Self-diffusion in the chalcogenide glass system SeGeAs

Journal of Non-Crystalline Solids 30 (1978) 211-220 © North-HoUand Publishing Company

SELF-DIFFUSION IN THE CHALCOGENIDE GLASS SYSTEM S e - G e - A s U. EICHHORN * and G.H. FRISCHAT Arbeitsgruppe Glas, Lehrstuhl fiir Glas und Keramik, Technisehe Universitat Clausthal, Germany

Received 10 April 1978

Se, As and Ge self-diffusion were investigated in three different glasses of the chalcogenide system Se-Ge-As by means of the radioactive tracers 7SSe, 73As and 71Ge. AI1D values (Se between 200 and 290°C, As between 240 and 290°C and Ge between 280 and 295°C) lay between 10-14 and 5 X 10-16 cm2 s-1. The diffusion profiles were analyzed using a chemical micro-etching technique. Roles of glass structure and possible diffusion mechanism are discussed.

1. Introduction There are many papers on diffusion in oxide glasses, see e.g. the reviews in [1,2]. Diffusion in non-oxide glasses has been investigated by some authors only [ 3 - 1 3 ] . Most of these papers deal with heterodiffusion, self-diffusion has been studied only for Cd and As in glassy CdGeAs2 [6,7] and for Ag in glasses o f the systems A s 2 S a Ag2 S, GeS2 - G e S - A g 2 S and P2 Ss - A g 2 S [ 12]. Self-diffusion processes can be studied by using radioactive or stable isotopes. In most cases the application o f a radioactive isotope combined with a sectioning method and a standard counting technique is much easier than the use of stable isotopes in conjunction with a mass spectrometric or a neutron activation technique for analysis of the diffusion profiles. The problem in investigating self-diffusion in oxide glasses arises from the fact that Si and O, the most important network forming constituents o f oxide glasses, do not have suitable radioactive isotopes. Thus, data on self-diffusion of network modifying ions, i.e. Na an Ca, are available, whereas data on self-diffusion o f network forming ions, i.e. Si and O, are scarce so far. Moreover, scattering in available data is great. In the field of non-oxide glasses it is much easier to choose glass forming systems with constituents having suitable radioactive isotopes. One important system is the chalcogenide system S e - G e - A s , which has a broad glass forming area in the Se-rich c o m e r [14,15]. Compared with oxide glasses Se has a bridging * Now associated with Jenaer Glaswerk Schott and Gen., Mainz, Germany. 211

212

U. Eichhorn, G.H. Frischat / Self~liffusion in the chalcogenide glass system

Table 1 Compositions and some physical data of the investigated glasses of the system Se-Ge-As. No.

Composition in at.-%

p in g cm-3

Tg in °C a)

8 15 26

50 Se 20 Ge 30 As 40 Se 40 Ge 20 As 25 Se 30 Ge 45 As

4.441 4.531 4.672

284 385 391

a) Measured by DTA. function in the glass network similar to O, Ge may behave like Si and As like P. It is the aim of this paper to investigate the self-diffusion of all constituents of this glass system and to add information on the dynamic structure of these glasses.

2. Investigated glasses The glass forming area of the chalcogenide system S e - G e - A s was investigated i.e. by [14,15]. Different compositions of this system were prepared using a rotating sealed-off SiO2 glass ampoule and melting temperatures up to 1050°C. Glass samples * of about 70 g could be obtained in this way. Composition of the glasses was checked by X-ray fluorescence and homogeneity by electron microprobe analysis. Table 1 contains the glasses on which self-diffusion was investigated. Several physical properties of these glasses are also listed in table 1. The annealed glasses were then prepared as planparallel slices of 15 × 15 mm 2 surface areas and with a thickness of 3 mm. The surfaces were ground and polished carefully. For further details concerning glass preparation and handling see ref. [ 16].

