COMPUTATION OF STRUCTURE AND ENERGY OF THE Σ3 (21(-1)) TILT BOUNDARY IN SILICON

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COMPUTATION OF STRUCTURE AND ENERGY OF THE Σ3 (21(-1)) TILT BOUNDARY IN SILICON

Mohammed Cheikh, A. Hairie, F. Hairie, G. Nouet, E. Paumier

To cite this version:

Mohammed Cheikh, A. Hairie, F. Hairie, G. Nouet, E. Paumier. COMPUTATION OF STRUC- TURE AND ENERGY OF THEΣ3 (21(-1)) TILT BOUNDARY IN SILICON. Journal de Physique Colloques, 1990, 51 (C1), pp.C1-103-C1-108. �10.1051/jphyscol:1990114�. �jpa-00230051�

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COLLOQUE DE PHYSIQUE

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

COMPUTATION OF STRUCTURE AND ENERGY OF THE X3 (217) TILT BOUNDARY IN SILICON

M. CHEIKH, A. HAIRIE, F. HAIRIE, G. NOUET and E. PAUMIER

Laboratoire d l E t u d e s et de Recherches sur les MatBriaux, CNRS U R A 1317.

Institut des Sciences d e la Matiere et du Rayonnement, Boulevard du Mar6chal Juin, F-14032 Caen Cedex, France

Rdsume

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On compare entre elles differentes determinatjons experimentales et theoriques du yecteur de translation t du joint de grains de flexion 2 3 (211) dans le silicium. Un 2al- cul utilisant le potentiel de Keating donne un vecteur t et une structure atomique en tres bon accord avec le calcul de liaison forte de Paxton et Sutton et avec les determinations experimentales de Bourret et al. sur le germanium. Cela con- firme la validite du modele de Papon et Petit pour la structure atomique de ce joint de grains.

Abstract

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Different experimental and+ theoretical determinations of the rigid body translation t in the Z 3 (211) tilt grain boundary in silicon aFe compared. A calculation using Keating's potential gives a t vector and an atomic structure in very good agreement with Paxton and Suttonts tight binding calculation and with experimental determinations on germanium by Bourret et al. his confirms the validity of Papon and Petit's model for the atomic structure of this grain boundary.

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INTRODUCTION

The grain boundary structure in diamond-structure semiconductors has been studied during last years by different ways from theoretical and experimental points of view. Now, it appears that the intrinsic atomic structure is not the direct origin of any special electronic structure able to explain the electronic activity observed on some grain boundaries. In particular, no states have been found in the gap o f germanium, due to dangling bonds /l/. The electronic activity of some grain boundaries in silicon is attributed to precipitates

/2/. Thus the determination of the atomic structure of a grain boundary is useful to study its effects on impurity mobility and preci- pitation. Such atomic structure determinations have been performed by electronic microscopy (a fringes or high resolution electron microscopy) associated with theoretical models and are in agreement with reconstructed structures. These reconstructed structures do not show any dangling bond in silicon or germanium. However, some pro- blems may arise concerning eventual disagreement between the different determinations relative to a particular grain boundary. As an example, we have chosen the 2 3 (211) tilt boundary in silicon for which a great number of studies have been published. We have compared the different structures which have been proposed. In particular, we have compared the rigid body translation they give for the displacements of the two crystals with respect to each other. With the aid of Keating's model we have calculated the rigid body translation and we have compared the results with the experimental and theoretical determinations already known.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1990114

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COLLOQUE DE PHYSIQUE

I I I

$ 0 ;

;

^d ^o ⁰ ⁰

O 1 1 O O 1 0 0

t o o ; 1 0 0

0

0 0

0 ; I

"

⁰ ⁰

0 1 I

9

^{0 :} ⁰ ^o ^o

0 0

--

0

C 0

o c l I d 0 1 o o

C A 0 :

1

I

?

^O0 ⁰ ⁰

n c " I

0 0 ;

,

^p ^{o (} ⁰ ⁰

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1 1 1 1

Fig. 1 : Three relaxed structures of Z3 (21i) twin boundary are shown : the symmetric one (a) by Vlachavas and Pond /3/ and the non symmetric ones (b) and (c) proposed by Fontaine and Smith /5/ and by Bourret and Bacmann /11/ respectively. The last one is the bl structure of Papon and Petit /13/ with a double period along [lil] and is obtained by Paxton and Sutton /14/. (The distances between the atoms and the (011) plane are given in units of lattice constant a).

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The unrelaxed structure of the Z3 (21z) grain boundary in diamond structure may be seen in Vlachavas and Pond /3/ and Pond /4/ papers.

