A NEW APPROACH OF AMORPHOUS

SEMICONDUCTORS STRUCTURE USING CURVED

SPACES

J. Sadoc, R. Mosseri

To cite this version:

J. Sadoc, R. Mosseri. A NEW APPROACH OF AMORPHOUS SEMICONDUCTORSSTRUCTURE USING CURVED SPACES. Journal de Physique Colloques, 1981, 42 (C4),pp.C4-189-C4-192. <10.1051/jphyscol:1981438>. <jpa-00220895>

HAL Id: jpa-00220895

https://hal.archives-ouvertes.fr/jpa-00220895

Submitted on 1 Jan 1981

HAL is a multi-disciplinary open accessarchive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come fromteaching and research institutions in France orabroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, estdestinee au depot et a la diffusion de documentsscientifiques de niveau recherche, publies ou non,emanant des etablissements d’enseignement et derecherche francais ou etrangers, des laboratoirespublics ou prives.

JOURNAL DE PHYSIQUE

CoZZoque C4, supple'ment au nOIO, Tome 42, octobre 1981 page C4-189

A NEW APPROACH OF AMORPHOUS SEMICONDUCTORS STRUCTURE U S I N G CURVED

SPACES

J.F. Sadoc and R. ~osseri*

Laboratoire de Physique des Sotides associe' au C. N . R. S., Universite' Paris- Sud, BGtiment 510, 91405 Orsay Cedex, France

* Laboratoire de Physique des Sotides - C.N.R.S., 1, place Arist ide Briand, 921 90 Meudon, France

Abstract.- We present a description of amorphous structures using regular arrangement in curved spaces to describe the local order. Defects and disor- der ariserrom the mapping of the curved spaces onto the euclidian space. Density variations are qualitatively explained by this description.

I. Introduction.- The current interest in amorphous semiconductor structural model is to try to go beyond the continuous random network (CRN) approach. The CRN model is known to describe qualitatively well the mean structure of most amorphous semi-con- ductorsbut it fails to account for observed or suppposed defects present in real ma- terials. Several new properties have been recently emphasized like the possible dua- lity and decoration transformations between networks (1) or the occurence of discli- nation line defects associated with ring parity (2). This paper presents a new des- cription of amorphous structures which starts from a different point of view. How- ever the above mentioned new aspects play a significant role in this model.

11. Ordered structures in curved spaces

1. Close packed structures.- It is known that a tetrahedral arrangement yields to the closest packing of 4 spheres. However a complete space filing with a packing of tetrahedra cinnot be realized. A perfect tiling'becomes possible-if the space iH given a certain curvature. This is similar to what happens in 2D with pentagons. A plane surface cannot be covered'by 5 fold rings without defects while this is possi- ble on a spherical curved surface leading to a dodecahedron. As in this 2D example where a regular polyhedron is the solution for the covering of a surface by regular pentagons, the covering of a 3D space by regular tetrahedra.is realized by a polyto- pe. The polytope obtained when packing tetrahedra is described by Coxeter (3), it is called (3,3,5), using standard notation, but we shall sometimes refer it asthe poly- tope "120" (it has 120 vertices and 600 cells).

We postulate that polytopes (and more generally regular tesselations in cur- ved spaces) are a model for an amorphous structure with a given local order. Defects and disorder arise from the mapping onto the euclidian space. Such a procedure has been previously described in different papers (4,5).

2. Tetracoordinated polytopes.- We shall start from the "120" polytope to build new polytopes which are attractive for the description of tetracoordinated semicon- ductors.

