IMPERFECT AMORPHOUS SOLID AND BIPOLARONIC GROUND-STATE

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IMPERFECT AMORPHOUS SOLID AND BIPOLARONIC GROUND-STATE

B. Chakraverty

To cite this version:

B. Chakraverty. IMPERFECT AMORPHOUS SOLID AND BIPOLARONIC GROUND-STATE.

Journal de Physique Colloques, 1981, 42 (C4), pp.C4-749-C4-752. �10.1051/jphyscol:19814164�. �jpa-

00220788�

CoLZoque C4, suppLdment au nOIO, Tome 42, octobre 1981 page C4-749

I M P E R F E C T AMORPHOUS S O L I D AND B I P O L A R O N I C GROUND-STATE

B.K. Chakraverty

Groupe des Transitions de Phases, C.N. R.S., B. P. 166, 38042 GrenobZe Cedex, France

Abstract

It is generally considered that the Polli-model of an infinite random network of per-.

fectly bonded amorphous solid does not explain the "real" amorphous silicon which con- tains dangling bonds, vacancies, voids and fine scale inhomogeneities. The questio:l naturally arises as to the nature of the predominant defect in a-Si that would explain possible Fermi-level pinning and the recombination characteristics. Presuming an iso- lated dangling bond

(4)

to be such a defect, ~dler-Elliott have postulated negative U centers on such defects to explain Fermi-level pinning and other properties. Recent experiments as well as detailed calculations do not however support the existence of negative U in a-silicon. In this communication I like to point out that basic defect

"unit" is not an isolated dangling bond, but a dangling bond cluster of which the simplest unit is a vacancy center

4

that has only two near-neighbours i.e. a center with two dangling bonds that can locally deform to give bonding. This stable bonded

6

center is a bipolaron and provides all the ingredients to understand a variety of two-electron states phenomena in a-Si. The neutral centers will be deep in the gap.

The two related charge states V; and

v;

with respectively one and three electrons will also be gap states and are responsible for light induced e.s.r. signal. The V$ center?

can trap two hydrogen atoms to give (SiH)2 complexes in contrast to Si-H bonds. A doubly ionised

9

^center

(v)

can trap two electrons to go into a metastable He-like configuration and can explain Staebler-Wronski effect. a-Si in general will contain both

4

centers as well as isolated dangling bonds ( ~ 9 ) whose mutual interaction can explain a variety of radiative and non-radiative phenomena. The neutral centers will tend to empty nearby

'Iq

centers, will cause light-induced e.s.r. quenching of the T?

centers. They will be also responsible for Staebler-lronski effect as well as for quenching of luminescence and photoconductivity.

INTRODUCTION

It is now admitted that amorphous silicon is far from perfect in the sense of the Polk-model of a perfectly connected tetrahedral network. Real amorphous silicon con- tains dangling bonds, vacancies, voids and inhomogeneities on fine scale as revealed by high resolution electron microscopy. Weaire-Thorpe model of the connected four- fold network has no defect states in the band gap. Results ( 1 ) on non-hydrogenated evaporated amorphous silicon shows a large density of unpaired spins. Hydrogen effu- sion experiments (2) on glow discharge a-Si:H reveal about one unpaired spin created for about a hundred hydrogen atoms given off and which suggest that most of the defect-spins are paired.

Adler (3) as well as Elliott (4) have suggested that the predominant defect in a-Si could be a negative charged dangling bond with two spin-paired electron (T3 center) and assume a negative correlation energy U. Considering that the bare on-site Coulomb repulsion energy (5) on a silicon sp3 orbital U is % 7 eV, it seems unlikely one will have a negative U. Unhybridisation, as suggested by Adler-Elliott can certainly occur and if it does, we get an Ueff still positive and is estimated at least 1 eV. Recent

luminescence experiments ( G ) and calculations (7) do not point out to negative U

either. An alternate defect model has been put forward by Hirose ( 8 ) et a1 that con- sist of a double vacancy. However creation energy of such a vacancy-pair is of the order of 7 eV, and is considered to be unlikely except in irradiated silicon.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19814164

