8.ElectronicPropertiesofSemiconductorInterfaces ElectronicPro · on the semiconductor side of the interface. This new depletion-layer concept immediately triggered a search for a

Electronic Pro175Part

A|8

8. Electronic Properties of Semiconductor Interfaces

Winfried Mönch

In this chapter, we discuss electronic prop-erties of semiconductor interfaces. Semicon-ductor devices contain metal–semiconductor,insulator–semiconductor, insulator–metal, and/orsemiconductor–semiconductor interfaces. Theelectronic properties of these interfaces deter-mine characteristics of the device. The bandstructure lineup at all these interfaces is deter-mined by one unifying concept, the continuum ofinterface-induced gap states (IFIGS). These intrin-sic interface states are the wave function tails ofelectron states that overlap the fundamental bandgap of a semiconductor at the interface; in otherwords, they are caused by the quantum mechan-ical tunneling effect. IFIGS theory quantitativelyexplains the experimental barrier heights of well-characterized metal–semiconductor or Schottkycontacts as well as the valence-band offsets ofsemiconductor–semiconductor interfaces or semi-conductor heterostructures. Insulators are viewedas semiconductors with wide band gaps.

8.1 Experimental Database....................... 1778.1.1 Barrier Heights of Laterally

Homogeneous Schottky Contacts .......... 1778.1.2 Band Offsets of Semiconductor

Heterostructures ................................. 180

8.2 IFIGS-and-Electronegativity Theory..... 181

8.3 Comparison of Experiment and Theory 1838.3.1 Barrier Heights of Schottky Contacts...... 1838.3.2 Band Offsets of Semiconductor

Heterostructures ................................. 184

8.4 Modifications of Schottky Contacts . ..... 1878.4.1 Nonalloyed Ohmic Contacts

or MUTIS Schottky Contacts ................... 1878.4.2 Atomic Interlayers ............................... 189

8.5 Graphene Schottky Contacts. ............... 190

8.6 Final Remarks .................................... 190

References ................................................... 191

In his pioneering article entitled Semiconductor Theoryof the Blocking Layer, Schottky [8.1] finally explainedthe rectifying properties of metal–semiconductor con-tacts, which had first been described by Braun [8.2],as being due to a depletion of the majority carrierson the semiconductor side of the interface. This newdepletion-layer concept immediately triggered a searchfor a physical explanation of the barrier heights ob-served in metal–semiconductor interfaces, or Schottkycontacts as they are also called in order to honor Schot-tky’s many basic contributions to this field.

The early Schottky–Mott rule [8.3, 4] proposed thatn-type (p-type) barrier heights were equal to the differ-ence between the work function of the metal and theelectron affinity (ionization energy) of the semiconduc-tor. A plot of the experimental barrier heights of variousmetal–selenium rectifiers versus the work functions ofthe corresponding metals did indeed reveal a linear cor-relation, but the slope parameter was much smaller thanunity [8.4]. To resolve the failure of the very simple and

therefore attractive Schottky–Mott rule, Bardeen [8.5]proposed that electronic interface states in the semi-conductor band gap play an essential role in the chargebalance at metal–semiconductor interfaces.

Heine [8.6] considered the quantum-mechanicaltunneling effect at metal–semiconductor interfaces andnoted that for energies in the semiconductor band gap,the volume states of the metal have tails in the semi-conductor. Tejedor and Flores [8.7] applied this sameidea to semiconductor heterostructures where, for ener-gies in the band-edge discontinuities, the volume statesof one semiconductor tunnel into the other. The con-tinua of interface-induced gap states (IFIGS), as theseevanescent states were later called, are an intrinsicproperty of semiconductors and they are the funda-mental physical mechanism that determines the band-structure lineup at both metal–semiconductor contactsand semiconductor heterostructures: in other words, atall semiconductor interfaces. Insulator interfaces arealso included in this, since insulators may be de-

© Springer International Publishing AG 2017S. Kasap, P. Capper (Eds.), Springer Handbook of Electronic and Photonic Materials, DOI 10.1007/978-3-319-48933-9_8

PartA|8

176 Part A Fundamental Properties

W

z

W

z

WFWcb

Wvb

WciΦBn

Metal /n – semiconductor

ΔWc

ΔWv

W rci

W rvi

W lvi

W lci

Semiconductor – semiconductor

a)

b)

Fig. 8.1a,b Schematic energy-band diagrams of(a) metal–semiconductor contacts and (b) semiconductorheterostructures. WF, Fermi level; ˚Bn, barrier height; Wv

and Wc, valence-band maximum and conduction-bandminimum, respectively; Wv and Wc, valence- andconduction-band offset, respectively; i and b, values at theinterface and in the bulk, respectively; r and l, right andleft side, respectively

scribed as wide-gap semiconductors. Figure 8.1 showsschematic band diagrams of an n-type Schottky contactand a semiconductor heterostructure.

The IFIGS continua derive from both the valence-and the conduction-band states of the semiconduc-tor. The energy at which their predominant characterchanges from valence-band-like to conduction-band-like is called their branch point. The position of theFermi level relative to this branch point then deter-mines the sign and the amount of the net charge in theIFIGS. Hence, the IFIGS give rise to intrinsic interfacedipoles. Both the barrier heights of Schottky contactsand the band offsets of heterostructures thus divide upinto a zero-charge-transfer term and an electric-dipolecontribution.

From a more chemical point of view, these interfacedipoles may be attributed to the partial ionic charac-ter of the covalent bonds between atoms right at theinterface. Generalizing Pauling’s [8.8] electronegativ-ity concept, the difference in the electronegativities ofthe atoms involved in the interfacial bonds also de-scribes the charge transfer at semiconductor interfaces.Combining the physical IFIGS and the chemical elec-tronegativity concept, the electric-dipole contributionsof Schottky barrier heights as well as those of het-erostructure band offsets vary proportional to the differ-ence in the electronegativities of the metal and the semi-conductor and of the two semiconductors, respectively.

The theoreticians appreciated Heine’s IFIGS con-cept at once. The initial reluctance of most experi-mentalists was motivated by the observation that thepredictions of the IFIGS theory only marked upper lim-its for the barrier heights observed with real Schottkycontacts [8.9]. Schmitsdorf et al. [8.10] finally resolvedthis dilemma. They found a linear decrease in the ef-fective barrier heights with increasing ideality factorsfor their Ag/n-Si(111) diodes. Such behavior has beenobserved for all of the Schottky contacts investigatedso far. Schmitsdorf et al. attributed this correlation topatches of decreased barrier heights and lateral dimen-sions smaller than the depletion layer width [8.10, 11].Consequently, they extrapolated their plots of effec-tive barrier height versus ideality factor to the idealityfactor determined by the image-force or Schottky ef-fect [8.12] alone; in this way, they obtained the barrierheights of the laterally homogeneous contacts. Thebarrier heights of laterally uniform contacts can alsobe determined from capacitance–voltage measurements(C=V) and by applying ballistic-electron-emission mi-croscopy (BEEM) and internal photoemission yieldspectroscopy (IPEYS). The I=V, C=V, BEEM, andIPEYS data agree within the margins of experimentalerror.

Mönch [8.13] found that the barrier heights oflaterally homogeneous Schottky contacts as well asthe experimentally observed valence-band offsets ofsemiconductor heterostructures agree excellently withthe predictions of the IFIGS-and-electronegativity the-ory.

Electronic Properties of Semiconductor Interfaces 8.1 Experimental Database 177Part

A|8.1

8.1 Experimental Database

8.1.1 Barrier Heights of LaterallyHomogeneous Schottky Contacts

I=V CharacteristicsThe current transport in real Schottky contacts occursvia thermionic emission over the barrier provided thedoping level of the semiconductor is not too high [8.14].For doping levels larger than approximately 1018 cm�3,the depletion layer becomes so narrow that tunnel orfield emission through the depletion layer prevails.The current–voltage characteristics then become ohmicrather than rectifying.

