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Structure of amorphous GexSe1−x and GexSeyZnz thin films: an EXAFS study
Journal of Non-Crystalline Solids 297 (2002) 156–172 www.elsevier.com/locate/jnoncrysol
Structure of amorphous GexSe1x and GexSey Znz thin films: an EXAFS study J. Choi, S.J. Gurman, E.A. Davis
*
Department of Physics and Astronomy, University of Leicester, University Road, Leicester LE1 7RH, UK Received 5 October 2001
Abstract Extended X-ray absorption fine structure (EXAFS) measurements have been made on thin films of a-Gex Se1x with 0:2 < x < 1. The results show that the Ge–Ge, Ge–Se and Se–Se bond lengths have values 2.45, 2.37 and 2.32 (all 0:03) , respectively and are independent of film composition. The partial atomic coordination numbers of Ge and Se suggest A that the films have a predominantly chemically ordered 4-2 coordinated covalent bond network structure throughout the whole composition range, as found by others for Ge–Se bulk glasses with x < 0:4. EXAFS data for a-Gex Sey Znz , independent of the comfilms show that the lengths of Ge–Zn and Se–Zn bonds are 2:57 0:05 and 2:44 0:03 A position. Results on the atomic coordinations reveal that Zn is fourfold coordinated and preferentially bonds to Se atoms. Ó 2002 Elsevier Science B.V. All rights reserved.
1. Introduction In recent years, a great deal of interest has been given to structural studies of chalcogenide glasses because of their distinct usefulness as electrical and optical components. One of the binary chalcogenides, Gex Se1x , has been studied by several workers in the amorphous form, either as bulk glasses or as thin films. Two main frameworks have frequently been used for considering the structure of this system: one is based on the Chemically Ordered Network model proposed by Lucovsky [1] and the other is based on Phillips’ constraint theory [2]. The first refers to
*
Corresponding author. Tel.: +44-166 252 3571; fax: +44116 252 2770. E-mail address: [email protected] (E.A. Davis).
nearest-neighbour coordinations (short-range order) whereas the second is concerned with glassforming ability and medium-range structure. Determination of the structure of these films, particularly their degree of chemical order, is not straightforward. Ge and Se atoms have very similar electron and X-ray scattering factors and the three possible types of bond, Ge–Ge, Ge–Se and Se–Se, are similar in length. X-ray diffraction can give only the mean bond length and the mean coordination. Results using this technique for bulk glasses, which exist only in the glass-forming region x < 0:4, favour a 4-2 coordinated network [3]. The extended X-ray absorption fine structure (EXAFS) technique is limited to providing nearest-neighbour information but should give more information than X-ray diffraction since both Ge and Se K-edge structures can be measured. Zhou et al. [4] performed EXAFS measurements on
0022-3093/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 3 0 9 3 ( 0 1 ) 0 0 9 3 7 - 1
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Gex Se1x bulk glasses ðx < 0:4Þ and provided data on the three bond lengths and the coordinations, which supported a chemically ordered 4-2 coordinated network model. In this work, we report EXAFS data on a range of sputtered a-Gex Se1x thin films with 0:2 < x < 1, which includes samples in the Ge-rich region of the system which can only be produced in the form of thin films. EXAFS data on Zn-alloyed films, a-Gex Sey Znz ðz < 0:24Þ, have also been obtained and analysed, in order to investigate the effects of the inclusion of a third atom on the properties of the films. ZnSe, in which both Zn and Se are fourfold covalently bonded, is a wide bandgap semiconductor, and so the inclusion of Zn could increase the bandgap (and the average Se coordination) allowing an extra degree of bandgap tuning. It is also possible that Zn could bond metallically, so driving an insulator–metal transition, as does Ti in amorphous Si [5]. In this case we would expect a high Zn coordination. The EXAFS experiments were carried out using the synchrotron radiation source at the CLRC Daresbury Laboratory, UK. Data analysis was made using EXCURV92 which is an improved fast curved-wave simulation program [6]. Structural information on bond lengths and their mean square deviations will be presented separately for the a-Gex Se1x and a-Gex Sey Znz systems. Results on the partial co-ordination numbers will be compared with two simple structural models, the chemically ordered bond network (OBN) model and the random bond network (RBN) model.
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pieces of Zn foils ð4 4 1 mm3 Þ onto a polycrystalline Ge target (400 diameter). The films were deposited onto mylar substrates to yield thicknesses of 0.5–2.5 lm. The thickness of the films was determined optically by analysing the fringes in reflection data [7]. The compositions of the films were determined by an energy dispersive X-ray analyser (SEM-EDAX) attached to a DS 130 scanning electron microscope. The amorphicity of the films was checked by a 100 keV transmission electron microscope. The EXAFS measurements of the films were carried out using the 2 GeV synchrotron radiation source at station 7.1 of the CLRC Daresbury Laboratory. The X-ray spectra beyond the Ge, Se and Zn K-edges were obtained in the region from 12 to 14 keV in transmission mode. The incident X-ray beam was monochromatized using a Si (1 1 1) double-crystal monochromator with harmonic rejection set at 80%. Before and after passing through the monochromator, the size of the beam was defined horizontally and vertically by two slits. Both the monochromator and slits were kept in evacuated chambers. The samples on their mylar substrates were folded several times to obtain the optimal thickness (40–50 lmÞ and inserted into a sample holder situated between two ionization chamber detectors. The ionization chambers, filled with Ar gas, measured the incident X-ray beam intensity I0 and the transmitted beam intensity It , respectively. Hence the absorption coefficient l was easily determined.
3. Data analysis 2. Experimental details The films used for EXAFS measurements were prepared by radio-frequency (rf)-sputtering at room temperature. The base pressure of the chamber was 2 107 mTorr and sputtering was in argon at a pressure of 3–6 mTorr. The rf power was 240 W, at a frequency of 13.56 MHz. A cosputtering method was employed for the deposition of binary a-Gex Se1x and ternary a-Gex Sey Znz films. The composition of the films was controlled by distributing Se pellets (3.5 mm diameter) and
The raw EXAFS data were recorded in the central computer of the Daresbury Laboratory and analysed using the computer programs available at the laboratory. Each transmission spectrum was first energy calibrated by the program EXCALIB and the calibrated data was normalized by the program, EXBACK. The background of the EXAFS signal was subtracted as follows. The pre-edge data was fitted by a first-order polynomial and the post-edge data was fitted by third-order polynomial to give a smoothly varying background absorption l0 , which was then
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subtracted to leave the EXAFS function vðEÞ. The function vðEÞ was converted to the k-space function vðkÞ and multiplied by k raised to some power n (of the order of 1–3) to yield a weighted function of approximately constant amplitude. The data from EXBACK were processed by the program EXCURV92, which finally enabled extraction of the structural information from the data. This program is based on the fast curved wave theory [6]. For the nearest-neighbour contributions, only single-scattering events need be considered. Theoretical curves were fitted to the experimental data by means of non-linear least-squares fitting. In the process of fitting, several parameters were involved. The main fitting parameters are: Rj (the nearest-neighbour bond length) and E0 (the absorption edge energy); correlated parameters which control the phase of the function vðkÞ, and the pair Nj (the number of neighbours in a given shell) and Aj (the Debye– Waller factor) which control the amplitude of vðkÞ. The parameters were continuously refined by iteration processes until the best fit between the experimental and theoretical curves was obtained. After consideration of possible different atom types as neighbours, i.e. changing the parameter Tj , curves giving the minimum fit index, FI, were chosen as the final result. The FI is defined by X 2 FI ¼ 1=100Np ½fvi ðtheo:Þ vi ðexp:Þgk n ; ð1Þ where Np is the number of data points in the spectrum and n is the weighting factor mentioned above. The uncertainties in the parameters were checked by a contour map which was also available in EXCURV92. A 95% confidence limit was always used. A theory using the statistical test by this contour map is clearly described in Joyner et al. [8]. The fitting range used for Gex Se1x films ran 1 for the Ge K-edge data and from k ¼ 1 to 12.5 A 1 for the Se K-edge data in from k ¼ 2 to 11:5 A order to filter noise from the spectra. Throughout the analysis of each EXAFS spectrum by the EXCURV92 program, the amplitude factor AFAC (the parameter which corrects for amplitude reductions arising from events such as multiple excitations) and VPI (the parameter which takes into account inelastic losses and the core-
hole lifetime) were fixed at 0.8 and )4.0 eV, respectively for the Ge and Se K-edges. These values were obtained from an analysis of results from a standard a-Ge sample. The parameter E0 , which adjusts for the position of the X-ray absorption edge, was chosen from the EXCALIB program and allowed to vary freely in the fitting procedure. The scattering phaseshifts of each neighbour atom type were calculated and applied in the fitting process. It is not possible to distinguish Ge and Se atoms on the basis of their electron scattering factors, which are extremely similar. Thus in the analysis we used the fitted bond lengths to identify the atom type: thus the shortest contribution was assumed to be due to Se–Se bonds, etc. The fitting ranges in k-space for the Gex Sey Znz 1 for films were selected to be from k ¼ 1 to 13:5 A 1 for the Ge K-edge spectra, from k ¼ 1 to 12:5 A 1 the Se K-edge spectra, and from k ¼ 1 to 10:5 A for the Zn K-edge spectra. Depending on the noise presented in the k-space EXAFS spectra, the fitting range of k was adjusted for better RDF fitting. Throughout an analysis of each EXAFS spectrum, the amplitude factor, AFAC, and the parameter, VPI, were fixed at 0.8 and )0.4 eV, respectively, for all three K-edges, while the other parameters were allowed to vary freely in the fitting procedure. Once again, the three components have very similar electron scattering factors and so the atoms types were assigned on the basis of bond length. In all cases no significant contribution was found with a so that Zn– bond length greater than about 2.6 A Zn bonds were excluded from all the fits. After using the three computer programs mentioned above, the set of structural information of the sample, i.e. the nearest bond-length, the nearest bond-type, the number of nearest neighbours and the mean-square deviation of the bond-length, together with their associated fitting uncertainties was finally obtained. 4. Results 4.1. a-Gex Se1x films X-ray absorption spectra for the Ge and Se K-edges of a-Gex Se1x films obtained from the
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experiments, were analysed using the computer programs described in Section 3. Some examples of the final EXAFS functions, vðkÞ, and the radial distibution fuctions (RDFs) for the Ge and Se Kedges of a-Gex Se1x films are presented in Fig. 1. As seen in the figures, the samples show only one strong peak in the RDFs. This implies that our films preserve short-range order primarily in the first shell of nearest neighbours and considerable structural disorder exists in higher shells. The almost total lack of more distant peaks in the RDF is a feature of EXAFS data (compare Fig. 1 with the RDFs obtained from neutron diffraction data by Petri et al. [9] for Ge33 Se67 bulk glasses). It arises from the lack of low-k data. The EXAFS 1 , the wavevector of an spectra start at k 1–2 A electron at the bottom of the conduction band. Peaks with strong disorder are therefore strongly attenuated by the Debye–Waller factor. The structural parameters obtained from the analysis of the EXAFS data are the nearest-
159
neighbour bond lengths, the mean square deviations in these (the EXAFS Debye–Waller factor) and the partial coordination numbers. The lengths of the Ge–Ge, Ge–Se and Se–Se bonds determined from the analyses are presented in Fig. 2 where the values obtained from samples with different composition are plotted versus the Ge content. The fitting uncertainly on these values . is about 0:02 A The mean square deviation in nearest-neighbour distances (i.e. bond lengths), the Debye– Waller factors r2 , are shown in Fig. 3. One of the fitting parameters, A, in the data analyses is related to this value, r2 , by the equation A ¼ 2r2 . The fitting uncertainty on these is about 20 104 A2 . The value of r2 is the half-width of the peak in the RDFs (the true RDFs: the Fourier transforms of the EXAFS include a great deal of extra broadening due to the finite data range) and is directly related to the amount of disorder in the bond lengths shown in Fig. 2.
