We have analyzed the atomic rearrangements underlying self-diffusion in
amorphous Si during annealing using tight-binding molecular dynamics
simulations. Two types of amorphous samples with different structural features
were used to analyze the influence of coordination defects. We have identified
several types of atomic rearrangement mechanisms, and we have obtained an
effective migration energy of around 1 eV. We found similar migration energies
for both types of samples, but higher diffusivities in the one with a higher
initial percentage of coordination defects.Comment: 9 pages, 4 figure

Iván Santos

L. Khriachtchev

Lourdes Pelaz

Luciano Colombo

Luis A. Marqués

English

arXiv

Producción CientíficaWe have analyzed the atomic rearrangements underlying self-diffusion in amorphous Si during annealing using tight-binding molecular dynamics simulations. Two types of amorphous samples with different structural features were used to analyze the influence of coordination defects. We have identified several types of atomic rearrangement mechanisms, and we have obtained an effective migration energy of around 1 eV. We found similar migration energies for both types of samples, but higher diffusivities in the one with a higher initial percentage of coordination defects.Ministerio de Economía, Industria y Competitividad (Project TEC2008-06069)Junta de Castilla y León (programa de apoyo a proyectos de investigación - Ref. VA011A09)HPC-EUROPA2 (Project 228398

Santos Tejido, Iván

Pelaz Montes, María Lourdes

Marqués Cuesta, Luis Alberto

Colombo, Luciano

Repositorio Documental de la Universidad de Valladolid

PHYSICAL REVIEW B 83, 153201 (2011)Elucidating the atomistic mechanisms driving self-diffusion of amorphous Si during annealingIván Santos,* Luis A. Marqués, and Lourdes PelazDepartamento de Electricidad y Electrónica, Universidad de Valladolid, E.T.S.I. de Telecomunicación, Paseo Belén 15,E-47011 Valladolid, SpainLuciano ColomboDipartimento di Fisica, Università degli Studi di Cagliari, Cittadella Universitaria, I-09042 Monserrato (CA), Italy(Received 23 November 2010; revised manuscript received 8 February 2011; published 14 April 2011)We have analyzed the atomic rearrangements underlying self-diffusion in amorphous Si during annealingusing tight-binding molecular dynamics simulations. Two types of amorphous samples with different structuralfeatures were used to analyze the influence of coordination defects. We have identified several types of atomicrearrangement mechanisms, and we have obtained an effective migration energy of around 1 eV. We found similarmigration energies for both types of samples, but higher diffusivities in the one with a higher initial percentageof coordination defects.DOI: 10.1103/PhysRevB.83.153201 PACS number(s): 07.05.Tp, 66.30.−h, 81.05.GcDespite the renewed interest in amorphous Si (a-Si) foroptoelectronic and photovoltaic applications,1 the atomic-scale understanding of its microstructural evolution duringprocessing (an issue of large technological impact) is stilla matter of debate. In particular, it has been found thatimpurity diffusion is greatly affected by modifications in thea-Si structure.2,3 These modifications mainly occur duringannealing, and they are directly related to microscopic changesof the amorphous matrix.4 Uncontrolled diffusion during thefabrication process results in the degradation of the finalperformance of devices. A better understanding of diffusionat the atomic level will help to overcome these negativeeffects.In this Brief Report, we have analyzed the atomic rearrange-ments underlying self-diffusion in a-Si during annealing. Wehave used tight-binding molecular dynamics (TBMD) sim-ulations within an sp3 orthogonal tight-binding approach,5,6and the Hamiltonian representation proposed by Kwon et al.7This representation has been successfully used for studyingdiffusion phenomena in crystalline Si (Refs. 8–10) (c-Si) andthe properties of a-Si.11–13 We have considered two modelsof a-Si, obtained by rather different computer simulations.On the one hand, a-Si was obtained by melting c-Si, andquenching the resulting liquid at a rate of 1013 K/s, which lieswithin the typical cooling rates used in molecular dynamicssimulations.14 On the other hand, a-Si was obtained usingthe algorithm developed by Wooten, Winer, and Weaire(WWW).15 We considered three quenched and two WWWcubic cells with 216 atoms. The structural differences betweenthese two types of a-Si simulation cells are well known:while the WWW algorithm generates a perfectly fourfoldcoordinated a-Si,15 quenched samples have an appreciableoccurrence of non fourfold coordinated atoms that dependson the quench rate.14 In our case, we had ∼80% and ∼20% offourfold and fivefold coordinated