CHARACTERIZATION OF THE INTERSTITIAL VOIDS IN THE STRUCTURAL MODEL OF AMORPHOUS SILICON DERIVED FROM THE DIAMOND-LIKE LATTICE

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1 Journl of Optoelectronics nd Advnced Mterils Vol. 5, No. 5, 3, p CHARACTERIZATION OF THE INTERSTITIAL VOIDS IN THE STRUCTURAL MODEL OF AMORPHOUS SILICON DERIVED FROM THE DIAMOND-LIKE LATTICE F. Sv * Ntionl Institute of Mterils Physics, Buchrest-Mgurele, P.O. Box MG. 7, Romni The simultion of interstitil void evolution in model of line silicon sujected to topologicl disordering reveled tht the void size distriution rodens nd shifts towrds smller men dimeter size, when the lttice disordering increses. The size distriution is not gussin nd the men dimeter of the voids is lower thn the line vlue. The clcultion of the structure fctor corresponding to void configurtion evidences the sence of the short nd long rnge order nd point out to the presence of the medium rnge order. (Received July 5, 3; ccepted August 8, 3) Keywords: Amorphous silicon, Intestitil voids, Medium rnge order, Modelling. Introduction Amorphous silicon (-Si) is prticulrly interesting mteril. With the dvent of the hydrogented morphous silicon, this non-line semiconductor ecme the most promising mteril for solr energy conversion. -Si ws the suject of considerle effort devoted to the mesurement of its structure, opticl, electricl nd virtionl properties [-5]. Recently, the possiility to hve the elementl silicon in severl llotropic forms, like cron, hs een demonstrted []. Yonezw et l. [7] hve shown tht the rditive recomintion rte is enhnced in morphous silicon nnostructures nd, therefore, the disorder is importnt for light emitting silicon. The fundmentl properties of morphous silicon require detiled knowledge of the tomic scle structure. As opposite to the line cse, there re limitless possile disordered structures ut no experimentl techniques tht provide tomic resolution similr to logrphy [8]. The wy to get informtion on the morphous structure is to clculte the one-dimensionl rdil distriution function (RDF) [9]. Nevertheless, the informtion otined from RDF is n verge on ll tomic configurtions in the mteril. The structurl models, either hnd-uilt or computer generted, gretly enlrge the informtion on the structure of the disordered mterils, especilly when used conjointly with the experimentl RDFs [9]. The morphous stte of germnium nd silicon ws thought, firstly, in terms of the microline models, nd then in terms of the continuous network models []. Lter, Wooten, Winer nd Weire [] used simple lgorithm for the systemtic computer genertion of disordered network models, strting with the simulted dimond structure (FC-), nd successfully rerrnging it y specil elementry processes. On the sis of the generted models the mentioned uthors hve investigted the topologicl conditions tht led to liztion []. Lst yers, n incresed ttention ws pid to the prolem of structurl voids in the disordered mterils with the purpose to explin some properties of the glsses. Thus, Elliott [3] explined the structurl origin of the first shrp diffrction pek in the diffrcted intensity curves of severl glsses through the void-sed model, while Jensen et l. [4] suggested tht voids re importnt for the interprettion of the positron nnihiltion lifetime dt in non-line chlcogenides. * Corresponding uthor: fsv@lph.infim.ro

2 7 F. Sv The presence nd the role plyed y the structurl voids in vrious metl-semiconductor lloys s e.g. Ge-Mo nd Ge-Au, re still under dete nd severl models sed on the Monte Crlo Metropolis nd reverse Monte-Crlo methods hve een discussed [5,]. Recently, Gskell [7] hs reviewed the structurl network glsses nd hs shown tht ordered (microline) nd rndom models hve oth strengths nd weknesses. Hlm et l. [8] hve shown tht in mny liquid lloys there re strong fluctutions of density t the tomic scle nd they cn e scried to the specific distriution of the voids. In this pper we report the results of the clcultion of interstitil void size distriution in model of morphous silicon derived from the line lttice of silicon y introducing step y step specil topologicl modifictions, clled deformon sttes.. Topologicl defects in perfect tetrhedrlly onded lttice. Model of morphous silicon If two neighoring toms in line silicon re interchnged fter reking nd re-forming only three onds (one common ond nd two onds with the neighors) then one gets devint onds emedded into perfect lttice. The distortion energy of the devint onds rpidly decreses y the relxtion of the lttice round the interchnged toms. The finl stte of distortion defines diffuse defect in the silicon lttice. This cn e considered s topologicl defect, nd Popescu [9] proposed to e clled deformon stte, or simply deformon. The schemticl illustrtion of the chnge of the positions of two toms while preserving ll covlent onds in the lttice, chrcteristic to the deformon stte, is shown in Fig Fig.. The topologicl chnges involved in the deformon stte;. initil stte; deformon stte. The modelling ws crried out on hnd-uilt model of line silicon with 3 toms. A numer ws ttched to ech tom in the originl lite. The coordintion of every tom ws listed in coordinte tle nd the covlently onded neighours were listed in neighour tle. Firstly, only one deformon ws introduced in the centre of the model y switching two onds. The nlysis of the topologicl defect thus formed hs shown tht in the line lttice chrcterized y -fold chir-like rings of toms do pper four 5-fold rings nd six 7-fold rings of toms. After introducing the defect stte, the whole (whose tom coordintes were susequently mesured on the model) ws energeticlly relxed, without oundry conditions, y using Monte Crlo computer procedure nd ond ending nd ond stretching potentils fter Keting [] with the elstic force constnts given y Mrtin []. The Keting potentil is simple sum of ond-stretching nd ond-ending potentils: V = i( j) 3α 3β 8d ( x i x j d ) + ( x )( ) cos i x j xk xi d i( j, k ) 8d where nd re the ond-stretching nd ond-ending force constnts, respectively, nd d is the strin-free equilirium ond length in the. For Si d =.35 nm. The sum i is over ll toms, j over the nerest neighours of i, nd k over ll nerest neighours not including j. γ is the idel tetrhedrl ngle: 9 o 8. The ond stretching force constnt is = 48.5 pj nd the rtio / =.85. γ ()

