Structure and physical properties of the glassy As2S3Gex system

Journal of Non-Crystalline Solids 20 (1976) 101-122 © North-Holland Publishing Company

STRUCTURE AND PHYSICAL PROPERTIES OF THE GLASSY As2S3Gex SYSTEM R. ANDREICHIN, M. NIKIFOROVA, E. SKORDEVA and L. YURUKOVA Institute of Solid State Physics, Bulgarian Academy of Sciences, Sofia, Bulgaria R. GRIGOROVICI, R. M.g,N,g,IL~, M. POPESCU and A. VANCU Institute of Physics, State Committee for Nuclear Energy, Bucharest-Mligurele, Romania Received 25 April 1975 Spectroscopical and structur,'d investigations directly reveal the presence of those structural units which were predicted by Myuller and coworkers to form the continuous network of As-S-Ge glasses. After refining Myuller's model to some extent, the variation with x of several physical properties (density, microhardness, electrical dark conductivity, photoconductivity, optical gap and first-neighbour coordination) in the whole series of As2SaGex glasses can be either understood qualitatively or even calculated quantitatively with the aid of additivity laws.

1. Introduction Ternary chalcogenide glasses of the type A v - BVI-c IV have attracted much attention both because of the relative easiness with which they can be obtained and because of the practical applications they offer. Of all the investigations, the most systematic are due to Myuller, Borisova et al. [ 1]. The importance of this group of papers resides in the interpretation of the results which is based on a unitary point of view. The glass is thought of as consisting of structural units of molecular size which are linked to each other at random in an ideal network by predominantly covalent bonds. Clustering at a scale of 10-20 A is admitted. Thermodynamic considerations are used in order to predict which bonds are formed and which not. For example in A s - S - G e glasses, the most probable structural units are, after Myuller, those listed in fig. la. Units l, 2 and 3 appear only in glasses very rich in S, As and Ge, respectively. Units 4 - 7 are the main constituents of most of these glasses [2], their relative contributions varying with composition so that all bonds are satisfied. The formation of As-Ge bonds is considered to be, if not excluded, at least extremely improbable. Electrical conductivity 0 = o 0 exp(-eo/kT) is considered to be governed on the one hand by the activation energy e0 which varies as the predominant bond energy and is also reflected in the width of the energy gap, and on the other by the preexponential factor 00 which varies with the degree of heterogeneity of the structure, being the lower the more the structural units which form the continuous network differ from each other in symmetry.

R. Andreichin et al. / Structural properties of the As2 $3 Gex system

102

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A series of physical quantities which characterize these glasse,~;like density, microhardness, electrical conductivity and others are supposed to be calculable on the basis of molecular additivity rules. The agreement reached in some cases is fairly good Similar points of view can also be found, for instance, in [3] and [4] which are, however, ~:oncerned with other glasses. Successful as these investigations have been, their conclusions remain largely conjectural because no direct proof of the actual existence of the, structural units supposed to form the network of the glass; is given. It is the aim of this paper to discuss those units lacking direct proofs of existence. We restricted ourselves to the study of a single system As2S3Ge:, c , which presents several advantages. Homogeneous glassy samples are relatively ea,,sy to obtain over a broad range of compositions, the optical edge and the vibrationa~l absorption spectrum ilie within an easily accessible spectral range, and X-ray diffraction data are relatively easy to interpret because of the significant difference in atomic number between the S and the As ~.r~dGe atoms, respectively. We included in our investigations a board variety of me',~,surements - structural, mechanical, electrical, photoelectrical and opticai - co~ering the whole range of x from 0 to 3.33 ( 0 - 4 0 at% Ge), the uFper limit of existenc,: of the glassy g~ate. We correlated all our various results in order to reach a better understanding of the way the addition of Ge to As2S 3 modifies the latter's properties *.

2. Sample preparation The glasses were synthesized from the elements. As and S were of 6n purity; Ge * Preparation of the samples, mechanical, electrical and photoelectrical measurements were performed in Sofia (see [5], [6]), structural and optical measurements in Bucharest. All measurements were performed at room temperature.

R. Andreichin et al. / Structural properties o f the As2 Sa C,ex system

103

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R. Andreichin et al. / Structural properties of the As2S3Ge x system

were single crystals of 40 f~-cm resistivity. The weighted elements were introduced into a quartz ampoule which was evacuated to 10 - 3 - 1 0 -4 torr and then sealed. The synthesis was carried out in a rocking furnace. The ampoules were held at the highest temperature of 900°C for 20 h, after which they were taken out of the furnace and cooled in air. The compositions synthesized and investigated are listed in table 1..All glasses were clear and homogeneous, their colour changing from dark red to a reddish orange and then back through dark red to nearly black with increasing Ge content, with the exception of the 5-10 at% Ge range in which they were turbid and their colour was a bright orange.

3. Structure As suggested by the conchoidal fracture and by examination in the metaUographical mJcroscope [5], X-ray diffraction measurements showed that, indeed, with the exception of the turbid ones, all samples were completely glassy. X-ray diffraction patterns were obtained on powdered samples with the aid of a Siemens Kristalloflex IV diffractometer with Mo K~ radiation [Smax = (4n sin 0)/X =-15 A -1 ]. Radial distribution functions (RDF) in electronic units were obtained by Fourier transformation using an ICL-1902 computer. Some improvements were achieved with respect to errors in the intensity diffracted at high angles with the aid of a variant of the procedure devised by Kaplow et al. [7]. A series of RDFs are represented in fig. 2 for samples of various compositions. With increasing Ge content the first peak of the RDF is increasing in area and shifting from 2.27 to 2.47 A (table 2). The modifications which occur further in the RDF will be discussed in section 8. The diffraction pattern of the turbid samples showed the presence of small quantities of crystalline As2S2 embedded in a glassy matrix. This is clearly shown in fig. 3. curve 2, where the hffraction lines of As2S2 are those indicated by Maruno[8].

