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X-ray emission spectra and electronic structure of amorphous silicon
Journal of Non-Crystalline Solids 70 (1985) 187-198 North-Holland, A m s t e r d a m
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X-RAY EMISSION SPECTRA AND ELECTRONIC STRUCTURE OF AMORPHOUS SILICON E.Z. K U R M A E V * and G. WIECH Sektion Physik der Universitgtt M~nchen, 8000 M~znchen 22, Fed. Rep. Germany Received 7 August 1984
X-ray K and L emission bands of c-Si and a-Si are reported and compared with available XPS and UPS measurements. The experimental results for a-Si are found to be consistent and in excellent agreement. From comparison of the experimental results with available electron densityof-states calculations based on different structure models of the amorphous state, we conclude that only ST-12 structure and the Polk-Boudreaux model provide results that are compatible with experiment. Furthermore we have studied the high energy L satellite band of c-Si and a-Si.
1. Introduction
Most of the progress in understanding the structure of amorphous materials has been achieved by studying non-crystalline silicon (a-Si) and germanium (a-Ge). Information about the short-range order (SRO) is contained in the radial distribution functions (RDF) obtained from X-ray scattering. The position, intensity and width of the features of the experimental RDF of Si [1,2] and Ge [3,4] show the preservation of SRO in these tetrahedrally bonded materials when going from the crystalline to the amorphous state. It is generally accepted that in a-Si and a-Ge each atom is surrounded by four other atoms (disregarding broken and dangling bonds); distortions of the bond lengths, bond angles, dihedral angles and topology, however, lead to a breakdown of long-range order (LRO). Because there exists no experimental method which provides direct access to the structure of amorphous materials, various structure models have been developed: the continuous random tetrahedral network (CRTN) models, the microcrystallite model, and models which are intermediate between CRTN and microcrystallite models. Based on these structure models radial distribution functions and the density of states (DOS) have been calculated and compared to the corrresponding experimental results.
* Permanent address: Institute of Metal Physics, Ural Science Centre, Academy of Sciences of the USSR, Sverdlovsk GSP-170, USSR. 0022-3093/85/$03.30 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
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The comparison of the calculated DOS curves with experimental results so far is almost entirely based on the XPS measurements of Ley et al. [5] and the UPS measurements of Pierce and Spicer [6]. XPS spectra of Si reflect the features of the total DOS, the s-like electrons being over-emphasized owing to the cross-section ratio of s- and p-like electrons o~: Op ~ 2 : 1. UPS depicts only the upper part of the valence band of a-Si due to the limited photon energy. More detailed information about the electronic structure of a-Si can be extracted from X-ray emission spectroscopy (XES) than from XPS and UPS. X-ray emission bands reflect the partial DOS, i.e. the K- and L-emission bands provide information on the p- and s-like electrons, respectively. The K- and L-emission bands of c-Si and a-Si were measured by Wiech and Z6pf [7] but so far these results have not been extensively used for an analysis of the amorphous state. The paper is organized as follows: in section 2 we describe sample preparation and the experimental conditions for taking the X-ray emission band and high energy satellite spectra. In section 3 the K- and L-emission bands are compared with available XPS measurements. The results for the high energy satellite are reported in section 4. In section 5 we give a description of the structure models and report available RDF results, and finally, in section 6 we discuss the compatibility of calculated RDF and DOS with experiment.
2. Experimental The samples of a-Si were prepared by evaporation in two different ways. In the first case a film of about 8000 A was evaporated onto a Cu-substrate, the temperature of the substrate being 100-200°C. The source-to-substrate distance was about 30 cm, and the evaporated material struck the substrate at near-normal incidence. The rate of deposition was about 50-60 ,~/s at a pressure of 10 -5 Torr. The samples were checked by X-ray diffraction, and good agreement was found with the results reported by Brodsky et al. [8]. In the second case a-Si was deposited onto a disk of a Si single crystal at a pressure of 2 × 1 0 - 6 Torr, whereas the other experimental conditions remained unchanged. The film thickness was 1 /~ and more. The amorphous state was established by electron diffraction. The spectra obtained for both kinds of samples were virtually identical. The K emission bands of c-Si and a-Si were measured with a Johann-type spectrometer using fluorescence excitation. The crystal was quartz cut parallel to the 1010 plane and bent to a radius of about 1 m. The X-ray tube was operated at 10-12 kV, and currents up to 350 mA were used. In the X-ray tube and in the spectrometer a vacuum better than 10 -5 Torr was obtained. In the region of the Si K-emission band the resolution of the spectrometer was about 0.6 eV. For the measurement of the Si Lz.3-emission band and the Si Lz.3-satellite a grazing incidence concave grating spectrometer was used (radius 2 m, 600
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lines/mm, blaze angle 1°31'). The spectra were excited by low-load electron bombardment (2-3 kV, 1-3 mA; area of sample 10-15 mm2). The pressure in the X-ray chamber was 10-7-10 -~ Torr, in the spectrometer about 10 -6 Torr. At 120 A the resolution was about 0.5 eV. If electron excitation is used with electron energies ranging between 2 kV and 3 kV, the Si L-emission bands probe a depth of about 1500 A to 2000 [9]. If fluorescence excitation is used as in the case of the Si K-emission bands, the probed depth is a multiple of these values, and therefore for the measurements of the Si K bands only samples of a-Si deposited on a copper substrate were used. The energy scales of the Si K- and Si L2,3-emission bands are aligned by the Si Ka-lines, which were also measured. The energies of the K a l lines of c-Si and a-Si are 1739.91 eV and 1739.92 eV, respectively.