The (5,3,3) polytope.- If we put a vertex at the center of each of the 600 cells of the (3,3,5) and forget the 120 original vertices, we obtain the dual poly- tope called (5,3,3)(3) or polytope "600". It contains 600 vertices and 120 cells which are dodecahedra (the dodecahedron is the dual polyhedron of the icosahedron). Each vertex which is four-fold coordinated, Belongs to three dodecahedra and six- five fold rings. The local order corresponds to the famous "amorphon" of Grigorovici. Stereoscopic views of parts of the (5,3,3) can be seen on fig 1. Although the amor- phon picture alone is now rarely used to describe the amorphous Si structure, the

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1981438

JOURNAL DE PHYSIQUE

(5,3,3) polytope may be of a great use to study the properties induced by the presence of 5- fold rings.

he "3 000" - polytope.- If we replace each vertex of the "600" polytope by a small centered tetrahedron of defined edge-length, we obtain a 3 000 tetracoordinated polytope. This structure contains a mixing of 5-fold and 6-fold rings, which can be seen on the stereoscopic view (fig 2). The local order corresponds to the hand built model of Dando- loff et a1 (6) and consists of packing of dode- cahedra and small clusters of 15 vertices called "barrelans". The method used in obtai- ning the 3 000-polytope startingfrom the (5,3,3) polytope is similar to a site decoration of a topological network.

Fig1-Viewo artofthe The "240" polytopef'.- Back to the (3,3,5) {5,3,5f ;ofytope.

polytope (the 120 12-fold coordinated vertF polytope), we now build a new tetracoordinated structure containing 6-fold rings only. This polytope is obtained using the same rule which allows to get the diamond structure starting from the FCC structure: that is to sa)r to put a new vertex in the center of some tetrahedral cells. In fact one tetrahedron over five will be centered. The obtained 120 new vertices belong to another (3,3,5) polytope as for the diamond structure case where the new vertices belong to another FCC structure. This is ano- ther example for the possible transformation from a closed packed structure to a 4-fold coordinated structure. The importance of such transformations has been recently pointed out by Zallen (7). The whole structure (called the "240" polytope) contains 240 vertices, even rings only, the shortest ones being dis- F i g 2 - View of a part of the torted 6 "boat" rings (fig 3). "3000" polytope. A

The three above illustrations are ortho- "barellan " is darkened. gonal maps of small parts of the polytopes.

111. Mapping procedure.- We now look at the way of producing realistic 3D structures. An orthogonal mapping of the whole polytope from the 3D curved space to the 3D euclidian space gives rise to large distortions of bond lengths and bond angles and thus it cannot be used here. Threrefore,we shall use a "star projec- tion" in order to minimize these distortions. A simple example of star mapping in 2D is the peeling of an orange down to a table. We have to pay the price for the small distortions by creating cuts into the structure : - line cuts for an orange (or any 2-sphere). This is illustrated on fig 4 ; - surface cuts for the polytope.

The star-mapped polytope looks like a "sea-urchin" with the atoms belonging to lobes. The.connectivity of the polyto e is retained ~nslde the lobe,the atoms on tge surface having dangling bonds.

F i g 3 - V i e w o f a p a r t of the "240" p o l y t o p e . A 6 f o l d r i n g i s d a r k e n e d .

On fig. 52 one can see a view of one lobe of the tetracoordinated"240"polytope map- 0' ped along the four tetrahedral directions. This stick and ball structure has been constructed using the nearest-neighbour relationships of the computationally mapped polytope.

It is interesting to note the relation between the number of cuts and the distortion in the structure : large length distortions are associated with small cut area (and vice versa).

It is necessary to fill all the space in order to obtain realistic models. This can be achieved by adding new replica of the mapped poly- tope close to the first one. It is always possi- ble to keep some local order continuity between the first and the second map in a limited region. However some discontinuities remain and give rise to internal surfaces in the structure. We obtain

- elastic distortions which do not alter the space filling structures with two kinds of defects: Fig 4 - Mapping of a sphere

local topology, onto the plane. The - walls, where the local order is destroyed, which local order is retai- are tiled with dangling bonds. ned in the lobes.

It is rather tempting then to saturate these un- satisfied bonds with hydrogen atoms. The hydrogen content can easily be varied by slightly changing the mapping procedure.

