) yields:

f0 0 ( ) rrx

y (6)

The negative sign in Eq. (6) had to be introduced because we changed from the moving coordinate system (ellipsometry) to the x,y,z coordinates fixed to the sample (RAS). Alternatively to the complex reflectance ratio 0, the impact of two different reflectances rx and ry (with x and y orthogonal to each other) to the polarization state of the reflected light can be described by r/r (defined by Eq. (3)), which is related to 0 by:

rr

2 11

0

0

(7)

02

2

rrrr

(8)

In case the surface is only weakly anisotropic, i.e., quadratic terms such as |r/r|<<1 can be neglected, one yields from Eq. (8):

8


Re ; Im arg rr

rr

1 0 0 (9)

Thus, in principle one could use a standard ellipsometer at normal incidence for detecting a weak anisotropic response on a semiconductor surface. However, for sensitivity reasons which are discussed below in more detail a special RAS optical setup should be used.For ellipsometric real-time analysis in most cases of practical importance the sample should be oriented in such a way (=45°) that the samples anisotropy cancels out (ellipsometry measures the projection of the samples optical properties to the line formed by the intersection of the surface and the plane of incidence [34]) and therefore under this condition Eq.(2) can be applied as for a completely isotropic sample. A different sample orientation, e.g., has to be chosen in two special cases: (i) for monitoring ellipsometry growth oscillations with monolayer periodicity [Error:Reference source not found] and (ii) when using a spectroscopic real-time ellipsometer for surface anisotropy measurements in the case of a substrate with highly precise wobble-free rotation. While the first item will be touched below, the second - that in principle is doable because precisely adjustable rotating sample holders are now available [Error: Reference source not found] - still remains to be done [35].

2.2 Multilayer structures and virtual substrate approach

Up to now we only discussed the optical properties of semiconductor samples with substrate-like optical properties. However, also for single or multilayer samples the basic ellipsometry and RAS equations (1) and (3), respectively, remain valid. The only necessary extension to be introduced is that now the complex reflectances rp, rs, rx and ry have to be calculated according to well known multilayer algorithms [36]. In

Fig. 3 Reduction of a multilayer system to a single layer (a) and definition of a virtual interface (b) or a virtual substrate (c) representing the integral effect of all subsurface interfaces

9

J.-T. Zettler

the case of only a single layer the familiar Airy formula results (for definitions see Fig.3):

r r Z rZ r r

Z e nj

id

nj j a

j

j

01 1 12

1 01 12

22

2

1

e e f/ ; sin

(10)

It can be shown that the reflectance of any multilayer system can be written in terms of a modified Airy formula (Fig. 1a):

r r Z rZ r r

N

N

01 1 1

1 01 11 (11)

More specifically, if a virtual interface is defined at a distance dv®0 below the surface, the integral effect of all subsurface interfaces of the sample can be represented by the reflectance rvN of the virtual interface [37] (Fig. 3b).

r r Z rZ r r

r rr r

v vN

v vN

vN

vN

01

01

01

011 1 (12)

Under certain conditions the four parameters defining the virtual interface (i.e., the complex parameters r1v,p and r1v,s) can be approximated by means of the only two parameters of a virtual substrate (i.e., real and imaginary part of ev, Fig. 3c). This virtual substrate approximation, introduced by Aspnes [Error: Reference source notfound] and recently comprehensively reviewed by the same author [Error: Referencesource not found], can be applied for semiconductor hetero-epitaxy in most cases because the dielectric functions of the materials involved often differ only slightly and therefore the contribution of the buried interfaces to the measured ellipsometric spectra remains small. The basic equation for calculating the dielectric function eo in a thin overlayer of thickness dv from an ellipsometric real-time measurement at the wavelength is given by [Error: Reference source not found]

e e

e e e

e f e

o

i d

212

12

1

8 sin

(13)

(14)

10


A linear approximation of Eq. (13) is [Error: Reference source not found]

e e e f

ee

eo

o

id

411

1

1sin (15)

which will be used in 2.4 to visualize the precision limits of this method.

If one or more layers in the sample are anisotropic more complicated but well-known multilayer matrix algorithms (see, e.g., [Error: Reference source not found]) would have to be applied. In case the optical axis of all layers are oriented in the same direction and parallel to the surface, the reflectances rx and ry for light polarized along the eigenaxis x and y, respectively, have to be calculated separately according to Eq. (11) thus yielding the normal reflectance anisotropy with Eq. (3). Using this procedure for a thin anisotropic layer on an absorbing substrate and assuming d1<<, Eq. (5) was derived in [Error: Reference source not found]. In case of a single interface anisotropy a formula similar to Eq. [Error: Reference source not found] can be given [38]. However, if more than one region of the sample (surface, interface or layer) contributes to the RAS spectrum a deconvolution becomes rather complicated and is in most cases beyond the time restrictions of real-time analysis. An example will be given below for ordered InGaP on GaAs where surface anisotropy and bulk anisotropy are superimposed.For symmetry reasons every hetero-interface should cause an interface anisotropy (e.g., the S4 improper rotations characteristic for the diamond and zinc-blende structure [Error: Reference source not found] cannot be applied to their (001) surfaces and interfaces). Furthermore, in case the thickness of the uppermost layer is less than the light's penetration depth, even isotropic interfaces modify the surface related r/r via Fabry-Perot oscillations. This indicates that for optically thin epitaxial layers RAS ceases to be an only surface sensitive method.

2.3 Morphology contributions to the Ellipsometry and RAS spectra

Roughness effects to the ellipsometric spectra are well known and effective medium approximations (EMA) have been successfully used to model these contributions [39]. For semiconductor epitaxial growth especially in device related processes, roughness is supposed to be restricted to sub-monolayer heights. However, when new processes are developed or formerly properly running processes have to be transferred to new growth chambers, often the growth parameters have to be optimized for yielding smooth surfaces and interfaces. Otherwise, in some cases well defined roughnesses have to be prepared: step bunching can be used for quantum wire preparation and Stranski-Krastanow growth mode is utilized for quantum dot preparation [40]. Therefore, some work was addressed in recent years to quantify the optical effects of roughness levels of the order of only a few monolayers which cannot be treated by conventional EMA. Aspnes [41] calculated the effect of surface steps to reflectance measurements and in [42] the combined effects of monolayer islands and

11

J.-T. Zettler

reconstruction was modeled. In the latter work the Bruggeman effective medium approximation [43] was extended to anisotropic (ellipsoidal) inclusions which can be adjusted to the morphology of growth surfaces. Generally, one has to start from the generalized effective medium formula [Error: Reference source not found]:

ee e e e e

e e e

q q f fq f f

A B h A A B B

h A B B A

( )( )

11 (16)

(e)

Fig. 4 Most commonly used ellipsometric configurations: (a) fixed Polarizer-Sample-rotating Analyser (PSA), (b) fixed Polarizer-Sample-fixed retarder-rotating Analyser (PSRA), (c) fixed Polarizer-Sample-PEM(0)-fixed Analyser (PSM(0)A, (d) fixed Polarizer-Sample-PEM(45)-fixed Analyser (PSM(45)A). In (e) the RAS set-up according to Aspnes [Error: Reference source notfound] is given.

12


which gives the effective dielectric function <e> of a mixture of the two "guest" material inclusions (with volume fraction fA and fB and dielectric function eA and eB in a "host" medium eh. The screening parameter q has a value between 0-1 and has to be calculated [44,Error: Reference source not found] depending on the mean shape of the inclusions.

2.4 Ellipsometry and RAS: hardware, systematic and random errors

Ellipsometers and RAS systems are currently commercially available with excellent performance characteristics. A detailed description of ex-situ systems and specific in-situ set-ups can be found in a number of books and review articles [Error: Referencesource not found,Error: Reference source not found,45,Error: Reference source notfound]. Therefore, only some aspects especially relevant for growth monitoring applications will be dealt with here. The intention of this section is to ease the decision of which kind of method and optical system is the best suited for monitoring a given growth situation. In that sense I will concentrate on a comparison between the basic types of ellipsometric and RAS setups suited for real-time studies. Special attention will be paid to the physical limits for the signal-to-noise ratio and the characteristic systematic errors of the several types of optical systems covering both rotating analyzer/polarizer ellipsometers as well as phase-modulated ellipsometers and their derivatives the reflectance anisotropy (difference) spectrometers. Fig. 4 gives an overview over the basic types of optical systems. In several studies the sources of systematic errors for these different types of ellipsometric set-ups are analyzed [Error: Reference source not found, 46]. In general it is accepted that the less optical components are used the smaller is the number of systematic errors that has to be compensated. For this reason the simple PSA ellipsometer in many cases gives the most precise data and most of the dielectric function reference data taken with this kind of ellipsometer by Aspnes and co-workers more than a decade ago still serve as an excellent reference. The implementation of a retarder, that gives an additional phase shift R, in the PSRA configuration, improves under certain conditions the signal-to-noise ratio but introduces - via depolarization and limited precision of alignment - additional systematic errors. The same holds for the photo-elastic modulator (PEM), which is the main optical component for phase-modulated ellipsometry (PSM(0)A and PSM(45)A set-up in Fig. 4). Even the best designed PEM (free of built in static strain, temperature stabilized and internally generating an ideal standing acoustic wave) is characterized by an inhomogeneous phase shift distribution over the light-beam cross section. The resulting depolarization can be avoided by restricting the beam diameter to only a few millimeters (i.e., a very small fraction of the acoustic wavelength). This, however, decreases the signal-to-noise ratio due to low throughput. For many ex-situ applications these sources of systematic errors and also the often non-sinusoidal phase modulation can be compensated by elaborate alignment procedures. However, in in-situ situations at least two more systematic errors have to be dealt with: phase shifts due to strained

13

J.-T. Zettler

windows and a less precisely defined angle of incidence. Keeping in mind that only a limited number of alignment parameters can be compensated by even highly sophisticated in-situ alignment procedures the most simple ellipsometric set-up should be used. This directly guides us to the PSA set-up that - with a rotating polarizer and a fixed analyser - allows for the application of parallel detector arrays. In fact this is presently the only type of real-time ellipsometer that delivers real-time spectra with less than 100ms time-resolution. PEM-based systems despite their high modulation frequency (50kHz) cannot be used for very fast spectroscopic measurement because the amplitude of the modulating acoustic wave

Fig. 5 Noise in the measured ellipsometric parameters arg() (a) and || (b) for the four different ellipsometry set-ups given in Fig. 4.

in the PEM has to be tuned to the wavelength with a time constant of several seconds.

While the absolute precision of ellipsometric measurements is limited by systematic errors, the detection of small changes on the surface of the growing sample is directly limited by the signal to noise ratio S/N of the given ellipsometric set-up. The following equation:

I t I I t I m tc s( ) cos sin 0 2 (17)

describes the time dependence of the intensity signal at the detector and is general for all ellipsometry and RAS systems discussed here (Fig. 4). It mirrors the fact that

14


ellipsometry and its derivative RAS can be regarded as modulation spectroscopic methods with the angular frequency either of the phase modulation (phase-modulated spectroscopic ellipsometry (PMSE), RAS; m=1) or of the modulation of the polarization azimuth (rotating analyzer ellipsometer (RAE), rotating polarizer ellipsometer (RPE); m=2). In general the sample parameters =rp/rs and r/r are determined by measuring the intensity ratios ac=Ic/I0 and as=Is/I0 [Error: Referencesource not found,Error: Reference source not found]. It is this normalization to the light intensity which makes these ellipsometric techniques so well suited to growth applications. And it is the modulation technique that allows for lock-in detection or digital Fourier analysis which gives the excellent signal-to-noise ratio ellipsometric techniques are known for. What is different for the specific ellipsometric set-ups in Fig. 4 is the way how || and arg() are derived from the measured intensity ratios ac

and as :

PSA:

11 1 2

aa

a

ac

c

s

c

; arg arccos(18)

PSRA:

11 1 2

aa

a

ac

c

s

cR; arg arccos (19)

PSM(0)A:

tan arcsin ;

arg arcsin ;

arg arccos ;

12 2 2

2

2

2

2

1

2

12 2

22 2

aJ

aJ

a J

a aa a

a J

a aa a

c

PEM

s

PEM

s PEM

s cs c

c PEM

s cc s

(20)

PSM(45)A:

tan arccos ;

arg arcsin

12 2

2

1

2

12

aJ

a J

a

c

PEM

s PEM

c(21)

RAS:

15

J.-T. Zettler

Re

Im arg

rr

aJ

rr

aJ

c

PEM

s

PEM

12

2

02

01

(22) (J1,2(PEM) are the Bessel functions of the amplitude PEM of the PEM's phase modulation). Obviously, for each set-up the complex reflectance ratio =rp/rs has to be calculated via specific and rather complicated trigonometric equations. These equations, which are given here assuming ideal optical and electronic components, are implemented in the ellipsometer control software and therefore usually one has not to care about them. However, the derivatives of Eqs. (18)-(21) tell us how a given intensity noise I shows up (via the noise in the intensity ratios ac and as) in the resulting (E) spectra:

dda

a dda

ac

cs

s (23)

The respective results for the specific ellipsometric set-ups are illustrated by Fig. 5 where an intensity noise of I/I=10-3 was assumed. With this very general characteristic of the different types of ellipsometers one can judge about their applicability to specific real-time monitoring tasks. In any case not only the noise in the measured ellipsometric parameters || and arg()=ps has to be analyzed but also the resulting noise in the sample parameters to be determined in-situ. As an example, Fig. 6 gives the resulting random errors in the measured bulk dielectric functions, which have to be calculated via [47]:

e

1 0 21

3

01

31

2 4

4 8

c cc

c

cc

cc

psps

psps

ps

coscos

sincos

(24)

and

e e

2 22

3

1

20 2

2

3

2 4

cc

cc

c ccps

pspscos

sin

(25)

with

cc

c c c ps0

2 2

32 1 2 3 1

4 1 2 sin tan ; ; cos,

f f

16


5

10

15

20

25

GaAs at 300K

a)

e 2

2 3 4 50.01

0.1

photon energy [eV]

PRSA

PSM(45)A

PSA

PSM(0)A

b)

e2

-10

0

10

20

30c)

e 1

2 3 4 50.01

0.1

d)PSA

PSM(45)A

PRSA

PSM(0)A

photon energy [eV]

e1

Fig. 6 Ellipsometric measurement of the GaAs bulk dielectric function: imaginary and real part of the bulk dielectric function (a,c) and corresponding noise for four different ellipsometry set-ups (b,d).

Maximum sensitivity in single wavelength mode can be reached by using an adjustable phase-shifting element (e.g. a Babinet-Soleil retarder) in conjunction with the polarizer adjusted to P=arctan|| for virtually shifting the measured towards values that can be detected with minimum noise (PRSA curve in Fig. 6b). This technique has been used for monitoring monolayer growth oscillations at 2.6 eV by ellipsometry [Error: Reference source not found]. The mechanical adjustments improving the S/N ratio are, however, not suited for fast spectroscopic measurements. Therefore and because of the limitations of PEM-based ellipsometers discussed above, PSA configurations are still widely used (with either the polarizer or analyser rotating). Due to the poor S/N ratio of PSA ellipsometers in the low-absorbance range, recently rotating compensator systems receive some interest again for constructing fast and sensitive in-situ ellipsometers [48].