For thermionic emission over the barrier, thecurrent–voltage characteristics of n-type Schottky con-tacts may be written as [8.13]

Ite D Is exp

�e0Vc

nkBT

��1� exp

��e0Vc

kBT

��; (8.1)

where

Is D AA�

RT2 exp

��˚ effBn

kBT

�(8.2)

is the saturation current and A is the diode area, A�

R isthe effective Richardson constant of the semiconductor,and kB, T , and e0 are Boltzmann’s constant, the tem-perature, and the electronic charge, respectively. Theeffective Richardson constant is defined as

A�

R D 4 e0kBm�

n

h3D AR

m�

n

m0; (8.3)

where AR D 120A cm�2 K�2 is the Richardson con-stant for thermionic emission of nearly free electronsinto vacuum, h is Planck’s constant, and m0 and m�

n arethe vacuum and the effective conduction-band mass ofelectrons, respectively. The externally applied bias Va

divides up into a voltage drop Vc across the depletionlayer of the Schottky contact and an IR drop at the se-ries resistance Rs of the diode, so that Vc D Va � IRs.For ideal (intimate, abrupt, defect-free, and, above all,laterally homogeneous) Schottky contacts, the effec-tive zero-bias barrier height ˚ eff

Bn equals the difference˚hom

Bn � ı˚0if between the homogeneous barrier height

and the zero-bias image-force lowering [8.13]

ı˚0if D e0

�2e20Nd

.4 /2"21"b"

30

�e0

ˇ̌V0i

ˇ̌� kBT�1=4

;

(8.4)

where Nd is the donor density, e0jV0i j is the zero-bias

band bending, "1 and "b are the optical and the bulk di-electric constant, respectively, and "0 is the permittivityof vacuum. The ideality factor n describes the voltage

dependence of the barrier height and is defined by

1� 1

nD @˚ eff

Bn

@e0Vc: (8.5)

For real diodes, the ideality factors n are generallyfound to be larger than the ideality factor

nif D�1� ı˚0

if

4e0jV0i j��1

; (8.6)

which is determined by the image-force effect only.The effective barrier heights and the ideality factors

of real Schottky diodes fabricated under experimen-tally identical conditions vary from one specimen tothe next. However, the variations of both quantities arecorrelated, and the ˚ eff

Bn values become smaller as theideality factors increase. As an example, Fig. 8.2 dis-plays ˚ eff

Bn versus n data for Ag/n-Si(111) contacts with.1� 1/i-unreconstructed and .7� 7/i-reconstructed in-terfaces [8.10]. The dashed and dash-dotted lines arethe linear least-squares fits to the data points. The lineardependence of the effective barrier height on the ideal-ity factor may be written as

˚ effBn D ˚nif

Bn � 'p.n� nif/ ; (8.7)

where ˚nifBn is the barrier height at the ideality factor

nif. Several conclusions may be drawn from this rela-tion. First, the ˚ eff

Bn �n correlation shows that more thanone physical mechanism determines the barrier heightsof real Schottky contacts. Second, the extrapolation of˚ eff

Bn versus n curves to nif removes all mechanisms that

0.75

0.72

0.69

0.66

0.631.0 1.1 1.2

Effective barrier height (eV)

Ideality factor

i

i

Ag/n-Si(111)Nd = 1 × 15 cm–3

T =

(1 × 1)

(7 × 7)

Fig. 8.2 Effective barrier heights versus ideality factorsdetermined from I=V characteristics of Ag/n-Si(111)-.7�7/i and -.1�1/i contacts at room temperature. The dashedand dash-dotted lines are the linear least-squares fits to thedata. (After [8.10])

PartA|8.1


1.0

0.5

01.0

0.5

0

–0.2

0.20x/zdep

z /zdep

V/V 0i

Fig. 8.3 Calculated potential distribution underneath andaround a patch of reduced interface potential embedded ina region of larger interface band-bending. The lateral di-mension and the interface potential reduction of the patchare set to two-tenths of the depletion layer width zdep andone-half of the interface potential of the surrounding re-gion. (After [8.13])

cause a larger bias dependence of the barrier height thanthe image-force effect itself from consideration. Third,the extrapolated barrier heights ˚nif

Bn are equal to thezero-bias barrier height ˚hom

Bn � ı˚0if of the laterally ho-

mogeneous contact.The laterally homogeneous barrier heights obtained

from ˚ effBn versus n curves to nif are not necessarily char-

acteristic of the corresponding ideal contacts. This isillustrated by the two data sets displayed in Fig. 8.2,which differ in the interface structures of the respec-tive diodes. Quite generally, structural rearrangementssuch as the .7� 7/i reconstruction are connected witha redistribution of the valence charge. The bonds inperfectly ordered bulk silicon, the example consid-ered here, are purely covalent, and so reconstructionsare accompanied by electric SiCq �Si�q dipoles.The Si(111)-.7� 7/ reconstruction is characterized bya stacking fault in one half of its unit mesh [8.15].Schmitsdorf et al. [8.10] quantitatively explained theexperimentally observed reduction in the laterally ho-mogeneous barrier height of the .7� 7/i with regard tothe .1�1/i diodes by the electric dipole associated withthe stacking fault of the Si(111)-.7� 7/ reconstruction.

Patches of reduced barrier height with lateral dimen-sions smaller than the depletion layer width that are em-bedded in large areas of laterally homogeneous barrierheight is the only knownmodel that explains a loweringof effective barrier heights with increasing ideality fac-tors. In their phenomenological studies of such patchySchottky contacts, Freeouf et al. [8.11] found that thepotential distribution exhibits a saddle point in front of

20

15

10

5

00.65 0.70 0.75 0.80 0.85

i

Ag/n-Si(111)

Number of diodes

Flat-band barrier height (eV)

(7 × 7)

(1 × 1)

i

Fig. 8.4 Histograms of flat-band barrier heights deter-mined from C=V characteristics of Ag/n-Si(111)-.7� 7/i

and -.1� 1/i contacts at room temperature. The data wereobtained with the same diodes discussed in Fig. 8.2.The dashed and dash-dotted lines are the Gaussian least-squares fits to the data. (After [8.10])

such nanometer-size patches of reduced barrier height.Figure 8.3 explains this behavior. The saddle-point bar-rier height strongly depends on the voltage drop Vc

across the depletion layer. Freeouf et al. simulated thecurrent transport in such patchy Schottky contacts andfound a reduction in the effective barrier height anda correlated increase in the ideality factor as they re-duced the lateral dimensions of the patches. However,they overlooked the fact that the barrier heights of thelaterally homogeneous contacts may be obtained from˚ eff

Bn versus n plots, by extrapolating to nif.It has to be mentioned that the effective barrier

heights and the ideality factors of real Schottky contactsgenerally vary as a function of temperature. The so-called Richardson plots ln.Is=T2/-versus-1=T will nei-ther result in correct values of effective barrier heightsnor will the effective Richardson constants obtainedequal the theoretical values because such graphs inher-ently assume the barrier heights to be independent oftemperature [8.16–18] in contrast to what is experimen-tally observed with real Schottky contacts.

C=V CharacteristicsBoth the space charge and the width of the depletionlayers at metal–semiconductor contacts vary as a func-tion of the externally applied voltage. The space-chargetheory gives the variation in the depletion layer capaci-tance per unit area as [8.13]

Cdep D�e20"b"0Nd

2

�e0

�ˇˇV0i

ˇˇ�Vc

�� kBT��1=2

:

(8.8)

Electronic Properties of Semiconductor Interfaces 8.1 Experimental Database 179Part

A|8.1

The current through a Schottky diode biased in thereverse direction is small, so the IR drop due to theseries resistance of the diode may be neglected. Con-sequently, the extrapolated intercepts on the abscissaof 1=C2

dep versus Va plots give the band-bending e0jV0i j

at the interface, and together with the energy distanceWn D WF �Wcb from the Fermi level to the conductionband minimum in the bulk, one obtains the flat-bandbarrier height˚ fb

Bn�˚homBn D e0jV0

i j CWn, which equalsthe laterally homogeneous barrier height of the contact.

