Relations between the structure of crystalline and amorphous CdGexAs2

JOURNALOF NON-CRYSTALLINESOLIDS3 (1970) 294-304 © North-Holland Publishing Co.

RELATIONS BETWEEN THE STRUCTURE AND AMORPHOUS

OF CRYSTALLINE

CdGexAs 2

L. (~ERVINKA Czechoslovak Academy of Sciences, Institute of Solid State Physics, Cukrovarnickd 10, Praha 6, Czechoslovakia and R. HOSEMANN and W. VOGEL Fritz-Haber-lnstitut der Max Planck-Gesellschaft, Faradayweg 4-6, 1 Berlin 33, Germany

Received 3 January 1970 A detailed discussion of the CdAs2 structure makes it possible to present a model of the crystalline CdAsz-type-to-chalcopyrite-typestructure transformation. Unoccupied A- and B-sites are introduced into the CdAs2 lattice. Macroscopic density measurements on the amorphous samples of the CdGezAs~ system are interpreted by a mechanism of gradual occupation of these A- and B-sites with Ge atoms. A rough interpretation of diffraction pictures taken on amorphous samples with x = 0.1 and 1.1 points to a close similarity of these amorphous samples with the CdAs2 nearest neighbours structure.

1. Introduction I t is well k n o w n t h a t s o m e t e r n a r y s e m i c o n d u c t i n g c o m p o u n d s o f the AUBIVCv type can be p r e p a r e d in the crystalline a n d a m o r p h o u s states 1). This is for instance the case with C d G e A s 2 - a c o m p o u n d which crystallizes in the chalcopyrite-like structure with lattice p a r a m e t e r s a = 5.942, c = 11.22, 12. c / a = 1.889, space g r o u p DEa , C d G e A s 2 was o b t a i n e d in the a m o r p h o u s state, too. H o w e v e r up to now no serious a t t e m p t was m a d e to study the structure o f the a m o r p h o u s phase, t h o u g h it shows interesting semiconducting p r o p e r t i e s a). A priori, it seems to be rather c o m p l i c a t e d to study the a m o r p h o u s structure o f a c o m p o u n d with three c o m p o n e n t s , having in m i n d t h a t the study o f m o r e simple a m o r p h o u s materials presents a serious p r o b l e m . In spite o f this we u n d e r t o o k this study because we h a d the possibility to study samples o f the whole C d G e x A s 2 system, a n d further we h a d the possibility to correlate results with k n o w n crystalline structures f o r m i n g the b o r d e r s o f this system, i.e. with the CdAs2 a n d C d G e A s 2 structure. 294

THE STRUCTURE OF CRYSTALLINE AND AMORPHOUS

CdGezAs~

295

2. Technology

Amorphous samples of this system were prepared by rapid cooling of a melt heated for some time to a temperature about 100°C to 200°C higher than the melting point. The obtained ingots had a diameter of about 3 m m and were up to 30 m m long. Detailed description of the preparation is given elsewhere3). The composition of these amorphous samples can be represented by the above-mentioned formula, where x varies from 0.02 to 1.2. 3. Discussion of the CdAs 2 structure

We find it useful to discuss here more profoundly the structure of CdAs 2. This structure was recently determined using powder samples, as reported in ref. 4. In figs. 1 and 2 are given the projections of this structure into the

CdAs2 a=Z96

cdO

As©

e-1,.67 x-0.48 [,~1 Asites

1

g]

F i g . 1.

~

[ol

Projection of the CdAs2 structure into the x y plane with the channels of A-sites. The numbers in brackets give the z-components of the B-sites.

and x z planes respectively. In this structure every Cd atom is surrounded by a tetrahedron of four As atoms at a distance of 2.69 A; e.g. placing the Cd atom into the origin (0, 0, 0), the four As atoms will have coordinates xy

(¼, x, 3), (x, ¼, 3), (¼, 2, 3), (2, ¼, 3), x = 0.06. The C d - A s distance is in good agreement with the reported covalent radius values s), for Cd 2.98 A, As 2.49 A, i.e. for the C d - A s distance one obtains the value 2.73 A. Cadmium and arsenic atoms are arranged spirally with a difference in the z-coordinate of ¼, but the nearest neighbour distance of the As-As spiral is 2.44 A and for the C d - C d distance 4.15 A. In this connection we like to point out that additionally to the As-As spiral there is a second character-

296

L. (~ERVINKAs R. HOSEMANN AND W. VOGEL

CelAss a=Z96

Cd 0 e-4.67

a

I~

"

•

As0

x=0.48 [,~1

-

i

j2 "

LI

"

i'

Fig. 2. Projection of the CdAs2 structure into t h e x z plane. Three systems o f CdAs4 t e t r a h e d r o n s are s h o w n ( , - - -, ...). I n every s y s t e m (CdAs)0 rings c a n be f o u n d (see later). These three systems interact with each o t h e r by m e a n s of a n ( A s - A s ) spiral, see e.g. arsenic a t o m s designed as ¼, ½ - - x , ¼, x . . . . .