4. Density The density p of the samples was determined by dipping in toluene. The measured values are listed in table 1 and represented by crosses versus composition in fig. 4a. The composition is plotted as logp ( p = 100 x/(5 + x ) at% Ge) in order to see what happens at low Ge content. An x scale is also provided. The density values given in [2] for six investigated compositions are represented in the same figure by dots. The dependence of p on p is rather complicated: a slight and slow increase is followed after p ~ 3 at% Ge by a rather steep decrease to a minimum at p ~ 12 at% Ge, after which p rises again, first slower until p ~ 25 at% Ge and then steeper until p ~ 4 0 a t % Ge.

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Table 2 Position and area of the first peak of the RDF in As2 S3Gex glasses. Glass no.

Composition

5

As2 S 3Geo.o2 s

11

As2 S3(;eo .681

14

p (at% Ge) 0.5

First peak of RDF Position r I (A)

Area A l (el. units)

2.27

6500

12

2.34

9700

As2 S 3Gel .667

25

2.40

12900

15

As2 S3Ge2.14

30

2.41

16100

16

As2S3Ge2.69

35

2.42

19200

17

As2 $3 Ge3.33

40

2.47

22600

106

R. Andreichin et aL / Structural properties of the AssS3 Gex system

4

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J l It. ill II ..., II $~

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5. Microhardness The microhardness H was measured by Hannemann's method using a load of 50 g. The values of H listed in table 1 are shown by crosses in fig. 4b. The values of H measured in [2] are represented in fig. 4b by dots after multiplication by a constant factor, which brings ~ e values obtained by the two different research groups into a best fit. There is an obvious similarity between the dependence of p and H on p, but also some notable differences, especially in the depth of the minimum of H and in the steepness of the subsequent increase between p = 12 and p = 25 at% Ge.

6. Electrical conductivity The dark conductivity o D (table 1 and fig. 4c, curve 1) shows two maxima as a function of p. The first lies at p ~, 0.1 at% Ge, after which o D comes back to its value in pure glassy As2S 3 over a broad composition interval. The second rather high and narrow peak lies at p = 15 at% Ge, after which o D drops again to the initial value in pure glassy As2S 3 at about 30 at% Ge only to increase again sharply by three orders of magnitude at 40 at% Ge.

7. Photoconductivity The photoconductivity o L under constant illumination (E = 1500 Ix, tungsten lamp) exhibits little variation with composition (table 1 and fig. 4c, curve 2). The

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0 LI 0"5 £0 # j ,#" / m~ /~ a , ~ m I d . % ~ Fill. 4. Physical properties of As2 S3Ge / glasses as a function of Ge content ( p = 100 xl(x + 5) at% Ge). (a) Density p : x experimental values (table 1); • experimental values after [2 ]; -~ calculated values, after table 7; .... calculated values after table 8. (b) Microhardness H: × measured values (table 1); • experimental values after [2], adapted for best fit with X. (c) Curve 1 electrical dark conductivity aD; curve 2 photoconductivity o L under illumination with white light (1500 Ix); curve 3 oL/OD; +, X, • measured values (table 1). (d) Main absorption edge htoo. X measured values (table 1); curve 1 assumed dependence of/~wo on composition in As~ S 3 - 1 x glasses; cuive 2 dependence of/~too on composition in S3Gex glasses (after [9 ]); calculated values (table 8). (e) Percental content Pi of various structural units: - after table 7; .... after table 8. 0~1

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108

IL Andreiehin et a£ / Structural properties of the As2S 3Gex System

ratio OL/OD (table 1 and fig. 4c, curve 3) therefore shows the usual behaviour, i.e. the ratio is the higher the lower o D. However, the dependence of the photocurrent on illumination (I 5 < E < 1500 Ix) follows a power law with an exponent K which clearly delimits three composition ranges (table 1)" g ~, ~ for 0 < p < 2; K = 0.8-0.9 for 2 < p < 15 and g = 0.4-0.5 for p >t 20 at% Ge

8. Optical absorption The position of the exponential absorption edge hco0 was evaluated from spectral transmission curves between 8000 and 20000 cm -1 . For the sake of comparison this was done by a procedure used by Kawamoto and Tsuchihashi [9], as shown schematically in fig. 5. This procedure is admissible only if all samples are of about tile same thickness which was more or less the case (0.2-O.3 ram). The procedure could also be applied only to clear glasses, because turbid samples display a reduction in the slope of the edge due to light scattering [10]. Therefore, the compositional range between 5 and 10 at% Ge could not be explored directly. However, the colour of powdered samples clearly showed a tendency to shift from red towards orange from 0 to 10 at% Ge. In fig. 4d, where ~w0 is plotted against log p, the 5-10 at% Ge region is marked by a shadowed area. Also shown (curve 2) are the values of hw 0 reported in [9] wltich deals with Ge-S glasses. Three composition ranges are clearly seen in fig. 4d. Within the first region (0-10 at% Ge) ~w0 increases slowly. In the second (10-25 at% Ge) h w 0 decreases, but more rapidly. In the third region (25-40 at% Go) which follows after a short anomalous behaviour, ~ 0 drops even more rapidly and is only slightly lower than that of the corresponding GexS 3 glasses. The ~w0 versus log p curve as a whole approximately mirrors the photoconductivity curve in fig. 4 c (curve 2). Spectral transmission and reflection was also recorded between 5 and 25/~m (2000 and 400 cm- 1) where the lattice vibrations already show up. In general, the reflection curves showed traces of the same structure as the transmission curves. In order to compare the optical properties of samples of different thicknesses (0.2 to

i--Fig. 5. Definition of absorption edgehtoo (after [9 ]).