3. X-ray emission spectra and their comparison to photo-emission measurements In fig. 1 the K and L2,3 emission bands of c-Si and a-Si are shown. The K emission band corresponds to transitions ls ~ 3p and reflects the N3p(E ) partial density-of-states distribution, whereas the L2,3 emission band (transition 2p --* 3s) reflects the N3s(E ) partial density-of-states distribution. At the top of the valence band of c-Si Si3p states are dominant and give the main contribution to the subband denoted by A (fig. lb). Si3s states are concentrated in the middle (B) and at the bottom (C) of the valence band (fig. la). The tailing of the spectra towards lower energies is due to Auger broadening, and the weak hump in the L band between 75 eV and 80 eV reflects the plasmon satellite. In going to the amorphous state (figs. lc, d) the twin structure (B and C) of the L band merges, new states emerge where the minimum used to be, forming a broad common peak, and also details in region A are smoothed out. Similar changes also apply to the K band: all fine structure between 1830 eV and 1835 eV has disappeared, and the valley at 1835 eV is completely filled in. Along with these smearing effects one observes that the centroid of region A is shifted towards higher photon energies (lower binding energies) by about 0.4 eV. The main peak of the K band of c-Si and a-Si is at 1836.1 eV and 1836.65 eV, respectively. The position of the peak is shifted no less than 0.55 eV (and is approximately 2 eV below the valence-band maximum) thus leading to a sharpening of the p-band edge. The high energy edge in the L spectrum is also much steeper in a-Si than in c-Si. At 98 eV the intensities of the L spectra of c-Si and a-Si are less than 30% and more than 40%, respectively, compared to the peak intensity. In addition there is a small step at about 100 eV, which is not observed in the L band of c-Si. These XES results are in excellent agreement with the XPS measurements of Ley et al. [5]. In fig. 2 the XPS results for c-Si and a-Si are reproduced, c-Si
E.Z. Kurmaev, G. Wiech / X-ray spectra and electronic structure of a-Si
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exhibits three distinct features at binding energies 2.2 eV, 6.6 eV and 9.2 eV (fig. 2a). The more tightly bound features reflect the s-part, the broad peak at 2.2 eV the p-part of the DOS. The energy separations of these features, 4.4 eV and 2.6 eV, compare well with the energy differences 4.1 eV and 2.5 eV extracted from the positions of peaks A, B and C of the X-ray K and L emission bands (figs. la, b). In going from c-Si to a-Si the two features in the s-part of the valence band
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X - ray spectra and electronic" structure o f a - Si
merge into one broad hump (fig. 2b) in a similar way as in the L band of a-Si (fig. lc). The pronounced peak closest to E v is maintained, but its centroid is shifted towards the Fermi energy by about 0.4 eV, and the peak by about 0.65 eV (now being approximately 1.8 eV below E v ) in good agreement with XES results. The UPS measurements of a-Si films [6] provide results which are in close agreement with the XES and XPS results. Due to low photon energies (11.7 eV) only the p-part of the valence band (top to - 5 eV) was measured. The electron distribution curves (EDC) of c-Si films exhibit some fine structure, whereas the EDCs of a-Si are strikingly featureless with a broad hump at about 1.75 eV below the valence band maximum. In recent UPS measurements (He II, 40.8 eV) Wesner and Eberhardt [32] observed an EDC of c-Si (annealed a-Si) with a three-peak fine structure which is present as well in the EDC of a-Si films, however with much less contrast. The first two peaks are closely related to features A and B in fig. 1 and corresponding features in fig. 2; the third peak at - 1 2 eV, however, has no equivalent in XES and XPS results. In the UPS measurements [6,32] the centroid of the p-part of the valence band is shifted towards the valence band maximum in going from c-Si to a-Si, as has been observed by XES and XPS.
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192
E.Z. Kurmaeo, G. Wiech / X-ray spectra and electronic structure of a-Si
4. The high energy satellite of the Si L2,3-emission band
Along with the L2, 3 emission bands of c-Si and a-Si the high energy satellites of both materials were measured. The high energy satellite arises from the radiative decay of a double ionization state, (L2.3)2 ~ Lz.3M [10]. Concerning the shape of the spectrum there exist some discrepancies [10,11]. In fig. 3 the high energy satellite and the parent band spectra of c-Si and a-Si are displayed. The position of the satellite and parent spectra was determined by matching a characteristic structure in the satellite with the corresponding structure in the L band. The resulting energy separation is (15.6 _+0.2) eV. The peak intensity of the satellites is only about 1.5% of that of the L bands. The satellite of c-Si (fig. 3a) exhibits four maxima ((105.3 _+0.1) eV, (109.3_0.1) eV, (113.9_+0.2) eV and (117.8 _+0.1) eV), whose intensity decreases with increasing photon energy. The gross features of the satellite band agree with previous work [10,11]. In the spectrum measured by Z6pf [11] the energy and the separation of the two main peaks ((105.2_+ 0.3) eV, (109.1 ± 0.3) eV; AE--3.9 eV) compare well with the present results, the structure of the high energy part, however, is not resolved. These features were observed by Hanson and Arakawa [10] (although less resolved), but the separation of the two low-energy peaks is only about 2.5 eV (which is identical with the peak separation in the L2, 3 emission band of c-Si). The high energy satellite of a-Si (fig. 3b) is similar to that of c-Si, all features, however, are smoothed out, and only two peaks at (105.7 + 0.1) eV, and (117.8 + 0.2) eV are observed. Regarding the changes of spectra in going from c-Si to a-Si there is close similarity between the high energy satellite and the L emission band. The satellites are situated on the high energy side of the L absorption edge. Since the absorption coefficient of Si is a function of the photon energy self-absorption effects may affect the spectrum. According to Hanson and Arakawa [10] self absorption has to be considered for a quantitative comparison of the intensities within the spectrum, but does not significantly change the observed spectrum.