As an example, Fig. 8.4 displays the flat-band bar-rier heights of the same Ag/n-Si(111) diodes that arediscussed in Fig. 8.2. The dashed- and dash-dotted linesare the Gaussian least-squares fits to the data fromthe diodes with .1� 1/i and .7� 7/i interface struc-tures, respectively. Within the margins of experimentalerror, the peak C=V values agree with the laterallyhomogeneous barrier heights obtained from the extrap-olations of the I=V data shown in Fig. 8.2. These dataclearly demonstrate that barrier heights characteristic oflaterally homogeneous Schottky contacts can be onlyobtained from I=V or C=V data from many diodesfabricated under identical conditions rather than froma single diode. However, the effective barrier heightsand the ideality factors vary as a function of the diodetemperature. Hence, the effective barrier heights andideality factors evaluated from the I=V characteris-tics for one and the same diode recorded at differenttemperatures are also suitable for determining the cor-responding laterally homogeneous barrier height [8.13].

Ballistic-Electron-Emission MicroscopyIn BEEM [8.19], a tip injects almost monoenergeticelectrons into the metal film of a Schottky diode. Thesetunnel-injected electrons reach the semiconductor asballistic electrons provided that they lose no energyon their way through the metal. Hence, the collectorcurrent Icoll is expected to set in when the ballistic elec-trons surpass the metal–semiconductor barrier; in otherwords, if the voltage Vtip applied between tip and metalfilm exceeds the local potential barrier ˚ loc

Bn .z/=e0. Belland Kaiser [8.20] derived the square law

Icoll.z/ D R�Itip�e0Vtip �˚ loc

Bn .z/�2

(8.9)

for the BEEM Icoll=Vtip characteristics, where Itip isthe injected tunnel current. BEEM measures local bar-rier heights; most specifically, the saddle-point barrierheights in front of nanometer-sized patches rather thantheir lower barrier heights right at the interface.

BEEM is the experimental tool for measuring spa-tial variations in the barrier height on the nanometer-scale. The local barrier heights are determined byfitting relation (8.9) to measured Icoll/Vtip characteris-

15

10

5

01.1 1.2 1.3 1.4

BEEM barrier height (eV)

Probability (%)

Pd/n-6H-SiCT = 293 K

Fig. 8.5 Histograms of local BEEM barrier heights of twoPd/n-6H-SiC(0001) diodes with ideality factors of 1:06(gray solid bars) and 1:49 (empty bars). The data were ob-tained by fitting the square law (8.9) to 800 BEEM Icoll=Vtip

spectra each. (After Im et al. [8.21])

tics recorded at successive tip positions along lateralline scans. Figure 8.5 displays histograms of the lo-cal BEEM barrier heights of two Pd/n-6H-SiC(0001)diodes [8.21]. The diodes differ in their ideality factors,1:06 and 1:49, which are close to and much larger, re-spectively, than the value nif D 1:01 determined solelyby the image-force effect. Obviously, the nanometer-scale BEEM histograms of the two diodes are identical,although their macroscopic ideality factors and there-fore their patchinesses differ. Two important conclu-sions were drawn from these findings. First, these datasuggest the existence of two different types of patches:intrinsic and extrinsic ones. The intrinsic patches mightbe correlated with the random distributions of the ion-ized donors and acceptors which cause nanometer-scalelateral fluctuations in the interface potential. A fewgross interface defects of extrinsic origin, which es-cape BEEM observations, are then responsible for thevariations in the ideality factors. Second, Gaussianleast-squares fits to the histograms of the local BEEMbarrier heights yield peak barrier heights of 1:27˙0:03 eV. Within the margins of experimental error, thisvalue agrees with the laterally homogeneous value of1:24˙0:09 eV, which was obtained by extrapolation ofthe linear least-squares fit to a ˚ eff

Bn versus n plot to nif.The nanometer-scale BEEM histograms and the macro-scopic I=V characteristics thus provide identical barrierheights of laterally homogeneous Schottky contacts.

Internal Photoemission Yield SpectroscopyMetal–semiconductor contacts show a photoelectric re-sponse to optical radiation with photon energies smallerthan the width of the bulk band gap. This effect is causedby photoexcitation of electrons from the metal over the

PartA|8.1


0.03

0.02

0.01

0.000.25 0.30 0.35 0.40

[Y(hω) × hω]1/2

Photon energy (eV)

Pt/p-Si(001)Na = 8 × 15 cm–3

T = 50 K

Fig. 8.6 Spectral dependence of the internal photoemis-sion yield of a Pt/p-Si(001) diode versus the photon energyof the exciting light. The dashed line is the linear least-squares fit to the data for photon energies larger than0:3 eV. (After Turan et al. [8.23])

interfacial barrier into the conduction band of the semi-conductor. Experimentally, the internal photoemissionyield, which is defined as the ratio of the photoinjectedelectron flux across the barrier into the semiconductorto the flux of the electrons excited in the metal, is mea-sured as a function of the energy of the incident photons.Consequently, this technique is called internal photoe-mission yield spectroscopy (IPEYS). Cohen et al. [8.22]derived that the internal photoemission yield varies asa function of the photon energy „! as

Y.„!/ / 1

„!�„! �˚ IPEYS

Bn

�2: (8.10)

Patches only cover a small portion of the metal–semiconductor interface, so the threshold energy˚ IPEYS

Bn will equal the barrier height ˚homBn of the later-

ally homogeneous part of the contact minus the zero-bias image-force lowering ı˚0

if .In Fig. 8.6, experimental .Y.„!/� „!/1=2 data for

a Pt/p-Si(001) diode [8.23] are plotted versus the energyof the exciting photons. The dashed line is the linearleast-squares fit to the data. The deviation of the ex-perimental .Y.„!/� „!/1=2 data towards larger valuesslightly below and above the threshold is caused by theshape of the Fermi–Dirac distribution function at finitetemperatures and by the existence of patches with bar-rier heights smaller and larger than ˚hom

Bn .

8.1.2 Band Offsets of SemiconductorHeterostructures

Semiconductors generally grow layer-by-layer, at leastinitially. Hence, core-level photoemission spectroscopy

(PES) is a very reliable tool and the one most widelyused to determine the band-structure lineup at semicon-ductor heterostructures. The valence-band offset maybe obtained from the energy positions of core-levellines in x-ray photoelectron spectra recorded with bulksamples of the semiconductors in contact and withthe interface itself [8.24]. Since the escape depths ofthe photoelectrons are on the order of just 2 nm, oneof the two semiconductors must be sufficiently thin.This condition is easily met when heterostructures aregrown by molecular beam epitaxy (MBE) and pho-toemission spectra (PES) are recorded during growthinterrupts. The valence-band discontinuity is then givenby (Fig. 8.7)

Wv D Wvir �Wvil D Wi.nrlr/�Wi.nlll/

C ŒWvbr �Wb.nrlr/�� ŒWvbl �Wb.nlll/� ;

(8.11)

where nrlr and nlll denote the core levels of the semi-conductors on the right (r) and the left (l) side of theinterface, respectively. The subscripts i and b charac-terize interface and bulk properties, respectively. Theenergy difference Wi.nrlr/�Wi.nlll/ between the corelevels of the two semiconductors at the interface isdetermined from energy distribution curves of pho-toelectrons recorded during MBE growth of the het-erostructure. The energy positions Wvbr �Wb.nrlr/ andWvbl �Wb.nlll/ of the core levels relative to the valence-band maxima in the bulk of the two semiconductors areevaluated separately.

z

W

Bulkleft Interface Bulkright

Wvbl – Wb(n lll)

Wvbr – Wb(nrlr)Wi (nl ll)

Wi (n rlr)

Wvir

WvilΔWv

Fig. 8.7 Schematic energy band diagram at semiconductorheterostructures. Wvb and Wvi are the valence-band max-ima and Wb.nl/ and Wi.nl/ are the core levels in the bulkand at the interface, respectively. The subscripts l and r de-note the semiconductors on the right and the on the leftside of the interface. Wv is the valence-band offset. Thethin dashed lines account for possible band-bending fromspace-charge layers

Electronic Properties of Semiconductor Interfaces 8.2 IFIGS-and-Electronegativity Theory 181Part

A|8.2

Another widely used technique for determiningband offsets in heterostructures is internal photoemis-

sion yield spectroscopy. The procedure for evaluatingthe IPEYS signals is the same as described in Sect. 8.1.1.

