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APPLICATION OF THE MOLECULAR ORBITAL SELF-CONSISTENT-FIELD METHOD TO THE
STUDY OF a-Si
L. Sansores, E. Cetina, J. Tagueña-Martínez
To cite this version:
L. Sansores, E. Cetina, J. Tagueña-Martínez. APPLICATION OF THE MOLECULAR ORBITAL
SELF-CONSISTENT-FIELD METHOD TO THE STUDY OF a-Si. Journal de Physique Colloques,
1981, 42 (C4), pp.C4-823-C4-826. �10.1051/jphyscol:19814181�. �jpa-00220807�
JOURNAL DE PHYSIQUE
CoZZoque C4, suppZdrnent au nO1O, Tome 42, octobre 1981 page C4-823
APPLICATION OF THE MOLECULAR ORBITAL SELF-CONSISTENT-FIELD METHOD TO THE STUDY OF a-Si
L.E. Sansores, E .A. Cetina and J . ~ a g u e i i a - ~ a r t i n e z
Institute de Investigaciones en MateriaZes, UNAM, Apartado PostaZ 70-360,
~6zico 20, D. F.
Abstract.- The molecular selt-consrstent-field method (MOSCFM) together with the cluster model has been proved very successfully to obtain electronic properties of sol~ds(1). The MOSCFM is
essentially a tight binding LC3-OCPIC.3 type of approximation an6 the use of the cluster model simplifies enormously the computa- tion in systems without symmetries. In this work the MOSCFM is applied to the study of amorphous silicon tetrahedrally coordi- nated clusters Si8H18, the role of the hydrogen being to satur- ate the bonds. The energy spectra, band gaps, bond indices and atomic orbital populations are calculated. The results are sat- isfactory and the method can be easily extended to study the hydrogenated amorphous silicon.
Introduction.- Many properties of the solids depend on the local environmentrather than on the large range order, that is why works that study clusters have given remarkably good results. In particular, Cartling(2) and later Hemstreet(3) using Xa scattered wave method have investigated the crystalline and doped Si. They have used a SiSHj7
+.-
cluster, where the central Si atom is tetrahedrally coordinated to four nearest-neighbor Si atoms, each of which is saturated by three hydrogen atoms at a distance equal to the normal Si-Si distance. The purpose of the hydrogens is to saturate the otherwise dangling bonds, not to simulate hydrogenated Si.
On the other hand,MOSCFM has been used very successfully to ob- tain electronic properties of solids. For instance, using semiempiri- cal complete neglect of differential overlap (CNDO) calculations, Bock et al(4) studied n-silanes molecules reproducing quite accurately ex- perimental results as the band gap.
In this work we have combined a CNDO calculation with a cluster model for the amorphous silicon. We have reproduced the above men- tioned, CNDO'S silanes results and those for the Si5H12 molecule. We only calculate the eigenvalues for k=O, which turn out to be in rea- sonable agreement with the theoretical band scheme for crystalline Si(5). To simulate the amorphous Si, we have chosen the Si8H18 tetra- hedrally coordinated molecule. We have also studied a Si10H20 cluster in order to analyze the effect of different cluster and ring sizes.
Our calculations give the energy spectra, band gaps, bond indices and atomic orbital population.
Model and Results.- Crystalline silicon presents atoms tetrahedrally
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19814181
JOURNAL DE PHYSIQUE
TABLE I
S t a g g e r e d E c l i p s e d
Bond I n d i c e s 2.805 3.289
( v a l e n c y )
c C e n t r a l s 1 . 7 8 2 1 . 5 6 8
4
S i a t o m s p 0 . 7 2 3 0.7553 i
2
E x t e r n a l s 1 . 7 8 7 1 . 7 9 42 8
S i a t o m s p 0 . 7 1 6 0.746l a ) ( b t ( c l
F i g . 1 S i l i c o n c l u s t e r ( a ) S t a g g e r e d p o s i t i o n ( b ) E c l i p s e d p o s i t i o n (c) D i h e d r a l a n g l e a marked i n a f r o n t a l v i e w o f t h e s t a g g e r e d c l u s t e r .
F i g . 2 E n e r g y l e v e l s f o r i n t e g e r v a l u e s o f t h e d i h e d r a l angles of the S i 8 H I 8 c l u s t e r .