The results given in Fig. 6 can be used, e.g., for analyzing the precision limits of ellipsometric real-time composition and growth rate measurements by means of the virtual substrate analysis. Fig. 7, which is based on a similar figure in [Error:Reference source not found], gives an schematic representation of the determination of the actual composition x and the actual growth rate d/t by real-time ellipsometry at E=2.6 eV during the growth of Al0.2Ga0.8As on GaAs. Rewriting Eq. (15) for a real-

17

J.-T. Zettler

time ellipsometric measurement of both growth-rate and composition yields (see Fig.7)

20 21 22 239

10

11

12

13

14

Al0.2Ga0.8As

AlxGa1-xAs10

<e>

o<e >(d)

x

d [A]

e

150

20

100

0.25

0.15

0.10

0.05

Im <

e >

Re < e >

Fig. 7 Schematic representation of the determination of the actual composition x and the actual growth rate d/t by real-time ellipsometry at E=2.6eV during the growth of Al0.2Ga0.8As on GaAs (according to [Error: Reference source not found]). The size of the open circles represents the random noise <e> assumed for this measurement.

e e e f

ee

eo

o

id

dt

411

1

1

1

sin

(26)

The length of e-<e> is scaled by the inverse growth rate d /t and therefore both the actual composition and the growth rate can be determined from the point of intersection of e-<e> with the e(x) line of AlxGa1-xAs. It can be shown that the error in the direction of eo -<e> is |<e>|/<e>. The noise in the ellipsometric measurement has been assumed here to be | <e>|=0.1 (i.e., significantly higher than what can be reached with an optimized set-up according to Fig. 6 only in order to ease the schematic representation. The resulting random errors in x and d/t are indicated in Fig. 7 (the relative errors of d/t and |eo-<e>| are the same). The random errors of this real-time measurement can be further decreased by fixing either the growth rate or the composition to known values for determining the actual composition [Error: Reference source not found] or the actual thickness [Error:Reference source not found]. However, at this level of ellipsometric analysis the impact of systematic errors, such as temperature effects, changing reconstructions, etc., can reduce the absolute precision of the real-time measurement.

18


As we have discussed above, RAS can be regarded as a direct derivative from ellipsometry. Thus, in principle one could use any standard ellipsometer at normal incidence for detecting a weak anisotropic response on a semiconductor surface. However, from Fig. 5 it becomes clear that for the small reflectance anisotropies of reconstructed semiconductor surfaces, i.e., for ||1 and arg00, only the PSM(45)A and the PRSA configurations give a sufficiently high S/N ratio. Furthermore, conventional ellipsometers work at high f-numbers because they are optimized for high precision oblique incidence measurements with nearly parallel light beams (the angle of incidence f is a crucial parameter in ellipsometric analysis!). This scales down the S/N ratio and therefore in most cases ellipsometers cannot resolve small anisotropies. For this reason, despite earlier attempts for normal incidence ellipsometry [49,50,51], a real break through in surface anisotropy sensing was reached only after Aspnes published his optical set-up for RDS/RAS [Error:Reference source not found] which is basically a PSM(45)A configuration with an decreased f-number (see Fig. 4e). This PSM(45)A configuration was chosen as the starting point for developing an optimized RAS set-up because it yields a maximum S/N ratio for arg0 and ||1 (see Fig. 5), i.e. for small reflectance anisotropies (see Eq.(9)).

For a given reflectance ratio =|rp/rs| exp(ips) the detected intensity in a PSM(45)A set-up is given by [Error: Reference source not found]:

I tI

J T

Jt

J T

Jt

PEM

PEM

ps PEM

PEM

( ) ( )

( )cos

sin ( )

( )sin

0

2

22 2

0

2

2

21 1

0

2

2

11

12

111

2

2

12

111

(27)

with T1 and T2 the damping constants of the electronic detection system at f= mod

and f=2mod, respectively and PEM the amplitude of the phase modulation by the photo-elastic modulator. For ellipsometry measurements PEM =2.405 rd is usually chosen because with J0(2.405)=0 Eq. (27) simplifies significantly [Error: Referencesource not found]. Assuming again small reflectance anisotropies, i.e. |r/r|2<<1 and changing to normal incidence, Eq. ( 2 7 ) transforms with Eqs. (6) and (9) into

19

J.-T. Zettler

0

1

2

3

4

5

6

num

ber o

f pho

tons

[1010

s-1]

2 3 4 50

5

10

15

r/r photon noise limit [10

-5]photon energy [eV]

Fig. 8 The number of photons per second as detected in a typical RAS set-up by using a UV-enhanced Si-detector and the resulting RAS resolution limit for an integration time of 0.1 seconds.

I tI

rr

rr

J T

J

rr

rr

t

rr

J T

J

rr

rr

t

PEM

PEM

PEM

PEM

( )Re

Re

( )

( )Re

Re

cos

Im ( )

( )Re

Re

sin

0

2 2

0

1 1

0

11

2

11

2

2

11

(28)

Only in case of very small reflectance anisotropies, i.e. |r/r|<<1, and with ideal electronic damping parameters (T1=T2=1) Eq. ( 2 8 ) can be replaced by

I tI

rr

J t rr

J tPEM PEM( ) Re ( ) cos Im ( ) sin0

2 11 2 2 2

(29)

that is basically what was given by Aspnes [Error: Reference source not found]. Some correcting terms for nonideal optical components are dropped here because they can easily be compensated for by rotating the sample azimuth by 90 degree as described below. In general, however, it is often not the very small reflectance anisotropy of the sample that decides whether Eq. ( 2 8 ) or Eq. ( 2 9 ) has to be applied but the larger offsets due to strained windows or non-ideal optical components. Thus, especially when the PEM modulation amplitude is set to values PEM¹2.405rd (e.g., PEM=1.8423rd for maximizing J1 or PEM=3.0521rd for maximizing J2 and thus improving the S/N ratio for Im(r/r) and Re(r/r) measurements, respectively) Eq. ( 2 8 ) should be used instead of Eq. ( 2 9 ) .

20


For real-time monitoring it is crucial to have a signal-to-noise ratio as high as possible for measurements on time scales as short as possible. Thus, a figure of merit for RAS systems S=(r/r)t½ can be defined with (r/r) the noise for a given integration time t. The presently reached performance is about S=10-5s½ [Error:Reference source not found]. This performance represents the physical limit for fully spectroscopic RAS systems because it is already limited by the photon's shot noise. In Fig. 8 the RAS photon shot-noise resolution limit for a typical RAS set-up (Fig. 4e) is given. The spectrum of the number of photon results from folding the Xe-arc lamp intensity spectrum with the samples reflectance, the detectivity spectrum of the UV-enhanced silicon detector and the transmittivity spectra of both the monochromator grating and the Glan-Air polarization prisms.

Similarly, also for SE a photon noise resolution limit can be determined. In a typical SE set-up about two orders of magnitude less photons can be detected per time unit due to the higher f-number and due to the reduced reflectance close to the Brewster angle. The resulting noise values correspond roughly to that what was given in Fig. 5, requiring, however, that in case of the PSA and PSRA configurations the angular frequency of the mechanically rotating prisms is highly stabilized.

Finally, I would like to point out that changing the polarizer azimuth away from the P=45 position (Fig. 4a-e) imposes a well defined (but virtual) change to the measured (E) and r/r(E) spectra, respectively. This can be used in ellipsometry for decreasing the noise by shifting virtually to values the ellipsometric system is most sensitive to. This procedure requires however that the change in polarizer azimuth does not significantly decrease the intensity. In RAS a small shift in P away from P=45 enables us to determine both the correct sign of the Re(r/r) spectrum and T2 in Eq. ( 2 8 ) . This gives, via the Kramers-Kronig relation, also the sign of the Im(r/r) spectrum and T1.

2.5 Kramers-Kronig relations

Epitaxial growth systems enable us to prepare ideally smooth surfaces free of adsorbates and oxides. Thus the bulk optical properties of these semiconductors can be directly measured by ellipsometry in terms of their bulk dielectric function eb. The real and imaginary part of the dielectric function, however, are not independent because they are correlated via the Kramers-Kronig relations [52]. The Kramers-Kronig relations are of very general validity. They enable us to find the real part z1 of the response function z()=z1+iz2 of a linear passive system if the imaginary part z2

of the response function is known at all frequencies, and vice versa.

z z d122 2

0

2( ) ( )

z z d212 2

0

2( ) ( )

(30)

(31)

Eqs.(30) and (31) can be applied to both e-1 and r/r, because e-1 is the response function between the internal electric fields in the solid and the resulting polarization

21

J.-T. Zettler

field and because the complex reflectance r() can be regarded as a response function between the incident and reflected waves. This is of fundamental importance for ellipsometry and RAS in-situ spectroscopic studies at growth systems, where window strain, window deposition, poor sample alignment, etc. often modify the spectra. The resulting systematic errors can be detected and sometimes compensated for by using the Kramers-Kronig consistency between the real and imaginary part of the spectra as an figure of merit for the goodness of the data. Furthermore, because it can be shown that energetically remote absorption contributes to Re[e()] only as a smoothly varying baseline, the complex dielectric function of a semiconductor can be completely given by its imaginary part and a small number of parameters modeling the UV absorption. Having in mind that for growth characterization an extended dielectric function data base has to be available for a wide field of compositions and temperatures, it becomes clear that usage of Eq.( 3 0 ) is also important for data reduction.

2.6 Coupling of the in-situ optics to the growth chamber

a) General considerationsUp to this point we have discussed the absolute precision and the S/N ratio typical

for the several ellipsometric and RAS setups irrespective whether they are used ex-situ or in-situ. For real-time applications some sources of systematic errors become less important as the oxide and roughness overlayers which otherwise often complicate the measurement of bulk dielectric functions. On the other hand additional alignment procedures have to be introduced for compensating the effects of residual window strain to the measured spectra. Furthermore, disturbing effects to the spectroscopic system such as process light, mechanical vibrations and growth process related electromagnetic signals have to be taken into account. Additional constraints on the optical design are often added by the limited space at the optical ports to the growth chambers. Some of these aspects are summarized in Fig. 9 where both RAS and SE are attached to a linear MOVPE reactor. The size of the optical systems is restricted to a minimum in order to fit completely into the exhausting closet that houses the MOVPE reactor. Both systems, RAS and SE utilize double-grating monochromators and UV-enhanced silicon detectors in order to cover

22


Fig. 9: Detailed RAS construction design (top, after [53]) and schematic drawing (bottom) of how both optical systems, RAS and ellipsometry, are attached to the MOVPE reactor (P polarizer prism, A analyzer prism, M monochromator, Xe xenon arc lamp, R retarder, F bandpass filter wheel, Si UV-enhanced silicon photodiode, PEM photoelastic modulator, PM photomultiplier, C chopper).

23

J.-T. Zettler

Fig. 10: RAS attached to a MBE system using a strain-free pyrometer window (after [Error:Reference source not found]).

the 1.1 eV to 5.3 eV spectroscopic range. The SE is in fact a double-monochromator system because the band-pass filter wheel in front of the detector serves as a polarization-independent second 'monochromator' that suppresses completely in conjunction with the light chopper the brightly shining light of the halogen lamp heating system. This configuration allows for ellipsometric measurements in the PSA (polarizer-sample-rotating analyser) mode which yields for absorbing samples, as discussed above, a sufficiently high absolute precision. The throughput of the RAS optical system is maximized by using large area (20x20mm2) Glan-air polarizing prisms and a focus length of the imaging mirrors that completely fills both the acceptance angles of the polarizing prisms and the f-number of the monochromator. Both, RAS and SE are coupled to the reactor through strain reduced custom-made and purged silica windows and small holes in the inner liner tube.

While both systems allow for single wavelength transient measurements with 100 ms time resolution, it takes typically 4 and 8 minutes to measure a complete spectrum (120 points) with these types of RAS and SE systems, respectively. The RAS measurement time is mainly determined by the scanning time constant of the PEM. The SE measurement is relatively slow due to the several mechanical components (shutter, grating, filter-wheel) to be moved.

24


Fig. 11: (a) Rotating polarizer type ellipsometer with diode-array parallel detection (after [Error:Reference source not found]), and (b) phase-modulated infra-red ellipsometer for in-situ studies (after [Error: Reference source not found]).

For RAS measurements on MBE systems (Fig. 10) usually no modifications to the growth chamber are necessary. The RAS spectra can be taken via the pyrometer port, which should be equipped with a commercially available strain-reduced window. For this configuration, where pyrometric temperature measurements are not feasible, it is necessary to measure the sample's temperature by means of the RAS set-up (see section 5.2).

Fast spectroscopic ellipsometers based on a spectrograph/array-detector using a rotating polarizer-sample-analyzer configuration have been developed and steadily improved in recent years by Collins and co-workers [Error: Reference source notfound]. These systems (Fig. 11a) allow for fully spectroscopic measurements (usually from 1.2 eV to 4 eV) in less than a second and are available in similar form

25

J.-T. Zettler

meanwhile also commercially. On the other hand due to the efforts of Drevillon and co-workers [Error: Reference source not found] the spectroscopic range available with phase-modulated ellipsometers for in-situ applications has been extended towards the IR and considerable improvements have been reached regarding the precision of phase-modulated spectroscopic ellipsometry (Fig. 11b). The application of phase-modulated IR ellipsometers especially for MOVPE and CBE systems should give new insight in the mechanisms how organic adsorbates and fractional components of the precursor gases influence the growth regime.

b) Alignment of the angle of incidence For RAS as a normal incidence technique the angle of incidence f is not a critical

parameter. For ellipsometry, however, f has to be determined with maximum precision. In ex-situ systems this is a rather simple geometric problem. For growth systems, however, where the sample position is usually not as well defined, the angle of incidence f is usually determined by fitting it to the measured (E) spectrum of a known sample. Changes in f during the deposition process due to thermal expansion of the sample holder are difficult to compensate. In case these thermal expansion effects are reproducible, f calibration by means of samples with known temperature dependence of their optical parameters should work quite well. Otherwise the use of an auxiliary laser to monitor the changing sample position was used successfully [Error: Reference source not found]. Also more importantly, the recent design of an ultrastable MBE manipulator was reported [Error: Reference source not found] that features a wobble amplitude of less than 0.02° an externally controllable substrate tilt and a significantly reduced thermal expansion. This kind of sample holder definitely allows for the realization of what often was promised by the optical in-situ techniques: real-time characterization during growth processes with rotating (usually with about one revolution/s) samples [Error: Reference source not found].

c) Compensation of phase shifts due to window strain The effect of residual strain on the window to the in-situ spectra has to be

compensated both in RAS and SE. For ellipsometry two different phase shifts are superimposed to the spectra because in this case there are two windows necessary. Both windows impose an additional phase shift 1,2 to the measurement which should be kept - by carefully selecting the windows - as small as possible. For correcting the effect of the windows, the Jones matrix equation for the transformation of the electric component of the electromagnetic light wave due to the sample:

EE

rr

PP

x

y

p

s

00

cossin (32)

has to be extended by the Jones matrices W1 and W2 of both windows:

EE

Wr

rW

PP

x

y

p

s

1 2

00

cossin (33)

26


with

Wi i

i ijj j j j j

j j j j j

cos cos sin sin sinsin sin cos cos sin

2 22 2

Assuming a linear j ( ) function

j j jc c j( ) ; , 0 0 12

and taking in-situ spectra of a known sample for a set of different polarizer azimuths yields the orientation of the optical axis j and the parameters c0j and c1j of both windows via a 6-parameter fit procedure. Once these window parameters are known, Eq. ( 3 3 ) can be inverted to yield the ellipsometric parameters of any further sample. This procedure provides stable and reproducible data when only small corrections to the window anisotropy parameters have to be measured. However, when a new window with completely unknown strain amplitude and orientation is implemented, this procedure has to be applied for a set of different samples and one has to check carefully whether the six window parameters found by the fitting procedure really represent the windows optical properties.

