Si K-edge and Ge K-edge X-ray absorption spectroscopy of the SiGe interface in [(Si)m(Ge)n]p atomic layer superlattices

Surface Science 291 (1993) 349-369 North-Holland

Si K-edge and Ge K-edge X-ray adsorption spectroscopy of the Si-Ge interface in [(Si),( Ge) Jp atomic layer superlattices A.P. Hitchcock,

T. Tyliszczak,

P. Aebi ’

I~ti~te for ~ute~~~ Research and Ontario Centre for careen

J.Z. Xiong, T.K. Sham, KM.

Baines,

Research, ~cMa~ter ~n~ver~~~,Hamilton, Canada

K.A. Mueller

Lkpartment of Chemistry, Uniuersity of We.stem Ontario, London, Ontario~ Canada

X.H. Feng, J.M. Chen 2, B.X. Yang 3 CSRF, SRC, University of Wsconsin-Madison, Stoughton, WJ USA

Z.H. Lu, J.-M. Baribeau

and T.E. Jackman

Institute for Microstructural Sciences, National Research Council, Ottawa, Canada Received 13 November 1992; accepted for publication 2 March 1993

The sensitivity of X-ray absorption near edge (XANES) spectra to the structure around the core excited atom has been explored by comparisons of the Si K-edge and Ge K-edge spectra of SiMe,, Ge(SiMe,),, Si(GeMe&, Si(SiMes),, Ge(Me), and Ge,(MeI, molecular compounds (Me = methyl); single crystal and amorphous Si; single crystal Ge; single crystal Si, _xGe, alloys, and [(Si),(Ge)J, atomic layer superlattices grown by molecular beam epitaxy. Systematic changes with changing en~ronment are detected. The spectral trends as well as comparison with spherical wave multiple scattering calculations of variable size z(Si), and SitGel, clusters (4 < n < 1901, indicate that many aspects of the near edge (O-50 eV) spectral features in the semiconductors are determined by structure far beyond the first coordination shell and that there are strong multiple scattering contributions. Two maxima separated by 0.80(3) eV are found as the lowest energy features in the Si K-edge spectrum of crystalline Si. These are attributed to 1s + 3p conduction band (CB) excitations. Even larger splittings are observed in the corresponding 1s -+ CB structure in Ge-rich Si,_,Ge, alloys and the atomic layer superlattice samples. The CB splitting varies systematically with the superlattice structure. The utility of the various components of the XANES signal for characterizing the Si-Ge interface in [(Si),(Ge),], superlattice samples is discussed.

1.Int~uction There is currently considerable development of advanced Si-Ge

interest in the semiconductor

i Present address: Institut de Physique, UniversitB de Fribourg, Fribourg, Switzerland. 2 Present address: Synchrotron Radiation Research Centre, Hsinchu, 30077 Taiwan, ROC. 3 Present address: CARS, Universi~ of Chicago, Chicago, IL, USA. Elsevier Science Publishers B.V.

materials with novel electrical and optoelectronic properties for device purposes [1,2]. Many of these devices require the preparation by molecular beam epitaxy or other growth techniques of single crystal multilayer materials with well-defined interfaces between pure or enriched Si and Ge layers. The quality of such structures is very dependent on the growth conditions employed 131. In order to investigate this, as well as to be able to follow the stability of such interfaces through subsequent annealing or other processing steps, it

350

A.P. Hitchcock et al. / Si K-edge and Ge K-edge X-ray absorption spectroscopy

is important to have techniques which can provide information about the local structure on an atomic scale. Over the past few years extended X-ray absorption fine structure (EXAFS) at the Ge K-edge has been used for this purpose [4-121. Recently we have been attempting to combine Ge K-edge EXAFS with Si K-edge EXAFS measured on the same sample in order to obtain a more accurate structural analysis of the Si-Ge interface in [(Si),(Ge),], atomic layer superlattice (ALS) samples. In the course of this work we have noted that there are systematic changes in the Si K near edge spectra (XANES) with the composition and structure of the ALS samples. In order to better understand these observations we have investigated the Si K near edge and Ge K near edge spectra of a number of molecular complexes which have a well-defined local environment of a Si or Ge atom, along with the spectra of single crystal Si, Ge and Si,Ge,_, alloys. This combination of samples provides a very striking example of the evolution of XANES spectra as the complexity of the local surroundings of the core excited atom increases from that of a weakly perturbed atom; through molecular species with one and two shells of well-defined backscattering neighbor atoms; to crystalline semiconductor solids, where there is effectively an infinite range of well-defined coordination shells. There have been relatively few materials whose Si K-edge or Ge K-edge spectra have been reported. The spectrum of pure Si (both crystalline and amorphous) has been studied extensively [13-191. The Si K-edge spectra of a number of molecular complexes have been reported [20-221. The study by Bouldin et al. [23] of GeH,, GeH,Cl and GeCl,, which identified the contribution of triangular Ge-Cl-Cl-Ge multiple scattering paths in GeCl,, is one of the few Ge K-edge spectral investigations of molecules. The work which approaches most closely to the present study is the very recent report by Woicik and Pianetta [24] of Ge K- and Si K-edge studies of single crystal Si, Ge and Si,Ge,_, alloys. The present results are in generally good agreement with those reported in the literature although there are some quantitative differences, which are discussed.

Generally, spectral features close to the onset of core excitation are described within an electronic structure model in terms of dipole excitations to unoccupied molecular orbitals (MOs) for molecules, or bands in the density of states (DOS) for solids. In particular, the K-edge spectra of solids are closely related to the partial density of unoccupied states of p-character [151, although modifications in energy and relative intensity may occur because of core hole relaxation effects. At higher energies, greater than about 10 eV above threshold, the most common description of X-ray absorption is a scattering picture which includes both single and multiple scattering paths [25,26]. Long range multiple scattering is particularly important in Si [13,14,17,19] and other diamond lattice semiconductors [15,27] because of their open framework structure. The relationships among the models and their applicability to different aspects of the XANES structure is a theme of this work. Experimental details are presented in section 2. Sections 3.1 and 3.2 present the Si K-edge and Ge K-edge spectra and their interpretation within electronic structure (MO, DOS) models. The Si K-edge spectra are some of the first results from a newly commissioned soft X-ray beam line [28]. The capabilities of this system (high resolution and excellent beam stability) have enabled acquisition of very high quality Si K-edge spectra. Section 3.3 describes multiple scattering calculations and evaluates their accuracy in reproducing various aspects of the Si K and Ge K XANES spectra. Section 3.4 discusses possible analytical applications of Si K-edge XANES for characterization of the geometric and electronic structure of the Si-Ge interface in Si-Ge superlattice structures.

2. Experimental The Si K-edge spectra were recorded using the Ontario Center for Materials Research-Canadian Synchrotron Radiation Facility (OCMR-CSRF) double crystal beam line 1281on the Aladdin ring at the Synchrotron Radiation Centre operated by the University of Wisconsin-Madison. The

A.P. Hitchcock et al. / Si K-edge and Ge K-edge X-ray absorption spectroscopy

351

nel plate. Since occasionally there are small energy shifts associated with changes in the position of the electron beam in the Aladdin storage ring, the energy scale was calibrated regularly by recording the c-Si (c~stalline Si) spectrum. The inflection point of the absorption edge of c-Si (determined by the peak in the first derivative)

monochromator was equipped with InSb crystals and has a resolution of 0.8 eV at the Si K-edge. The Si K-edge spectra of the single crystal semiconductor materials were recorded with total electron yield (TEY) detection, either by measuring the sample current directly or by measuring the ejected electron current with a biased chan-

Table 1 Source, sample preparation and detection technique used for samples studied Model complexes

Species

Source

Prep.