An alternative mapping procedure consists of the introduction of disclination lines. Indeed these defects are associated with a change of the local curvature (8) and ring parity. This method leads to structural models presenting a smaller density of dangling bonds.

Density variation in a Sil-xgx.- It has

previously been observed by several authors (9) that the variation of density in Sil-xHx compounds

display two different behaviours when x increases, in spite of the large scattering of experimental data. The gross features of this variation (fig 6) are : - for x >0.1, the density exhibits a decrease when the H content increases. A linear approxi- mation can qualitatively describesthis beha- viour. A remarkable ~oint is that the extrapola- tion of this variation to the zero H content leads to a value for the density significantly higher than the a-Si one ; Fig 6 - a-Si-H density.

- for x < 0.1, we suppose a smooth variation bet- Experimental values are taken from dif-

ween the two experimental values for x = 0 and ferent authors (see x = 0.1. ref 9).

These results have to be explained by topo- logical arguments since the Si-Si first distance is nearly constant for all compositions. The cur- ved space description presented in this paper can provide a qualitative explanation for the density variation. We have shown that defects are necessa- * Fig 5 : see on the next page. rily present in the form of internal cuts or dis- clinations lines. A variable amount of dangling

C4- 192 JOURNAL DE PHYSIQUE

or weak bonds are associated with these defects. The structure can accommodate itself to the incorporation of H atoms without a large change of the density. Indeed post-hydrogenation experiments (10) show that as much as 10 % of H atoms can be bon- ded into a pure a-Si matrix.

For x >0.1, we have to infer to the presence o f new internal surface cuts in order to bond more H atoms. All dangling bonds covering these new cuts are H saturated, leading to linear dependence of the density. In such structures the Si atoms, gathered in dense regions, have their local order similar to the ideal one in curved space, e.g. to the polytope short range order. This can explain why the extrapolated intercept of the density variation curve with the x = 0 axis leads to a value different from the crystalline case and even from the pure a-Si one. The obtained value refers to the density of the ideal structure, the polytope density. Among the three tetracoordinated polytopes, the so-called "240" polytope has a density about 5 % higher than the c-Si density and thus it is a good candidate for an a.Si-H structural model. It has to be noticed that this polytope contains many distorted boat shaped six fold rings with dihedral configurations intermediate bet- ween the eclipsed and staggered one. X-ray diffraction experiments (11) have shown that these configurations are frequent in a-Si H I-x x'

B I B L I O G R A P H Y

(1) - WRIGHT A.C., CONNELL G.A.N. and ALLEN J.W., Journ. N. Cryst. Sol., 42 (1980) 69.

(2) - RIVIER N., Philos. Magn., 40 (1979) 859. (3) - COXETER H.S.M., Regular Polytopes, Dover Publications, New York (1973).

(4) - KLEMAN M., SADOC J.F., J. de Phys. Lett., 40 (1979) L 569. (5) - SADOC J.F., Journ. N. Cryst. Sol., 44 (1981) 1.

(6) - DANDOLOFF R. et al, Journ. Non Cryst. Sol., 2, 5 (1980) 537. (7) - ZALLEN Z., Fluctuation Phenomena, ed. E.W. Montroll, J.L. Lebowitz (North

Holland - Amsterdam (1979)). (8) - HARRIS W.F., Scientific America, 237 vol 6 .(1977) 3.

(9) - JOHN P., ODEH I.M. et al, J. Phys. C : Sol. State Physics, 16 (1981) 309. (10) - D1EUMEGAR.DE D., DUBREUIL D., PROUST N., Proceedings 0f 8th International

Vacuum Congress, Le Vide, 201 (1980) 731. (11) - MOSSRU R., SELLA D., DIXMIER J., Phys. Stat. Sol. (a), 52, 1979) 475.

F i g 5 - One l o b e o f t h e 240-po ly tope s t a r mapped o n t o t h e 21 e u c l i d i a n space .