The just-described procedure, that works well for SE, in principle can also be applied for RAS. Even if RAS uses only one window, due to the usually inhomogeneous strain distribution over the window area, in this case also two different phase shifts are imposed to the light before and after reflection from the sample. In case the sample can be rotated, however, the effect of the window can be compensated more easily. Turning the samples azimuth by 90° inverts the sign of r/r. Thus the average spectrum [0.5(r/r(=0)+r/r(=90))] describes the window's anisotropy contribution while [0.5(r/r(=0)-r/r(=90))] yields the samples RAS spectrum without window effects.

Generally, when RAS or SE spectra of the sample have been taken utilizing a specific compensation of window effects one has to check if this has been done correctly. This check can be performed by comparison to the spectra of a known sample or by using the Kramers-Kronig consistency between either Re(r/r) and Im(r/r) in RAS or e1 and e2 in ellipsometry.

3 ON THE MICROSCOPIC ORIGIN OF THE SPECTROSCOPIC FEATURES

Assuming properly aligned optical systems both bulk and surface dielectric function can be measured even at elevated temperatures with excellent precision by SE and RAS, respectively. As compared to these experimental results the theory of the bulk and surface dielectric function is still less developed. However, recent conceptual and computational progress in theory of dielectric functions contributed significantly to the closing of this gap.

27

J.-T. Zettler

3.1 The dielectric function of the isotropic semiconductor bulk

Theoretically, the imaginary and real parts of the bulk dielectric function can be calculated directly from the semiconductor's band structure and the Kramers-Kronig relation, respectively. Empirical pseudo-potential methods, as applied by Chelikowski

2 3 4 50

5

10

15

20 (a)

300K800K

150K

1000K

0K

e 2

photon energy [eV]

2 3 4 50

5

10

15

20

25 (b) E2E0'

E1+1E1

761K

522K

907K

300K

e 2

photon energy [eV]

Fig. 12: Imaginary part of the GaAs bulk dielectric function at various temperatures: (a) calculated (after A. Shkrebtii [54]) and (b) measured.

and Cohen [55] gave, however, only qualitative agreement to the measured spectra. Therefore, line-shape analysis (LSA) in the framework of parabolic band approximation [56,57] has been widely used to analyze the second derivative of the bulk dielectric function spectra instead of the directly measured spectra itself. This technique yields the bulk critical points (CP's) and band structure calculations are used only to identify the different types of critical points by assigning them to specific transitions within the band structure (The main bulk critical points of GaAs are indicated for the 300 K spectrum in Fig. 12b). LSA can be used to track directly the changes in the semiconductor's band structure with temperature and composition.

28


Temperature increase characteristically broadens the spectra and downshifts the CP energies (see Fig. 12b) mainly due to the thermal expansion of the lattice (i.e., a reduced overlap of the bonding orbitals) and due to the electron-phonon interaction. In case of ternary and quaternary semiconductors the CP energies shift, to first order, linearly with composition and the features in the dielectric function spectra are inhomogeneously broadened with respect to binary and elementary systems due to random microscopic fluctuations in composition (Fig. 39b gives an example).

Very recent progress in theoretical work and the emergence of more powerful computers brought the calculated spectra of elementary and binary semiconductors remarkably close to the experimental ones even if some partially rough approximations (restriction to single-particle solutions and neglection of spin-orbit splitting) often still have to be used for computational reasons. Regarding the bulk dielectric function at growth temperatures, which is of particular importance for our purposes, it is of advantage that excitonic effects are less significant. Under these conditions ab-initio pseudo-potential calculations in the local density approximation give, after some correcting gap shift, a generally good agreement to the experiment in the case where thermal expansion and electron-phonon interaction have been taken into account properly [Error: Reference source not found] (Fig. 12a gives very recent results of work that still is in progress [Error: Reference source not found]). Remaining differences between theory and experiment are most prominent close to the E1 critical points of the group IV and III-V semiconductors which are known from both line-shape analysis studies [58] and calculations in the effective-mass approximation [59,60] to be significantly influenced by excitonic effects. This, and the only small improvements reached by both the recently introduced so-called quasi-particle corrections to the single-particle energies and local field effect corrections [Error: Reference source not found], indicates that taking into account many-body excitonic effects is most crucial for obtaining a more satisfactory theoretical description of the semiconductor bulk dielectric functions.

3.2 The surface dielectric anisotropy

The anisotropic surface dielectric response of cubic semiconductors is caused by directed surface dipoles which in the case of reconstructed surfaces originate mainly from the local dimer arrangement. However, even nonreconstructed surfaces are expected to give an anisotropic reflectance response because in general the broken bonds of the terminated bulk are anisotropically directed. There are only two exceptions of importance: (111) surfaces and single stepped group IV (001) surfaces with domains that usually cancel out in anisotropy. As a consequence RAS spectra in most cases can be correlated with the surface structure. Such a correlation can be established in principle by theoretical calculations of the anisotropic dielectric response of the surface. To preserve as in the bulk case translational symmetry also for the calculation of the surface properties mostly a slab geometry is used where N atomic layers and the equivalent of M layers of vacuum (N,M=10...30) are repeated along the direction perpendicular to the surface. Because additionally due to the surface reconstruction the respective surface unit cell is usually significantly larger with respect to the ideal bulk termination, essentially larger numbers of atoms have to be taken into account to model the surface realistically. Moreover, because the

29

J.-T. Zettler

Fig. 13: Comparison between the calculated surface dielectric anisotropy (dotted) and measured data (drawn) for a Ga rich (4x2) reconstructed GaAs (001) surface (after [Error: Reference sourcenot found]).

2 3 4 5

0

1

2

3

(a)

(2x4), 883K

(2x4), 833K

r/r

[10-3

]

photon energy [eV]

2 3 4 5

-2

0

2

4

6

8

10(b)

2(2x4)

3(2x4)

r/r

[10-3

]

photon energy [eV]

Fig. 14: RAS spectra of a GaAs (001)-(2x4) surface: (a) measured with the reconstruction assigned by RHEED (after [Error: Reference source not found]) and (b) calculated assuming a (2x4) and a 2(2x4) surface unit mesh (after [Error: Reference source not found]).

30


Fig. 15: Local density of states of the Si (001)-(2x1) surface (after [61]). The dimer related surface state extends over about 3 atomic layers.

surface optical properties depend critically on the details of the real atomic surface configuration, total energy minimization with respect to the bond length's and directions in the surface region in any case has to be the starting point. The early works of Chang et al. [62,63] on the GaAs (001) surface was based on an empiricaltight binding model and used a simplified (2x1) and (1x2) model for the (2x4) and (4x2) reconstruction, respectively. They gave already a qualitative agreement to the experimental spectra and the origin of the main characteristic features in the surface dielectric anisotropy eod could be assigned to the structural details of the dimer configurations characteristic for the main GaAs (001) surface reconstructions. Later on the same authors tried to improve their calculations by using more realistic structures of the (2x4), c(4x4) and (4x2) surface unit cells and by performing total energy minimization taking into account at least bond angle relaxation in the uppermost atomic layers [Error: Reference source not found]. This gave a significantly improved agreement of the measured and calculated surface dielectric anisotropy amplitudes. Especially for the Ga-rich (4x2) reconstruction the experimental data have been tracked by the calculation reasonably well, except for a rigid shift of 0.5 eV (Fig. 13). In the case of the As-rich (2x4) reconstruction the agreement has been not as convincing. However, an anisotropic surface transition close to the characteristic 2.5 eV reflectance anisotropy feature of this surface was clearly identified. The energy position of this surface transition is very close to the E1

bulk critical point which, as discussed above, is significantly influenced by excitonic effects. Energy position and temperature dependence of this surface transition (Fig.14a) indicate that beyond the single-electron description on which these calculations

31

J.-T. Zettler

have been based, an anisotropic screening of the excitonic E1 bulk state due to the surface structure could also effect the optical anisotropy of this surface. This would explain why even very recent results of Shkrebtii [Error: Reference source not found], based on a 20 layer slab configuration and an sp3s* tight-binding algorithm, allowing for the complete relaxation of the surface, could not completely resolve the discrepancy between the measured and calculated surface dielectric anisotropy of the (2x4) reconstructed GaAs (001) surface (Fig. 14).

For symmetry reasons any hetero-interface should cause an interface anisotropy - similar to the unreconstructed (by H-termination) GaAs (001)-(1x1) surface, which gives a small but non-vanishing surface anisotropy [64]. Additionally, over a very limited range of monolayers buried interfaces may also influence the dimer configuration at the surface. This is straight forward for nonideal (graded, rough) interfaces but also for ideally abrupt ones where the dimer configuration at the surface is expected to change rather gradually with overlayer coverages of only a few monolayers. From calculations of the local density of surface states for each of the uppermost monolayers (Fig. 15 gives an example) it becomes clear that for hetero-epitaxial growth - irrespective to quantum confinement effects - at least 2-5 monolayers have to be grown before the dimer related surface states reach their steady state parameters.

2 3 4

E1+1

E1

E1+1

E1

T=300Kr/r do

ped -

r/r

undo

ped

(10-3

)

photon energy [eV]

1

T=875K

Fig. 16: Surface field induced RAS signatures of a GaAs (001) surface. In order to separate only the field induced LEO signature, for both temperatures the difference of the RAS spectra of two samples (undoped and doped with n=2*1018cm-3) is displayed here.

Fig. 17: Piezo-electric contribution to the linear electro-optic effect in the reflectance anisotropy. Bonds in (-110) planes are stretched, those in (110) planes are compressed.

32


3.3 Field effects to the reflectance anisotropy spectra

For highly doped III-V and II-VI (001) semiconductors the linear electro-optic effect (LEO) causes characteristic RAS signatures close to the E1 and E0' bulk critical points [65,66,67,68,69] (Fig. 16). The linear electro-optic effect, that scales linearly with the static electric field for symmetry reasons [Error: Reference source not found], has been empirically assigned to a shift in oscillator strength from the E1 towards the E1+1

bulk critical points [Error: Reference source not found]. Its origin was correlated to the Franz-Keldysh like surface-field effects [Error: Reference source not found] and the RAS signatures have been directly compared to intermediate field electro-reflectance experiments [Error: Reference source not found]. However, electroreflectance studies on differently doped GaAs samples performed by Cardona et al. [70] revealed a significant redshift in the E1 and E1+1 energy position for doping concentrations higher than some 1017cm-3, i.e., exactly in that doping range that causes the RAS LEO signatures. Therefore, one should expect that high-field effects contribute to the characteristic LEO signature in the RAS spectra. Two of them shall be discussed here: (i) piezo-electric effects and (ii) the unscreening of the impurities, i.e., dopants, in the depletion layer as recently used for explaining the doping induced redshift in the E1 and E1+1 bulk CP's [71].

A piezo-electric effect is caused by the the surface field via the asymmetric distortion of the bonds in the space charge region of partially ionic semiconductors (see Fig. 17). These internally strained bonds in the surface space-charge region recently have shown up in optical pump-probe experiments on GaAs (001) surfaces [Error: Reference source not found]: subpicosecond laser pulse generated free carriers screened the surface field on a time scale much shorter than the oscillation period of the optical phonons causing the strained atomic layers to relax quasi-instantaneously thus exciting coherent phonons which have been monitored by Cho et al. [72] via 8.8 THz reflectance oscillations. A different and polarization dependent response of the amplitudes of the GaAs E1 and E1+1 bulk critical points under uniaxial strain applied along the [111] direction has been observed in the early piezo-electroreflectance experiments of Pollak and Cardona [73]. However, in the linear optical experiments discussed here, these piezo-electric effects would give contributions to the RAS signatures which are at least 2 orders of magnitude smaller than observed.

The unscreening of the charged dopants in the depletion layer was recently used to explain the doping induced redshift in the GaAs E1 and E1+1 bulk CP's both in ellipsometric [Error: Reference source not found] and electroreflectance studies [74]. Three characteristic effects, namely the different peak shifts for pinned and unpinned surfaces, the different peak shifts for p- and n-doped GaAs as well as a saturation in the peak shift at very high doping levels could be explained [Error: Reference sourcenot found]. Calculations of the slope of the CP's redshift with dopant concentration by second order perturbation theory with a simplified parabolic band model gave good agreement to the experimental data. Lukes et al. [Error: Reference source not found], concerned with experiments sensing only the isotropic unscreening effect, used the

33

J.-T. Zettler

isotropic potential of a point charge as second order perturbation term in their calculations. In the space charge region, however, it is the distortion of this point charge fields by the charges in the surface states that generates the space charge field. This distorted and unscreened field of the dopant atoms should effect the bonds along [110] and [-110] differently, depending on whether the dopant atom is at a group III or group V site. In addition to the characteristic LEO line shapes (Fig. 16) there are two more experimental results that support the assumption that anisotropic broadening of the E1 and E1+1 excitonic bulk CP's (at lower temperatures) and the anisotropic peak shift (at higher temperatures) could be caused by this unscreening effect. First, there is at very high doping levels a significant deviation from the linear behavior of the LEO amplitude (after passing a maximum it decreases again at very high doping levels [75]) that cannot be explained by the reduced depth of the space charge region that gives only a saturation effect [Error: Reference source not found]. Secondly, for RAS experiments performed by Sobiesierski et al. [76] with silicon delta-doped GaAs in MBE an unusual change in the LEO amplitude has been reported during the subsequent overgrowth with undoped GaAs: during the overgrowth of the delta-doped Si layer with undoped GaAs the LEO signature increased in amplitude until about 64 ML GaAs had been deposited and subsequently it decreased exponentially. This experimental result, that has been observed to be independent of the doping level, is consistent to the assumption that the LEO signal arises predominantly from the delta-doped layer. Initially, the free carrier screening is decreased until the GaAs layer is about one Debye length thick and subsequently the LEO amplitude decreases due to the reduced transmittance of the overlayer.

Summarizing the present knowledge on the field effect contributions to the RAS spectra one can state: (i) There is a relatively small range of doping concentrations (some 1016 cm-3 up to some 1018 cm-3 in case of Si doped GaAs(001)) where at room temperature a characteristic RAS signature is found that scales in amplitude linearly with the doping concentration and that is apparently caused by a relative shift of excitonic oscillator strength between the E1 and E1+1 bulk critical points. This signature changes in sign when p-doped samples are used instead of n-doped. (ii) The changes in the LEO signature with increasing temperature and under very high doping conditions are not yet completely understood. However, there is some indication that unscreening effects, used recently for the interpretation of ellipsometric results on highly doped GaAs samples, could contribute.

4 STUDYING BASIC EPITAXIAL GROWTH PROCESSES BY MEANS OF OPTICAL TECHNIQUES

In the 1960's techniques for the epitaxial growth of GaAs were developed. Mainly two techniques proved to be capable of growing low dimensional structures: the deposition of Ga and As that were evaporated from solid sources in UHV (MBE [77]) and the decomposition of organometallic gases at higher pressures (MOVPE [78]). Meanwhile epitaxial growth methods for a wide field of elementary, binary, ternary and quaternary semiconductors have been introduced but still GaAs usually serves

34


as a prototype system when basic growth studies are performed. Since in MBE the well established UHV techniques can be used to study the mechanisms controlling the growth, the analysis of the GaAs (001) surface was mostly done on MBE grown samples. The most important experimental techniques for those studies have been reflection high-energy electron diffraction (RHEED) and modulated beam mass spectrometry. With these techniques it was soon established that the GaAs (001) surface is As terminated under MBE growth conditions [Error: Reference source notfound,Error: Reference source not found,79].