Edge

Phase

Detection mode

Si(Me).+ Si(SiMe,), SitGeMe,), Ge(SiMes), Ge(SiMe,),

Petrarch Systems Synthesis ‘) Synthesis a) Synthesis a) Synthesis a1

Si K Si K Si K Si K GeK

gas gas gas gas sol

Ion~at~on yield Ionization yield Ionization yield Ionization yield Thin film TEY

GetMel,

Toronto Res. Co. Synthesis a) Virginia Semiconductor Inc. IMS, NRC (prep. in situ) IMS, NRC MBE b, MBE

PVW PWJ P=P Pvan Thin film evap. from acetone soln. None None Oxide etch ‘)

GeK Ge K Si K

liq liq sol

Transmission Transmission Transmission

Oxide etch ‘) In situ evap. None None Oxide etch ‘)

Si K Si K GeK Ge K Si K

sol sol sol sol sol

Sampie current TEY Sample current TEY TEY (rotation) TEY (rotation) Sample current TEY

Ge,(Me& c-Si 2 pm wafer c-Si 1 mm wafer a-Si 1000 A/Ag c-Ge Si,Ge, alloys

ttSi),(GeI,l,

atomic rzlyersuperlattices

Code Grown on Ge(lQQ) 7.51

752 754

Grown on SifiQO) 674 698 700 867 1016

mtm,) d,

n(n,)

d,

P

(m - 11-l

Sample preparation and spectral acquisition Prior to Si K-edge measurements using channelplate TEY detection the samples were etched to remove oxides ‘). The Ge K-edge spectra were measuring using TEY (rotation) on as-prepared samples.

4.2(4)

8.2(8)

24

0.31

2.3(2) 1.9(2)

12.5(12) 6.5(6)

48 40

0.77 1.11

9.3(4) 6.6(6) 8.0(8) 20.002) 12.102)

3.7(2) 2.0(2) 2.2(2) 6.6(S) 2.2(2)

24 48 100 8 50

0.12 0.18 0.14 0.052 0.091

(As above)

a) Prepared for this study as described in the test. b, Molecular beam epitaxy (Institute for Microstructural Sciences, NRC, Ottawa). ‘) HF (1MI for 5 s followed by distilled water rinse was used to remove Si oxides. NaOCI (commercial bleach solution) for 5 s followed by a distilled water rinse was used to remove Ge oxides, where appropriate. For the ALS and alloy samples both etch procedures were required to remove Si oxide signals in the Si K-edge spectra. d, The m, n values are those measured by X-ray diffraction [34,35], while the ma, no values are the target values.

352

A.P. Hitchcock et al. / Si K-edge and Ge K-edge X-ray absorption spectroscopy

has been set to 1839.2 eV. This value is derived independently from a careful calibration of the monochromator energy scale against the main resonances in gaseous SF, (2486.0 eV>, CH,Cl (2823.4 eV) and Ar (3203.5 eV>, all of which are well accepted calibration features. This value for the inflection point of the Si K-edge spectrum of c-Si agrees with that recommended in tabulated summaries of elemental absorption threshold energies 1291and that reported by some other investigators 1183. However, it is almost 2 eV lower than that reported by Woicik and Pianetta [24]. This discrepancy indicates there is still some uncertainty in absolute spectral energies at the Si K-edge. Based on the stability of the monochromator energy scale, the energy scales of the Si K-edge of different species are accurate relative to each other within 0.2 eV. The Si K-edge spectra of the molecular species were obtained in the gas phase with detection of an ionization current. For Ge(SiMe,), the same result was obtained when the total electron yield (sample current) was recorded from the solid sample deposited as a powder on a conducting substrate. The spectrum of c-Si was measured in transmission, using a 2 pm thick single crystal wafer with a (001) orientation (Virginia Semiconductor Inc.) (fig. 11, and in total electron yield (TEY), using a 1 mm thick single crystal Si wafer (fig. 2). The TEY and transmission spectra of c-Si were found to be essentially identical. Details of the source, preparation and detection procedures for all samples are summarized in table 1. The Ge K-edge spectra were recorded at the Cornell High Energy Synchrotron Radiation Source (CHESS) operating at 5.2 GeV. At X-ray energies around the Ge K-edge (11.1 keV), energy-dispersed diffraction from single crystals causes artifacts. In order to suppress these artifacts the total electron yield spectra have been recorded using a He ionization detector with sample rotation 1301.This ionization detector was used to record the spectrum of Ge(SiMe), in the form of a thin film deposited by evaporation from an acetone solution. The spectra of the liquid GeMe, and Ge,Me, samples were recorded using the conventional transmission technique with a thin (< 1 mm path length) liquid cell. Calibra-

tion of the energy scales ( f 0.2 eV) of the spectra of the molecular complexes was achieved by simultaneously recording the spectrum of Ge powder and setting the inflection point of its absorption edge to 11104 eV [29]. Tetramethylgermane (GeMe,) and tetramethylsilane (SiMe,) were used as received from the Toronto Research Co. and Petrarch Systems Inc. Tetrakis(trimethylsilyl)silane [Si(SiMe,),] [31] and tetrakis(trimethylsilyl)germane [Ge(SiMe,),] [32] were synthesized according to published procedures. Tetrakis(trimethylgermyl)silane [Si(GeMe,),] was synthesized from silicon tetrachloride, trimethylgermyl chloride and lithium in diethyl ether/hexamethylphosphoramide in 19% yield 1331. Hexamethyldigermane [Ge,(Me),] was obtained as a by-product of this reaction. All synthesized compounds were fully characterized by nmr and mass spectrometry, as outlined in the relevant publications 131-331. Their purity is estimated to be > 95% based on ‘H nmr spectroscopy. Ano amorphous Si (a-Si> film approximately 1000 A thick was prepared by in situ evaporation onto a clean Ag substrate at room temperature. The epitaxial atomic layer superlattice (ALS) and single crystal alloy samples were grown in a VG Semicon V80 MBE system on Czochralski Si(100) or Ge(100) wafers [341. Prior to alloy or superlattice growth a thick epitaxial Si or Ge buffer layer was grown to ensure identical initial conditions. Growth procedures have been described in detail elsewhere [341. X-ray diffraction [35], Raman and cross-section transmission electron microscopy measurements have established the Ge and Si concentrations and nominal layer thicknesses [3,341. The probing depth for total electron yield detection [36] at the Si K-edge is bias dependent, N 50 A in this case. The thickness of the superlattice0 in the [(Si),(Ge),], ALS samples (100 to 1000 A depending on the values of m, n, p - see table 1) was such that the Si K-edge spectrum of an ALS grown on a Si substrate could be recorded with negligible contribution from the underlying Si substrate. This was not the case at the Ge K-edge, whzre the depth sensitivity is greater than 2000 A and thus only ALS samples grown on Si substrates could be measured. When mak-

353

A.P. Hitchcock et al. / Si K-edge and Ge K-edge X-ray absorption spectroscopy

ing Si K-edge measurements it was impoortant to remove any Si or Ge cap (typically 50 A in the as-prepared materials) as well as any surface o%ide, since the presence of native oxide (of N 10 A thickness) caused significant changes in the spectrum. The cap was removed by controlled anodic oxidation followed by standard selective etch procedures for Si and Ge oxides.

