Electron band structure of α-ZnIn2S4 and related polytypes

Solid State Communications, Vol. 29, pp. 235—238. Pergamon Press Ltd. 1979. Printed in Great Britain. ELECTRON BAND STRUCTURE OF a-ZnIn2 S4 AND RELATED POLYTYPES F. Aymerich, F. Meloni and G. Mula Istituto di Fisica dell’Universitâ, Cagliari, Italy and Gruppo Nazionale di Struttura della Materia del CNR, Italy (Received 25 September 1978 by F. Bassani) Pseudopotential calculations have been carried out for the a, (3 and polytypic forms of the layer semiconductor ZnIn2 S4, respectively, corresponding to space groups C~,C~and D~d.The required form factors are consistent with those used in our previous calculations for ZnS and CdIn2 S4. The band structure of the a phase, the only one up to now for which optical data are available, compares quite satisfyingly with very recent photoemission and reflectivity experimental data. The computed band structures of the j3 and ~yphases are very alike; on the contrary, interesting differences exist between these structures and the a phase which could easily be verified by experimental investigations. 11B’ 11C~ AMONGZnIn the ternary semiconductors of the A 2 family, 2S4 is of special interest because it is the one with a layer structure. This feature stimulated in the last few years several experimental investigations [1—4]; very recent reflectivity [5] and photoemission [6] experiments made possible a fIrst understanding of the electron band structure of this compound. Up to now, however, no theoretical calculation has been reported. In this paper we fill this gap by reporting on a pseudopotential band calculation for ZnIn2 S4 and by starting an analysis of the effects due to the polytypism characteristic of this crystal structure. Besides, possibly accounting for some divergences in the experimental data, this analysis should stimulate further experimental work because we show that some easily detectable differences should indeed exist in the electron properties of these polytypes. The basic element of all the polytypes of Znln2 S4 is a pack made up from seven atomic layers characterized by the following stacking sequence:

hhcchhcchhcc. Zn atoms occupy half of the tetrahedral holes inside each hh pair of S layers whereas In atoms occupy the corresponding holes of cc pairs. Furthermore, In atoms must also be put into half the octahedral holes of hc pairs whereas the holes inside the ch pairs are empty and explain the perfect cleavage properties of these crystals. This structure is so far the only one which appears to have been considered in the aforementioned experimental investigations [1—6] We shall study in addition two other polytypes, namely f3, whose space group is C~[8] and y, which corresponds [7] to space group D~d.Polytype 13 is a one-pack structure characterized by the hhhh stacking sequence for the S layers, while polytype -y corresponds to the two-pack arrangement S—In~—S—Inç~ —S—Zn—S—S—Zn—S—Inp—S—1n1.—S ,

S—Zn—S—ln~—S—In~—S,

with a hhhhhhhh stacking of S layers. In Table I we report lattice constants and atomic coordinates for the unimolecular a and f3 polytypes and for the bimolecular

where the index ~2means octahedral and r tetrahedral sites. The various polytypes differ in the number of packs per unit cell as well as in the arrangement of S layers. What we shall call the a phase and which corresponds [7] to the rhombohedral space group ~ is a three-pack structure characterized by the alternate succession of pairs of S layers arranged as in the cubic hexagonal close-packed structure with analogous close-packed pairs. In formula this arrangement of the 12 S layers which are needed to build the unit cell of the structure can be written as follows:

y polytype. Our calculations followed the method previously used by these authors for the ternary compounds [9] CdIn2 Se4, CdIn2Te4, ZnIn2 Se4 and Znln2Te4, as well as for [10] CdIn2S4. In r space our model pseudopotential may be written 2 )r 1 as sinfollows: (cr) 2Z*r_l . (I) V(r) = a exp (— br As in the aforementioned papers the atomic parameters a, b and c have been taken from reference [11], where they were evaluated from an extensive fitting of the —

235

236

ELECTRON BAND STRUCTURE OF a-ZnIn2S4

Vol. 29, No. 3

Table 1. Atomic coordinates and lattice constants for a, j3and -y polytypes of ZnIn,S4 a(C~~)

