Atomic arrangement in the glassy semiconductor Ge30As20Se50

i

Mat. Res. Bull., Vol. 21, pp. 1167-1174, 1986. Printed in the USA. 0025-5408/86 $3.00 + .00 C o p y r i g h t (e) 1986 Pergamon Journals Ltd.

ATOMIC ARRANGEMENT

IN THE GLASSY SEMICONDUCTOR

Ge3oAS2oSe50

N. de la Rosa Fox, L. Esquivias and R. Jim@nez-Garay Departamento de Fisica Fundamental. Facultad de Ciencias Apartado 40. Puerto Real. C~diz. Spain

(Received June 25, 1986; Communicated by J. M. Garcla-Rmz)

ABSTRACT Two

tridimensional

models

of Ge30 AS2oSe50

amorphous alloy have been

built by theoretical simulation of the experimental Radial Distribution Function (RDF) calculated from the X-ray diffraction data of a powder sample of the studied alloy. The models are discussed from topological and geometric point of view and an analysis of the main structural parameters is carried out in order to proposed a real average structure of the material. Both models fit the experimental RDF and abide by the geometrical conditions. But a model formed by clusters of tetrahedra with some overlapping linked to each other by As and Se chains has been considered more probable from topological considerations. This model has a better agreement with the shortrange order supposed from the RDF preliminary analysis, glass transition temperature and electronic structure. MATERIALS INDEX: glassy semiconductor,

atomic structure~

Ge3oAS2oSe50

INTRODUCTION

The main technological interest of the chalcogenide glasses is due to the semiconductor behavior of this kind of materials. The electrical switching and memory effects (i) as well as the photostructural changes and optical memory (2) are some of its differential properties. A structural study could further knowledge of their physical properties. This paper is a continuation of the line undertaken in an earlier work (3). There are two reasons why this study particularly attracts our attention: firstly, the glass forming tendency (which is the inverse of the minimal quenching rate to avoid crystallization) depends strongly on the average coordination number since it imposes important topological restrictions (4). It is well know that among dozens of crystalline compounds IV-VI and V-VI. Be combines only with Ge or As with coordination numbers which satisfy

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the 8-N rule(5).Moreover, experimental results (6) show that the average coordination number of the present alloy is greater than those theoretically calculated as an average of the standard values of the elements, i.e. 4, 3 and 2 for the Ge, As and Se respectively. A priori, a coordination number increase can be expected and it would be interesting to determine the behavior of every element in this sense. Secondly, defect give rise to dangling bond states in the gap (i.e. localized), the correlation energies of which are positive in four-fold coordinated atoms and negative in two-fold coordinated (7). If the atom is three-fold coordinated, both positive and negative correlation energy defects exist. A negative correlation energy gives rise to a pinning of the Fermi level in the midgap which makes doping of these materials difficult. EXPERIMENTAL

According to the composition desired, elements of high purity were weighed and introduced into a quartz ampoule. The ampoule was then evacuated, sealed and heated in a rotatory furnace. Afterwards, it was quenched in ice water. A standard X-ray diffraction diagram did not show any crystallinity remains. X-ray diffraction intensities were collected using a scintillation counter. Averaged values lay within 5% of the mean. Data were corrected for background, polarization and multiple scattering, were later normalized using the high-angle method (8), and the Compton scattering was subtracted. OPERATIVE

METHOD

In order to create the model, the results of the RDF(r) analysis (6) was taken into consideration. The area under first maximum is consistent with a short-range order in which the Ge, As and Se atoms have, respectively 4, 3 and 2 as the most probable coordination number with aproximately 10% of the As atoms four-fold coordinated. The spherical geometry was selected because the essential feature of the RDF(r) is that it is only an r-dependent function. A shpere of 20 ~ diameter was considered adequate to represent the macroscopic material from a statistical viewpoint. The technique is based on the Metropolis MonteCarlo method (9) with some modifications (i0) described in earlier structural work whose results justify their use (3,11). The initial model is built by laying down geometrical and topological conditions inferred from the RDF(r) analysis only. A theoretical diffraction experiment is simulated in such a way that the model is the convolution of gaussian curves in the way proposed by Renninger et al. (12). In order to compare the experimental result with the theoretical one, we have used a probability function (13) which, multiplied by the experimental RDF(r), simulates what would be obtained if a sample with the same shape and size as the model had been employed for the experiment. Under these conditions, both functions have been compared. The mean standard deviation serves as criterion to decide the model's validity, ~2 being defined as: ~2 = 1/N ! IRDFmod(ri)-RDFexp(ri) 2 l N being the number of points where comparison is accomplished. The refinement process consist, essentially, in moving an atom, randomly designed, in an aleatory direction. If the new position keeps the geometrical and coordination conditions and improves the fitting of the calculated RDF(mod) with respect to the experimental one, it is accepted and the process starts again.

