INTERFACE JUNCTIONS AND SIMMETRY

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INTERFACE JUNCTIONS AND SIMMETRY

E. Doni, Ph. Komninou, G. Bleris, Th. Karakostas, P. Delavignette

To cite this version:

E. Doni, Ph. Komninou, G. Bleris, Th. Karakostas, P. Delavignette. INTERFACE JUNC- TIONS AND SIMMETRY. Journal de Physique Colloques, 1990, 51 (C1), pp.C1-121-C1-125.

�10.1051/jphyscol:1990117�. �jpa-00230274�

COLLOQUE DE PHYSIQUE

Colloque Cl, supplement au n o l , Tome 51, janvier 1990

E.G. DONI, PH. KOMNINOU, G.L. BLERIS, TH. KARAKOSTAS and P. DELAVIGNETTE*

Department of Physics, Aristotle University of Thessaloniki, GR-540 06 Thessaloniki. Greece

"service de Physique des Surfaces, Universite Libre de Bruxelles, C.P.

234, Bd du Triomphe, B-1050 Bruxelles, Belgique

Rbumc!

-

Des jonctions triples de haute symdtrie sont examinees par MET dans le silicium. Les propriQds de symdtrie des grains et de leurs interfaces sont dtudides sur base du modble de CSL.

Des jonctions de flexions suivant < 110> de type t(3,3,9), 1(3,9,27a) et t(3,27a,81 d) sont examinees;

elles contiennent toutes une t = 3 avec interface {l 11 ). La relation des interfaces avec les CSL et la symdtrie des jonctions triples est analysee en details.

Abstract

-

High symmetry triple junctions in polysilicon observed by TEM are presented. The sym- metry properties of their grains and interfaces are studied with the use of the CSL model. The ex- amples concern triple junctions of c 1 10> tilt boundaries with the CSL configurations of t(3,3,9), t(3,9,27a) and t(3,27a,81d). In all the cases the 1 = 3 twin with interface the (111) plane is at least one of the components. The connection of the interfaces with the CSLs and the symmetry of the triple junction is analytically discussed.

1

-

INTRODUCTION

Polycrystalline Si forms generally planar grain boundaries. From a previous study of GBs in polysilicon using transmission electron microscopy (TEM), we have found that some systematic symmetry properties exist be- tween the grains in the triplets of thermodynamically favorable boundaries /l-3/. The method used for the study of these triplets is based on the analytical form of the CSL rotation matrix R describing each bicrystal /4/

and on the symmetry of the corresponding CSL in relation to the symmetry of the parent lattice /5-6,'. A theoretical study of triple junctions, which has been appeared recently, resulted to some analytical expressions of the matrix elements of one of the CSL rotation matrices describing a bicrystal in the junction as the product of the other two matrices and also to a symmetry classification of the triple junctions in the cubic system 17-8/.

In this paper, we analyse high symmetry interfaces in polysilicon. The examples given concern the triplets of

< 110> tilt boundaries with the CSL configurations of t(3,3,9), 1(3,9,27a) and t(3,27a,81d) which are the most commonly observed in this material. Each junction contains the t = 3 twin with interface the {l 11) plane as at least, one of the components and the interfaces are microscopically special faces for each grain. By the term

"special" face we characterize a boundary face which can be repeated by symmetry. A triple junction of such boundaries is called "special triple junction".

2

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THE c 110> TILT GRAIN BOUNDARIES IN POLYCRYSTALLINE Si

The majority of the observed intergrowing GBs in polysilicon form junctions composed by 1=3" bicrystals. In these junctions the adjacent grains are in perfect CSL orientation relationship. In all the cases the t = 3 twin is at least one of the components.

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The most commonly observed junction is the t=3,3,9 special triple junction, where the interfaces of t = 3 twins are the { l 11) planes, the t = 9 being the (221) plane. All the interfaces are special faces for each grain.

Two different configurations of this system have been observed and are shown in Fig. l a and l b in edge-on orientation. In both cases the common intersection is the c 110> axis for all the component grains.

- A second typical example of special triple junction is the 1=3,9,27a junction which is usually formed as an in- tergrowing system of crystallites between two large grains with a perfect t=27a relationship, intersecting along the < 110> axes, as it is illustrated in Fig. 2. The interfaces of the t=27a CSLs are the (552) planes, the inter- faces of t = 9 are the (221)/(411) planes, while the t = 3 twin has the { l 11) interface. All the interfaces are also special faces for each grain.