(3(Cj~)

Referred to rhombohedral axes

Referred to

Referred to

hexagonal axes

hexagonal axes

0.0, 0.0, 0.692 1/3,2/3,0.069

±(1/3,

mr

0.396, 0.396, 0.396 0.937,0.937,0.937

Inç~ 5(1) S(2) S(3) S(4)

0.166, 0.166, 0.166 0.040,0.040, 0.040 0.294, 0.294, 0.294 0.459,0.459,0.459 0.872, 0.872, 0.872

2/3, 1/3, 0.382 0.0, 0.0, 0.007 0.0, 0.0, 0.495 1/3, 2/3,0.269 1/3, 2/3, 0.754

±(

a~ c~

3.85 A 37.06 A

3.85 A 12.34 A

3.85 A 24.68 A

Zn

*

In S

2/3, 0.594)

±(l/3,2/3,0.094) 0

0 , 0.250) 2/3, 0.6935) ±(1/3, 2/3, 0.4375) ±(l/3,2/3,O.1938) ±(1/3, 2/3, 0.9375) ,

±(1/3,

Hexagonal cell.

Table 2. Pseudopotential parameters used in our calculations for all the polytypes

Zn

y(D~d)

a

b

C

5.14657 5.58037 7.28303

0.265 1 0.2260 0.2532

1.502 1.382 2.250

degenerate F3. As usual in ternary compounds the valence band is split into two parts, a lower one which comes F and an from upper the one S s-orbitals which comes and forms from four S p-orbitals. F~levelsAs at 3.2 3.2 5.6

optical spectra of zincblende 111—V and Il—VI cornpounds. There pseudopotential (1) was screened by the semiconductor Schulze and Unger [12] dielectric func~ tion; here, owing to the high value of the c0 lattice constant (37.06 A for the a phase), we prefer to use the free-electron Lindhard function. This corresponds to a larger screening at small k vectors and should be cornpensated by a slight variation of the parameters with respect to the values established in reference [11]. We were able to limit these modifications to the variation of the Sc parameter alone, which has been brought from 1.85 to 2.25. In Table 2 we report all the pseudopotential parameters used in our calculations, including the values of the effective ionic charges Z~.In this case we chose for the effective charge of the Zn atoms a typical value used for tetrahedral compounds (e.g. [9] Znln2 Se4) while that one of In atoms has been adjusted in order to fit the lowest direct optical gap. Not unexpectedly this adjustment leads to a higher ionicity in this compound than in purely tetrahedral ones; the effective charge of S atoms is of course determined by the charge neutrality requirement. The resulting band structure of the a phase is given in Fig. 1. In the relevant range of energies the low symmetry of the C3,~point group leads to the occurrence at F ofjust two types of irreducible representations, namely the totally symmetric one F1 and the doubly

can be seen more clearly from Fig. 2 we can distinguish in the upper valence band the nearly flat doubly degenerate bands coming from S p~and p~-orbita1s from the more rapidly varying non degenerate bands coming from S p~-orbitals.Since the two uppermost valence bands in the a phase have F3 symmetry at F we should have no cation s-contributions to them: this is exactly what has been found by Cerrina etal. [6] for their A photoemission peak. The opposite behaviour of their lower B, C, D peaks is again easily explained by our valence band structure: these peaks must in fact come also from the bands originating from S p~-orbita1s,which have F1 symmetry at F and, therefore, can include some cation s-contribution. On the whole the structure of the photoemission spectrum is in good agreement with our theoretical results, though the total width of our upper valence band seems to be somewhat less than it should. The lowest conduction band level has a F1 symmetry and should come mainly from cation, probably In, s-orbitals. The direct absorption edge corresponds to a F1,~—F3~ transition of 2.94 eV. The lowest direct transitions at Z (3.78 eV) and V (4.83 eV) points compare quite well with the higher transitions of 3.72 and 4.54 eV found in the reflectivity spectrum by Kisiel etal. [5] . Finally their peak at 5.61 eV should be attributed to bulk transitions. Though density of states calculations are clearly needed to confirm the above analysis we feel that the overall structure of our conduction band too is essentially correct. The last point to be discussed refers to the changes that can be found in (3and y polytypes. The calculations