Meanwhile the detailed structure of the GaAs(001) surface is, at least for the main reconstructions and after recent years intensive discussions [Error: Reference sourcenot found,Error: Reference source not found,Error: Reference source not found,Error:Reference source not found,Error: Reference source not found] well known. Especially the development of UHV-scanning tunnel microscopy (UHV-STM) enabled one to clarify what atomic structures are responsible for the RHEED and LEED patterns characteristic for the specific reconstructions.

As compared to the MBE process, in the early 1990s the understanding of the MOVPE surface processes was still rather limited. The resulting urgent need for in-situ characterization techniques applicable also for gas-phase growth techniques was the driving force for the improvement of the optical techniques since the late 1980s. Again Aspnes and co-workers contributed the most to the solution of this problem by developing their RDS(RAS) system from an optimized normal incidence ellipsometry set-up but early results from both Samuelssons group [80] in Lund and Berkovits in St. Petersburg [Error: Reference source not found] also contributed to the opening of this field of research. With the application of this new and highly surface sensitive technique soon it became clear that for GaAs (001) irrespective to the different ambient and pressure conditions the same surface reconstructions are present in MBE and MOVPE, respectively. This result, reported by Kamiya et al. [81] caused intensive discussions. However, after Kiskers grazing incidence X-ray scattering experiments [82] had verified that even characteristic long range order reconstruction exists at MOVPE surfaces, it is now generally accepted that there are much more similarities than differences between MBE and MOVPE growth.

It is important to point out that while in MBE mainly well established knowledge could be verified and utilized by RAS experiments, in MOVPE the basic research on the details of epitaxial growth required considerable stimulation and sometimes provided surprising results from RAS investigations. Recently, following advances in the correlation of RAS signatures with a specific state of the surface, RAS has been able to add some more details also to MBE related knowledge. For this reason in this chapter we concentrate on the RAS contributions to the broadening of basic knowledge on growth processes both in MOVPE and MBE.

4.1 Static surfaces

Under UHV conditions on an ideally prepared and adsorbate-free semiconductor (001) surface, in most cases, dimer bonds are formed which minimize the total energy of the surface and usually introduce a specific geometrical anisotropy to the surface region. At elevated temperatures of 300°C to 700°C as typically used for epitaxial semiconductor growth of compound semiconductors these surfaces have to

35

J.-T. Zettler

be stabilized by a flux of group V or group VI atoms for III-V and II-VI semiconductors, respectively. By adjusting this stabilizing flux that compensates the temperature dependent out-diffusion from the sample's surface, the chemical potential of the surface, i.e. the surface stoichiometry, can be set. Under these conditions the state of the surface is termed static. Stable surface stoichiometries, i.e., less sensitive to the stabilizing flux, usually are correlated with homogeneously reconstructed (single domain) surfaces. In some cases a quite accurate experimental determination of these surface reconstructions was possible by combined RHEED and STM investigations using well equipped MBE systems. With this experimental background, surface structures can be directly assigned to RAS spectra measured at the same

Fig. 18: RAS spectra and the related surface dimer configuration on reconstructed GaAs (001) surfaces. surfaces thus establishing the experimental basis for the interpretation of spectra taken elsewhere. However, only in a few cases (e.g., [Error: Reference source notfound]) has the assignment of RAS signatures directly to the surface structure by STM, presently the best available structural tool, been applied. Therefore simultaneous surfaces characterization by diffraction experiments (mostly RHEED [83,84], low energy electron diffraction (LEED) [85] and grazing incidence x-ray scattering (GIXS) [Error: Reference source not found]) and RAS still contributed the most to the correlation between reflectance anisotropy signatures and geometrical structure. Some ambiguities in this correlation, the fact that in some cases surfaces with the same periodicity cause slightly different RAS spectra, are now mostly resolved. Nevertheless, often the STM data from such surfaces also show very

36


different structural images for very similar diffraction periodicities. In such cases the contribution of reconstructed domains is usually found which are superimposed differently in RAS and diffraction experiments. While obviously the direct assignment of surface structures to RAS spectra with STM measurements has to be preferred, empirical correlations still are of importance because from surfaces under typical high temperature growth conditions STM data are only accessible after sophisticated quenching procedures have been applied [Error: Reference source not found].

Fig. 18 shows typical RAS spectra of a number of GaAs(001) surface reconstructions together with the proposed stick and ball models of the surface unit meshes [86,Error: Reference source not found]. The surface dimers obviously cause oscillator like anisotropic absorption features with characteristic resonance energies (about 2.6 eV at 500°C for the As dimers and about 2.0 eV for the Ga dimers) [Error: Reference source notfound]. While the shape of the spectra is highly sensitive to the detailed structure of the surface unit mesh the amplitude of specific RA structures directly mirrors the absolute surface density of the related reconstruction domains. Thus, once a database containing the correlation of the RAS signatures with structure has been comprehensively established, the status of not too complicated surface configurations (i.e. homogeneously reconstructed surfaces or those with only two types of reconstruction domains) can be determined by deconvolution of the measured RAS spectra. Specifically, if the shape of the RAS spectra indicates the presence of a characteristic dimer configuration of [n´m] symmetry and if additionally the amplitudes of the RA signatures testify that their surface density is close to 100 percent, RAS can give a very strong indication that the surface in fact is [n´m] reconstructed even if the long range order is not directly sensed.

37

J.-T. Zettler

Fig. 19: Assignment of GaAs (001) RAS spectra taken in in MOVPE to the related surface reconstruction: (a) the RAS signature of a (4x2) reconstructed surface in MOVPE (drawn) is compared to a spectra taken in MBE (dashed), where RHEED was used as reference. (b,c) gives the respective GIXS scans (after [Error:Reference source not found]).

The correlation between RAS signatures and surface reconstruction has been used by Kamiya and co-workers to verify that even under gas phase conditions as typical for MOVPE growth the GaAs (001) surface reconstructs. The authors prepared a fairly complete range of GaAs (001) surface configurations under MOVPE conditions which afterwards have been proven by the GIXS studies of Kisker et al. [Error:Reference source not found] to be reconstructed as predicted by RAS (Fig. 19). Under conditions typical for MOVPE growth of GaAs, however, it turned out that practically for the complete range of epitaxy parameters the As rich c(4x4) reconstruction is present at the surface. This unified description of GaAs (001) surfaces both under MBE and MOVPE conditions is summarized by the surface phase diagram in Fig. 20 that was established by Kamiya et al. [Error: Referencesource not found].

Fig. 20: Surface phase diagram established by RAS measurements both in MBE and MOVPE (after [Error: Reference source not found]).

Additionally to the temperature and the stabilizing fluxes, the surface stoichiometry is influenced by monolayer steps on the surface. Experiments with vicinal III-V

38


surfaces in MOVPE indicate that with increasing miscut angle, i.e. with increasing step density, the outdiffusion of the group V element is enhanced. Fig. 21 shows that for vicinal surfaces at elevated temperatures the characteristic RAS minimum downshifts from 2.6 eV to 2.0 eV indicating that the As dimers of the singular surfaces are replaced at least partially by Ga dimers on the high off-cut (6°) sample. This effect was interpreted by Ploska et al. [Error: Reference source not found] by means of Ga rich surface domains close to the steps. A similar effect of the monolayer steps can be observed under MBE conditions (see below). Because the outdiffusion from the sample depends on the bond strength between the atoms involved, one finds, as expected, chemical shifts with the bulk stoichiometry of ternary semiconductors not only in the energy positions of the RAS features but also in the surface stoichiometry. In Fig. 22 the chemical shift of the As dimer related RAS minimum with the composition of AlGaAs was studied. In these experiments temperature and As2 flux have been chosen so that for all compositions the surfaces remained well within the c(4x4) phase of the surface phase diagram. If the conditions are differently chosen, the chemical shift in the energy position of both the RAS features and in the surface stoichiometry can be observed at once. Fig. 23, that gives the RAS spectra of InGaAs on GaAs, may serve as an example of this kind of situation. In this experiment, however, a further parameter influences the surface dimer configuration: InGaAs is lattice mismatched to the GaAs substrate and thus the energy position of the evolving InGaAs (2´4)-like RAS signature is shifted towards the related value for GaAs because the lattice constant of GaAs is imposed on the InGaAs layer.

39

J.-T. Zettler

2 3 4 5

-2

0

2 775K

0° 1°off (B) 6°off (B)

energy (eV)

-2

0

2 825KRe(r

/<r>

) (1

0-3)

-2

0

2 875K

-2

0

2 925K

-4

-2

0

2

4

6

1

0.5

x=0

(a)

E1 (AlxGa1-xAs)

c(4x4)T=510°C

Re

( 2 (r

[-110

] - r [1

10])

/ <r>

) (1

0-3)

2 3 40

5

10

15

20

0.5 1x=0

(b)

photon energy [eV]

<e2>

Fig. 21: RAS spectra of vicinal and singular GaAs (001) surfaces in MOVPE (after [87]).

Fig. 22: Reflectance anisotropy (after [Error:Reference source not found]) (a) and effective dielectric function (after [88]) (b) of AlxGa1-xAs.

2 3 4 5

-2

-1

0

1

2

3 InAs(unstrained)

10 ML InxGa1-xAs on GaAs(001)

T= 775 K

x=0.18

x=0.11

x=0.06

GaAs

Re

( r /

<r>

) ( 1

0 -3 )

Energy (eV)

Fig. 23: RAS spectra of InxGa1-xAs on GaAs (after [89]).

40


2 3 4 5

-2

-1

0

1

2

3

2

InAs (unstrained)

deposited InAs (in ML)

1.5

1

0.5

0

photon energy [eV]

Re

(r/r)

[10-3 ]

Fig. 24: RAS spectra of strained InAs monolayers on GaAs (after [90]).

41

J.-T. Zettler

Finally, Fig. 24 shall underline that in some cases the thickness of an epitaxial layer also influences the dimer configuration at the surface. Because the wave functions of the dimer related electronic surface states are extended over several atomic layers, a hetero-interface influences the details of surface reconstruction until about 5 monolayers are grown. This effect, that was already discussed in section 3, has been observed not only for InAs on GaAs but also for AlAs on GaAs [91] and InGaAs on GaAs [Error: Reference source not found].

Obviously one has to conclude from the RAS experiments on static III-V semiconductor (001) surfaces that there is a fairly large number of epitaxial parameters that influences via the changing dimer configuration the shape and amplitude of RAS spectra: temperature, stabilizing group V flux, bulk composition of compound semiconductors, strain, surface step density and buried hetero-interfaces.

Only one of the parameters influencing the dimer configuration at stabilized surfaces can be changed more or less abruptly: closing the shutters of the group V sources in MBE or switching between the lines of different group V precursors in MOVPE enables us to systematically study the kinetics of desorption processes (e.g. Se desorption from MBE grown ZnSe surfaces [92]) and surface exchange reactions (e.g. As to P exchange by PH3 supply to GaAs (001) in MOVPE [Error: Referencesource not found], Fig. 25).

0 10 20 30 40 50

2 * 10 -3

E= 2.5 eV

PH3

AsH3

755 K

775 K

795 K

Re

( r /

<r>

)

Time (s)

Fig. 25: As to P exchange by PH3 exposure to GaAs (001) in MOVPE (after [93]). An activation energy of 1.64 eV was determined from an Arrhenius plot of the exchange rates [Error:Reference source not found].

42


4.2 Surfaces during growth

When homoepitaxial III-V semiconductor growth is initiated, i.e., if group III atoms are supplied additionally to the surface, the chemical potential of the surface is changed. The effective group V overpressure is reduced because a part of the stabilizing group V atoms are now used to let the crystal grow. Additionally, unless carefully chosen growth conditions ensure ideal two-dimensional step-flow growth (e.g., by optimized temperatures, vicinal substrates, very low growth rates), the growth surface tends to be microscopically rough as compared to the annealed static one and the density of surface steps is increased. As we have seen from the basic studies on static surfaces, both the reduction of group V stabilization and the increased density of surface steps cause the surface to become less group-V-rich. The respective growth induced changes can be followed by RAS immediately and

1 2 3 4 5 6

c)

growth rate (nm/h)

500

1

0

50

25

200

100

75

1000

900

T=770K

Re(r

/<r>

) (1

0-3)

Energy (eV)

0.0 0.2 0.4 0.6 0.80.6

0.8

1.0

1.2

1.4

1.6

1.8d)

T=770K

As [

ML]

growth rate [ML/s]

Fig. 26: RAS measurements of the As surface coverage on GaAs (001) during MBE growth: (a) Substrate temperature dependence of the RAS level at 2.65 eV for the GaAs (001) surface without (circles) and with growth (triangles). See Fig. 28 for definitions. (b) Effective As dimer coverage as derived from the data in (a) assuming the RAS level to vary linear with ; (c) RAS monitoring the changing surface dimer configuration for various growth rates. (d) Effective As dimer coverage derived from the data in (c). ((a,b) after [Error: Reference source not found], (c) after [94]).

43

J.-T. Zettler

sensitively because it senses predominantly the changing dimer configuration and is less sensitive to the long range order of the surface structures. This valuable advantage as compared to the diffraction based techniques was utilized in the experiments summarized by Fig. 26 where the state of the surface during GaAs (001) growth was monitored through the shape of the RAS spectra. In these studies [Error:Reference source not found,Error: Reference source not found] the influence of both growth temperature (Fig. 26a) and growth rate (Fig. 26c) to the geometric structure and stoichiometry of the growth surface was investigated. In Fig. 26b and Fig. 26d the reduced As dimer coverage could be quantified during growth. In this analysis it was used that on surfaces with domains of different reconstruction a linear interpolation between the reference spectra of homogeneously reconstructed surfaces can be applied [Error: Reference source not found]. From both experiments it is obvious that the c(4x4) reconstructed surface in MBE is highly unstable when Ga is supplied and that the dimer configuration of the (2x4) reconstruction is typical under MBE growth conditions.

For a number of reasons the MOVPE and MOMBE growth of GaAs from gas sources is more complex as compared to MBE. This is mainly because the decomposition of the precursor gases is at least a partially surface catalytic process and therefore the status of the surface influences the growth kinetics. Additionally, in most MOVPE systems the sample temperature also controls the decomposition of both the group III and group V precursor gases. Thus changes in sample temperature cause changes both in outdiffusion and in the stabilizing group V overpressure. Moreover, under certain conditions the presence of highly reactive radicals which result from the decomposed precursor gases additionally influences the stoichiometry of the growth surfaces. According to Fig. 27 three well distinguished surface phases are observed, which distinguishes it from MBE, where GaAs growth usually takes place on a (2x4) reconstructed surface. The phase boundaries are directly correlated to the decomposition of the precursor gases. The boundary between phase II and phase I marks the line where with increasing temperature the increasingly decomposed arsine overcompensates the Ga species supplied to the surface. The boundary between phase II and phase III represents a transition in growth conditions where either by an oversupply of TMG or by only partial TMG decomposition at low temperatures the surface is covered by TMG or other adsorbates which hinder the surface catalytic TMG decomposition. While high quality GaAs layers usually are grown under phase I conditions the surface dimer configuration in phase II has been concluded from RAS studies to be characterized by coexisting surface domains with As and Ga dimers.

44

Characterization of epitaxial semiconductor growth 45

J.-T. Zettler

1.1 1.2 1.3 1.4 1.5

0.1

1

10

(b)pa

rtial

pre

ssur

e TM

Ga

(Pa)

Temperature (K)

T -1 (10-3 K-1)

phase I c(4x4)phase IIphase III

950 900 850 800 750 700 650

Fig. 27: Surface phase diagram taken by RAS in MOVPE (after [Error: Reference source notfound], see text for explanation).

