- Email: [email protected]
Ionicity and bonding in a-Si1−yNy
174
Journal of Non-Crystalline Solids 127 (1991) 174-185 North-Holland
Ionicity and bonding in S.C. Bayliss
a
a-Sil_yNy
a n d S.J. G u r m a n b
a Department of Physics, Loughborough Uniuersity of Technology, Loughborough, UK b Department of Physics and Astronomy, Uniuersity of Leicester, Leicester, UK Received 25 April 1990 Revised manuscript received 24 September 1990
The homopolar and heteropolar contributions to the bonding have been calculated for the amorphous non-stoichiometric binary semiconductora-Si1_yNy. The Penn gap for 0 < y <1 has then been calculated for two possible structural models: the random bond network and the ordered bond network. Comparisons of these values with those obtained from optical data for this system suggest that the structure of a-SiI _yNy is ordered. EXAFS data for this system give independent evidence for the existence of an ordered network. The XANES part of the EXAFS spectra have been used to profile the CB DOS, giving rise to an experimentally determined CB-VB DOS, fitted to optical data and in agreement with values of the Penn gap.
1. Introduction There have been many determinations of the ionicity of materials based on the approach of Phillips [1] and its extension by Levine [2]. All of these calculations relate to ordered crystalline systems where, for a system AnBm, each A - B bond in the material is the same. In the majority of cases, only one type of bond is present. The procedure involves separating the average energy gap Eg (the Penn gap) of the material into heteropolar, C, and homopolar, Eh, parts. The fractional ionicity, Fi, and covalency, Fc, are then obtained using (Levine [2])
E 2 = E~ + C 2, F~ = C 2 / E 2,
(1)
F~ = E Z / E 2.
(2)
In amorphous materials the situation is more complicated. Firstly, because of the disorder, all three types of bond (AA, AB and BB) will in general occur in a binary compound, even at the stoichiometric composition. The numbers of bonds present will depend on their strengths and have to be determined statistically. Further, each bond may not be completely determined by type (e.g.
AB) alone but may depend on the local environment of A and B atoms, i.e. the bonds may be altered by interactions between them. These interactions can therefore introduce a composition-dependence into the bond strength, which can be seen in the composition dependence of vibrational frequencies as measured by I R spectroscopy, and therefore into the ionicity. As an example, consider the amorphous silicon alloy S i l _ y N y : H . Each silicon will be four-fold coordinated in the simplest model, but each of the four atoms may be Si, N or H. The numbers of each on a given Si atom will vary with y. A similar situation will exist for the nitrogen atoms, the total coordination of which will be assumed to be 3. The contributions for these different bonds to the total E h and C have to be summed, taking into account the possible effects of the local environment. In this paper we describe calculations of the Penn gap of amorphous Si 1_yNy made using the two standard models of the structure of amorphous compounds, these being the two limiting cases of a general model (Gurman [3]). They are the ordered bond network model (OBN) in which the number of heteropolar bonds is maximised and the ran-
0022-3093/91/$03.50 © 1991 - Elsevier Science Publishers B.V. (North-Holland)
S.C. Bayliss, S.J. Gurman / lonicity and bonding in a-Si t _ yNy
dom bond network model (RBN) in which the numbers of different bonds present is statistical and depends on the concentration alone (Phillip [4]). The numbers of Si-Si, Si-N and N - N bonds present in amorphous Si x_yNy in these two models have been given earlier (Piggins et al. [5]) and are reproduced in section 3. In section 5, we describe EXAFS data for thinfilm samples of amorphous Si x_yNy:H prepared by a glow discharge process. Our results show that the bonding in these materials is classified by the OBN, the number of Si-N bonds being maximised. We have previously determined the Penn gap for these samples from optical data (Davis et al. [6]) using the method of Wemple and DiDomenico [7]. We compare calculated and experimental values of the Penn gap to obtain the ionicity of the system.
2. The Penn gap, Eg Phillips and van Vechten [8] defined an average energy gap (or Penn gap) for a crystal by considering the low energy electronic susceptibility, X, as a sum of contributions from the different types of bond present: × = Z~-xj, J
(3)
where fj. is the fraction of bonds of type j in the crystal. The bond contributions, Xj, may be found using the static refractive n(O) of a crystal containing bonds of type j only: 2 2 __ X 2j = Ep,j/Eg,j - n (0) 2 - 1,
(4)
where Eg,j is the average energy gap (the Penn gap) in the crystal and Ep, j is the plasmon energy for the appropriate valence electron density. Phillips and van Vechten considered only elemental crystals and AB compounds. The theory of the Penn gap in stoichiometric crystals of general composition AraB, was developed by Levine [2]. In this theory, Eg is separated into heteropolar, C, and homopolar, E h, contributions as in Phillips [1]. The division is given as eq. (1) and when E h and C are known the ionicity of the bond may be determined by use of eq. (2). Levine [2] gives
175
expressions for E h and C in stoichiometric crystals of general composition AmBn (n > m): E h =
39.74/d 2"48 eV,
C = 1 4 " 4 b e - k s r ° [ Zar o
(5)
mnZb]r o
eV,
(6)
in which d (.~) is the nearest-neighbour distance (the bond length), ro = d / 2 and d = ra + rb, with ra and r b the cation and anion radii respectively. Z a (Zb) is the number of valence electrons on the cation (anion), exp(-ksro) is the Thomas-Fermi screening factor with k s derived from the average valence electron density and b is a factor of order unity introduced by Levine as a correction to simple Thomas-Fermi screening and depending on the average coordination number N~: b = 0.089Nc 2.
(7)
The expression for the homopolar contribution E h comes from a study of Eg for pure covalent bonds such as are found in elemental crystals. The heteropolar contribution C is due to the difference in the screened Coulomb potentials of the two ion cores: 14.4 is the energy (in eV) due to the Coulomb interaction of two electron charges separated by 1 A. In Phillips' original formulation of this theory [1], the covalent radii of the atoms appeared in the denominators of eq. (6), Phillips arguing that the bond charge was mainly located at the point where the two atomic spheres touched (although he used ro in the screening factor!). Levine [2] showed that better agreement with experiment, in the case of AB compounds, was obtained by using ro in both denominators, i.e. that the bond charge was located half way between atoms. This form has the further advantage that only interatomic distances are used in the theory, avoiding recourse to the possibly ill-defined covalent radii. The factor n / m that appears in eq. (6) was introduced by Levine [2] when he extended the theory from the consideration of AB compounds to that of AraB. compounds. This factor originates in the argument that in an A,,B, compound the valence charge density is not located half way between atoms but that the valence electrons spend more time on atom B, by a factor of n / m , than on atom A, or, equivalently, that the
176
S. C Bayliss, S.J. Gurman / lonicity and bonding in a.Si t _ y Ny
valence charge density is located closer to B than to A, the mean position being mro/n from B. Levine [2] also provides a justification for the value of b, which was left as an arbitrary constant by Phillips [1], in terms of a correction to simple Thomas-Fermi screening. The theory developed by Levine was shown by him (Levine [2]) to provide a good description of the static refractive index n(0) and the fractional ionicity F~ of the bonds over a very wide range of stoichiometric crystals. In all the crystals considered, only one type of bond is present. In this paper, we extend the use of Levine's theory to the case of non-stoichiometric amorphous binary semiconductors, where all three possible bonds, A-A, A - B and B-B, may occur. We describe this extension in the next section.
3. The Penn gap in amorphous semiconductor alloys We wish to use the theory of the Penn gap, as developed by Levine [2], to calculate the Penn gap, and the static dielectric constant, in non-stoichiometric binary amorphous semiconductors. This involves calculating E h and C for each bond and also calculating fj, the fractions of each type of bond present. We assume that the bondlengths and the total coordination of each atom type are independent of composition. These assumptions are tested for the case of Si l_yNy in section 6. The homopolar contribution to the Penn gap, Eh, is given by eq. (5) and depends only on the bond lengths; thus, in our model, it is independent of composition. Each of the three bond types present in an Al_xBx alloy will have a characteristic value of E h. The heteropolar contribution, C, will be non-zero only for AB bonds, for which it is given by eq. (6). We take the n/m factor to be the ratio of the total coordinations of the two types of atoms NA/NB in accordance with Levine's [2] interpretation of this factor. Thus the factor in square brackets in eq. (6) is independent of composition in our model. However, C will vary with composition through the composition variation of the parameters b and k s. For a n AI_yBy com-
pound with total atomic coordinations NA and N B we have, from eq. (7), b = 0.089[(1 - y ) N A +yNB] 2.
