Materials Science and Engineering B71 (2000) 213–218

Defect-related growth processes at an amorphous/crystallineinterface: a molecular dynamics study

B. Weber *, D.M. Stock, K. GartnerInstitut fur Festkorperphysik, Friedrich–Schiller-Uni6ersitat Jena, Max-Wien-Platz 1, D-07749 Jena, Germany

Abstract

The structure of the interface between amorphous Si and {100}Si and its change during thermal annealing at 1000 K isinvestigated using classical molecular dynamics simulations. The defect structure of the interface can be reduced to two complexdefect structures which contain dimers. The two defect structures are proved to be only two interface modifications of atopological defect of crystalline silicon called bond defect. The annealing of the bond defect at the interface contributes tocrystallization where an uncompleted [110] ledge of a {111} terrace is completed and simultaneously a ledge perpendicular to thisledge is opened. This process is discussed within the kink-model of crystallization. © 2000 Elsevier Science S.A. All rights reserved.

Keywords: Molecular dynamics simulations; A/c interface; Crystallization; Defects

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1. Introduction

Solid state crystallization at amorphous/crystalline(a/c) interfaces in silicon induced by thermal annealing(solid phase epitaxy — SPE) or by high energy ionirradiation (ion beam induced epitaxial crystallization— IBIEC) is investigated extensively. The main experi-mental results of SPE and IBIEC are reviewed by Olsonand Roth [1] and by Priolo et al. [2], respectively. Tounderstand the processes responsible for the crystalliza-tion different models (reviewed for example in [3] forSPE and in [4] for IBIEC) have been developed wherethe creation or transport of different types of defectsat/or to the a/c interface are suggested to be the rate-limiting process in epitaxial growth. Up to now thekinetics of interface motion and the microscopic struc-ture of the defects at the a/c interface responsible forcrystallization are not fully understood. Priolo et al. [5]stated that similar effects are observed in SPE andIBIEC. Therefore, similar processes should be operativein the two cases. They assume that the same defectresponsible for thermal annealing is also responsible forIBIEC. According to the model of Williams and Elli-

man [6] this defect should be a kink which is formed on[110] ledges at {111} terraces of the a/c interface.Investigations of the dependence of the SPE rate onhydrostatic compression [3] as well as on uniaxial stressin the interface plane [7] imply that defect formationor/and motion at the a/c interface are the substantialcontribution to the rate-limiting process. IBIEC experi-ments under channeling conditions [8] led to the sameconclusion. The dangling bond model of Spaepen andTurnbull [9] and the kink-model [6] meet this con-straint. Priolo et al. [5] stated that kinks are structuraldeformations at the a/c interface and do not exist awayfrom the interface, they generate, diffuse and annihilateat the interface. Moreover, the kinks generate andannihilate in pairs which coincides with the behavior ofthe defects postulated in the Jackson model [10] forIBIEC.

Because the atomic structure of the a/c interfacecannot be investigated by experimental methods, molec-ular dynamics (MD) simulations of the a/c interfaceplay an important role. Simulations should be doneusing quantum mechanical methods, but it is onlypossible for very small systems and very short times.The investigation of sufficiently large systems over timescales in the order of nanoseconds is only possible byclassical MD simulations using empirical potentials.Spaepen [11] and Saito and Ohdomari [12] investigated

* Corresponding author. Tel.: +49-3641-647316; fax: +49-3641-947302.

E-mail address: obw@rz.uni-jena.de (B. Weber)

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the structure of hand-built a-Si/{111}Si and a-Si/{100}Si interface models, respectively. Investigations ofcrystallization processes at an a/c interface by classicalMD simulations based on empirical potentials havebeen done by different authors [13–18]. Bernstein et al.[19] investigated the structural features of the a/c inter-face by MD simulations based on a combination of anempirical potential and a non-orthogonal tight-bindingmodel. In [13,14] it could be shown that crystallizationproceeds by attaching Si atoms at kink sites along [110]ledges. In [15–17,19] the existence of dimers as a char-acteristic feature at the a-Si/(001)Si interface wasshown. Moreover, in [15] it was demonstrated that theexistence of the dimers at the interface is related to thebond defect found by Tang et al. [20] and Cargnoni etal. [21] in crystalline silicon as metastable defectconfiguration after incomplete recombination of a va-cancy and an interstitial with a barrier of its thermalannealing of �1.1 eV.