5. Structure models and radial distribution functions
In this section we describe available structure models and the RDF based on them. The agreement of the calculated RDF with the experimental RDF is a necessary prerequisite of any usable structure model and its applicability to studies of other physical properties, such as DOS. In the continuous random tetrahedral network (CRTN) model suggested by Polk and Boudreaux (PB) [12,13] and Connell and Temkin (CT) [14] the amorphous phase consists of a completely disordered structure, whereas each atom is approximately tetrahedrally coordinated with its nearest neighbours. In
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193
this type of CRTN structure models finite networks have been built up containing about 200-500 atoms. But even in clusters of that size a large fraction of atoms is still close to the surface. Therefore, other CRTN models employ a unit of a certain number of atoms satisfying periodic boundary conditions in order to avoid surface effects [15,16]. A quite different approach to the structure of a-Si and a-Ge has been suggested by Joannopoulos and Cohen [17,18]. These authors have studied a series of crystalline polytypes of Si and Ge to find out how changes in the topology of the local environment are reflected in the electronic structure, and whether these materials are useful to serve as structural models for a-Si and a-Ge. It has been assumed that a mixture of microcrystallites of various polymorphs will reflect the properties of the amorphous state. Another model of amorphism is intermediate between the CRTN model and the microcrystallite model: the complex band structure (CBS) model of amorphous structure [19]. CBS structure of a-Si is based on polytypes of c-Si. The amorphous structure is obtained by displacing the atoms from their lattice sites by a small arbitrary amount. Generalization is obtained by considering a model based upon a weighted average of at least two structures [20]. Based on these structure models different physical properties, in particular the RDF and the density of states (DOS), have been calculated and compared to the corresponding experimental results. Using their hand-built CRTN models Polk and Boudreaux [13] and Connell and Temkin [14] calculated the RDF of a-Si and a-Ge, respectively. The RDF fit the gross structure in the experimental RDF [1-4] up to about 6 A, (first three peaks). Shevchik calculated the RDF of a-Ge based on a computer generated CRTN model [21], and he claims his calculations fit all the major peaks in the experimental RDF [3] occurring up to about 10 A. Despite the overall agreement of calculated and experimental RDF, there exist noticeable differences in details. Based on the microcrystallite model Weinstein and Davis [22] calculated the RDF of a series of polymorphs of Ge with diamond (FC-2), wurtzite (2H-4), Si III (Si BC-8), Ge Ill (Ge ST-12), and clathrate I and II structure. Along with the RDF they calculated the electron diffraction function which is one step closer to experimental data than RDF. Whereas the diffraction functions of the polymorphs are in poor agreement with the experimental results for sputtered Ge [3], a combination of 60% Si III and 40% clathrate II quite acceptably reproduces the diffraction data. Therefore these authors suggest that the structure of a-Ge can best be represented by a statistical microcrystallite model, the crystallite diameter being about 15 A. Applying the concept of CBS model of amorphous structure Boyce and McCloughrey [20] calculated the RDF and the X-ray scattering function of a-Si. The authors used a combination of two Si polymorphs. The best agreement with experiment [2] was obtained for a pure distorted wurtzite structure, although there is some disagreement with respect to the heights of the peaks. Whatever structure model has been applied, none of the calculated RDF
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E.Z. Kurmae~, G. Wiech / X-ray spectra and electronic structure of a-Si
really reproduces the experimental data, and even the R D F of different structure models lead to a similar RDF. On the other hand the agreement of a calculated R D F with the experimental R D F is a necessary prerequisite of any usable structure model. Since the R D F is a one-dimensional representation of a three-dimensional structure, distortions in the bond angles and slight changes in the bond lengths will not emerge in the R D F peak representing nearest neighbours. Such changes, however, will affect the strength of the bonds and consequently also the electronic structure. The DOS therefore seems to be a quantity more sensitive to structural disorder than RDF.
6. Comparison of experimental results to calculated DOS It has been shown in section 3 that the transition from c-Si to a-Si is accompanied by substantial changes of the electronic structure, and that the experimental results of XES, XPS and UPS for a-Si are in excellent agreement regarding the features of DOS. In this section we compare the experimental
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results with available DOS calculations to find out which model best fits the experimental data. As will be shown, of all the DOS based on the microcrystallite model and the CRTN model only two are compatible with experiment: the ST-12 structure and the Polk-Boudreaux C R T N model. In fig. 4 are shown the calculated DOS of c-Si [17] and of a-Si based on the ST-12 structure [17,25] and the Polk-Boudreaux model [23]. 6.1. Polymorphs o f silicon
The distortions of the different polymorphs of c-Si (diamond or FC-2) can be characterized as follows: Wurtzite or 2H-4 has no bond-length and bondangle distortions. It has only six-membered rings and 25% of the dihedral angles are in cis and 75% in trans position. BC-8 contains bond-length and bond-angle disorder, but has only even-membered rings. ST-12 is an interesting polymorph, because the Si atoms possess two different types of environment and because of the large fraction of fivefold (and also sevenfold) rings. The DOS for the 2H-4 (wurtzite) [17,18] and BC-8 [17,18,23] structures do not reproduce the experimental data, in that they exhibit too much structure and resemble the DOS of c-Si, which is shown in the top panel of fig, 4. The DOS for the 2H-4 structure suggests conclusions which contrast with those of Boyce and McCloughrey [20], who concluded from the agreement of their calculated R D F with experiment that pure (distorted) wurtzite could serve as a base for the microcrystallite model. The DOS of ST-12 has been calculated by several authors [17,18,23-26]. The results of Joannopoulos and Cohen [17,18] (fig. 4b) and Ching et al. [23] are in good agreement. The DOS exhibit a broad band at lower energies (s-region) and new states near the gap which sharpen the edge of the p-region, in agreement with experiment. The calculations, however, do not reflect the valley between the s- and the p-region, and the spike at about - 7 eV resembles c-Si (fig. 4a). This spike and other fine structure in the calculated DOS, however, may be smoothed out if the DOS curve is folded by a Gaussian of fwhm 0.5 eV or more. This valley and also the broad s-region are present in the DOS of Robertson (fig. 4c). In the ST-12 DOS of Kelly and Bullett [24] the p-peak is shifted towards the top of the valence band, the s-region, however, is in disagreement with other calculated DOS and resembles that of c-Si. The merging of the twin-peak structure in the s-region is generally attributed to the presence of odd-membered rings, while the origin of the shift of the p-peak and the emerging of new states at the top of the valence band is still a subject of debate. Joannopoulos and Cohen [17,18] attribute the latter effect to bond-angle variations. To study the effects of bond-angle variations and rings, and their influence on the p-like region in more detail the Bethe lattice method was applied, and the DOS along with the local DOS of p and s orbitals was calculated [27]. The results for the s-region confirmed that the smoothing out is to be attributed to effects of ring topology. It was also found that the shift of