(8)
k s, the Thomas-Fermi screening parameter, is a function of the average electron density only, and hence may be calculated from the composition and the density of the compound, or from measured plasmon energies. In order to calculate the fractions of the different bonds present in the amorphous alloy, we need either experimental data or a model of the structure. Two limiting models of the bond arrangement in amorphous semiconductor alloys are in general use. One is the ordered bond network (OBN) model in which the number of AB bonds is maximised and the other is the random bond network (RBN) model, originally described by Phillip [4], in which the bond distribution is statistical. In the RBN, the partial coordination numbers N,7, the number of j atoms bonded to an i atom, depend only on the composition
Nij=cjN~,
i, j = A , B
(9)
where c is a fractional composition and N, is the total coordination of an atom of type i. The numbers of each bond present are obtained by assigning half a bond to the atoms at its ends and summing over all atoms. The bond fractions fj then come by normalising these numbers to the total numbers of bonds. Thus, for a binary alloy of composition Al_yBy we obtain (CA= 1 - - y , CB = y ) fAA = 3(1 --y)2NA/~_,,
(10)
lab = ½y(1 - - y ) ( N a + Ns)/Y'., f . . = ½y2N
/E,
E = 3(1 --y)NA + ½yNB, where Y'. is the total number of bonds present. In the OBN we maximise the number of AB bonds present. For a compound AI_yBy, this means that B atoms are coordinated entirely by A atoms if y is less than the stoichiometric value, or A atoms are coordinated entirely by B atoms if y is greater than this value. This assumption, to-
S.C Bayliss, S.J, Gurman / lonicity and bonding in a-Si I yNy
gether with the total coordinations NA and N B, and the bond consistency condition CANAB = CBNBA
(11)
enable us to calculate the partial coordination N,j and hence the bond fractions fj. The bond consistency condition merely states that the number of AB bonds is the same whether looked at from an A or a B atom. Thus, for an alloy A l_yBy we obtain fAA = ½[(1 - y ) N A
-yN.]/E
U~
fAB = y N B / ~.,
< N---B'
fB~ = 0
(12) fAA=0 f . . = (1 - y ) N . / E f..
> N--BB'
½[yN n - ( 1 - - y ) N A ] / ~ _ , (13)
with E having the same form as in the RBN. With these expressions for the bond fractions, and the energy gap contributions due to each bond, we may calculate the Penn gap for any amorphous alloy by use of eqs. (3) and (4). In so doing, we take the plasmon energy Ep~ which appears in eq. (4) as the plasmon energy for the alloy as a whole. Thus, we write X
=
Ep2 ~ f J E g , s2,
i.e.
Eg 2 = ~-'~fjE -g2j .
J
(14)
loys and an interpretation of the experimental data in terms of the Penn model. All of the samples were thin films of the alloy deposited on Coming 7059 or quartz substrates. Films of a - S i l _ y N y : H used for optical and EXAFS measurements were produced by the glow discharge decomposition of silane and ammonia and were kindly provided by Profs. Spear and LeComber of the University of Dundee. Details of their preparation and composition can be found in Dunnett et al. [9]. These films contain a few percent of hydrogen. Optical data were also obtained from films produced by rf sputtering of a 99.999% pure polycrystalline silicon target in an atmosphere of a r g o n - n i t r o g e n or a r g o n - n i t r o g e n - h y d r o g e n . Their preparation and characterisation is described by Davis et al. [6]. These films contain from 1-5% argon and from 0-6% hydrogen. Optical data for these films, in the form of reflection and transmission coefficients as a function of photon energy, were obtained using a double-beam Perkin-Elmer 330 spectrophotometer. The static refractive index n (0) was obtained from these data by extrapolation to zero photon energies: detailed information may be found in the paper by Davis et al. [6]. The Penn gap for the films, Eg, was calculated using eq. (15) from the experimental n (0) values and the plasmon energies as measured by Karcher et al. [10]. The values of Eg as a function of composition are given by Davis et al. [6].
J
Thus, the energy gaps for the individual bonds, Eg, j are summed in the form of inverse squares. The Penn gap for the compound Eg is then related to the static refractive index by a form analogous to eq. (4): X = n(0) 2 - 1 = E o2/ E ~2 = Ep]F_,fjEgj. 2 -2
(15)
J
4. Amorphous Si l_
177
yNy:H
We describe here a study of the optical and structural properties of amorphous Si 1_yNy : H a l -
5. EXAFS experiment and data analysis Extended X-ray absorption fine structure (EXAFS data for the S i K edge ( - 1 8 4 0 eV) were collected for samples in the composition range 0 < y < 0.57 (i.e. from Si to SiaN4) using the 2 GeV Synchrotron Radiation Source at the Daresbury Laboratory. Beam currents during data taking were between 150 and 250 mA. The experiments were performed on beamline 3.4 (SOXAFS) which has a Cr-plated mirror to focus the beam at the sample. The energy of the X-ray beam was defined using an InSb double-crystal monochromator with harmonic rejection set at 70%. The
S.C. Bayliss, S.J. Gurman / Ionicity and bonding in a-Si/_ yNy
178
incident beam intensity was monitored using an A1 foil. Absorption at the sample was measured by the electron drain current method, a modification of the total electron yield method (Elam et al. [11]). This technique measures the electron drain needed to earth the sample after electron emission and thus requires a path for electrical conduction. The samples available were deposited on (insulating) Coming 7059 glass and so a border of silver-based conducting paint was applied to the samples which were then clamped in a copper sample holder, thus producing a conducting pathway through the front of the sample. Although 7059 glass contains silicon, it is unlikely that any SiK edge signal from the substrate contributes to the data since the drain current method samples only the first 100 .~ or so below the surface and the Sil_yNy films were approximately 1 I~m thick. The angle between the incident beam and the sample surface was set to optimise the counting statistics, a value of about 45 ° being used. The software on beamline 3.4 produces as output a signal proportional to the total absorption coefficient /~(E) as a function of photon energy. The EXBACKV program (Morrell et al. [12]) was used to fit low-order polynomials to the pre- and post-edge data to represent the smooth atomic absorption background. These were then subtracted from the spectra in the normal way to give the EXAFS function x(E). A simplified version of the EXAFS function for K edges, which shows clearly the structural information contained in the spectrum, may be written as
x(k)
A(k) E k
]
~ l f ~ ( ~ r ) Ie-2°?k~e-2Rj/x
X sin(2kRj + 28 + ~j),
(16)
where k, the photoelectron wavevector, is related to the photon energy by h2 k 2 = (ho~ - E~dge) + E 0 2rn
(17)
E 0 being an energy offset, the difference between the energy of a k = 0 photoelectron and the lowest unoccupied energy level. The energy of the edge,
E~dge, was taken to lie at the maximum in the first derivative of/x(E). Nj is the number of identical atoms in a shell of radius Rj about the absorbing atom, each of which has a backscattering amplitude I fj(~r) I. This is a function of both atom type and photoelectron energy. A(k) is a factor that corrects for amplitude reductions due to events that result in absorption but not EXAFS, such as multiple excitations. In practice it is always taken to be energy-independent. The first exponential term is the Debye-Waller factor which provides a description of the effects of thermal and static disorder in the sample, a2 being the mean square deviation in the interatomic distance Rj. The second exponential term accounts for losses due to inelastic scattering, 2~ being the elastic mean free path of the photoelectron. This is modelled in terms of a constant imaginary part of the potential, ~, so that ~ = k/~. This reproduces the standard v~- variation of electron mean free paths. The phaseshift experienced by the photoelectron during its passage through the emitting atom potential is 8, while ~j is the phase of the backscattering factor. For our samples, structural information was obtained by multi-parameter fitting of the experimental data to an EXAFS function calculated using the single-scattering curved wave theory (Gurman et al. [13]). The program used was the standard Daresbury package EXCURV88 (Binsted et al. [14]). For the successful application of this theory, it is necessary to use a reliable set of scattering data. The scattering phase shifts used were calculated within EXCURV88 for each atom type. These were checked by analysing EXAFS data for crystalline Si and Si3N 4 taken during the same experimental shifts as our amorphous sampies. These standard samples also yielded values for the amplitude reduction factor A(k) and the mean free path parameter Vi. The EXCURV88 fitting routine uses a non-linear least-squares fit of the fast curved-wave theory to the experimental data. The variable parameters are the interatomic distances Rj and the energy offset E 0, which together fix the phase of Xi and the coordination numbers Nj and Debye-Waller parameter of , which control the amplitude of XThe data range used in the fits was energies from
179
S.C. Bayliss, S.J. Gurman / Ion±cityand bonding in a-S±t _ yNy
0.018|
o.ol6t-----T O.Ol/.1--
A2
0.012 .... o.olo
....
--
F--
,---
l_z-, __/--
:-
0.008 ..... i - -,-'-~ - I~- - T 0.006 . . . ~; /--i-f
-
~
o.oot. ....
0.002 ..... i--~,~--- ' ' 0.000 . . . . . . 0 2 3 t, 5 N2
7 8
Fig. 1.95% significanceregion (thick line) on a contour map of the fit index plotted as a function of two correlated fitting parameters A2 and N2 (202 and N for the second shell, i.e. for Si-Si bonds) for a-S±x_yNy : H with y = 0.13. 15 to 600 eV above the absorption edge. The program varies selected parameters until a minim u m in the fit index is resulted. The fit index used, FI, is defined by up 1 FI= ~ Y] ([Xi(CalC) - x i ( e x p ) ] k n } 2, i=1
(18) where Np is the number of points and n a kweighting factor used to equalise the contribution of all points to FI. A non-trivial problem encountered when using this type of curve-fitting approach is the estimation of the uncertainties in the fitted parameters. This problem is complicated by the presence of correlations between parameters, especially the pairs (R j, Eo) and (Nj, of), introduced by the finite data range. We have used the statistical test
described by Joyner et al. [15] to estimate these uncertainties, since this test is an integral part of EXCURV88. This test, as implemented in EXCURV88, provides a plot of the 95% significance region ( + 40 uncertainty) on a contour map of the fit index plotted as a function of two correlated fitting parameters. An example is shown as fig. 1. The test may also be used to determine whether the addition of further shells of scattering atoms is justified. In all cases described here (except a-S±) only two shells were found to contribute significantly to the EXAFS.