Fig. 1. The k 3 -weighted EXAFS function v and Fourier transform (FT) for an a-Ge0:66 Se0:34 film at the (a) Ge K-edge and (b) Se Kedge.
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Fig. 2. First-shell bond distances, R, determined from the Ge and Se K-edge data versus Ge atomic percentage in a-Gex Se1x films. The or less. (a) Ge–Ge bonds; (b) Ge–Se bonds: Ge K-edge data (diamonds), Se K-edge data (crosses); (c) Se–Se uncertainties are 0:02 A bonds.
Values of the partial coordination numbers obtained from the Ge and Se K-edge experiments are presented in Table 1 and in Figs. 4 and 5, respectively. The data are plotted as a function of Ge concentration. We note that the AB coordination numbers obtained from the two sets of edge data must obey the bond consistency equation: cA NAB ¼ cB NBA ;
ð2Þ
which states that the number of AB bonds must be the same whether viewed from the A or B end. In Eq. (2) ci is an atomic concentration and Nij the partial coordination of j atoms round an i atom. In our results, the values of NSeGe obtained from the Se K-edge data are always consistent with the of NGe–Se obtained from the Ge K-edge data.
4.2. a-Gex Sey Znz films EXAFS measurements on 11 ternary alloys of a-Gex Sey Znz films were also carried out using the SRS beamline at station 7.1 in the CLRC Daresbury Laboratory. Since the compositions of films have no regularity, we represent these as aGex Sey Znz for convenience. In fact, the main aim of these measurements was to probe any structural differences that might result from Zn alloying a-Gex Se1x films. Examples of the final EXAFS functions, vðkÞ and radial distribution functions obtained by Fourier transformations of the K-edge data are shown in Fig. 6. In all the RDFs, only one strong peak is present, suggesting that preservation of short-range order is confined to the first shell. This
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Fig. 3. Composition dependence of the mean square deviation in bond lengths obtained from the Ge and Se K-edge data for a2 . (a) Ge–Ge bonds; (b) Ge–Se bonds: Ge K-edge data (crosses), Se K-edge Gex Se1x thin films. The uncertainties are 20 104 A data (squares); (c) Se–Se bonds.
typical feature implies considerable disorder beyond the first shell. The bond lengths between the component atoms were determined from the final fits and are presented in Fig. 7. Again, the fitting un. The certainty on these values is about 0:02 A values are plotted, for convenience, as a function of the Zn content in the samples. Hence values obtained from samples having the same Zn content but with otherwise different compositions are sometimes presented together at the same value of z. The mean square deviations in the bond lengths, i.e. the Debye–Waller factors, r2 , are shown in Fig. 8, again as a function of Zn content. The fitting uncertainty on these in about 20 2 . 104 A
The partial coordination numbers obtained from the Ge, Se and Zn K-edge experiments are presented in Tables 2–4.
5. Discussion 5.1. a-Gex Sey Znz films 5.1.1. Bond lengths The Ge–Ge bond lengths were found to have an , The average Ge–Ge average of 2:45 0:03 A bond length, 2.45 A, is slightly longer than the [10]. known crystalline tetrahedral value, 2.44 A However, considering the experimental error, the agreement between the two values suggests that the nearest-neighbour bond lengths between Ge
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Table 1 Coordination number results for a-Gex Se1x films x
Bond
Ne
NOBN
NBN
Bond
Ne
NOBN
NRBN
0.21
Ge–Ge Ge–Se Ge–Ge Ge–Se Ge–Ge Ge–Se Ge–Ge Ge–Se Ge–Ge Ge–Se Ge–Ge Ge–Se Ge–Ge Ge–Se Ge–Ge Ge–Se Ge–Ge Ge–Se Ge–Ge Ge–Se
0 4.5 0.3 0 4.3 0.2 0.2 0.4 3.7 0.5 2.2 0.2 2.2 0.3 2.7 0.4 1.1 0.3 2.4 0.2 1.2 0.2 3.2 0.4 1.0 0.2 3.7 0.3 0.6 0.3 4.1 0.4 0.2 0.2 3.6 0.5 0
0 4 0 4 0 4 1.75 2.25 1.9 2.1 2.5 1.5 3.0 1.0 2.25 0.75 3.8 0.2 4 0
1.4 2.6 1.75 2.25 1.9 2.1 2.5 1.5 2.6 1.4 2.9 1.1 3.2 0.8 3.4 0.6 3.8 0.2 4 0
Se–Ge Se–Se Se–Ge Se–Se Se–Ge Se–Se Se–Ge Se–Se Se–Ge Se–Se Se–Ge Se–Se Se–Ge Se–Se Se–Ge Se–Se Se–Ge Se–Se Se–Ge Se–Se
0.9 0.4 1.2 0.4 1.6 0.2 0.3 0.4 1.7 0.2 0.3 0.4 2.0 0.1 0 1.3 0.4 0.4 0.2 1.6 0.3 0.3 0.2 1.8 0.2 0.4 0.3 1.8 0.1 0.1 0.2 1.7 0.4 0.1 0.2
1.05 0.95 1.65 0.35 1.9 0.1 2 0 2 0 2 0 2 0 2 0 2 0
0.7 1.3 0.8 1.2 0.95 1.05 1.25 0.75 1.3 0.7 1.45 0.55 1.6 0.4 1.7 0.3 1.9 0.1
0.29 0.32 0.47 0.49 0.57 0.66 0.73 0.91 1.00
Ne denotes the fitted values of partial coordination numbers. NOBN and NRBN refer to the ordered and random bond network models, respectively. A value of zero in the Ne column means that adding that contribution definitely worsened the fit.
Fig. 4. Partial coordination numbers obtained from the Ge K-edge data versus Ge atomic percentage in a-Gex Se1x thin films. The solid and dashed lines are the OBN and RBN modelled results, respectively.
atoms are the same in crystalline and amorphous samples. The bond lengths of the Ge–Se and Se– Ge bonds, obtained independently from analyses of the Ge and Se K-edge data, respectively, were both found to be consistent and to have a value of . This value is significantly about 2:37 0:03 A , in shorter than the crystalline value, 2.44 A ZnSe [10], where Se is fourfold coordinated. There
is also weak evidence for a slight lengthening of this bond as the Ge content of the films increases. The Se–Se bond lengths in samples with different , again in compositions average to 2:32 0:03 A good agreement with the known crystalline value, , in Se [10]. The overall results are consistent 2.31 A with those obtained on bulk glasses [4] and suggest that the bond lengths are unaffected by the type of
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163
Fig. 5. Partial coordination numbers obtained from the Se K-edge data versus Ge atomic percentage in a-Gex Se1x thin films. The solid and dashed lines are the OBN and RBN modelled results, respectively.
bonds surrounding each atom. The amorphous nature of the samples does not therefore arise from variations of bond lengths between atoms. 5.1.2. Debye–Waller factors Generally, in the case of amorphous material, the experimentally-determined Debye–Waller factor has contributions from both thermal and static disorder. If we assume that the crystalline state has only thermal disorder, the static disorder in the amorphous material can be easily determined by subtracting the value obtained from a crystalline standard. The Ge–Ge Debye–Waller factors in Fig. 3 show little variation with Se content but are generally higher than that of the a-Ge sample 2 Þ and increase up to about 70 ð40 104 A 2 . This implies that even though the values 104 A contain contributions from both thermal and static disorder, the static disorder in the Ge–Ge bond length is higher a-Gex Se1x films than in a-Ge. This result is not entirely surprising. a-Ge has an amorphous structure based on the tetrahedral bond, and the addition of two-fold coordinated selenium is expected to increase the disorder in the system. The Debye–Waller factors for Ge–Se and Se–Ge bonds are independent of composition, 2 . This having an average value of 40 104 A implies that the disorder in these samples is similar over the whole composition range. Note that the values determined from both the Ge and Se
K-edges are consistent with each 2other. Compar to that of a-Ge ing the average value 40 104 A 2 4 ð40 10 A Þ, suggests that there is a fairly small static disorder in the lengths of Ge–Se bonds. The Ge–Se bonds are stronger than are the Ge–Ge bonds [11] so the lower Debye–Waller factor is not unexpected. As seen in Fig. 3, the Debye–Waller factors for Se–Se bonds are distributed from 2 to 40 104 A 2 with varying germa5 104 A nium content. However, except for the sample containing only 20% Ge, the Se–Se contribution is very weak so that Debye–Waller factors for this bond are probably unreliable. The lack of second-shell data is caused by the large value of the Debye–Waller factors for that shell. As seen in Fig. 1, all the RDFs show only one distinct peak. However, the well-preserved short-range order of the first shell implies that the large disorder in the second shells is mainly related to a spread in the bond angles [12]. 5.1.3. Coordinations The degree of chemical order present in an amorphous material is highly significant for understanding the atomic structure of the material. It can be provided by EXAFS data in the form of partial nearest-neighbour coordination numbers. In Figs. 4 and 5, the variations of the partial coordination numbers, calculated on the basis of two limiting structural models, the random bond
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Fig. 6. The k 3 -weighted EXAFS function v and Fourier transform (FT) for a-Ge49 Se38 Zn13 film at the (a) Ge K-edge, (b) Se K-edge and (c) Zn K-edge.