In this paper classical MD simulations are used toinvestigate the role of the bond defect in epitaxialgrowth at an a-Si/(001)Si interface. The relation be-tween the annealing of the bond defect and the kinkmodel of epitaxial growth will be shown.

2. MD simulations

The simulations were done with a standard MD code[22], where the interaction of the Si atoms is describedby the Stillinger–Weber interatomic potential [23]. Theintegration of the equations of motion is performedusing the velocity form of the Verlet algorithm and atime step of 0.3892 fs. The a-Si/(001)Si interface systemhas a size of 8×8×10 unit cells (5120 atoms) withperiodic boundary conditions in x and y direction anda free surface and two fixed bottom planes in z direc-tion. It is prepared by melting and cooling of the upperhalf of the MD cell. The preparation procedure isdescribed in detail in [14]. Crystallization at the inter-face was initiated by thermal annealing of the system at1000 K over 400 ps.

3. Results and discussion

The structure of the a/c interface and its changeduring annealing at 1000 K has been investigated fordifferent annealing times up to 400 ps. In all cases thesame characteristic structures and structural changeswere observed. Typical situations are given in Figs. 1and 2 which show top views of five (001) atomic layersof the a/c interface at two different annealing times(117and 137 ps). As already found by Bernstein et al. [19]and discussed in [15] for differently prepared interfacesystems, the interface is not confined to a single atomic

layer, but the transition from the crystalline to theamorphous state extends over several (6–8) atomiclayers. The two lower layers in Figs. 1 and 2 areperfectly crystalline ones. The overlaying layers show

Fig. 1. Five atomic layers of the a-Si/(001)Si interface annealed at1000 K for 117 ps. The two lower layers are perfectly crystalline ones.The black and grey circles mark defect regions of type I and II. Thebold drawn bonds mark the [110] chains where the (111) doublelayers shown in Figs. 4 and 5 intersect the (001) interface.

Fig. 2. Same atomic layers as in Fig. 1 after further annealing at 1000K for 20 ps. The marked atoms and bonds have the same meaning asin Fig. 1.

B. Weber et al. / Materials Science and Engineering B71 (2000) 213–218 215

Fig. 3. Part of crystalline Si (a), same part containing the relaxedatomic configuration of the bond defect at 0 K (b) and the (001)projection (c) and (100) projection (d) of the bond defect with somesurrounding crystalline atoms. The two black circles represent therotated atoms A and A%, the grey circles with the border representatoms which form dimers with one black atom, and the grey atomswithout the border mark defect rings visible in the [001] projections.

structure I corresponds to the structural feature ob-served in the interface model of Saito and Ohdomari[12] and the defect structure II is connected with dimerssimilar to those on a (2×1) reconstructed free {100}surface. Such dimers were also observed in tight-bind-ing MD simulations of an a-Si/(001)Si interface byBernstein et al. [19]. Our results show that (lookingfrom the c-Si side of the interface) the defect structureII always starts with the dimer which means that thedimers are important for the transition from the crys-talline order to the random network of the a-Si. This isalso supported by the results of MD simulations of lowtemperature layer deposition on reconstructed {001}Sisurfaces [16,17]. They show that the dimers are respon-sible for the growth of amorphous layers which hasbeen observed experimentally during low temperatureMBE also [24].

Because at all annealing times investigated the inter-face exhibits two characteristic defect structures, thepossible processes during annealing are reduced to an-nihilation of these two defect structures which providescrystallization and to the transformation between thetwo defect structures. This can be seen by comparisonof Figs. 1 and 2, where the interface structure in Fig. 2is obtained after 20 ps annealing of the structure shownin Fig. 1. During this annealing step the defect structureI and two defect structures of type II annihilate. Forillustration the corresponding black atoms, though theybecome ordered, are still marked by black circles in Fig.2. Besides the annihilation, one defect structure of typeI is generated (see Fig. 2) by the transformation of adefect structure of type II (see Fig. 1, only the dimer ofthis structure is visible) into type I.

