Electronic and structural properties of amorphous Si1−xAlx

Journal of Non-Crystalline Solids 77 & 78 (1985) 91-94 North-Holland, Amsterdam

91

ELECTRONIC AND STRUCTURAL PROPERTIES OF AMORPHOUS S i 1 _ x A l x J.A.

VERGES

D e p a r t a m e n t o de F i s i c a del C a n t o b l a n c o , 28049 M a d r i d ,

Estado Spain*

S61ido,

Universidad

Aut6noma,

S e v e r a l random B e t h e l a t t i c e s capable of simulating the atomic structure o f a m o r p h o u s S i 1 _ x A l x a r e d e f i n e d and t h e c o r r e s p o n d ing density of electronic s t a t e s and s t a t i s t i c a l distribution of static charges analysed.

Recently,

the metal-insulator

has been s t u d i e d conductivity

at

of

MIT d e p e n d i n g

doing the

T ~ OK i s

random n e t w o r k : ly

i)

coordinated

near the rise

to

ii)

In t h i s

ces one s t a t e

the

in

filles

the

electron

gap.

3.

describe

order

lattices

of RBL's

it

in

as t h e MIT o f

doping

heavily

forming of all

the

the tetrahedral-

which with

requirements

band

gives

doped c - S i .

only

three

bond t h a t

produ-

the dangling

w i d e n s as x i n c r e a s e s

eventuallity,

ways

a p p e a r s an i m p u r i t y

of

The i n t e r a c t i o n

with

2 (RBL's)

the alloy.

and p o s s i b l y

t h e MIT w o u l d have a o n e -

these

by means o f constitute i).

have been used t o model

The s t u d y

of

the electronic

Bethe lattices an e x t e n s i o n

random n e t w o r k s

(see Figure

ciated

gap.

x

A1 atoms i n

e v e r y A1 atom has a d a n g l i n g

In t h a t

semiconductors

they

valence

of

Si atoms

case,

same n a t u r e

a-Sil_xAl

T h e r e a r e two d i f f e r e n t

on t h e c o o r d i n a t i o n

In t h i s

in

character.

structure

tradition

observed.

a new band t h a t

Random B e t h e mic

the

(MIT)

When x r e a c h e s ~ O . 2 , m e t a l l i c

the evolution

its

case,

bonds p r o d u c e s

of

band,

a MIT o f

I.

A1 can s u b s t i t u t e

network.

valence

A1 can s a t i s f y

bonds.

transition

experimentally

which

The s t u d y

RBL's c o n f i r m s

of

do n o t the

the

(BL's)

of

has a l o n g

standard

BL's

possess s h o r t

electronic

qualitative

the ato-

structure because

range

structure picture

asso-

developed

above. The method d e v e l o p e d Green's

function

in

Ref.2

has been used t o

on an atom s u r r o u n d e d

obtain

by a RBL. A1 i s

the

characteri-

* Work s u p p o r t e d i n p a r t by t h e C o m i s i 6 n A s e s o r a de I n v e s t i g a c i 6 n Cient~fica y T~cnica of the Spanish Ministry o f E d u c a t i o n and Science, under contract No.2068/83. 0022-3093/85/$03.30 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

J.A. Verges/ Properties of amorphous Si l.xAlx

92

sed by i t s

atomic

levels,

to the corresponding rences

being Si-Al

Si-Si

ones.

between A1 and Si a r e i n c l u d e d

tronegativity,

and i i )

t h e a v e r a g e d LDOS on a g i v e n studied.

The d i s t r i b u t i o n spectra

in

the calculation:

i)

elec-

of

b r a n c h e s o f t h e RBL g i v e s

by a f i x e d

static

charges

configuration

the stacan be

has been o b t a i n e d

from

some amorphous a l l o y s 4.

The a v e r a g e d LDOS o f

# ~F

in

equal

t h e main d i f f e -

t y p e o f atom. A l t e r n a t i v e l y ,

c h a r g e on an atom s u r r o u n d e d

core level

interactions

way, o n l y

connectivity.

The a v e r a g e o v e r r a n d o m l y g e n e r a t e d tic

and A I - A I

In t h i s

several

RBL's i s

shown in

Figures

2 and 3.

i-

.

(a)

OB I

u~ uJ

(a) 0.6

L O O f i on t

At

, I

I,."-

u~

0.4

I..L O

0.2 • Si a t o m

oA[

atom

(b)

m o

0.4 o

(b) LDOEII o n Si

,EF

0.2

0.0 2-8-G -64

FIGURE I Schematic representation of the RBL's used in t h i s work to model the atomic structure of a-Si1_ x Al×. Only the c o n n e c t i v i t y of the l a t t i c e is relevant since the employed Hamiltonian does not include disorder e f f e c t s associated with bond length or bond angles f l u c t u a t i o n s .