R. Andreichin et aL/ Structural properties o f the As2SsGe x system

109

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1.5 mm), the optical absorption coefficient ~ was calculated from the transmittance by admitting a constant reflectance R 0 = 1 - T 0, where T O is the constant transmittance between 5 and 6.5 jura. The results are shown for four selected samples in fig. 6. Pure glassy As2S3 shows a rather broad, probably complex absorption band at 4 3 0 - 4 9 0 cm - l ascribed by Tsuchihashi and Kawamoto [4] mainly to the As-S bond, a stronger and narrower peak at about 680 c m - l and a weak one at 960 cm-1 both also assigned in [4] to the A s - S bond. Addition of Ge is seen to have the folI

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110

R. Andreichin et aL / Structural properties of the As2 SaGex System

lowing effects: the 455 cm -1 band shows a flight tendency to shift towards lower energies and to increase in intensity. Both the 680 and the 960 cm -1 bands, however, gradually decrease in intensity, while two bands at 800 and 1290 cm -1 first sharply increase in intensity and then, for x > 1.7, start shifting towards lower wave numbers, reaching at x = 3.33, 755 and 1250 cm -1 , respectively. Mention must also be made of the appearance of a narrow absorption band at 1540 cm-1. Its intensity increases sharply with the addition of relatively small amounts of Ge ( < 20 at%), Cu (< 1 at%) and Sn (< 1.5 at%) (fig. 7). Its shape and position are independent of the nature of the dopant and must therefore be at. tributed to a molecular grouping containing only As and S atoms.

9. Discussion of optical and structural data The best starting point for a discussion is the optical absorption measurements. As already stated, the main absorption bands in the IR spectrum of glassy As2S 3 are assigned to the As-S bond [4]. A more detailed understanding of the meaning of this spectrum in terms of structure and lattice vibrations is given by the analysis of the far IR spectrum of glassy As2S 3 due to Lucovsky and Martin [ 11 ]. They show that there is a weak coupling between the four vibrations V l - V 4 of the AsS 3 pyramids (I, I1, Ill in fig. 8) and the three fundamental modes v~, v~, v~ of the As-S-As chains, so that they can be calculated separately; As2Se 3 is also considered. The fit between experiment and theory for both As2S3 and As2Se 3 is excellent and includes in the latter case, the v~, v~ and v~ frequencies. Confidence may t f therefore be expressed in the calculated frequencies v I and v2 in As2S3 which are not known experimentally. Table 3 contains the calculated and observed frequencies in As2S 3 as well as possible assignments for the 400-1100 cm- 1 range not covered by Lucovsky and Martin, but investigated in [12] and by us. The vibrations are supposed to be harmonic, i.e. higher harmonics are multiples of the fundamentals and there are no intercombination bands. In order to understand the modifications in the absorption spectrum due to the addition of Ge and described in section 8, we make use of the assignments given by Kawamoto and Tsuchihashi in [9] who show that the Ge-S bonds give rise in As

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Fig. 8. Structural model of glassy As2$3 after Lucovskyand Martin [ 11].

iZ Andreichin et al. / Structural properties of the As2S3Ge x system

111

Table 3 Vibrational spectrum of As2 $3 glass. Mode I

v2 f

Structure As-S-As

Vcalc ( c m - l ) after [ 11 ]

Vexp (cm- 1 ) a)

Samples

55

v4

AsS 3

133

120-150

v2

AsS3

162

164

vl

As-S-As

218

v3

AsSa

310

310

vI

AsS3

344

344

v3

As-S-As

438

2v'l

As-S-As

436

3v2

AsS3

486

2v 3

AsS3

620

2v I

AsS3

688

3v'l

As-S-As

654

0.2-1.5 mm;

4v2

AsS3

648

this work;

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ASS:;

1032

3v 3

AsS3

93(J

4Jl

As-S-As

872

5~1

As-S-As

109~

!

I

th~-n films after [11]

455 vs

bulk samples, 680 vs

thickness

see also [121 960 w

a) vs = very strong, w = weak.