6. EXAFS results The structural parameters obtained from a curve-fitting analysis of the EXAFS from four samples of amorphous Sil_yNy and one of amorphous Si are summarised in table 1. These were obtained using the values A ( k ) = 0.7 and V, = - 4 eV obtained from analysis of standard samples. A typical fit to k 3 x ( k ) and its Fourier transform are shown in fig. 2. As always with EXCURV88 output, the Fourier transform is phase-corrected (taken with respect to 2 k R + 28 + ~kl) so that peaks appear at their true distances. Figure 1 shows a contour plot of the fit index for this data, showing the 95% confidence region ( + 40 uncertainty) for the amplitude parameters for the Si-Si coordination. The strong correlation between N and 0 2 is apparent from this figure. The bondlengths for both Si-Si and S i - N show no significant variation with composition and are the same as those found in the crystals and in
Table 1 Structural parameters obtained from a curve-fitting analysis of the EXAFS from four samples of Six_yNy y
Si-Si R a)
N
02
Si-N R a)
N
X10-4~ 2
0.57 0.43 0.33 0.13 0.~
2.35 2.34 2.36 2.34 2.33
") +0.02 A.
1.0±1.0 1.4±1.0 2.3±1.0 4.0±1.0 4.0±1.0
75±50 50±50 65±25 75±25 45±35
02
and
Si total N
one sample of a-S± Calc. NN_Si
X10-4~ 2
1.71 1.73 1.72 1.67(±0.05)
2.9±1.0 2.0±1.0 1.5±0.5 1.0±0.5
30±30 75±50 1~±50 75±50
3.9±1.5 3.4±1.5 3.8±1.2 5.0±1.2 4.0±1.0
2.2±0.8 2.7±1.3 3.0±1.0 6.7±3.3
S.C. Bayliss, S.J. Gurman / Ionicity and bonding in a-Sil -
180 1.2- a
7-
1.1-
6-
b
5~
lO-
4-
o8-
2-
0.7-
1-
0.6-
O-
/!
,, ,
-1
o3_5
-3 i/,,
0.2-
- 5 -
,
~
i /i
'
0.5-
01
yNy
'
,1
~,/ 'v
-6-
0.0 "'/~ Fig. 2. (a) Fit to k3x(k) for Sil_yNy: H with y = 0.13. (b) Fourier transform of k3x(k) over the range 3 - 1 2 ,/k-1 for a-Si l_yNy: H with y = 0.13. Dashed line is theoretical fit, solid line is experimental data.
amorphous Si. (The weak contribution from the S i - N coordination bonds for y = 0.13 is less well defined than the others.) Therefore, we may assume that the covalent bonds are well-defined entities and are unaffected by the type of the other bonds on the same Si atom. This conclusion is consistent with the Si 2p XPS data of Ingo et al. [16]. A thermodynamic analysis of these data (Gurman [3]) shows the nitrogen atoms to be randomly distributed amongst the silicon atoms, i.e. that there is effectively no interaction between bonds on a given Si atom. The mean square deviations in the bond length, 02, are also given in table 1. For Si-Si bonds these are independent of composition and only a little larger than the value found in a-Si, which is itself almost identical to that in crystalline silicon. A calculation using the Einstein model with a Si-Si stretch frequency of 300 c m - : gives a room temperature thermal contribution of 0.0040 k 2 t o 0 2 for this bond. Therefore, there is very little static disorder in the Si-Si bond length in our samples. There is, however, considerable static disorder in the S i - N bond length, for which the thermal contribution to o 2 is only 0.0015 ./k2 if we take the stretch frequency to be about 900 cm -1. The degree of static disorder is independent of composition except possibly close to the stoichiometric
composition Si3N 4 ( y = 0.57). We feel it is not unreasonable that at stoichiometry there is slightly less disorder, as is indicated by a drop in a 2 for y = 0.57 (table 1). The absence of any strong second neighbour contribution (Si-Si would be expected to occur at 3.0 .~) shows that there is a large amount of bond angle variation. To lower this contribution below the noise level, as we observe it in our data, requires 02 > 0.04 A 2 corresponding to a bond angle variation of at least + 10 °. This is a typical value for thin film samples of amorphous covalent materials. The partial coordination numbers which we obtain are somewhat imprecise due to the short data range which arises from the weak backscattering power for high energy electrons shown by all light atoms. This short data range gives rise to strong correlations between N and 02 and hence large uncertainties on both. They do, however, clearly favour an ordered bond model (OBN) in which the number of S i - N bonds is maximised. Our results are compared to ordered and random bond models in fig. 3. This conclusion is perhaps more clearly shown if we calculate the number of Si atoms bonded to each N atom by use of the bonding consistency equation (1 - Y)Nsi_ N = y N y _ s i ,
(19)
S.C. Bayliss, S.J. Gurman / lonicity and bonding in a-Si I _ y N y
"~
r,.
//
si I "x
composition. If we take the N - N bond length as 1.2 ,~, twice the covalent radius as determined from the Si-Si and Si-N bond lengths, then we may immediately calculate the value of E h for the three bond types. E h is also independent of composition
/z/
//-'/
x
~" /
I
/ x\x\
.
02
014
Eh: Si-Si 4.8 eV; Si-N 10.4 eV; N - N 31.4 eV;
x\\
iI "
0.6
i x
, I
08
Y
Fig. 3. Partial coordination numbers obtained from EXAFS data as a function of y in a-Sil_yNy:H: O, Si-Si coordination; o, Si-N coordination. Solid hne denotes ordered bond model, dashed hne denotes random bond model.
which merely states that the number of Si-N bonds is the same whether viewed from an Si or a N atom. The calculated NN_si is also given in table 1 and is seen to be consistent with 3, the expected total coordination of N, in all cases. The total coordination of Si is also seen to be consistent with 4 in all cases: the effects of the hydrogen content will be totally swamped by our uncertainties. The structure of amorphous thin films of Si l_yNy: H has previously been the subject of an EXAFS analysis by Mobiho and Fihpponi [17]. These authors used empirical scattering data derived from Fourier-filtered spectra from amorphous Si and amorphous Si 3N4 . T h e y report only the interatomic distances and the relative coordination (Nsi_N//Nsi_si in our notation): no values of Debye-Waller factors are given. Mobilio and Filipponi conclude that the interatomic distances for Si-Si and Si-N bonds are essentially independent of composition and equal to the values in the standards. Their relative coordination values are in good agreement with the ordered bond model. These conclusions are in line with our own results.
7. The Penn gap in amorphous
181
Si I _
yNy:H
The EXAFS data give us the bond lengths for Si-N and Si-Si bonds: these are independent of
(20)
C is only non-zero for Si-N bonds. The terms in the square bracket of eq. (6) are composition independent and are all known. The value of b is given by eq. (8), assuming total coordinations Nsi = 4 and N N = 3. The value of k s is equal to 7.45 × 108 nls/3 ~-1 where n s is the total valence electron density, which we determine by use of the plasmon energies as measured by Karcher et al. [10]. The value of C is found to vary slowly with composition, being about - 7 eV. Our calculated value is plotted in fig. 4 along with the Penn gap for each bond as a function of composition. With the individual bond contributions Eg, j
E(eV) 2O
t
Eg : Eh N-N et 31.4eV
18 16 14 12
•
"
"
•
•
•
•
.:Cg
Si IN
Eh Si-N
10 x
8
X
X X
X
X
6
X
X X
X X
x
x-C S i - N
Eg=Eh Si-Si 4 2
0'2
6.4
6.6 ~8
~'.o 4'2
1'4
~×
Fig. 4. Calculated Penn gap as a function of composition for Si-Si, Si-N and N - N bonds. The heteropolar bond energy C for Si-N bonds, and homopolar bond energies E h for Si-Si and Si-N bonds are also shown.
182
S.C. Bayliss, S.J. Gw'man
/ lonicity and bonding in a-Si t _ ylVy
8. XANES results
E9 (e~
12
+ .H-
10
+
4,
+
o
o
o
++-P
%+
o÷
+o
8
+
6+++~t
o
•
•
•
•
o
~°•
.+
z
0'2 ~
d6 0'8 11o i'.2 i'.~
Fig. 5. Calculated Penn gap as a function of composition for the OBN (o) and RBN (e) models. The experimental data of Davis et al. [6] are also shown ( + ).
known, we can calculate Eg for the alloy using eq. (15) and the bond fractions. The results for the RBN and the OBN models are plotted in fig. 5 together with the experimental data of Davis et al. [6]. We see that the two models give very different predictions for the Penn gap and that the OBN results are in good agreement with the experimental data. Our EXAFS results show that Si a_yNy is almost completely chemically ordered, with S i - N bonds being favoured. The optical data, interpreted using our extension of Levine's [2] theory of the Penn gap, also show this to be the case. Thus, we argue that our description of the Penn gap is reasonable, and that optical studies can give information on the structure of amorphous semiconductor alloys. Our analysis completely neglects the effects of any hydrogen which may be present in the experimental films. The films measured by Davis et al. [6] contained no hydrogen or only a few percent of hydrogen, as noted in fig. 5. The effects of a few percent of hydrogen on the bond fractions, and hence on Eg, will be very small, and the experimental data show that the changes in Eg due to hydrogen are less than the scatter of the data points. Therefore, we feel justified in neglecting the hydrogen content of the films.
