Calculated atomic structures of ZnS, ZnSe and ZnTe (110) surfaces

(~)

0038-1098/93 $6.00+. 00 P e r g a m o n Press Ltd

Solid State C o m m u n i c a t i o n s , Vol. 87, No. 11, pp. 1001-1004, 1993. Printed in G r e a t Britain.

CALCULATED

ATOMIC STRUCTURES

OF ZnS, ZnSe AND

ZnTe

(110) S U R F A C E S

L E A . Alves

Fundaf~o de Ensino Superior de Sflo Jo~o del Rei - DCNA T 36300-000, Sfto Jo~o del Rei, MG, Brasil K. W a t a r i a n d A.C. Ferraz

Instituto de Ffsica da Universidade de S~o Paulo CP.20516 - 01498-970, Sdo Paulo, SP, Brasil (Received J u n e 10, 1993 by Cylon E.T. Gongalves da Silva)

In this p a p e r we describe a systematic study of t h e atomic g e o m e t r y of Z n S , Z n S e and Z n T e (110) surfaces. W e analyse t h e t r e n d for t h e equilibrium atomic structures in connection with t h e ionicity of t h e materials. W e report calculations which are b a s e d on the density-functional theory (DFT), t h e local-density aproximation ( L D A ) for t h e exchangecorrelation a n d t h e self-consistent ab-initio p s e u d o p o t e n c i a l approach.

Theoretical Framework

0.005 eV/A. T h i s c o r r e s p o n d s to a n u m e r i c a l u n c e r t a i n t y of a t o m i c positions of l e s s t h a n 0 . 0 5 A. The s i n g l e - p a r t i c l e o r b i t a l s f o r t h e valence e l e c t r o n s w e r e expanded in plane w a v e s by u s i n g b a s i s s e t s w i t h c u t - o f f s in t h e kinetic e n e r g y (k + G) z equal to 10Ry. The s u m m a t i o n over f o u r M o n k h o r s t - P a c k [12] k - p o i n t s of t h e i r r e d u c i b l e p a r t of t h e s u r f a c e Brillouin zone w a s u s e d to r e p l a c e t h e Brillouin zone i n t e g r a t i o n s . The Atomic Geometry

We u s e t h e d e n s i t y - f u n c t i o n a l t h e o r y t o g e t h e r with the local-density approximation for the exchange-correlation functions [1,2]. The e l e c t r o n - g a s d a t a f o r t h e LDA a r e t a k e n f r o m Ceperly and Alder [3] as p a r a m e t r i z e d by P e r d e w and Zunger [4]. The electron-ion interaction is described by norm-conserving, fully separable a b - i n i t i o p s e u d o p o t e n t i a l s [5]. They a r e b a s e d on relativistic all-electron calculations for the free atom by solving the Dirac equation s e l f - c o n s i s t e n t l y [6,7]. In o r d e r to d e s c r i b e t h e s u r f a c e s we u s e t h e slab s u p e r c e l l m e t h o d [8]. Each slab c o n s i s t s of e i g h t (IIO1 planes. The l a t t i c e c o n s t a n t s a r e f i x e d a t t h e bulk t h e o r e t i c a l equilibrium values, a n d a r e given f o r t h e t h r e e s y s t e m s in Table I. The t h e o r e t i c a l l a t t i c e c o n s t a n t s f o r ZnS and ZnSe a r e a b o u t 77. s m a l l e r t h a n t h e e x p e r i m e n t a l ones and f o r ZnTe 47.. T h e s e d i s c r e p a n c i e s a r e to be a t t r i b u t e d to t h e m i s s i n g c o n t r i b u t i o n of t h e Zn 3d s t a t e s w h i c h a r e c o n s i d e r e d a s f r o z e n core s t a t e s and t h u s hidden in t h e p s e u d o p o t e n t i a l s . In our c a l c u l a t i o n s we did not consider the non-linear core e x c h a n g e - c o r r e l a t i o n c o r r e c t i o n s [9,10]. Since o u r m a i n i n t e r e s t is in t h e c h a n g e s which o c c u r a t t h e II-VI(IIO) s u r f a c e s , we g e n e r a t e d a p s e u d o p o t e n t i a l of a zinc a t o m by r e g a r d i n g i t s 3d o r b i t a l s as core o r b i t a l s and by choosing s u i t a b l e core radii and an electron configuration sXpy which is able to r e p r o d u c e t h e e x p e r i m e n t a l bulk s t r u c t u r a l c o n s t a n t o f t h e II-VI compounds w i t h i n minor e r r o r s . We used v a c u u m r e g i o n s w i t h a t h i c k n e s s equivalent to s i x a t o m i c layers. T h e s e choices have been proven to be a d e q u a t e f o r d e s c r i b i n g t h e bulk region a n d f o r minimizing the interaction between contiguous s u r f a c e s [IlL The c e n t r a l t w o l a y e r s of t h e slab w e r e kept f i x e d a t t h e bulk p o s i t i o n s and t h e t h r e e o u t e r m o s t l a y e r s of a t o m s on both s i d e s of t h e slab w e r e r e l a x e d to g e o m e t r i e s given by t h e c a l c u l a t e d t o t a l - e n e r g i e s and f o r c e s . The equilibrium g e o m e t r y is i d e n t i f i e d when all f o r c e s a r e s m a l l e r t h a n