atoms, respectively, using abond cutoff for determining the local atomic coordination aslong as 2.8 Å. The aim of considering two different models ofa-Si is to investigate the possible role of coordination defectson the microstructure evolution during annealing. Generatedsamples were rapidly heated at the desired temperature andstabilized during 5 ps before analyzing the dynamics ofthe system. Then, we performed constant temperature andvolume simulations for total times ranging from 1.5 to 4 ns.The temperature range was chosen between 900 and 1300 K,since for higher temperatures, a-Si transforms into liquid.11We performed velocity rescalings every 103 time steps to keepthe temperature of the cell constant. Equations of motion wereintegrated using the velocity-Verlet algorithm16 with a timestep of 1.5 fs. Periodic boundary conditions were applied inall directions.To analyze self-diffusion, we evaluated the atomic mean-squared displacement (MSD) asMSD(t) =N∑i=1|ri(t) − ri(0)|2N, (1)with N the number of atoms in the simulation cell, and ri(t)the position of atom i at time t . A representative plot of thetime evolution of the MSD in the case of quenched a-Siat several temperatures is shown in Fig. 1. At temperatureslower than 1000 K, the atomic MSD slowly increases withtime by means of small steps separated by long plateaus.As temperature increases, the steps are higher and plateausbecome shorter. Bearing in mind that abrupt changes in theMSD have been correlated to transitions among differentconfigurations of the Si self-interstitial in c-Si,17 we paidattention to atomic trajectories when abrupt changes in theMSD occurred in some of the simulations performed. Weused the fast Fourier transformation (FFT) to filter out thermalvibrations for identifying relevant atomic movements in oursimulations. The FFT is applied to atomic trajectories to obtainthe frequency spectrum. Since frequencies associated to latticevibrations are much higher than those associated to atomicrearrangements, an inverse FFT in which high frequencies areneglected is performed to obtain filtered atomic trajectoriesand keep only those events that really induce microstructuralchanges. Contrary to atomic diffusion in c-Si, where thenumber of stable and saddle configurations is limited, theunderlying amorphous network in a-Si varies as diffusionevents take place. The initial atomic configuration before153201-11098-0121/2011/83(15)/153201(4) ©2011 American Physical SocietyBRIEF REPORTS PHYSICAL REVIEW B 83, 153201 (2011) 0 5 10 15 20 0  0.5  1  1.5  2  2.5MSD (Å2 )Time (ns)1300 K1200 K1150 K1100 K1000 K950 KFIG. 1. (Color online) Representative plot for the MSD in the caseof quenched a-Si as a function of time for different temperatures.diffusion events differs one from another, and so it does thepath followed by the atoms that move. This fact results in a dis-tribution of energy barriers, as reported in theoretical studies ofthe configurational energy landscape in a-Si.18 Nevertheless,we could identify several common features in the observedatomic rearrangements that allowed us to classify them.By analyzing the broken and newly formed bonds andthe atomic displacements, we have identified five differenttypes of basic mechanisms, namely: bond break (BB), bondswitch (BS), frustrated bond switch (FBS), kick-out (KO),and vacancy-like (VL). The rearrangements shown in Fig. 2are representative examples of the prototypical mechanismsidentified. The features that define these mechanisms, whichwill be described in the following, were used to classifythe rearrangements that took place during the simulations ofannealing.The BB only involves one atom (A) in the rearrangement.When one of its bonds is broken (bond A–B), the influenceof the rest of its neighbors causes the atom A to movein the opposite direction to the broken bond. It forms anew bond with another atom (C) which was initially at asecond-neighbor distance. Atomistic models have proposedthe BB as a possible mechanism for the creation oflight-induced defects in hydrogenated a-Si.19 The BS consistsof the interchange of two neighbors (C, D) between two neigh-boring atoms (A, B): the bonds A–D and B–C are switchedto become A–C and B–D. While the BS mechanism was onlyconjecture to date,18 in the present study, by analyzing theTBMD trajectories, we provide evidence that it indeed occursand is responsible for large local rearrangements. Furthermore,our results also indicate that BS in a-Si can be produced bythermal atomic motions in addition to light illumination, asproposed by Wagner et al.20 The BS has a special relevance inboth c-Si and a-Si. The so-called IV pair is a point defect in c-Sithat can be generated and recombined through a BS.8,21 Thisdefect plays an important role in