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165
Fig. 7. First-shell bond distances obtained from the Ge, Se and Zn K-edge data versus Zn atomic percentage in a-Gex Sey Znz films. The or less. (a) Ge–Ge bonds (diamonds) Se–Se bonds (crosses); (b) Ge–Se bonds: Ge K-edge data (diamonds), uncertainties are 0:02 A Se K-edge data (crosses); (c) Se–Zn bonds: Se K-edge data (diamonds), Zn K-edge data (crosses), (d) Ge–Zn bonds; Ge K-edge data (diamonds), Zn K-edge data (crosses).
network model (RBN) and the chemically ordered bond network model (OBN) are co-plotted with the experimental results for comparison purposes. In the RBN model it is assumed that each component atom (Ge or Se in our system) combines with any other atom independent of any chemical preference and purely statistically. This means that all types of bond have an opportunity of being formed at any composition, but their concentrations are weighted statistically by the number of each type of atom present. Thus in our a-Gex Se1x films, Ge–Ge, Ge–Se and Se–Se firstneighbour bonds, appropriately weighted, are allowed at all compositions, except of course for the end members. In the OBN, on the other hand it is assumed that each component combines according
to its chemical preference. In our system, the heteropolar bond, Ge–Se, is energetically preferred [11] so that the number of these bonds is maximized at all compositions in the OBN. We return to the partial coordination-number data shown in the top box of Fig. 4. Experimentally, the partial coordination number, NGe–Ge , i.e. the number of Ge atoms surrounding Ge, starts to appear from a Ge content of about 30% and increases with increasing Ge content up to a maximum of about 4. This result clearly shows that Ge–Ge bonds are not present in the Se-rich region ð0 < Geð%Þ < 33Þ as would be expected on the RBN model. Indeed the variation of the partial coordination number, NGe–Ge , with composition agrees well with the theoretical curve for the OBN
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Fig. 8. Composition dependence of the mean square deviation in bond lengths obtained from Ge, Se and Zn K-edge data for a2 . (a) Ge–Ge bonds (diamonds), Se–Se bonds (crosses); (b) Ge–Se bonds: Ge KGex Se1x films. The uncertainties are 0:02 104 A edge data (diamonds), Se K-edge data (crosses); (c) Se–Zn bonds: Se K-edge data (diamonds), Zn K-edge data (crosses); (d) Ge–Zn bonds; Ge K-edge data (diamonds), Zn K-edge data (crosses).
model. In the bottom box of Fig. 4, the variation of the partial coordination number, NGe–Se , is also in good agreement with that expected according to the OBN model. In this model, the number of Ge– Se bonds is maximized so that NGe–Se ¼ 4 until a Ge content of 33%, at which point the stoichiometric composition GeSe2 exists. Beyond this point, although the number of Ge–Se bonds is still maximized, Ge–Ge bonds are forced to replace Ge–Se bonds because insufficient Se atoms are present. It should be noted that the total coordination number of Ge, i.e. the sum of the partial coordination numbers NGe–Ge and NGe–Se , lies close to four within experimental error throughout the whole composition range. These results amply demon-
strate that each Ge atom has a coordination number of 4 (i.e. makes four covalent bonds with its neighbours, whether these be Ge or Se) independent of composition as predicted by Mott’s 8 N rule [13]. Fig. 5 shows the partial coordination numbers of Se obtained from Se K-edge experiments. The variations of partial coordination numbers, NSe–Se and NSe–Ge , again also agree well with the OBN modelled results. However, the values of NSe–Ge and NSe–Se in the Ge-rich region ðGeð%Þ > 33Þ show some departure from the OBN modelled results suggesting that chemical order is not quite complete. Actually, a similar behaviour was found in the results on the partial coordination numbers, NGe–Ge in Fig. 4. If chemical ordering is preserved,
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Table 2 Ge K-edge results for a-Gex Sey Znz films Gex Sey Znz
Bond type
Ne
NOBN
NRBN
6
Ge–Ge Ge–Se Ge–Zn
1.3 0.6 2.4 0.6 0
1.7 2.3 0
2.1 1.6 0.3
32
10
Ge–Ge Ge–Se Ge–Zn
3.2 0.5 0.6 0.4 0.1 0.1
3.5 0.5 0
2.7 0.8 0.5
49
38
13
Ge–Ge Ge–Se Ge–Zn
3.3 0.3 0.5 0.3 0
3.5 0.5 0
2.4 1.0 0.6
54
27
19
Ge–Ge Ge–Se Ge–Zn
3.6 0.2 0.4 0.2 0
3.6 0 0.4
2.5 0.6 0.9
40
40
20
Ge–Ge Ge–Se Ge–Zn
3.1 0.7 0.4 0.6 0.4 0.2
4.0 0 0
2.2 0.9 0.9
53
24
23
Ge–Ge Ge–Se Ge–Zn
2.9 0.6 0.0 0.2 0.9 0.5
3.2 0 0.8
2.5 0.5 1.0
x
y
36
56
58
z
Ne denotes the fitted values of partial coordination numbers. NOBN and NRBN refer to the ordered and random bond network models, respectively. A value of zero in the Ne column means that adding that contribution definitely worsened the fit.
mechanical constraints will obviously increase, so that the bonding network may become more random. We note that the partial coordination numbers determined from the Ge and Se K-edge data are consistent with one another. To within their uncertainties, the two values xNGe–Se , and ð1 xÞNSe–Ge are equal. Since both represent the number of Ge–Se bonds this must be the case. This result provides an internal consistency check on the fitted results. The total coordination number on selenium, i.e. the sum of NSe–Ge , and NSe–Se is maintained at the value of around 2 within the experimental error over the whole composition range. This figure clearly confirms that the coordination numbers of Ge and Se are maintained at the values of 4 and 2, respectively, independent of composition. The EXAFS results of Zhou et al. [4] for bulk glasses with x < 0:4 were interpreted in terms of complete chemical order, i.e. the data were found to fit the OBN model. The values they obtained for bond lengths and Debye–Waller factors are very
similar to ours. The differences in partial coordination numbers are also not large, as may be seen by comparing our results with the prediction of the OBN model (see Table 1) and it may be that this early analysis missed some weak contributions. A more recent neutron diffraction study of a bulk GeSe2 glass by Petri et al. [9] showed some homonuclear Ge–Ge and Se–Se bonding at distances very similar to those found here. The Ge–Ge coordination of 0.25 and the Se–Se coordination of 0.20 are a little lower than our values. The variation of optical bandgaps of this system [14] can be understood in terms of a chemically ordered bond network model. The slow variation in the optical gap on the Ge-rich side with x lying between 0.5 and 1 corresponds closely to the composition range in which Ge–Ge bonds predominate over others ð0:42 < x < 1Þ. The rapid rise in the gap occurs in the region where Ge–Se bonds begin to exert their influence on the electronic band structure. Below x ¼ 0:22, Se–Se bonds dominate the structure and the optical gap falls slowly from its maximum value at the GeSe2
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Table 3 Se K-edge results for a-Gex Sey Znz films Gex Sex Znz
Bond type
Ne
NOBN
NRBN
6
Se–Ge Se–Se Se–Zn
1.0 0.4 1.0 0.5 0.5 0.2
1.6 0 0.4
1.0 0.8 0.2
32
10
Se–Ge Se–Se Se–Zn
1.0 0.5 0.2 0.2 1.0 0.2
0.8 0 1.2
1.3 0.4 0.3
49
38
13
Se–Ge Se–Se Se–Zn
0.7 0.4 0 1.3 0.4
0.7 0 1.3
1.2 0.5 0.3
54
27
19
Se–Ge Se–Se Se–Zn
0.5 0.5 0 2.0 0.3
0 0 2.0
1.2 0.3 0.5
40
40
20
Se–Ge Se–Se Se–Zn
0.4 0.6 0.2 0.2 1.6 0.8
0 0 2.0
2.2 0.9 0.9
53
24
23
Se–Ge Se–Se Se–Zn
0.5 0.5 0 2.0 1.0
0 0 2.0
1.2 0.3 0.5
x
y
36
56
58
z
Ne denotes the fitted values of the partial coordination numbers. NOBN and NRBN refer to the ordered and random bond network models, respectively. A value of zero in the Ne column means that adding that contribution definitely worsened the fit.
composition to that of amorphous Se. The cusp in the optical gap which occurs at the stoichiometric composition, and which is sharp in the case of bulk glasses [14] is somewhat rounded off in the case of our thin films. This is a further indication of a degree of chemical disorder in thin film samples. Indeed, the variation in band gap with composition can be closely modelled using the coordination numbers given here [15]. Therefore, considering the overall results, we can safely conclude that our a-Gex Se1x films have an almost completely chemically ordered 4-2 covalent bond network structure throughout the whole composition range. 5.2. a-Gex Sey Znz films 5.2.1. Bond lengths First of all, the lengths of the Ge–Ge, Ge–Se and Se–Se bonds are worth comparing to those found for the a-Gex Se1x samples. The Ge–Ge independent of bond lengths are 2:45 0:03 A composition. These values are the same as those
obtained for a-Gex Se1x samples, which implies that Zn-alloying does not affect the lengths of the Ge–Ge bonds. As seen in Fig. 7, the bond lengths of Ge–Se and Se–Ge were found to be 2:40 independent of composition. Compared to 0:03 A , which were obtained for the value, 2:37 0:03 A the a-Gex Se1x samples, these results suggest a slight lengthening of this bond on the addition of Zn. Also, the lengths of the Se–Se bonds were , again the same as the found to be 2:32 0:03 A obtained for the a-Gex Se1x value 2:32 0:03 A samples. Now let us look at the bond length data relating directly to bonds involving Zn atoms. As seen in Fig. 7, the Ge–Zn bond lengths have an average of essentially independent of compo2:57 0:05 A sition, and the Zn–Se and Se–Zn bond lengths , again with were both found to be 2:44 0:03 A no obvious variations with composition. If we assume that all bonds are covalent, we can calculate the expected bond length from the radii of the individual atoms [16]. From the well-known crystalline bond lengths of Ge–Ge, Se–Se, Zn–Zn
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169
Table 4 Zn K-edge results for a-Gex Sey Znz films Gex Sey Znz
Bond Type
Ne
NOBN
NRBN
6
Zn–Ge Zn–Se Zn–Zn
0 4.6 0.4 0
0 4.0 0
1.9 1.8 0.3
32
10
Zn–Ge Zn–Se Zn–Zn
0.5 0.3 3.5 0.4 0
0 4.0 0
2.7 0.8 0.5
49
38
13
Zn–Ge Zn–Se Zn–Zn
0 4.2 0.5 0
0 4.0 0
2.4 0.9 0.7
54
27
19
Zn–Ge Zn–Se Zn–Zn
1.0 0.5 3.2 0.6 0
1.1 2.9 0
2.5 0.6 0.9
40
40
20
Zn–Ge Zn–Se Zn–Zn
0.8 0.5 3.1 0.5 0
0 4.0 0
2.2 0.9 0.9
53
24
23
Zn–Ge Zn–Se Zn–Zn
2.0 1.0 2.0 1.0 0
1.9 2.1 0
2.5 0.5 1.0
x
y
36
56
58
z
Ne denotes the fitted values of partial coordination numbers. NOBN and NRBN refer to the ordered and random bond network models, respectively. A value of zero in the Ne column means that adding that contribution definitely worsened the fit.