8.2 IFIGS-and-Electronegativity Theory

Because of the quantum-mechanical tunneling effect,the wave functions of bulk electrons decay exponen-tially into vacuum at surfaces or, more generally speak-ing, at solid–vacuum interfaces. A similar behavioroccurs at interfaces between two solids [8.6, 7]. In en-ergy regions of Schottky contacts and semiconductorheterostructures where occupied band states overlapa band gap, the wave functions of these electronswill tail across the interface. The only difference tosolid–vacuum interfaces is that the wave function tailsoscillate at solid–solid interfaces. Figure 8.8 schemat-ically explains the tailing effects at surfaces and semi-conductor interfaces. For the band-structure lineup atsemiconductor interfaces, only the tailing states withinthe gap between the top valence and the lowest conduc-tion band are of any real importance since the energyposition of the Fermi level determines their chargingstate. These wave function tails or interface-inducedgap states (IFIGS) derive from the continuum of thevirtual gap states (ViGS) of the complex semiconductorband structure. Hence, the IFIGS are an intrinsic prop-erty of the semiconductor.

The IFIGS are made up of valence-band andconduction-band states of the semiconductor. Their netcharge depends on the energy position of the Fermilevel relative to their branch point, where their characterchanges from predominantly donor- or valence-band-

a)

b)

Metal, Semiconductor Vacuum z

ψ ψ*

ψ ψ*

Metal, Semiconductor Semiconductor z

Fig. 8.8a,b Wave functions at clean surfaces (a) and atmetal–semiconductor and semiconductor–semiconductorinterfaces (b) (schematically)

like to mostly acceptor- or conduction-band-like. Theband-structure lineup at semiconductor interfaces isthus described by a zero-charge-transfer term and anelectric dipole contribution.

In a more chemical approach, the charge transfer atsemiconductor interfaces may be related to the partlyionic character of the covalent bonds at interfaces.Pauling [8.8] described the ionicity of single bonds indiatomic molecules by the difference between the elec-tronegativities of the atoms involved. The binding ener-gies of core-level electrons are known to depend on thechemical environment of the atoms or, in other words,on the ionicity of their chemical bonds. Figure 8.9displays experimentally observed chemical shifts forSi(2p) and Ge(3d) core levels induced bymetal adatomson silicon and germanium surfaces as a function of thedifference Xm �Xs between the Pauling atomic elec-tronegativity of the metal and that of the semiconductoratoms. The covalent bonds between metal and substrateatoms still persist at metal–semiconductor interfaces, asab-initio calculations [8.25] have demonstrated for theexample of Al/GaAs(110) contacts. The pronouncedlinear correlation of the data displayed in Fig. 8.9 thusjustifies the application of Pauling’s electronegativityconcept to semiconductor interfaces.

0.5

0.0

–0.5

–1 10

Adatom-induced core-level shift (eV)

Electronegativity difference Xm–Xs

Si(111)Si(001)Ge(111)Ge(001) Au

Ag

SnIn

Cs

Fig. 8.9 Chemical shifts of Si(2p) and Ge(3d) core levelsinduced by metal adatoms on silicon and germanium sur-faces, respectively, as a function of the difference Xm �Xs

in the metal and the semiconductor electronegativities inPauling units. (After [8.13])

PartA|8.2


The combination of the physical IFIGS and thechemical electronegativity concept yields the bar-rier heights of ideal p-type Schottky contacts andthe valence-band offsets of ideal semiconductor het-erostructures as

˚Bp D ˚pbp � SX.Xm �Xs/ (8.12)

and

Wv D ˚pbpr �˚

pbpl CDX.Xsr �Xsl/ ; (8.13)

respectively, where ˚pbp D Wbp �Wv.� / is the energy

distance from the valence-band maximum to the branchpoint of the IFIGS or the p-type branch-point energy.It has the physical meaning of a zero-charge-transferbarrier height. The slope parameters SX and DX are ex-plained at the end of this section.

The IFIGS derive from the ViGS of the com-plex band structure of the semiconductor. Their branchpoint is an average property of the semiconductor. Ter-soff [8.26] calculated the branch-point energies ˚

pbp

of Si, Ge, and 13 of the III–V and II–VI com-pound semiconductors. He used a linearized augmentedplane-wave method and the local density approxima-tion. Such extensive computations may be avoided.Mönch [8.27] applied Baldereschi’s concept [8.28] ofmean-value k-points to calculate the branch-point en-ergies of zincblende-structure compound semiconduc-tors. He first demonstrated that the quasi-particle bandgaps of diamond, silicon, germanium, 3C-SiC, GaAs,and CdS at the mean-value k-point equal their averageor dielectric band gaps [8.29]

Wdg D „!pp"1 � 1

; (8.14)

where „!p is the plasmon energy of the bulk valenceelectrons. Mönch then used Tersoff’s ˚p

bp values, calcu-lated the energy dispersion of the topmost valence bandin the empirical tight-binding approximation (ETB),and plotted the resulting branch-point energies at themean-value k-point versus the widths of the dielec-tric band gaps Wdg. The linear least-squares fit to thedata of the zincblende-structure compound semicon-ductors [8.30]

˚pbp D 0:449Wdg � ŒWv.� /�Wv.kmv/�ETB (8.15)

indicates that the branch points of these semiconductorslie 5% below the middle of the energy gap at the mean-value k-point kmv. Table 8.1 displays the calculated p-type branch-point energies of the Group IV elementalsemiconductors, of SiC, of III–V and II–VI compoundsemiconductors and of some I–III–VI2 chalcopyrites.

Table 8.1 Optical dielectric constants, widths of the di-electric band gap, and branch-point energies of diamond-,zincblende, and chalcopyrite-structure semiconductors.(After [8.26, 29, 30])

Semiconductor "1

Wdg (eV) ˚pbp (eV)

C 5:70 14:40 1:77Si 11:90 5:04 0:36a

Ge 16:20 4:02 0:18a

3C-SiC 6:38 9:84 1:443C-AlN 4:84 11:92 2:97AlP 7:54 6:45 1:13AlAs 8:16 5:81 0:92AlSb 10:24 4:51 0:533C-GaN 5:80 10:80 2:37GaP 9:11 5:81 0:83GaAs 10:90 4:97 0:52GaSb 14:44 3:8 0:163C-InN – 6:48 1:51InP 9:61 5:04 0:86InAs 12:25 4:20 0:50InSb 15:68 3:33 0:22ZnS 5:14 8:12 2:05ZnSe 5:70 7:06 1:48ZnTe 7:28 5:55 1:00CdS 5:27 7:06 1:93CdSe 6:10 6:16 1:53CdTe 7:21 5:11 1:12CuGaS2 6:15 7:46 1:43b

CuInS2 6:3* 7:02 1:47b

CuAlSe2 6:3* 6:85 1:25b

CuGaSe2 7:3* 6:29 0:93b

CuInSe2 9:00 5:34 0:75b

CuGaTe2 8:0* 5:39 0:61b

CuInTe2 9:20 4:78 0:55b

AgGaSe2 6:80 5:96 1:09b

AgInSe2 7:20 5:60 1:11b

� "1 D n2, a [8.26], b [8.29]

A simple phenomenologicalmodel of Schottky con-tacts with a continuum of interface states and a constantdensity of states Dis across the semiconductor band gapyields the slope parameter [8.31, 32]

SX D AX1C e20

"i"0Disıis

� ; (8.16)

where "i is an interface dielectric constant. The pa-rameter AX depends on the electronegativity scalechosen and amounts to 0:86 eV=Miedema-unit and1:79 eV=Pauling-unit. For Dis!0, relation (8.16) yieldsSX!AX or, in other words, if no IFIGS were present atthe metal–semiconductor interfaces one would obtainthe Schottky–Mott rule. The extension ıis of the inter-face states may be approximated by their charge decay

Electronic Properties of Semiconductor Interfaces 8.3 Comparison of Experiment and Theory 183Part

A|8.3

length 1=2qis. Mönch [8.32] used theoretical Dmigs and

qmigs data for metal-induced gap states (MIGS), as the

IFIGS in Schottky contacts are traditionally called, andplotted the .e20="0/D

migs =.2q

migs / values versus the optical

susceptibility "1 �1. The linear least-squares fit to thedata points yielded [8.32]

AX

SX� 1 D 0:1."1 � 1/2 ; (8.17)

where the reasonable assumption "i � 3 was made.To a first approximation, the slope parameter DX

of heterostructure band offsets may be equated withthe slope parameter SX of Schottky contacts, since theIFIGS determine the intrinsic electric-dipole contribu-tions to both the valence-band offsets and the barrierheights.