X-ray absorption near-edge structure (XANES) is the name given to structure appearing within 0-50 eV above an absorption edge. Such structure on a K edge reflects the p-like ( l s - p transition) density of empty final states in the region close to the atomic nucleus, where the initial ls state is localised. Thus, the XANES on the Si K edge gives us information on the p-like part of the conduction bond local density of states on the silicon atom. XANES is thus complementary, at least in part, to XPS data which gives information on the valence band density of states. We have measured the Si K edge XANES on samples of Si l_yNy produced by a glow discharge process. (Such data form part of the EXAFS data set.) These are shown in fig. 6 together with XPS data (Karcher et al. [10]) from sputtered samples of approximately the same composition. In plotting our data on the same energy scale as the XPS data, we have the problem of relating the two energy scales, because of the possibility of a chemical shift in the ls state occurring. In fig. 6 we have plotted our absorption data under two different assumptions. The solid line assumes no chemical shift of the ls state with increasing nitrogen content, so that E v lies 1834.5 eV above the ls state. This value was obtained from the band gap in amorphous silicon. The dashed line assumes a l s chemical shift (to deeper binding energies with increasing nitrogen content) of the same magnitude as the 2s shift measured by Karcher et al. [10]. Such a shift aligns our XANES data well with the Tauc gap in Sia_yNe as measured by Davis et al. [6] and the OJDOS spectra of Piggins et al. [18]. In the discussion that follows, we always refer to these shifted spectra. The transition matrix elements for Si K edges XANES and XPS are different. In the XPS data, the Si3s and N2s cross-sections are about ten times larger than the Si 3p and N 2 p cross-sections, which are approximately equal (Karcher et al. [10]). Thus s states are strongly enhanced in the XPS. In the XANES, we see only the p-like LDOS on the silicon atom: thus non-bonding states such as the N 2p~ (the lone pair) and N 2s will contribute very weakly if at all. Our discussion of the two
S.C. Bayliss, S.J. Gurman / Ionicity and bonding in a-Si I _ yNy
183
IETI
XPS
XANES
a
-20
-16
-1
-8
-
E~
/.
12
16
20
24
eV
ET
II
/
///
~~
I
I
-20
~
-16
L
-12
i
~
-8
-4
\l
I
;
I
Er
4
8
12
I E"
L
1~5
[
I
20
eV
.... '.
/ l1lit
I
-20
I
-16
I
-12
I
I
-8
-4
~,.I
E~,
I
I
I
[
I
I
4.
8
12
16
20
24
eV
Fig. 6. XANES (this work) and XPS (Karcher et al. [10]) data for a-Si] _ y N y : H plotted on same graph assuming (i) no chemical shift of the l s state (solid line) and (ii) a l s chemical shift of same magnitude as the 2s shift measured by Karcher et al. [10] (dashed line). (a) y = 0.0; (b) y = 0.32; (c) y = 0.59.
S.C. Bayliss, S.J. Gurman / lonicity and bonding in a-Si I _ yNy
184
sets of data is thus largely in terms of peak positions, not intensities. The data shown in fig. 7 show that the XANES and XPS peak positions are approximately mirror images of one another, exactly as we expect from a simple bonding-antibonding picture with the Fermi level at mid-gap. Thus for y = 0 we have XPS peaks at - 3 eV and at about - 9 eV and XANES peaks at 3 and 10 eV. The XPS data show the double-peak structure of the sp3 valence band, whilst the XANES data show a similar structure in the conduction band. For amorphous Si3Na ( y = 0 . 5 7 ) we see a similar mirrored structure, with the lone pair contribution missing in the XANES and the N 2 s * contribution much weakened, as we expect. The peaks show a double-peak structure in the Si-N bond DOS, identified by Karcher et al. as arising from hybridised Sisp 3 bonds with N2pxy bonds in the valence band, plus a lone pair peak near E F, and the corresponding anti-bonding structure in the conduction band. Data from non-stoichiometric compositions show a similar mirrored structure, with the Si-Si contribution at + 3 eV falling, and
t
201_
o
o N2s"
15L 10 ~ Si-Sit5 E,
Si-N"
9. Conclusions i
i
i
i
i
I
N2pz*N2Pxy
-15 '
!
-20L
the Si-N structure at + 6 eV rising, as the nitrogen content increases. The structure at +(10-12 eV) comes from both bonds and shows less change. None of the peaks appears to move in energy as the composition varies. The local DOS on the Si atom as calculated by Martin-Moreno et al. [19] show a similar behaviour with nitrogen content. We may also compare our Penn gap calculations with the XPS and XANES data. For a single, symmetric bonding-antibonding pair, the average energy gap will be that between the centres of the bands. Thus, the Penn gap for this case will span the peaks in the DOS above and below the Fermi energy. In the case of Si-Si and Si-N bonds, the DOS is dominated by the strong peak at the top of the valence bands (Martin-Moreno et al. [19]) and the Penn gap will then be approximately equal to the energy difference between this contribution in the valence and conduction bands. The experimental data shown in fig. 7 show this energy difference to be about 5 eV in amorphous silicon and about 14-16 eV in amorphous Si3N 4. The calculated DOS of Martin-Moreno et al. gives values of 5 and 10 eV. The OJDOS of Piggins et al. [18] gives similar values to the calculated DOS. This discrepancy at high y may be due to crosssection or matrix element effects as mentioned above. The invariance of peak positions with nitrogen content is shown in the calculated DOS, the XANES data and the Penn gap results for the individual bond contributions.
o
o
o
N 2s
Fig. 7. XANES and XPS peak positions for a-Si 1_yNy : H as a function of y, with suggested band assignments.
We have calculated the homopolar and heteropolar contributions to the bonding for a-Sil_yNy based on the method of Levine [2]. Calculated values of the Penn gap for RBN and OBN models show large differences especially for high values of y where discrepancies of - 5 eV are obtained. Comparison of the calculated Penn gap with experimentally obtained values suggests that the system exhibits ordered bonding, supported independently by EXAFS data. XANES data have been interpreted in terms of the CB DOS which, in conjunction with XPS (VB) data of Karcher et al. [10], have given rise to an experimentally de-
s.c. Bayliss, S.J. Gurman / lonicity and bonding in a-Si I rNy
t e r m i n e d V B - C B D O S . T h i s D O S has b e e n fitted to optical gap d a t a of D a v i s et al. [6] a n d is in a g r e e m e n t w i t h v a l u e s of P e n n gap a n d O J D O S d a t a of P i g g i n s et al. [19]. T h e v a r i a t i o n of p e a k p o s i t i o n s w i t h c o m p o s i t i o n suggests a s y m m e t r i c a l o p e n i n g of the gap as y is increased, i n a g r e e m e n t w i t h the electrical d a t a of Spear et al. [20].
References [1] [2] [3] [4] [5]
J.C, Phillips, Phys. Rev. Lett. 20 (1968) 550. B.F. Levine, Phys, Rev. B7 (1973) 2591. S.J. Gurman, Philos. Mag. (1990) in press. H.R. Phillip, J. Non-Cryst. Solids 8-10 (1972) 627. N. Piggins, E.A. Davis and S,C. Bayliss, J. Non-Cryst. Solids 97&98 (1987) 1047. [6] E.A. Davis, N. Piggins and S.C. Bayliss, J. Phys. C 20 (1987) 4415. [7] S.H. Wemple and M. DiDomenico Jr. Phys. Rev. B3 (1971) 1338. [8] J.C. Phillips and J.A. van Vechten, Phys. Rev. Lett. 22 (1969) 705.
185
[9] B. Dunnett, D.I. Jones and A.D. Stewart, Philos. Mag. B53 (1986) 159. [10] R. Karcher, L. Ley and R.L. Johnson, Phys. Rev. B30 (1984) 1896. [11] W.T. Elam, J.P. Kirkland, R,A. Neiser and P.D. Wolf, Phys. Rev. B38 (1988) 26. [12] C. Morrell, J.T.M. Baines, J.C. Campbell, G.P. Diakun, B.R. Dobson, G.N. Greaves and S.S. Hasnain, eds., Daresbury EXAF Users' Manual (internal publication). [13] S.J. Gurman, N. Binsted and I. Ross, J. Phys. C17 (1984) 143. [14] N. Binsted, S.J. Gurman and J.W. Campbell, SERC Daresbury Laboratory EXCURV 88 Program (1988). [15] R.W. Joyner, K.J. Martin and P. Meehan, J. Phys. C20 (1987) 4005. [16] G.M. Ingo, N. Zacchetti, D. della Sala and C. Coluzza, J. Vac. Sci. Technol. A7 (1989) 3048. [17] S. Mobilio and A. Filipponi, J. Non-Cryst. Solids 97&98 (1987) 365. [18] N. Piggins, S.C. Bayliss, E.A. Davis and T. Shen, J. Phys. CM1 (1989) 8111. [19] L. Martin-Moreno, E. Martinez, J.A. Verges and F. Yndurain, Phys. Rev. B35 (1987) 9683. [20] W.E. Spear, B. Durmett and P.G. LeComber, Mater. Res. Sci. Symp. Proc. 95 (1987) 39.