describing the amorphizationand the recrystallization processes of Si.21 In addition, theso-called concerted-exchange diffusion mechanism in c-Sican be regarded as a combination of three consecutive BSsinvolving the same pair of atoms.22 Moreover, the BS is thefundamental movement within the WWW bond network forthe generation of a-Si from c-Si.Due to rearrangements induced in the surroundings, some-times the neighbor interchange is not totally completed in theBS event. This feature is manifested through the identificationof a FBS rearrangement, which is shown in Fig. 2. The bondsA–D and B–C break as it occurs in the BS, and the bondB–D is formed. However, atom A does not bond to atom Cbut rather to atom E, which is a second neighbor of atom B.Although at the end of the movement the newly formed bondsare A–E and B–D, this type of rearrangement has a BS nature.During the KO event, one atom (A) displaces another one (B)from its position. As a consequence of this rearrangement,atom C is also displaced in this particular case. This kind ofmovement is similar to that occurring during the diffusion of Siself-interstitials in c-Si.8,17,23 Finally, in the VL, only one atom(A) moves as in the BB, but in the VL, the distance traveledis longer. In the case of the VL, atom A seeks open spacesin the network, and changes most of its neighbors during thedisplacement. This movement resembles the vacancy diffusionmechanism in c-Si where an atom moves toward the emptyFIG. 2. (Color online) Snapshots of representative atomic movements in the observed rearrangement mechanisms. See text for details.153201-2BRIEF REPORTS PHYSICAL REVIEW B 83, 153201 (2011)800 1000 1200 14000204060020406080Temperature (K)Relativefrequency(%)BBBSKOVLQuenched a-SiWWW a-SiFIG. 3. (Color online) Statistics of the observed basic diffusionmechanisms. Lines are to guide the eye.space associated with a vacancy.24 It is worth noting that,although the BB and the BS events found here agree with theobservations of previous theoretical static studies,18 neither theKO nor the VL events were reported.In order to evaluate the relevance of the observed mecha-nisms, we have represented in Fig. 3 the relative frequency ofa given event as a function of temperature. Since sometimes itis difficult to distinguish between the FBS and the BS, wehave gathered FBS events within the BS group. We havefound that the BB rearrangement is the more frequent eventin both samples at the analyzed temperatures. The BS hasan important contribution to atomic rearrangements at lowtemperatures, especially in quenched a-Si, but its relevancediminishes as temperature increases. The relative frequencyof the KO events increase with temperature, while in the caseof VL, the increase is less. In general, it can be inferred fromFig. 3 that coordination defects favor BS events, while KO andVL events take place when the temperature is high enough. Allthese rearrangements caused the steps in the MSD observedin Fig. 1. Small steps at low temperatures are associated withisolated rearrangements involving small displacements of fewatoms. As temperature increases, the higher steps are related toan increment of the complexity of rearrangements involving alarger number of atoms, which can be regarded as a successionof several “basic rearrangements,” with BB the usual triggeringevent.We have also calculated the atomic diffusivity d(T ) fromthe MSD at different temperatures using the Einstein relationd(T ) = limt→∞MSD(t)6t. (2)10−910−810−710−6 8  9  10  11  12  13  141400 1300 1200 1100 1000 900Diffusivity  (cm2 s−1 )(kB T)−1 (eV−1)Temperature (K)dQuenched = 2.8×10−4 cm2s−1 exp( −0.86 eV/ KB T )dWWW = 4.2×10−4 cm2s−1 exp( −0.95 eV/ KB T )WWW aSiQuenched aSiFIG. 4. (Color online) Average atomic diffusivities at each tem-perature of the samples considered. Straight lines and equations showthe result of the Arrhenius data fit.In Fig. 4 we represent the average diffusivity at each tem-perature for the samples considered. Quenched samples havehigher atomic diffusivities than WWW ones. This may be dueto their higher initial structural distortion, which appears toenhance atomic rearrangement events. Data can be describedwith an Arrhenius behavior within the temperature rangeanalyzed asd(T ) = d0 exp(− EmkBT), (3)where d0 is the diffusivity prefactor, Em is the effectivemigration energy for self-diffusion in a-Si, kB is the Boltzmannconstant, and T is the temperature. The result of the Arrheniusfits is shown in Fig. 4. The obtained effective migrationenergies are 0.86 eV and 0.95 eV for quenched and WWWa-Si, respectively. These energies are of the order of magnitudeof the migration energies of point defects in c-Si.8,9,17,23,24 Inaddition, as we described above, we also observed analogouslocal