, respectively [10]), we can (2.44, 2.31 and 2:66 A calculate the expected covalent radii of the Ge, Se and Zn atoms simply by dividing the above bond lengths by two, which gives the values 1.22, respectively. Hence, by adding the 1.16 and 1.33 A radii, the bond lengths of Ge–Zn and Zn–Se can respectively. be estimated to be 2.55 and 2.49 A Compared these ‘ideal’ covalent bond lengths with and 2.44 A reour experimental results (2.57 A spectively), the agreement is fair. Of course the bonding in zinc is metallic, not covalent and so the radii of Zn in the compounds is expected to differ from that in the element. The Ge–Zn bond length for Zn whilst the gives a covalent radius of 1:33 A , if we use the Zn–Se bond length gives 1:29 A covalent radii of Ge and Se as given above. These two values are in reasonable agreement. 5.2.2. Debye–Waller factors The Ge–Ge Debye–Waller factors show no significant trend with increasing Zn content in the 2 , is samples. The average value, 60 104 A
2 Þ, suggesting higher than that of a-Geð40 104 A that, in the Zn-alloyed films, there is more static disorder in the Ge–Ge bond lengths than in a-Ge. The addition of Zn does not, however, increase r2 for Ge–Ge bonds as may be seen by comparing Figs. 3 and 8. The Ge–Se Debye–Waller factors are nearly constant, scattered around an average 2 , independent of composivalue of 50 104 A tion. Comparing this to the average value obtained 2 Þ, suggests from a-Gex Se1x samples ð40 104 A that the a-Gex Sey Znz films have more static disorder in the Ge–Se bond lengths than a-Gex Se1x films. The Debye–Waller factors of the Se–Se bond 2 for all samples. In lengths are about 60 104 A a-Gex Se1x samples the highest factor was 40 2 ; hence these Debye–Waller factors may 104 A indicate an increase of disorder in the Se–Se bond lengths resulting from the Zn-alloying. However, the Se–Se contribution is very weak in all samples except those with the lowest Zn content, so that the Debye–Waller factrors are probably unreliable.
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We now look at the Debye–Waller factors of the bond lengths containing Zn atoms. As seen in Fig. 8, the Debye–Waller factors of 2 the Ge–Zn whilst the bond lengths are about 50 104 A data from the Zn K edge gives about 80 2 . The uncertainties on these figures are 104 A 2 , so they are just consistent. about 20 104 A The Ge–Zn contribution is strongest at high Zn contents and we find a Debye–Waller factor of 2 here, indicating a fair amount about 80 104 A of static disorder in these bonds. The Debye– Waller factors of the Zn–Se and Se–Zn bond lengths show nearly constant values2 indepen and 60 dent of Zn concentration: 95 104 A 2 4 10 A respectively, again just consistent within their errors. These are rather high values, suggesting a high degree of static disorder in these bonds, which are apparently the strongest bonds in the system. In view of the agreement found for the bond lengths between the Zn–Se and Se–Zn bonds, the above Debye–Waller factors seem to carry an unexpected discrepancy in their average values. However, if we consider the general fitting results of EXAFS spectra presented in Fig. 6, we can notice that the Zn K-edge spectra generally show much larger discrepancies between the experimental data and the theoretical curves. Hence we suppose that the larger Debye–Waller factors of the Zn–Se bond lengths result from experimental or analytical errors in the Zn K-edge experiments. 5.2.3. Coordinations So far we have examined the EXAFS results from the point of view of bond lengths and their degree of disorder as a function of composition. We now look into the local structure of the aGex Sey Znz films by means of data on the partial coordination numbers. The partial coordination numbers obtained from the Ge, Se and Zn K-edge experiments are presented in Tables 2–4. Since our main interest is to investigate the degree of chemical order in the films, with the experimental partial coordination number, Ne , the calculated partial coordination numbers, based on two limiting structural models (OBN and RBN), are also presented as NOBN and NRBN . In calculating the partial
coordination number, NOBN , the chemical preference of bonding was decided on the basis of the bond energy and the electro-negativity. Thus, first the number of Zn–Se bonds and then the number of Ge–Se bonds were maximized at all compositions in the calculation of NOBN . Zn–Zn bonds were explicitly forbidden in this model. As seen in Table 2, the Ge K-edge data show that, at almost all compositions, the nearest neighbours of the Ge atoms are predominantly Ge atoms. This is largely due to a concentration constraint: all the samples are highly Ge-rich except for that with lowest Zn content. Furthermore, because of the relatively large difference in electronegativity, most of Se atoms bond with Zn atoms, leaving the remaining Ge bonds to bond with Zn atoms. The experimental partial coordination numbers do not agree exactly with any of the modelled results. However, comparatively speaking, the OBN modelled coordination numbers, NOBN , correspond better to the experimental values, Ne , than do the RBN modelled results, NRBN . The OBN model was set up to maximize Zn-Se bonds so, to a large degree, we argue that this controls the Ge environment. The Se K-edge data in Table 3 also show that in the degree of agreement with the experimental values, the OBN-modelled partial coordination numbers are much better than the RBN-modelled ones. Examination of the nearest-neighbour types indicates that the probed Se atoms are mostly combined with Zn atoms, which confirms the existence of the chemical preference in making a bond. The Zn K-edge data in Table 4 also show results supporting the OBN model. The nearest neighbours of the Zn atoms are almost all Se atoms as we expect in the OBN model, and the experimental partial coordination numbers agree comparatively well with the calculated coordination numbers based on the OBN model. Again we note that the partial coordinations obtained from the several edges are internally consistent, in that the number of each type of heteronuclear bond is the same, to within the uncertainties, when calculated from either end atom. The total coordination numbers of the Ge atoms are comparatively well preserved at all
J. Choi et al. / Journal of Non-Crystalline Solids 297 (2002) 156–172
compositions, having the average value of 4. The total coordination numbers of Zn atoms were also found to be 4, independent of composition. Those of Se atoms were found to be about 2.3, which is slightly higher than the expected value of 2. These results indicate that each Ge atom forms a covalent bond, having the coordination number 4 predicted by Mott’s 8 N rule. However, the total coordination number, 4, of Zn atom is the unexpected result from the viewpoint of the Mott’s 8 N rule, because a Zn atom has an electronic structure of [Ar] 3d10 4s2 [17], which means that the outer sub-shell of the Zn atom is filled. We speculate that the introduced Zn atoms adopt 4-fold coordination by the excitation of outer electrons. The slight increase of Se total coordination number from 2 could resulted from the large differences in electro-negativities between Se and Zn atoms which may cause the instant transfer of electrons from a Zn atom to a Se atom and an extra coordination to the covalent environment of Se atoms. In ZnSe, both Zn and Se are fourfold-coordinated and the high mean Se coordination may be due to the presence of some four fold-coordinated Se in our samples. The result that Zn is 4-fold coordinated up to Zn content of 24% explains why the addition of this metal does not reduce the bandgap of the alloys [14] or introduce a metal–insulator transition. One would expect a reduction in the bandgap only if zinc adopted a higher metallic-like coordination rather than being tetrahedrally bonded as in the present system. In the crystalline phase, ZnSe is a wide bandgap semiconductor (Eg 2:8 eV) with the zinc-blende structure [18], and we speculate that the introduced Zn replaces Ge to make a mixed Ge–Se/Zn–Se semiconductor system. The band gap does not increase on the addition of Zn because, although the Zn bonds primarily to Se, the Se atoms remain largely or entirely two fold coordinated. This results in the samples being dominated by Ge–Ge bonds, which keep the band gap at a low value only slightly greater than that of a-Ge [15]. Considering the overall results, we come to the conclusion that, though the order is not complete, the a-Gex Sey Znz films surely have chemical order in their structure, and each component combines
171
by covalent bonds, having coordination numbers, 4 (Ge), 2 (Se), and 4 (Zn). Therefore, the structure of our a-Gex Sey Znz films can be described as a partially chemically-ordered covalent bond network structure. 6. Conclusions EXAFS experiments were performed on aGex Se1x films ð0:2 < x < 1Þ and data obtained from both the Ge and Se K edges analysed. The lengths of Ge–Ge, Ge–Se and Se–Se bonds were , 2:37 0:03 A and found to be 2:45 0:03 A 2:32 0:03 A, respectively, independent of composition, in the binary alloys, and these bond lengths are nearly the same as those found in crystalline materials. Partial coordination numbers obtained for each componenent atom were compared with values calculated from two structural models, the OBN and the RBN. The results suggest that the a-Gex Se1x films have a chemically ordered 4-2 covalent network structure throughout the whole composition range. EXAFS measurements were also carried out on ternary alloys of a-Gex Sey Znz films ðz < 0:24Þ. The addition of Zn did not affect the lengths of the Ge– Ge or Se–Se bonds but caused a slight increase in the Ge–Se and Se–Se bond lengths. The bond lengths of Ge–Zn and Zn–Se were found to be and 2:44 0:03 A , both indepen2:57 0:05 A dent of composition. The values agree well with the calculated ideal covalent bond lengths within the experimental error. The total coordination number of Zn atom was found to be four, with Zn atoms preferentially bonded to Se atoms. Comparison of the partial coordination numbers with modelled results, suggest that the structure has a large degree of chemical order, with Zn–Se bonding favoured, though the order is not complete. Acknowledgements EPSRC is acknowledged for partial support of this work. The authors would like to thank Mr G.L.C. McTurk for the SEM-EDAX measurements.
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References [1] G. Lucovsky, T.M. Hayes, in: M.H. Brodsky (Ed.), Amorphous Semiconductors, Springer, Berlin, 1979. [2] J.C. Phillips, J. Non-Cryst. Solids 34 (1979) 153. [3] P. Armand, A. Ibanez, E. Phylippot, Q. Ma, D. Raoux, J. Non-Cryst. Solids 150 (1992) 371. [4] W. Zhou, M. Paesler, D.E. Sayers, Phys. Rev. B 43 (1991) 2315. [5] S.J. Gurman, B.T. Williams, J.C. Amiss, J. Phys. CM 12 (2000) 5981. [6] S.J. Gurman, N. Binsted, I. Ross, J. Phys. C 17 (1984) 143. [7] J.I. Cisneros, G.B. Rego, M. Tomyiama, S. Bilac, J.M. Goncalves, A.E. Rodriguez, Z.P. Arguello, Thin Solid Films 100 (1983) 155. [8] R.W. Joyner, K.T. Martin, P. Meehan, J. Phys. C 20 (1987) 4005. [9] I. Petri, P.S. Salmon, H.E. Fischer, Phys. Rev. Lett. 84 (2000) 2413.
[10] Data from ICSD Databank, CLRC Daresbury Laboratory. [11] R.T. Sanderson, Chemical Bonds and Bond Energy, Academic Press, New York, 1971. [12] M.A. Paesler, D.E. Sayers, R. Tsu, J. Gonzalez-Hernandez, Phys. Rev. B 28 (1983) 4550. [13] N.F. Mott, E.A. Davis, Electronic Processes in Non-Crystalline Materials, Oxford University, Oxford, 1979. [14] J. Choi, A. Singh, E.A. Davis, S.J. Gurman, J. Non-Cryst. Solids 198–200 (1996) 680. [15] S.J. Gurman, J. Choi, E.A. Davis, J. Non-Cryst. Solids 230 (1998) 833. [16] J.C. Phillips, Bonds and Bands in Semiconductors, Academic Press, New York, 1973. [17] A. Beiser, Concepts of Modern Physics, 4th Ed., McGrawHill, New York, 1987. [18] A. Feltz, Amorphous Inorganic Materials and Glasses, VCH, New York, 1993.