We now t u r n to t h e a n a l y s i s of t h e e q u i l i b r i u m atomic geometries obtained after relaxing the ll-Vl(ll0) s u r f a c e s . All s u r f a c e s r e l a x s u c h t h a t t h e g r o u p II s u r f a c e a t o m moves i n w a r d and t h e g r o u p Vl a t o m moves outward. As will be d i s c u s s e d l a t e r in t h i s section, in a s i m i l a r w a y a s in t h e case of III-V(II0) surfaces [11] the driving m e c h a n i s m f o r t h i s a t o m i c r e a r r a n g e m e n t is t h a t , u n d e r t h e coordination conditions of t h e s u r f a c e , t h e g r o u p II a t o m p r e f e r s a m o r e p l a n a r , sp 2 - like bonding s i t u a t i o n w i t h i t s t h r e e g r o u p Vl n e i g h b o r s a n d t h e g r o u p VI a t o m p r e f e r s a p - b o n d i n g w i t h i t s three group II neighbors. Schematically the r e l a x a t i o n is s h o w n in Fig. I, which also d e f i n e s t h e s t r u c t u r a l p a r a m e t e r s which a r e given in T a b l e s I a n d II. Although our r e s u l t s f o r t h e s t r u c t u r a l p a r a m e t e r s a r e in good g e n e r a l a g r e e m e n t w i t h low-energy electron diffraction [LEED] analysis [13], t h e r e a r e some i m p o r t a n t d i s a g r e e m e n t s w h i c h will d e s e r v e a l a t e r d i s c u s s i o n in t h i s paper. The g e n e r a l f e a t u r e s t h a t we would like to e m p h a s i z e are: a) The r e s u l t s of LEED a n a l y s i s reveal t h a t t h e II-VI(IIO) s u r f a c e s r e l a x w i t h t h e s u r f a c e c a t i o n s moving inward and the surface anions being d i s p l a c e d o u t w a r d , as s h o w n in Fig. 1. T h i s well known r e s u l t is r e p r o d u c e d by our c a l c u l a t i o n s . b) Among t h e v a r i o u s s t r u c t u r a l p a r a m e t e r s , t h e relative displacement A is t h e m o s t a c c u r a t e l y l,J. d e t e r m i n e d by LEED i n t e n s i t y a n a l y s i s to within _+O,OSA. Our calculated values for A are 1,~ 1001

|002

ZnS, ZnSe AND ZnTe(110) SURFACES

a)