1’“‘I’“‘I”“I”“I”“I” A

53-K

3. Results and discussion 3.1. Si K-edge studies

Fig. 1 presents the Si K-edge spectra of four molecular species (Si(Me),, Ge(SiMe,),, Si(SiMe,),) and c-Si. Of these Si(GeMe,),, molecular spectra, only that of SiMe, has been reported previously [20,21]. The present result for SiMe, is in good agreement with those published. A linear background has been subtracted from the as-recorded spectra and the average continuum intensity at 1860 eV has been set to a constant value (i.e. the spectra have a normalized edge jump). The energies of the absorption threshold (defined as the knee at the onset of the Si K-edge signal) and the first one or two peaks are summarized in table 2. Each molecular spectrum exhibits a prominent edge resonance at the absorption threshold which we associate with states corresponding to Si 1s promotion to cr* orbitals of appreciable Si 3p character. Similar edge resonances have been reported in the Si K-edge spectra of Six,, X = Cl, F, CH, [21]; SiMe,Cl,_, (x = O-4) [22]; and in the Ge K-edge spectra of GeCI, and GeH,Cl 1231. In the latter series of molecules, the intensity and position of the edge resonances depend on the number of non-hydrogen first shell neighbors. The systematics of the intensity and position of the edge resonances are consistent with an interpretation in terms of 1s + a*(A-B) transitions associated with the presence of A-B bonds (i.e. Si-C, Si-Si, Si-Ge (this work); Si-C, Si-Cl [22]; or Ge-Cl [23]). Thus the peak at 1841.5 eV observed in all species containing Si-C bonds is associated with Si 1s + u *(Si-C) transitions. The 1841.5 eV peak in Si(GeMe,), cannot logically be

-J J....l....l....l....l..~ 1840

1850

1860

Photon Energy WI Fig. 1. Si K-edge spectra of SiMe,, GefSiMe,),, Si(CeMe,),, Si(SiMe,),, recorded using ionization yield in the gas phase, compared to the absorption spectrum of c-Si recorded in transmission. In each case a background extrapolated from below the onset has been subtracted and the continuum intensity at 1860 eV set to 1.0. The dashed lines indicate the onset for absorption. The arrows indicate low energy shoutders discussed in the text.

ascribed to a*(Si-C) since this species does not contain a Si-C bond. We note the 1841.5 eV peak is significantly weaker in Si(GeMe,), than in the other species. We propose that this feature is a higher energy Si 1s --f a*(Si-Ge) transition. Analogous transitions may underlie the u*(Si-C) resonance in Si(SiMe,), and Ge(SiMe,),. The spectra of Si(SiMe,), and Si(GeMeJ, each exhibit a shoulder at 1840 eV which is attributed to low energy u*(Si-Si) or u*(Si-Ge) resonances (see the arrows in fig. 1. The shoulder in Si(GeMe,), is readily visible if one views the

354

A.P. Hitchcock

et al. / Si K-edge and Ge K-edge X-ray absorption

figure at a small angle). The spectrum of Si(SiMe,), is very similar to that of the sum of the spectrum of SXGeMe,), plus four times the spectrum of Ge(SiMe,),. This suggests that the XANES features associated with Si-Si and Si-Ge bonds are rather similar. Because there is only one third the number of Si-Si as Si-C bonds in Si(SiMe,),, the u *(Si-Si) is proportionately weaker than the o*(Si-C) resonance. The occurrence of low-lying core + u* transitions in systems containing bonds between third row elements has been noted in other studies. For example the Si2p (L2J spectra of SXSiMe,), and

Table 2 Energies

and splittings

for characteristic

Single crystal semiconductor

Si K-edge

c-Si

Si,Me, exhibit low energy Si 2p -+ a*(Si-Si) transitions whose intensity is proportional to the number of Si-Si bonds [37]. Distinct S 1s -+ u*(S-S) and S 1s + a*@-C) resonances have also been identified in the S K-edge spectra of Me-S,-Me (n = 1, 2, 3) compounds [381. Fig. 2 compares the spectra of: a dilute alloy of Si in Ge (Si,,,Ge,,); [(Si),(Ge>,l,,/Ge(lOO), and [(Si),(Ge>,],,,/Si(lOO) ALS samples; and amorphous and crystalline Si (a-Si and c-Si). Fig. 2 also plots the partial density of unoccupied p-symmetry states (p-DOS), as given by calculations of the ground state band structure of c-Si [441. The

features

solids E thr a’

Species

spectroscopy

First max.

E(1) - Ethr

This work

[24]

E (eV)

TW

[24]

[46] b,

TW

Second

max.

TW

Splitting [241

[491

1838.0

1840.0

1840.4

2.4

2.2

2.0

1841.2

0.80(3)

1.0

1.1

1838.5 1838.5 1838.4

1840.4 1840.1 1840.1

1.9 1.6 1.7

1.8 1.5 -

1.3 1.3

1841.6 1841.8 1841.8

1.25(3) 1.71(3) 1.73(3)

1.5 1.7 1.8

1.4 1.8 1.8

1838.1 1838.0 1838.2

_ _

1840.2 1840.2 1840.2

2.1 2.2 2.0

-

-

1841.5 1841.7 1841.6

Splitting 1.25(3) 1.47(3) 1.49(3)

l’(2) d’ 0.33 0.55 0.52

1837.9 1838.0 1837.7 1838.0

_ _ _ _

1840.3 1840.3 1840.3 1840.4

2.4 2.3 2.6 2.4

1841.4 1841.4 1841.4 1841.3

1.04(3) 1.04(3) 1.02(3) 0.91(3)

0.204 0.208 0.196 0.160

Alloys

Sb.5Ge0.5 Si&%.Y Si o.&co.~~ Superlattices #751 #752 #754

on Ge ‘)

Superlattices #674 #698 #700 #lo16

on Si

Molecular compounds Species SiMe, Ge(SiMe,), Si(GeMe,), Si(SiMe,),

E tbr =) 1840.3 1840.1 1839.5 1839.4

Peak 1 [o*(Si-Si), _ 1840.4 1840.2

a*(Si-Ge)]

Peak 2 [a*(Si-C)] 1841.8 1841.7 (1841.6) ‘) 1841.6

by the intersection of straight lines fit to the pre-edge and to the rising slope of the a) E ,hr is the threshold energy as determined absorption edge. Woicik and Pianetta [24] define this point as the onset of Si 1s + CB transitions - see fig. 42 of ref. [24]. b, Separation of the threshold energy and the first maximum in the band structure calculation [46]. ‘) All data were taken from normal incidence spectra to avoid polarization shifts [48]. d, Peak to peak intensity at 1840.8 eV in the first derivative of the spectrum. ‘) This feature is attributed to o*(Si-Ge) (see text).

A.P. Hitchcock et al. / Si K-edge and Ge K-edge X-ray absorption spectroscopy

Si-K

PL

J....l....l....l....l....l, 1850 1840 Photon Energy

186[ (ev)

Fig. 2. Comparison of the Si K-edge spectra of a Si,.,Ge,,, single crystal alloy, [(Si),(Ge),], on Ge, [(Si)s(Ge),],, on Si, amorphous Si (a-S& crystalline Si (c-Si), all recorded by sample current TEY, and the calculated density of p-unoccupied states (p-DOS) [44]. The p-DOS has been aligned at the second peak maximum.

maxima in the p-DOS are aligned with the near edge features of c-Si. As for the molecular spectra, a linear background has been subtracted from the as-recorded spectra and the average continuum intensity at 1860 eV has been set to a constant value (i.e. the spectra have a normalized edge jump). The threshold energy, which Woicik and Pianetta interpret as the onset of Si 1s --j conduction band (CB) transitions [24], as well as the energies of the first two peaks are listed in table 2, in comparison to literature counterparts where available. There is a difference of almost 2 eV between our absolute energies and those of Woicik and Pianetta [24]. We believe this is the