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the p-peak and the sharpening of the edge are caused by some kind of bond-angle distortion, while dihedral-angle distortions are not very important. Tanake and Tsu [28] have studied the influence of bond length changes, bond angle changes and dihedral angle deviations on the electronic structure of c-Si. The authors find that bond length changes lead to a broadening of states (about 0.2 eV) in the s-region and that bond angle changes shift the p-peak towards the top of the valence band due to a destabilisation of binding energies, while dihedral angle deviations cause a bump structure of DOS in the p-like region of the valence band. The latter conclusions agree with those of Joannopoulos [27], but are being questioned by Singh [29] and Robertson [25,26], who attribute the sharpening of the p-region to dihedral angle distortion. 6.2. C R T N model
Ching et al. [23] and Kelley and Bullett [24] have calculated the DOS of a-Si based on CRTN models. The DOS of the periodic G-54 structure [23] (fig. 4d) shows the same gross features as experiment, the p-peak, however, is too broad, and the peak of the s-region is too narrow and positioned too close to the bottom of the valence band. The DOS for the periodic H-61 structure [23] exhibits no gap between the valence and conduction band, and therefore the H-61 structure is unsuitable. The CRTN model of Connell and Temkin (CT) [14] contains only even-membered rings. Therefore the features of the s-region of the DOS are not smoothed out [23,24] and resemble c-Si. Moreover the p-region does not exhibit a sharp edge. The CT model therefore is not a good model for a-Si. The refined model of Polk and Boudreaux (PB) contains even- and odd-membered rings. As in the case of ST-12 structure (figs. 4b, c) the DOS based on the PB CRTN model (fig. 4d) exhibits a broad s-region (due to five-fold rings), and a sharpened p-edge, with a maximum of the p-region about 2 eV below the top of the valence band [23,24], in accordance with experiment. From discussion it follows that only PB CRTN (and to some extent also G-54) and the ST-12 structure are acceptable candidates for models of a-Si (figs. 4b-d). Both structures have even- and odd-membered rings as well, and topological disorder seems to be responsible for a smooth s-band. Moreover these structure models contain bond length, bond angle and dihedral angle disorder, which lead to the shift and sharpening of the p-peak. Rewesz [30] emphasizes that in a CRTN structure the wide ranges of bond lengths and bond angles appear to be incompatible with sp 3 hybridization characteristic of c-Si, and that therefore d-orbitals of Si participate in bonding. If d-orbitals were participating in bonding they would contribute to the top part of the DOS of the valence band. Indeed, for the X-ray L emission band one observes a considerable contribution of new states at the high energy edge in going from c-Si to a-Si (fig. lc), which in part may be d-like. In a recent paper Papaconstantopoulos [31] has calculated the partial DOS of s-, p-, and
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d-like electrons in c-Si, and it is interesting to note that even in the case of c-Si d-like electrons contribute to the bonds. Rewesz [30] therefore suggested as a model of a-Si a mixture of local configurations the extremes of which resemble c-Si and BC-8 (Si III). In section 5 it has been mentioned that a mixture of 60% Si III and 40% clathrate II reproduces many of the features of Shevchik's diffraction curve of a-Ge. On the other hand it must be emphasized that a mixture of Si III and c-Si will hardly reproduce the DOS of a-Si. Even the DOS of Si III [17,23] retains much of the individual features of c-Si, while the observed features of the s-region of a-Si have drastically changed in going from c-Si to a-Si.
7. Conclusions The analysis of experimental and theoretical results for a-Si has shown that the experimental data of XES, XPS and UPS are in excellent agreement and that, of all the DOS calculations based on different polymorphs of c-Si and on C R T N models, only the ST-12 structure and the PB C R T N model reproduce the basic features of a-Si. We believe that new experiments (XES, XPS, UPS) should be performed to obtain even more reliable and trustworthy experimental data. In particular the influence of differently prepared a-Si samples and of the variation of the experimental conditions during sample preparation on the spectra should be studied in detail. On the other hand refined models are necessary. Based on these models the DOS of p-like and s-like electrons should be calculated as well as X-ray K and L emission bands. Calculated local DOS permit a better comparison with measured emission bands than the total DOS, and therefore provide better insight into the bonding properties, One of the authors (E.Z.K.) thanks the Academy of Sciences of the USSR and Deutsche Forschungsgemeinschaft for financial support.
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W.F. Hanson and E.T. Arakawa, Z. Phys. 251 (1972) 271. E. Z~Spf, Thesis Universitgt M~nchen (1972). D.E. Polk, J. Non-Crystalline Solids 5 (1971) 365. D.E. Polk and D.S. Boudreaux, Phys. Rev. Lett. 31 (1973) 92. G.A.N. Connell and R.J. Temkin, Phys. Rev. B9 (1974) 5323. D. Henderson, J. Non-Crystalline Solids 16 (1974) 317. g. Guttman, Bull. Am. Phys. Soc. 22 (1977) 64, AIP Conf. Proc. 31 (1976) 268. J.D. Joannopoulos and M.L. Cohen, Phys. Rev. B7 (1973) 2644. J.D. Joannopoulos and M.L. Cohen, in Solid State Physics 31, eds., H. Ehrenreich, F. Seitz and D. Turnbull (Academic Press, New York-San Francisco-London, 1976) p. 71. B. Kramer, Phys. Stat. Sol. (b)47 (1971) 501. B. Kramer, K. Maschke and P. Thomas, Phys. Stat. Sol. (b)48 (1971) 635. J.F. Boyce and J.K. McCloughrey, Phys. Stat. Sol (b)63 (1974) 569. N.J. Shevchik, Phys. Star. Sol (b)58 (1973) 111. F.C. Weinstein and E.A. Davis, J. Non-Crystalline Solids 13 (1973/74) 153. W.Y. Ching, C.C. Lin and L. Guttman, Phys. Rev. B16 (1977) 5488. M.J. Kelly and D.W. Bullett, J. Non-Crystalline Solids 21 (1976) 155. J. Robertson, Adv. Phys. 32 (1983) 361. J. Robertson, Phys. Rev. B28 (1983) 4647. J.D. Joannopoulos, Phys. Rev. B16 (1977) 2764. K. Tanaka and R. Tsu, Phys. Rev. B24 (1981) 2038. J. Singh. Phys. Rev. B23 (1981) 4156. A.G. Rewesz, Phys. Star. Sol. (a)60 (1980) 619. D.A. Papaconstantopoulos, Phys. Rev. B27 (1983) 2569. D. Wesner and W. Eberhardt, Phys. Rev. B28 (1983) 7087.