r e l a x a t i o n is a n a l o g o u s to t he r e l a x a t i o n of t h e III-V(IlO) s u r f a c e s which ha s been i n t e r p r e t e d in t e r m s of t he r e h y b r i d i z a t i o n of t he s u r f a c e bonds [11]: t h e s u r f a c e group V a t om c h a n g e s i nt o a m o r e p - l i k e c o n f i g u r a t i o n and t he s u r f a c e g r o u p Ill a t o m 2 i nt o a more sp like c o n f i g u r a t i o n w i t h r e s p e c t t o t h e i r bulk sp 3 c o n f i g u r a t i o n . In t h i s w a y t h e t op l a y e r g e o m e t r y l i e s b e t w e e n t he bulk g e o m e t r y ( t e t r a h e d r a l bonding) and t he g e o m e t r y o b t a i n e d by putting t he cation and the anion in their r e s p e c t i v e s m a l l molecule c o n f i g u r a t i o n s , e.g. t h e p l a n a r Gall molecule w i t h 120 bond a n g l e s and t h e

{) Top view

2d

Vol. 87, No. 11

3

p y r a m i d a l AsH

3

molecule w i t h bond a n g l e s of 92,1 °, o

t h u s c l os e t o 9 0 . In Table II we d i s p l a y t h e bond a n g l e s o b t a i n e d in our p r e s e n t c a l c u l a t i o n f o r t h e II-VI(llO) surfaces together with the angles o b t a i n e d f o r t h e III-V(llO) s u r f a c e s in r e f e r e n c e II. As can be seen t h e a ngl e c¢ is b i g g e r in II-Vl compounds t h a n in III-V compounds. On t h e o t h e r hand t h e a n g l e ~ is c l o s e r t o 90 a s one goe s f r o m p h o s p h o r compound to a r s e n i c compound in III-V compounds (e.g. f r o m GaP t o GaAs) or f r o m s u l p h u r compound t o s e l e n i u m compound and t h e n to t e l u r i u m compound in II-Vl compounds. In o r d e r t o u n d e r s t a n d these features, besides the influence of the repulsion between the chemical bonds one has to take in account the ionic character of these bonds which increases from III-V to II-Vl compounds [14]. For the more ionic zinc-blend semiconductors, the attractive Coulomb forces between the outward relaxed surface anions and the inward relaxed surface cations should reduce the relaxation caused by covalent forces. Following Kasowski et al. [IS] we compare in Table II the trends of the angle and the Coulomb energy Ze2/ca., where a is the

l%J_.:___; ° F i g u r e 1. Atomic geometry for II-VI s e m i c o n d u c t o r (110) s u r f a c e s (a) Top view of t h e s u r f a c e unit cell. (b) Side view of the f i r s t t h r e e l a y e r s of t h e (110) s u r f a c e . Open c i r c l e s a r e a n i o n s and h a t c h e d c i r c l e s a r e cations, a is t h e 1

t h e o r e t i c a l bulk l a t t i c e c o n s t a n t and do = ~ ~/2 ao.

zinc-blend theoretical lattice constant, Z is the longitudinal effective charge [16], e is the electron's charge, and c is the dielectric c o n s t a n t . As can be seen in Table II, f o r compounds w i t h a common c a t i on, t h e a ngl e cc d e c r e a s e s , g e t t i n g c l o s e r to 9 0 , when t h e Coulomb e n e r g y d e c r e a s e s . Moreover t h i s f a c t is r e f l e c t e d in t h e t r e n d of t h e c a l c u l e d t i l t a ngl e ~), a l s o shown in T a b l e II, w hi c h i n c r e a s e s when t he Coulomb e n e r g y decreases. It is worth noting also that the calculated relative displacement At,±, in Z of the

systematically smaller than the experimentally d e r i v e d ones. c) The t i l t a n g l e ~ is a p a r a m e t e r which has been t h e s u b j e c t of many e x p e r i m e n t a l i n v e s t i g a t i o n s [13]. Our c a l c u l a t e d v a l u e s a r e in f a i r a g r e e m e n t w i t h t h e e x p e r i m e n t a l ones, which a r e d e t e r m i n e d w i t h a p r e c i s i o n of 10Z. d) As shown in Fig. I the s u r f a c e s r e l a x in such a way that th e c a t i o n s move i n w a r d to an approximately planar, threefold coordination with i t s anion n e i g h b o r s , w h e r e as t h e u p p e r m o s t a n i o n s move outward into a corresponding pyramidal c o n f i g u r a t i o n w i t h i t s t h r e e c a t i o n neighbors. This

theoretical

lattice parameter

higher Coulomb energies.