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Ge30As20Se50

1169

Models were built k e e p i n g in mind the results of the former work (3) where we show that the Ge-As and Ge-Ge bonds must be present in the alloy. To maintain this hypothesis, any movement involving breaking of Ge-X bonds was prohibited. MODELS DESCRIPTION

AND RESULTS

A first model built under the condition that all the Ge atoms be four-fold coordinated, evolved from an initial standard deviation of 2.3103 to a final value of 0.0546 having accomplished a total of 669 valid movements and using 22908 aleatory numbers. This model may be described as a very distorted tetrahedranetwork, specially near the boundary of the sphere due to the p r o t e c t i o n of the Ge-X bonds. A second model was g e n e r a t e d taking into account that the atoms in the sphere's periphery may be considered bonded with hypothetical external neighbors, provided that they are found at a minimal first neighbor distance from the boundary, d e t e r m i n e d by the lower limit of the RDF(r) first peak at r=2.10 ~. In this way 22 positions were chosen with highest coordination (four), embedded in a sphere of 7.90 ~ radius and 22 positions with smaller c o o r d i n a t i o n in the r e m a i n i n g annulus for Ge atoms. The same rule was used for the Se atoms with positions of c o o r d i n a t i o n ~ 2 . The As atoms were randomly designed. For the model refinement, similar restrictions to the formed model were imposed. After 879 valid movements, the standard deviation went down from 2.2807 to 0.0511, for which 26430 aleatory numbers were necessary. After refinement of thermal vibration parameters, the standard deviation became 0.0333 and 0.0320 for both p e r f o r m e d models, respectively. The geometrical fitting of the RDF's curves are shown in FIG. i. As can be seen, both are s a t i s f a c t o r y enough to be considered representative of the real average structure. Nevertheless, from topological considerations, the second one may be considered more probable than the first. Effectively, the imposed restrictions in the sphere's periphery give rise to a greater relaxation of the atomic positions. This constrained situation, would allow further tridimensional development without involving continuity problems, whereas in the first mode], the tetrahedra distortion in the sphere's periphery, would cause discontinuities in its tridimensional development.

FIG. 2 and overlapping first model

The tetrahedra situations of the models are schematized in 3. As can be expected of the high Ge percentage, they are fitted one into another. Furthermore, several atomic chains, unlike the appear in the second one as independent structural units.

COORDINATION TABLE I collects the resulting coordination distributions of atoms in both models. The first value being that of the "packed" model and the second one that of the "relaxed" model. If we consider that the 8-N rule must be fulfilled, the models present a total of 46 and 77 dangling bonds in the packed and relaxed models, respectively, that to a large extent belong to atoms which are at the sphere's periphery and which could be therofore satisfied by atoms outside the sphere. However, there is 14.3% and 17.1% for the packed and relaxed model, respectively, which are not in an appropiate situation to be satisfied with external neighbors. But a number of dangling bonds may always be expected in these glasses as a consequence of the way they are prepared.

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Vol.

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I0

8.C 5.63.2O.,E--

~'- - 1 . 6 t~

-~" -4.0

-

O. --1 •

,

-4.0

2

I 4

I

FIGURE Reduced

I 6

l

I , 8 r(~,)

10

1

experimental RDF's (solid line) and those of the model (dashed line) for the p e r f o r m e d models

TABLE Coordination

distribution

I

of the atoms

Type of atom

4

3

Coordination 2

Ge

43-22

1-13

As

1-2

5-14

Se

2-0

36-44

11-0

in both models

1

0

0-9

0-0

0-0

14-11

9-2

0-0

21-27

4-3

In TABLE II the p e r c e n t a g e of dangling bonds per type of atom on the total are give. Although the p a c k e d model has less coordination defects, this is to be expected due to the maintenance of four-fola c o o r d i n a t i o n of all the Ge atoms during the whole r e f i n e m e n t process. On the other and, the results in TABLE I seem to show a better agreement with the average coordinations already seen in the RDF(r) p r e l i m i n a r y analysis (6), indicating the increase of the average As atoms coordination which agrees with the Grigorivici results (14). Another characteristic of the packed model is the appearance of a certain number of o v e r c o o r d i n a t e d Se atoms. On principle, all of them may be a t t r i b u t e d to the existence of valence alternation pair (VAP) (15) but this it is not possible s i n c e the density of these o v e r c o o r d i n a t e d atoms in the model is two orders of magnitud greater than its c o r r e s p o n d i n g standard value.

Ge30As20Se50

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×

A(

S kj~e FIGURE 2 Spatial representation of the framework of continous tetrahedra and chains for the packed-model TABLE II Percentage of dangling bonds per type of atom Type of atom

dangling bonds (%) packed relaxed

Ge

2.2

40.2

As

67.4

16.9

Se

30.4

42.9

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N. DE LA ROSA FOX, et al.