0 4

8

ENERGY (eV) FIGURE 2 Averaged local densities of states f o r the RBL depicted in F i g . l a when the atomic aluminium concentration is 20%.

ZA. Verges/Properties of amorphous Sil_xAlx Figure ties

2 shows t h e (see Figure

ce band b u t , the

apart

LDOS o f

network

of

ing

Ib).

parameter

~-

this

a BL w i t h

fact,

both

coordinated

results

for

the

In a b i n a r y

06 _ ( o )

"~:1

alloy

_(c)

in

LDOS a r e v e r y

the

valen-

similar

BL d e s c r i b i n g

to

a regular

atoms). second t y p e o f

RBL's a r e

as a f u n c t i o n

t h e number o f

~=0.5

A1 i m p u r i -

are created

(the

They have been p l o t t e d

(.

substitutional

case h o l e s

impurities

tetrahedrally

Figure co uJ

from

3 the

for

In t h i s

a BL w i t h o u t

In F l g u r e (see

results

la).

93

of

crossed

_(e)4=0.25

shown

the mixSi-AI

.(g){=0.125

p-

u~ LI.. C) >.

0A

02

(b)

W~

(d)

(f)

(h)

0.~

c~ .__1

- ~

0.2

o o

0.0 -12

_.J

-~

~

-12

/. -12

-~

-/4

ENERGY

/,. -12

-/.

/~

(eV)

FIGURE 3 Averaged local densities o f s t a t e s on A1 ( u p p e r h a l f ) and Si ( l o w e r h a l f ) f o r t h e t y p e o f RBL's d e p i c t e d i n F i g . l b . The a l u m i n i u m concentration i s 20%. The Fermi l e v e l l i e s a l w a y s in t h e gap (E F 0 eV) a t T = OK. bonds can v a r y termined

from

0 (segregation,

by t h e c o n c e n t r a t i o n

bonds t h a t

it

forms

of

pure

BL's

is

g)

comes f r o m

(perfect

obtained.

the

~ the dangling

electronic binding

mixing,

is

~ = 1).

a maximum v a l u e For ~ ÷ 0 the

de-

In c o n c l u s i o n , is

bonds t h a t

For h i g h e r

and a t y p i c a l

behaviour

result

t h e gap ( s e e p a n e l

dangling

coordination.

recovered.

a metallic

filles

between the

threefold

bond band n a r r o w s

structure

parameters

~ = O) t o

each e l e m e n t and t h e number o f

The hand t h a t

interaction

main a t A1 atoms w i t h of

of

re-

values

semiconductor for

expected

our tight-

only

if

A1

segregates. Finally,

in

Figure

4 the

static

charge

distributions

are

shown.

J.A. Verges/ Properties of amorphous Si l_xAlx

94

(a)

,_ -r LU~

(b)

I --AL--

I --Si-

I

I

I

I

At1

I

-SiI

I.--t~

I--

I

IF

2.6 2.8 3.0 3.8 &0 4.2 STATIC CHARGE

i

I

2.@ 3.0 4g ON ATOMS

4.2

FIGURE 4 S t a t i s t i c a l d i s t r i b u t i o n of s t a t i c charges on Al and Si atoms for the two types of RBL's depicted in F i g . l . The mean values are nAl=2.90 and nsi=4.02 in case (a), and nAi=2.83 and nsi=4.O4 in case (b).

The h i s t r o g r a n s have been e x t r a c t e d from 100 d i f f e r e n t atomic conf i g u r a t i o n s around each atom. The r e s u l t s show t h a t , c o n t r a r i l y to what we expected, the d i s t r i b u t i o n i s wider For t e t r a h e d r a l l y coo r d i n a t e d AI. This i m p o r t a n t q u a n t i t a t i v e d i f f e r e n c e (which does not appear in the s t a t i c charge d i s t r i b u t i o n on Si) allows f o r experimental d e t e r m i n a t i o n of the l o c a l environment of A1 in the amorphous a l l o y . REFERENCES D.J. Bishop, E.G. Spencer, J.P. Phys. Soc. 29 (1984) 343. J.A. Verges, Phys,Rev. L e t t .

Garno and R.C. Dynes, Bull.Am.

53 (1984) 2270.

D. A l l a n and J.D. Joannopoulos, Theory of e l e c t r o n i c s t r u c t u r e , i n : The Physics of Hydrogenated Amorphous S i l i c o n I I , eds. J.D. Joannopoulos and G. Lucovsky ( S p r i n g e r , B e r l i n , 1984) pp. 5-60. 4) L. Ley~ Photoemission and o p t i c a l p r o p e r t i e s , i n : The Physics of Hydrogenated Amorphous S i l i c o n I I , eds. J,D. Joannopoulos and G. Lucovsky ( S p r i n g e r , B e r l i n , 1984) pp.61-168.