In early Gedanken experiments, Schottky contactsand semiconductor heterostructures were assembledby gradually approaching the respective two solids in

vacuum [8.3, 33]. As long as a vacuum gap exists be-tween the two surfaces facing each other, the vacuumlevel Wvac is the appropriate reference and, for ex-ample, the work function Wvac �WF of the metal andthe electron affinity Wvac �Wc or the ionization en-ergy Wvac �Wv of the semiconductor may be used todescribe the charge distribution and the energy-bandalignment in such a metal–vacuum–semiconductor ar-ray. As the vacuum gap is closed, that is, an intimateSchottky contact is made, chemical bonds betweenmetal and semiconductor atoms will have formed at thenow intimate metal–semiconductor interface. Hence,the work function of the metal as well as the elec-tron affinity or the ionization energy of the semi-conductor are inappropriate reference properties, butinstead the electronegativities of the metal and thesemiconductor may be used to describe the electricdipole layer at Schottky contacts [8.34]. The samearguments also hold for semiconductor heterostruc-tures.

8.3 Comparison of Experiment and Theory

8.3.1 Barrier Heights of Schottky Contacts

Experimental barrier heights of intimate, abrupt, clean,and (above all) laterally homogeneous Schottky con-tacts on n-Si, n-GaAs, n-GaN, and SiO2, as an examplefor insulators, are plotted in Figs. 8.10 and 8.11 versusthe difference in the Miedema electronegativities of themetals and the semiconductors. Miedema’s electroneg-ativities [8.35] are preferred since they were derivedfrom properties of metal alloys and intermetallic com-pounds, while Pauling [8.8] considered covalent bondsin small molecules. The p- and n-type branch-pointenergies, ˚p

bp D Wbp �Wv.� / and ˚nbp D Wc �Wbp, re-

spectively, add up to the fundamental band-gap energyWg D Wc �Wv.� /. Hence, the barrier heights of n-typeSchottky contacts are

˚homBn D ˚n

bp C SX.Xm �Xs/ : (8.18)

The electronegativity of a compound is taken as the ge-ometric mean of the electronegativities of its constituentatoms.

First, the experimental data plotted in Figs. 8.10and 8.11 clearly confirm that the different experimentaltechniques, I=V, C=V, BEEM, IPEYS, and PES, yieldbarrier heights of laterally homogeneous Schottky con-tacts which agree within the margins of experimentalerror.

Second, the experimental Si, GaAs, and GaN dataare quantitatively explained by the branch-point en-ergies (8.15) and the slope parameters (8.17) of theIFIGS-and-electronegativity theory. As was alreadymentioned in Sect. 8.1.1, the stacking fault, whichis part of the interfacial Si(111)-.7� 7/i reconstruc-tion [8.15], causes an extrinsic electric dipole in addi-tion to the intrinsic IFIGS electric dipole. The latter oneis present irrespective of whether the interface struc-ture is reconstructed or .1� 1/i-unreconstructed. Theextrinsic stacking fault-induced electric dipole quanti-tatively explains the experimentally observed barrier-height lowering of 76˙ 2meV [8.10].

Third, the IFIGS line in Fig. 8.11a was drawnusing the branch-point energy calculated for cubic 3C-GaN since relation (8.15) was derived for zincblende-structure compounds only. However, the Schottky con-tacts were prepared on hexagonal wurtzite-structure2H-GaN. The good agreement between the experimen-tal data and the IFIGS line indicates that the p-typebranch-point energy seems to be rather insensitive to thespecific bulk lattice structure of the semiconductor. Thisconclusion is further justified by the barrier heights oflaterally homogeneous Schottky contacts on cubic 3C-SiC and its hexagonal polytypes 4H and 6H [8.13] aswell as by the experimentally observed band-edge dis-continuities of semiconductor heterostructures, whichwill be discussed in Sect. 8.3.2.

PartA|8.3


1.0

0.8

0.6

0.4–3 –2 –1 0

2 3 4 5

1

Schottky barrier height (eV)

Electronegativity difference Xm – XSi

Electronegativity(Miedema)

a)

1.0

0.9

1.1

0.8

0.7

0.6–3 –2 –1 0 1 2

2 3 4 5 6


Electronegativity difference Xm – XGaAs


b)

Metal/n-Si Metal/n-GaAsPt

Ag-(1×1)i

Al-(1×1)i

Pb-(1×1)i

Pb-(7×7)iAl-(7×7)iAg-(7×7)i

Na-(3×1)i

Na-(7×7)i

Cs-(7×7)i

Au

Ir

IFIGS theory IFIGS theory

TiMnSb

Cs

Ni

PtAu

PdAl

Fig. 8.10a,b Barrier heights of laterally homogeneous n-type silicon (a) and GaAs Schottky contacts (b) versus thedifference in the Miedema electronegativities of the metals and the semiconductors. The � and �, 4, Þ, and 5 symbolsdifferentiate the data from I=V , BEEM, IPEYS, and PES measurements, respectively. The dashed and the dash-dottedlines are the linear least-squares fits to the respective experimental data. The solid IFIGS lines are drawn with SX D0:101 eV=Miedema-unit and ˚

pbp D 0:36 eV for silicon (a) and with SX D 0:08 eV=Miedema-unit and ˚

pbp D 0:5 eV for

GaAs (b). (After [8.13])

1.5

1.0

0.5

0.0–4 –3 –2 –1 0

2 3 4 5 6

1


Electronegativity difference Xm – XGaN


a)

5

4

3

2–3 –2 –1 0

3 4 5 6


Electronegativity difference Xm – XSiO2


b)

Metal/n-GaN

Ti

Cs

Pb Cu

Co Ni

PtAg Mo

Au Pd

IFIGS theory

Metal/SiO2

TiMg

Cu

CrNi

PtAg Au

Pd

HfAl

W

Fig. 8.11a,b Barrier heights of laterally homogeneous n-GaN(0001) (a) and SiO2 Schottky contacts (b) versus the dif-ference in the Miedema electronegativities of the metals and the semiconductors. (a) The solid IFIGS line is drawnwith SX D 0:29 eV=Miedema-unit and ˚

pbp D 2:37 eV. (a,b) The �, �, 4, and 5 symbols differentiate the data from

I=V , C=V , IPEYS, and PES measurements. The dashed lines are the linear least-squares fits to the respective data.(After [8.13, 36])

8.3.2 Band Offsets of SemiconductorHeterostructures

In the bulk and at interfaces of sp3-coordinated semi-conductors, the chemical bonds are covalent. The

simplest semiconductor–semiconductor interfaces arelattice-matched heterostructures. However, if the bondlengths of the two semiconductors differ, then the in-terface will respond with tetragonal lattice distortions.Such pseudomorphic interfaces are under tensile or

Electronic Properties of Semiconductor Interfaces 8.3 Comparison of Experiment and Theory 185Part

A|8.3

compressive stress. If the strain energy becomes toolarge, then it is energetically more favorable to releasethe stress by the formation of misfit dislocations. Suchmetamorphic interfaces are almost relaxed.

In contrast to isovalent heterostructures, the chem-ical bonds at heterovalent interfaces require specialattention, since interfacial donor- and acceptor-typebonds may cause interfacial electric dipoles [8.37].No such extrinsic electric dipoles will exist normal tononpolar (110) interfaces. However, polar (001) inter-faces behave quite differently. Acceptor bonds or donorbonds normal to the interface would exist at abrupt het-erostructures. But, for reasons of charge neutrality, theyhave to be compensated by a corresponding density ofdonor bonds and acceptor bonds, respectively. This maybe achieved by an intermixing at the interface which, onthe other hand, causes extrinsic electric dipoles. Theircomponents normal to the interface will add an extrinsicelectric-dipole contribution to the valence-band offset.