3. Tracer experiments The following radioactive isotopes were used for the investigations **: 7SSe

(ru2 = 120.4 d), 71Ge (rl/2 = 11.4 d) and 7aAs (rl/2 = 80.3 d). All isotopes emit characteristic X-ray spectra due to decay with orbital electron capture. One drop of an aqueous solution of the radioactive isotope (total amounts: about 10-7 g in the case of 7SSe, 10-6 g in the case of 71Ge and 10-s g in the case of 73As) was put on the surface of the glass specimen ***. This was covered with an identical disc to prevent loss of active material (sandwich specimen) and heated in a furnace in dry and purified N2 atmosphere. After heat treatment about 1 mm of the material was ground away from the edges and outer surfaces of the specimens to avoid the influ* The raw materials Se, Ge and As were of 5N quality. Supplier of the isotopes: Amersham Buchler, Braunschweig, Germany. *** The radioisotopes were supplied as Na27 s SeO3 in aqueous solution, H373ASO4 in 0.04 m HC1 solution, and Na271 GeO3 in 1.4 m NaOH solution. * *

U. Eichhorn, G.H. Frischat / Self~liffusion in the chalcogenide glass system

213

ence of any surface diffusion process. The specimens were carefully cleaned and sectioned by etching off thin layers parallel to the surface, see next section. The residual activity [17] of the sample after each layer had been ground away was measured with a scintillation counter, using a discriminator for the corresponding emission peaks of the spectra, the specimen being placed in a lead chamber to reduce background. 4. Sectioning method Fig. 1 shows an example of 7SSe diffusion in glass 8 at 216°C. Despite of an annealing time of 12 weeks total penetration depth of the isotopes did not exceed

"7 E

o

(,3

lO3

\

o o

O-tS crr~ls

102755e Glass 8 T=260 °C, t=2016h

10t Penetration depth x Ipm

Fig. 1. Residual activity following diffusion of 7s Se in glass 8 (Ses oGe2 o As3o), T = 260°C, t = 2016 h. The solid line was drawn according to eq. (2) with D = 2.51 X 10 -1 s cm2/s.

214

u. Eichhorn, G.H. Frischat / Self-diffusion in the chalcogenide glass system

about 6/am at that temperature. Similar small diffusion depths were also obtained for 71Ge and 73As. Early attempts to measure these profiles using a mechanical microgrinding technique failed. Therefore, a special chemical microetching technique had to be developed [18]. CP4 solution [19] * was used as an etchant, the limit of this method was reached, when thickness of the etched layer and surface roughness caused by etching (inspected by optical interferometry and scanning electron microscopy) were comparable. This surface roughness was always between 0.2 and 0.3 /am, thus accurate analysis of profiles with diffusion depths of~>2 to 3/am was possible, for further details see ref. [18]. The lowest limit of diffusion coefficient was thus around 5 × 10-16 cm2/s.

5. Method of evaluation

For diffusion processes like those shown in fig. 1, Fick's second diffusion law holds. With the initial and boundary conditions of an instantaneous source (tracer film thicknesses were <0.1/am [ 18]) one obtains the following concentration distribution in the glass [20] c(x, t) -

Co e x p ( _ x 2 /4Ot) (nDt) l/2

(1)

where c is the concentration of the tracer, t is the diffusion time, D is the diffusion coefficient, x is the penetration depths normal to the surface, and Co is the initial concentration of the tracer at the surface at t = 0. Residual activity measured after etching away a thickness, x, of sample may be written as [ 17] I(x, t) = Io erfc(x/2(Dt)a/2) ,

(2)

where Io is the initial activity. Evaluation of D for a special experiment was possible by solving eq. (2) numerically by computer.

6. Diffusion results

7SSe diffusion was investigated between 200 and 290°C, 7aAs diffusion between 240 and 290°C and 71Ge diffusion between 280 and 295°C. Fig. 2 shows a typical Arrhenious plot of 7SSe diffusion in glass 8 (SesoGe2oAs3o) and table 2 contains all Do and Q values obtained for 7SSeand 73Asdiffusion. Since penetration depths of 71Ge were too small, no temperature dependence could be obtained. Some of the DGe values measured between 280 and 295°C are listed in table 3. Fig. 3 contains a

* Chemical Polishing Etchant 4 (45.45 vol.-% HNO3, 27.27% CH3 COOH, 27.27% HF (48%) 0.5% Br).