GeSx (1.25 < x < 5) glasse,; to a strong band at 4 6 0 - 4 8 0 cm-1 anddo another strong band which shifts with decreasing S/Ge ratio from 790 to 755 cm -1 . No measurements seem to have: been performed beyond 1200 cm -1 . The bands appearing in our measurements (fig. 6) can clearly be attributed to the formation of an increasing number of G e - S bonds, while the shift of the 790 and 1290 cm -1 bands towards lower frequ~;ncies at high Ge contents can be attributed to the same structural changes which o~.'cur necessarily in Ge-rich GeS x glasses, i.e. to the forma tion of increasing numbers of Ge-Ge bonds. This implies that no G e - A s bonds are formed. The appearance of Ge-15 bonds must induce the formation of direct As-As bonds, thus reducing the namber of As-S bonds. The gradual disappearance of the 680 and 960 cm -1 bands reflects this phenomenon. The conservation of the 455 cm -1 band which seems to contradict this conclusion is explained by the fact that this frequency is found both in glassy As2S 3 and G e - S glasses. To be sure of this interpretation a search for possible evidence of the formation of Ge-As bonds must be made. As far as we are aware, nothing is known about the

112

K Andreichin et al. / Structural properties o f the As2SsGe x system

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[141). optical vibrations in Ge-As glasses or in related crystals. However, from the papers by Goryunova et al. [13] and by Abraham et al. [14] on the absorption spectra of glassy CdGexAs2 alloys and crystalline CdGeAs 2 and CdAs 2, the arrangement shown in fig. 9 emerges: some absorption bands are present in both crystalline CdAs 2 and CdGeAs2. The other bands which appear in CdGeAs2 only, must therefore be assigned to the Ge-As bond. The same absorption bands are also present in the amorphous phases. As shown in table 4, none of these frequencies or their harmonics show up with increasing Ge content in the As2S 3 Gex glasses. The strongest band at 680 cm-1 should compensate the weakening of the As-S band at the same frequency with increasing x. This does not happen either. It may be concluded, therefore, that the As and Ge atoms are almost exclusively linked to each other through ;,Jtermediary S atoms. Finally, As-As bonds could show up optically in the composition range in which As atoms are bound not only to each other, but also to S atoms. Such groupings start forming at low Ge co~tent and cease to exist at relatively high Ge content, where practically no S is left over to be bound to the As atoms, i.e. at about 20at% Ge (fig. 4e). Other elements such as Cu, Sn, Ag which readily combine with S must be expected to have the same effect. Indeed, the Ig absorption spectrum of realgar (As2S2) is practically identical to that of orpiment (As2S3) [ 15] except for a supplementary narrow band found by us at 1386 cm - I (fig. 10) which may be attributed to the =S2=As-As=S2= group. We may therefore tentatively assign the narrow 1540 cm -1 absorption band which appears in Ge-, Cu-and Sn.doped glassy As2S 3 (figs. 6 and 7) at low concentrations and disappears again at more than 20 at% Ge, to the same = S 2 = A s - A s = S 2 = group, its frequency being shifted towards higher energies due to the different way in which the neighbouring atoms are attached to this group in glassy As2S3Gex and in crystalline As2S2, respectively. Hitherto, the spectroscopic results provide partial evidence in favour of Myuller Table 4 Vibrational frequencies of the Ge-As bond (see fig. 9).

Mode

vI

v2

v3

v4

2v2

3v2

2v3

3v3

(cm-Z) a)

94 w

154 m

27¢ s

670 vs

308

462

548

828

a) w = weak, m - medium, s = strong, vs = very strong

IL Andreichin et al. / Structural properties o f the As2S3Ge x system

#o

6#-

113

T

1

20-

OL

n /5OO

I

I

I

tz~O0

/30O

1200

l

1100 cm -f

Fig. 10. Optical transmission of KBr-embedded realgar (As2 $2).

and Borisova's views on the structural units in A s - S - G e glasses. The molecular species As2S3, As2S 2, GeS 2 and GeS show up either in the IR absorption spectrum or in the shift of the absorption edge, but there is no evidence for the presence of amorphous As and Ge (a-As and a-Ge) clusters. However, an analysis of the structural results may provide evidence for all structural units including a-As and a-Ge. Indeed, if the evolution of the RDFs with increasing Ge content (fig. 2 and table 2) is followed, the increase inarea and the shift of the position of the first peak is first noticed. This can be ascribed qualitatively to the increase of the average number of effective electrons pet atom and of the mean interatomic distance, respectively, i,a the newly formed As-As and Ge-Ge bonds (dAs_ s ~. dGe_ S = 2.26 A,; dAs_As = 2.50 A;dGe_Ge "-"2.45 •). The shift towards higher r of the second peak with increasing p up to 30 at% Ge (fig. 2) is due to the increase of the number of both GeS 2 and a-As structural units. The shift in the opposite direction of this peak between 30 and 40 at% Ge can clearly be linked with an increased content in GeS units replacing those of GeS 2. The interpretation of the changes in the RDF between 5 and 6 A is more relevant. First, the reversal in the height of the 5.2-5.4 and 5.8-6.0 peaks when passing from 0.5 to 12 at% Ge correlates well with the similar reversal observed by Renninger and Averbach in [ 16] (fig. 3) in passing from As2Se 3 to As2Se 2 glasses. A comparison between the diffracted intensity curves of our glassy As2S 3 and As2S3 + 12 at% Ge glasses also si~ows that it clearly reflects the change in the angular distribution of the diffraction lines when passing from crystalline As2S 3 to crystalline As2S 2 (fig. 3, curves 1 and 3). These seem to indicate that the presence of As2S2 structural units is near its peak around 10-12 at% Ge, in contradiction with Myuller and Borisova's structural formulae (table 7, last column). The shift towards higher r of the peak

