BONDING AT SEMICONDUCTOR INTERFACES

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BONDING AT SEMICONDUCTOR INTERFACES

M. Schlüter

To cite this version:

M. Schlüter. BONDING AT SEMICONDUCTOR INTERFACES. Journal de Physique Colloques,

1985, 46 (C4), pp.C4-331-C4-333. �10.1051/jphyscol:1985436�. �jpa-00224686�

JOURNAL DE PHYSIQUE

Colloque C4, supplement au n04, Tome 46, avril 1985 page C4-331

BONDING AT SEMICONDUCTOR INTERFACES

M. Schliiter

AT&T BeZZ Laboratories, Murray HiZZ, New Jersey 07974, U.S.A.

EXTENDED ABSTRACT

In

m t r a s t to simple

metals,

Semiconductors have to

be

viewed as

molecular netwaks

with valence dectrcms strongly amcentrated near atoms and along bands.

Disturbing these

networks

results (with increasing perturbation strength) in bending, stretching and breaking of the bonds. This simple picture has to be augmented by intermediate situations, such as

the

formation

of new

types of bands which can stabiIize conf@rations with changed atomic cmdination numbers.

Typically, the energy

required

to campletely

break

a semiconductor bond

is -1

eV/atam. Large elastic distartims can therefore be accanmodated to avoid breaking

of bonds

or to favor

the

fmmtion

of

new types of weaker bonds. A beautiful example

al this

behavior

is the

formation of m-bonds in order to stabilize the Si(ll1) (2x1) surface? Similar situations can be expected for internal interfaces and grain boundaries.

To k e t i c a l l y

describe

strongly defamed semicanductors in a reliable fashian it

is necessary

to

consider

rehybridization

af

atomic wawfuncticms,

i s . quantum-

mechanical descriptions

are needed

beyond qualitative descriptions

based on

pair-

wise

interactions alone? Several classes

of approaches are

possible: a) the simulation

of

rehybridization by three-body interactions? b)

the

empirical tight- binding band structure approach4 and

c)

the s e l f d s t e ~ ~ t

density functional approach:

which

often

is m m W with

the use of

first principles

normcansaving

pseudopotentials!

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1985436

C4-332 JOURNAL DE PHYSIQUE

In

addition to atomic structure and bonding gecanetries, modifications in

the

electronic structure

near the semimducting

gap are

of

interest. Gmpletely ruptured bonds introduce deep states in

the

gap, like it is eg.

the

case

f a

vacancies7

a some

surfaces?

J k p

states

can

be

seen

by capacitance

a

optical spectroscopy

or

by spin

resonance.

Partial rebonding

modifies these

electronic states and tends to delocalize them and to remove them from the gap region?.7

Weaker

perturbations, like

some

perfectly bonded hetmjunctions7

do

not induce localized states in the

gap

at all. The question about a threshold strength (a loss

cb

symmetry)

cb

the perturbation

for

introducing localized electranic states in

the

gap has nd been answea-ed in much generality although a large

number

d individual case studies exists?-l4

1)

K.

C. Pandey, Phys.

Rev.

Lett. 47,1913 (1981), and ibid. 49,223 (1982).

2) H.

J.

M6Uer and H. H. Singer, preprint.

3)

E.

Pearson, T. Takai, T. Halicioglu and

W. k T i e r ,

preprint.

4)

D. J.

Chadi, Phys.

Rev.

Lett. 41,1062 (1978).

5) M. Schliiter and L.

J.

Sham, Physics Today,

February

1982,

p. 36.

6) G.

B.

Bachelet,

D. R.

Hamann and M:Schliiter, Phys.

Rev.

B26, 4199 (1982).

7) G.

k Baraff, E

0.

Kane

and M. Schliiter, Phys.

Rev.

B21,5662 (1980).

8) M. Schliitet in Festkiirperpobleme

XVIII,

p. 155,

J.

Treusch (ed.), Vieweg, Braunschweig (1978).

9)

R. E. Thornson

and

D. J.

Chadi, Phys.

Rev.

829,889 (1984).

10)

J. R.

Chelikwsky and

J.

C. Spence, Phys.

Rev.

B30,694 (1984).

11)

J. E. Noxthrup

and M. L.

Cohen,

Phys.

Rev.

823,2563 (1981).

12) S. G. Louie, these proceedings.

13)

L. F. Mattheiss and

J. R. Patel,

Phys.

Rev., B23,5384

(1981).

14)

J. R. Chelikowsky, Phys.

Rev. Lett. 49,1569 (1982).

DISCUSSION

D. A s t : Two comments: ( i ) It is known experimentally from EBIC s t u d i e s t h a t t h e svmmetricZ=9 g r a i n boundary i n S i is not e l e c t r i c a l l y a c t i v e . ( i i )

From RDF o f d S i it i s known experimentally t h a t b a / a f 5% b u t t h a t bond angle f l u c t u a t i o n s can be l a r g e

--

20'.

M. Schluter: ( i ) This then a g r e e s with C h a d i f s tight-binding r e s u l t s . ( i i ) Amorphous S i is one example f o r l e a r n i n g about bonding changes, b u t it i s n o t exhaustive. A t s u r f a c e s and i n t e r f a c e s , s t e r i c c o n s t r a i n t s can be q u i t e d i f f e r e n t and "neww bonding c o n f i g u r a t i o n s can occur. However, a s you mention t h e r e i s a h i e r a r c h y o f f o r c e s ; bond-bending f o r c e s , although s t a b i l i z i n g t h e t e t r a h e d r a l s t r u c t u r e a r e about one o r d e r o f magnitude smaller than bond s t r e t c h i n g f o r c e s .

A.P. Sutton: Chadils c a l c u l a t i o n o f

2

=9 (221 ) involved 150 atoms/unit c e l l r e s u l t i n g i n t h e d i a g o n a l i s a t i o n o f a 600 x 600 matrix ( s e v e r a l times during t h e c a l c u l a t i o n ) . How many atoms/unit c e l l a r e t r a c t a b l e with t h e d e n s i t y f u n c t i o n a l approach?

M. Schluter: We a r e c u r r e n t l y experimenting with minimal b a s i s s e t s o f - 8 o r b i t a l s p e r S i (Gel atom. This b a s i s y i e l d s cohesive p r o p e r t i e s with l e s s than

-10% e r r o r . So, 50 t o 100 a t o m d u n i t c e l l can be t r e a t e d on computers l i k e a Cray-I. Space is one c o n s i d e r a t i o n , b u t computer-time i s another one. Density f u n c t i o n a l c a l c u l a t i o n s need self-consistency i n t e r a c t i o n s and a r e roughly one t o two o r d e r s o f magnitude more computer-time i n t e n s i v e than e m p i r i c a l tight-binding c a l c u l a t i o n s .