C4-750 JOURNAL DE PHYSIQUE

A d e e p i n s i g h t i n t o a-Si c a n be g a i n e d by e n q u i r i n g i n t o two r e l a t e d f i e l d s

-

f r e e s u r f a c e s o f c r y s t a l l i n e s i l i c o n and i r r a d i a t e d s i l i c o n . I n b o t h c a s e s , we s e e no e v i d e n c e o f TT c e n t e r ; on t h e c o n t r a r y b o t h (100) and (111) s u r f a c e d a n g l i n g bonds r e c o n s t r u c t i n t o d i m e r s , w h i l e d i m e r s a r e s e e n i n double-vacancy complexes o f i r r a - d i a t e d s i l i c o n . S i l i c o n i s a non-polar m a t e r i a l ; b e c a u s e of i t s f u n d a m e n t a l l y cova- l e n t n a t u r e i f a n y t h i n g it w i l l t e n d t o r e a r r a n g e i t s d e f e c t s i n t o bonds o r s i n g l e t p a i r s t a t e , where c h a r g e t r a n s f e r i n g c a n be a v o i d e d . S i p o l a r o n s ( 9 ) a r e j u s t s u c h an u n i t .

BIPOLARONS AND V: CENTERS

F i g . 1 shows a t y p i c a l b i p o l a r o n e n v i s a g e d ( c a l l e d a V$ c e n t e r ) c r e a t e d o u t o f two non-near neighbour s p 3 o r b i t a l s around a s i n g l e doubly-coordina- t e d vacancy ( i n t h e nomenclature V s t a n d s f o r a vacancy, t h e sub- s c r i p t 2 f o r i t s c o o r d i n a t i o n ) . The b a s i c assumption i s t h a t i n a-Si we have a v a r i e t y o f weak- bonds w i t h o n l y two o r t h r e e n e i g h b o u r c o n E i g u r a t i o n s i n which vacancy c r e a t i o n i s e a s i e s t a t a c o n f i g u r a t i o n o f o n l y two n e i g h - bour atoms % and

?.

The b i p o l a - ron bond a-b s e r v e s e s s e n t i a l l y a s a b r i d g e between two d i s c o n -

Fig :I ^{V ;} C e n t e r a n d b e n t bond

n e c t e d b u t o t h e r w i s e 4"Si- o r d e r e d domains. A bouncl s i n g l e t s t a t e w i l l be a c h i e v e d p r o v i d e d t h e t r a n s f e r i n t e g r a l Tab i s a p p r e c i a b l e w i t h r e s p e c t t o t h e i n t e r - s i t e Coulomb r e p u l s i o n Vab. The b i p o l a r o n bond

( b l > ) shown i n F i g . 1 i s a b e n t bond, c o n t a i n i n g e q u a l amount of 0 and n c h a r a c t e r ( b t > = ( 0 ^{2 il)/}

fi).

T h i s i s i n c o n t r a s t t o t h e p u r e 0 - c h a r a c t e r of t h e near-neigh- b u r sp3 i n t e r a c t i o n i n p u r e s i l i c o n . The t u n n e l l i n g i n t e g r a l Tab a t r a b = 4 i s e v a l u a t e d by t h e u s u a l e x t e n d e d Hiickel method, used r e c e n t l y by H a r r i s o n ( 1 0 ) . tie have :

Tab =

(

's

-

^€3) _{where S i s} t h e o v e r l a p i n t e r a c t i o n f o r t h e b e n t bond 1

-

s 2 _E

-

^E i s t h e s - p promotion e n e r g y .