114

R. Andreichin et al. / Structural properties o f the As2S3Ge x system

at 5.6 A in the 35 at% Ge RDF to 5.8 A in the 40 at% Ge RDF is clearly due to an increase of the number of GeS units replacing GeS2 units, but in order to account for the position of this particular p~al,: i~t all RDFs between 25 and 40 at% Ge, a notable contribution due to a-As clusters now seems necessary. An even more convincing feature in favour of the existence of a-As clusters is the appearance beyond 25 at% Ge of the small peak at ~4.7 A which seems to be assignable only to a-As after the disappearance of all signs of the presence of an As2S 3-type short-range order. We would therefore conclude that a-As clusters show up somewhere near 20 at% Ge. This contradicts the structural formulae given in [2], where a-As clusters should appear at a Ge content as low as 5 at% (table 7, last column). As to the presence of a-Ge clusters, signs of their existence can also be detected in Ge-rich Ge-S glasses. Indeed, in the RDF of glassy GeS 2 (x = 1.5) obtained by Rowland et al. ([17], fig. 3), the positions of the first and second peak match the sum of the covalent radii of Ge and S (2.26 A) and the corresponding secondneighbour tetrahedral distance of 3.67 A, respectively. However, in the RDF of the GeSI.38 (x = 2.18,p = 31 at% Ge) glass ([17], fig. 4) the first peak has slightly shifted nearer the Ge-Ge distance of 2.45 A, while the second peak shows a clear shoulder at 4.0 A, i.e. the second-neighbeur tetrahedral distance in a-Ge. In our glasses the presence of a-Ge clusters shows up for the first time in the obvious broadening of the sec,3nc~ pe~3kin the 35 at% Ge RDF and culminates in the split of this peak in the 40 at% Ge RDF. Therefore the presence of a-Ge clusters is again detected later than predicted in [2], i.e. at about 25 at% Ge (cf. table 7, last column). Thus the structural measurements provide the direct proof we have aimed at for the existence of all the structural units predicted by Myuller. However, some quantitative discrepancies have appeared between our results and his predictions. We therefore tried to find compositional formulae similar to those devised by Myuller but based on our optical and structural results, and to check them by calculating with the aid of additivity laws the values of various physical quantities in order to compare them with the experimental results.

10. Composition and density We began by using our density data (table 1, fig. 4a) to perform this check. In writing compositional formulae, we restricted ourselves first to Myuller's six molecular species marked by asterisks in table 5. Writing thus the compositional formula of the As2S 3Gex glass as As2S3Gex = c I As2S 3 + c 3As2S 2 + c 5As 2 + c 6GeS 2 + c 7 G e S + c 8 G e

(1)

we chose not to use more than three components for a given composition. This perfectly defines the three coefficients c i, if x is increased and a new species added when a preceding one disappears; or, x may be decreased continuously.

R. Andreichin et al. / Structural properties of the As2 $3 Gex system

115

Table 5 Structural units, their molecular weights and densities used in density calculations. Unit

Structural

Molecular weight

no.

unit

M

1" 2

As2S3 As3S4

246.10 353.12

3'

As2 $2

214.04

4 5* 6* 7* 8*

As2 S

181.98 149.92 136.72 104.66 72.60

AS2

GeS2 GeS Ge

Densityp (g cm -3)

M/p

3.18 3.31 3.28 3.60 4.93 2.70 3.50 5.35

77.4 106.7 65.3 50.3 30.4 50.5 29.9 13.6

The average density of the glass can be calculated from the relation of additivity

p=

MAs2S 3 "t"XMGe

i

,

(2)

ciMi/Pi

where M i is the molecular weight of the/-species, c i its compositional coefficient and Pi its density in the glassy or amorphous state. The values of Pi given in table 5 are taken from the literature ([6] for a-As2S3; [18] for a-As; [9] for a-GeS 2 and a-GeS; [ 19] for a-Ge) except that of glassy As2S 2 which is not available directly. We evaluated this value from the densities of the orpiment [20] and regular [21] crystals by assuming that p(a-As2S2) = p(a-As2S3) [p(cr-As2S2)]/[(p(cr-As2S3)] = 3.18(3.59/3.48)= 3.28 g cm -3 . This calculation proved quite successful in the x > 1.5 range, but failed to describe the experimental densities below x = 1.5. Two main questions are raised in connection with this calculation. First, if the structural model of the glass is indeed a continuous random network, then an additivity law is expected to hold, but we should not restrict ourselves to molecular species selected as structural units on the ground that they are able to form crystals. It may help to introduce some intermediary 'molecules' like As3S 4 and As2S (fig. l) to give a higher degree of continuity to the structural changes between As2S 3 and As2 (table 5). The second question is that of the densities to be ascribed to these species. A

R. Andreichin et aL / Structural properties of the As2S3Ge x system

116

Fig. 11. D e n s i t y o f c r y s t a l l i n e (1) a n d glassy (2) phases in t h e S - A s s y s t e m . × , +, ~ e x p e r i m e n t a l values; - o -

i n t e r p o l a t e d values ( f o r l i t e r a t u r e , see t e x t ) .

Table 6 Compositional coefficients

ci in A s 2 S s G e x g J a s ~ s a f t e r f o r m u l a (3).

Structural units

As2 $3

As3 $4

As2 $2

As2 S

As2

GeS2

GeS

Ge

Compositional

Cl

c2

c3

c4

Cs

c6

c7

Cs

2(x-l) 1 1

x x x x 3-x -

2x-3 3

coefficients Composition range 0 0.167 0.5 1.0 1.5 3.0





l-6x -

. .

4x 1 - 2x . . . .

3 x - 0.5 2(I-x) . .