Several relaxed structures have been proposed for this grain boundary for interpretation of the observations by a fringes /3, 5-9/

measurements in Si or by high resolution electron microscopy in Ge /10, 11/. As noticed by Vlachavas and Pond /3/ the symmetric structure shown in Fig. la ("reflection twinv1) containing 5 and 7 membered cycles is not the only possible one. Non symmetric structures characterized by some displacement of the twin crvstal with respect to the matrix one are also possible. In such "translation twinw structures, the displacement is characterized by the rigid body translation vector t. Two of them are often used and they are repre- sented in Fig. lb /5, 6, 12/ and lc /11, 13, 14/. They differ from the symmetric one by a different disposition of the 5 and 7 membered cycles. They have been proposed to explain a fringes measurements

/ 5 , 12/ and electron microscopy observations /11, 13/.

The rigid body translation vector is usually given by its components t4 and t, respectively parallel and perpendicular to the boundary plane (21?). It is useful to note that a component along tilt axis [Oll] is sometimes given. Such a component may be obtained by the most precise measurement method using a fringes. It may be also obtained by high resolution microscopy if it is possible to observe similar specimens of different orientations /10/.

In the following discussion we compare results obtained on silicon or germanium : they have the same crystalline structure and moreover, they have elastic properties leading to Keating's potentials characterized by the same ratio of stretching to bending components.

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COMPARAISON'BETWEEN EXPERIMENTAL RESULTS

The comparison between the different experimental determinations is shown in Fig. 2 giving tg and tl components reported in the littera- ture. Before discussing on this graph, it is necessary to note that the two axis scales is 0.la (a : crystalline parameter) which amounts to 0.5

A

for silicon and germanium. Thus, the difference between the extreme values of t4 and tl remains small. This graph shows that the majority of the experimental results are ve5y close to each other. Another remark is that some of them give a t vector close to 1/4 [ ~ l i ] . This may be explained by the tendency for the atoms to recover their tetrahedral coordination where it is not fullfilled in the unrelaxed structure /12/. At first sight, it may be surprising that somewhat different relaxed structures as shown in Fig. lb and Ic lead to nearly the same rigid body translation vector. Among the experimental results cited above, those obtained from electron microscopy observations need models to be interpreted.

Those models as well as theoretical ones give tg and t, components shown in Fig. 3. The remarks noted for the discussion about Fig. 2 remain valid here. Taking these remarks into account, Fig. 3 shows that the different theoretical determinations are close to each other. However, some discrepancies exist and it seemed useful to us to clarify their origin.

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Cl-106 COLLOQUE DE PFIYSIQUE

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COMPARISON BETWEEN CALCULATED RESULTS

We compare our results deduced from Keating's potential with that of Paxton and Sutton /14/, of Kohyama et al. /15/ and that of Bourret et al. /10/ who used the three structures shown in Fig. 1. When using Keating's potential it is necessary to recall that it depends on two parameters ^ct and p : the first one a describing pure bond stretching and the second one p describing a mixing of bond bending and bond stretching /16/. The ratio p/& is the same for silicon and germanium. These parameters may be fitted on the elastic constants C I 1 , Cl, and C44 : in that case these values lead to the correct

-, 3

value of the compressibility K = and to a fairly good Cl ¹ ⁺2c12 ^-

agreement with the k=O translrerse optic mode but not with the trans- verse acoustic mode at Brillouin-zone boundary. On the contrary a and p may be chosen for reproducing the phonon spectrum through large portions of the Brillouin-zone, with the restriction that the correct value of K is retained /16/. The second fitting procedure leads to almost the same & value but to a p value reduced by a fac- tor of 3. Moreover, the elastic constants are no longer well fitted.

The calculation has been made with the two sets of a and p values giving a result labeled "elasticw and another one labeled "phononsI1.

A first striking feature of the graph in Fig. 3 is that the tl component of

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is only slightly sensitive to this modification of the p value. A-second remark is that the first set of parameters values gives a t vector which coincides exactly with the result of Paxton and Sutton /14/. These authors used a tight-binding approximation with a recursion method. Thus with a rather simple method we find a result obtained by somewhat more sophisticated methods.

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DISCUSSION AND CONCLUSION

The comparison between Figures 2 and 3 shows a rather close agreement between the experimental results of Fontaine and Smith /6/, Bourret and Bacmann ^/10/,Rocher and Labidi / S / , Labidi ^/7/and Komninou et al. / 9 / and the theoretical result of Paxton and Sutton /14/ and ours. This agreement is a first test of the models. But, as we have already noted, it is difficult to distinguish between the different structures since they give t vectors close to each other.