187
X-RAY EMISSION SPECTRA AND ELECTRONIC STRUCTURE OF AMORPHOUS SILICON E.Z. K U R M A E V * and G. WIECH Sektion Physik der Universitgtt M~nchen, 8000 M~znchen 22, Fed. Rep. Germany Received 7 August 1984
X-ray K and L emission bands of c-Si and a-Si are reported and compared with available XPS and UPS measurements. The experimental results for a-Si are found to be consistent and in excellent agreement. From comparison of the experimental results with available electron densityof-states calculations based on different structure models of the amorphous state, we conclude that only ST-12 structure and the Polk-Boudreaux model provide results that are compatible with experiment. Furthermore we have studied the high energy L satellite band of c-Si and a-Si.
1. Introduction
Most of the progress in understanding the structure of amorphous materials has been achieved by studying non-crystalline silicon (a-Si) and germanium (a-Ge). Information about the short-range order (SRO) is contained in the radial distribution functions (RDF) obtained from X-ray scattering. The position, intensity and width of the features of the experimental RDF of Si [1,2] and Ge [3,4] show the preservation of SRO in these tetrahedrally bonded materials when going from the crystalline to the amorphous state. It is generally accepted that in a-Si and a-Ge each atom is surrounded by four other atoms (disregarding broken and dangling bonds); distortions of the bond lengths, bond angles, dihedral angles and topology, however, lead to a breakdown of long-range order (LRO). Because there exists no experimental method which provides direct access to the structure of amorphous materials, various structure models have been developed: the continuous random tetrahedral network (CRTN) models, the microcrystallite model, and models which are intermediate between CRTN and microcrystallite models. Based on these structure models radial distribution functions and the density of states (DOS) have been calculated and compared to the corrresponding experimental results.
* Permanent address: Institute of Metal Physics, Ural Science Centre, Academy of Sciences of the USSR, Sverdlovsk GSP-170, USSR. 0022-3093/85/$03.30 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
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The comparison of the calculated DOS curves with experimental results so far is almost entirely based on the XPS measurements of Ley et al. [5] and the UPS measurements of Pierce and Spicer [6]. XPS spectra of Si reflect the features of the total DOS, the s-like electrons being over-emphasized owing to the cross-section ratio of s- and p-like electrons o~: Op ~ 2 : 1. UPS depicts only the upper part of the valence band of a-Si due to the limited photon energy. More detailed information about the electronic structure of a-Si can be extracted from X-ray emission spectroscopy (XES) than from XPS and UPS. X-ray emission bands reflect the partial DOS, i.e. the K- and L-emission bands provide information on the p- and s-like electrons, respectively. The K- and L-emission bands of c-Si and a-Si were measured by Wiech and Z6pf [7] but so far these results have not been extensively used for an analysis of the amorphous state. The paper is organized as follows: in section 2 we describe sample preparation and the experimental conditions for taking the X-ray emission band and high energy satellite spectra. In section 3 the K- and L-emission bands are compared with available XPS measurements. The results for the high energy satellite are reported in section 4. In section 5 we give a description of the structure models and report available RDF results, and finally, in section 6 we discuss the compatibility of calculated RDF and DOS with experiment.
2. Experimental The samples of a-Si were prepared by evaporation in two different ways. In the first case a film of about 8000 A was evaporated onto a Cu-substrate, the temperature of the substrate being 100-200°C. The source-to-substrate distance was about 30 cm, and the evaporated material struck the substrate at near-normal incidence. The rate of deposition was about 50-60 ,~/s at a pressure of 10 -5 Torr. The samples were checked by X-ray diffraction, and good agreement was found with the results reported by Brodsky et al. [8]. In the second case a-Si was deposited onto a disk of a Si single crystal at a pressure of 2 × 1 0 - 6 Torr, whereas the other experimental conditions remained unchanged. The film thickness was 1 /~ and more. The amorphous state was established by electron diffraction. The spectra obtained for both kinds of samples were virtually identical. The K emission bands of c-Si and a-Si were measured with a Johann-type spectrometer using fluorescence excitation. The crystal was quartz cut parallel to the 1010 plane and bent to a radius of about 1 m. The X-ray tube was operated at 10-12 kV, and currents up to 350 mA were used. In the X-ray tube and in the spectrometer a vacuum better than 10 -5 Torr was obtained. In the region of the Si K-emission band the resolution of the spectrometer was about 0.6 eV. For the measurement of the Si Lz.3-emission band and the Si Lz.3-satellite a grazing incidence concave grating spectrometer was used (radius 2 m, 600
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189
lines/mm, blaze angle 1°31'). The spectra were excited by low-load electron bombardment (2-3 kV, 1-3 mA; area of sample 10-15 mm2). The pressure in the X-ray chamber was 10-7-10 -~ Torr, in the spectrometer about 10 -6 Torr. At 120 A the resolution was about 0.5 eV. If electron excitation is used with electron energies ranging between 2 kV and 3 kV, the Si L-emission bands probe a depth of about 1500 A to 2000 [9]. If fluorescence excitation is used as in the case of the Si K-emission bands, the probed depth is a multiple of these values, and therefore for the measurements of the Si K bands only samples of a-Si deposited on a copper substrate were used. The energy scales of the Si K- and Si L2,3-emission bands are aligned by the Si Ka-lines, which were also measured. The energies of the K a l lines of c-Si and a-Si are 1739.91 eV and 1739.92 eV, respectively.