2x- 1 3-2x

x-3

1~ Andreichin et al. / Structural properties o [ the As2 $3 Ge x system

o% +

+ ~

o%

<

oo

÷

÷

+

117

+ OQ

o% +

eel

<

<

¢,1

,X, o%

o)

,..~ ¢~1 ~'~ O0 ,-~ ~ ~ ~ ¢~1 ~ ~ ~ ¢ ~ ~ " ~ ~ " t ~ ~ ¢~1 ~ ~D O0 ~ O0 ¢¢~ t'~ ~ " ~ •-~ ,-~ ,-~ ¢~1 ¢'4 ¢'4 ¢~1 ¢¢~ ¢¢~ ¢ ~ ~Y ~P "¢~ w~ ~ ~ ~ ~ ~D " ~ ¢¢~ tt~ P~ " ~ 4 " ÷ ÷ ÷ ÷ + - I - , ÷ ÷ ÷ + ÷ ÷ ÷ ÷ ÷ + ÷ ÷ - 1 - ÷ ÷ 4 - ÷ ÷ ÷ ÷ ÷ o) oo

0

0 0

°!

÷

÷

÷

÷

-t"

+

-I-

+

÷

÷

÷

÷

÷

÷

÷

÷,÷

÷

÷

÷

÷

÷

÷

4-

÷

118

R. Andreichin et al. / Structural properties o / t h e As2SaGe x system '~

graphical r~presentation of the dependence of density on composition in both the crystalline and the glassy state in the As-S system is given in fig. I l (after [20]-[23] for the crystalline phases AS2S3, As2S 2, As4S3, As4S and after [4], [24], [25] and [ 18] for the glassy As--S system and a-As). There is an obvious parallelism between the shape of the p versus composition curves in the two states which both seem to display a peak in density somewhere between As2S3 (40 at% As) and As2S 2 (50 at% As). We therefore tentatively included the structural units As3S4 and As2S in the scheme with the densities 3.31 and 3.60 gcm 3 we obtained by interpolation in fig. I 1 on curve 2. The compositional formula of the glass now became AS2S3Gex = c I As2S3 + c 2 As3S4 + c 3 As2S2 + c4 As2S + c 5 As 2 + c 6 GeS 2 + c? GeS + c 8 Ge,

(3)

while the average density is again given by eq. (2). The resulting expressions for the compositional coefficients c i are given in table 6, while table 7 contains their numerical values as well as the percental concentrations Pi of the eight molecular species and the calculated average densities/~, which are displayed as full curves in fig. 4e and 4a, respectively. The last column of table 7 contains Myuller and Borisova's compositional data as given in [2 I. I he calculated values fit the experimental densities quite well, though some improvement still seems desirable. The relative success achieved by introducing the intermediary structural units As3S4 and As2S suggests that it may help even more to replace the discrete structural units which contain As and S by a continuously varying species. We therefore replaced eq. (3) by As2S3Gex = As2S3_2x + xGeS 2 ,

(4)

the dependence of p(As2S3_2x ) on x re:~lting from curve 2 in fig. 11 which also provides values of 0 for As2S 3, As3S4, As2S2, As2S and As2 in agreemen~ with those in table 5. In the composition range 1.5 < x < 3.0, two different ~tructural units which contain Ge and S come into play. The triangular shapes of the Pi versus PGe curves in fig. 4e are obviously only a first approximation to reality. A more realistic shape would be, for example, Gaussian curves covering the same areas as the triangles with PGeS2 and PGeS summing up to 1 --PAs2 for 1.5 < x < 3.0. This gives PGeS2 = 0 . 5 3 4 e x p [ - - l . 1 0 2 ( x - 1.5) 2]

f o r x > 1.5 ;

F,7,eS -- 0.705 exp[-l.034(x - 3.0) 2]

for x < 3.0.

(5)

The Pi versus PGe curves for As2S 3 - 2x, GeS2 and GeS now assume the shapes of the broken curves in fig. 4e. The numerical data of c i and Pi (for As2S3_2x, GeS2 and GeS) in dependence on x are summarized in table 8 together with the new calculated densities also shown by the broken curve in fig. 4a. This curve is in even

R. Andreichin et al. / Structural properties o f the As2S3Ge x system

119

Table 8 Calculated composition, density and absorption edge of As2 S3Gex glasses after formulae (2), (4)(5),(6).

0 0,015 0.025 0.050 0.075 0.100 0.125 0.150 0.167 0.200 0.25 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20 1.30 1.40 1.50 1.75 2.00 2.50 3.00

p (at% Ge)

Composition Pi (molar%)

a(As2S3-2x) after fig. 11

Calc.density ~(g cm -3)

Calc. absorpt. edge hwo(eV)

0 0.299 0.496 0.990 1.475 1.96 2.44 2.90 3.22 3.84 4.76 5.66 7.40 9.09 10.7 12.3 13.8 15.3 16.7 18.0 19.4 20.6 21.9 23.1 25.9 28.6 33.3 37.5