In order to study the structural changes during theannealing, especially with respect to the kink-model ofcrystallization, the two defect structures at the a/cinterface are analyzed in more detail. In our previouswork [15] it has been shown that the two defect struc-tures found at the a-Si/(001)Si interface can be under-stood in terms of the bond defect which is illustrated inFig. 3. In Fig. 3a a section of perfectly crystalline Si isshown, where the characteristic six-membered rings areclearly visible. Fig. 3b shows the same section after theatoms A and A% (marked by black circles) switchedtheir bonds (breaking the bonds AB% and A%B andforming the new bonds AB and A%B% due to the rotationof atoms A and A% in the (110) plane) according to themodel of Wooten et al. [25] to construct a randomnetwork of covalently bonded material. This defectstructure has been relaxed at room temperature andquenched dynamically to 0 K. It has the same configu-ration as the defect structure obtained by Tang et al.[20] after incomplete recombination of an interstitial-vacancy pair and by Motooka et al. [26] after introduc-ing a divacancy-di-interstitial pair into crystalline Si as

defect regions the atoms of which are marked by blackand grey circles. As can be seen in both figures, thereare two different complex defect structures and somesingle dimers. The defect structure I (see Fig. 1) can becharacterized by a pair of atoms rotated out of the�1( 10� chain (marked by black circles) and by onefive-membered ring, one seven-membered ring and twodistorted six-membered rings of atoms. Each of thesefour rings of atoms include one or both of the rotatedatoms. For illustration the other atoms in these ringsare marked by grey circles without border. The defectstructure II (see Fig. 1) can be characterized by a dimer(formed by two neighboring atoms of adjacent �110�chains and marked by a pair of a black circle and agrey circle with border) and by two five-membered andtwo seven-membered rings of atoms marked by greycircles without border (the role of the second blackatom is described later). As can be seen, the layers inFig. 1 contain one defect structure of type I and fivedefect structures of type II, and the layers in Fig. 2contain one defect structure of type I and three defectstructures of type II. Beside these complex defect struc-tures there are also some single dimers present in Figs.1 and 2. However, these dimers appear in the upper(fifth) atomic layer. The inclusion of the sixth atomiclayer (not shown) proves that these dimers are only thelower part of the defect structure of typ II. This meansthat there exist no isolated single dimers and all thedefect structures found can be reduced to only twodifferent types of complex defect structures. The defect

B. Weber et al. / Materials Science and Engineering B71 (2000) 213–218216

basic step to construct a-Si. The defect structure of Fig.3b is a topological but not a number defect which hasno reminiscence of its origin and thus named as bonddefect [21]. Characteristics of the bond defect are theformation of five- and seven-membered rings (four five-membered rings and 16 seven-membered rings) and theoccurence of dimer bonds between atoms A and B andatoms A% and B%. Viewing the bond defect with itscrystalline surroundings in �001� and �100� directionand cutting the atoms on top of the two rotated atomsA and A% (which simulates a bond defect on top of a{100} surface) yields the configurations shown in Fig.3c and d, respectively. Looking in �010� direction

yields a configuration similar to that of Fig. 3d. Com-paring Fig. 3c and d with Figs. 1 and 2 it is obviousthat the defect structures found at the a-Si/(001)Siinterface are just the same as shown in Fig. 3c and dwhere the corresponding atoms are marked in the sameway. Therefore, the defect structures I and II at theinterface can be explained by two orientations of thebond defect, where the bond between the two rotatedatoms is oriented either nearly parallel (Fig. 3d) ornearly perpendicular (Fig. 3c) to the interface. There-fore, the two defect structures I and II will be calledparallel and perpendicular interface configuration ofthe bond defect, respectively. Because the bond defect isobviously a basic element for understanding the struc-ture of the a/c interface, the structural changes at theinterface during annealing as described above should beattributed to changes of the bond defect. The annihila-tion of the defect structures I and II visible by compar-ing Figs. 1 and 2 can be considered to be theconsequence of the annealing of the correspondingbond defect, and the transformation of the defect struc-ture of type II into typ I is caused by a change of theorientation of the bond defect. While the latter processprovides only a changed defect structure at the interfacethe annihilation of the bond defect results in crystalliza-tion. The annihilation path of the bond defect at theinterface was found to be similar to that described byCargnoni et al. [21] for the annihilation of the isolatedbond defect in the Si crystal, but it depends on the localstructure of the amorphous atoms in the overlyinglayers.