Vol. 21, No. 10

%

@As ©Se FIGURE

3

Spatial r e p r e s e n t a t i o n of the framework of tetrahedra clusters and independent chains (black bonds) for the relaxed model

BONDING

DISTANCES

the models

for

The average bonding distance are shown in TABLE III.

(ABD)

of

different

bonds

present

in

The Ge-Ge ABD in both models is very near to the 2.44 ~ obtained bond in Continous Random Network (CRN) models on G e x S e l _ x amorphous

this

alloy. The in bond

AND ANGLES

mean

models

value but

of Ge-As

near

to

the

ABD sum

in GeAs 2

crystalline

of covalent

radii

is 2.45 ~, being (SCR).

The values

lower of the

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Ge30As20Se50

1173

Ge-Se ABD in both models are similar to the mean value of the three s t a n d a r d distances in TABLE III. The As-As ABD are not r e p r e s e n t a t i v e , due to the small number of these bonds in the models. For the As-Se bond we found an ABD similar to the 2.36 ~ of BCR. Finnaly, the mean value of the two standard distances of Se-Se bond c o i n c i d e s with the ABD in the models. The second model shows atomic chains as i n d e p e n d e n t structural units with a majority of Se atoms. These chains have been c o n s i d e r e d as a separate phase, and their Se-Se ABD was 2.39 ~ more near to the 2.40 ~ in Se amorphous phase.

TABLE

III

A v e r a g e d b o n d i n g distances of d i f f e r e n t p r e s e n t in both models

Bond

packed

relaxed

SCR*

standard

bonds

distances

(A)

Ref.

Ge-Ge

2.46±0.14

2.45±0.13

2.44

2.54 a-Ge 2.45 c-Ge 2.44 C R N - G e x S e I _ x

14 14 16

Ge-As

2.43±0.17

2.40±0.08

2.42

2.45 GeAs 2 crystalline

17

Ge-Se

2.46±0.16

2.42±0.10

2.38

2.37 hexagonal GeSe 2 2 59 o r t h o r h o m b i c GeSe 2 2.38 C R N - G e x B e I _ x

18 19 16

As-As

2.32±0.01

2.35+0.16

2.40

2.49 a-As 2.51 rhombohedral

20 21

As-Se

2.38~0.09

2.38±0.09

2.36

Se-Se

2.37±0.10

2.38+0.06

2.32

As

2.41

average in As2Se 3 crystalline 2.40 a-Se 2.34 C R N - G e x S e I _ x

22 23 16

A v e r a g e d b o n d i n g angles are 1080 and 1120 respectively, for both models. Both are in a g r e e m e n t with the h y p o t h e s i s of packing and relaxing respectively. They are a c c e p t a b l e since the first d i s t o r t i o n that one may expect in an amorphous material is in the b o n d i n g angles.

CONCLUSIONS Both models are valid from a formal v i e w p o i n t and described the real average s t r u c t u r e of the m a c r o s c o p i c material. It may be c o n s i d e r e d as a clusters d i s t r i b u t i o n of distorted tetrahedra, some of them overlapping, centered on Ge atoms, the clusters being linked to each other by Se and As chains. The most important d i f f e r e n c e between the availables models lies in the way the initial model has been generated. The former one, which we called "packed", has all the bonds of the Ge atoms satisfied. In the second one, s o - c a l l e d "relaxed", only those Ge atoms s i t u a t e d at a distance greater then 2.10 A (minimal first n e i g h b o r distance) from the sphere's p e r i p h e r y have all their bonds satisfied, s u p p o s i n g that the rest may be linked with hypothetical external neighbors. The

geometrical

parameters,

such

as

the

averaged

b o n d i n g distances

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N. DE LA ROSA F O X , e t 8/.

Vol. 21, No. I0

and angles, do not present remarkables differences. The bonding distances are a little shorter than those of the G e 2 o A S 4 o S e 4 0 (3) which may be related to the greater stability of the present alloy indicated temperature (305°C and 341°C, respectively (24)).

by a glass

transition

The way as they reproduce the first sharp diffraction peak (FSDP), related to the medium-range order, was checked in an earlier paper (25). The attempt was unsuccessful and no difference was found. Nevertheless, the fitting of the theoretical interference functions, corresponding to the models, with regard to the experimental one was better in the relaxed model. Finnaly, we conclude that although both models fit the experimental RDF and abide by the geometrical conditions, the so-called relaxed model better reflects the topological conditions supposed for this alloy from the previous RDF analysis, glass transition temperature and electronic structure. ACKNOWLEDGEMENT

We thank M. Gavin West for his help in the completion of the paper. REFERENCES 1.

2. 3. 4.

5. 6. 7. 8.

9. i0. ii. 12. 13 14 15 16 17 18 19 20 21 22 23 24 25.

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