Structure of amorphous GexSe1x and GexSey Znz thin films: an EXAFS study J. Choi, S.J. Gurman, E.A. Davis
*
Department of Physics and Astronomy, University of Leicester, University Road, Leicester LE1 7RH, UK Received 5 October 2001
Abstract Extended X-ray absorption fine structure (EXAFS) measurements have been made on thin films of a-Gex Se1x with 0:2 < x < 1. The results show that the Ge–Ge, Ge–Se and Se–Se bond lengths have values 2.45, 2.37 and 2.32 (all 0:03) , respectively and are independent of film composition. The partial atomic coordination numbers of Ge and Se suggest A that the films have a predominantly chemically ordered 4-2 coordinated covalent bond network structure throughout the whole composition range, as found by others for Ge–Se bulk glasses with x < 0:4. EXAFS data for a-Gex Sey Znz , independent of the comfilms show that the lengths of Ge–Zn and Se–Zn bonds are 2:57 0:05 and 2:44 0:03 A position. Results on the atomic coordinations reveal that Zn is fourfold coordinated and preferentially bonds to Se atoms. Ó 2002 Elsevier Science B.V. All rights reserved.
1. Introduction In recent years, a great deal of interest has been given to structural studies of chalcogenide glasses because of their distinct usefulness as electrical and optical components. One of the binary chalcogenides, Gex Se1x , has been studied by several workers in the amorphous form, either as bulk glasses or as thin films. Two main frameworks have frequently been used for considering the structure of this system: one is based on the Chemically Ordered Network model proposed by Lucovsky [1] and the other is based on Phillips’ constraint theory [2]. The first refers to
*
Corresponding author. Tel.: +44-166 252 3571; fax: +44116 252 2770. E-mail address: [email protected] (E.A. Davis).
nearest-neighbour coordinations (short-range order) whereas the second is concerned with glassforming ability and medium-range structure. Determination of the structure of these films, particularly their degree of chemical order, is not straightforward. Ge and Se atoms have very similar electron and X-ray scattering factors and the three possible types of bond, Ge–Ge, Ge–Se and Se–Se, are similar in length. X-ray diffraction can give only the mean bond length and the mean coordination. Results using this technique for bulk glasses, which exist only in the glass-forming region x < 0:4, favour a 4-2 coordinated network [3]. The extended X-ray absorption fine structure (EXAFS) technique is limited to providing nearest-neighbour information but should give more information than X-ray diffraction since both Ge and Se K-edge structures can be measured. Zhou et al. [4] performed EXAFS measurements on
0022-3093/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 3 0 9 3 ( 0 1 ) 0 0 9 3 7 - 1
J. Choi et al. / Journal of Non-Crystalline Solids 297 (2002) 156–172
Gex Se1x bulk glasses ðx < 0:4Þ and provided data on the three bond lengths and the coordinations, which supported a chemically ordered 4-2 coordinated network model. In this work, we report EXAFS data on a range of sputtered a-Gex Se1x thin films with 0:2 < x < 1, which includes samples in the Ge-rich region of the system which can only be produced in the form of thin films. EXAFS data on Zn-alloyed films, a-Gex Sey Znz ðz < 0:24Þ, have also been obtained and analysed, in order to investigate the effects of the inclusion of a third atom on the properties of the films. ZnSe, in which both Zn and Se are fourfold covalently bonded, is a wide bandgap semiconductor, and so the inclusion of Zn could increase the bandgap (and the average Se coordination) allowing an extra degree of bandgap tuning. It is also possible that Zn could bond metallically, so driving an insulator–metal transition, as does Ti in amorphous Si [5]. In this case we would expect a high Zn coordination. The EXAFS experiments were carried out using the synchrotron radiation source at the CLRC Daresbury Laboratory, UK. Data analysis was made using EXCURV92 which is an improved fast curved-wave simulation program [6]. Structural information on bond lengths and their mean square deviations will be presented separately for the a-Gex Se1x and a-Gex Sey Znz systems. Results on the partial co-ordination numbers will be compared with two simple structural models, the chemically ordered bond network (OBN) model and the random bond network (RBN) model.
157
pieces of Zn foils ð4 4 1 mm3 Þ onto a polycrystalline Ge target (400 diameter). The films were deposited onto mylar substrates to yield thicknesses of 0.5–2.5 lm. The thickness of the films was determined optically by analysing the fringes in reflection data [7]. The compositions of the films were determined by an energy dispersive X-ray analyser (SEM-EDAX) attached to a DS 130 scanning electron microscope. The amorphicity of the films was checked by a 100 keV transmission electron microscope. The EXAFS measurements of the films were carried out using the 2 GeV synchrotron radiation source at station 7.1 of the CLRC Daresbury Laboratory. The X-ray spectra beyond the Ge, Se and Zn K-edges were obtained in the region from 12 to 14 keV in transmission mode. The incident X-ray beam was monochromatized using a Si (1 1 1) double-crystal monochromator with harmonic rejection set at 80%. Before and after passing through the monochromator, the size of the beam was defined horizontally and vertically by two slits. Both the monochromator and slits were kept in evacuated chambers. The samples on their mylar substrates were folded several times to obtain the optimal thickness (40–50 lmÞ and inserted into a sample holder situated between two ionization chamber detectors. The ionization chambers, filled with Ar gas, measured the incident X-ray beam intensity I0 and the transmitted beam intensity It , respectively. Hence the absorption coefficient l was easily determined.
3. Data analysis 2. Experimental details The films used for EXAFS measurements were prepared by radio-frequency (rf)-sputtering at room temperature. The base pressure of the chamber was 2 107 mTorr and sputtering was in argon at a pressure of 3–6 mTorr. The rf power was 240 W, at a frequency of 13.56 MHz. A cosputtering method was employed for the deposition of binary a-Gex Se1x and ternary a-Gex Sey Znz films. The composition of the films was controlled by distributing Se pellets (3.5 mm diameter) and
The raw EXAFS data were recorded in the central computer of the Daresbury Laboratory and analysed using the computer programs available at the laboratory. Each transmission spectrum was first energy calibrated by the program EXCALIB and the calibrated data was normalized by the program, EXBACK. The background of the EXAFS signal was subtracted as follows. The pre-edge data was fitted by a first-order polynomial and the post-edge data was fitted by third-order polynomial to give a smoothly varying background absorption l0 , which was then
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subtracted to leave the EXAFS function vðEÞ. The function vðEÞ was converted to the k-space function vðkÞ and multiplied by k raised to some power n (of the order of 1–3) to yield a weighted function of approximately constant amplitude. The data from EXBACK were processed by the program EXCURV92, which finally enabled extraction of the structural information from the data. This program is based on the fast curved wave theory [6]. For the nearest-neighbour contributions, only single-scattering events need be considered. Theoretical curves were fitted to the experimental data by means of non-linear least-squares fitting. In the process of fitting, several parameters were involved. The main fitting parameters are: Rj (the nearest-neighbour bond length) and E0 (the absorption edge energy); correlated parameters which control the phase of the function vðkÞ, and the pair Nj (the number of neighbours in a given shell) and Aj (the Debye– Waller factor) which control the amplitude of vðkÞ. The parameters were continuously refined by iteration processes until the best fit between the experimental and theoretical curves was obtained. After consideration of possible different atom types as neighbours, i.e. changing the parameter Tj , curves giving the minimum fit index, FI, were chosen as the final result. The FI is defined by X 2 FI ¼ 1=100Np ½fvi ðtheo:Þ vi ðexp:Þgk n ; ð1Þ where Np is the number of data points in the spectrum and n is the weighting factor mentioned above. The uncertainties in the parameters were checked by a contour map which was also available in EXCURV92. A 95% confidence limit was always used. A theory using the statistical test by this contour map is clearly described in Joyner et al. [8]. The fitting range used for Gex Se1x films ran 1 for the Ge K-edge data and from k ¼ 1 to 12.5 A 1 for the Se K-edge data in from k ¼ 2 to 11:5 A order to filter noise from the spectra. Throughout the analysis of each EXAFS spectrum by the EXCURV92 program, the amplitude factor AFAC (the parameter which corrects for amplitude reductions arising from events such as multiple excitations) and VPI (the parameter which takes into account inelastic losses and the core-
hole lifetime) were fixed at 0.8 and )4.0 eV, respectively for the Ge and Se K-edges. These values were obtained from an analysis of results from a standard a-Ge sample. The parameter E0 , which adjusts for the position of the X-ray absorption edge, was chosen from the EXCALIB program and allowed to vary freely in the fitting procedure. The scattering phaseshifts of each neighbour atom type were calculated and applied in the fitting process. It is not possible to distinguish Ge and Se atoms on the basis of their electron scattering factors, which are extremely similar. Thus in the analysis we used the fitted bond lengths to identify the atom type: thus the shortest contribution was assumed to be due to Se–Se bonds, etc. The fitting ranges in k-space for the Gex Sey Znz 1 for films were selected to be from k ¼ 1 to 13:5 A 1 for the Ge K-edge spectra, from k ¼ 1 to 12:5 A 1 the Se K-edge spectra, and from k ¼ 1 to 10:5 A for the Zn K-edge spectra. Depending on the noise presented in the k-space EXAFS spectra, the fitting range of k was adjusted for better RDF fitting. Throughout an analysis of each EXAFS spectrum, the amplitude factor, AFAC, and the parameter, VPI, were fixed at 0.8 and )0.4 eV, respectively, for all three K-edges, while the other parameters were allowed to vary freely in the fitting procedure. Once again, the three components have very similar electron scattering factors and so the atoms types were assigned on the basis of bond length. In all cases no significant contribution was found with a so that Zn– bond length greater than about 2.6 A Zn bonds were excluded from all the fits. After using the three computer programs mentioned above, the set of structural information of the sample, i.e. the nearest bond-length, the nearest bond-type, the number of nearest neighbours and the mean-square deviation of the bond-length, together with their associated fitting uncertainties was finally obtained. 4. Results 4.1. a-Gex Se1x films X-ray absorption spectra for the Ge and Se K-edges of a-Gex Se1x films obtained from the
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experiments, were analysed using the computer programs described in Section 3. Some examples of the final EXAFS functions, vðkÞ, and the radial distibution fuctions (RDFs) for the Ge and Se Kedges of a-Gex Se1x films are presented in Fig. 1. As seen in the figures, the samples show only one strong peak in the RDFs. This implies that our films preserve short-range order primarily in the first shell of nearest neighbours and considerable structural disorder exists in higher shells. The almost total lack of more distant peaks in the RDF is a feature of EXAFS data (compare Fig. 1 with the RDFs obtained from neutron diffraction data by Petri et al. [9] for Ge33 Se67 bulk glasses). It arises from the lack of low-k data. The EXAFS 1 , the wavevector of an spectra start at k 1–2 A electron at the bottom of the conduction band. Peaks with strong disorder are therefore strongly attenuated by the Debye–Waller factor. The structural parameters obtained from the analysis of the EXAFS data are the nearest-
159
neighbour bond lengths, the mean square deviations in these (the EXAFS Debye–Waller factor) and the partial coordination numbers. The lengths of the Ge–Ge, Ge–Se and Se–Se bonds determined from the analyses are presented in Fig. 2 where the values obtained from samples with different composition are plotted versus the Ge content. The fitting uncertainly on these values . is about 0:02 A The mean square deviation in nearest-neighbour distances (i.e. bond lengths), the Debye– Waller factors r2 , are shown in Fig. 3. One of the fitting parameters, A, in the data analyses is related to this value, r2 , by the equation A ¼ 2r2 . The fitting uncertainty on these is about 20 104 A2 . The value of r2 is the half-width of the peak in the RDFs (the true RDFs: the Fourier transforms of the EXAFS include a great deal of extra broadening due to the finite data range) and is directly related to the amount of disorder in the bond lengths shown in Fig. 2.