OCd

( ~ Ge O A S o ~

CdAs~

,-- ~s~._, CdC-eAs 2

Fig. 3. The transformation from crystalline CdAs2 (a) to CdGeAs= (b). (a) The atoms 1, 6, 7, 8 and 9 build up one of the spirals, parallel to the c-axis.Three B-sites ( × ) with adjacent strongly deformed As4 tetrahedra are drawn. (b) The spiral 1, 6, 7, 8, 9 is broken up by the Ge atoms, which fill up the B-sites. The As4 tetrahedra turn by about ± 45° and loose their deformation, without breaking one of the tetrahedra bonds. New types of spirals (AsGeAsCd)n in all three directions arise, for instance 1, 2, 3, 4, 5.

THE STRUCTURE OF CRYSTALLINE AND AMORPHOUS

CdGexAsa

297

istic formation in this structure, i.e. (Cd-As) spirals (fig. 3a). Four of these spirals form a kind of tetrahedron with four spatially distorted planes of (Cd-As)6 rings, see figs. 4 and 5. The whole lattice is then composed from three quasi-independent sets of these (Cd-As)6 rings; the three systems of rings interact with each other only by means of As-As spirals as can be seen from figs. 2 and 3a. We shall now designate as A-sites the empty channels with coordinates (¼, ¼, z) and (¼, ¼, z) (see fig. l) and as B-sites the unoccupied positions in the middle of the Cd-Cd distance in the z-direction, which will then have the coordinates (0, 0, 0), (0, 5, ¼), (5, ½, ½) and (½, 0, ¼) (see the crosses in figs. 3a and 6b). In the same way as deformed As tetrahedra surround each Cd atom, such tetrahedra of As atoms are around the empty B-site. For example a B-site with coordinates (½, ½, ½) is surrounded with an As tetrahedron having

Cd As2

[CdAs] 6 rings

cd0

AsO

Fig. 4. The same as fig. 1, but with lines indicating the chemical bonding. 4 spirals parallel to the c-axis can be seen.

coordinates (¼, 5 - x, ~), ( 5 - x, ¼, ~), (¼, 5 + x, ~a), (5 + x, ¼, ~) (figs. 1 and 3a). The B-site-to-As distance is 2.28/~,. The important difference between these tetrahedra and those surrounding the Cd atoms, is that the former are more contracted in the z-direction. In the B-site tetrahedron the two As-As pairs are neighbours of the above-mentioned As-As spiral with a distance of 2.44 ,~,, while in the Cd-surrounding tetrahedron the As-As distance is 4.10 A with a distance ¼c in the c-direction. The As-As distance which is parallel with the x y plane is the same in both tetrahedra and is equal to 4.09 A, see fig. 6. In the same figure is also shown the difference between As tetra-

298

L. CERVINKA,R. HOSEMANNAND W. VOGEL

hedra surrounding B-sites and Cd-sites. These two kinds of tetrahedra build up the whole structure and play an important role, if Ge atoms are introduced. 4. The CdGeAs 2 structure and the crystalline CdAs2-to-CdGeAs2 transformation The CdGeAs 2 structure 2) is shown in figs. 3b, 7 and 8. It can be described in such a way that As atoms form a little deformed face-centered cubic lattice and Ge and Cd atoms together form another deformed face-centered cubic lattice shifted from the arsenic one by (¼, ¼, ~). Comparing figs. 3a and 3b we

CdAss [CdAs]6rings

Cd0 As0

[

'

~

Y

i I i

I

Y

~-~'~

1 I

! Fig. 5.

A perspective representation o f fig. 4, illustrating that the four spirals build up

4 nonplanar (CdAs)o rings.

see that the C d - G e structure of CdGeAs2 is absolutely the same as the Cd-B-site structure, if it is affine deformed. The As4 tetrahedra, on the other hand, during the transition from CdAs2 to CdGeAs2 turn along the c-axis by a b o u t + 4 5 ° and - 4 5 ° vice versa without cracking any of the B-tetrahedra bonds. In fig. 3b, for instance, the arrow at the Ge atom 4 points to the left, the arrow of the adjacent Ge atom at the left points to the right, indicating the rotation of the two tetrahedra into the position of fig. 3a. On the basis of the preceding discussion of the CdAs2 structure, namely using B-site and Cd-site bricks, we can present now the model of the CdAs2-

THE STRUCTURE OF CRYSTALLINE A N D AMORPHOUS

CdGexAs2

299

Cd,4s 2 - B R I C K STRUCTURE

As 0

Q

x

Q

'/a b Fig. 6. (a) Projection of B- and Cd-site bricks into the xy plane. There are two orientations of these bricks. A-site "holes" are clearly visible. (b) A projection of B- and Cd-site bricks into the (110)-plane. CdGeAs 2

a=Sq4

c=1122 x=159

[~I

t~ i-

Fig. 7.