The valence-band offsets at nonpolar heterostruc-tures of compound semiconductors should equal thedifference in the branch-point energies of the two semi-conductors in contact provided the intrinsic IFIGSelectric-dipole contribution can be neglected, see rela-tion (8.13). This assumption is justified for heterostruc-tures among the elemental Group IV semiconductorsGe and Si, SiC, and the III–V and II–VI compounds –with the nitrides and the oxides being excepted – be-cause the elements that constitute these semiconductorsare all placed in the middle of the Periodic Table sothat their electronegativities only differ slightly. Fig-ure 8.12a displays respective experimental results fordiamond- and zincblende-structure semiconductors asa function of the difference in the calculated branch-point energies given in Table 8.1. The dashed lineclearly demonstrates that the experimental data areexcellently explained by the theoretical branch-pointenergies or, in other words, by the IFIGS theory.

As an example of lattice-matched and isovalentheterostructures, Fig. 8.13 shows valence-band offsetsof Al1�xGaxAs/GaAs heterostructures as a function ofthe alloy composition x. The IFIGS branch-point en-ergies of the alloys were calculated assuming virtualcations [8.30] and were found to vary linearly as a func-tion of composition between the values of AlAs andGaAs. More refined first-principles calculations yieldedidentical results [8.38–40]. Figure 8.13 reveals that thetheoretical IFIGS valence-band offsets excellently fitthe experimental data.

Figure 8.12b displays valence-band offsets of meta-morphic heterostructures versus the difference in thebranch-point energies of the two semiconductors. Thedashed line indicates that the experimental results areagain excellently described by the theoretical IFIGS

2.0

1.5

1.0

0.5

0.0

0.0 0.5 1.0 1.5 2.0

2.0

1.5

1.0

0.5

0.0

0.0 0.5 1.0 1.5 2.0

a) Heterostructures: non-polarValence-band offset (eV)

Difference of branch-point energies (eV)

b) Heterostructures: metamorphicValence-band offset (eV)

Difference of branch-point energies (eV)

Ge/CdSGe/ZnSe

ZnSe/GaAs CdSe/ GaSb

GaAs/InAs

AlP/GaPAlAs/GaAs

Ge/GaAs

InAs/GaSb

ZnS/Ge2H-GaN/GaAs

2H-GaN/6H-SiC

2H-GaN/3C-SiC

2H-GaN/2H-AlN

AlSb/ZnTe

Si /Ge

ZnTe/CdTe

Fig. 8.12a,b Valence-band offsets at nonpolar (110)-oriented (a) and metamorphic semiconductor heterostruc-tures (b) versus the difference between the p-type branch-point energies of the semiconductors in contact. (Af-ter [8.13])

0.6

0.4

0.2

0.00.0 0.5 1.0

Composition x

Valence-band offset (eV)

IFIGS theory

Al1–xGaxAs/GaAs

Fig. 8.13 Valence-band offsets of lattice-matched and iso-valent heterostructures as a function of alloy composi-tion x. (After [8.13])

data. This is true not only for heterostructures betweencubic (C) zincblende- and hexagonal (H) wurtzite-

PartA|8.3


structure compounds but also for wurtzite-structureGroup III nitrides grown on both cubic 3C- and hexag-onal 6H-SiC substrates. These observations suggest thefollowing conclusions. First, all of the heterostructuresconsidered in Fig. 8.12b are only slightly (if at all)strained, although their lattice parameters differ by upto 19:8%. First-principles calculations [8.41] revealedthat misfit dislocations change the valence-band off-sets of metamorphic heterostructures by less than 0:1 eVonly. Second, the calculations of the IFIGS branch-pointenergies assumed zincblende-structure semiconductors.These values, on the other hand, reproduce the experi-mental valence-band offsets irrespective of whether thesemiconductors have zincblende, wurtzite, or, as in thecase of 6H-SiC, another hexagonal-polytype structure.These findings again support the conclusion drawn fromthe GaN Schottky barrier heights in the previous sectionthat the IFIGS branch-point energies are rather insensi-tive to the specific semiconductor bulk lattice structure.

Quite generally, the contribution of the IFIGSelectric-dipole term SX.Xsl �Xsr/ to the valence-bandoffset Wv of heterostructures may not be neglected.A simple rearrangement of terms in relation (8.13) gives

Wv � SX.Xsr �Xsl/ D ˚pbpr �˚

pbpl : (8.19)

For heterostructres of one and the same semiconductor,the valence-band offsets less the IFIGS-related electric-dipole contributions thus vary as the p-type branch-point energies of the respective other semiconductors.Figure 8.14 displays experimental valence-band offsetsof SiO2 heterostructures minus the respective electric-dipole contributions as a function of the calculatedbranch-point energies of the respective other semicon-ductors [8.26, 30] (Table 8.1); the SX value of SiO2 wasadopted from Fig. 8.11b. The linear least-squares fit hasa slope parameter of 0:94˙ 0:07 which value is closeto 1 as is to be expected from (8.19), and its intercepton the ordinate gives the empirical p-type branch-pointenergy of SiO2 as 3:73˙ 0:07 eV.

Figures 8.15 and 8.16 display experimental Wv �SX.Xsemi �XSi,Ge,GaN/ data of Si, Ge, and GaN het-erostructures as a function of the branch-point energiesof the other semiconductors and insulators involved.For the semiconductors, the calculated values [8.26,30] were taken again while for the insulators empiri-cal values [8.42–44] were considered. Again, the slopeparameters of the linear least-squares fits (0:97˙ 0:03,0:90˙ 0:04, and 0:87˙ 0:04) are close to 1, the valueexpected from (8.19). The empirical p-type branch-point energies result as 0:30˙ 0:09 eV for Si, 2:34˙0:4 eV for GaN, and 0:08˙ 0:10 eV for Ge. Within themargins of experimental error, these empirical valuesexcellently agree with the calculated ones (Table 8.1).

–2

–1

0

–3

–430 1 2

∆Wv – SX(Xsemi – XSiO2) (eV)

Branch-point energy Φpbp(semi) (eV)

GaNZnS

SiC

CdTeSi

SiO2 heterostructures

Fig. 8.14 Experimental valence-band offsets of SiO2 het-erostructures minus the respective IFIGS electric-dipolecontributions as a function of the calculated p-type branch-point energies of the respective other semiconductors. Thedashed line is the linear least-squares fit to the data points.(After [8.42])

2

3

4

1

0

2

3

4

1

0

430 1 2

∆Wv – SX(Xsemi – XSi) (eV)

SX(Xsemi – XSi)(eV)


ZnO

SiC

Si3N4

HfO2

Al2O3

Y2O3

ZrO2

SrTiO3

SiO2

IFIGS theory

InN

GaAsGe

InAs

Si heterostructures

Fig. 8.15 Experimental valence-band offsets of Si het-erostructures minus the respective IFIGS electric-dipolecontributions (�) and the IFIGS electric-dipole contri-butions (�) as a function of calculated and empiricalp-type branch-point energies of the respective other semi-conductors and insulators, respectively. The dashed anddash-dotted lines are the linear least-squares fits to the datapoints. (After [8.43])

Figure 8.15 also displays some of the IFIGSelectric-dipole contributions SX.Xsemi �XSi/ in Si het-erostructures. The example of SiO2/Si heterostructuresdemonstrates that this intrinsic dipole term measures1:3 eV and this large value thus amounts to approxi-mately 30% of the total valence-band offset.