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A different example concerning the t=3,27a,81d junction is given in Fig. 3. The common intersection axis is the < 110> axis. The only special face is the (1 1 1) interface of the t = 3 GB, while the 1=27a and t = 8 1 d GBs are not macroscopically planar but have also the character of the intergrowing crystallite systems.

( l ) work supported by the No ST2J 0289 European Community Contract

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1990117

Cl-122 COLLOQUE DE PHYSIQUE

a b

Fig. 1

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a. b. Two different configurations of the Z=3,3,9 triple junction in edge-on orientation.

Fig. 2 - A Z=3,9,27a junction as an intergrowing system of crystauites between two large Z=27a grains in edge-on orientation. a. TEM micrograph. b. Schematic illustration.

Fig. 3 - A Z=3,27a,81d triple junction. The 2 = 3 CSL is the only one having a special face.

3

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SYMMETRY PROPERTIES OF TRIPLE JUNCTIONS

In a given crystal lattice the possible special triple junctions with a symmetry axis as a common intersection can be constructed theoretically using the following steps:

a. All the multiple lattices of the parent lattice containing this symmetry axis are constructed and classified in an increasing Z value according to their symmetry. The different variants of each multiple lattice, within the parent lattice, are determined in connection with their generating groups /5/. Therefore each multiple lattice is taken in all its equivalent orientations by symmetry.

For analysing the examples of Fig. 1 and 2 the symmetry elements, transformed in their different variants, of X = 3 , E = 9 and Z=27a multiple lattices are given in Tables 1,2 and 3.

In these tables, H is the maximal invariant subgroup, defining the common symmetry between the multiple lat- tice and the parent cubic lattice, in the system of the parent lattice; h is an element, defined also within the parent lattice, corresponding to a 180' operator such that: a bicrystal having as CSL the corresponding mul- tiple lattice is formed by its action. The symmetry group

GC%

of the

CSL

/6/ is given by the relation:

The elements of H and h are transformed from one variant to another through the relations:

and

where g is the corresponding generating element of the variant, i= 1,2, ...,p and p =

1

^G

I / (

H

1,

the index of H in G (G is the symmetry group of the parent lattice), for all the variants.

A common intersection axis is found from the section:

where Hi and Hiare taken from equation (2).

Cl-124 COLLOQUE DE PHYSIQUE

b. In order to construct all the possible junctions of a given triplet of t values about this common axis all the combinations of the variants having as an intersection this axis are considered. The special junction is formed by the construction of the special faces of the corresponding boundaries in each grain.

Table 1

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The symmetry elements of the t = 3 multiple lattice transformed in the four different variants of t = 3 . The different variants are represented by the subscript i, i= 1,2,3,4 and the superscript 3 represents the t value.

3 ~ i , i = 1,2,3,4 3hi = C2ri

r, = [ l 1 l] , [121], ['ill], [ l 151 r2 = [ l i l ] , [121], [ Z i i ] , [iTZ?]

r3 = [~ITI, [j_ZTl, [PIT], [l121 r4 = [l 1 l] , [121], [21 l] , [TlZ]

Table 2

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The symmetry elements of the t = 9 multiple lattice transformed in the twelve different variants of 1=9.

The different variants are represented by the subscript i, i= 1 ,...,l2 and the superscript 9 represents the E value.

'Hi, i = 1 ,...,l2 9h.= I

c

^{zrr . 'Hi, i = 1 ,...,l2 'hi = C,,}

9 ~ 1 =

t

E, C,

1

r, =

[z!T],

[:TT] 9 ~ 7 =

1 ^E,

,C,

1

^{r, =} [2i2], [l471 'H, =

t

E, C,,

1

r2 = [1221, = {

E,

,C,

1

r8 = [!22], [ T i l l 'H3 =

t

E, ,C, ) r3 = [212], [T~I] =

t

E, C

,

^{} rg =} [ 2 g l , [l411 'H, =

t

E,

I

^{r4 =} [1$2], [~III _gHiO 9~ ₌ = { E,

E, , ¹

r,, = [2211, [l141 'H5 =

4

E, ) r, = [212], [T4i]

g,,''

i

E, C,, } r,

,

⁼ t2211, [l141

{E,C2f} r, = [I 221, [4TT] 12 = { E,

1

rl, = [221], [ i l Z ]

Table 3

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The symmetry elements of 1=27a multiple lattice transformed in the twelve different variants of t=27a. The different variants are represented by the subscript i, i=1,

...,

12 and the superscript 27 represents the t value.