It is well known from RHEED oscillation experiments in MBE that after the initiation of island growth in layer-by-layer growth mode the morphology of the surface oscillates between being smooth and half covered with monolayer islands. While RHEED directly senses these morphology oscillations, the RAS spectra are significantly less sensitive to the surface morphology [Error: Reference source notfound,Error: Reference source not found]. However, as discussed above, the dimer configuration is modified in domains close to the surface steps. Therefore RAS is also capable of measuring growth oscillations with monolayer periodicity by sensing the resulting oscillations in dimer coverage [95,Error: Reference source not found,Error:Reference source not found,Error: Reference source not found] (Fig. 28 and Fig. 29).

46


Fig. 28: RAS transient of 15 ML GaAs growth at 610°C in MBE (top), monitored at a photon energy of 2.65 eV. The insert shows an enlargement of the first growth oscillation and gives the definition of characteristic RAS levels (used in Fig. 26a) and of the RAS oscillation amplitude. The temperature dependence of the latter is given in the lower part (filled squares, left axis) where the corresponding variation in the effective As surface coverage (open squares, right axis) is added (after [Error: Reference source not found]).

For monitoring RAS oscillations with a time resolution of some 100 ms usually a photon energy is chosen where the surface dielectric anisotropy responses most sensitively to the changing dimer configuration. Fig. 28a gives a typical transient that monitors at 2.65 eV the homoepitaxial growth of 14 ML GaAs in MBE. The initial sharp decrease in the RA level marks predominantly the decrease in As coverage due to the presence of Ga atoms on the surface. The subsequent oscillations mirror the oscillating step density during the initially coherent island growth. In MBE growth of GaAs RAS oscillations can be monitored practically for all substrate temperatures. They disappear only in a small and slightly growth rate dependent temperature range

47

J.-T. Zettler

(in Fig. 28b this is about 540°C) due to the nonmonotonic dependence of the 2.6 eV RAS signal on the As surface coverage.

2 3 4 5-2

-1

0

1

2

3

4

T = 500° CPTMGa = 0.52 PaPAsH3

= 71 Pa

0.5 ML grown 1.0 ML grown c(4x4) before growth

Re(r

/r) [1

0 -3 ]

photon energy [eV]

2 3 4-2

-1

0

1

2

3

4 80 % Ga dimer domains in c(4x4) 30 % Ga dimer domains in c(4x4) c(4x4)

Re(r

/r) [1

0-3]

photon energy [eV]

Fig. 29: RAS growth oscillations in MOVPE: (a) spectral shape of the first RAS oscillation as derived from a multi-transient experiment and (b) model calculations assuming step induced oscillations in the surface dimer coverage (after [Error: Reference source not found]).

The situation is different in MOVPE (Fig. 29) where RAS oscillations can be monitored only under conditions specific for phase II of the surface phase diagram in Fig. 27. In Fig. 29a RAS transients have been taken at several photon energies and from the first oscillation period of these multi-transient experiments the spectra have been composed. The model calculations in Fig. 29b indicate that the status of the surface oscillates between being more (high density of steps) and less (smooth surface) covered with Ga dimer domains which coexist with c(4x4)-like domains under the given growth conditions.

48


RAS oscillations opened not only an interesting field of applications for real-time control but also allowed one to study the surface mobility of the Ga species in MOVPE [Error: Reference source not found] which turned out to be significantly higher than in MBE. Furthermore, by studying the transition temperatures from island growth mode to step-flow growth by taking RAS oscillations at differently off-cut vicinal substrates, the temperature dependent island spacing in MOVPE growth could be determined [Error: Reference source not found].

5 EXAMPLES OF GROWTH MONITORING AND GROWTH CONTROL

Despite the fact that a number of questions about the correlation between the details of the growth process and the respective response of the optical spectra still remain to be answered, there are some practical aspects that already can be taken advantage of in standard growth operations. However, monitoring the growth process of a real semiconductor device is in most cases generally different as compared to the basic studies discussed in chapter 4. There, for surface science applications, it was relatively easy to handle the fact that both ellipsometry and especially RAS spectra are sensitive to a fairly large number of growth parameters. For studying a specific surface effect one had simply to keep the contributions from all the other parameters fixed. While this can be done quite easily for a bare semiconductor surface, in case of a growing complex semiconductor device it is not feasible as it is well known, e.g., for the sample temperature that often varies unintentionally due to the changing emissivity of the growing device structure. Therefore, usually one has to decide what level of real-time spectroscopy to use for the specific growth task. In the early stage of process development and process optimization, when switching times and flow rates have to be determined or processes have to be adopted to a new growth apparatus, optical in-situ techniques, even at their present level of development, can contribute significantly. If afterwards the growth process for preparing a certain device structure runs smoothly and reproducably, in-situ analysis in some cases is no longer necessary. While this is certainly the most desirable situation regarding cost efficiency and usability of the growth system, with rising complexity and decreasing thickness of the layers often the next level of real-time spectroscopy applications becomes increasingly important: process monitoring, i.e. sensing any deviation from the optimum growth procedure by application of spectroscopic techniques highly sensitive to the just grown uppermost atomic layers. This at least enables us to detect instantaneously when the process runs out of the acceptable limits (e.g., in MOVPE the bubbler source may fail, or deposition on the liner tube may change the temperature profile, etc.). Costs for the further processing of the wafers are avoided this way and the problem can be fixed by the operator without unnecessary delays. Finally, the ultimate target of optical real-time applications goes far beyond simple process monitoring: optical closed loop control by sensing the absolute values of the critical sample parameters and their subsequent use for tight process control.

49

J.-T. Zettler

In this section we discuss the present status of real-time spectroscopy for the three levels of application: process development, process monitoring and process control.

5.1 Surface preparation before growth

After a standard wet chemical treatment of the substrate and is transfer to the growth chamber, oxide desorption and buffer growth are usually the starting procedures in all epitaxial systems. To study the oxide desorption from a GaAs surface in MOVPE, RAS and SE transients can be taken while heating up the sample under arsine flow (Fig. 30). The SE transients were monitored at the E0´ transition (4.7 eV) of the bulk semiconductor GaAs (Fig. 30a). The RAS transients were taken at 2.6 eV (Fig. 30b) because this photon energy yields the maximum difference in reflectance anisotropy between the oxidized and c(4´4) reconstructed GaAs (001) surface. The origin of the reflectance anisotropy of the oxidized surface is not completely understood yet but presumably the bond configuration directly at the semiconductor-oxide interface is responsible.

In the experiments summarized by Fig. 30, the oxide desorbs during an initial heating procedure (A). After buffer growth at 650°C (B) the sample was cooled down to room temperature (C) and re-oxidized (D) in order to repeat the oxide desorption (E) - this time from a smooth GaAs-oxide interface. The general decrease of the SE signal is due to the changing bulk dielectric function with temperature (Fig. 30a). Therefore, in Fig. 30d the oxide thickness transients, as derived from the ellipsometry transients, are added. After the initial oxide desorption (A) a surface roughness of about one monolayer remains. Keeping the substrate under As stabilization at 650°C and/or starting GaAs buffer growth (B) results in the formation of an atomically flat surface as can be seen from the ellipsometry transient (C). From the oxide thickness transient (E) it is obvious that the contribution of the oxide desorption process itself to the surface roughness is marginal.

50


The RAS transient of the initial oxide desorption (A) is difficult to interpret due to the complex roughness contributions to the RAS signal. Therefore we concentrate on the RAS and SE transients taken during the second oxide desorption (E) from the smooth buffer surface. The RAS signal changes and approaches that of the bare, c(4´4) reconstructed surface (C) between 320°C and 500°C. On the other hand the oxide thickness is reduced to zero already between 250°C and 400°C (transient (E) in Fig. 30d). This indicates inhomogeneous oxide desorption (320-400°C) and the following formation of As dimers (400-500°C).

Performing the same experiment under various conditions, i.e., under carrier gas flow only (H2 or N2 in MOVPE with pAsH3=0 or in a MBE system) gives increased oxide desorption temperatures. In MBE the GaAs oxide desorbs at about 580°C, i.e., at a temperature well above that found under MOVPE conditions. This is because in MBE no hydrogen radicals are present. In MOVPE these H radicals are generated during the arsine decomposition and obviously catalyze the oxide desorption.

4.0 4.5 5.0

15

20

490oCdox=0nm

350oCdox=1.1nm

RTdox=1.1nm

photon energy [eV]

(a)

<e2>

2 3 4

-2

-1

0

1

2

photon energy [eV]

500oCdox=0.0nm

c(4x4)

350oCdox=1.1nm (b)

Re(r

/r) (1

0-3)

18

20

22

24

26 (c)

E=2.6eV

E=4.7eV

<e2>

E

DC

BA

0.2

0.4

0.6

0.8

1.0 (d)

roughness beforebuffer growth

A

E

oxid

e th

ickn

ess

(nm

)

0 100 200 300 400 500 600 700-4

-3

-2

-1

0

1

B

D

(e)E

C

A

temperature (oC)

Re(r

/r) (1

0-3)

Fig. 30: Oxide desorption and buffer growth in MOVPE (after []). The photon energy is chosen differently to ensure the maximum sensitivity for both ellipsometry (a) and RAS (b). In (c) and (e) the respective real-time transients are displayed and (d) gives the oxide thickness as measured in real-time by the SE transients in (c). See text for details.

51

J.-T. Zettler

5.2 Measurement of surface temperature and pre-growth surface reconstruction

The measurement of the actual surface temperature during semiconductor epitaxy still is a crucial aspect for device growth. Besides thermo-couples mainly optical methods such as pyrometry [96], scatterometry [97], and laser interferometry [98] have been applied. While thermo-couples can give a relevant temperature under optimum conditions (e.g., in an IR heated stationary MOVPE susceptor) in MBE sample holders, they usually do not and in rotating susceptor systems in MOVPE they cannot. Pyrometers became a standard tool for the determination of the sample temperature but fail for lower temperatures and in MOVPE systems where the susceptor is heated by IR radiation. Therefore it has been of interest to test and apply the in-situ optical techniques RAS and ellipsometry also for temperature measurements. This had to be done especially for RAS because in MBE usually the pyrometer port is used for the RAS set-up.

RAS is, as the surface reconstruction itself, highly sensitive to a number of growth parameters, a fact which complicates the measurement of a single parameter like the surface temperature. Therefore, generally the bulk beneath the surface is the desirable region for temperature sensing and either a spectroscopic ellipsometer [99] or precise reflectance measurements could be used for substrate temperature measurements. From the bare substrate after buffer growth this yields temperature corrections for the thermo-couple (Fig. 31) which apply also during the subsequent growth of the complete semiconductor structure when optical real time analysis is used to monitor parameters not as 'trivial' as the sample temperature. Reflectance spectra can be derived from the RAS raw data by a simple procedure: Using the known reflectance of the sample at room temperature, the relative changes in the intensity spectra I0(E) (see Eq. ( 1 7 ) with increasing temperature can be converted into the monitoring reflectance spectra of Fig. 31a. For both reflectance based (Fig.31a) and for ellipsometric temperature calibration (Fig. 31b) the derivatives of the spectra are analyzed and the temperature is determined from the spectral position of the bulk critical points which shift significantly with temperature (Fig. 12).

Finally, after oxide desorption, buffer layer growth and temperature calibration the substrate is well prepared for the growth of a semiconductor structure. At this point shape and amplitude of the RAS spectrum often give a clear indication whether the substrate preparation has been successful or not. This is because the RAS spectra are directly related to the dimer configuration at the surface which is highly sensitive to deviations from the ideally smooth, homogeneously reconstructed starting surface. Additionally, unintended background doping also would show up because the resulting surface field causes, via the linear electro-optic effect, characteristic signatures in the RAS spectra.

52


96[?] Pyritte, technical report, Sentech Instruments, 1995 .

97[?] S.R. Johnson, C. Lavoie, T. Tiedje, and J. Mackenzie, J. Vac. Sci. Technol. B 11, 1007 (1993).

98[?] H. Sitter, G. Glanner, and M. Herman, Vacuum 46, 69 (1995).

26[?] R.M.A. Azzam and N.M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977).

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29[?] M. Wassermeier, V. Bressler-Hill, R. Maboudian, K. Pond, X.-S. Wand, W.H. Weinberg, and P.M. Petroff, Surf. Sci. 278, L147 (1992).

30[?] T. Hashizume, Q.K. Xue, A. Ichimiya, and T. Sakurai, Phys. Rev. Lett. 73, 2208 (1994).

31[?] T. Hashizume, Q.K. Xue, A. Ichimiya, and T. Sakurai, Phys. Rev. B 51, 4200 (1995).

32[?] D.E. Aspnes, Y.C. Chang, A.A. Studna, L.T. Florez, H.H. Farrell, and J.P. Harbison, Phys. Rev. Lett. 64, 192 (1990).

52[?] J.D. Jackson, Classical Electrodynamics (John Wiley and sons, New York, 1975).

62[?] Y. Chang and D.E. Aspnes, J. Vac. Sci. Technol. B 8, 896 (1990).

63[?] Y. Chang, S. Ren, and D.E. Aspnes, J. Vac. Sci. Technol. A 10, 1856 (1992).

1 [?] D.E. Aspnes, J.P. Harbison, A.A. Studna, L.T. Florez, and M.K.Kelly,J. Vac. Sci. Technol. A 6, 1327 (1988).

2 [?] D.E. Aspnes, Mat. Sci. Engineering B 30, 109 (1995).

3 [?] Characterization of Epitaxial Semiconductor Layers by Electromagnetic Radiation,edited by G. Bauer and W. Richter (Springer Verlag, Berlin, 1995).

2 3 4 50.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9(a)

E1(RT)

873 K

RT

Ref

lect

ance

[]

photon energy [eV]

300 400 500 600 700 800 9002.85

2.90

2.95

3.00

3.05

3.10

3.15

3.20

Temperature (K)

E 1 CP

pos

ition

(eV

)

0 100 200 300 400 500-70

-60

-50

-40

-30

-20

-10

0 (b)

T sam

ple -

Tth

erm

ocou

ple (

K)

Tthermocouple (°C)

2.6 2.8 3.0

-200

-150

-100

-50

0

50

100

150sample temperaturedetermined by ellipsometry:

452°C 432°C 472°C exp.)

photon energy E [eV]

d2 e 2 /

dE2 [e

V-2]

Fig. 31: Calibration of the temperature reading of a thermo-couple located in the sample holder by means of optical in-situ spectroscopy: (a) Temperature of a InP substrate measured by means of an RA spectrometer (after [Error: Reference source not found]). The first derivative of the reflectance spectrum (derived from the RAS raw data) is used to sense the energy position of the E1 bulk critical point. (b) GaAs substrate temperature measured by SE (after [] (method) and [(data)). The insert shows the accuracy of the evaluation procedure using the second derivative of the ellipsometric spectra.

53

J.-T. Zettler

5.3 Growth rate measurement

Growth rate and the actual layer thickness certainly are the presently most often determined sample parameters by in-situ techniques. Both, RHEED and RAS oscillations yield layer thicknesses of quantum well structures on a sub-monolayer scale [Error: Reference source not found,Error: Reference source not found]. Fig.32a gives the RAS transient during the growth of 10 ML of InxGa1-xAs (x=0.11). The general shape of this RAS transient can be explained by a shift from the GaAs/c(4´4) level (pregrowth) via the (2´4) InGaAs level (during growth) to the c(4´4) / (2´4) InGaAs level (after growth). Monolayer oscillations due to the

4 [?] D.E. Aspnes, Thin Solid Films 233, 1 (1993). 5 [?] B. Drevillon, Prog. Crystal Growth and Charact. 27, 1 (1993).