Electronic Properties of Semiconductor Interfaces 8.4 Modifications of Schottky Contacts 187Part

A|8.4

–1

0

1

–23 40 1 2

∆Wv – SX(Xsemi – XGaN) (eV)


2

4

0

3 40 1 2

∆Wv – SX(Xsemi – XGe) (eV)


a) b)

SiO2

Al2O3

In0.28Ga0.72N

In0.17Al0.83N

Al0.3Ga0.7N, Al0.17Ga0.83N

HfO2

TiO2

SiCGaAs

Si3N4

IFIGS theory

IFIGS theory

InN

C

MgOZnO

HfO2

TiO2

GaAs

MgOZnO

ZnSZnSe

AIN

InP

Si InAs

GaPIn0.53Ga0.47As

Al0.52In0.48PCdTe

ZrO2 Al2O3

GaN heterostructures Ge heterostructures

Fig. 8.16a,b Experimental valence-band offsets of GaN (a) and Ge heterostructures (b) minus the respective IFIGSelectric-dipole contributions as a function of the calculated and empirical p-type branch-point energies of the respectiveother semiconductors and insulators, respectively. The dashed lines are the linear least-squares fits to the data points.(After [8.43])

Table 8.2 Fundamental band gaps Wg and empirical branch-point energies ˚nbp and ˚

pbp as obtained from barrier heights

of Schottky contacts and valence-band offsets of heterostructures, respectively [8.13, 36, 42–46]

Semiconductor Wg (eV) ˚nbp (eV) ˚

pbp (eV) ˚n

bp C ˚pbp (eV)

Si 1:12 0:80˙ 0:01 0:30˙ 0:09 1:10Ge 0:66 0:59˙ 0:01 0:08˙ 0:10 0:67GaN 3:39 1:12˙ 0:03 2:34˙ 0:09 3:46GaAs 1:42 0:90˙ 0:01 0:68˙ 0:11 1:58InP 1:34 0:50˙ 0:02 0:86˙ 0:11 1:36SiO2 8:7�8:9 4:95˙ 0:19 3:73˙ 0:07 8:68TiO2 3:3�3:5 1:13 .˙0/ 2:34˙ 0:36 3:47HfO2 5:7�6:0 4:01˙ 0:19 2:27˙ 0:14 6:28Al2O3 6:7�7:0 4:38˙ 0:34 2:98˙ 0:26 7:36Ga2O3 4.9 1:34˙ 0:08 3:57˙ 0:50 4.91

As was already mentioned, the p- and n-typebranch-point energies, ˚p

bp D Wbp �Wv.� / and ˚nbp D

Wc�Wbp, respectively, add up to the fundamental band-gap energyWg D Wc �Wv.� /. Table 8.2 shows empir-ical ˚n

bp and ˚pbp values that were obtained from ex-

perimental barrier heights of n-type Schottky contactsand valence-band offsets of heterostructures, respec-tively; see, for example, Figs. 8.10, 8.11, 8.14–8.16,8.19. Within the margins of experimental error, the em-

pirical p- and n-type branch-point energies of thesesemiconductors and insulators indeed add up to thewidths of their fundamental band gaps. These findingsagain strongly support the IFIGS-and-electronegativityconcept of the band-structure alignment at semiconduc-tor interfaces. The empirical ˚n

bp values are of specialimportance since they were evaluated from experimen-tal barrier heights with no other input than the metal andsemiconductor electronegativities.

8.4 Modifications of Schottky Contacts

8.4.1 Nonalloyed Ohmic Contactsor MUTIS Schottky Contacts

Ideal metal–semiconductor or Schottky contacts aregenerally rectifying while genuine low-resistance orohmic contacts are obtained with p-type Ge and GaSb

and n-type InN, InAs, and InSb only because theirIFIGS branch points are close to their valence-bandmaxima and above their conduction-band minima, re-spectively (Table 8.1). Recently, Connelly et al. [8.47,48] studied a new path towards Ohmic contacts. Theyavoided alloying and demonstrated that the resistance of

PartA|8.4


10–3

10–2

10–1

100

101

43210

Contact resistance ratio

Si3N4 thickness (nm)

Fig. 8.17 Contact resistance ratio of Al/Si3N4/n-GaAsSchottky contacts versus the thickness of the Si3N4 inter-layer. (After [8.49])

Si Schottky contacts is considerably lowered by ultra-thin Si3N4 layers placed between the metal and silicon.As a typical example, Fig. 8.17 displays the contactresistance of Al/Si3N4/n-GaAs Schottky contacts nor-malized to the value of the intimate Al/n-GaAs contactin dependence on the insulator thickness [8.49]. Theinitial dramatic decrease of the contact resistance isaccompanied by a gradual reduction of the Schottkybarrier heights to a then constant value while the sub-sequent rise is easily attributed to the increasing tunnelresistance through the then thicker insulator interlayers.

Figure 8.18 schematically shows the energy-banddiagram of ideal metal-ultrathin insulator–semi-conductor or MUTIS structures resulting from theIFIGS-and-electronegativity concept. It is assumed thatthe electronegativity of the insulator is intermediatebetween the values of the metal and the semiconductor.In order to avoid that the IFIGS of the metal–insulatorand the insulator–semiconductor interface overlap thethickness of the insulator has to be larger than four tofive times the decay length at the IFIGS branch point ofthe insulator. Theoretical calculations found these dacaylengths to range between 0:09 and 0:28 nm [8.50]. Thepronounced minimum value of the contact resistanceratio displayed in Fig. 8.17 is compatible with thisestimate. Considering (8.12) and (8.13), one obtains

WF �W iv D ˚

pibp � SiX.Xm �Xi/ (8.20)

at the metal–insulator interface and

WF �W iv D Wv CWs

g �˚ sBn

D ˚pibp �˚

psbp C SiX.Xs �Xi/CWs

g �˚ sBn

(8.21)

Metal Insulator Semiconductor

∆Wv

W sv

W iv

W sbp

WFWF

W sc

W ic

ΦsBn

Φ pi

Φ ps

bp

bp

IFIGSdipoles

Energy

Position

Fig. 8.18 Band-structure lineup at metal-ultrathin insu-lator–semiconductor (MUTIS) structures (schematically)with the assumption Xm < Xi > Xs. On the semiconductorside the extension of the band-bending regime is not drawnto scale. (After [8.50])

at the insulator–semiconductor interface where the sub-and superscripts m, i, and s indicate metals, insula-tors, and semiconductors, respectively. Ws

g designatesthe width of the fundamental band gap of the semicon-ductor. A rearrangement of (8.20) and (8.21) then givesthe effective n-type barrier heights of the MUTIS struc-tures as

˚ sBn D Ws

g �˚psbp C SiX.Xm �Xs/

D ˚nsbp C SiX.Xm �Xs/ (8.22)

The effective n-type barrier height of an ideal n-typeMUTIS structure is thus determined by the n-typebranch-point energy ˚ns

bp of the semiconductor and theslope parameter SiX of the insulator. The optical di-electric constant "1 of Si3N4, and the same holds forother insulators such as Al2O3, Ge3N4, and MgO, isconsiderably smaller than the respective values of semi-conductors as, for example, Ge, Si, and GaAs and,hence, (8.17) gives SiX > SsX for the slope parameters.The insertion of the ultrathin insulators in MUTIS con-tacts thus alleviates the pinning of the Fermi levelin comparison with the respective intimate MS con-tacts. Furthermore, (8.22) reveals that Ohmic ratherthan rectifying n-type MUTIS contacts will be obtainedprovided metals are chosen such that their electroneg-ativities are sufficiently smaller than the values of therespective semiconductors.