Fig. 1. The k 3 -weighted EXAFS function v and Fourier transform (FT) for an a-Ge0:66 Se0:34 film at the (a) Ge K-edge and (b) Se Kedge.
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Fig. 2. First-shell bond distances, R, determined from the Ge and Se K-edge data versus Ge atomic percentage in a-Gex Se1x films. The or less. (a) Ge–Ge bonds; (b) Ge–Se bonds: Ge K-edge data (diamonds), Se K-edge data (crosses); (c) Se–Se uncertainties are 0:02 A bonds.
Values of the partial coordination numbers obtained from the Ge and Se K-edge experiments are presented in Table 1 and in Figs. 4 and 5, respectively. The data are plotted as a function of Ge concentration. We note that the AB coordination numbers obtained from the two sets of edge data must obey the bond consistency equation: cA NAB ¼ cB NBA ;
ð2Þ
which states that the number of AB bonds must be the same whether viewed from the A or B end. In Eq. (2) ci is an atomic concentration and Nij the partial coordination of j atoms round an i atom. In our results, the values of NSeGe obtained from the Se K-edge data are always consistent with the of NGe–Se obtained from the Ge K-edge data.
4.2. a-Gex Sey Znz films EXAFS measurements on 11 ternary alloys of a-Gex Sey Znz films were also carried out using the SRS beamline at station 7.1 in the CLRC Daresbury Laboratory. Since the compositions of films have no regularity, we represent these as aGex Sey Znz for convenience. In fact, the main aim of these measurements was to probe any structural differences that might result from Zn alloying a-Gex Se1x films. Examples of the final EXAFS functions, vðkÞ and radial distribution functions obtained by Fourier transformations of the K-edge data are shown in Fig. 6. In all the RDFs, only one strong peak is present, suggesting that preservation of short-range order is confined to the first shell. This
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161
Fig. 3. Composition dependence of the mean square deviation in bond lengths obtained from the Ge and Se K-edge data for a2 . (a) Ge–Ge bonds; (b) Ge–Se bonds: Ge K-edge data (crosses), Se K-edge Gex Se1x thin films. The uncertainties are 20 104 A data (squares); (c) Se–Se bonds.
typical feature implies considerable disorder beyond the first shell. The bond lengths between the component atoms were determined from the final fits and are presented in Fig. 7. Again, the fitting un. The certainty on these values is about 0:02 A values are plotted, for convenience, as a function of the Zn content in the samples. Hence values obtained from samples having the same Zn content but with otherwise different compositions are sometimes presented together at the same value of z. The mean square deviations in the bond lengths, i.e. the Debye–Waller factors, r2 , are shown in Fig. 8, again as a function of Zn content. The fitting uncertainty on these in about 20 2 . 104 A
The partial coordination numbers obtained from the Ge, Se and Zn K-edge experiments are presented in Tables 2–4.
5. Discussion 5.1. a-Gex Sey Znz films 5.1.1. Bond lengths The Ge–Ge bond lengths were found to have an , The average Ge–Ge average of 2:45 0:03 A bond length, 2.45 A, is slightly longer than the [10]. known crystalline tetrahedral value, 2.44 A However, considering the experimental error, the agreement between the two values suggests that the nearest-neighbour bond lengths between Ge
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Table 1 Coordination number results for a-Gex Se1x films x
Bond
Ne
NOBN
NBN
Bond
Ne
NOBN
NRBN
0.21
Ge–Ge Ge–Se Ge–Ge Ge–Se Ge–Ge Ge–Se Ge–Ge Ge–Se Ge–Ge Ge–Se Ge–Ge Ge–Se Ge–Ge Ge–Se Ge–Ge Ge–Se Ge–Ge Ge–Se Ge–Ge Ge–Se
0 4.5 0.3 0 4.3 0.2 0.2 0.4 3.7 0.5 2.2 0.2 2.2 0.3 2.7 0.4 1.1 0.3 2.4 0.2 1.2 0.2 3.2 0.4 1.0 0.2 3.7 0.3 0.6 0.3 4.1 0.4 0.2 0.2 3.6 0.5 0
0 4 0 4 0 4 1.75 2.25 1.9 2.1 2.5 1.5 3.0 1.0 2.25 0.75 3.8 0.2 4 0
1.4 2.6 1.75 2.25 1.9 2.1 2.5 1.5 2.6 1.4 2.9 1.1 3.2 0.8 3.4 0.6 3.8 0.2 4 0
Se–Ge Se–Se Se–Ge Se–Se Se–Ge Se–Se Se–Ge Se–Se Se–Ge Se–Se Se–Ge Se–Se Se–Ge Se–Se Se–Ge Se–Se Se–Ge Se–Se Se–Ge Se–Se
0.9 0.4 1.2 0.4 1.6 0.2 0.3 0.4 1.7 0.2 0.3 0.4 2.0 0.1 0 1.3 0.4 0.4 0.2 1.6 0.3 0.3 0.2 1.8 0.2 0.4 0.3 1.8 0.1 0.1 0.2 1.7 0.4 0.1 0.2
1.05 0.95 1.65 0.35 1.9 0.1 2 0 2 0 2 0 2 0 2 0 2 0
0.7 1.3 0.8 1.2 0.95 1.05 1.25 0.75 1.3 0.7 1.45 0.55 1.6 0.4 1.7 0.3 1.9 0.1
0.29 0.32 0.47 0.49 0.57 0.66 0.73 0.91 1.00
Ne denotes the fitted values of partial coordination numbers. NOBN and NRBN refer to the ordered and random bond network models, respectively. A value of zero in the Ne column means that adding that contribution definitely worsened the fit.
Fig. 4. Partial coordination numbers obtained from the Ge K-edge data versus Ge atomic percentage in a-Gex Se1x thin films. The solid and dashed lines are the OBN and RBN modelled results, respectively.
atoms are the same in crystalline and amorphous samples. The bond lengths of the Ge–Se and Se– Ge bonds, obtained independently from analyses of the Ge and Se K-edge data, respectively, were both found to be consistent and to have a value of . This value is significantly about 2:37 0:03 A , in shorter than the crystalline value, 2.44 A ZnSe [10], where Se is fourfold coordinated. There
is also weak evidence for a slight lengthening of this bond as the Ge content of the films increases. The Se–Se bond lengths in samples with different , again in compositions average to 2:32 0:03 A good agreement with the known crystalline value, , in Se [10]. The overall results are consistent 2.31 A with those obtained on bulk glasses [4] and suggest that the bond lengths are unaffected by the type of
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Fig. 5. Partial coordination numbers obtained from the Se K-edge data versus Ge atomic percentage in a-Gex Se1x thin films. The solid and dashed lines are the OBN and RBN modelled results, respectively.
bonds surrounding each atom. The amorphous nature of the samples does not therefore arise from variations of bond lengths between atoms. 5.1.2. Debye–Waller factors Generally, in the case of amorphous material, the experimentally-determined Debye–Waller factor has contributions from both thermal and static disorder. If we assume that the crystalline state has only thermal disorder, the static disorder in the amorphous material can be easily determined by subtracting the value obtained from a crystalline standard. The Ge–Ge Debye–Waller factors in Fig. 3 show little variation with Se content but are generally higher than that of the a-Ge sample 2 Þ and increase up to about 70 ð40 104 A 2 . This implies that even though the values 104 A contain contributions from both thermal and static disorder, the static disorder in the Ge–Ge bond length is higher a-Gex Se1x films than in a-Ge. This result is not entirely surprising. a-Ge has an amorphous structure based on the tetrahedral bond, and the addition of two-fold coordinated selenium is expected to increase the disorder in the system. The Debye–Waller factors for Ge–Se and Se–Ge bonds are independent of composition, 2 . This having an average value of 40 104 A implies that the disorder in these samples is similar over the whole composition range. Note that the values determined from both the Ge and Se
K-edges are consistent with each 2other. Compar to that of a-Ge ing the average value 40 104 A 2 4 ð40 10 A Þ, suggests that there is a fairly small static disorder in the lengths of Ge–Se bonds. The Ge–Se bonds are stronger than are the Ge–Ge bonds [11] so the lower Debye–Waller factor is not unexpected. As seen in Fig. 3, the Debye–Waller factors for Se–Se bonds are distributed from 2 to 40 104 A 2 with varying germa5 104 A nium content. However, except for the sample containing only 20% Ge, the Se–Se contribution is very weak so that Debye–Waller factors for this bond are probably unreliable. The lack of second-shell data is caused by the large value of the Debye–Waller factors for that shell. As seen in Fig. 1, all the RDFs show only one distinct peak. However, the well-preserved short-range order of the first shell implies that the large disorder in the second shells is mainly related to a spread in the bond angles [12]. 5.1.3. Coordinations The degree of chemical order present in an amorphous material is highly significant for understanding the atomic structure of the material. It can be provided by EXAFS data in the form of partial nearest-neighbour coordination numbers. In Figs. 4 and 5, the variations of the partial coordination numbers, calculated on the basis of two limiting structural models, the random bond
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Fig. 6. The k 3 -weighted EXAFS function v and Fourier transform (FT) for a-Ge49 Se38 Zn13 film at the (a) Ge K-edge, (b) Se K-edge and (c) Zn K-edge.