and Vab = 2 S T~~ S P

I n t h i s way we o b t a i n : Tab = 0 . 2 5 eV Vab = 0.06 eV

The s i n g l e t s t a t e o f t h e V$ i s s t a b i l i s e d w i t h r e s p e c t t o a T3 c e n t e r (whose e n e r g y 0 i s t a k e n a s z e r o of r e f e r e n c e ) by Eat, = Vab - J where J i s t h e exchange i n t e g r a l

4 T~~~ / U e f f . T h i s g i v e s u s a bound s t a t e a t

-

0.18 eV. The one ( ~ 3 )

,

two

(9)

and t h r e e

(3)

e l e c t r o n c e n t e r s w i t h t h e i r g r o u n d - s t a t e c o n f i g u r a t i o n e n e r g i e s a r e shown i n T a b l e 1 . D e t a i l s w i l l b e p u b l i s h e d e l s e w h e r e . T h e i r e s t i m a t e d v a l u e s a r e a l s o shown, u s i n g Ueff 1 eV. Here C: a r e t h e c r e a t i o n o p e r a t o r s , s t h e s p i n - s t a t e s and

[ 0 > t h e vacuum s t a t e ,

IG>

t h e g r o u n d - s t a t e , S t h e o v e r a l l s p i n s t a t e .

F i g . 2a g i v e s t h e p o s i t i o n s of ,:v V: and V; i n t h e s i l i c o n g a p , assuming t h e gap t o be 2 eV ( o f t h e o r d e r o f t h e d i r e c t g a p ) , t h a t we have p l a c e d s y m m e t r i c a l l y a r o u n d 0 . I n Fig. 2 a , d o t t e d d e n s i t y o f s t a t e s

6

and V; s i g n i f y t h a t t h e s e s t a t e s w i l l e x i s t o n l y i f t r a n s f e r o c c u r s between two

4

c e n t e r s . F i g . 2b shows t h e s i t u a t i o n when we have b o t h

4

c e n t e r s a s w e l l a s i s o l a t e d d a n g l i n g bonds, t h e

~9

c e n t e r s . Now t h e

s e r v e d (Kaplan e t a 1 ( I l ) , S t r e e t e t a 1

( 6 ) ) . The hv c o r r e s p o n d i n g t o t h c p r o c e s s i s (hv = AE = E V ~ + E ~ $ + - ~ E V ~ = 0.8 eV) :The e . s . r . s i g n a l s c o r r e s p o n d i n g t o V T and V$ c e n t e r s w i l l o c c u r a t f i x e d g - v a l u e s i n c o n s t r a s t t o what i s e x p e c t e d from b a n d - t a i l s t a t e s .

t y p e s of d e f e c t s , a1 though i n e v a p o r a - t e d amorphous f i l m s N T ~ >> N V ~ ( t h e dan- g l i n g bonds w i l l p r e d o m i n a t e ) .

T h e r e a r c s e v e r a l l i g h t i n d u c e d e f f e c t s t h a t can be u n d e r s t o o d from F i g s . 2 a , 2b and 2c.

I . l i g h t - i n d u c e d e . s . r . s i g n a l : AS F i g .

2. Light-quenched e . s . r . : When t h e r e i s d a r k e . s . r . a s i n F i g . 2 b , due t o d a n g l i n g bonds, a s i n e x o d i f f u s e d s i l a n e f i l m s , we o b s e r v e a l a r g e q u e n c h i n g o f e . s . r . s i g n a l

(Kaplan e t a 1 ( 1 2 ) ) due t o band-gap l i g h t . F i g . 2b shows how t h i s c a n a r r i v e i n a two s t e p p r o c e s s

I

' I

v+ I I

2 \ ' 1

I 1.2

I

Luminescence

a ) V2 0 + hv -> V; + e l e c t r o n i n t h e c o n d u c t i o n band b) V; + T$ -t T; + V$

2a shows, l i g h t w i l l p o p u l a t e

~2

and V;

I

l e v e l s , t h r o u g h t h e r e a c t i o n 2V?O+hv+

0

V; + VT. S i n c e V; and V Z have u n p a i r e d

.