Table I S t r u c t u r a l p a r a m e t e r s for the surface r e l a x a t i o n as defined in F i g u r e 1. For each compound t he f i r s t line c o r r e s p o n d s t o t h e LEED a n a l y s i s [13] a

(h)

A

I,I

A

l,y

A

2, I

(h)

(A)

(A)

d

12,1

d

23,1

d

12,y

(A)

{A)

(A)

(o)

ZnS

5.410 5.027

0.59 0.43

4.19 4.05

0.00 0.07

1.53 1.33

1.91 1.84

3.15 2.84

26.0 23.9

ZnSe

5.668 5.259

0.69 0.50

4.43 4.21

0.00 0.07

1.52 1.39

2.00 1.91

3.35 2.98

29.0 25.4

ZnTe

6.104 5.883

0.72 0.63

4.75 4.72

0.00 0.09

1.64 1.47

2. 15 2. 13

3.59 3.36

28.5 28.4

a.,

is

smaller

for

1003

ZnS, Z n S e A N D ZnTe(110) S U R F A C E S

Vol. 87, No. 11

Table II Calculated lattice

tilt

constant

a 0'

angle

o~, relative

bond

angles

at

displacement the

anions

Atx

and

in at

% of cations

located a t the f i r s t layer, and ZeZ/ea° in eV (see text).

w

AI / a

~

g

~

ZeZ/eao

(o)

(Z)

(o)

(.)

(°)

GaP

27.8

10.6

92.3

114.1

122.0

0.442

OaAs

28.6

11.4

90.8

112.1

122.3

0.255

InP

29.2

11.3

91.4

113.7

122.4

0.582

(eV)

InAs

30.7

12.0

90.1

112.5

123.3

0.235

ZnS

23.9

8.5

95.6

119.4

117.9

1.809

ZnSe

25.4

9.5

94.2

120.6

116.0

1.225

ZnTe

28.4

10.7

92.4

121.8

llS. I

0.924

Therefore, based on our calculations we propose that the relaxation of the II-VI(ll0) s u r f a c e s , although smaller than the r e l a x a t i o n of the III-V(II0) s u r f a c e s due to the competition between covalent and ionic forces, is driven essentially by the same mechanism: the g r o u p VI atom tends to a p-bonding with its t h r e e g r o u p II neighbors, f o r m i n g a pyramidal geometry. This proposal is in agreement with theoretical conformational analyses [17] which predict pyramidal geometries f o r the ions (SH3) ÷ and

i)

(Sell3) ÷ with

bond

angles

equal

iv)

respectively. findings.

These

values

are

to very

94,5 ° and close

to

ii)

iii)

93" our

v)

Summary We have r e p o r t e d p a r a m e t e r - f r e e calculations of the s u r f a c e c r y s t a l l o g r a p h y of various II-VI compounds, namely ZnS(ll0), ZnSe(ll0), and ZnTe(ll0). The top t h r e e layers of our s u r f a c e s a r e relaxed according to the f o r c e s on the atoms, using an "optimized s t e e p e s t descent" method t o g e t h e r with a C a r - P a r r i n e l l o [18] approach f o r bringing the wave f u n c t i o n s to self-consistency. Summarizing our r e s u l t s and comparing them to the r e s u l t s of LEED analysis, we observe:

vi)

vii)

The r e s u l t s of LEED reveal t h a t the II-VI(II0) s u r f a c e s r e l a x with the s u r f a c e cations moving inward and the s u r f a c e anions being displaced outward; this r e s u l t is reproduced by our calculations; the r e l a x a t i o n of the II-VI(II0) s u r f a c e s is analogous to the r e l a x a t i o n of the III-V(II0) surfaces; our calculated values f o r A and the t i l t l,J.