U. Eichhorn, G.H. Frischat / Self-diffusion in the chalcogenide glass system -

10-I~

T

215

I°C

280

260

2~ 0

220

L

I

I

,

2~0

? 5

C3

3

10-15

6

6

75Se, Glass 8

1046

I

7,8

T

7,9

2,0 •, 1031TIff -!

I

2,1

Fig. 2. Temperature dependence o f 7s Se diffusion in glass 8 (SesoGe20As3o) according to D = D O e x p ( - Q / R T ) , D O = frequency factor, Q = activation energy. The figures at the error bars represent the n u m b e r of m e a s u r e m e n t s done at special temperature.

Table 2 D o and Q values o f 7s Se and 73As diffusion in different glasses of the system S e - G e - A s Glass No.

Isotope

D o in cm 2 s -1

Q in kJ mole -1

8 15 26 8 15 26

75Se 75Se 75Se 73As 73As 73As

(1.8 (1.6 (2.0 (1.5 (2.3 (1.6

69.7 71.0 72.2 83.6 86.1 72.7

± ± ± ± ± ±

0.5) 0.9) 0.4) 0.2) 0.2) 0.5)

X X X X X X

10 - s 10-8 10 -a 10 -a 10 -8 10 -8

± 1.3 ± 2.1 +- 1.3 +- 0.5 +- 0.5 ± 2.1

216

U. Eichhom, G.H. Frischat / Self~liffusion in the chalcogenide glass system

Table 3 Some diffusion data of 7z Ge obtained for glasses 15 and 26 Glass No.

T in °C

D in cm 2 s-1

15 15 15 26 26 26 26

280 290 295 280 285 290 295

4.9 6.6 8.0 7.2 8.7 1.1 1.5

X 10 -z6 X 10 -z6 X 10 -z6 × 10-16 X 10 -16 x 10 - I s X 10 -zs

TI °C

4

10 -14 ,

280

260

I

240

I

200 L

I

E tj

l 1045755e

Gloss15 Gloss26

10-161

1:8

1'~

2:0

2'.I

• tO31TIK-I

Fig. 3. Comparison of 7 s Se diffusion in glasses 8 (Se s oGe 2 oAsa o), 15 (Se4 oGe4oAs2 o) and 26 (Se2 s Gea oAs4 5).

U. Eichhorn, G.H. Frischat / Self-diffusion in the chalcogenide glass system .

280

1o -I,~

[

260

T I °C

21.0

l

217

220

[

i

200 i

I0 -T&

o

10-I6

Glass 15

718

755e

2:0

,b D

2:7

1031T/K -l

Fig. 4. Comparison o f 7 5 Se, 71 Ge and 7 3 As diffusion in glass 15 (Se 4 o Ge 4 0 As2 0).

comparison of 7SSe diffusion data in glasses 8, 15 and 26 and fig. 4 shows a comparison of 7s Se, 73As and 7 i Ge diffusion data in glass 15. All D values are below 10-14 cm2/s. Despite of the chemical microetching technique D G e values are obtainable at higher temperatures only. Difficulties arose also from the relatively short half-life of 7~Ge of 11.4 d compared to the much longer diffusion anneal times. To use 6aGe would be preferable (71/2 = 275 d), however, this isotope is not yet commercially available. Accurate diffusion coefficients could be obtained by the chemical etching technique only, if the total penetration depths of tracer were at least 2/am. In the case of Ge self-diffusion this was a restrictive condition. Therefore, an ion-etching technique of higher resolution would be preferable here. However, such techniques still involve many difficulties [21]. 7. Discussion The three glasses investigated here are quite different with respect to their location in the glass forming area. Whereas glass 8 (SesoGe2oAs3o) is situated in the cen-

218

U. Eichhorn, G.H. Frischat / Self-diffusion in the chalcogenide glass system

s_o\ AI~

2

~. / - - \ As

I

/Aa

3 JAs

,, i',,,

\//

" IAs.',

\'~-s ....... As

1

....