Experimental barrier heights of Si3N4/n-Si and in-timate n-Si Schottky contacts are plotted versus theelectronegativity difference Xm �XSi in Fig. 8.19. The

Electronic Properties of Semiconductor Interfaces 8.4 Modifications of Schottky Contacts 189Part

A|8.4

1.2

0.8

0.6

1.0

0.4

0.2

0.0–2 –1 0

3 4 5 6

1


Electronegativity difference Xm – XSi


Ti

Ti

Pb

Al

Al

Er

Na

Pt

Ag

Mg

Au

Ir

IFIGS theory

Intimate contacts

With Si3N4 layer

Fig. 8.19 Schottky barrier heights of intimate metal/n-Si(from Fig. 8.10a) and metal/Si3N4/n-Si versus the differ-ence Xm �XSi of the metal and the Si electronegativities.The full and the dashed lines are the predictions of theIFIGS theory and the linear-least squares fits to the exper-imental data, respectively. (After [8.50])

thickness of the Si3N4 layers measured approximately1 nm and is thus sufficiently larger than the esti-mated decay length of the IFIGS at their branch point.Within the margins of experimental error, the exper-imental barrier heights of the metal/Si3N4/n-Si junc-tions clearly confirm prediction (8.22) of the IFIGS-and-electronegativity concept in that the MUTIS bar-

1.0

0.8

0.6

0.4

0.2

0.0

2.5

2.0

1.5

1.0

0.5

0.0–2 –1 0 1


Electronegativity difference Xm – XSi (Miedema unit) Electronegativity difference Xm – XC (Miedema unit)

a)

–3 –2 –1 0

Effective barrier height (eV)b)

Pb

Pb

Mg

Mg

Mg

Er

Hf

Sn

Ti

IFIGS theory

IFIGS theory

Intimate p-Si

0.30 eV

0.16 eV

(111)

(001)

Al

Al

Au

Au

FeNi

InTa Zn

Cu W

Pt

Clean interfaces

H-doped interfaces

Intimate p-diamond

Fig. 8.20a,b Barrier heights of p-Si (a) and p-diamond Schottky contacts (b) with and without H-interlayers. The fulland the dashed lines are the predictions of the IFIGS theory and the linear least-squares fits to the experimental data,respectively. (After [8.50])

rier heights are determined by the branch-point en-ergy of the semiconductor and the slope parameter ofthe insulator. This observation most directly demon-strates the alleviation of the Fermi-level pinning inMUTIS structures in comparison with intimate MS in-terfaces.

8.4.2 Atomic Interlayers

The barrier heights of metal–semiconductor contactsmay also be modified by atomic interlayers. Figure 8.20displays barrier heights of p-type silicon and diamondSchottky contacts without and with hydrogen inter-layers [8.48, 50, 51]. Irrespective of the metals used,the H-induced modifications amount to � 1:4 eV forp-diamond(001) but to C0:3 eV for p-Si(111) and toC0:16 eV for p-Si(001) Schottky contacts. In contrastto the insertion of ultrathin insulators, the H-interlayersdo not alter the slope parameters SX.

The metal-independent H-induced modificationsof the Schottky barrier heights were explained bythe partial ionic character of the covalent bonds be-tween the H atoms and the interface atoms of thesubstrates [8.52]. The electronegativity of hydrogenranges between the values of silicon and carbon, that is,XSi < XH < XC [8.8]. Hence, the partial ionic characterof covalent Si–H and C–H bonds differs in sign, andH�q-SiCq but HCq-C�q bonds will exist at sili-con and diamond interfaces, respectively. The oppositedirections of the H-induced interface dipoles easilyexplain why the H-induced variations of the barrier

PartA|8.6


height exhibit different signs with p-Si and p-diamondSchottky contacts.

These early conclusions were excellently confirmedby the recent observation that F-interlayers reduce thebarrier heights of n-Ge Schottky contacts and do notchange the slope parameter SX [8.53]. The electroneg-ativity of F is larger than the one of Ge so thatF�q-GeCq dipoles are to be expected at F-dopedGe interfaces. These dipoles will reduce the barrier

heights of metal/F:n-Ge Schottky contacts while, aswith H:p-Si contacts, an increase would be observedwith metal/F:p-Ge interfaces. The reduction of the bar-rier height observed with Fe/S:n-Ge contacts [8.54] iseasily explained along the same lines.

The experimental data presented in Fig. 8.20and [8.53] clearly demonstrate that atomic interlayers inSchottky contacts cause no depinning of the Fermi leveland no alleviation of the Fermi-level pinning either.

8.5 Graphene Schottky ContactsGraphene (Gr) is a single layer of sp2-bonded car-bon atoms arranged in a hexagonal crystal lattice.The remaining 2pz orbitals are perpendicular to thegraphene plane and form contiguous � and �� bandsso that graphene may be described as a zero-overlapsemimetal. As the conventional metal-semiconductorcontacts discussed in the preceding chapters graphene-semiconductor contacts indeed exhibit rectifying prop-erties. However, conventional and Gr Schottky contactsdiffer in that the bonds between the metal and thesemiconductor atoms are covalent while the bondsbetween graphene and semiconductor substrates areof van der Waals type. Mönch [8.55] verified thatthe experimental barrier heights of intimate Gr con-tacts on conventional n-type semiconductors as wellas on layered n-MoS2 agree with the values pre-dicted by (8.17) and (8.18) but do not follow the

Schottky–Mott rule. Hence, electric dipoles exist atGr-semiconductor interfaces because graphene has alarger electronegativity than the semiconductors, withSiO2 being the only exemption. The respective elec-tronic charge transfer from the semiconductors towardsthe more electronegative Gr layer was also confirmedby theoretical calculations (see Refs. cited in [8.55]).The barrier heights of graphene Schottky contacts arethus explained by the � and �� wave-function tailsof the graphene across the interface in the energyrange where the �–�� bands of the graphene overlapthe band gap of the semiconductor. The IFIGS-and-electronegativity concept thus also explains the bandstructure lineup at graphene-semiconductor interfacesrather than the Schottky–Mott rule as assumed in al-most all the articles reporting barrier heights of suchcontacts.

8.6 Final Remarks

The local density approximation to density functionaltheory (LDA-DFT) is the most powerful and widelyused tool in theoretical studies of the ground-stateproperties of solids. However, excitation energies suchas the width of the energy gaps between the valenceand conduction bands of semiconductors cannot becorrectly obtained from such calculations. The funda-mental band gaps of the elemental semiconductors C,Si, and Ge as well as of the III–V and II–VI compoundsare notoriously underestimated by 25�50%. However,it became possible to compute quasi-particle energiesand band gaps of semiconductors from first princi-ples using the so-called GW approximation for theelectron self-energy [8.56, 57]. The resulting band-gapenergies agree to within 0:1�0:3 eV with experimentalvalues.

For some specific metal–semiconductor contacts,the band-structure lineup was also studied by state-of-

the-art ab-initio LDA-DFT calculations. The resultingLDA-DFT barrier heights were then subjected to a-posteriori corrections, which consider quasi-particleeffects and, if necessary, spin–orbit interactions andsemicore-orbital effects. However, comparison of thetheoretical results with experimental data gives an in-consistent picture. The mean values of the barrierheights of Al- and Zn/p-ZnSe contacts, which werecalculated for different interface configurations usingab-initio LDA-DF theory and a-posteriori spin–orbitand quasi-particle corrections [8.58, 59], agree withthe experimental data to within the margins of ex-perimental error. The same conclusion was reachedfor Al/AlxGa1�xAs Schottky contacts [8.60]. However,ab-initio LDA-DFT barrier heights of Al-, Ag-, andAu/p-GaN contacts [8.61, 62], as well as of Al– andTi/3C-SiC(001) interfaces [8.63, 64], strongly deviatefrom the experimental results.

Electronic Properties of Semiconductor Interfaces References 191Part

A|8

As already mentioned, ab-initio LDF-DFT valence-band offsets of heterostructures [8.39–41] reproducethe experimental results well. The same holds formean values of LDF-DFT valence-band offsets com-puted for different interface configurations of GaN- andAlN/SiC-heterostructures [8.65–69].

The main difficulty, which the otherwise extremelysuccessful ab-initio LDF-DFT calculations encounterwhen describing semiconductor interfaces, is not theprecise exchange-correlation potential, which may beestimated in the GW approximation, but their remark-able sensitivity to the geometrical and compositionalstructure right at the interface. This aspect is more

serious at metal–semiconductor interfaces than at het-erostructures between two sp3-bonded semiconductors.The more conceptual IFIGS-and-electronegativity the-ory, on the other hand, quantitatively explains notonly the barrier heights of ideal Schottky contactsbut also the valence-band offsets of semiconduc-tor heterostructures. Here again, the Schottky con-tacts are the more important case, since their zero-charge-transfer barrier heights equal the branch-pointenergies of the semiconductors, while the valence-band offsets are determined by the differences in thebranch-point energies of the semiconductors in con-tact.

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