6 [?] R.W. Collins, I. An, H. Nguyen, Y. Li, and Y. Lu, in Real-time spectroscopic ellipsometry studies of the nucleation, growth, and optical functions of thin films, part I:

tetrahedrally bonded materials (Academic Press, Orlando, 1994), p. 49. 7 [?] E. Irene, Thin Solid Films 233, 96 (1993). 8 [?] C. Pickering, in Handbook of crystal growth 3, part B: Growth mechanisms and dynamics, edited by D. Hurle (ELSEVIER, Amsterdam, 1994), p. 819. 9 [?] M.A. Herman and H. Sitter, Molecular Beam Epitaxy (Springer Series in Materials

Science, Berlin, 1989). 10[?] K. Ploog, Angewandte Chemie 100, 611 (1988). 11[?] B.A. Joyce, Rep. Prog. Physics 48, 1637 (1985). 12[?] L. Däweritz and K. Ploog, Semicond. Sci. Technol. 9, 123 (1994).

13[?] N. Kobayashi and Y. Horikoshi, Jap. J. Appl. Phys. 29, L702 (1990).

14[?] N. Kobayashi and Y. Horikoshi, Jap. J. Appl. Phys. 30, L319 (1991).

15[?] D.E. Aspnes, J. Vac. Sci. Technol. A 14, 960 (1996).

16[?] G.N. Maracas, C.H. Kuo, S. Anand, R. Droopad, G. Sohie, and T. Levola, J. Vac. Sci. Technol. A 13, 727 (1995). 17[?] J.-T. Zettler, T. Wethkamp, M. Zorn, M. Pristovsek, C. Meyne, K. Ploska,

and W. Richter, Appl. Phys. Lett. 67, 3783 (1995).

18[?] D.E. Aspnes, W. Quinn, M. Tamargo, M. Pudensi, S. Schwarz, M. Brasil, R. Nahory, and S. Gregory, Appl. Phys. Lett. 60, 1244 (1992).

19[?] J. Rumberg, J.-T. Zettler, K. Stahrenberg, K. Ploska, W. Richter, L. Däweritz, P. Schützendübe, and M. Wassermeier, Surface Science 337, 103 (1995).

54


oscillating As dimer coverage in island growth mode are clearly resolved and again, as discussed in section 3, it takes several monolayers to be grown (about 5) until there is no more direct influence from the GaAs substrate to the InGaAs dimer configuration. The equivalence of the during-growth and after-growth RAS level is coincidentally here because of the nonmonotonic dependence of the 2.6 eV RAS level to the As surface stoichiometry (see a). At higher volume fractions of In both the during-growth and after-growth status of the InGaAs surface is (4´2)-like. The surface is then completely covered by group III dimers and RAS oscillations cannot be measured. Besides the chemical shift towards InAs we regard the strain induced In segregation at the surface to be responsible for this effect.

20[?] C.H. Kuo, S. Anand, R. Droopad, K.Y. Choi, and G.N. Maracas,J. Vac. Sci. Technol. B 12, 1214 (1994).

21[?] R. Dorn and H. Lüth, Phys. Rev. Lett. 33, 1024 (1974).

22[?] M. Kuball, M. Kelly, P. Santos, and M. Cardona, Phys. Rev. B 50, 8609 (1994). 23[?] M. Wassermeier, J. Behrend, J.-T. Zettler, K. Stahrenberg, W. Richter, and K.H. Ploog, Phys. Rev. B 53, 13542 (1996).

24[?] R.D. Sole, in Photonic probes of surfaces, edited by P. Halevi (Elsevier Science B.V., Amsterdam, 1994), p. 133.

25[?] P.Y. Yu and M. Cardona, Fundamentals of semiconductors (Springer Verlag, Berlin, 1996).

33[?] K. Hingerl, D.E. Aspnes, I. Kamiya, and L.T. Florez, Appl. Phys. Lett. 63, 885 (1993).

34[?] D.E. Aspnes, J. Opt. Soc. Am. 70, 1275 (1980).

35[?] While processing this manuscript two different approaches for dealing with rotating and wobbling samples have been published at the International Conference on SpectroscopicEllipsometry, Charleston, USA, 1997: (i) rigidly and actively reducing the wobbleamplitude for ellipsometric RAS measurements in a MOVPE system: M. Ebert, G.D. Powel,K.A. Bell and D.E. Aspnes, submitted to Thin Solid Films; and (ii) passively compensatingthe effect of sample wobbling to RAS and ellipsometry measurements: K. Haberland,O. Hunderi, M. Pristovsek, J.-T. Zettler, and W. Richter, submitted to Thin Solid Films.

36[?] M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1980).

37[?] D.E. Aspnes, J. Opt. Soc. Am. A 10, 974 (1993).

38[?] T. Yasuda, D. Aspnes, D. Lee, C. Bjorkman, and G. Lucovsky, J. Vac. Sci. Technol. A 12,1152 (1994).

39[?] D.E. Aspnes, Thin Solid Films 89, 249 (1982).

40[?] D. Bimberg, M. Grundmann, N.N.Ledentsov, S. Ruvimov, P. Werner, U. Richter,

55

J.-T. Zettler

J. Heydenreich, V. Ustinov, A. Egorov, A. Zhukov, P. Kopev, and Z. Alferov, Thin Solid Films, accepted for publication.

41[?] D.E. Aspnes, Phys. Rev. B 41, 10334 (1990).

42[?] J.-T. Zettler, J. Rumberg, K. Ploska, K. Stahrenberg, M. Pristovsek, W. Richter, M. Wassermeier, P. Schützendübe, J. Behrend, and L. Däweritz , phys. stat. sol. (a) 152,

35 (1995).

43[?] D.A.G. Bruggeman, Annalen der Physik 24, 637 (1935).

44[?] J.A. Osborn, Physical Review 67, 351 (1945).

45[?] A. Röseler, Infrared Spectroscopic Ellipsometry (Akademie-Verlag, Berlin, 1990).

46[?] D.E. Aspnes and A. Studna, Applied Optics 14, 220 (1975).

47[?] J.-T. Zettler, T. Dittrich, and L. Schrottke, phys. stat. sol. (a) 119, K91 (1990).

48[?] R. Collins, private communication .

49[?] M. Cardona, F.H. Pollak, and K.L. Shaklee, J. Phys. Soc. Jap. 21, 89 (1968).

50[?] R.M.A. Azzam, Opt. Comm. 19, 122 (1976).

51[?] R.M.A. Azzam, Opt. Act. 24, 1039 (1977).

53[?] J. Rumberg, diploma thesis, Technische Universität Berlin, 1996.

54[?] A. Shkrebtii, Proceedings of the International Conference on SpectroscopicEllipsometry, Charleston, USA, May 1997, to be published in Thin Solid Films.

55[?] M. Cohen and J. Chelikowski, Electronic Structure and optical properties of semiconductors (Springer, Berlin, 1989).

56[?] M. Cardona, Modulation Spectroscopy (Academic Press, New York, 1969).

57[?] D.E. Aspnes, in Handbook on Semiconductors, edited by M. Balkanski (North-Holland Publishing Company, Amsterdam, 1980), p. 109.

56


0 10 20 30 40 50

1

(a)(2x4)-like3

5 ML

1c(4x4) / (2x4)

endbeginof growth

In0.11Ga0.89As As stabilised

GaAs As stabilised c(4x4)

Re

( r /

<r>

) [1

0-3]

time (s)

11

12

13

14

15

16fit (dashed) yields r=0.139 nm/s

<e1>

<e2>

(b)

ellipsometry, E=2.8eV

<e>

0 100 200 300 400

0.43

0.44

0.45

0.46

0.47

time [s]

fit (dashed) yields r=0.145 nm/s

(c)

DC(RAS), normalized to R(GaAs), E=2.6eV

refle

ctan

ce R

58[?] P. Lautenschlager, M. Garriga, S. Logothetidis, and M. Cardona, Phys. Rev. B 35, 9174 (1987).

59[?] B. Velicky and J. Sak, phys. stat. sol. 16, 147 (1966).

60[?] E.O. Kane, Phys. Rev. 180, 852 (1969).

61[?] T.-H. Shen, C. Mathai, and R. Williams, in Second EPIOPTIC Workshop on optical characterization of semiconductor surfaces and interfaces (Berlin, Germany, 1991).

64[?] N. Esser, P. Santos, M. Kuball, M. Cardona, M. Ahrens, D. Pahlke, W. Richter,F. Stietz, J. Schaefer, and B. Fimland, J. Vac. Sci. Technol. B 13, 1 (1995).

65[?] V. Berkovits, I. Makarenko, T. Minashvili, and V. Safarov, Sov. Phys. Semicond. 20, 654 (1986).

66[?] S. Acosta-Ortiz and A.Lastras-Martinez, Phys. Rev. B 40, 1426 (1989).

67[?] H. Tanaka, E. Colas, I. Kamiya, D.~E. Aspnes, and R. Bhat, Appl. Phys. Lett. 59, 3443 (1991).

68[?] H. Farrel, M. Tamargo, T. Gmitter, A. Weaver, and D.E. Aspnes, J. Appl. Phys. 70, 1033 (1991).

69[?] K. Knorr, A. Rumberg, M. Zorn, C. Meyne, T. Trepk, J.-T. Zettler, W. Richter, P. Kurpas, and M. Weyers, in Proceedings of the International Conference on Indium

Phosphide and related Materials (Schwäbisch Gmünd, Germany, 1996).

70[?] M. Cardona, K. Shaklee, and F. Pollak, Phys. Rev. 696, 154 (1967).

71[?] M. Kuball, M. Kelly, M. Cardona, K. Köhler, and J. Wagner, Phys. Rev. B 49, 16569 (1994).

72[?] G.C.Cho, W. Kütt, and H. Kurz, Phys. Rev. Lett. 65, 764 (1990).

73[?] F. Pollak and M. Cardona, Phys. Rev. 172, 816 (1968).

74[?] F. Lukes, S. Gopalan, and M. Cardona, Phys. Rev. B 47, 7071 (1993).

57

J.-T. Zettler

Fig. 32: In-situ growth rate measurements by RAS monolayer oscillations (a) (after [Error:Reference source not found]) and Fabry-Perot oscillations (after [Error: Reference source notfound]) in ellipsometry (b) and reflectance (c).

While with RHEED of course one can not measure layer thicknesses after the oscillations have disappeared due to increasingly incoherent growth, the optical in-situ techniques are able to measure growth rates also at this stage via Fabry-Perot oscillations. While this is well known and straight forward for in-situ ellipsometry [Error: Reference source not found], the RAS raw data have to be transformed for

75[?] A. Rumberg, D. Fischer, P. Kurpas, M. Weyers, and W. Richter, unpublished.

76[?] Z. Sobiesierski, D. Westwood, and D. Woolf, J. Vac. Sci. Technol. B 14, 3065 (1996).

77[?] A. Cho, J. Appl. Phys. 42, 2074 (1971).

78[?] H. Manasevit, Appl. Phys. Lett. 12, 156 (1968).

79[?] C.T. Foxon and B.A. Joyce, Surf. Sci. 50, 434 (1975).

80[?] J. Jönsson, K. Deppert, and L. Samuelson, J. Cryst. Growth 124, 30 (1992).

81[?] I. Kamiya, D.E. Aspnes, H. Tanaka, L.T. Florez, J.P. Harbison, and R. Bhat, J. Vac. Sci. Technol. B 10, 1716 (1992).

82[?] D.W. Kisker, G.B. Stevenson, I. Kamiya, P.H. Fuoss, D.E. Aspnes, L. Mantese, and S. Brennan, phys. stat. sol. (a) 152, 9 (1995).

83[?] I. Kamiya, D.E. Aspnes, L.T. Florez, and J.P. Harbison, Phys. Rev. B 46, 15894 (1992).

84[?] S.J. Morris, J.-T. Zettler, K.C. Rose, D.I. Westwood, D.A. Woolf, R.H. Williams, and W. Richter, J. Appl. Phys. 77, 3115 (1995).

85[?] U. Resch, S.M. Scholz, U. Rossow, A.B. Müller, and W. Richter, Appl. Surf. Sci. 63, 106 (1993).

86[?] H.H. Farrell and C.J. Palmström, J. Vac. Sci. Technol. B 8, 903 (1990).

87[?] K. Ploska, M. Pristovsek, W. Richter, J. Jönsson, I. Kamiya, and J.-T. Zettler, phys. stat. sol. (a) 152, 49 (1995).

88[?] C.H. Kuo, S. Anand, H. Fathollahnejad, R. Ramamurti, R. Droopad, and G.N. Maracas, J. Vac. Sci. Technol. B 13, 681 (1995).

89[?] M. Zorn, Jönsson, A. Krost, W. Richter, J.-T. Zettler, K. Ploska, and F. Reinhardt, J. Cryst. Growth 145, 53 (1994).

90[?] E. Steimetz, J.-T. Zettler, F. Schienle, T. Trepk, T. Wethkamp, W. Richter,

58


this purpose into reflectance spectra as discussed above for temperature measurements. In Fig. 32 the MOVPE growth of strained InGaAs on GaAs is monitored. Fabry-Perot oscillations allow for growth rate measurements even under these conditions (Fig. 32b,c) and from the growing layer's refractive index gained as an additional parameter in this measurement the actual composition can be determined. For growth systems where only ellipsometry optical ports are available it is of importance that monolayer growth oscillations have also been recently taken by ellipsometry [Error: Reference source not found] (Fig.33). Consequently, both optical techniques discussed here can potentially measure in-situ growth rates and thicknesses for the complete range from submonolayers up to microns.

and I. Sieber, Appl. Surface Science 107, 203 (1996). 91[?] M. Wassermeier, I. Kamiya, D.E. Aspnes, L.T. Florez, J.P. Harbison, and P.M. Petroff,

J. Vac. Sci. Technol. B 9, 2263 (1991).

92[?] J.-T. Zettler, H. Wenisch, K. Stahrenberg, B. Jobs, D. Hommel, and W. Richter,J. Vac. Sci. Technol. B 14, 2757 (1996).

93[?] M. Zorn, J. Jönsson, W. Richter, J.-T. Zettler, and K. Ploska, phys. stat. sol. (a) 152, 23 (1995).

94[?] K. Ploska, J.-T. Zettler, W. Richter, J. Jönsson, F. Reinhardt, J. Rumberg, M. Pristovsek, M. Zorn, D. Westwood, and R.H. Williams, J. Cryst. Growth 145, 44 (1994). 95[?] J.P. Harbison, D.E. Aspnes, A.A. Studna, L.T. Florez, and M.K. Kelly, Appl. Phys. Lett. 52, 2046 (1988).

99[?] R. Droopad, C.H. Kuo, S. Anand, K.Y. Choi, and G.N. Maracas, J. Vac. Sci. Technol. B 12,1211 (1994).