Journal of Non-Crystalline Solids 127 (1991) 174-185 North-Holland
Ionicity and bonding in S.C. Bayliss
a
a-Sil_yNy
a n d S.J. G u r m a n b
a Department of Physics, Loughborough Uniuersity of Technology, Loughborough, UK b Department of Physics and Astronomy, Uniuersity of Leicester, Leicester, UK Received 25 April 1990 Revised manuscript received 24 September 1990
The homopolar and heteropolar contributions to the bonding have been calculated for the amorphous non-stoichiometric binary semiconductora-Si1_yNy. The Penn gap for 0 < y <1 has then been calculated for two possible structural models: the random bond network and the ordered bond network. Comparisons of these values with those obtained from optical data for this system suggest that the structure of a-SiI _yNy is ordered. EXAFS data for this system give independent evidence for the existence of an ordered network. The XANES part of the EXAFS spectra have been used to profile the CB DOS, giving rise to an experimentally determined CB-VB DOS, fitted to optical data and in agreement with values of the Penn gap.
1. Introduction There have been many determinations of the ionicity of materials based on the approach of Phillips [1] and its extension by Levine [2]. All of these calculations relate to ordered crystalline systems where, for a system AnBm, each A - B bond in the material is the same. In the majority of cases, only one type of bond is present. The procedure involves separating the average energy gap Eg (the Penn gap) of the material into heteropolar, C, and homopolar, Eh, parts. The fractional ionicity, Fi, and covalency, Fc, are then obtained using (Levine [2])
E 2 = E~ + C 2, F~ = C 2 / E 2,
(1)
F~ = E Z / E 2.
(2)
In amorphous materials the situation is more complicated. Firstly, because of the disorder, all three types of bond (AA, AB and BB) will in general occur in a binary compound, even at the stoichiometric composition. The numbers of bonds present will depend on their strengths and have to be determined statistically. Further, each bond may not be completely determined by type (e.g.
AB) alone but may depend on the local environment of A and B atoms, i.e. the bonds may be altered by interactions between them. These interactions can therefore introduce a composition-dependence into the bond strength, which can be seen in the composition dependence of vibrational frequencies as measured by I R spectroscopy, and therefore into the ionicity. As an example, consider the amorphous silicon alloy S i l _ y N y : H . Each silicon will be four-fold coordinated in the simplest model, but each of the four atoms may be Si, N or H. The numbers of each on a given Si atom will vary with y. A similar situation will exist for the nitrogen atoms, the total coordination of which will be assumed to be 3. The contributions for these different bonds to the total E h and C have to be summed, taking into account the possible effects of the local environment. In this paper we describe calculations of the Penn gap of amorphous Si 1_yNy made using the two standard models of the structure of amorphous compounds, these being the two limiting cases of a general model (Gurman [3]). They are the ordered bond network model (OBN) in which the number of heteropolar bonds is maximised and the ran-
0022-3093/91/$03.50 © 1991 - Elsevier Science Publishers B.V. (North-Holland)
S.C. Bayliss, S.J. Gurman / lonicity and bonding in a-Si t _ yNy
dom bond network model (RBN) in which the numbers of different bonds present is statistical and depends on the concentration alone (Phillip [4]). The numbers of Si-Si, Si-N and N - N bonds present in amorphous Si x_yNy in these two models have been given earlier (Piggins et al. [5]) and are reproduced in section 3. In section 5, we describe EXAFS data for thinfilm samples of amorphous Si x_yNy:H prepared by a glow discharge process. Our results show that the bonding in these materials is classified by the OBN, the number of Si-N bonds being maximised. We have previously determined the Penn gap for these samples from optical data (Davis et al. [6]) using the method of Wemple and DiDomenico [7]. We compare calculated and experimental values of the Penn gap to obtain the ionicity of the system.
2. The Penn gap, Eg Phillips and van Vechten [8] defined an average energy gap (or Penn gap) for a crystal by considering the low energy electronic susceptibility, X, as a sum of contributions from the different types of bond present: × = Z~-xj, J
(3)
where fj. is the fraction of bonds of type j in the crystal. The bond contributions, Xj, may be found using the static refractive n(O) of a crystal containing bonds of type j only: 2 2 __ X 2j = Ep,j/Eg,j - n (0) 2 - 1,
(4)
where Eg,j is the average energy gap (the Penn gap) in the crystal and Ep, j is the plasmon energy for the appropriate valence electron density. Phillips and van Vechten considered only elemental crystals and AB compounds. The theory of the Penn gap in stoichiometric crystals of general composition AraB, was developed by Levine [2]. In this theory, Eg is separated into heteropolar, C, and homopolar, E h, contributions as in Phillips [1]. The division is given as eq. (1) and when E h and C are known the ionicity of the bond may be determined by use of eq. (2). Levine [2] gives
175
expressions for E h and C in stoichiometric crystals of general composition AmBn (n > m): E h =
39.74/d 2"48 eV,
C = 1 4 " 4 b e - k s r ° [ Zar o
(5)
mnZb]r o
eV,
(6)
in which d (.~) is the nearest-neighbour distance (the bond length), ro = d / 2 and d = ra + rb, with ra and r b the cation and anion radii respectively. Z a (Zb) is the number of valence electrons on the cation (anion), exp(-ksro) is the Thomas-Fermi screening factor with k s derived from the average valence electron density and b is a factor of order unity introduced by Levine as a correction to simple Thomas-Fermi screening and depending on the average coordination number N~: b = 0.089Nc 2.
(7)
The expression for the homopolar contribution E h comes from a study of Eg for pure covalent bonds such as are found in elemental crystals. The heteropolar contribution C is due to the difference in the screened Coulomb potentials of the two ion cores: 14.4 is the energy (in eV) due to the Coulomb interaction of two electron charges separated by 1 A. In Phillips' original formulation of this theory [1], the covalent radii of the atoms appeared in the denominators of eq. (6), Phillips arguing that the bond charge was mainly located at the point where the two atomic spheres touched (although he used ro in the screening factor!). Levine [2] showed that better agreement with experiment, in the case of AB compounds, was obtained by using ro in both denominators, i.e. that the bond charge was located half way between atoms. This form has the further advantage that only interatomic distances are used in the theory, avoiding recourse to the possibly ill-defined covalent radii. The factor n / m that appears in eq. (6) was introduced by Levine [2] when he extended the theory from the consideration of AB compounds to that of AraB. compounds. This factor originates in the argument that in an A,,B, compound the valence charge density is not located half way between atoms but that the valence electrons spend more time on atom B, by a factor of n / m , than on atom A, or, equivalently, that the
176
S. C Bayliss, S.J. Gurman / lonicity and bonding in a.Si t _ y Ny
valence charge density is located closer to B than to A, the mean position being mro/n from B. Levine [2] also provides a justification for the value of b, which was left as an arbitrary constant by Phillips [1], in terms of a correction to simple Thomas-Fermi screening. The theory developed by Levine was shown by him (Levine [2]) to provide a good description of the static refractive index n(0) and the fractional ionicity F~ of the bonds over a very wide range of stoichiometric crystals. In all the crystals considered, only one type of bond is present. In this paper, we extend the use of Levine's theory to the case of non-stoichiometric amorphous binary semiconductors, where all three possible bonds, A-A, A - B and B-B, may occur. We describe this extension in the next section.
3. The Penn gap in amorphous semiconductor alloys We wish to use the theory of the Penn gap, as developed by Levine [2], to calculate the Penn gap, and the static dielectric constant, in non-stoichiometric binary amorphous semiconductors. This involves calculating E h and C for each bond and also calculating fj, the fractions of each type of bond present. We assume that the bondlengths and the total coordination of each atom type are independent of composition. These assumptions are tested for the case of Si l_yNy in section 6. The homopolar contribution to the Penn gap, Eh, is given by eq. (5) and depends only on the bond lengths; thus, in our model, it is independent of composition. Each of the three bond types present in an Al_xBx alloy will have a characteristic value of E h. The heteropolar contribution, C, will be non-zero only for AB bonds, for which it is given by eq. (6). We take the n/m factor to be the ratio of the total coordinations of the two types of atoms NA/NB in accordance with Levine's [2] interpretation of this factor. Thus the factor in square brackets in eq. (6) is independent of composition in our model. However, C will vary with composition through the composition variation of the parameters b and k s. For a n AI_yBy com-
pound with total atomic coordinations NA and N B we have, from eq. (7), b = 0.089[(1 - y ) N A +yNB] 2.