100As2 $3 98.5As2S2.97 + 1.5GeS2 97.6As2S2.9s + 2.40eS2 95.2As2S2.9o + 4.80eS2 93.0As2S2.ss + 7.0GeS2 90.9As2S2.8o + 9.1GeS2 88.9As2S2.TS + I I.IGeS2 87.0As2S2.7o + 13.0GeS 2 85.7As2S2.67 + 14.30eS2 83.3As2S2.6o + 16.70eS2 80.0As2 $2.5o + 20.0GeS2 76.9As2 $2.4o + 23.10eS2 71.4As2 $2.2o + 28.60eS2 66.7As2S2.c~ + 33.20eS2 + 0.1GeS 62.5As2Si.8 +37.3GES2 + 0.2GeS 58.8As2S1. 6 +40,90eS2 + 0.3GeS 55.6As2Sl. 4 +43.90eS2 + 0.5GeS 52.6As2Si.2 + 46.70eS2 + 0.TGeS 50.0As2Sl.o + 48.8GES2 + 1.2GeS 47.6As2So.a + 50.7GES2 + 1.7GeS 45.5As2So.6 +52.1GES2+ 2.4GeS 43.5As2So.4 + 53.00eS2 + 3.5GeS 41.7As2So.2 + 53.4GES2 + 4.9GeS 40.0As2 + 53.4GES2 + 6.6GeS 36.7As2 + 49.3GES2 + 14.0GeS 33.3As2 + 40.7GES2 + 26.0GeS 28.6As2 + 17.7GES2 + 53.7GES 25.0As2 + 4.50eS2 + 70.5GeS

3.18 3.19 3.20 3.22 3.24 3.26 3.28 3.29 3.31 3.34 3.37 3.39 3.39 3.28 3.24 3.27 3.35 3.47 3.60 3.79 4.01 4.27 4.57 4.93 4.93 a.93 ,:~,.93 4~.93

3.18 3.19 3.19 3.20 3.21 3.22 3.23 3.24 3.25 3.26 3.27 3.26 3.23 3.12 3.07 3.07 3.10 3.13 3.17 3.22 3.27 3.34 3.39 3.45 3.36 3.39 3.63 3.74

1.96 1.96 1.97 1.99 2.00 2.02 2.03 2.04 2.05 2.06 2.09 2.11 2.14 2.17 2.04 1.94 1.89 1,84 1.7", 1.75 1.73 1.70 1.67 1.~5 1.64 1.54 1.26 1.11

b e t t e r agreement with the experimental data over the whole range o f As2S3Ge x glasses.

11.

Composition and o t h e r

physical properties

It n o w seems w o r t h while to look into the dependence of o t h e r physical properties of the As2S 3 Ge x glasses on their Ge content as displayed in fig. 4b--d. The microhardness H w o u l d be expected to increase regularly w h e n Ge is added progressively, due to the transition from trigonal to tetrahedral connectivity as

120

R. Andreichin et al. / Structurzl properties of the As 2S3 Gex system

happens in As2Se3Gex glasses [26]. However, the effect of the anomalous decrease in density at about 10 at% Ge due to looser structural packing prevails, so that H follows the variations of p closely. The effect is probably enhanced by the presence of As2S 2 crystallites in the glassy matrix. On the other hand, the reduction in slope in the H versus p curve beyond 25 at% Ge seems to indicate that little is to be gained in microhardness when the whole network is already tetrahedrally interconnected. As to the electrical conductivity o D its first increase at very low Ge content can be attributed tentatively to the bridging effect of the tetrahedrally coordinaged Ge atoms introduced into a trigonally interconnected network. However, with increasing Ge content, the diversity of structural elements of different symmetries also increases and this must lead, after Myuller, to a decrease in mobility and, consequently, in o D, too. Predominantly tetrahedral coordination starts again with the inclusion of mainly As2 s 2 and GeS 2 structural units (see fig. 1) at x = 0.5, and may result in the o D peak at x - 0.9 followed by a new decrease in conductivity when other structural units reappear. Therefore, this peak is probably a mobility effect again. The sharp and vet37strong increase in o D at x = 2.8 is obviously linked to the rapid narrowing of the energy gap and is probably a carder concentration effect. Photoconductivity OL (fig. 4C, curve 2) follows the variation of the optical gap closely, increasing when the gap decreases and vice versfi. This is easily understandable because, the measurements being performed in white light, the photocurrent will be the higher, the larger the useful spectral interval. While the interpretation of the H, o D and OL data was purely qualitative and conjectural, the variation of the width of the optical gap, as shown in fig. 4d, can be obtained quantitatively by a simple calculation based on an additivity law if the dependence of the gap width on composition in both the As-S and the Ge-S glassy systems is known. We calculated the width hw 0 of the optical gap with the aid of an additivity law of the form flwo(As2S3Gex) = Pl ~/'~0 (As2S3-2x) + P2 ~Wo (GeS2) + P3 tiWo (GeS), (6) where Pl, P2 and P3 are taken from table 8. The basic data hco0(GeS2) = 2.60 eV and hco0(GeS ) = 1.25 eV were taken from [9]. In the As2S3_2x series, hw 0 was assumed to stay constant between As2S 3 and As2S2 and to vary linearly with log x between x = 0.5 and x = 1.5 from ~Wo = 1.96 eV for As2S 2 to ~i¢o0 = 0.45 eV for a-As. This latter value results by extrapolation of the log c~versus energy curve given by Greaves et al. [27] t o a = 3 cm -1, a value which approximately corresponds to 7 ~ 0 as defined in fig. 5 for samples 0.2-0.3 mm thick. The fit of the calculated curve (full curve in fig. 4d) with the experimental data is quite satisfactory and confirms that only a continuous network and not a mixture of small crystaUites can describe the structure of, at least, this type of glasses. Indeed, one would expect the effective energy gap in a mixture of crystaUites to be given by thee narrowest gap in the components rather than by a weighted average of the gaps of the components. Fina!!y, let us come back to the structural data. We used the structural formula

R. Andreichin et al. / Structural properties of" the As2S3 Gex system

121

e/em~i i~ A,t t.O(

t.I01

p ~

Fig. 12. Area A 1 (electronic units) under the first peak of the RDF of As2S3Gex glasses in dependence of the Ge content p. + experimental values (table 2); ~ calculated values using compositional formula (3) and data of table 7. (3) and the data of table 7 in order to calculate the areas of the first peak of the RDF of As2S3Ge x glasses with varying p. The results are plotted against p in fig. 12 (full curve) and compare well with the measured areas of the first peak (A 1) in the RDFs of the glasses investigated by X-ray diffraction (table 2).