3. X-ray emission spectra and their comparison to photo-emission measurements In fig. 1 the K and L2,3 emission bands of c-Si and a-Si are shown. The K emission band corresponds to transitions ls ~ 3p and reflects the N3p(E ) partial density-of-states distribution, whereas the L2,3 emission band (transition 2p --* 3s) reflects the N3s(E ) partial density-of-states distribution. At the top of the valence band of c-Si Si3p states are dominant and give the main contribution to the subband denoted by A (fig. lb). Si3s states are concentrated in the middle (B) and at the bottom (C) of the valence band (fig. la). The tailing of the spectra towards lower energies is due to Auger broadening, and the weak hump in the L band between 75 eV and 80 eV reflects the plasmon satellite. In going to the amorphous state (figs. lc, d) the twin structure (B and C) of the L band merges, new states emerge where the minimum used to be, forming a broad common peak, and also details in region A are smoothed out. Similar changes also apply to the K band: all fine structure between 1830 eV and 1835 eV has disappeared, and the valley at 1835 eV is completely filled in. Along with these smearing effects one observes that the centroid of region A is shifted towards higher photon energies (lower binding energies) by about 0.4 eV. The main peak of the K band of c-Si and a-Si is at 1836.1 eV and 1836.65 eV, respectively. The position of the peak is shifted no less than 0.55 eV (and is approximately 2 eV below the valence-band maximum) thus leading to a sharpening of the p-band edge. The high energy edge in the L spectrum is also much steeper in a-Si than in c-Si. At 98 eV the intensities of the L spectra of c-Si and a-Si are less than 30% and more than 40%, respectively, compared to the peak intensity. In addition there is a small step at about 100 eV, which is not observed in the L band of c-Si. These XES results are in excellent agreement with the XPS measurements of Ley et al. [5]. In fig. 2 the XPS results for c-Si and a-Si are reproduced, c-Si
E.Z. Kurmaev, G. Wiech / X-ray spectra and electronic structure of a-Si
190
exhibits three distinct features at binding energies 2.2 eV, 6.6 eV and 9.2 eV (fig. 2a). The more tightly bound features reflect the s-part, the broad peak at 2.2 eV the p-part of the DOS. The energy separations of these features, 4.4 eV and 2.6 eV, compare well with the energy differences 4.1 eV and 2.5 eV extracted from the positions of peaks A, B and C of the X-ray K and L emission bands (figs. la, b). In going from c-Si to a-Si the two features in the s-part of the valence band
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X - ray spectra and electronic" structure o f a - Si
merge into one broad hump (fig. 2b) in a similar way as in the L band of a-Si (fig. lc). The pronounced peak closest to E v is maintained, but its centroid is shifted towards the Fermi energy by about 0.4 eV, and the peak by about 0.65 eV (now being approximately 1.8 eV below E v ) in good agreement with XES results. The UPS measurements of a-Si films [6] provide results which are in close agreement with the XES and XPS results. Due to low photon energies (11.7 eV) only the p-part of the valence band (top to - 5 eV) was measured. The electron distribution curves (EDC) of c-Si films exhibit some fine structure, whereas the EDCs of a-Si are strikingly featureless with a broad hump at about 1.75 eV below the valence band maximum. In recent UPS measurements (He II, 40.8 eV) Wesner and Eberhardt [32] observed an EDC of c-Si (annealed a-Si) with a three-peak fine structure which is present as well in the EDC of a-Si films, however with much less contrast. The first two peaks are closely related to features A and B in fig. 1 and corresponding features in fig. 2; the third peak at - 1 2 eV, however, has no equivalent in XES and XPS results. In the UPS measurements [6,32] the centroid of the p-part of the valence band is shifted towards the valence band maximum in going from c-Si to a-Si, as has been observed by XES and XPS.
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192
E.Z. Kurmaeo, G. Wiech / X-ray spectra and electronic structure of a-Si
4. The high energy satellite of the Si L2,3-emission band
Along with the L2, 3 emission bands of c-Si and a-Si the high energy satellites of both materials were measured. The high energy satellite arises from the radiative decay of a double ionization state, (L2.3)2 ~ Lz.3M [10]. Concerning the shape of the spectrum there exist some discrepancies [10,11]. In fig. 3 the high energy satellite and the parent band spectra of c-Si and a-Si are displayed. The position of the satellite and parent spectra was determined by matching a characteristic structure in the satellite with the corresponding structure in the L band. The resulting energy separation is (15.6 _+0.2) eV. The peak intensity of the satellites is only about 1.5% of that of the L bands. The satellite of c-Si (fig. 3a) exhibits four maxima ((105.3 _+0.1) eV, (109.3_0.1) eV, (113.9_+0.2) eV and (117.8 _+0.1) eV), whose intensity decreases with increasing photon energy. The gross features of the satellite band agree with previous work [10,11]. In the spectrum measured by Z6pf [11] the energy and the separation of the two main peaks ((105.2_+ 0.3) eV, (109.1 ± 0.3) eV; AE--3.9 eV) compare well with the present results, the structure of the high energy part, however, is not resolved. These features were observed by Hanson and Arakawa [10] (although less resolved), but the separation of the two low-energy peaks is only about 2.5 eV (which is identical with the peak separation in the L2, 3 emission band of c-Si). The high energy satellite of a-Si (fig. 3b) is similar to that of c-Si, all features, however, are smoothed out, and only two peaks at (105.7 + 0.1) eV, and (117.8 + 0.2) eV are observed. Regarding the changes of spectra in going from c-Si to a-Si there is close similarity between the high energy satellite and the L emission band. The satellites are situated on the high energy side of the L absorption edge. Since the absorption coefficient of Si is a function of the photon energy self-absorption effects may affect the spectrum. According to Hanson and Arakawa [10] self absorption has to be considered for a quantitative comparison of the intensities within the spectrum, but does not significantly change the observed spectrum.