355

result of a different choice of absolute energy calibration. The Si K-edge XANES spectra of the semiconductors are quite different from those of the molecular species. The threshold energy of the Si K-edge in each of the semiconductors is 1.3(l) eV lower than that of Si(SiMe,), or Si(GeMe,), and 2.1(l) eV lower than that in SiMe, and Ge(SiMe,), (see dashed lines in fig. 1). This shift was unexpected since, in previous comparisons of the inner-shell excitation spectra of species with similar local chemical environments, such as free and surface adsorbed molecules, identical spectral features were found at essentially identical energies [39,40]. The offset between the Si Kedges of molecular and semiconductor materials, which is also observed at the Ge K-edge (see section 3.21, probably reflects the fact that the HOMO-LUMO separation in the molecules is larger than the band gap in the semiconductor solids. If the Si 1s binding energy and any core hole relaxation effects are similar in the molecules and semiconductors, the greater gap energy should lead to a higher energy absorption threshold in the molecular species. The reduced threshold energy in Si(SiMe,), or Si(GeMe,), suggests the “gap” in these species may be approaching that of bulk Si. In the multiple scattering calculations (section 3.3.1) there is evidence for a decrease of the threshold energy as the size of the cluster increases, consistent with the observed offset between the molecular clusters and c-Si. It would be interesting to study experimentally the size dependence of the Si K-edge spectra of Si, molecular clusters, produced either synthetically or by molecular beam techniques, in order to study the convergence of the K-edge resonance structure to that of bulk Si. Recently the Ar2p spectra of variable size argon clusters have been shown to interpolate systematically between the Ar2p spectra of atomic and solid argon [411. It is also possible that core excitons play a role in establishing a lower energy threshold for the semiconductor spectra. However, at the Si L-edge, the core exciton energy of crystalline Si is only 40 meV [42]. Any core exciton associated with the Si K-edge would be expected to have a comparable binding energy and thus should not play any

356

A.P. Hitchcock et al. / Si K-edge and Ge K-edge X-ray absorption spectroscopy

significant role in shifting the threshold or giving rise to detectible features. The sharp threshold resonance in the molecular compounds is replaced in all of the single crystal semiconductor materials cc-%, alloys and [(Si),(Ge),], ALS) by a broad peak which has a distinct splitting. This splitting is also evident in several of the published c-Si spectra [14,241. The splitting in the Si K-edge spectrum of the reconstructed Si(ll1) surface 1431is identical to that we find for Si(100). Woicik and Pianetta [241 have attributed this splitting as arising from structure in the conduction band (CB) density of states. For c-Si the magnitude of the CB splitting and the relative intensity of the two components are in good agreement with the shape of the ground state density of unoccupied p states of Si predicted by numerous band structure calculations [13,15,44-471, as illustrated in fig. 2. In a local picture, the Td site symmetry would be expected to give rise to a three-fold degeneracy of the Si 3p conduction band and thus one might naively expect a single Si 1s + 3p transition at the central Si atom of a SiSi, cluster. However, in the crystal lattice the translational symmetry lowers the effective site symmetry which leads to a removal of the degeneracy and the creation of structure in the conduction band in the ground state of Si [45]. According to band structure calculations, the energies of the two CB components vary with the direction of the Bloch states into which the transition occurs (see fig. 8-8 of ref. 1451).This dispersion should only be observed by final state momentum resolved techniques, such as inverse photoemission, in which the direction of the CB electron is well defined. Absorption and total electron yield measurements integrate over all directions of the CB electron. Thus the peak represents an average CB energy. Comparisons of the Si K-edge spectra of c-Si, a-Si and partially crystalline Si provide direct experimental information on the range of crystalline order which is needed to introduce the CB splitting and other spectral fe$ures 113,241. The Si K-edge spectrum of a 1000 A thick amorphous Si film (a-Si) (fig. 2) does not exhibit the CB splitting or the fine structure between 1842 and 1862 eV, although it does contain a weak, broad

maximum at about the same energy as the CB feature in c-Si. As Woicik and Pianetta [24] have shown very clearly, superposition of the c-Si and a-Si spectra shows that this same broad maximum lies underneath the two sharp CB structures in the Si K-edge spectrum of c-Si. The split CB structures are simply absent in a-Si. This agrees with density of states calculations for a-Si [49]. The extent of degradation of the CB peak splitting and the higher energy multiple scattering features depends on the degree of non-crystallinity of Si. Thus in porous Si [50] the CB-splitting is lost but most of the other multiple scattering XANES features of c-Si (those between 1843 and 1860 eV) are retained, whereas both types of features disappear in fully amorphous Si. This observation indicates that the CB splitting is the Si K-edge spectral feature which is most sensitive to long range order. In a multiple scattering picture, the CB-splitting can be associated with the overlap of a large number of specific multiple scattering paths (see section 3.3) which are absent in a small unit such as Si(SiMe,),, or highly damped in ospecies in which the medium range order (4-8 A) is poor. Thus the CB splitting at the Si K-edge spectrum is a feature of spatially-extended aspects of the electronic structure [24,45]. The CB splitting also occurs in inverse photoemission spectra. Jackson et al. [51] clearly detect two features in the X-ray inverse photoemission (BIS) spectrum of Sic111) which do not appear in the BIS spectrum of a-Si. The separation of the CB features in the BIS spectrum is 1.4 eV rather than the 0.8 eV which we observe at the Si K-edge. The difference is ascribed to the influence of the Si 1s core hole. Chelikowsky et al. [521 have found good agreement between X-ray inverse photoemission and band structure calculations. Straub et al. and other groups [53] have reported the valence shell inverse photoemission spectra of Ge(ll1) and Si(ll1) surfaces. In this case the CB splitting of bulk Si detected by inverse photoemission is 0.3 eV larger than that observed in the optical excitation spectrum of c-Si, again indicating that the CB-splitting is influenced by relaxation effects associated with the presence of a hole in the occupied DOS.

A.P. Hitchcock et al. / Si K-edge and Ge K-edge X-ray absorption spectroscopy

As with c-Si, two closely spaced maxima form the first part of the Si K-edge spectra of both crystalline alloys and the Si-Ge ALS samples (fig. 2). In fact the CB splitting is much larger in the spectra of Ge-rich alloys or ALS than in c-Si (see table 2). The translational symmetry in the AL,S is highly anisotropic. It effectively disappears in the alloys. Thus the explanation of the CB splitting used for c-Si [45] cannot apply in the same fashion to the alloy or ALS samples. In these materials the multiple scattering picture provides a clearer description. The Si,ssGe,ss alloy has the largest CB splitting (1.73(3) eV> of any of the materials we have studied. Using comparisons of the Si K-edge spectra of c-Si with those of Si,,Ge,, and alloys, Woicik and Pianetta [24] have Si0.1Gel.N noted that the magnitude of the CB splitting increases with increasing Ge content. They propose that the splitting in very dilute Si-in-Ge alloys should be similar to that in the conduction band density of states of pure Ge. This is indeed the case [531. Alloys of intermediate composition, such as Si,,,Ge,,,, should have CB splittings between those of c-Si and c-Ge. Comparison with band structure calculations for SiGe 146,491 support this viewpoint (see table 2). The magnitude of the Si 1s + CB splitting in the ALS species depends on their composition and structure. ALS samples with thick Si layers (m > 4, as in KSi),(Ge),l,,, [W,(Ge),l,,, have CB splitKSi),(Ge), lIoo and [(Si),,(Ge&,) tings around 0.8 eV, similar to that in c-Si. Values up to 1.5 eV are found in samples with very thin Si layers (m = 2, as in [(S&oe),,],, and [(Si>2(Ge&,>. The increase in splitting varies systematically with increased Ge content (see section 3.4) suggesting that, although the CB splitting requires a regular local structure about the Si 1s ionized Si atom in order to allow reinforcement of multiple scattering paths, the energetics are affected by the proportion of Ge and Si atoms in the spatial region over which the multiple scattering occurs. This interpretation is consistent with the dependence on Ge content of the CB splitting in alloys. If a perfect epitaxial structure was achieved, the Si atoms in the m = 2 samples would have Ge atoms as 50% of their