F i g . 2. D e f e c t l e v e l s i n t h e gap.

.r;,4., Y L I L c I c L I L C . S . Y . W O U I ~ be ob-

The second p r o c e s s i s r e c o m b i n a t i o n of t h e d a n g l i n g bond e l e c t r o n w i t h a V$ c e n t e r . We n o t e t h a t i n t h e a b s e n c e o f V% c e n t e r s , a s i n e v a p o r a t e d amorphous f i l m s t h i s r e c o m b i n a t i o n w i l l n o t o c c u r and i n r e a l i t y no l i g h t q u e n c h i n k o f e . s . r . s p i n s i s s e e n w i t h e v a p o r a t e d amorphous f i l m s .

C4-752 JOURNAL DE PHYSIQUE

3. The last light-induced effect we shall talk about is the quenching of the 1.20 eV lrlo~inescence. We suggest that the luminescence is, as in Fig. 2c, due to light exci- ted conduction electrons falling into the V centers. This strong luminescence will be quenched, if the process b) of the previius aragraph occurs i.e. if

19

^{spin cen-}

ters already exist in large quantity so as to Tg + Y$ ⁺ T; +

VY

reaction predomina- tes. Increase of temperature would also quench this luminescence due to increased temperature-induced tunnelling of the T? centers into the

~3

levels. Besides the in- tense 1.2 eV luminescence, recombination

3

^{to V$} center will give an emission at

1 . 1 eV. If we add the 1.4 eV band-gap luminescence as well as that due to conduc- tion band electron to dangling band levels, we expect to see altogether four lunines- cence lines ; a group of four lines has recently been reported by EruyZre et a1 (13).

VZ centers also will serve as shallow electron traps providing for dispersive trans- port.

Space does not permit us to talk of V2 centers ++ ; strong illuminations will create these centers which in turn could capture two electrons to go into a metastable he- lium like configuration in the gap and may be the reason for the Staebler-llronski effect. VZ and

~3

formation will also be responsible for hindering the doping of donors and acceptors respectively. Finally strong proton-proton repulsion in a (SiH)2 complex within a

~4

center will provide weaker-sites for hydrogen seen in the effu- sion experiments (2).

References

I Thomas P.A., Brodsky M.H., Kaplan D. and Lepine D., Phys. Rev. B

18

(1978) 3059.

2 Biegelsen D.K., Street R.A., Tsai C.C. and Knights J.C., Phys. Rev. B

3

⁽¹⁹⁷⁹⁾

4839.

Also Zellama K., Germain P., Squelard S., Bourdon B., Fontenille J. and Danielou R., Phys. Rev. B, 1981, to be published.

3 Adler D., Phys. Rev. Lett.

41

(1978) 1755.

4 Elliott S.R., Phil. Mag. B

2

(1978) 325.

5 Casula F. and Selloni A., Solid State Comm.

37

^{(1981) 495.}

6 Street R.A. and Biegelsen D.K., 8th International Conference on Amorphous Semi- conductors, J . of Non-Crystalline Solids

2-%

^{(198C) 651.}

7 Allen D.C. and Joannopoulos J.D., Phys. Sev. Lett.

5

(1980) 43.

8 Hirose M. et al, 8th International Conference on Amorphous Semiconductors, 3 . of Non-Crystalline Solids

35-36

(1980) 297.

Hirose M., These Proceedings.

9 Chakraverty B.K., Sienko 11.J. and Bonnerot J., Phys. Rev. B

17

(1978) 3781.

10 Harrison M.A., Phys. Rev. B

3

^{(1981) 5230.}

1 1 Kaplan D., Proceedings 14th International Conference on the Physics of Semiconduc- tors, Edinburgh 1978.

12 Friedrich A. and Kaplan D., 8th International Conference on Amorphous Semiconduc- tors, J. of Non-Crystalline Solids

35-36

(1980) 657.

13 BruySre J.C. et al, These Proceedings.