Vol. 29, No. 3

ELECTRON BAND STRUCTURE OF a-ZnIn2S4

1

0~0

leVi E

237

________

__________________________________________________________________ _____________ ____________

~

Zn in2 S

00 —50 -100

_______

__________________

v

zr

ASD

Fig. 1. Band structure of a-ZnIn2 S4 (C~~). are absent in the (3polytype are clearly exhibited. On 60

1

E

1 1

____________

1 1

1

-----~

1

1

the contrary some relevant differences exist between these results and the already examined a polytype band structure: the maximum of the valence band has now F1 symmetry instead of F3, the ener~gap raises to 3.4 eV. A last feature is the completely flat behaviour of the doubly degenerate bands along the F—Z direction. In summary we may say that the electron band

(eVi

20

3

.

00

—

20

.

3 3 1

~

___________

i

—.——~

~

~z:~EE~E -

1 -40

1

structure of the a polytype of the layer semiconductor Znln 2 S4 computed with the model pseudopotential method [11] is in good agreement with the available photoemission [6] and reflectivity [5] data. The calculations have been extended to two other polytypes of the same compound and show that easily

j

cx

- --

experimentally These findings should detectable stimulate differences more refined should exist. experimental studies and pave the way for more detailed calculations including electron charge density and

,~-_.

1

___________

1 z

density of state distributions. Work is in progress in this direction.

___________

r

REFERENCES

z

Fig. 2. Band structure along the F—Z axis for a, (3 and -y polytypes of Znln2 S4. The dashed lines refer to the -y polytypes band structure which has been “unfolded” in the Brillouin zone of the jl polytype. The dashed lines have been omitted in the case of overlap with the solid lines. have been made with the same parameters used for the a polytype, though slightly different values for the effective ionic charges are conceivable. The band structure of the -y polytype turns out to be very alike to that one of (3 polytype and may be thought of as obtained from the latter one by a folding along the F—Z axis plus a small perturbation. This is apparent from Fig. 2 where the (3band structure is compared with a “double zone” -y band structure; in this plot the discontinuities due to the Fourier coefficients which

1.

2. 3. 4. 5. 6. 7.

8.

E. Gombia, N. Romeo, G. Sbreveglieri &

C. Paorici, Phys. Status Solidi (a) 34, 651(1976). M.Guzzi&G.Baldini,J. Luminesc. 9,514 (1975). A. Cingolani, M. Ferrara, A. Minafra, F. Adducci & P. Tantalo, Phys. Status Solidi (a) 23, 367 (1974). A. Serpi,J. Phys. D9, 1881 (1976). A. Kisiel, M. Turowski, T. Zeppe & W. Girant, Ternary Compounds, p. 259. Inst. Phys. Conf. Ser. 35, Bristol (1977). F. Cerrina, I. Abbati, L. Braicovich, F. Levy & G. Margaritondo, Solid State Commun. 26, 99 (1978). F. Donika, S.1. Radautsan, G.A. Kiosse, S.A. Semiletov, T.V. Donika & I.G. Mustya, Soy. Phys.—Cryst. 16, 190 (1971). F. Donika, S.I. Radautsan, S.A. Semiletov, T.V. Donika, 1G. Mustya & V.F. Zhitar’, Soy. Phys.—Cryst. 15, 695 (1971).

238 9. 10.

ELECTRON BAND STRUCTURE OF a-ZnIn2S4 F. Meloni, F. Aymerich, G. Mula & A. Baldereschi, Helv. Phys. Acta. 49, 687 (1976). A. Baldereschi, F. Meloni, F. Aymerich & G. Mula, Ternary Compounds, p. 193. Inst. Phys. Conf. Ser. 35, Bristol (1977).

11. 12.

Vol. 29, No. 3

F. Aymerich, F. Meloni & G. Mula,Phys. Rev. BiS, 3980 (1977). K.R. Schulze & K. Unger,Phys. Status Solidi 66, 491 (1974).