5. Structure models and radial distribution functions
In this section we describe available structure models and the RDF based on them. The agreement of the calculated RDF with the experimental RDF is a necessary prerequisite of any usable structure model and its applicability to studies of other physical properties, such as DOS. In the continuous random tetrahedral network (CRTN) model suggested by Polk and Boudreaux (PB) [12,13] and Connell and Temkin (CT) [14] the amorphous phase consists of a completely disordered structure, whereas each atom is approximately tetrahedrally coordinated with its nearest neighbours. In
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193
this type of CRTN structure models finite networks have been built up containing about 200-500 atoms. But even in clusters of that size a large fraction of atoms is still close to the surface. Therefore, other CRTN models employ a unit of a certain number of atoms satisfying periodic boundary conditions in order to avoid surface effects [15,16]. A quite different approach to the structure of a-Si and a-Ge has been suggested by Joannopoulos and Cohen [17,18]. These authors have studied a series of crystalline polytypes of Si and Ge to find out how changes in the topology of the local environment are reflected in the electronic structure, and whether these materials are useful to serve as structural models for a-Si and a-Ge. It has been assumed that a mixture of microcrystallites of various polymorphs will reflect the properties of the amorphous state. Another model of amorphism is intermediate between the CRTN model and the microcrystallite model: the complex band structure (CBS) model of amorphous structure [19]. CBS structure of a-Si is based on polytypes of c-Si. The amorphous structure is obtained by displacing the atoms from their lattice sites by a small arbitrary amount. Generalization is obtained by considering a model based upon a weighted average of at least two structures [20]. Based on these structure models different physical properties, in particular the RDF and the density of states (DOS), have been calculated and compared to the corresponding experimental results. Using their hand-built CRTN models Polk and Boudreaux [13] and Connell and Temkin [14] calculated the RDF of a-Si and a-Ge, respectively. The RDF fit the gross structure in the experimental RDF [1-4] up to about 6 A, (first three peaks). Shevchik calculated the RDF of a-Ge based on a computer generated CRTN model [21], and he claims his calculations fit all the major peaks in the experimental RDF [3] occurring up to about 10 A. Despite the overall agreement of calculated and experimental RDF, there exist noticeable differences in details. Based on the microcrystallite model Weinstein and Davis [22] calculated the RDF of a series of polymorphs of Ge with diamond (FC-2), wurtzite (2H-4), Si III (Si BC-8), Ge Ill (Ge ST-12), and clathrate I and II structure. Along with the RDF they calculated the electron diffraction function which is one step closer to experimental data than RDF. Whereas the diffraction functions of the polymorphs are in poor agreement with the experimental results for sputtered Ge [3], a combination of 60% Si III and 40% clathrate II quite acceptably reproduces the diffraction data. Therefore these authors suggest that the structure of a-Ge can best be represented by a statistical microcrystallite model, the crystallite diameter being about 15 A. Applying the concept of CBS model of amorphous structure Boyce and McCloughrey [20] calculated the RDF and the X-ray scattering function of a-Si. The authors used a combination of two Si polymorphs. The best agreement with experiment [2] was obtained for a pure distorted wurtzite structure, although there is some disagreement with respect to the heights of the peaks. Whatever structure model has been applied, none of the calculated RDF
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E.Z. Kurmae~, G. Wiech / X-ray spectra and electronic structure of a-Si
really reproduces the experimental data, and even the R D F of different structure models lead to a similar RDF. On the other hand the agreement of a calculated R D F with the experimental R D F is a necessary prerequisite of any usable structure model. Since the R D F is a one-dimensional representation of a three-dimensional structure, distortions in the bond angles and slight changes in the bond lengths will not emerge in the R D F peak representing nearest neighbours. Such changes, however, will affect the strength of the bonds and consequently also the electronic structure. The DOS therefore seems to be a quantity more sensitive to structural disorder than RDF.
6. Comparison of experimental results to calculated DOS It has been shown in section 3 that the transition from c-Si to a-Si is accompanied by substantial changes of the electronic structure, and that the experimental results of XES, XPS and UPS for a-Si are in excellent agreement regarding the features of DOS. In this section we compare the experimental
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E.Z. Kurmaev, G. Wiech / X-ray spectra and electronic structure of a-Si
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results with available DOS calculations to find out which model best fits the experimental data. As will be shown, of all the DOS based on the microcrystallite model and the CRTN model only two are compatible with experiment: the ST-12 structure and the Polk-Boudreaux C R T N model. In fig. 4 are shown the calculated DOS of c-Si [17] and of a-Si based on the ST-12 structure [17,25] and the Polk-Boudreaux model [23]. 6.1. Polymorphs o f silicon
The distortions of the different polymorphs of c-Si (diamond or FC-2) can be characterized as follows: Wurtzite or 2H-4 has no bond-length and bondangle distortions. It has only six-membered rings and 25% of the dihedral angles are in cis and 75% in trans position. BC-8 contains bond-length and bond-angle disorder, but has only even-membered rings. ST-12 is an interesting polymorph, because the Si atoms possess two different types of environment and because of the large fraction of fivefold (and also sevenfold) rings. The DOS for the 2H-4 (wurtzite) [17,18] and BC-8 [17,18,23] structures do not reproduce the experimental data, in that they exhibit too much structure and resemble the DOS of c-Si, which is shown in the top panel of fig, 4. The DOS for the 2H-4 structure suggests conclusions which contrast with those of Boyce and McCloughrey [20], who concluded from the agreement of their calculated R D F with experiment that pure (distorted) wurtzite could serve as a base for the microcrystallite model. The DOS of ST-12 has been calculated by several authors [17,18,23-26]. The results of Joannopoulos and Cohen [17,18] (fig. 4b) and Ching et al. [23] are in good agreement. The DOS exhibit a broad band at lower energies (s-region) and new states near the gap which sharpen the edge of the p-region, in agreement with experiment. The calculations, however, do not reflect the valley between the s- and the p-region, and the spike at about - 7 eV resembles c-Si (fig. 4a). This spike and other fine structure in the calculated