'. \ / i Ge

Ue--

, i

_bg__x_s,o_ / I I\

/

I

4

5 ~s~

-~

\;'1--\~/.. .be

I/

\1 --be

/.

.......

--~

be

6

7

',\

71',

..... -#I /

....

/

X

~

/

!

--

/

:/ :/ ,~ei--,~el

Fig. 5. Possible structural units in glasses of the system Se-Ge-As [22]. 1: SeSe2/2, 2: AsAs3/3, 3: GeGe4/4, 4: AsSe3/2, 5: GeSe4/2, 6: As2Se4/2, 7: GeSe2/2,

ter, glasses 15 (Se4oGegoAs2o) and 26 (Se~sGe30As4s) are near the borders of the glass forming region. According to Myuller's structure chemical principles [22] glasses of the system S e - G e - A s may contain different short-range oder groupings, see fig. 5. Depending on actual overall composition the relative portions of these different units may vary. Pernot [23] gave relations for their approximate calculation. According to these glass 8 can be approximately characterised by 50 GeSe4/2 • 20 AsSe3/2 • 30 AsAs3/3, glass 15 by 50 GeSe4/2 • 25 GeGe4/4 • 25 AsAs3/3 and glass 26 by 30 GeSe4/2 • 20 GeGe4/4 • 50 AsAs3/2 *. Despite of these possible differences in short-range structure of the glasses self-diffusion coefficients of the components are not very different, see the comparison for Dse in fig. 3. There is especially no indication of a non-linear dependence of self-diffusion coefficients on composition as has been found for other physical properties, e.g. elastic moduli [24]. However, data on more glasses are needed to clarify this compositional influence. On the other hand the results display Dse > D n s > D G e , see fig. 4. If one considers that bonds in these glasses are highly covalent, this is in line with the fact that the covalent radii increase in the order rse < rAs < rGe. Inspection of the experi* For the case that GeSe2/2 units are formed instead of GeSe4/2, structure chemical compositions of glasses 15 and 26 axe 80 GeSe2/2 • 20 AsAs3/3 and 50 GeSe2/2 • 5 GeGe4/4 - 45 AsAs3/3, respectively.

U. Eichhorn, G.H. Frischat / Self-diffusion in the chalcogenide glass system

219

Table 4 Entropy factors (AS/R), calculated according to eq. (3)

(AS/R), glass 8 (AS/R), glass 15 (AS]R), glass 26

7SSe

73As

-9.6 -10.0 -9.9

-7.5 -7.3 -10.2

mentally obtained data demonstrates both unusually low frequency factors Do (between about 10-7 and 10- a c m 2 s-l) and activation energies Q (between about 70 and 85 kJ mole-l), see table 2. Comparison with other self-diffusion data on glasses shows similarities with oxygen self-diffusion in lead borate and lead borosilicate glasses only [25]. The conclusion there was that O diffuses as an atom rather than as an ion and an estimation of the energy of migration displayed that its value coincided with the experimentally determined activation energy, thus the energy of defect formation was considered to be negligible. Perhaps similar conditions could hold for the diffusion of the constituents investigated here. All of them are thought to diffuse as atoms and their function in non-oxide glass structure is considered similar as that of the bridging element oxygen in oxide glasses. Further information on mechanism may be obtained from application of Zener's theory [26]. According to this

Do = 7fva 2 exp(AS/R) ,

(3)

where 3' is a structural parameter, f is the correlation factor, v is the vibrational frequency of the diffusing particle, a is the jumping distance and (AS/R) is the diffusion entropy factor. Do is known from experiment. Estimating appropriate values for the other parameters (3' = 1/6 for a four-point m o d e l , f = 1 *), v = (2.9 - 4.3) × 1012 s -1 ** and a ~ 2.4 A [27], this calculation leads to the (AS/R) values listed in table 4. As may be seen all (AS/R) values are negative, similar to what has been found for O diffusion in the above mentioned oxide glasses [25]. According to experience with data for self-diffusion in crystalline materials this negative diffusion entropy factors could suggest an interstitial mechanism in these glasses. However, quite a different approach cannot be excluded, since the discussion of possible diffusion mechanisms in non-crystalline matter is still in the beginning, see also [28]. Acknowledgement The financial support of the Deutsche Forschungsgemeinschafl (DFG), BonnBad Godesberg, is gratefully acknowledged. * Nothing is known so far about correlation effects of diffusion in non-oxide glasses. ** Calculated from Debye temperatures 0 D [24].