The comparison with theoretical determinations in Fig. 3 allows some conclusions about this distinction. The results obtained by Bourret et al. /10/ using the reflection twin structure (Fig. la) studied by Pond et al. /12/ or the translation twin structure (Fig. lb) proposed by Fontaine and Smith /5,6/ show some discrepancies with respect to other calculation results. That means tQat these structures are not able to give the experimental values of t components. The calculation of Bourret et al. using Papon et Petit model gives a rather low value of tl. This value was used by Mauger et al. /4/ and by Kohyama et al. /15/ for their electronic structure determinations.

Another way of comparing results between them is to compare the positions of the atoms. The comparison between Paxton and Sutton /14/ or Kohyama et al. /15/ results with ours do not show any signi- ficant deviations in atomic positions. Comparing our results with those of Bourret et al. /10/ we obtain of course a good agreement with the simulated image they obtained with Keating's potential applied to Papon and Petit model of figure lc /13/. Moreover, the

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PARALLEL TO 1.1.

[+l-i+il

-- EXPERIMENTAL RESULTS

I I;iyiNTFiItiE

[0+1-11/4

PERPENDICULAR TO G .B.

1+2+1-11 0.0a

0.Ba 0 :'!a 0 .'?a 8 h a

Fig. 2 : Comparison between the different ezperimental determinations of the rigid body translation vector t in Si (Vlachavas and Pond / 3 / , Fontaine and Smith /5, 6 / , Labidi / 7 / , Rocher and Labidi

/8/, Komninou et al. / g / ) and in Ge (Bourret et al. /10/). A box

indicates the precision when it is known.

PARALLEL T E . G 5

[ + l - l t i l

-- COIPUTATIONS --

k S o N T w N E m o u ~ m ~ t 9 8 ,

0.0a

L G c i O N D hi BouRRET

Hsi

PERPENDICULAR TO G .B.

1+2+1-11

0. 0.ia 8 .'2a

8

h a

0.2a

-

- -

Fig. 3 : Comparison between the theoretical determination of the rigid body translation vector given by Paxton and Sutton /14/, Kohyama et al. /15/, by the different models used by Bourret et al.

0 and calculated by us with Keatingls model using the two sets of parameters values fitted on elastic constants and on phonon spectrum / 16/.

(

phonons OUR RESULTS

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C l - l 0 8 COLLOQUE DE PHYSIQUE

agreement is good with the observed high resolution electron microscopy image published by Bourret et al. /10/.

In conclusion the present discussion is in favour of the Papon and Petit bl model /13/ giving the structure shown in figure lc. The same conclusion is obtained by Komninou et al. /g/.

REFERENCES

/l/ Mauger, A., Bourgoin, J.C., Allan, G., Lannoo, M., Bourret A.

and Billard, L., Phys. Rev. B 35 (1987) 1267.

/2/ Ihlal, A. and Nouet, G., Polycrystalline Semiconductors, Edi- ted by Moller, H.J., Strunk, H.P. and Werner, J.H., Springer Proceedings in Physics 35, Springer Verlag Berlin (1989) 77.

/3/ Vlachavas, D. and Pond, R.C., Inst. Phys. Conf. Ser., NO60 (1981) 159.

/4/ Pond, R.C., J. Phys. Coll. C1 43 (1982) 51.

/5/ Fontaine, C. and Smith, D.A., Appl. Phys. Lett. 40 (1982) 153.

/6/ Fontaine, C. and Smith, D.A., Grain boundaries in semiconductors (1982) 39.

/7/ Labidi, M., These de 3eme Cycle (1983).

/8/ Rocher, A. and Labidi, M., Rev. Phys. Appl. 21 (1986) 201.

/9/ Komninou, Ph., Karakostas, Th. and Delavignette, P., J. Mat.

Sci. (1989) to be published.

/10/ Bourret, A., Billard, L. and Petit, M., Inst. Phys. Conf. Ser.

76 (1985) 23.

/11/ Surret, A. and Bacmann, J. J., Grain boundary structures and related phenomena, Trans. Jap. Inst. Met. (1986) 125.

/12/ Pond, R.C., Bacon, D.J. and Bastaweesy, A.M., Inst. Phys. Conf.

Ser. 67 (1983) 253.

/13/ Papon, A.M. and Petit, M., Scripta Met. 19 (1985) 391.

/14/ Paxton, A.T. and Sutton, A.P., J. Phys. C 21 (1988) L 481.

/15/ Kohyama, M., Yamamoto, R., Watanabe, Y., Ebata, Y. and Kinoshita, M - , J. Phys. C 21 (1988) L 695.

/16/ Baraff, G.A., Kane, E.O. and Schluter, M., Phys. Rev. B (1980) 5662.