357

first shell contacts. For samples with m > 4 there is a relatively small proportion of Ge atoms in the average local environment of Si. Thus the spectra of the ALS samples with thicker Si layers should be similar to that of c-Si, as observed. Along with changes in the separation of the threshold resonances, the second maximum at 1841.5 eV is more intense in ALS samples with a larger proportion of the Si atoms at the Si-Ge interface, and thus with a larger average first shell Ge content. Although this maximum occurs around the same energy as the main a*(Si-C) resonance in the molecular compounds, we do not believe there is any direct connection between the interpretation of these features in semiconductors and molecules (aside from both having a dominant Si3p orbital character). The analytical potential for both the CB splitting and the relative peak intensity is explored in section 3.4. Compared to c-Si, the interface samples, particularly [(Si),(Ge&,, exhibit a different pattern of higher energy multiple scattering structure (> 1842 eV) although they do exhibit a similar number of features. The changes in this region of the spectrum are discussed in section 3.3. In addition to a chemical and structural sensitivity, the conduction band component of the Si K-edge spectra of single crystal strained-AL,S samples exhibits a polarization dependence, i.e. a small but distinct sensitivity to sample orientation [48]. By contrast the polarization dependence of the Si K-edge spectra of Si,Ge,_, alloys or relaxed-ALS is much weaker than that of the strained-ALS materials. The interpretation of this polarization dependence in terms of the strained Si environment in the ALS samples will be reported elsewhere [48]. For consistency, only spectra recorded with normal incidence have been included in this work. 3.2. Ge K-edge spectra Fig. 3 presents the Ge K-edge spectra of Ge(SiMe,),, GeMe, and Ge,Me,, compared to that of pure c-Ge. To our knowledge this is the first time any of these molecular spectra have been reported. The edge resonance in Ge(SiMe,), is considerably more prominent than that in ei-

A.P. Hitchcock et al. / Si K-edge and Ge K-edge X-ray absorption spectroscopy

358

ther Ge,Me, or GeMe,. The Ge K-edge spectrum of GeMe, has a well-resolved second peak about 10 eV above the first peak which could be the first EXAFS oscillation for Ge-C scattering, which is expected to be strong at low energy. Ge,Me, may also have a higher energy component but it is much weaker and less well resolved than in GeMe,. This may be related to overlap and/or interference of the Ge-C and the Ge-Ge scattering signal. The increasing complexity of the Ge K-edge XANES with increasing range over which there are well-defined backscattering neighbors parallels the observations at the Si K-edge. The Si K-edge XANES of the molecular species are generally richer than those of the Ge

IL c-S

(as-recorded)

-4 _J

Ge-K

I....I.*..I....I...

11140

11100 Photon

Energy (eV)

Fig. 4. Ge K-edge spectra of a Ge,,ISi,,, alloy; [Ws(Ge&,, Wi)9(Ge),124and [(Si),,,(Ge),], ALS structures grown on Si, and c-Ge recorded using TEY with sample rotation. The Si K-edge spectrum of pure Si, as-recorded and smoothed to match the Ge K-edge width (based on the lo-90% jump) is also plotted, aligned at the Ge K-edge threshold energy. In each case a background extrapolated from below the onset has been subtracted and the intensity of the continuum set to a constant value.

i

Ge-K

J I....I....I....I...

11140 11100 Photon Energy (eV) Fig. 3. Background subtracted and continuum normalized Ge K-edge spectra of Ge(SiMe,),, GeMe,, GezMe,, and c-Ge. The spectra of GeMe, (e) and Ge,Me, CL”) were recorded using transmission while those of Ge(SiMe,), (s) and c-Ge were recorded using TEY with sample rotation. In each case a background extrapolated from below the onset has been subtracted and the intensity of the continuum set to a constant value.

compounds, because of the higher intrinsic resolution at the Si K-edge. Interestingly, at the Si K-edge, the main edge resonance in molecular complexes with Si-Ge bonds is less prominent than in species with Si-C bonds whereas at the Ge K-edge the opposite is true - i.e. in the Ge K-edge spectra the main peak in Ge(SiMe,),, which we attribute to a a*(Ge-Si) resonance, is more intense than that in GeMe, or Ge,Me, which we attribute to a*(Ge-C) resonances. Fig. 4 compares the Ge K-edge spectra of a Si-rich Ge,,,Si,, alloy; three different Si-Ge superlattice samples, [W,(Ge),l,,, [(Si),(Ge),l,,,

A.P. Hitchcock et al. / Si K-edge and Ge K-edge X-ray absorption spectroscopy

and c-Ge. As with the molecular [(Si),,(Ge),l,; compounds, the Ge K-edge features in the semiconductors are much broader than those at the Si K-edge because the higher energy Ge K-shell core hole has a shorter lifetime and thus a larger natural linewidth. In general there is less detail apparent in a given energy width of the Ge spectrum than in the comparable energy width of the Si spectrum. In order to demonstrate the relative sensitivity of the Si and Ge near edge spectra, fig. 4 also presents the spectrum of c-Si after it has been aligned at the Ge K-edge. In addition to the as-recorded c-Si spectrum, fig. 4 also plots the c-Si spectrum after it has been smoothed until it has an edge width similar to that of the Ge K-edge spectra. It is evident that the Ge K-edge provides less information about unoccupied electronic structure than the Si K-edge; in particular the CB splitting is completely washed out. While the lack of detail at the Ge K-edge is mainly the result of the large natural linewidth, some of the broadening in our spectra may be instrumental since Oyanagi et al. [54] have recently reported somewhat better resolved Ge K-edge spectra of Si-Ge ALS materials. While some detail is lost, the smoothed and aligned c-Si spectrum nicely illustrates the dominant influence of the nature of the backscattering environment on XANES, and thus its local structural sensitivity, since the relative location and intensities of spectral features in the smoothed c-Si spectrum match almost exactly with those in the Ge K-edge spectrum of the Ge,~,Si,, dilute alloy. This shows directly that the presence of successive shells of Si backscatterers and their geometrical arrangement around the core excited atom are the critical factors in establishing the XANES structure, and that the nature of the core excited atom (i.e. Ge or Si) is of relatively little importance. Since the valence electron distribution of Si and Ge and thus the contribution of the core excited atom to the scattering phase is similar, this may be a phenomenon peculiar to the Si-Ge system. Also, even in systems with the same valence, one might encounter large differences in cases where there are large differences in electron correlation, such as in comparisons of core excitation spectra of very heavy and very

359

light atoms in the same group of the periodic table. In general the Ge K-edge spectra of the semiconductors have a larger number, but weaker features, than those of the molecular compounds. As at the Si K-edge, the onset of Ge K-edge excitation in the semiconductor spectra occurs about 1.5 eV below that of the molecular species. As discussed in section 3.1, this threshold energy shift reflects the fact that the HOMO-LUMO gap in the molecules is smaller than the band gap in the semiconductor materials. The Ge K-edge XANES structure associated with a Si-only environment (e.g. that in the Ge0.rSill.9 alloy) is quite distinct from that observed in the molecular compounds, the XANES of the ALS samples or that in pure Ge. The Ge K-edge XANES of the ALS sample with the thinnest Ge layer and thus the largest nearest neighbor Si content ([(Si),(Ge&,& is most like that of the Si-rich alloy, Ge,,Si,, while the Ge K-edge spectrum of the ALS with the thickest Ge layer ([(Si),,(Ge),],) is most like that of c-Ge. Overall there is a systematic evolution of the spectral shape from that of a pure Ge environment in c-Ge to that of a nearly pure Si environment in the dilute Ge-in-Si alloy. This indicates that, even at the modest intrinsic resolution of the Ge K-edge, XANES remains sensitive to the local environment. While the shape and energy distribution of the spectral features changes, the position of the threshold of the Ge K-edge of the semiconductor materials does not change when going from a Ge-rich to a Si-rich environment (as also found for the Si K-edge threshold 1241, see table 2). Therefore, the bottom of the conduction band in the superlattice samples is likely at a similar energy to that of c-Si and c-Ge. This observation is consistent with other measurements which indicate that there is no band offset in the superlattice samples relative to pure Ge 1551. 3.3. Multiple scattering calculations of Si and Ge K-edge XANES 3.3.1. Calculational details

In the multiple scattering (MS) model X-ray absorption fine structure is viewed as the result