220

U. Eichhorn, G.H. Frischat / Self-diffusion in the chalcogenide glass system

References [1] G.H. Frischat, Ionic Diffusion in Oxide Glasses, (Trans Tech. Publ., Aedermannsdorf/ Switzerland, 1975). [2] R. Terai and R. Hayami, J. Non-Crystalline Solids 18 (1975) 217. [3] F.F. Kharakorin and V.V. Aksenov, Soy. Phys. Semicond. 1 (1967) 805. [4] K.A. Arseni, B.I. Boltaks and T.D. Dzhafarov, Phys. Star. Sol. 35 (1969) 1053. [5] S. Murano, T. Yamada, M. Noda and Y. Kondo, Japan J. Appl. Phys. 10 (1971) 653. [6] V.V. Aksenov and F.F. Kharakhorin, Sov. Phys. Semicond. 7 (1974) 1231. [7] F.F. Kharakhorin and V.V. Aksenov, Sov. Phys. Semicond. 7 (1974) 1233. [8] B.I. Boltaks, Z.U. Borisova et al., Phys. Stat. Sol. A 30 (1975) 731. [9] P. Siiptitz and I. Willert, Phys. Stat. Sol. A 28 (1975) 223. [10] E.A. Lebedev, P. Siiptitz and I. Willert, Phys. Star. Sol. A 28 (1975) 461. [11] V.K. Biktimirova, B.I. Boltaks et al., Soy. Phys. Semicond. 8 (1975) 1412. [12] Y. Kawamoto and M. Nishida, Phys. Chem. Glasses 18 (1977) 19. [13] P. Stiptitz, in: Proc. 1 lth Inter. Congress on Glass, Prague 1977, Vol. II, 337. [14] J.A. Savage and S. Nielson, Phys. Chem. Glasses 6 (1965) 90. [15] L.A. Baidakov, in: Sofid State Chemistry, eds. R.L. MyuUer and Z.U. Borisova (Consultants Bur., New York, 1966)p. 194. [ 16 ] U. Eichhorn, Dissertation, Technische Universit/it Clausthal (1977). [17] G.H. Frischat and H.J. Oel, Z. Angew. Phys. 20 (1966) 195. [18] G.H. Frischat and K. Remmers, in: Non-Crystalline Solids, ed. G.H. Frischat (Trans Tech. Publ., Aedermannsdorf/Switzerland 1977) p. 447. [19] A.F. Bogenschiitz, ,~tzpraxis fiir Halbleiter (Hauser, Miinchen, 1967). [20] W. Jost and K. Hauffe, Diffusion (Dr. Dietrich Steinkopff, Darmstadt, 1972) p. 28. [21] H. Bach, Radiation Effects 28 (1974) 215. [22] R.L. MyuUer, in: Solid State Chemistry, eds. R.L. Myuller and Z.U. Borisova (Consultants Bur., New York, 1966) p. 1. [23] F. Pernot, Verres Refract. 27 (1973) 45. [24] U. Tille, G.H. Frischat and K.-J. Leers, in: Non-Crystalline Solids, ed. G.H. Frischat (Trans Tech. Publ., Aedermannsdorf/Switzerland 1977) p. 631. [25] H.A. Schaeffer and H.J. Oei, Glastechn. Ber. 42 (1969) 493. [26] C. Zener, in: Imperfections in Nearly Perfect Crystals (Wiley, New York 1952) p. 289. [27] H. Krebs and H. Welte, J. Solid State Chem. 2 (1970) 182. [28] G.H. Frischat, see ref. [1 ], p. 97.