(8)
k s, the Thomas-Fermi screening parameter, is a function of the average electron density only, and hence may be calculated from the composition and the density of the compound, or from measured plasmon energies. In order to calculate the fractions of the different bonds present in the amorphous alloy, we need either experimental data or a model of the structure. Two limiting models of the bond arrangement in amorphous semiconductor alloys are in general use. One is the ordered bond network (OBN) model in which the number of AB bonds is maximised and the other is the random bond network (RBN) model, originally described by Phillip [4], in which the bond distribution is statistical. In the RBN, the partial coordination numbers N,7, the number of j atoms bonded to an i atom, depend only on the composition
Nij=cjN~,
i, j = A , B
(9)
where c is a fractional composition and N, is the total coordination of an atom of type i. The numbers of each bond present are obtained by assigning half a bond to the atoms at its ends and summing over all atoms. The bond fractions fj then come by normalising these numbers to the total numbers of bonds. Thus, for a binary alloy of composition Al_yBy we obtain (CA= 1 - - y , CB = y ) fAA = 3(1 --y)2NA/~_,,
(10)
lab = ½y(1 - - y ) ( N a + Ns)/Y'., f . . = ½y2N
/E,
E = 3(1 --y)NA + ½yNB, where Y'. is the total number of bonds present. In the OBN we maximise the number of AB bonds present. For a compound AI_yBy, this means that B atoms are coordinated entirely by A atoms if y is less than the stoichiometric value, or A atoms are coordinated entirely by B atoms if y is greater than this value. This assumption, to-
S.C Bayliss, S.J, Gurman / lonicity and bonding in a-Si I yNy
gether with the total coordinations NA and N B, and the bond consistency condition CANAB = CBNBA
(11)
enable us to calculate the partial coordination N,j and hence the bond fractions fj. The bond consistency condition merely states that the number of AB bonds is the same whether looked at from an A or a B atom. Thus, for an alloy A l_yBy we obtain fAA = ½[(1 - y ) N A
-yN.]/E
U~
fAB = y N B / ~.,
< N---B'
fB~ = 0
(12) fAA=0 f . . = (1 - y ) N . / E f..
> N--BB'
½[yN n - ( 1 - - y ) N A ] / ~ _ , (13)
with E having the same form as in the RBN. With these expressions for the bond fractions, and the energy gap contributions due to each bond, we may calculate the Penn gap for any amorphous alloy by use of eqs. (3) and (4). In so doing, we take the plasmon energy Ep~ which appears in eq. (4) as the plasmon energy for the alloy as a whole. Thus, we write X
=
Ep2 ~ f J E g , s2,
i.e.
Eg 2 = ~-'~fjE -g2j .
J
(14)
loys and an interpretation of the experimental data in terms of the Penn model. All of the samples were thin films of the alloy deposited on Coming 7059 or quartz substrates. Films of a - S i l _ y N y : H used for optical and EXAFS measurements were produced by the glow discharge decomposition of silane and ammonia and were kindly provided by Profs. Spear and LeComber of the University of Dundee. Details of their preparation and composition can be found in Dunnett et al. [9]. These films contain a few percent of hydrogen. Optical data were also obtained from films produced by rf sputtering of a 99.999% pure polycrystalline silicon target in an atmosphere of a r g o n - n i t r o g e n or a r g o n - n i t r o g e n - h y d r o g e n . Their preparation and characterisation is described by Davis et al. [6]. These films contain from 1-5% argon and from 0-6% hydrogen. Optical data for these films, in the form of reflection and transmission coefficients as a function of photon energy, were obtained using a double-beam Perkin-Elmer 330 spectrophotometer. The static refractive index n (0) was obtained from these data by extrapolation to zero photon energies: detailed information may be found in the paper by Davis et al. [6]. The Penn gap for the films, Eg, was calculated using eq. (15) from the experimental n (0) values and the plasmon energies as measured by Karcher et al. [10]. The values of Eg as a function of composition are given by Davis et al. [6].
J
Thus, the energy gaps for the individual bonds, Eg, j are summed in the form of inverse squares. The Penn gap for the compound Eg is then related to the static refractive index by a form analogous to eq. (4): X = n(0) 2 - 1 = E o2/ E ~2 = Ep]F_,fjEgj. 2 -2
(15)
J
4. Amorphous Si l_
177
yNy:H
We describe here a study of the optical and structural properties of amorphous Si 1_yNy : H a l -
5. EXAFS experiment and data analysis Extended X-ray absorption fine structure (EXAFS data for the S i K edge ( - 1 8 4 0 eV) were collected for samples in the composition range 0 < y < 0.57 (i.e. from Si to SiaN4) using the 2 GeV Synchrotron Radiation Source at the Daresbury Laboratory. Beam currents during data taking were between 150 and 250 mA. The experiments were performed on beamline 3.4 (SOXAFS) which has a Cr-plated mirror to focus the beam at the sample. The energy of the X-ray beam was defined using an InSb double-crystal monochromator with harmonic rejection set at 70%. The
S.C. Bayliss, S.J. Gurman / Ionicity and bonding in a-Si/_ yNy
178
incident beam intensity was monitored using an A1 foil. Absorption at the sample was measured by the electron drain current method, a modification of the total electron yield method (Elam et al. [11]). This technique measures the electron drain needed to earth the sample after electron emission and thus requires a path for electrical conduction. The samples available were deposited on (insulating) Coming 7059 glass and so a border of silver-based conducting paint was applied to the samples which were then clamped in a copper sample holder, thus producing a conducting pathway through the front of the sample. Although 7059 glass contains silicon, it is unlikely that any SiK edge signal from the substrate contributes to the data since the drain current method samples only the first 100 .~ or so below the surface and the Sil_yNy films were approximately 1 I~m thick. The angle between the incident beam and the sample surface was set to optimise the counting statistics, a value of about 45 ° being used. The software on beamline 3.4 produces as output a signal proportional to the total absorption coefficient /~(E) as a function of photon energy. The EXBACKV program (Morrell et al. [12]) was used to fit low-order polynomials to the pre- and post-edge data to represent the smooth atomic absorption background. These were then subtracted from the spectra in the normal way to give the EXAFS function x(E). A simplified version of the EXAFS function for K edges, which shows clearly the structural information contained in the spectrum, may be written as
x(k)
A(k) E k
]
~ l f ~ ( ~ r ) Ie-2°?k~e-2Rj/x
X sin(2kRj + 28 + ~j),
(16)
where k, the photoelectron wavevector, is related to the photon energy by h2 k 2 = (ho~ - E~dge) + E 0 2rn
(17)
E 0 being an energy offset, the difference between the energy of a k = 0 photoelectron and the lowest unoccupied energy level. The energy of the edge,
E~dge, was taken to lie at the maximum in the first derivative of/x(E). Nj is the number of identical atoms in a shell of radius Rj about the absorbing atom, each of which has a backscattering amplitude I fj(~r) I. This is a function of both atom type and photoelectron energy. A(k) is a factor that corrects for amplitude reductions due to events that result in absorption but not EXAFS, such as multiple excitations. In practice it is always taken to be energy-independent. The first exponential term is the Debye-Waller factor which provides a description of the effects of thermal and static disorder in the sample, a2 being the mean square deviation in the interatomic distance Rj. The second exponential term accounts for losses due to inelastic scattering, 2~ being the elastic mean free path of the photoelectron. This is modelled in terms of a constant imaginary part of the potential, ~, so that ~ = k/~. This reproduces the standard v~- variation of electron mean free paths. The phaseshift experienced by the photoelectron during its passage through the emitting atom potential is 8, while ~j is the phase of the backscattering factor. For our samples, structural information was obtained by multi-parameter fitting of the experimental data to an EXAFS function calculated using the single-scattering curved wave theory (Gurman et al. [13]). The program used was the standard Daresbury package EXCURV88 (Binsted et al. [14]). For the successful application of this theory, it is necessary to use a reliable set of scattering data. The scattering phase shifts used were calculated within EXCURV88 for each atom type. These were checked by analysing EXAFS data for crystalline Si and Si3N 4 taken during the same experimental shifts as our amorphous sampies. These standard samples also yielded values for the amplitude reduction factor A(k) and the mean free path parameter Vi. The EXCURV88 fitting routine uses a non-linear least-squares fit of the fast curved-wave theory to the experimental data. The variable parameters are the interatomic distances Rj and the energy offset E 0, which together fix the phase of Xi and the coordination numbers Nj and Debye-Waller parameter of , which control the amplitude of XThe data range used in the fits was energies from
179
S.C. Bayliss, S.J. Gurman / Ion±cityand bonding in a-S±t _ yNy
0.018|
o.ol6t-----T O.Ol/.1--
A2
0.012 .... o.olo
....
--
F--
,---
l_z-, __/--
:-
0.008 ..... i - -,-'-~ - I~- - T 0.006 . . . ~; /--i-f
-
~
o.oot. ....
0.002 ..... i--~,~--- ' ' 0.000 . . . . . . 0 2 3 t, 5 N2
7 8
Fig. 1.95% significanceregion (thick line) on a contour map of the fit index plotted as a function of two correlated fitting parameters A2 and N2 (202 and N for the second shell, i.e. for Si-Si bonds) for a-S±x_yNy : H with y = 0.13. 15 to 600 eV above the absorption edge. The program varies selected parameters until a minim u m in the fit index is resulted. The fit index used, FI, is defined by up 1 FI= ~ Y] ([Xi(CalC) - x i ( e x p ) ] k n } 2, i=1
(18) where Np is the number of points and n a kweighting factor used to equalise the contribution of all points to FI. A non-trivial problem encountered when using this type of curve-fitting approach is the estimation of the uncertainties in the fitted parameters. This problem is complicated by the presence of correlations between parameters, especially the pairs (R j, Eo) and (Nj, of), introduced by the finite data range. We have used the statistical test
described by Joyner et al. [15] to estimate these uncertainties, since this test is an integral part of EXCURV88. This test, as implemented in EXCURV88, provides a plot of the 95% significance region ( + 40 uncertainty) on a contour map of the fit index plotted as a function of two correlated fitting parameters. An example is shown as fig. 1. The test may also be used to determine whether the addition of further shells of scattering atoms is justified. In all cases described here (except a-S±) only two shells were found to contribute significantly to the EXAFS.