angle ~ ave systematically smaller than the values f r o m LEED analysis; our calculated values f o r the tilt angle a r e s m a l l e r than the predicted values f o r the III-V(II0) s u r f a c e s ; our calculations a r e sensitive to the ionicity of the m a t e r i a l s and the r e s u l t s a r e in agreement with previous arguments which predict that the relaxation angle w of zinc-blend ( 1 1 0 ) s u r f a c e s should depend on ionicity [15]; the calculated bond angles at the II-VI(ll0) s u r f a c e s a r e bigger than the bond angles at the III-V(I10) s u r f a c e s . This r e s u l t r e f l e c t s the f a c t t h a t the ionic f o r c e s t r y to reduce the r e l a x a t i o n caused by the covalent f o r c e s ; a p p a r e n t l y the LEED analysis are not sensible enough to the ionicity of the s y s t e m s since they give about the same value 0~ -= 28 f o r all zinc-blende (110) s u r f a c e s .

References [I] [2] [3] [4] [5]

P.Hohenberg and W. Kohn, Phys. Rev. 136, B864(1964). W. Kohn and L.J. Sham, Phys. Rev. 140, AI133(1965). D.M. Ceperley and B.I. Alder, Phys. Rev. Lett, 45, 566(1980). P. Perdew and A. Zunger, and M.L. Cohen, J. Phys. Cl2, 4409(1979). R. Stumph, X. Gonze, and M. Scheffler:"A list of separable norm-conserving, ab-initio pseudopotentials", Fritz Haber Institut,research report, April 1990, unpublished; X. Gonze, P. Ktickell, and M. Scheffler, Phys. Rev. Bl2, 4200(1975).

[6]

[7] [8] [9] [I0] [II]

D.R. Hamann, M. Schltlter, and C. Chiang, Phys. Rev. Lett. 43, 4494(1979), G.B. Bachelet, D.R. Hamann, and M. Schlfiter, Phys. Rev. B26, 4199(1982). L.Kleinman and D.M. Bylander, Phys. Rev. Lett. 45, 1425(1982). M. Schltlter, J.R. Chelikowsky, S.G. Louie, and M.L. Cohen, Phys. Rev. Bl2, 4200(1975) S.G. Louie, S. Froyen, and M.L. Cohen, Phys. Rev.B26, 1738(1982). G.E. Engel and R.J. Needs, Phys. Rev. B41, II, 78"/6(1990). J.L.A. Alves, J. Hebenstreit, and M. Scheffler, Phys. Rev. B44, (6188(1991).

I004 [12] [13]

[14]

Vol. 87, No. l 1

ZnS, Z n S e A N D Z n T e ( 1 1 0 ) S U R F A C E S H.J. Monkhorst and J.D. Pack, Phys. Rev. BI3, 5188(1976). C.B. Duke, "Surface P r o p e r t i e s of Electronic Materials" D.A. King & D.P. Woodrif eds. Elsevier 1986 - C h a p t e r 3. The Phillips ionicities f o r GaP, GaAs, InP, InAs, ZnS, ZnSe, ZnTe a r e 0.374, 0.310, 0.421, 0.357, 0.623, 0.676 and 0.576, respectively. See, f o r i n s t a n c e , F. Bechstedt and R. Enderlein, "Semiconductor Surfaces and I n t e r f a c e s " (Akademic Verlaq, Berlin, 1988).

[15]

[16]

[17]

R.V. Kasowski, M.-H. Tsai and J.D. Dow, J. Vac. Sci. Technol. 85,4, 953(1987).M.-H. Tsai, R.V. Kasowski and J.D. Dow, Solid S t a t e Commun. 64, 2, Z31[1987). The ionicity is a p p r o x i m a t e l y p r o p o r t i o n a l to Z; see G. Lucovsky, R.M. Martin and E. B u r s t e i n , Phys. Rev. B4, 1367(1971). D.A. Dixon and D.S. Marynick, J.Am. Chem. Soc

99, 6101(1977); J. Chem. 2471(1985). [18]

R.CaF and 2471(1985).

M. Parrinello,

Phys. 71, 2860(1979). Phys.

Rev.

Lett.S5,