12. Conclusions This detailed and many-sided investigation of the glassy As2S3Ge x system provides not only direct evidence in favour of the existence of the structural units postulated on thermodynamical grounds to form the building blocks of fheir structural network by Myuller and coworkers, but also achieves some essential improvements in the compositional formulae of these glasses as well as in the quantitative agreement between the measured values of various physical quantities and those calculated with the aid of molecular additivity laws.

References [ 1] R.L. Myuller, in: Solid State Chemistry, ed. Z.U. Borisova (Consultants Bureau, New York, 1966) p. i.

122

R. Andreichin et al. / Structural properties o f the As2 $3 Gex s'ystem

12l ILL. Myuller, V.N. Timofeeva and Z.U. Borisova, in: Solid State Chemistry, ed. Z.U. Borisova (Consultants Bureau, New York, 1966) p. 46. A.R. Hfltcm, C.E. Jones and M. Brau, Phys. Chem. Glasses 7 (1966) 105. 131 S. Tsuchihashi and Y. Kawamoto, J. Non'Crystalline Solids 5 (1971) 286. 14l R. An d~eichin, M. Nikiforova, E. Skordeva and L. Yurukova, Konf. amorL, zhidk, i 151 stekloobrazn, poluprovodn., ed. R. Andreichin (Bulg. Akad. of Sciences, Sofia, 1972) p. 15. [61 IL Andreichin, M. Nikiforova, E. Skordeva and L. Yurukova, Proc. Conf. Amorphous Semicond., ed. P. Suptitz (Akad. Wissensch. DDR, Reinhardsbrunn, 1974) p. 228. [7] R. Kaplow, S.L. Strong and B.L. Averbach, Phys. Rev. 138A (1965) 1336. [81 S. Maruno, Jap. J. Appl. Phys. 7 (1968) 1434. [91 Y. Kawamoto and S. Tsuchihashi, J. Amer. Ceram. Soc. 54 (1971) 131. [101 A. Vancu, St. Sladaru and R. Grigorovici, Proc. 5th Int. Conf. on Amorphous Liquid Semicond., Garmisch-Partenkirchen, 1973, ed. J. Stuke and W. Brenig (Taylor and Francis, London, 1974) p. 631. G. Lucovsky and R.M. Martin, J. Non-Crystalline Solids 8 - 1 0 (1972) 185. [111 [121 M. Onomichi, A. Toshihiro and K. Kudo, J. Non-Crystalline Solids 6 (1971) 362. [131 N.A. Goryunova, E.F. Gross, L.B. Zlatkin and E.K. lvanov, J. Non-Crystalline Solids 4 (1970) 57. 1141 A. Abrah~im, I. Gregora, A. Hrub~, M. Maty~, L. Stoura;:, J. Tauc, V. Vorli~ek and M. Zav6towi, Proc. 10th Int. Conf. Phys. Semicond., Cambridge (Mass.), 1970, ed. S.P. Keller, J.C. Hensel and F. Stern (US Atomic Energy Commission) p. 784. [15] S. Maruno, J. Chem. Soc. Jap. 71 (1968) 670. [16] A.L. Renninger and B.L. Averbach, Phys. Rev. 8B (1973) 1507. [~71 S.C. Rowland, S. Narasimhan and A. Bienenstock, J. Appl. Phys. 43 (1972) 2741. llal H. Krebs and R. Steffen, Z. anorg, allg. Chemie 327 (1964) 224. [191 D.E. Polk, J. Non-Crystalline Solids 5 (1971) 365. [201 N. Morimo!o, Mineral. J. (Sapporo) 1 (1954) 160. [211 T. lto, N. Morimoto and R. Sadanaga, Acta Cryst. 5 (1952) 775. [22] H.J. Whitefield, J. Chem. Soc. Amer. 10 (1970) 1800. [231 J. Zdenek, C. Laforet, P. Picot and J. F6raud, Bull. Soc. Fr. Mineral. Cristallogr. 96 (1973) 131. [24] M. Tanaka and T. Minami, Jap. J. Appl. Phys. 4 (1965) 939. [25] T. Minami, M. Hattori and M. Tanaka, Yogyo-Kyokai-Shi 78 (1970) 101. [26] E.V. Shkol'nikov and Z.U. Borisova, Vestnik Leningrad. Univ., Seriya Fiz. i Khim., no. 4, 1966, p. 120. [27] G.N. Greaves, J.C. Knights and E.A. Davis, Proc. 5th Conf. on Amorphous Liquid Semicond., Garmisch-Partenkirchen, 1973, ed. J. Stuke and W. Brenig (Taylor and Francis, London, i974) 369.