-t

Projection of CdGeAs2 structure into the x y plane.

300

L. ~ E R V I N K A , R. H O S E M A N N A N D W . V O G E L

to-chalcopyrite transformation. A gradual occupation of B-sites by Ge atoms is accompanied with a corresponding removal of the B-site tetrahedra deformation. Introducing then the correct dimensions of the Cd and B-site bricks which correspond to the new CdGeAs2 lattice parameters, we arrive directly to this structure, see figs. 3, 7 and 8.

CclGeAse a=5.94

Cd0

GeQ AsQ

c=17.22 x=1.69

[,~I

x I-

tl

I

Fig. 8. Projection of the CdGeAs~ structure into the

xz plane

5. The measurement of the macroscopic density The measurement of the macroscopic density is presented in fig. 9. Starting with amorphous samples with x = 0 the density increases. This can be explained in such a way that Ge atoms occupy at the beginning only the Asites. This process, having no remarkable influence on an enlargement of the lattice, introduces local lattice distortions. Coming to an x-value of approx. 0.2 we arrive just to a limiting value of distortions above which the Ge atoms begin to occupy the B-sites, too. This process leads to an enlargement of the lattice in the c-direction, as illustrated by figs. 3a and 3b. As it was observed (see fig. 9), the density is nearly constant in the range of xvalues from the value 0.2 to 0.6. This nearly constant course can then be explained by a mutual compensation of the two, above already mentioned, processes, namely the A- and B-site occupation. In the range of densities

THE STRUCTURE OF CRYSTALLINE AND AMORPHOUS

CdGezAsz

301

between 0.6 and 0.7 a step-like decrease in the density value is observed. The reason of this j u m p has not been quite clear until now. One explanation may be given in the following way: We can suppose that from a given value ( x = 0 . 6 ) the tendency decreases rapidly that Ge atoms occupy the A-sites. Since the amount x = 0 . 6 of occupied B-places produces large enough lattice distortions, now within a certain range of x-values the occupation of B-sites is preferred. This process evokes then just the observed j u m p of the density to smaller values. To explain the difference between the densities of the amorphous and crystalline states for x = 1, we must suppose that in this case all Ge atoms are built into the B-sites. To test the reliability of the A-site occupation process, we calculated the density under the assumption that 5% of Ge atoms are embedded into the lattice without enlarging it. Results are presented in table I. This increase is approx. 1% and is in agreement with the measurement. I

S [g/cma2

I

I

I

I

I

I

CclGexAs 2

6.00 Qo.O"-'----O.______._._O 5.80 E

5.60 5.40

0 amorphous

t

I-1 crystatline

5. 20 5,00

I

I

I

0

02

0.4

I 06

I I I I 0.8 1,0 "1.2 composition x

Fig. 9. Macroscopic density in the CdGezAsz systems as a function of the germanium content x. Density was measured with the hydrostatic method using xylene as the liquid. Accuracy of measurement is ± 0.02 g/cma.

6. Study of the radial electron density distribution To obtain a first and rough estimate of possible differences in amorphous structures of the system CdGe~As2, two cases with the greatest difference possible in the x-value, i.e. x = 0 . 1 and x = l . 1 , were chosen. The results are presented in fig. 10 and tables 2 and 3. F r o m these results the following conclusions can be drawn: The position of the first maximum can be in both

302

L. (~ERVINKA, R. HOSEMANN AND W. VOGEL

TABLE 1 Comparison of the measured and calculated density for several samples of the CdGexAs~ system Density Measured Smeas Differ. (g/cm a) (%)

Sample

CdAs~ crystalline

Calculated Differ. (g/cm a) (~o) Seale

5.86

5.88 0.5

CdGeo.osAs~ amorphous

5.89

CdAs2 crystalline

5.86

1.5 5.97 5.88

5.0 CdGeAs~ crystalline

5.58

CdGeAs2 crystalline

5.58

4.8 5.61

2.5 CdGeAs2 amorphous

5.72

TABLE 2 Interpretation of the position of the first maximum Composition

Pairs

d (A)

(N/V) × 100

GeAs, CdAs

2.41

4.1

GeAs, CdAs

2.65

4.1

AsAs

2.44

2.0

CdAs

2.69

4.1

do (~)