In the following the structural rearrangements whichare connected with the annihilation of the bond defectand result in crystallization will be discussed for theexample of the annihilation of the defect structure I inFig. 1. According to the kink model, the crystallizationat a {100} a/c interface takes place by the motion of thekinks in {111}-oriented terraces along [110] ledges. Inorder to compare the results with this model the struc-tural changes caused by annihilation of the bond defectare studied by analyzing all equivalent {111} doublelayers intersecting the defect structure I in Fig. 1. Fig.4a shows the (111) double layer which intersects the toplayers of the (001) interface region of Fig. 1 along the�1( 10� chain marked by the bold bonds and Fig. 4bshows the same double layer after the annealing step of20 ps corresponding to Fig. 2. In Fig. 5 the (11( 1)double layer which intersects the interface along the�110� chain marked by the bold black bonds is shownbefore (a) and after (b) annealing of the bond defect.The �1( 10� and �110� chains marked by bold bonds inFigs. 4 and 5 correspond to that marked in Figs. 1 and2. The indication of the defect atoms in Figs. 4 and 5also corresponds to that in Figs. 1 and 2. The boldbonds in Fig. 4a indicate an uncompleted �1( 10� ledge.It is clearly visible that this ledge is interrupted by the

Fig. 4. The (111) double layer which intersects the a/c interfaces ofFig. 1a and Fig. 2b at the marked �1( 10� chain. The atoms and bondsare marked as in Fig. 1.

Fig. 5. The (11( 1) double layer which intersects the a/c interfaces ofFig. 1a and Fig. 2b at the marked �110� chain. The atoms and bondsare marked as in Fig. 1.

B. Weber et al. / Materials Science and Engineering B71 (2000) 213–218 217

five- and the seven-membered ring belonging to thebond defect which forms a pair of kinks. After an-nealing of the bond defect (Fig. 4b) the bonds of thetwo black atoms have rearranged which is accompa-nied with the formation of two six-membered ringsalong the ledge considered and connected with theannihilation of the two kinks. In Fig. 5 it can be seenwhat happens in the (11( 1) plane which intersects thedefect structure along the �110� ledge. Before anneal-ing (Fig. 5a) the �110� ledge is interrupted by oneseven-membered ring belonging to the bond defect.Due to the annealing of the bond defect this seven-membered ring transforms into a crystalline six-mem-bered ring (see Fig. 5b) where one of the two blackdefect atoms is incorporated and simultaneously apair of new kinks is created on top of the crystallizedrow by the other black defect atom. In this way anew ledge has been opened, where the new kinks al-ready moved to both sides and caused further crystal-lization. From these results follows that theannihilation of a bond defect at the interface causes apairwise annihilation of two kinks and simultaneouslya pairwise generation of two kinks in the next (001)layer which initiates crystallization by the motion ofthe kinks along a ledge perpendicular to the closedone. Analyzing the structure of the a/c interface atdifferent times during annealing over a period of �400 ps the two described interface configurations ofthe bond defect and the belonging kinks were foundin each case. That means that these defect structurescan be annihilated and generated at the interface in aselfsustaining process without the presence of addi-tional defects. This result is similar to the results ofMD simulations of low temperature MBE [16,17]where amorphous layers are formed. In this casedimers which are responsible for the growth of theamorphous layer occur at the (001) interface even ifthe interface moves.

It is interesting to note that the crystallization pro-cesses during thermal annealing as discussed abovehave also been observed in the case of ion beaminduced crystallization [15] which has been simulatedby starting recoils with energies well below the dis-placement threshold energy within the interface re-gion. This indicates that the same basic processesshould be responsible for the SPE and the IBIECwhich agrees with the assumption of Priolo et al. [5].

4. Conclusion

It has been shown that the parallel and perpendicu-lar interface configurations of the bond defect are theprominent defects at the a-Si/(001)Si interface whichintroduce topological disorder with five- and seven-membered rings. The annealing of a bond defect at

the interface results in the formation of six-memberedrings and provides crystallization. Within the kinkmodel discussed in [5,6] the existence of a bond defectat the interface is equivalent with the existence ofpairs of kinks in [110] ledges of {111} terraces. Theannealing of a bond defect at the interface causes theannihilation of a pair of kinks in a [110] ledge andsimultaneously the generation of a pair of new kinksin a [110] ledge perpendicular to the previous onewhich initiates crystallization along this new ledge.From this fact it may be concluded that during thethermal annealing the [110] ledges grow in alternatingdirections which seems to be different from the usualpicture of stepwise growth. Maybe this is an explana-tion for the micro-facetting of the a-Si/(001)Si inter-face found by MD simulations [13,18] and for thefinite interface roughness determined experimentally[27].

Acknowledgements

We acknowledge the financial support of theDeutsche Forschungsgemeinschaft, contract Ga 459/5-1.

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