360

A.P. Hitchcock et al. / Si K-edge and Ge K-edge X-ray absorption spectroscopy

of constructive and destructive interference between direct and elastically backscattered components of the final state wavefunction which energy-modulates the transition probability. One must consider both single scattering (one outand-back trajectory to a single neighbor) and multiple scattering (paths involving two or more scattering events from one or more neighboring atoms). In the near edge region multiple scattering generally becomes of increasing importance. The calculational procedures needed to get good predictive ability in the region close to threshold approach those used for KKR band structure determinations [56,57]. Thus there is a close connection between spectral interpretations within electronic (band) and geometric (MS) oriented models. The Feff program [58-601 (version 5.03) has been used to calculate Si K-edge and Ge K-edge spectra of clusters representative of both the molecular and semiconductor compounds. Feff uses a spherical wave backscattering function and treats the scattering potential and self-energy corrections in an explicit fashion [58,59]. It has a very efficient procedure for selecting the most important multiple scattering paths. This has allowed us to include multiple scattering with up to 8 scattering events (“legs”) per path, for clusters with as many as 13-shells (190 atoms) surrounding the core ionized atom. Even the most complex calculation executed in acceptable times (< 3 h) with relatively modest computational power (33MHz 486DX with 20 Mb RAM). The path filter makes Feff one of the most efficient ways currently available for accurate predictions of Xray absorption spectra. Feff calculations of Si(GeMe,), and Ge(SiMe,), were carried out using geometries estimated from similar species. Since the interaction between adjacent molecules is weak and the intermolecular vibrational amplitude correspondingly large, little structure is expected from scattering outside of the molecule. However, the strong, directed bonds in the single crystal semiconductor materials mean that backscattering is important over a much larger range, In order to test for convergence of the computed spectrum we have explored the influence of cluster size on

the Feff prediction of the XANES spectra of c-Si and c-Ge. We have also investigated the dependence of the predicted spectrum on the complexity of scattering path (number of legs per path) and the criterion used in the path filter to select the most significant paths. In the case of the latter parameter, we initially used the default criterion, 2.5%-4.0%, where the first number indicates the minimum intensity of a rapid plane-wave estimate of the path amplitude relative to the first shell signal (less intense signals are ignored), while the second number indicates the corresponding cutoff used in the final spherical wave calculation. This was found to be perfectly adequate for predicting structure above 50 eV but lower path criteria were found to make significant improvements in the agreement with experiment at lower energies. For these calculations we have used path filter criteria of 0.7%1.0%. This is the minimum value compatible with computational limitations for the largest clusters. Details of the geometries and program parameters are given in table 3. The calculated k-space results were first converted to E-space and then shifted by a small amount (4 eV in Si, 5 eV in Ge) to provide the best match to experiment of the structure above 30 eV. These energy shifts are very similar to the E, values determined in an EXAFS analysis and are in good agreement with other estimates [24]. Fig. 5a shows the Feff prediction of the evolution of the Si K-edge XANES of Si clusters as a function of cluster size between a one-shell species (SiSi,) and a cluster consisting of a Si atom surrounded by 13-shells of Si atoms in the diamond lattice geometry (a 19 A diameter cluster with 191 atoms). For each of these calculations paths of up to 6 legs were allowed. Note that the l-shell result (SiSi,) is rather similar to the Si K-edge spectrumof Si(GeMe,), (fig. 1). The corresponding cluster size investigation (l-13 shells) for c-Ge is shown in fig. 5b. The calculations for larger clusters clearly provide a much better match to experiment than those for the smaller clusters. The region close to threshold is most sensitive to the cluster size, consistent with the long range of low energy electrons in solids. Even the 13-shell result does not reproduce all of

A.P. Hitchcock et al. / Si K-edge and Ge K-edge X-ray absorption spectroscopy

361

Table 3 Geometries and parameters for Feff 5.03 calculations Species

Geometry

Si(GeC&

RSi_Ge = 2.389 ;i

Eo 0

a)

T/O,

b,

N leg

# paths ‘)

4.0

290/150

6

60/44

0.0

290/150

6

37/23

4.0

290/658

6

7/7 33/24 77/58 32/23 77/65 443/294 884/338

RGe_C = 1.946 A

Ge(SiC&

Si(Si...) l-shell 2-shell 3-shell 4-shell 5-shell IO-shell 13-shell

Rsi-oe = 2.389 A Rsi_c = 1.875 ;i 0 Rsi_si = 2.352 A

2-6 d,

Ge(Ge...) l-shell 2-shell 4-shell 5-shell lo-shell 13-shell

RGe_Ge = 2.450 z&

GetSi...) (13-shell)

RSi_Ge = 2.352 A

SitGe...)

RSi_Ge = 2.450 i

(13-shell)

5.0

290/658

6

7/5 22/12 53/47 64/58 258/173 312/192

5.0

290/352

8

140/111

4.0

290/352

8

599/404

R,i_si = 2.352 w

RG~-G~ =

2.450 A

a) The Feff spectra are computed in k-space, converted to E-space and shifted by the indicated E, value, which was chosen to obtain best match to experiment over the higher energy region. b, Sample temperature and Debye temperature, in K. ‘) The calculation considered all paths containing up to N,_ segments with a total path length of less than 10 A CR,,,,). A rapid plane-wave calculation was used to estimate the contribution of each path relative to the first shell scattering. If the given path contributed less than 1.0% it was ignored. After identifying all paths contributing at greater than 0.7% of first shell, full spherical wave calculations were carried out. Those paths having an intensity greater than 1.0% of first shell were retained (path filter of 0.7-1.0). This column lists the number of retained paths, with those meeting the plane-wave criterion first and the spherical wave criterion second. d, The spectra presented in fig. 6 were computed using Nren values of 2, 3, 4 and 6. The #paths refers to the N,,, = 6 calculation.

the experimental features, in particular the CB peaks at thresholds which lie below the k-space origin of the Feff calculation. In Feff studies of diatomic molecules [61] a very large number of multiple scattering events (> 13 as opposed to 6 in this case) were required in order to reproduce the u* resonance close to threshold. It is also possible that some of the features not predicted by the 13-shell calculation are in fact KM double excitation transitions, since these have been identified in the Si K-edge spectra of some molecular

species [20-223. We also find that Feff 5.03 systematically overestimates the higher shell and longer path length multiple scattering contributions for Si and Ge. This is an important source for the discrepancy between calculation and experiment below 30 eV. A very recent version of the Feff code calculates the atomic background including multi-electron excitations, uses an improved potential, and has a provision for calculating bound state structure below k = 0. This improves the precision at low energies and extends

362

A.P. Hitchcock et al. / Si K-edge and Ge K-edge X-ray absorption spectroscopy

the calculation into the region of the Si 1s -+ CB transitions. The results of these more accurate calculations will be reported in a future paper. Given the need to use as large a cluster size as possible to produce reasonable match to experiment for c-Si and c-Ge, clusters with 13-shells surrounding the core excited atom were used to calculate the Feff spectra for Si in an all-Ge environment and Ge in an all-Si environment (approximating the dilute alloys, although the first shell distances were not corrected). Sainctavit et

I

1

I

I

I

al. [14] report that the 8th shell has very strong multiple scattering contributions because of the focusing effect. They suggest that shells beyond the 8th are not very important. However, if the goal is to compute all aspects of the X-ray absorption spectrum including the structure very close to threshold, our results suggest that clusters even larger than 13 shells are required. Fig. 6 illustrates how the spectrum of a 13-shell Si cluster evolves as more extended multiple scattering paths are introduced. For each of these

I

I

I

I

/

,

I

(4

04

c-Si

c-Ge

# shells

I

I

I

0

20

40

Energy

above

I

I

I

60

60

0

Threshold

(eV)

Energy

I

20

I

40

above

/

60

I

60

Threshold

1

100

I

120

(eV)

Fig. 5. (a) Comparison of the experimental Si K-edge XANES of c-Si with the results of multiple scattering calculations (Feff 5.03) on clusters where the core excited Si atom is surrounded by the indicated number of shells of Si atoms arranged as in the diamond lattice structure of silicon. There are 191 Si atoms in the 13-shell system. This is the spectrum of only the central Si. (b) Comparison of the experimental Ge K-edge XANES of c-Ge with Feff 5.03 results for clusters where the core excited Ge atom is surrounded by the indicated number of shells of Ge atoms arranged as in the diamond lattice structure of germanium.