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165
Fig. 7. First-shell bond distances obtained from the Ge, Se and Zn K-edge data versus Zn atomic percentage in a-Gex Sey Znz films. The or less. (a) Ge–Ge bonds (diamonds) Se–Se bonds (crosses); (b) Ge–Se bonds: Ge K-edge data (diamonds), uncertainties are 0:02 A Se K-edge data (crosses); (c) Se–Zn bonds: Se K-edge data (diamonds), Zn K-edge data (crosses), (d) Ge–Zn bonds; Ge K-edge data (diamonds), Zn K-edge data (crosses).
network model (RBN) and the chemically ordered bond network model (OBN) are co-plotted with the experimental results for comparison purposes. In the RBN model it is assumed that each component atom (Ge or Se in our system) combines with any other atom independent of any chemical preference and purely statistically. This means that all types of bond have an opportunity of being formed at any composition, but their concentrations are weighted statistically by the number of each type of atom present. Thus in our a-Gex Se1x films, Ge–Ge, Ge–Se and Se–Se firstneighbour bonds, appropriately weighted, are allowed at all compositions, except of course for the end members. In the OBN, on the other hand it is assumed that each component combines according
to its chemical preference. In our system, the heteropolar bond, Ge–Se, is energetically preferred [11] so that the number of these bonds is maximized at all compositions in the OBN. We return to the partial coordination-number data shown in the top box of Fig. 4. Experimentally, the partial coordination number, NGe–Ge , i.e. the number of Ge atoms surrounding Ge, starts to appear from a Ge content of about 30% and increases with increasing Ge content up to a maximum of about 4. This result clearly shows that Ge–Ge bonds are not present in the Se-rich region ð0 < Geð%Þ < 33Þ as would be expected on the RBN model. Indeed the variation of the partial coordination number, NGe–Ge , with composition agrees well with the theoretical curve for the OBN
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Fig. 8. Composition dependence of the mean square deviation in bond lengths obtained from Ge, Se and Zn K-edge data for a2 . (a) Ge–Ge bonds (diamonds), Se–Se bonds (crosses); (b) Ge–Se bonds: Ge KGex Se1x films. The uncertainties are 0:02 104 A edge data (diamonds), Se K-edge data (crosses); (c) Se–Zn bonds: Se K-edge data (diamonds), Zn K-edge data (crosses); (d) Ge–Zn bonds; Ge K-edge data (diamonds), Zn K-edge data (crosses).
model. In the bottom box of Fig. 4, the variation of the partial coordination number, NGe–Se , is also in good agreement with that expected according to the OBN model. In this model, the number of Ge– Se bonds is maximized so that NGe–Se ¼ 4 until a Ge content of 33%, at which point the stoichiometric composition GeSe2 exists. Beyond this point, although the number of Ge–Se bonds is still maximized, Ge–Ge bonds are forced to replace Ge–Se bonds because insufficient Se atoms are present. It should be noted that the total coordination number of Ge, i.e. the sum of the partial coordination numbers NGe–Ge and NGe–Se , lies close to four within experimental error throughout the whole composition range. These results amply demon-
strate that each Ge atom has a coordination number of 4 (i.e. makes four covalent bonds with its neighbours, whether these be Ge or Se) independent of composition as predicted by Mott’s 8 N rule [13]. Fig. 5 shows the partial coordination numbers of Se obtained from Se K-edge experiments. The variations of partial coordination numbers, NSe–Se and NSe–Ge , again also agree well with the OBN modelled results. However, the values of NSe–Ge and NSe–Se in the Ge-rich region ðGeð%Þ > 33Þ show some departure from the OBN modelled results suggesting that chemical order is not quite complete. Actually, a similar behaviour was found in the results on the partial coordination numbers, NGe–Ge in Fig. 4. If chemical ordering is preserved,
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167
Table 2 Ge K-edge results for a-Gex Sey Znz films Gex Sey Znz
Bond type
Ne
NOBN
NRBN
6
Ge–Ge Ge–Se Ge–Zn
1.3 0.6 2.4 0.6 0
1.7 2.3 0
2.1 1.6 0.3
32
10
Ge–Ge Ge–Se Ge–Zn
3.2 0.5 0.6 0.4 0.1 0.1
3.5 0.5 0
2.7 0.8 0.5
49
38
13
Ge–Ge Ge–Se Ge–Zn
3.3 0.3 0.5 0.3 0
3.5 0.5 0
2.4 1.0 0.6
54
27
19
Ge–Ge Ge–Se Ge–Zn
3.6 0.2 0.4 0.2 0
3.6 0 0.4
2.5 0.6 0.9
40
40
20
Ge–Ge Ge–Se Ge–Zn
3.1 0.7 0.4 0.6 0.4 0.2
4.0 0 0
2.2 0.9 0.9
53
24
23
Ge–Ge Ge–Se Ge–Zn
2.9 0.6 0.0 0.2 0.9 0.5
3.2 0 0.8
2.5 0.5 1.0
x
y
36
56
58
z
Ne denotes the fitted values of partial coordination numbers. NOBN and NRBN refer to the ordered and random bond network models, respectively. A value of zero in the Ne column means that adding that contribution definitely worsened the fit.
mechanical constraints will obviously increase, so that the bonding network may become more random. We note that the partial coordination numbers determined from the Ge and Se K-edge data are consistent with one another. To within their uncertainties, the two values xNGe–Se , and ð1 xÞNSe–Ge are equal. Since both represent the number of Ge–Se bonds this must be the case. This result provides an internal consistency check on the fitted results. The total coordination number on selenium, i.e. the sum of NSe–Ge , and NSe–Se is maintained at the value of around 2 within the experimental error over the whole composition range. This figure clearly confirms that the coordination numbers of Ge and Se are maintained at the values of 4 and 2, respectively, independent of composition. The EXAFS results of Zhou et al. [4] for bulk glasses with x < 0:4 were interpreted in terms of complete chemical order, i.e. the data were found to fit the OBN model. The values they obtained for bond lengths and Debye–Waller factors are very
similar to ours. The differences in partial coordination numbers are also not large, as may be seen by comparing our results with the prediction of the OBN model (see Table 1) and it may be that this early analysis missed some weak contributions. A more recent neutron diffraction study of a bulk GeSe2 glass by Petri et al. [9] showed some homonuclear Ge–Ge and Se–Se bonding at distances very similar to those found here. The Ge–Ge coordination of 0.25 and the Se–Se coordination of 0.20 are a little lower than our values. The variation of optical bandgaps of this system [14] can be understood in terms of a chemically ordered bond network model. The slow variation in the optical gap on the Ge-rich side with x lying between 0.5 and 1 corresponds closely to the composition range in which Ge–Ge bonds predominate over others ð0:42 < x < 1Þ. The rapid rise in the gap occurs in the region where Ge–Se bonds begin to exert their influence on the electronic band structure. Below x ¼ 0:22, Se–Se bonds dominate the structure and the optical gap falls slowly from its maximum value at the GeSe2
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Table 3 Se K-edge results for a-Gex Sey Znz films Gex Sex Znz
Bond type
Ne
NOBN
NRBN
6
Se–Ge Se–Se Se–Zn
1.0 0.4 1.0 0.5 0.5 0.2
1.6 0 0.4
1.0 0.8 0.2
32
10
Se–Ge Se–Se Se–Zn
1.0 0.5 0.2 0.2 1.0 0.2
0.8 0 1.2
1.3 0.4 0.3
49
38
13
Se–Ge Se–Se Se–Zn
0.7 0.4 0 1.3 0.4
0.7 0 1.3
1.2 0.5 0.3
54
27
19
Se–Ge Se–Se Se–Zn
0.5 0.5 0 2.0 0.3
0 0 2.0
1.2 0.3 0.5
40
40
20
Se–Ge Se–Se Se–Zn
0.4 0.6 0.2 0.2 1.6 0.8
0 0 2.0
2.2 0.9 0.9
53
24
23
Se–Ge Se–Se Se–Zn
0.5 0.5 0 2.0 1.0
0 0 2.0
1.2 0.3 0.5
x
y
36
56
58
z
Ne denotes the fitted values of the partial coordination numbers. NOBN and NRBN refer to the ordered and random bond network models, respectively. A value of zero in the Ne column means that adding that contribution definitely worsened the fit.
composition to that of amorphous Se. The cusp in the optical gap which occurs at the stoichiometric composition, and which is sharp in the case of bulk glasses [14] is somewhat rounded off in the case of our thin films. This is a further indication of a degree of chemical disorder in thin film samples. Indeed, the variation in band gap with composition can be closely modelled using the coordination numbers given here [15]. Therefore, considering the overall results, we can safely conclude that our a-Gex Se1x films have an almost completely chemically ordered 4-2 covalent bond network structure throughout the whole composition range. 5.2. a-Gex Sey Znz films 5.2.1. Bond lengths First of all, the lengths of the Ge–Ge, Ge–Se and Se–Se bonds are worth comparing to those found for the a-Gex Se1x samples. The Ge–Ge independent of bond lengths are 2:45 0:03 A composition. These values are the same as those
obtained for a-Gex Se1x samples, which implies that Zn-alloying does not affect the lengths of the Ge–Ge bonds. As seen in Fig. 7, the bond lengths of Ge–Se and Se–Ge were found to be 2:40 independent of composition. Compared to 0:03 A , which were obtained for the value, 2:37 0:03 A the a-Gex Se1x samples, these results suggest a slight lengthening of this bond on the addition of Zn. Also, the lengths of the Se–Se bonds were , again the same as the found to be 2:32 0:03 A obtained for the a-Gex Se1x value 2:32 0:03 A samples. Now let us look at the bond length data relating directly to bonds involving Zn atoms. As seen in Fig. 7, the Ge–Zn bond lengths have an average of essentially independent of compo2:57 0:05 A sition, and the Zn–Se and Se–Zn bond lengths , again with were both found to be 2:44 0:03 A no obvious variations with composition. If we assume that all bonds are covalent, we can calculate the expected bond length from the radii of the individual atoms [16]. From the well-known crystalline bond lengths of Ge–Ge, Se–Se, Zn–Zn
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Table 4 Zn K-edge results for a-Gex Sey Znz films Gex Sey Znz
Bond Type
Ne
NOBN
NRBN
6
Zn–Ge Zn–Se Zn–Zn
0 4.6 0.4 0
0 4.0 0
1.9 1.8 0.3
32
10
Zn–Ge Zn–Se Zn–Zn
0.5 0.3 3.5 0.4 0
0 4.0 0
2.7 0.8 0.5
49
38
13
Zn–Ge Zn–Se Zn–Zn
0 4.2 0.5 0
0 4.0 0
2.4 0.9 0.7
54
27
19
Zn–Ge Zn–Se Zn–Zn
1.0 0.5 3.2 0.6 0
1.1 2.9 0
2.5 0.6 0.9
40
40
20
Zn–Ge Zn–Se Zn–Zn
0.8 0.5 3.1 0.5 0
0 4.0 0
2.2 0.9 0.9
53
24
23
Zn–Ge Zn–Se Zn–Zn
2.0 1.0 2.0 1.0 0
1.9 2.1 0
2.5 0.5 1.0
x
y
36
56
58
z
Ne denotes the fitted values of partial coordination numbers. NOBN and NRBN refer to the ordered and random bond network models, respectively. A value of zero in the Ne column means that adding that contribution definitely worsened the fit.