2 7 ~ = { E, C2a

1

r

,

= [552], [ j i s ] 2 7 ~ -

2 7 ~

-

2 7 ~ ⁷ - { E l C,- ,} r7 = [E%], [l371

2 - {ElC2d} r2 = [ ~ ~ I , [ ~ ~ ~ I 8 - ( E$ '2, r8 = [255], [511]

2 7 ~ 3 = { E,

1

r3 = [525], [is11 2 7 ~ g = { E, C } rg = [?g$], [l511 2 7 ~ 4 = { E,

1

r4 = (2551, 151 l ]

2 : ~ ~ ~

^{= { E,}

¹

^{rfo =} [552], [l151

=

4

E, C., r5 = [5251, [T5Tl H,, =

E,

CPb) r,, = [552], [TT51 2 7 ~ 6 = { E,

1

r, = (2551, [51 l] 2 7 ~ 1 2 = { E, r,, = [5521, [ i l s ]

Based on these, the experimental examples are characterized as follows:

a. The I=3,3,9 special triple junction.

From Tables 1 and 2 and accordin to equation (4) the variants of I = 3 and t = 9 CSLs with the C (701 axis)

%

common are the 3 ~ , , 3 ~ 2 , 'H and HS. Since the t = 3 has as a special face in all the rains the @l

2

l} plane, the specific indices of these pTanes in each variant are taJen from Table 1 and are: in H the (1 11) and in 3 ~ 2 the ( l 17) in Fig. l a and in 3 ~ 1 the (1 11) and in 3 ~ 2 the (1 11) in Fig. l

b.

(The equivalent bylinversion kelernents have also be taken into account). For t = 9 the specific indices are: in 'H5 the (212) and in 'Hg the (212) in both Fig. l a and lb. The combinations of these special faces correspond to the dihedral angles of the configura- tions of Fig. 1.

b. The 1=3,9,27a special triple junction.

Following the same procedure the intergrowing system of Fig. 2 is analysed.

Ibis

system forms two special triple junctions with the CSL configuration of 2(3,9,27a). By considering the C,, (101 axis) as the common axis in both junctions the boundary planes of the I = 3 , t = 9 and t=27a CSLs are found from the combinations of the variants 3 ~ 1 , 3 ~ 2 , 9 ~ 5 , 'Hg, 2 7 ~ and 2 7 ~ 9 , which have the C,, element common. The specific indices for each special face are taken from ~ & l e s 1, 2 and 3. These indices for th_e planes of the boundaries of the first junction l-in Fig. 2 are: in 3 ~ 1 the (1 1 l), in 3~ the (1 l l ) , in 'H the (141), in 9 ~ g the (141), in 2 7 ~ the (525) and in ,$H, the (5

I

5). The specific indices of the planes of theBoundaries of the second iunction h - i n Fio. 21

are: in 3 ~ 1 the (11 l), in 3 ~ 2 the ( l i l ) , in 'H5 the

@is),

in 'Hgthe (2i2), in 27~, the (525) and in 2 7 ~ 9 the (525).

All these are illustrated schematically in Fig. 2b.

c. The 1=3,27a,81 d triple junction.

In this junction of the three large grains the 1 = 3 boundary is the coherent twin and the 1=27a is expected to have the characteristics of that of Fig. 2. Since the boundary of the Z=81 d contains also a system of intergrow- ing crystallites, a possible theoretical explanation, on the basis of the ideas of this work, may also be given.

Each intergrowing crystallite of the 1=81d might form a system of 1(9,9,81d) or E(3,27a,81d) CSLs. Thus, the system of 1=3,27a,81d CSLs is microscopically analysed to a system of triple junctions composed of com- binations of 1 =3" bicrystals about a common < 1 10 > axis.

4

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CONCLUSION

The symmetry properties of <110> triple junctions in polysilicon have been analysed. In all the examples the model of the perfect CSL orientation relationship between the grains has been adopted. The boundaries were special faces (macroscopically or microscopically) for each of the component grains and were also normal to the 180' rotation axes describing the adjacent bicrystals. It has been prooven that there is a well defined rela- tion between the existing intergrowing crystalline systems which is a group

-

subgroup connection typical to any disymmetrization

-

symmetrization process.

REFERENCES

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/3/ Komninou, Ph., PhD Thesis. Univ. of Thessaloniki, Greece (1987).

/4/ Bleris, G.L. and Delavignette, P., Acta Cryst.

A37

(1981) 779.

/5/ Van Tendeloo, G. and Amelinckx, S., Acta Cryst.

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(1974) 431.

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110

(1988) 383.

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