atomic rearrangements in both c-Si and a-Si. Thesefacts are consequences of the similar short-range atomicenvironment that both phases of silicon share.The evaluated migration energy captures the statisticalaverage behavior of different atomic rearrangements in adynamical system. Calorimetric4 and conductivity25 measureson a-Si have revealed the existence of activation energybarriers ranging from ∼0.25 eV to ∼2.7 eV. Theoretical staticstudies of the configurational energy landscape in a-Si haveshown that there exists a distribution of energy barriers forthe saddle point and for the energy difference between initialand final configurations.18 In spite of this complexity, it hasbeen demonstrated that in amorphous materials, the combinedeffect of both distributions can result in an Arrhenius diffusionbehavior.26,27In conclusion, we have studied, from an atomistic pointof view, the microstructure evolution of a-Si during annealingusing TBMD simulations. The evaluation of the MSD togetherwith the analysis of atomic trajectories enabled us to make asynopsis of the type and relevance of rearrangement events153201-3BRIEF REPORTS PHYSICAL REVIEW B 83, 153201 (2011)occurring during annealing. Despite the variety of mechanismsfound, an effective migration energy of ∼1 eV was obtainedfrom the Arrhenius plot of the atomic diffusivities thatencompasses their average behavior in self-diffusion in a-Si.This energy could be used in Monte Carlo simulations of themicrostructure evolution of a-Si in order to access time scalesthat go beyond molecular dynamics simulations.The authors thank L. Bagolini for providing the WWWa-Si cells. This work was partially funded by HPC-EUROPA2under Project No. 228398 with the support of the EuropeanCommission Capacities Area - Research InfrastructuresInitiative, Spanish DGI under Project No. TEC2008-06069,and Junta de Castilla y León under Project No. VA011A09(IS, LAM, LP).*ivasan@tel.uva.es1L. Khriachtchev, Silicon Nanophotonics (World Scientific,Singapore, 2008).2S. Coffa, J. M. Poate, D. C. Jacobson, W. Frank, and W. Gustin,Phys. Rev. B 45, 8355 (1992).3S. Mirabella, D. DeSalvador, E. Bruno, E. Napolitani, E. F. Pecora,S. Boninelli, and F. Priolo, Phys. Rev. Lett. 100, 155901 (2008).4S. Roorda, W. C. Sinke, J. M. Poate, D. C. Jacobson, S. Dierker,B. S. Dennis, D. J. Eaglesham, F. Spaepen, and P. Fuoss, Phys. Rev.B 44, 3702 (1991).5L. Colombo and M. Rosati, Comput. Phys. Commun. 128, 108(2000).6L. Colombo, Comput. Mater. Sci. 12, 278 (1998).7I. Kwon, R. Biswas, C. Z. Wang, K. M. Ho, and C. M. Soukoulis,Phys. Rev. B 49, 7242 (1994).8M. Tang, L. Colombo, J. Zhu, and T. Diaz de la Rubia, Phys. Rev.B 55, 14279 (1997).9L. Colombo, Annu. Rev. Mater. Res. 32, 271 (2002).10M. Cogoni, B. P. Uberuaga, A. F. Voter, and L. Colombo, Phys.Rev. B 71, 121203 (2005).11V. Rosato and M. Celino, J. Appl. Phys. 86, 6826 (1999).12P. Biswas, Phys. Rev. B 65, 125208 (2002).13D. A. Drabold, Y. Li, B. Cai, and M. Zhang, Phys. Rev. B 83,045201 (2011).14M. Ishimaru, S. Munetoh, and T. Motooka, Phys. Rev. B 56, 15133(1997).15F. Wooten, K. Winer, and D. Weaire, Phys. Rev. Lett. 54, 1392(1985).16W. C. Swope et al., J. Chem. Phys. 76, 637 (1982).17L. A. Marqués, L. Pelaz, P. Castrillo, and J. Barbolla, Phys. Rev. B71, 085204 (2005).18F. Valiquette and N. Mousseau, Phys. Rev. B 68, 125209(2003).19M. Stutzmann, W. B. Jackson, and C. C. Tsai, Phys. Rev. B 32, 23(1985).20L. K. Wagner and J. C. Grossman, Phys. Rev. Lett. 101, 265501(2008).21L. A. Marqués, L. Pelaz, M. Aboy, L. Enriquez, andJ. Barbolla,Phys. Rev. Lett. 91, 135504 (2003).22K. C. Pandey, Phys. Rev. Lett. 57, 2287 (1986).23M. Posselt, F. Gao, and H. Bracht, Phys. Rev. B 78, 035208(2008).24P. M. Fahey, P. B. Griffin, and J. D. Plummer, Rev. Mod. Phys. 61,290 (1989).25J. H. Shin and H. A. Atwater, Phys. Rev. B 48, 5964 (1993).26Y. Limoge and J. L. Bocquet, Phys. Rev. Lett. 65, 60 (1990).27K. Mussawisade, T. 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Elucidating the atomistic mechanisms driving self-diffusion of amorphous Si during annealing

Crossref

Physical Review B

We have analyzed the atomic rearrangements underlying self-diffusion in amorphous Si during annealing
using tight-binding molecular dynamics simulations. Two types of amorphous samples with different structural
features were used to analyze the influence of coordination defects. We have identified several types of atomic
rearrangement mechanisms, and we have obtained an effectivemigration energy of around 1 eV.We found similar
migration energies for both types of samples, but higher diffusivities in the one with a higher initial percentage
of coordination defects

SANTOS I

MARQUES LA

PELAZ L

COLOMBO, LUCIANO

Archivio istituzionale della ricerca - Università di Cagliari