59

J.-T. Zettler

5.4 In-situ measurement of the composition of compound semiconductors

There are a number of different ways for determining the composition of compound layers from the in-situ optical data. At first there is a direct link to the just discussed growth rate measurements because both monolayer oscillations and Fabry-Perot oscillations sense also the composition. Monolayer oscillations can give the actual composition of a III-III-V ternary compound semiconductor grown on the respective binary III-V substrate via the relative change in growth rate which is usually limited by the group III element's supply [Error: Reference source not found]. For example, the compositions determined from the real-time transient in Fig. 32a agreed within less than 1 percent with those determined afterwards using ex-situ X-ray analysis. Similarly, from Fabry-Perot oscillations not only the growth rate but also the actual complex refractive index of the growing layer is measured. An essential requirement is a precise and comprehensive database of the high temperature optical data, which change in most cases significantly with composition, the latter can be determined in parallel to the growth rate.

More precise results can be gained from the analysis of the complete ellipsometric spectra than from the single wavelength transient experiments. For calibrating the flux ratios in MBE or the relative partial pressure ratios in MOVPE usually test layers thick enough for precise measurements of the critical point spectral positions have to be prepared. Because the position of the bulk critical points is highly sensitive to the composition (see, e.g., Fig. 22), the flux ratios can usually be calibrated to reach the targeted compositions with a precision better than one percent. In contrast to the

0 5 10

13.65

13.70

13.75

time [s]

EllipsometryE= 2.65 eV

<e2>

-4.0

-3.5

-3.0

-2.5

b)

a)

RASE= 2.65 eV

GaAs(001)pTMGa= 0.33PaT = 500°C

Re

( r[1

10] -

r [110

] / r )

[10

-3 ]

20.65

20.70

20.75

c)

3 ML2 ML1 MLTMGa on

EllipsometryE= 2.65 eV

<e1>

Fig. 33: Monolayer oscillations in ellipsometry (after [Error: Reference source not found]).

60


analogous ex-situ calibrations, a complete calibration curve can be taken on only one sample and in only one growth run. However, for lattice mismatched systems this requires that the optical data can be derived precisely also from rather thin layers in order to avoid the relaxation of the layers.

Once the sources and fluxes are calibrated one usually has to assume that the system works stable at least for a reasonable period of time. For some applications, however, even small drifts and fluctuations in composition cannot be tolerated. In this kind of situation composition control in closed-loop mode using ellipsometry and a virtual substrate approach [Error: Reference source not found] is the only alternative and I refer to section 5.7 for some more details. In general, sensitive in-situ measurements of the composition of compound semiconductors can only be performed if the optical parameters measured (refractive index, E1 gap position, etc.) change significantly with composition. Unfortunately, this rather trivial requirement is in some cases not realized and, more unfortunately, these cases are exactly those where in-situ composition measurements are urgently needed: during the growth of lattice matched III-V compound semiconductors on binary substrates. The physical reason for this dilemma, that has been discussed in detail for InGaP-on-GaAs growth by Lee et al. [100], is that the chemical shifts in the spectra of ternary III-V's mostly combine an upshift of the optical gap energies with a downshift in the lattice constant since the increasing optical gaps mirror an increase in bond strength. Hence, in case the composition targeted for lattice matched growth deviates towards a positive (negative) lattice mismatch the optical gaps should shift to lower (higher) energies. Additionally, the positive (negative) lattice mismatch additionally imposes a compressive (tensile) stress to the growing layer which is known to upshift (downshift) the gap energies. Consequently, in most cases the natural chemical shift of the gap energies of the unstrained materials is compensated by the strain effects and what has been successfully done in the field of in-situ AlGaAs composition control is far from being directly transferable to systems involving strain effects. Very recent results of Roth et al. in MBE [101] and of Zorn et al. in MOVPE [102] demonstrated, however, that by application of high-precision in-situ ellipsometry even feed-back controlled growth of InGaAs lattice matched to InP is feasable. Moreover, as discussed in the next section there are still a number of different ways that in-situ spectroscopy can contribute even to this obviously tough subject of lattice matched growth control.

5.5 Optimization of switching sequences

For many semiconductor devices abrupt and atomically flat interfaces have to be prepared. The problem is, that abrupt transitions and defined composition gradients often can not be easily achieved under high temperature conditions because of interdiffusion and defect formation. In order to keep these effects to an acceptably small level extensive empirical optimizations of purging cycles are performed. Often the performance of the final device is used as a sensor for assessing whether the chosen regime is successful or not. Alternatively or at least in support, RAS can be applied to clarify the changes imposed to the surface during the purging times.

61

J.-T. Zettler

50 60 70-2

-1

0

1

2

3

4

(a/a = +14.3*10-4)

(a/a = -4.7*10-4)

with H2 purge

no H2 purgeGaAs

Re

(r/r

) at 2

.6 e

V [

10-3]

time [s]

-2

-1

0

1

2

3

4

InGaP-growthPH3H2

2 3 4 5-3

-2

-1

0

1

2

3

t=9s: GaAs / PH3

t=5s: GaAs / H2 purged

t<0s: GaAs during growth

Re(r

/r) [1

0-3]

photon energy [eV]

Fig. 34: Multi-transient RAS experiment for clarifying the surface status during the purging cycles at an GaAs-InGaP interface (after [Error: Reference source not found]).

Fig. 34 gives an example: the growth of InGaP, nominally lattice matched to GaAs, has been monitored by RAS [103]. During this experiment the influence of additional H2

purging sequence before supplying phosphine and subsequently TMIn and TMGa has been studied. Fig. 34a gives the real-time RAS transients which can be interpreted by means of the spectra in Fig. 34b which display the result of a multi-transient experiment performed for reference. These spectra have been composed from transients taken at 20 different photon energies each lasting only a few seconds in order to avoid permanent damage to the GaAs surface. From these data the state of the surface during GaAs growth, during H2 purge and during PH3 purge can be

62


assigned to be of phase II character (see Fig. 27), (2x4)-like As dimer covered (see Fig. 18) and phosphorus/gallium-dimer covered (see Fig. 41 and Fig. 18), respectively. Returning to Fig. 34a, one can conclude that the higher (lower) RAS level after H2 and PH3 purge (PH3 purge only) is related to a higher (lower) P-dimer/group-III-dimer ratio that obviously persists also during the subsequent growth of InGaP. Apparently, growth under less P stabilized conditions results in a slightly more In-rich InGaP layer. The experiment summarized by Fig. 34 underlines that (i) multi-transient RAS experiments can contribute significantly to the understanding of the surface processes during purging cycles and (ii) that by using RAS at a well selected photon energy the surface stoichiometry during the growth of compound semiconductors represents a further option for real-time control of bulk composition.

5.6 In-situ measured dopand concentrations

As has been discussed in section 3.3, doping concentrations in the 1017 to 1019cm-3

range cause characteristic signatures in the RAS spectra due to the linear electro-optic effect. Under certain conditions and for devices where this range of doping concentrations is of importance, this can be used for in-situ measurements of the doping concentration. The utilization of these field dependent RAS features for contactless measurements of dopant concentrations were even suggested in the late 1980s [Error: Reference source not found,Error: Reference source not found]. First in-situ results have been reported by Tanaka et al. [Error: Reference source notfound] and Farrell et al. [Error: Reference source not found] for GaAs and ZnSe, respectively.

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Fig. 35: Correlation of in-situ measured LEO signatures to the dopant concentration: (a) bulk doping of GaAs (after [Error: Reference source not found]) and (b) Si delta layer in GaAs after overgrowth with a 64ML thick undoped layer (after [Error: Reference source not found]).

The lower limit of about 1017 cm -3 is usuallly due to the signal-to-noise ratio of a typical RAS system and should be further decreased by the future implementation of double-modulation techniques, which are already used in ex-situ ellipsometry [104,Error: Reference source not found]. The upper limit results from at least two effects: (i) the surface space charge region becomes smaller than the penetration depth of the sensing light [Error: Reference source not found] and (ii) the excitonic shape of the bulk critical point structures sensed by this optical measurement of doping levels is increasingly broadened due to the high fields and carrier scattering by the ionized dopants.

For quantitative measurements the sample should be cooled down to temperatures below 100°C. Additionally, bandpass filters have to be added to the RAS set-up in order to reduce the total intensity of light that otherwise would screen the surface fields causing the linear electro-optic effect. In Fig. 35a the variation of sign and amplitude of the GaAs LEO signature in the RAS spectra with bulk dopant concentration is displayed [Error: Reference source not found]. In the experiments summarized by Fig. 35b the concentration of electrically active dopants in Si delta doped layers of GaAs of varying Si concentration was studied at growth temperatures (400°C) [Error: Reference source not found]. In the latter work the thickness of an undoped GaAs overlayer has been carefully chosen in order to assure a maximum sensitivity of the excitonic LEO signature to the dopant concentration in the delta-doped Si layer (see section 3.3).

64


5.7 In-situ monitoring of epitaxial growth of quantum sized structures

Up to now examples have been given regarding the real-time spectroscopy during the planar growth of semiconductor layers. Because quantum wells (QWs) and superlattices (SLs) represent samples also to be grown in an epitaxial layer-by-layer growth mode there is no basic difference to that which has been discussed above regarding the real-time characterization of more macroscopic structures. However, because growth has to be controlled now on a sub-monolayer scale, the contribution of both random and systematic errors to the measurement has to be kept to an absolute minimum. Closed-loop control by means of the real-time spectroscopic data has become the ultimate aim. RAS monolayer oscillations have been used in MOVPE to count in real-time every single monolayer deposited during the growth of a 30 period InGaAs/GaAs superlattice [Error: Reference source not found] (Fig. 36). The assignment of the monolayer numbers to the oscillations in Fig. 36b, i.e., the interpretation of the phase of the RAS oscillations, is based on the analysis given above for the interpretation of Fig. 29 and Fig. 32a. In this experiment even the composition of the InGaAs well layers can be monitored in-situ via the oscillation period as described in section 5.4. The persistence of the oscillations throughout the growth of the complete device verifies that the intermediate purging cycles enabled the surface to recover from eventually emerging submonolayer roughening during growth. The thickness of wells and barriers, the composition of the InGaAs layers and the sharpness of the interfaces have been verified by X-ray diffraction profiles taken ex-situ afterwards [Error: Reference source not found].

65

J.-T. Zettler

For quantum well growth processes not displaying RAS or ellipsometry monolayer oscillations the usage of the virtual substrate technique enables one to control the well and barrier layer thickness on a submonolayer level. This has been utilized by Maracas et al. for the MBE growth of GaAs/AlGaAs quantum wells [Error: Referencesource not found] where the Ga and Al shutters have been controlled by the ellipsometer. In case the growth rate is well known, the composition of the surface AlGaAs monolayer can be measured and looped-back to the source fluxes in order to track a designed composition profile, as has been demonstrated by Aspnes et al. in an experiment paving the way for optical closed-loop control [Error: Reference sourcenot found] (Fig. 37).

66


1200 1210 1220 1230 1240

-8

-6

-4

-2

T= 775 KE= 2.6 eV

SL period 26 10987654

32

1

54

32

1

10 ML5 MLTMInTMGaAsH3

Re

( r

/ <r

> ) (

10

-3 )

Time (s)

0 500 1000

-8

-6

-4

-2

30 SL periodsa)

b)

Re

( r

/ <r

> ) (

10

-3 )

67

J.-T. Zettler

Fig. 36: (a) RAS response during the growth of a InGaAs(5ML)/GaAs(10ML) superlattice with 30 periods. (b) Magnification of the monitoring RAS signal during the growth of the (arbitrary chosen) 26th period. Monolayer oscillations are seen for each individual layer in the superlattice. (after [Error: Reference sourcenot found]).

Fig. 37: Data for a parabolic well, grown under closed-loop control by CBE. Top: data and target values of x. Middle: difference between data and target values. Bottom: control voltage (after [Error: Reference source not found]).

2 3 4 50

5

10

15

20

250

2(a)

4


photon energy [eV]

<e 2>

4.4 4.5 4.6 4.7

25.0

25.5

2

1

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5

10

15

20

25GaAs substrate

20

5

0(c)

QDs of height h on wetting layer: calculated ellipsometry spectra

h in ML

<e2>

photon energy [eV]

68


2 3 4 5-2

-1

0

1

2

3

4

5


4

2.6

1.5

1

0.5

0

(b)

photon energy [eV]

T=775KpTMI=0.34PapAsH3

=100Pa

Re

(r/r)

[10

-3 ]

2 3 4 5-2

-1

0

1

2

3

4

5

h in ML

0

(d)

5

10

QDs of height h on wetting layer: calculated RAS spectra

20

15

Re(r

/r) [

10-3]

photon energy [eV]

100[?] H. Lee, D. Biswas, M. Klein, H. Morkoc, D. Aspnes, B. Choe, J. Kim, and C. Griffith, J. Appl. Phys. 75, 5040 (1994).

101[?] J.A. Roth, J.-J. Dubray, D.H. Chow, P.D. Brewer, and G.L. Olson, Proc. of the ‘9th Int'l. Conf. on InP and related Materials’, Hyannis, MA, USA (1997).

102[?] M. Zorn, T. Trepk, M. Klein, J.-T. Zettler, and W. Richter, ‘European Workshop on MOVPE VII", Berlin, Germany, 1997.

103[?] K. Knorr, A. Rumberg, P. Kurpas, M. Weyers, J.-T. Zettler, and W. Richter, unpublished.

104[?] J.-T. Zettler, H. Mikkelsen, K. Leo, H. Kurz, R. Carius, and A. Förster, Phys. Rev. B 46, 15955 (1992).

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Fig. 38: InAs-on-GaAs Stranski-Krastanow growth in MOVPE: (a,c) measured and modeled ellipsometry spectra and (b,d) measured and modeled RAS spectra (after [Error: Referencesource not found]).

For the growth of quantum dot (QD) systems recently the preparation of self-arranging QD arrays in Stranski-Krastanow mode gained considerable interest. The targeted structures, combining a high area density of the QDs with a high uniformity in size and distribution, can be prepared only under well selected and tightly controlled growth parameters. On the other hand, the detailed mechanisms ruling the formation of these complex semiconductor structures are still under discussion. Therefore, both RAS and ellipsometry recently have been applied [Error: Referencesource not found] to study in-situ the Stranski-Krastanow growth of strained InAs on GaAs in MOVPE. As can be seen in Fig. 38, both techniques turned out to be highly sensitive to the different stages of quantum dot formation. Until a thickness of about two monolayers is reached, the RAS signatures at 2.6 eV monitor the changing dimer coverage on top of the strained layer-by-layer InAs growth. The subsequent transition to 3-dimensional growth is mirrored by significant changes both in the RAS and ellipsometry spectra (Fig. 38a,b). In Fig. 38c,d these measured data are compared to model calculations based on a modified effective-medium description allowing for an at least qualitative interpretation of the emerging spectral features during the formation of the 3-dimensional InAs islands.