RI (/~) x : 0.1 x = 1.l

2.53

CdGeAs2

2.64

2.62

2.61

CdAsz

N = number of distances inside the elementary cell; V = volume of the elementary cell, see table 4; d = first and second smallest atomic distance in the structure; do = value of weighted medium, calculated from the first and second atomic distance; R~ -- position of the first maximum in the electron density distribution curve.

cases e x p l a i n e d o n l y o n t h e basis o f t h e C d A s 2 n e a r e s t n e i g h b o u r s t r u c t u r e (see tables 2 a n d 4), i.e. o n t h e existence o f C d A s 4 t e t r a h e d r a (distance C d A s = 2.69 A ) a n d A s - A s - s p i r a l s (distance A s - A s = 2.44 ,~). T h e t e n d e n c y o f t h e c o o r d i n a t i o n n u m b e r t o increase w i t h i n c r e a s i n g x - v a l u e is u n d e r s t a n d a b l e so t h a t the b u i l d i n g - i n o f G e a t o m s i n t o t h e v a c a n t A - a n d B-sites,

THE STRUCTURE OF CRYSTALLINE AND AMORPHOUS

CdGezAsa

303

TABLE 3

Differences in radial density distribution curves in the system CdGezAs~ Composition x Coordination number RI (A) Rn (~) R = R I I - - RI (A) Halfwidth of the 1st maximum (A)

0

I

l

I

I

I

0.7

1.4.

2.1

28

3.5

0.1 4.7 2.64 3.99 1.35 0.45 I

1.1 5.2 2.62 4.02 1.40 0.60 I

4.2 4.9 DISTANCE

[

5.6 R [,~]

I

6.3

7.0

Fig. 10. Radial electron density distribution for two samples from the CdGe=As2 system with x ~ 0.1 and x = 1.1. For comparison the density distributions of atomic distancies for crystalline CdAs~ and CdGeAsa are plotted in the upper part of the figure (see also table 4). a c c o m p a n i e d with a strong disturbance o f the lattice, enhances the p r o b a bility o f d e v e l o p m e n t of higher c o o r d i n a t i o n of Cd a n d Ge atoms (CdAs 6 or GeAs6 octahedra) leading to a slight increase of the observed c o o r d i n a t i o n number.

304

L. C'ERVINKA, R. HOSEMANN A N D W. VOGEL TABLE

4

Density distribution of atomic distances in CdAs~ and CdGeAs2 CdGeAsz

(V =

~,~)

N

(N/V) x 100

16 16 4 48 20 8 2 12 8 12 8 8 8 14 4 17

4.1 4.1 1.0 12.2 5.1 2.0 0.5 3.0 2.0 3.0 2.0 2.0 2.0 3.5 1.0 4.3

2.4l 2.65 3.94 4.09 4.20 4.25 4.51 4.64 4.71 4.77 4.84 4.97 5.09 5.61 5.63 5.94

395/~z)

CdAs2

( V = 295/~3)

d(l~) N

(N/V) × 100

2.44 2.69 3.56 3.68 3.82 4.07 4.09 4.10 4.15 4.68 4.92 5.30 5.74 6.09

6 12 8 2 4 16 2 2 12 1 8 4 4 16

2.0 4.1 2.7 0.7 1.4 5.4 0.7 0.7 4.1 0.3 2.7 1.4 1.4 5.4

N = number of distances inside the elementary cell. V = volume of the elementary cell.

7. Conclusions

Our results illustrate the role of Ge atoms in the CdGexAs 2 system from the point of view of the development of the amorphous structure. Germanium atoms placed into the CdAs 2 A- and B-sites strongly disturb the principal formations of this structure, i.e. (Cd-As)6 rings and (As-As) spirals. This idea is clearly illustrated by our interpretation of the measurement of the macroscopic density in this system, by the presented model of the CdAs2-to-CdGeAs2 crystalline transformation and finally by the interpretation of the first maximum of the electron density distribution curves for x=0.1 and 1.1. References 1) A. S. Borshevskij, N . A . Goryunova, F. P. Kesamanly and D . N . Nasledov, Phys. Status Solidi 21 (1967) 9. 2) H. Pfister, Acta Cryst. 11 (1958) 221. 3) L. ~ervinka, A. Hrub3~, M. Maty~i~, T. ~ime~ek, J. ~k~icha, L. ~toura~, J. Tauc, V. Vorli6ek and P. H6schl. J. Non-Crystalline Solids 4 (1970) 258. 4) L. (~ervinka and A. Hrub~,, Acta Cryst., to be published. 5) L. Pauling, The Nature of the Chemical Bond (Cornell Univ. Press, Ithaca, N.Y., 1961).