A.P. Hitchcock et al. / Si K-edge and Ge K-edge X-ray absorption spectroscopy 1

,

I

I

I

I

backscattering by Si atoms. Fig. 7a plots the Feff calculation for the local structure of the Ge(SiMe,), molecule (4 first shell Si, 12 second shell C) and the recorded Ge K-edge spectrum of this species. All three spectral features are reproduced. The result calculated without multiple

c-Si 13 shella #

363

legs

k;

I-

z? x

-

Backscattering

34

by Si

c-Si

1

I

I

I

I

I

0

20

40

60

60

100

Energy

above

Threshold

(eV)

Fig. 6. Dependence on the complexity of the scattering path (maximum number of legs per path) of the Si K-edge spectrum of a Si atom at the centre of a 13-shell Si cluster according to Feff 5.03 calculations. The bottom plot corresponds to single scattering.

calculations the path filter criterion was 0.7%1.0%. The importance of triangular paths involving the first shell is emphasized by the fact that the largest changes occur between the 2- and 3-leg result. However, there is further evolution of the spectral shape below 20 eV even between the 4- and 6-leg calculation. 3.3.2, Results of multiple scattering XANES calculations

Fig. 7 compares experimental spectra for systems involving

and calculated predominantly

I

I

I

I

I

0

20

40

60

60

Energy

above

Threshold

(eV)

Fig. 7. Comparison of experimental results (darker lines) to Feff 5.03 multiple scattering calculations (lighter lines) for systems involving Si backscattering. (a) Comparison of Feff calculation for Ge(SiC,),, with the Ge K-edge spectrum of Ge(SiMe,),. (b) Comparison of Feff calculations for Si surrounded by 13 shells of Si and Ge surrounded by 13 shells of Si, with the Si K-edge spectrum of c-Si and the Ge K-edge spectrum of a single crystal Gea,tSi,,, alloy. The calculated spectra are energy shifted by 4 eV to obtain best match to experiment above 20 eV. The underlined atom in the label indicates the core ionized atom. See table 3 for details of the geometries and parameters used in the calculations.

364

A.P. Hitchcock et al. / Si K-edge and Ge K-edge X-ray absorption spectroscopy

scattering (path = 2 in Feff) is very similar to that presented in fig. 7a. Thus multiple scattering effects are weak in Ge(SiMe,),, a not unexpected result given the small size of the system and thus limited number of scattering paths; the fact that the vibrational amplitudes are probably much larger than in the semiconductors; and that C backscattering is weak relative to that by Si or Ge. This result is consistent with the relatively weak multiple scattering signal that was demonstrated experimentally in the comparison of the Ge K-edge spectra of GeH,, GeH,Cl and GeCl,

WI. In fig. 7b the Feff result for Si surrounded by 13-shells of Si atoms is reported, in comparison to the experimental Si K-edge spectrum of c-Si and the Ge K-edge spectrum of the Ge,,Si,,, alloy, two species in which the first shell is (almost) exclusively Si. The Feff result for Ge surrounded by 13 shells of Si (using the structural parameters for c-Si) is also presented in fig. 7b. These two Feff calculations are remarkably similar, differing mainly in the first 4 eV, with the core excited Si exhibiting stronger signal close to threshold than core excited Ge. This indicates that the nature of the backscatterer is much more critical than the identity of the central atom. This conclusion was also reached on the basis of the experimental comparisons presented in section 3.2. This result is consistent with the theoretical results of Miiller et al. [62], which indicate that the spatial symmetry around the core excited atom is a very important factor in determining XANES. As noted earlier, the Si K-edge spectra of c-Si and that of the Ge,,,Si,,, alloy are similar except below 10 eV. Clearly the spectral features in the XANES region are dominated by the geometry and type of backscatterer. From this work we find that the very sharp Si 1s + CB structures observed in the Si K-edge XANES cannot be explained using Feff 5.03 to calculate single and multiple scattering paths in the first 13 shells. The continued fraction expansion multiple scattering treatment of the Si Kedge spectrum of a Si,, cluster reported by Filipponi [19] provides a better match to the c-Si spectrum at low energies but it also does not reproduce the CB splitting. The relatively poor

agreement between the Feff 5.03 result and the c-Si spectrum close to threshold and the apparent non-convergence with cluster size suggests there are significant long range single and higher order multiple scattering contributions. The fact that essentially all of the XANES structure is washed out in amorphous Si (fig. 2) indicates that the intensity and the definition of the spectral structure associated with multiple scattering is dependent on the quality of the angular correlations since these are more strongly affected than bond lengths in the amorphous material. The reduced angular correlation is one manifestation of the longer range disorder which plays a central role in the difference between c-Si and a-Si and thus in destroying the XANES in the amorphous material. A detailed analysis of multiple scattering in both c-Si and a-Si has been presented by Bianconi et al. [13]. In agreement with our results (fig. 6) they find a very strong multiple scattering contribution in c-Si from triangular paths which involve the first and second coordination shells. This signal is almost completely eliminated in the spectrum of a-Si because of the large variation in the bond angles in an amorphous continuous random network material as compared to a single crystal material with very low defect density. The long range sensitivity of the threshold structure in Si K-edge XANES is also demonstrated by the cluster calculations for c-Si and a-Si reported by Bose et al. [63]. They find that a cluster of at least 400 atoms is needed to reproduce the DOS of c-Si. Calculations of the local DOS associated with different sites in an a-Si cluster did not reveal any simple correlation with local structure. Interestingly the calculations of Bose et al. [63] suggest that multiple scattering is still occurring in a-Si but that the long range contributions to the XANES overlap in such a way as to wash out observable structure. Fig. 8 compares experimental and calculated spectra for systems involving predominantly backscattering by Ge atoms. The Si K-edge spectrum of Si(GeMe,), is compared to the Feff calculation of Si(GeC,), in fig. 8a. While the Feff calculation forSi(GeC,), does predict a large resonance at threshold, as observed experimentally, the level of agreement between calculation

A.P. Hitchcock et al. / Si K-edge and Ge K-edge X-ray absorption spectroscopy r

/

/

I

I

I

Feff

/

Si(GeCg)q -

b)

!

0

Energy

/

20

I

40

above

I

60

/

80

Threshold

s

100

t

120

(eV)

Fig. 8. Comparison of experimental results (darker lines) to Feff 5.03 multiple scattering calculations (lighter lines) for systems involving Ge backscattering. (a) Comparison of Feff calculation for Si(GeC,), with the Si K-edge spectrum of SifGeMe,), (energy shift = 0). (b) Comparison of Feff calculations for Ge surrounded by 13 shells of Ge and Si surrounded by 13 shells of Ge, with the Ge K-edge spectrum of c-Ge and the Si K-edge spectrum of a Si,,Ge,, single crystal alloy. A 5 eV shift was used to obtain best match of calculation and experiment. The underlii.inthelabel indicates the core ionized atom. See table 3 for details of the geometries and parameters used in the calculations.