5.8 Ordering effects in ternary III-V semiconductors

As mentioned above, because we are dealing here with cubic semiconductors, bulk optical anisotropies are usually only a second order effect. However, for some ternary compound semiconductors bulk ordering effects along the [111] directions cause bulk related features in the monitoring RAS spectra [105,106]. Bulk ordering, described by an ordering parameter 0<h<1, tends to impose a superlattice structure to the crystal that reduces the symmetry from Td to C3v. It is now well established that the surface dimer configuration at the growth surface plays a major role in ordering [107,108]. Especially the ordering induced effects to the near-band-gap optical anisotropies have been studied intensively both experimentally [109] and theoretically [110]. For in-situ monitoring of ordering processes, however, the above band-gap region is more suitable. Therefore in Fig. 39 the bulk dielectric anisotropy of InGaP, grown lattice matched on GaAs (001) by MOVPE, is analyzed [Error: Referencesource not found]. Ellipsometric measurements have been performed ex-situ on an oxidized sample at room temperature (Fig. 39a). By using the amplitude of the Fabry-Perot oscillations in the low energy range of the spectra as a sensor for the oxide thickness (this can be done by checking the Kramers-Kronig consistency to the high-energy region) the layer thickness, oxide thickness and the mean bulk dielectric function have been determined (Fig. 39b). The analysis of the RAS spectra of ordered InGaP samples (Fig. 39c) yields, in conjunction with the ellipsometry data in Fig. 39b, the bulk dielectric function anisotropy (Fig. 39d). The influence of the

70


semiconductor-oxide interface anisotropy has been taken into account by an interface dielectric anisotropy, measured on a disordered InGaP sample (Fig. 39c, dotted lines). The comparison of the obtained bulk dielectric anisotropy to the first derivative of the mean bulk dielectric function indicates that mostly an anisotropy in the gap energies contributes to the RAS spectra of the ordered InGaP. Additionally, anisotropic broadening of the excitonic E1 and E0' CPs modifies the bulk dielectric anisotropy spectrum. How significant these broadening effects are one can judge by comparing the InGaP e2 spectrum to those of the binary systems of InP and GaP which are added for reference in Fig. 39b. For InGaAs ordering induced anisotropy of the broadening parameters of the E1 and E1+1 transitions has been found to be the dominating effect [Error: Reference source not found]. For InGaP, however, according to Fig. 39d, a dichroism of the E1 and E0’ critical point thresholds dominates the above-bandgap optical anisotropy. This is of importance for future feed-back controlled growth of latticed matched InGaP on GaAs: the bulk dielectric function between the E1 and E0’ critical points (i.e. at about 4 eV at room temperature) is insensitive to the ordering parameter and therefore ellipsometrically controlled lattice matched growth (demonstrated recently for the InGaAs/InP system [Error:Reference source not found,Error: Reference source not found]) should be possible also for the InGaP/InP system, irrespective to the ordering parameter of the growing layer.

0.1

0.2

0.3

0.4

0.5

0.6

0.7 (a)

tan Y

-0.9

-0.8

-0.7

-0.6

-0.5

-0.4

cos

2 3 4 5

5

10

15

20

25

30 E0'

E1

E0

(b)

e1

e2

e

photon energy [eV]

-8

-6

-4

-2

0

2

4

6 (c)

Im

Re

r/r

[10-3

]

2 3 4 5

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6 (d)

de2/dE

e2

e []

and

de/d

E [-

0.00

5eV-1

]

photon energy [eV]

Fig. 39: Ordered InGaP: ellipsometry spectra of an oxidized sample (a). The respective modeled spectra (dotted) result from an analysis that gives the mean bulk dielectric function of the InGaP (b). The room temperature RAS spectra of an ordered (drawn) and a disordered (dotted) InGaP

71

J.-T. Zettler

sample are given in (c). The bulk dielectric anisotropy derived from (b) and (c) is compared in (d) to the first derivative of the mean bulk dielectric function (after [Error: Reference source notfound]). In (b) the bulk dielectric function spectra e2 of InP (dashed) and GaP (dotted) are given for reference.

6 MODELLING THE DIELECTRIC FUNCTION OF SEMICONDUCTORS

Establishing a precise and comprehensive database of the room-temperature (RT) dielectric functions of the technologically most important semiconductors has been the subject of intensive work of various groups during the last two decades. A considerable part of the presently used RT semiconductor dielectric function reference data has been published (and made available also as data files) by D. Aspnes and coworkers. The first attempts to have this data available not only as lengthy data files but instead as a set of only a few parameters from which the complete dielectric function can be calculated originate back to 1984 where Erman et al. [111] used a simple seven oscillator approach to result in an approximation of the measured GaAs dielectric function over most of the spectrum. Presently, this need for compact data parametrization becomes yet more urgent, because dielectric function data have been (and still have to be) taken for a wide field of temperatures and compositions. This is because ellipsometric real-time characterization of the growth process means not only the fast accumulation of spectra but also the real-time correlation of the gained data with a comprehensive database in order to gain directly parameters such as layer thickness, sample temperature and compound composition. Because presently the establishment of an fairly complete experimental data base for growth characterization is work in continuous progress, I am going now to briefly review what has been reached in the development of algorithms for compact

105[?] J.S.Luo, J. Olson, K. Bertnes, M. Raikh, and E. Tsiper, J. Vac. Sci. Technol. B 12, 2552 (1994).

106 [?] B.A. Philips, I. Kamiya, K. Hingerl, L.T. Florez, D.E. Aspnes, S. Mahajan, and J.P. Harbison, Phys. Rev. Lett. 74, 3640 (1995).

107[?] B.A. Philips, A.G. Norman, T.Y. Tseong, S. Mahajan, G.R. Booker, M. Skowronski,J.P. Harbison, and V.G. Keramidas, J. Cryst. Growth 140, 249 (1994).

108[?] H. Murata, S.H. Lee, I.H. Ho, and G.B. Stringfellow, J. Vac. Sci. Technol. B14, 3013 (1996); 109[?] J.S. Luo, J.M. Olson, S.R. Kurtz, D.J. Arent, K.A. Bertness, M.E. Raikh, and E.V. Tsiper,

Phys. Rev B 51, 7603 (1995).

110[?] S. Froyen and A. Zunger, Phys. Rev. Lett. 66, 2132 (1991);S.-H. Wei and A. Zunger, Phys. Rev. B49, 14337 (1994).

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dielectric function data description and fast growth parameter interpolation. In general such algorithms should smoothly fit not only the measured spectra but also their first and second derivative at the main bulk critical points. Kramers-Kronig consistent analytic expressions including a minimum number of parameters should be only used in order to assure fast computation.

As has been discussed in section 2, theoretically first-principles ab-initio calculations could give the dielectric functions using as input parameter little more than only the type of atoms involved in the formation of the semiconductor crystal. Even if we assume that the immense progress in this field continues, we probably have to accept that the time restrictions of real-time analysis call for simpler and easy-to-handle algorithms. However and as we will see below, there is a great deal to learn from these theoretical approaches because often the most physical models are those which describe our data with a minimum number of parameters.

In contrast to ab-initio calculations we can start off for reaching the targetted compact data description and fast parameter interpolation by using extended tables of experimental data which have to be linearly interpolated, as used by Snyder et al. [112] for the AlGaAs alloy system. Here a fairly huge number of parameters, i.e. the complete set of experimental data for some selected compositions, is used within a very fast interpolation sceme. Harmonic oscillators (HOs) replacing the extended data tables [Error: Reference source not found,113,Error: Reference source not found] have been successfully applied to reduce the number of parameters for the description of a typical semiconductor dielectric function to less than 30 without increasing the computation time significantly. While at first glance this HO method is physically appealing, the replacement of the electronic transitions arising from an extended region of the semiconductor's Brillouin zone by only a single harmonic oscillator each is at a high price: the artificially broadened oscillators hinder modelling correctly the sharp onset of absorption at the E0 band gap and thus the HO model is only accurate at energies above the E0 region. But it is the spectroscopic region close to and below the E0 gap of the semiconductors that is mostly used for Fabry-Perot oscillation based real-time thickness measurements. To avoid this dilemma we have to return to the above mentioned ab-initio approach. Starting from this basic idea that characteristic features of the semiconductor's band structure should be directly used for modelling its dielectric function, Cardona [Error: Reference source not found] and Aspnes [Error: Reference source not found] developed the critical-point parabolic band model (CPPB). This approach was extremely successful for analyzing the second or third derivative like spectra as typically gained by modulation spectroscopic methods and also for the determination of energetic position and type of bulk critical points from ellipsometry spectra. While this CPPB model was never intended to fit the ellipsometric spectra directly, recently Kim and coworkers [114] extended it by taking into account the full analytic form of the combined electronic density of states, the separate contribution of several valence and conduction bands as well as the effect of non-Lorenzian broadening. In [Error: Reference source not found] these authors

111[?] M. Erman, J. Theeten, P. Chambon, S. Kelso, and D. Aspnes, J. Appl. Phys. 56, 2664 (1984).

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could show that this model gives an excellent quantitative agreement with experimental results for the GaAs dielectric function and for its derivatives with respect to the photon energy. Kim et al. applied their model also to the AlGaAs alloy system [115]. While every single dielectric function spectrum was described by 37 parameters, for the interpolation scheme for all compositions (x=0...1) in the 1.5 eV to 6.0 eV range they had to use 119 Parameters in total. This is, as the reader might expect, too large a set of parameters for fast real-time analysis, even if the complete set of model parameters is controled by the single composition parameter x. However, Kim et al. [Error: Reference source not found,Error: Reference source notfound] showed that by avoiding the use of artificially broadened oscillators and by using a description directly related to the combined electronic density of states it is possible to model the electron's contribution to the dielectric function spectra correctly over the entire photon energy range from the IR up to 6 eV. Using this result, in [116] a model has been developed that in some sense compromises the HO model with a description based on the combined electronic density of states. In Fig. 40 the temperature dependent dielectric function of InP is given as an example. Harmonic oscillators have been used here only for the description of the relatively sharp excitonic lineshapes in the dielectric function spectra. The contribution of transitions originating from other regions of the Brillouin zone is, as has be seen from ab-initio pseudo-potential calculations in the local density approximation (Fig. 12), significantly less structured, especially above room-temperature. Therefore, this broad 'background' contribution was taken into account by a cubic spline function with only a small number of set points that does allow for the proper description of the dielectric function close to and below to the E0 fundamental gap. The total number of parameters to be adjusted to yield the temperature dependent dielectric function of InP within this spline/oscillator model is only 22 and because there are analytic expressions for the Kramers-Kronig integrals of cubic spline functions [117], the calculation time is not significantly increased with respect to HO model.

74


0

5

10

15

20 InP T=298K

<e2>

2 3 4 50

5

10

15

20T=823K

<e2>

photon energy [eV]

2 3 4 5-10

-5

0

5

10

15

20

25

measured

<e>

photon energy [eV]

2 3 4 5-10

-5

0

5

10

15

20

25

calculated from database

<e>

photon energy [eV]

Fig. 40: InP(T) data base by the spline/harmonic ocillator model. A cubic spline /harmonic oscillator model is used for parameterizing the measured dielectric functions at room temperature (a) and 823K (b). In (c) the measured spectra are given for RT, 423, 523, 623, 723 and 823K and compared to the respective interpolated spectra in (d).

The above starting point for discussing the bulk dielectric function data base was that there is an increasingly complete set of temperature dependent and composition

112[?] P. Snyder, J. Woolam, S. Alterovitz, and B. Johs, J. Appl. Phys. 68, 5925 (1990).

113[?] H. Yao, P. Snyder, and J. Woolam, J. Appl. Phys. 70, 3261 (1991).

114[?] C. Kim, J. Garland, H. Abad, and P. Raccah, Phys. Rev. B 45, 11749 (1992).

115[?] C. Kim, J. Garland, and P. Raccah, Phys. Rev. B 47, 1876 (1993).

116[?] M. Zorn, T. Trepk, J.-T. Zettler, C. Meyne, K. Knorr, T. Wethkamp, M. Klein, W. Richter,

B. Junno, M. Miller, and L. Samuelson, submitted to Appl. Phys. A .

117[?] J.-T. Zettler, T. Trepk, L. Spanos, Y.-Z. Hu, and W. Richter, Thin Solid Films 233,402 (1993).

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dependent experimental data at least for the most important semiconductors. The situation for the surface dielectric functions, necessary for modeling RAS spectra, is however different. To date there are not yet so many groups active in this field. But there are also more general difficulties which have to be overcome to reach at least an experimental basis for a RAS data base. Fig. 41, which gives the temperature shift of a (2x1) reconstructed InP surface, may serve as an example. The amplitude of the P dimer related structure increases in the low temperature range with temperature and only above 300°C it starts to decrease and to broaden as expected. This is because there a superposition of the well known thermal broadening of the dielectric function features with the temperature dependent phosphine decomposition that causes a variation in phosphorus stabilization during this experiment. Consequently, carefully performed systematic studies are needed in MBE and CBE systems for establishing this kind of surface dielectric anisotropy data. RHEED has to be available as reference and - in the best case - direct transfer to UHV-STM characterization is desirable.

2 3 4 5

-4

-2

0

2

4

6

8

10625 K

photon energy [eV]

pPH3= 100 PaR

e (r

[110

] -r [1

10] /

<r>

) (10

-3)

875 K

RT

Fig. 41: Measured RAS spectra of InP(001) for various temperatures under fixed phosphine partial pressure.

7 SUMMARY AND OUTLOOK

We have shown that optical spectroscopic techniques specifically reflectance anisotropy and ellipsometry have reached a level of reliability and precision that until recently has been regarded far beyond the physical limits of optical methods. Because they can be applied as well in gas phase environments as under UHV conditions they allow for the first time comparative in-situ studies in all three main epitaxial techniques: MBE, MOMBE and MOVPE. They can deliver important basic but also very practical information about the epitaxial growth process: layer thickness, stoichiometry, temperature, doping concentrations, ordering and morphology parameters can be obtained. Even in very stable growth environments such knowledge is extremely useful when installing new or modifying existing growth processes. The effort necessary to arrive at satisfactory growth conditions is estimated to be reduced by a considerable factor already with today's level of monitoring capabilities. Irrespective of the significant progress that was reached in optical real-time characterization there is still a wide field of challenging tasks to be

76


tackled: (i) parallel detection of both ellipsometric and RAS spectra on time scales comparable to the growth of only a few monolayers has to be reached - with signal-to-noise ratios, absolute precision and photon energy range as available in the most advanced scanning systems. (ii) Simplified and affordable polarization and anisotropy sensors should be developed because in many cases status sensing on a rather low level can already contribute significantly to cost reductions in device production lines. (iii) The remarkable success of single wavelength virtual interface and virtual substrate techniques for up to now only a few very specific test cases should be broadened by applying these techniques really spectroscopically. Intelligent algorithms should select the most sensitive wavelengths, utilize internal Kramers-Kronig checks and adjust the mode of analysis (Fresnel or minimal data analysis) to the actual stage of the growth. And, (iv) besides these applied aspects of ellipsometry and RAS, there are, as discussed in sections 3 and 4, a number of basic physical questions that remain to be solved. The still not completely solved problem of the contribution of many-particle effects to the optical spectra may serve as an example.

Acknowledgements

It is a pleasure to acknowledge the contributions of a large number of hard working diploma students and PhD students at the University of Technology in Berlin. At least my main collaborators in the work discussed in this article shall be mentioned here: K. Knorr, M. Zorn, E. Steimetz, M. Pristovsek, who performed the most part of the experiments at the MOVPE system; J. Rumberg, T. Wethkamp and T. Trepk who contributed to the improvements of the spectroscopic systems. W. Richter and N. Esser are thanked for countless helpful and stimulating discussions. Collaborations with colleagues in the MBE groups at the Paul-Drude-Institut Berlin and at the University of Wales in Cardiff and those in the MOMBE laboratory at the University of Lund contributed substantially to our results in real-time control of MOVPE growth. G. Jungk, Z. Sobiesierski and J.B. Mullin are thanked for carefully reading and correcting the manuscript. The author is also grateful to A. Shkrebtii for a critical reading of section 3.

Part of this work was supported by the Deutsche Forschungsgemeinschaft (Sonderforschungsbereich 296), by the Bundesministerium für Forschung und Technologie (BMFT 01 BT 310/835) and by the DAAD.

References

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Documents

\begin{thebibliography}{100} - TU Berlin · Web viewWith these techniques it was soon established that the GaAs(001) surface is As terminated under MBE growth conditions [77,27,]