0--
-lo--
--- - - ---
- ---___-__---- -
- _ _ __ __________---
, --===== E-^----================ - -
CRYSTALLINE S i BAND GAP
I-====-=---
---- --- --- - --- ----
- --- ---- --- -
--- - -,
--- -
----_
-____---- ---
--
- -_=- ---3z---z--r-=f---
-- --
---- ----_ ---
--- -,=
----==----=E=3==----rZ-- -
---
_---_---- -
--
-_ _ __ --
--__---
-
-
-----
-__-_--_--_---
-
-A_----_----_--_ -
2 5 2 2 2 4
2
196f
168j 140 w 0
112 8 4 5 6 2 8 0
-30.00 -23.00 -16.00 -9.00 - 2 . 0 0
ENERGY ( r v )
Fig.3 Energy levels histogram of the Si8H18 cluster. All integer dihedral angles have been considered. Cell w i d t h = 0.25 ev.
- 3 0 . 0 0 -23.00 16.00 - 9 . 0 0 - 2 . 0 0
ENERGY ( r v )
Fig.4 Energy levels histogram of the Si10H2Q cluster with 5 and 6 atom rings. Cell width=0.25 ev.
C4-826 JOURNAL DE PHYSIQUE
bonded in what is called a staggered position. The amorphous silicon preserves the coordination and the interatomic distances change very little, but there are important angular changes: the dihedral angles varies from a staggered to an eclipsed position (see fig. 1).
Our model consists of a Si8H18 cluster, where the silicons are as in figure 1 and all the free bonds of the external Si have been saturated with H. Using the CNDO method we have calculated the energy levels for every integer value of the dihedral angle from 60" to 0'. The energy levels are shown in fig. 2, for the even angles. It is very interesting to see how new states appear inside the gap. There is also a jump of the levels at 40° and 20'. This effect is related to the so called rotation barriers. Enerqetically some positions are more favorable than others and the crystalline one is the most favor- able of all. We have analysed the total energy of the system and it is consistent with this result. Considering that the amorphous system presents all the possible diheral angles, in fig. 3 an histogram is shown where all the configurations have the same probability of occur- rence. This histogram is clearly related to the density of states. An interesting structure appears on the border of the band gap.
It has been pointed out the importance of the ring size for the properties of the amorphous systems(6). In the crystalline Si only
6 atoms rings are present, while in the amorphous case 5 and 7 atom rings can appear due to the eclipsed situation. In order to study the ring size effect, a SiZOHZO cluster was considered. First the en- ergy Spectra of a 6 atom ring that appear in crystalline Si was calcu- lated. Then with 4 rotations a 5 atom ring was created (this reduces the cluster to a Si9H18 molecule). Both results are combined to sim- ulate the amorphous denslty of stated,fig. 4. Again, new states ap- pear in the gap, giving a very good qualitative description of the effect of disorder.
The bond indices and atomic orbital population for the eclipsed andstaggered Si8H18 are shown in Table I.
Conclusions: We have presented a relatively simple CNDO calculation of a cluster model for the amorphous silicon. Our work gives a good description of the disorder in the energy spectra in the appearance of new states within the energy band.
The main difference of the Si8H18 and Si10H20 results is that the band gap is smaller in the bigger cluster. This is due to the fact that SilOHZO involves more than one unit cel1,thus new levels appear reducing the AE33.43 ev. result. It is clear that in the Si,,H,, there are many possible intermediate configurations that we
A "
-"
have not considered yet. Research is in progress for the hydrogenated a-Sir using the SilQH20 molecule as Johnson et al(7) have done in smaller clusters uslng X method.
a References:
1.- PERKINS P.G., STEWART J. J.P., J.C.S. Faraday I1
16
(1980) 520 2.- CARTLING B.G., J. Phys. C: Solid State Phys.8
(1975) 3171 3.- HEMSTREET L.A., Phys. Rev. B15
(1977) 8344.- BOCK H., ENSSLIN N., FEHER F., FREUND R., J Am. Chem. SOC.
98:3
(1976) 668
5.- COHEN M.L., BERGSTRESSER T.K., Phys. Rev.
141
(1966) 789 6.- THORPE M.F., WEARIE D., ALBEN R., Phys. Rev. B 7 (1973) 3777 7.- JOHNSON K.H., KOLARI H.J., DE NEUFVILLE J.P.,MGREL
D.L., ~ h y s .Rev. B