DOS, however, may be smoothed out if the DOS curve is folded by a Gaussian of fwhm 0.5 eV or more. This valley and also the broad s-region are present in the DOS of Robertson (fig. 4c). In the ST-12 DOS of Kelly and Bullett [24] the p-peak is shifted towards the top of the valence band, the s-region, however, is in disagreement with other calculated DOS and resembles that of c-Si. The merging of the twin-peak structure in the s-region is generally attributed to the presence of odd-membered rings, while the origin of the shift of the p-peak and the emerging of new states at the top of the valence band is still a subject of debate. Joannopoulos and Cohen [17,18] attribute the latter effect to bond-angle variations. To study the effects of bond-angle variations and rings, and their influence on the p-like region in more detail the Bethe lattice method was applied, and the DOS along with the local DOS of p and s orbitals was calculated [27]. The results for the s-region confirmed that the smoothing out is to be attributed to effects of ring topology. It was also found that the shift of
196
E.Z. Kurmaev, G. Wiech / X-ray spectra and electronic structure of a-Si
the p-peak and the sharpening of the edge are caused by some kind of bond-angle distortion, while dihedral-angle distortions are not very important. Tanake and Tsu [28] have studied the influence of bond length changes, bond angle changes and dihedral angle deviations on the electronic structure of c-Si. The authors find that bond length changes lead to a broadening of states (about 0.2 eV) in the s-region and that bond angle changes shift the p-peak towards the top of the valence band due to a destabilisation of binding energies, while dihedral angle deviations cause a bump structure of DOS in the p-like region of the valence band. The latter conclusions agree with those of Joannopoulos [27], but are being questioned by Singh [29] and Robertson [25,26], who attribute the sharpening of the p-region to dihedral angle distortion. 6.2. C R T N model
Ching et al. [23] and Kelley and Bullett [24] have calculated the DOS of a-Si based on CRTN models. The DOS of the periodic G-54 structure [23] (fig. 4d) shows the same gross features as experiment, the p-peak, however, is too broad, and the peak of the s-region is too narrow and positioned too close to the bottom of the valence band. The DOS for the periodic H-61 structure [23] exhibits no gap between the valence and conduction band, and therefore the H-61 structure is unsuitable. The CRTN model of Connell and Temkin (CT) [14] contains only even-membered rings. Therefore the features of the s-region of the DOS are not smoothed out [23,24] and resemble c-Si. Moreover the p-region does not exhibit a sharp edge. The CT model therefore is not a good model for a-Si. The refined model of Polk and Boudreaux (PB) contains even- and odd-membered rings. As in the case of ST-12 structure (figs. 4b, c) the DOS based on the PB CRTN model (fig. 4d) exhibits a broad s-region (due to five-fold rings), and a sharpened p-edge, with a maximum of the p-region about 2 eV below the top of the valence band [23,24], in accordance with experiment. From discussion it follows that only PB CRTN (and to some extent also G-54) and the ST-12 structure are acceptable candidates for models of a-Si (figs. 4b-d). Both structures have even- and odd-membered rings as well, and topological disorder seems to be responsible for a smooth s-band. Moreover these structure models contain bond length, bond angle and dihedral angle disorder, which lead to the shift and sharpening of the p-peak. Rewesz [30] emphasizes that in a CRTN structure the wide ranges of bond lengths and bond angles appear to be incompatible with sp 3 hybridization characteristic of c-Si, and that therefore d-orbitals of Si participate in bonding. If d-orbitals were participating in bonding they would contribute to the top part of the DOS of the valence band. Indeed, for the X-ray L emission band one observes a considerable contribution of new states at the high energy edge in going from c-Si to a-Si (fig. lc), which in part may be d-like. In a recent paper Papaconstantopoulos [31] has calculated the partial DOS of s-, p-, and
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d-like electrons in c-Si, and it is interesting to note that even in the case of c-Si d-like electrons contribute to the bonds. Rewesz [30] therefore suggested as a model of a-Si a mixture of local configurations the extremes of which resemble c-Si and BC-8 (Si III). In section 5 it has been mentioned that a mixture of 60% Si III and 40% clathrate II reproduces many of the features of Shevchik's diffraction curve of a-Ge. On the other hand it must be emphasized that a mixture of Si III and c-Si will hardly reproduce the DOS of a-Si. Even the DOS of Si III [17,23] retains much of the individual features of c-Si, while the observed features of the s-region of a-Si have drastically changed in going from c-Si to a-Si.
7. Conclusions The analysis of experimental and theoretical results for a-Si has shown that the experimental data of XES, XPS and UPS are in excellent agreement and that, of all the DOS calculations based on different polymorphs of c-Si and on C R T N models, only the ST-12 structure and the PB C R T N model reproduce the basic features of a-Si. We believe that new experiments (XES, XPS, UPS) should be performed to obtain even more reliable and trustworthy experimental data. In particular the influence of differently prepared a-Si samples and of the variation of the experimental conditions during sample preparation on the spectra should be studied in detail. On the other hand refined models are necessary. Based on these models the DOS of p-like and s-like electrons should be calculated as well as X-ray K and L emission bands. Calculated local DOS permit a better comparison with measured emission bands than the total DOS, and therefore provide better insight into the bonding properties, One of the authors (E.Z.K.) thanks the Academy of Sciences of the USSR and Deutsche Forschungsgemeinschaft for financial support.
References [1] S.C. Moss and J.F. Graczyk, in Proc. Tenth Int. Conf. on Physics of Semiconductors, Cambridge, Massachusetts, 1970, eds., S.P. Keller, J.C. Hensel and F. Stern, CONF-700801 (US AEC Div. of Techn. Inf., Springfield, Va., 1970) p. 658. [2] S.C. Moss and J.F. Graczyk, Phys. Rev. Lett. 23 (1969) 1167. [3] N.J. Shevchik and W. Paul, J. Non-CrystallineSolids 8-10 (1972) 381. [4] R.J. Temkin, W. Paul and G.A.N. Connell, Adv. Phys. 22 (1973) 581. [5] L. Ley, S. Kowalczyk,R. Pollak and D.A. Shirley, Phys. Rev. Lett. 29 (1972) 1088. [6] D.T. Pierce and W.E. Spicer, Phys. Rev. B5 (1972) 3017. [7] G. Wiech and E. ZOpf, in Band Structure Spectroscopy of Metals and Alloys, eds., D.J. Fabian and L.M. Watson (AcademicPress, London-New York, 1973) p. 629. [8] M.H. Brodsky, R.S. Title, K. Weiser and G.D. Petit, Phys. Rev. B1 (1970) 2632. [9] L. Hoffmann, G. Wiech and E. Zrpf, Z. Phys. 229 (1969) 131.
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E.Z. Kurmaev, G. Wiech / X-ray spectra and electronic structure of a- Si
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