, respectively [10]), we can (2.44, 2.31 and 2:66 A calculate the expected covalent radii of the Ge, Se and Zn atoms simply by dividing the above bond lengths by two, which gives the values 1.22, respectively. Hence, by adding the 1.16 and 1.33 A radii, the bond lengths of Ge–Zn and Zn–Se can respectively. be estimated to be 2.55 and 2.49 A Compared these ‘ideal’ covalent bond lengths with and 2.44 A reour experimental results (2.57 A spectively), the agreement is fair. Of course the bonding in zinc is metallic, not covalent and so the radii of Zn in the compounds is expected to differ from that in the element. The Ge–Zn bond length for Zn whilst the gives a covalent radius of 1:33 A , if we use the Zn–Se bond length gives 1:29 A covalent radii of Ge and Se as given above. These two values are in reasonable agreement. 5.2.2. Debye–Waller factors The Ge–Ge Debye–Waller factors show no significant trend with increasing Zn content in the 2 , is samples. The average value, 60 104 A
2 Þ, suggesting higher than that of a-Geð40 104 A that, in the Zn-alloyed films, there is more static disorder in the Ge–Ge bond lengths than in a-Ge. The addition of Zn does not, however, increase r2 for Ge–Ge bonds as may be seen by comparing Figs. 3 and 8. The Ge–Se Debye–Waller factors are nearly constant, scattered around an average 2 , independent of composivalue of 50 104 A tion. Comparing this to the average value obtained 2 Þ, suggests from a-Gex Se1x samples ð40 104 A that the a-Gex Sey Znz films have more static disorder in the Ge–Se bond lengths than a-Gex Se1x films. The Debye–Waller factors of the Se–Se bond 2 for all samples. In lengths are about 60 104 A a-Gex Se1x samples the highest factor was 40 2 ; hence these Debye–Waller factors may 104 A indicate an increase of disorder in the Se–Se bond lengths resulting from the Zn-alloying. However, the Se–Se contribution is very weak in all samples except those with the lowest Zn content, so that the Debye–Waller factrors are probably unreliable.
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We now look at the Debye–Waller factors of the bond lengths containing Zn atoms. As seen in Fig. 8, the Debye–Waller factors of 2 the Ge–Zn whilst the bond lengths are about 50 104 A data from the Zn K edge gives about 80 2 . The uncertainties on these figures are 104 A 2 , so they are just consistent. about 20 104 A The Ge–Zn contribution is strongest at high Zn contents and we find a Debye–Waller factor of 2 here, indicating a fair amount about 80 104 A of static disorder in these bonds. The Debye– Waller factors of the Zn–Se and Se–Zn bond lengths show nearly constant values2 indepen and 60 dent of Zn concentration: 95 104 A 2 4 10 A respectively, again just consistent within their errors. These are rather high values, suggesting a high degree of static disorder in these bonds, which are apparently the strongest bonds in the system. In view of the agreement found for the bond lengths between the Zn–Se and Se–Zn bonds, the above Debye–Waller factors seem to carry an unexpected discrepancy in their average values. However, if we consider the general fitting results of EXAFS spectra presented in Fig. 6, we can notice that the Zn K-edge spectra generally show much larger discrepancies between the experimental data and the theoretical curves. Hence we suppose that the larger Debye–Waller factors of the Zn–Se bond lengths result from experimental or analytical errors in the Zn K-edge experiments. 5.2.3. Coordinations So far we have examined the EXAFS results from the point of view of bond lengths and their degree of disorder as a function of composition. We now look into the local structure of the aGex Sey Znz films by means of data on the partial coordination numbers. The partial coordination numbers obtained from the Ge, Se and Zn K-edge experiments are presented in Tables 2–4. Since our main interest is to investigate the degree of chemical order in the films, with the experimental partial coordination number, Ne , the calculated partial coordination numbers, based on two limiting structural models (OBN and RBN), are also presented as NOBN and NRBN . In calculating the partial
coordination number, NOBN , the chemical preference of bonding was decided on the basis of the bond energy and the electro-negativity. Thus, first the number of Zn–Se bonds and then the number of Ge–Se bonds were maximized at all compositions in the calculation of NOBN . Zn–Zn bonds were explicitly forbidden in this model. As seen in Table 2, the Ge K-edge data show that, at almost all compositions, the nearest neighbours of the Ge atoms are predominantly Ge atoms. This is largely due to a concentration constraint: all the samples are highly Ge-rich except for that with lowest Zn content. Furthermore, because of the relatively large difference in electronegativity, most of Se atoms bond with Zn atoms, leaving the remaining Ge bonds to bond with Zn atoms. The experimental partial coordination numbers do not agree exactly with any of the modelled results. However, comparatively speaking, the OBN modelled coordination numbers, NOBN , correspond better to the experimental values, Ne , than do the RBN modelled results, NRBN . The OBN model was set up to maximize Zn-Se bonds so, to a large degree, we argue that this controls the Ge environment. The Se K-edge data in Table 3 also show that in the degree of agreement with the experimental values, the OBN-modelled partial coordination numbers are much better than the RBN-modelled ones. Examination of the nearest-neighbour types indicates that the probed Se atoms are mostly combined with Zn atoms, which confirms the existence of the chemical preference in making a bond. The Zn K-edge data in Table 4 also show results supporting the OBN model. The nearest neighbours of the Zn atoms are almost all Se atoms as we expect in the OBN model, and the experimental partial coordination numbers agree comparatively well with the calculated coordination numbers based on the OBN model. Again we note that the partial coordinations obtained from the several edges are internally consistent, in that the number of each type of heteronuclear bond is the same, to within the uncertainties, when calculated from either end atom. The total coordination numbers of the Ge atoms are comparatively well preserved at all
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compositions, having the average value of 4. The total coordination numbers of Zn atoms were also found to be 4, independent of composition. Those of Se atoms were found to be about 2.3, which is slightly higher than the expected value of 2. These results indicate that each Ge atom forms a covalent bond, having the coordination number 4 predicted by Mott’s 8 N rule. However, the total coordination number, 4, of Zn atom is the unexpected result from the viewpoint of the Mott’s 8 N rule, because a Zn atom has an electronic structure of [Ar] 3d10 4s2 [17], which means that the outer sub-shell of the Zn atom is filled. We speculate that the introduced Zn atoms adopt 4-fold coordination by the excitation of outer electrons. The slight increase of Se total coordination number from 2 could resulted from the large differences in electro-negativities between Se and Zn atoms which may cause the instant transfer of electrons from a Zn atom to a Se atom and an extra coordination to the covalent environment of Se atoms. In ZnSe, both Zn and Se are fourfold-coordinated and the high mean Se coordination may be due to the presence of some four fold-coordinated Se in our samples. The result that Zn is 4-fold coordinated up to Zn content of 24% explains why the addition of this metal does not reduce the bandgap of the alloys [14] or introduce a metal–insulator transition. One would expect a reduction in the bandgap only if zinc adopted a higher metallic-like coordination rather than being tetrahedrally bonded as in the present system. In the crystalline phase, ZnSe is a wide bandgap semiconductor (Eg 2:8 eV) with the zinc-blende structure [18], and we speculate that the introduced Zn replaces Ge to make a mixed Ge–Se/Zn–Se semiconductor system. The band gap does not increase on the addition of Zn because, although the Zn bonds primarily to Se, the Se atoms remain largely or entirely two fold coordinated. This results in the samples being dominated by Ge–Ge bonds, which keep the band gap at a low value only slightly greater than that of a-Ge [15]. Considering the overall results, we come to the conclusion that, though the order is not complete, the a-Gex Sey Znz films surely have chemical order in their structure, and each component combines
171
by covalent bonds, having coordination numbers, 4 (Ge), 2 (Se), and 4 (Zn). Therefore, the structure of our a-Gex Sey Znz films can be described as a partially chemically-ordered covalent bond network structure. 6. Conclusions EXAFS experiments were performed on aGex Se1x films ð0:2 < x < 1Þ and data obtained from both the Ge and Se K edges analysed. The lengths of Ge–Ge, Ge–Se and Se–Se bonds were , 2:37 0:03 A and found to be 2:45 0:03 A 2:32 0:03 A, respectively, independent of composition, in the binary alloys, and these bond lengths are nearly the same as those found in crystalline materials. Partial coordination numbers obtained for each componenent atom were compared with values calculated from two structural models, the OBN and the RBN. The results suggest that the a-Gex Se1x films have a chemically ordered 4-2 covalent network structure throughout the whole composition range. EXAFS measurements were also carried out on ternary alloys of a-Gex Sey Znz films ðz < 0:24Þ. The addition of Zn did not affect the lengths of the Ge– Ge or Se–Se bonds but caused a slight increase in the Ge–Se and Se–Se bond lengths. The bond lengths of Ge–Zn and Zn–Se were found to be and 2:44 0:03 A , both indepen2:57 0:05 A dent of composition. The values agree well with the calculated ideal covalent bond lengths within the experimental error. The total coordination number of Zn atom was found to be four, with Zn atoms preferentially bonded to Se atoms. Comparison of the partial coordination numbers with modelled results, suggest that the structure has a large degree of chemical order, with Zn–Se bonding favoured, though the order is not complete. Acknowledgements EPSRC is acknowledged for partial support of this work. The authors would like to thank Mr G.L.C. McTurk for the SEM-EDAX measurements.
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References [1] G. Lucovsky, T.M. Hayes, in: M.H. Brodsky (Ed.), Amorphous Semiconductors, Springer, Berlin, 1979. [2] J.C. Phillips, J. Non-Cryst. Solids 34 (1979) 153. [3] P. Armand, A. Ibanez, E. Phylippot, Q. Ma, D. Raoux, J. Non-Cryst. Solids 150 (1992) 371. [4] W. Zhou, M. Paesler, D.E. Sayers, Phys. Rev. B 43 (1991) 2315. [5] S.J. Gurman, B.T. Williams, J.C. Amiss, J. Phys. CM 12 (2000) 5981. [6] S.J. Gurman, N. Binsted, I. Ross, J. Phys. C 17 (1984) 143. [7] J.I. Cisneros, G.B. Rego, M. Tomyiama, S. Bilac, J.M. Goncalves, A.E. Rodriguez, Z.P. Arguello, Thin Solid Films 100 (1983) 155. [8] R.W. Joyner, K.T. Martin, P. Meehan, J. Phys. C 20 (1987) 4005. [9] I. Petri, P.S. Salmon, H.E. Fischer, Phys. Rev. Lett. 84 (2000) 2413.
[10] Data from ICSD Databank, CLRC Daresbury Laboratory. [11] R.T. Sanderson, Chemical Bonds and Bond Energy, Academic Press, New York, 1971. [12] M.A. Paesler, D.E. Sayers, R. Tsu, J. Gonzalez-Hernandez, Phys. Rev. B 28 (1983) 4550. [13] N.F. Mott, E.A. Davis, Electronic Processes in Non-Crystalline Materials, Oxford University, Oxford, 1979. [14] J. Choi, A. Singh, E.A. Davis, S.J. Gurman, J. Non-Cryst. Solids 198–200 (1996) 680. [15] S.J. Gurman, J. Choi, E.A. Davis, J. Non-Cryst. Solids 230 (1998) 833. [16] J.C. Phillips, Bonds and Bands in Semiconductors, Academic Press, New York, 1973. [17] A. Beiser, Concepts of Modern Physics, 4th Ed., McGrawHill, New York, 1987. [18] A. Feltz, Amorphous Inorganic Materials and Glasses, VCH, New York, 1993.