6. EXAFS results The structural parameters obtained from a curve-fitting analysis of the EXAFS from four samples of amorphous Sil_yNy and one of amorphous Si are summarised in table 1. These were obtained using the values A ( k ) = 0.7 and V, = - 4 eV obtained from analysis of standard samples. A typical fit to k 3 x ( k ) and its Fourier transform are shown in fig. 2. As always with EXCURV88 output, the Fourier transform is phase-corrected (taken with respect to 2 k R + 28 + ~kl) so that peaks appear at their true distances. Figure 1 shows a contour plot of the fit index for this data, showing the 95% confidence region ( + 40 uncertainty) for the amplitude parameters for the Si-Si coordination. The strong correlation between N and 0 2 is apparent from this figure. The bondlengths for both Si-Si and S i - N show no significant variation with composition and are the same as those found in the crystals and in
Table 1 Structural parameters obtained from a curve-fitting analysis of the EXAFS from four samples of Six_yNy y
Si-Si R a)
N
02
Si-N R a)
N
X10-4~ 2
0.57 0.43 0.33 0.13 0.~
2.35 2.34 2.36 2.34 2.33
") +0.02 A.
1.0±1.0 1.4±1.0 2.3±1.0 4.0±1.0 4.0±1.0
75±50 50±50 65±25 75±25 45±35
02
and
Si total N
one sample of a-S± Calc. NN_Si
X10-4~ 2
1.71 1.73 1.72 1.67(±0.05)
2.9±1.0 2.0±1.0 1.5±0.5 1.0±0.5
30±30 75±50 1~±50 75±50
3.9±1.5 3.4±1.5 3.8±1.2 5.0±1.2 4.0±1.0
2.2±0.8 2.7±1.3 3.0±1.0 6.7±3.3
S.C. Bayliss, S.J. Gurman / Ionicity and bonding in a-Sil -
180 1.2- a
7-
1.1-
6-
b
5~
lO-
4-
o8-
2-
0.7-
1-
0.6-
O-
/!
,, ,
-1
o3_5
-3 i/,,
0.2-
- 5 -
,
~
i /i
'
0.5-
01
yNy
'
,1
~,/ 'v
-6-
0.0 "'/~ Fig. 2. (a) Fit to k3x(k) for Sil_yNy: H with y = 0.13. (b) Fourier transform of k3x(k) over the range 3 - 1 2 ,/k-1 for a-Si l_yNy: H with y = 0.13. Dashed line is theoretical fit, solid line is experimental data.
amorphous Si. (The weak contribution from the S i - N coordination bonds for y = 0.13 is less well defined than the others.) Therefore, we may assume that the covalent bonds are well-defined entities and are unaffected by the type of the other bonds on the same Si atom. This conclusion is consistent with the Si 2p XPS data of Ingo et al. [16]. A thermodynamic analysis of these data (Gurman [3]) shows the nitrogen atoms to be randomly distributed amongst the silicon atoms, i.e. that there is effectively no interaction between bonds on a given Si atom. The mean square deviations in the bond length, 02, are also given in table 1. For Si-Si bonds these are independent of composition and only a little larger than the value found in a-Si, which is itself almost identical to that in crystalline silicon. A calculation using the Einstein model with a Si-Si stretch frequency of 300 c m - : gives a room temperature thermal contribution of 0.0040 k 2 t o 0 2 for this bond. Therefore, there is very little static disorder in the Si-Si bond length in our samples. There is, however, considerable static disorder in the S i - N bond length, for which the thermal contribution to o 2 is only 0.0015 ./k2 if we take the stretch frequency to be about 900 cm -1. The degree of static disorder is independent of composition except possibly close to the stoichiometric
composition Si3N 4 ( y = 0.57). We feel it is not unreasonable that at stoichiometry there is slightly less disorder, as is indicated by a drop in a 2 for y = 0.57 (table 1). The absence of any strong second neighbour contribution (Si-Si would be expected to occur at 3.0 .~) shows that there is a large amount of bond angle variation. To lower this contribution below the noise level, as we observe it in our data, requires 02 > 0.04 A 2 corresponding to a bond angle variation of at least + 10 °. This is a typical value for thin film samples of amorphous covalent materials. The partial coordination numbers which we obtain are somewhat imprecise due to the short data range which arises from the weak backscattering power for high energy electrons shown by all light atoms. This short data range gives rise to strong correlations between N and 02 and hence large uncertainties on both. They do, however, clearly favour an ordered bond model (OBN) in which the number of S i - N bonds is maximised. Our results are compared to ordered and random bond models in fig. 3. This conclusion is perhaps more clearly shown if we calculate the number of Si atoms bonded to each N atom by use of the bonding consistency equation (1 - Y)Nsi_ N = y N y _ s i ,
(19)
S.C. Bayliss, S.J. Gurman / lonicity and bonding in a-Si I _ y N y
"~
r,.
//
si I "x
composition. If we take the N - N bond length as 1.2 ,~, twice the covalent radius as determined from the Si-Si and Si-N bond lengths, then we may immediately calculate the value of E h for the three bond types. E h is also independent of composition
/z/
//-'/
x
~" /
I
/ x\x\
.
02
014
Eh: Si-Si 4.8 eV; Si-N 10.4 eV; N - N 31.4 eV;
x\\
iI "
0.6
i x
, I
08
Y
Fig. 3. Partial coordination numbers obtained from EXAFS data as a function of y in a-Sil_yNy:H: O, Si-Si coordination; o, Si-N coordination. Solid hne denotes ordered bond model, dashed hne denotes random bond model.
which merely states that the number of Si-N bonds is the same whether viewed from an Si or a N atom. The calculated NN_si is also given in table 1 and is seen to be consistent with 3, the expected total coordination of N, in all cases. The total coordination of Si is also seen to be consistent with 4 in all cases: the effects of the hydrogen content will be totally swamped by our uncertainties. The structure of amorphous thin films of Si l_yNy: H has previously been the subject of an EXAFS analysis by Mobiho and Fihpponi [17]. These authors used empirical scattering data derived from Fourier-filtered spectra from amorphous Si and amorphous Si 3N4 . T h e y report only the interatomic distances and the relative coordination (Nsi_N//Nsi_si in our notation): no values of Debye-Waller factors are given. Mobilio and Filipponi conclude that the interatomic distances for Si-Si and Si-N bonds are essentially independent of composition and equal to the values in the standards. Their relative coordination values are in good agreement with the ordered bond model. These conclusions are in line with our own results.
7. The Penn gap in amorphous
181
Si I _
yNy:H
The EXAFS data give us the bond lengths for Si-N and Si-Si bonds: these are independent of
(20)
C is only non-zero for Si-N bonds. The terms in the square bracket of eq. (6) are composition independent and are all known. The value of b is given by eq. (8), assuming total coordinations Nsi = 4 and N N = 3. The value of k s is equal to 7.45 × 108 nls/3 ~-1 where n s is the total valence electron density, which we determine by use of the plasmon energies as measured by Karcher et al. [10]. The value of C is found to vary slowly with composition, being about - 7 eV. Our calculated value is plotted in fig. 4 along with the Penn gap for each bond as a function of composition. With the individual bond contributions Eg, j
E(eV) 2O
t
Eg : Eh N-N et 31.4eV
18 16 14 12
•
"
"
•
•
•
•
.:Cg
Si IN
Eh Si-N
10 x
8
X
X X
X
X
6
X
X X
X X
x
x-C S i - N
Eg=Eh Si-Si 4 2
0'2
6.4
6.6 ~8
~'.o 4'2
1'4
~×
Fig. 4. Calculated Penn gap as a function of composition for Si-Si, Si-N and N - N bonds. The heteropolar bond energy C for Si-N bonds, and homopolar bond energies E h for Si-Si and Si-N bonds are also shown.
182
S.C. Bayliss, S.J. Gw'man
/ lonicity and bonding in a-Si t _ ylVy
8. XANES results
E9 (e~
12
+ .H-
10
+
4,
+
o
o
o
++-P
%+
o÷
+o
8
+
6+++~t
o
•
•
•
•
o
~°•
.+
z
0'2 ~
d6 0'8 11o i'.2 i'.~
Fig. 5. Calculated Penn gap as a function of composition for the OBN (o) and RBN (e) models. The experimental data of Davis et al. [6] are also shown ( + ).
known, we can calculate Eg for the alloy using eq. (15) and the bond fractions. The results for the RBN and the OBN models are plotted in fig. 5 together with the experimental data of Davis et al. [6]. We see that the two models give very different predictions for the Penn gap and that the OBN results are in good agreement with the experimental data. Our EXAFS results show that Si a_yNy is almost completely chemically ordered, with S i - N bonds being favoured. The optical data, interpreted using our extension of Levine's [2] theory of the Penn gap, also show this to be the case. Thus, we argue that our description of the Penn gap is reasonable, and that optical studies can give information on the structure of amorphous semiconductor alloys. Our analysis completely neglects the effects of any hydrogen which may be present in the experimental films. The films measured by Davis et al. [6] contained no hydrogen or only a few percent of hydrogen, as noted in fig. 5. The effects of a few percent of hydrogen on the bond fractions, and hence on Eg, will be very small, and the experimental data show that the changes in Eg due to hydrogen are less than the scatter of the data points. Therefore, we feel justified in neglecting the hydrogen content of the films.