and experiment is considerably worse than Ge(SiMe,), (fig. 7a). The reason for this is known. Fig. 8b compares the Feff calculations a 13-shell Ge cluster with the experimental

for not of Ge

365

K-edge spectrum of c-Ge. The ~rresponding calculation for Si at the centre of a 13-shell cluster of Ge is also presented. As in the case of an all-Si environment (fig. 8b), the XANES predicted for these two ciusters (each with an a&Ge environment) is almost identical beyond 10 eV above threshold. This further supports the notion that it is the type and structure of the backscatterer, not the nature of the absorbing atom, which determines the 2LANES structure [62]. The Si K-edge spectrum of a Si,,,Ge,,, alloy is also shown in fig. 8b. The lower frequency components of this rather noisy spectrum are similar to those in the XANES of Ge and both are well reproduced by the Feff calculation. The agreement between Feff and experiment for c-Ge is better than that for c-Si. Perhaps this is largely because of the lower intrinsic resohrtion at the Ge K-edge which masks possible finer features, such as those in the experimental Si K-edge XANES of c-Si and Si,,,,Ge0,,5. Presumably the larger natural linewidth associated with the more rapid decay of the Ge core hole blurs the structure associated with closely spaced states and/or longer scattering paths. Another factor may be that the backscattering amplitude for Ge is much smaller than that of Si at low k (the backscattering $mpIitude function for Ge has a minimum at 4 A-‘, about 50 eV above the edge [6]). The greater ability of Si to scatter low energy electrons leads to a greater multiple scattering contribution and thus to a longer range sensitivity (i.e. beyond the first 13-shells of neighboring atoms) of the Si K-edge spectral structure. 3.4. Application ~~Lys~

of XANES

to Si-Ge

inter&e

Clearly Si K-edge spectra are sensitive to the average structure around Si in crystalline alloy [24] and Si-Ge superlattice materials. Thus they have considerable potential for assisting structural analysis of the interface. The Si 1s + CB splitting appears to be the most promising feature for anaIytica1 applications. Fig. 9 investigates the systematics of the energy separation and the intensity of the second component as a function of

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A.P. Hitchcock et al. / Si K-edge and Ge K-edge X-ray absorption spectroscopy

ALS and alloy composition (see table 2 for numerical values). We have chosen to use the parameter (m - 11-l to express the systematic compositional variation of the local environment in the ALS species. (m - 11-i is the ratio of Ge to Si in the first coordination shell (No,/Nsi) in an [(Si),(Ge),], ALS, assuming perfect epitaxy and an abrupt interface. Detailed analysis of the polarization dependence suggests that the CB energy splitting may be partly associated with changes in the intensity of different spectral components with ALS composition rather than shifts in the position of a single spectral transition. However, for this study we have chosen to present a phenomenological analysis of the measured energy splitting to illustrate the sensitivity of the CB transitions to ALS structure. The intensity of the second component is measured as the peak-to-peak intensity at 1840.8 eV in the first derivative spectrum. This is proportional to the size and sharpness of the leading edge of the second peak. The spectra were continuum normalized and were all recorded at normal incidence to eliminate polarization dependent aspects [48]. Fig. 9 shows clearly that the energy separation and the intensity of the second component correlate in similar ways with changes in the local environment of Si in the ALS samples. This, along with much of the previous spectral interpretation, would suggest that average chemical composition (i.e. amount of Ge in the first few shells surrounding a Si atom) is the controlling factor. However, we note that strain may be as, or even more, important. The data plotted with open symbols in fig. 9 is from samples where the superlattice is grown on Si, whereas the data plotted with filled symbols is from samples where the superlattice is grown on Ge. In the former case most Si layers are unstrained whereas in the latter all the Si layers are strained (the 3 filled points correspond to as-grown strained epitaxial materials with (Si), or (Si), layers). Thus it is possible that strain may be a key factor in establishing the details of Si 1s + CB transitions. Indeed, the local distortions (strain) caused by the intrinsically larger size of a Ge atom may be the “mechanism” through which the details of the Si

I

I

I

I

9 i

0 0 i

+

-

I

I

I

I

0.0

0.4

0.6

1.2

(m-1)-l

Fig. 9. Energy separation of the Sils + CB features (left scale) and intensity of the second CB feature (right scale), as evaluated by the peak-to-peak variation at 1840.8 eV in the first derivative of the (continuum normalized) Si K-edge spectra of c-Si and seven [(Si),(Ge),], ALS samples. The open symbols (circles and triangles) are for samples grown on Si whereas the closed symbols are for samples grown in Ge. The strain distortion relative to the growth direction is opposite for these two situations. The spectral parameters (see table 2 for numerical values) are plotted as a function of (m - l)- ‘, which is the ratio of average number of Si-Ge to Si-Si bonds in the first shell of the Si atoms, assuming a perfect interface. Experimental X-ray diffraction values of m, the average thickness of each Si layer, are used (see table 1).

K-edge spectrum are linked to chemical composition, as found in alloys for example. Our recent polarization studies [48] show that the sense of the polarization dependence is inverted between strained ALS samples grown on a Si substrate and those grown on a Ge substrate. The tetragonal distortion is in the opposite sense in these two cases (i.e. there is an in-plane expansion and an

A.P. Hitchcock et al. / Si K-edge and Ge K-edge X-ray absorption spectroscopy

out-of-plane contraction for Si grown on Ge and vice versa for Ge grown on Si). This suggests there may be a close relationship between the near threshold features and the strain in the ALS layers. Since the strain distortions in thin (Si), layers in Ge can be removed by thermal annealing, studies of the changes in spectral shape and polarization dependence between strained and relaxed samples offer a strong possibility of being able to determine the relative importance of composition and strain in controlling the details of the Si 1s --+CB transitions. Fig. 9 suggests that the Si K-edge conduction band structure may be very useful for measuring average local composition and the effects of strain on the band structure of epitaxial Si-Ge superlattice structures. This proposal is closely related to a recent suggestion that features in the SiL,, near edge spectrum of Si, _xGe, alloys can be used to measure the alloy composition [64]. Features in Si L,, electron energy loss spectra (EELS) recorded in an electron microscope have been attributed to Si2p --j CB transitions. In particular, they are attributed to excitations to flat bands of s- and d-character which are those which contribute strongly to SiL,, spectra. Batson and Morar [64] have analyzed their results by assuming that the band structure of the alloys will be a linear interpolation of those of pure Si [45,46,65] and pure Ge [46]. They claim to be able to estimate alloy compositions with an accuracy of 5% from the relative intensities.

4. Conclusions This work has presented a detailed picture of how near edge features in K-shell X-ray absorption spectra change with the development of an extended geometric and electronic structure. The relative merits of an electronic structure (MO or band structure) versus a scattering picture for describing different energy regimes of X-ray absorption spectra have been explored. It appears that an “electronic state” (DOS or MO) picture is more appropriate right at the edge (< 10 eV) whereas above 10 eV the signal is better described within a “scattering” picture. At the same

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time these results clearly show that most XANES features, even those down to 10 eV above threshold, can be accurately reproduced by multiple scattering calculations if they are carried out in sufficient detail. Because of the importance of quite long range scattering in determining the threshold structure of the near edge spectra of semiconductor materials, the spectra of small molecular complexes are relatively poor models. Systematic differences in the near edge spectra of Si-Ge multilayer structures (particularly at the Si K-edge) occur with changes in the average environment of the Si or Ge atom. The Si 1s + CB features are found to be particularly sensitive to the interface structure (composition and/or strain) and thus have potential for providing useful information on mixing at the interface either during growth or after annealing. Based on our comparison of the Si K-edge and Ge K-edge results, it would appear that lower energy core edges which have a smaller natural linewidth may be even better suited than the K-edges for extracting quantitative structural information from XANES. In this regard it would be of interest to study the Si L,, [24,66] and Ge L,, [67] spectra of model compounds and interface materials. At the same time, analysis of the Ge K-edge and Si K-edge extended fine structural signal from ALS samples will continue to provide quantitative local structural information [9-121.

Acknowledgements

We thank the staff of SRC and CHESS (both funded by the National Science Foundation) for their expert operation of these facilities and for generous assistance when required. The Feff 5.03 multiple scattering code was provided by Dr. J.J. Rehr, along with useful advice on its operation. This research has been sponsored financially by the Ontario Centre for Materials Research and NSERC (Canada). Acknowledgement is made to the Donors of the Petroleum Research Fund, administered by the American Chemical Society for the partial support of this research.

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