X-ray absorption near-edge structure (XANES) is the name given to structure appearing within 0-50 eV above an absorption edge. Such structure on a K edge reflects the p-like ( l s - p transition) density of empty final states in the region close to the atomic nucleus, where the initial ls state is localised. Thus, the XANES on the Si K edge gives us information on the p-like part of the conduction bond local density of states on the silicon atom. XANES is thus complementary, at least in part, to XPS data which gives information on the valence band density of states. We have measured the Si K edge XANES on samples of Si l_yNy produced by a glow discharge process. (Such data form part of the EXAFS data set.) These are shown in fig. 6 together with XPS data (Karcher et al. [10]) from sputtered samples of approximately the same composition. In plotting our data on the same energy scale as the XPS data, we have the problem of relating the two energy scales, because of the possibility of a chemical shift in the ls state occurring. In fig. 6 we have plotted our absorption data under two different assumptions. The solid line assumes no chemical shift of the ls state with increasing nitrogen content, so that E v lies 1834.5 eV above the ls state. This value was obtained from the band gap in amorphous silicon. The dashed line assumes a l s chemical shift (to deeper binding energies with increasing nitrogen content) of the same magnitude as the 2s shift measured by Karcher et al. [10]. Such a shift aligns our XANES data well with the Tauc gap in Sia_yNe as measured by Davis et al. [6] and the OJDOS spectra of Piggins et al. [18]. In the discussion that follows, we always refer to these shifted spectra. The transition matrix elements for Si K edges XANES and XPS are different. In the XPS data, the Si3s and N2s cross-sections are about ten times larger than the Si 3p and N 2 p cross-sections, which are approximately equal (Karcher et al. [10]). Thus s states are strongly enhanced in the XPS. In the XANES, we see only the p-like LDOS on the silicon atom: thus non-bonding states such as the N 2p~ (the lone pair) and N 2s will contribute very weakly if at all. Our discussion of the two
S.C. Bayliss, S.J. Gurman / Ionicity and bonding in a-Si I _ yNy
183
IETI
XPS
XANES
a
-20
-16
-1
-8
-
E~
/.
12
16
20
24
eV
ET
II
/
///
~~
I
I
-20
~
-16
L
-12
i
~
-8
-4
\l
I
;
I
Er
4
8
12
I E"
L
1~5
[
I
20
eV
.... '.
/ l1lit
I
-20
I
-16
I
-12
I
I
-8
-4
~,.I
E~,
I
I
I
[
I
I
4.
8
12
16
20
24
eV
Fig. 6. XANES (this work) and XPS (Karcher et al. [10]) data for a-Si] _ y N y : H plotted on same graph assuming (i) no chemical shift of the l s state (solid line) and (ii) a l s chemical shift of same magnitude as the 2s shift measured by Karcher et al. [10] (dashed line). (a) y = 0.0; (b) y = 0.32; (c) y = 0.59.
S.C. Bayliss, S.J. Gurman / lonicity and bonding in a-Si I _ yNy
184
sets of data is thus largely in terms of peak positions, not intensities. The data shown in fig. 7 show that the XANES and XPS peak positions are approximately mirror images of one another, exactly as we expect from a simple bonding-antibonding picture with the Fermi level at mid-gap. Thus for y = 0 we have XPS peaks at - 3 eV and at about - 9 eV and XANES peaks at 3 and 10 eV. The XPS data show the double-peak structure of the sp3 valence band, whilst the XANES data show a similar structure in the conduction band. For amorphous Si3Na ( y = 0 . 5 7 ) we see a similar mirrored structure, with the lone pair contribution missing in the XANES and the N 2 s * contribution much weakened, as we expect. The peaks show a double-peak structure in the Si-N bond DOS, identified by Karcher et al. as arising from hybridised Sisp 3 bonds with N2pxy bonds in the valence band, plus a lone pair peak near E F, and the corresponding anti-bonding structure in the conduction band. Data from non-stoichiometric compositions show a similar mirrored structure, with the Si-Si contribution at + 3 eV falling, and
t
201_
o
o N2s"
15L 10 ~ Si-Sit5 E,
Si-N"
9. Conclusions i
i
i
i
i
I
N2pz*N2Pxy
-15 '
!
-20L
the Si-N structure at + 6 eV rising, as the nitrogen content increases. The structure at +(10-12 eV) comes from both bonds and shows less change. None of the peaks appears to move in energy as the composition varies. The local DOS on the Si atom as calculated by Martin-Moreno et al. [19] show a similar behaviour with nitrogen content. We may also compare our Penn gap calculations with the XPS and XANES data. For a single, symmetric bonding-antibonding pair, the average energy gap will be that between the centres of the bands. Thus, the Penn gap for this case will span the peaks in the DOS above and below the Fermi energy. In the case of Si-Si and Si-N bonds, the DOS is dominated by the strong peak at the top of the valence bands (Martin-Moreno et al. [19]) and the Penn gap will then be approximately equal to the energy difference between this contribution in the valence and conduction bands. The experimental data shown in fig. 7 show this energy difference to be about 5 eV in amorphous silicon and about 14-16 eV in amorphous Si3N 4. The calculated DOS of Martin-Moreno et al. gives values of 5 and 10 eV. The OJDOS of Piggins et al. [18] gives similar values to the calculated DOS. This discrepancy at high y may be due to crosssection or matrix element effects as mentioned above. The invariance of peak positions with nitrogen content is shown in the calculated DOS, the XANES data and the Penn gap results for the individual bond contributions.
o
o
o
N 2s
Fig. 7. XANES and XPS peak positions for a-Si 1_yNy : H as a function of y, with suggested band assignments.
We have calculated the homopolar and heteropolar contributions to the bonding for a-Sil_yNy based on the method of Levine [2]. Calculated values of the Penn gap for RBN and OBN models show large differences especially for high values of y where discrepancies of - 5 eV are obtained. Comparison of the calculated Penn gap with experimentally obtained values suggests that the system exhibits ordered bonding, supported independently by EXAFS data. XANES data have been interpreted in terms of the CB DOS which, in conjunction with XPS (VB) data of Karcher et al. [10], have given rise to an experimentally de-
s.c. Bayliss, S.J. Gurman / lonicity and bonding in a-Si I rNy
t e r m i n e d V B - C B D O S . T h i s D O S has b e e n fitted to optical gap d a t a of D a v i s et al. [6] a n d is in a g r e e m e n t w i t h v a l u e s of P e n n gap a n d O J D O S d a t a of P i g g i n s et al. [19]. T h e v a r i a t i o n of p e a k p o s i t i o n s w i t h c o m p o s i t i o n suggests a s y m m e t r i c a l o p e n i n g of the gap as y is increased, i n a g r e e m e n t w i t h the electrical d a t a of Spear et al. [20].
References [1] [2] [3] [4] [5]
J.C, Phillips, Phys. Rev. Lett. 20 (1968) 550. B.F. Levine, Phys, Rev. B7 (1973) 2591. S.J. Gurman, Philos. Mag. (1990) in press. H.R. Phillip, J. Non-Cryst. Solids 8-10 (1972) 627. N. Piggins, E.A. Davis and S,C. Bayliss, J. Non-Cryst. Solids 97&98 (1987) 1047. [6] E.A. Davis, N. Piggins and S.C. Bayliss, J. Phys. C 20 (1987) 4415. [7] S.H. Wemple and M. DiDomenico Jr. Phys. Rev. B3 (1971) 1338. [8] J.C. Phillips and J.A. van Vechten, Phys. Rev. Lett. 22 (1969) 705.
185
[9] B. Dunnett, D.I. Jones and A.D. Stewart, Philos. Mag. B53 (1986) 159. [10] R. Karcher, L. Ley and R.L. Johnson, Phys. Rev. B30 (1984) 1896. [11] W.T. Elam, J.P. Kirkland, R,A. Neiser and P.D. Wolf, Phys. Rev. B38 (1988) 26. [12] C. Morrell, J.T.M. Baines, J.C. Campbell, G.P. Diakun, B.R. Dobson, G.N. Greaves and S.S. Hasnain, eds., Daresbury EXAF Users' Manual (internal publication). [13] S.J. Gurman, N. Binsted and I. Ross, J. Phys. C17 (1984) 143. [14] N. Binsted, S.J. Gurman and J.W. Campbell, SERC Daresbury Laboratory EXCURV 88 Program (1988). [15] R.W. Joyner, K.J. Martin and P. Meehan, J. Phys. C20 (1987) 4005. [16] G.M. Ingo, N. Zacchetti, D. della Sala and C. Coluzza, J. Vac. Sci. Technol. A7 (1989) 3048. [17] S. Mobilio and A. Filipponi, J. Non-Cryst. Solids 97&98 (1987) 365. [18] N. Piggins, S.C. Bayliss, E.A. Davis and T. Shen, J. Phys. CM1 (1989) 8111. [19] L. Martin-Moreno, E. Martinez, J.A. Verges and F. Yndurain, Phys. Rev. B35 (1987) 9683. [20] W.E. Spear, B. Durmett and P.G. LeComber, Mater. Res. Sci. Symp. Proc. 95 (1987) 39.