3 Chrcteriztion of the interstitil voids in the structurl model of morphous silicon derived from the 77 The Keting potentil provides good semiempiricl description of the onding forces with only two prmeters. Centrl ond-stretching forces re not enough for stilizing tetrhedrlly onded structure, hence the ond-ending term is essentil. In the first stge of modelling we introduced second deformon in the sme simulted lttice nd the new stte of distortion ws determined fter the relxtion of the whole model. Then, we continued the process y introducing new deformons: 3, 5,, 5,, 5, 3, 33, 38, 45, 5, 55,, 4, 9, 75, 8, 85, 89, 95,, 5,, 5, 5, 3 nd 38 deformons for the finl stte of the line model. After every new group of deformons introduced in the lttice, the coordinte tle nd the neighor tle were updted. The relxed network in every cse ws nlysed in detil. Fig. shows the vrition of the distortion energy per mole of silicon s function of the numer of deformons introduced in c-si model. It is remrkle the synergic effect induced y high numer of deformons. The totl distortion energy increses non-linerly. The increse of distortion energy is not proportionl to the numer of deformons, ut shows tendency to sturtion. Distortion energy ( -7 J) Numer of deformons Fig.. The distortion energy of the c-si model vs the numer of deformons. 3. Method for the clcultion of the void-size distriution An interstitil void in lttice or network is defined s tht region situted in-etween the toms, tht corresponds to the sphere of mximum dimeter, which cn e introduced in the free spce delimited y the tomic neighourhood []. The void size distriution represents the distriution of the dimeters of ll the spheres tht cn e introduced in the lttice or network without notle superposition (prtil superposition of round 5- % of the dimeter ws permitted, thus ccounting for eventully non-sphericl, elongted voids). A specil computer progrm run in FORTRAN ws devised to this purpose. 4. Results 4. Void distriution. Chrcteriztion 8 No. of voids 5 def. 55 def Dimeter of voids (nm) 5 def. D men (nm) No. of deformons Dispersion of dimeters (nm) c No. of deformons Fig. 3.. The distriution of the void dimeters;. the men dimeter of voids versus the numer of deformons introduced in the silicon lttice; c. the dispersion (r.m.s.) of the void dimeters s function of the numer of deformons introduced in the silicon lttice.

4 78 F. Sv Fig. 3 shows the chrcteristic of the void system in the silicon model. The distriution of the void dimeters () rodens nd moves towrds smll vlues when the model ecomes disordered y introducing more deformons into the lttice. The men dimeter () moves down to vlue of ~.8 nm. In the sme time the r.m.s. devition of the void dimeter (c) increses up to vlues of ~.4 nm. It seems tht the model tends to limit of disorder when no four fold rings of toms re permitted. This rule ws imposed to our model during the disordering procedure. 4. Structurl chrcteriztion of the silicon model nd of its voids The structure fctor of the silicon model with vrious numers of deformon is shown in Fig. 4. Fig. 4 shows the theoreticl interference function clculted for model defined y the void centres, where the void centers consist of silicon toms. The most importnt feture of the void ssemly is the vnishing of the oscilltions specific to line lttice (for lrge rnge of the scttering vector) nd those specific to short-rnge order (for high vlues of scttering vectors). 3 S(Q) 5 def. 55 def. 5 def Q (nm - ) S(Q) def. 55 def. 5 def Q (nm - ) Fig. 4.. The structure fctor of the model with vrious numer of deformons;. Theoreticl interference function clculted for model defined y the void centres. The differentil rdil distriution function of the silicon model nd of its imge of voids were clculted nd represented in Fig. 5 for different numer of distorting deformons in the silicon lttice. While the tom DRDF is in good greement with the experimentl function, the void DRDF show less pronounced structurl detils. The existence of low nd rod mximum round the vlue of.37 nm speks in fvour of some ordering of the voids round the network toms. DRDF 4 5 def. 55 def. 5 def r (nm) DRDF 5 def def def r (nm) Fig. 5.. Differentil rdil distriution function of the silicon model;. Differentil rdil distriution function of the model defined y the void centres.

5 Chrcteriztion of the interstitil voids in the structurl model of morphous silicon derived from the 79 The void configurtion could e not completely t rndom. Some ordering proly exists nd this cn e relted to the medium rnge order in the morphous mteril. The extension of this order hs een nlysed y determining the network of possile onds etween voids nd clculting the hypotheticl distriution of dihedrl ngles etween voids. The results re shown in Fig.. As esily oserved, the dihedrl ngle correltion is rpidly lost when the numer of deformons in the c- Si increses. The complete loss of dihedrl ngle correltion mens tht the voids re rther correlted t distnces lrger thn.54 nm, corresponding to the verge distnce etween the end voids tht define the dihedrl ngle. Numer of dihedrl ngles deformons 55 deformons 89 deformons 5 deformons 5 5 ω ( o ) Fig.. Dihedrl ngle distriution in the system of voids. 5. Discussion The interstitil void distriution in model of morphous silicon is n importnt prmeter relted to the properties of silicon. Nkhmnson [3] hs shown tht the min properties of morphous silicon cn e understood y supposing tht network of intimtely relted nnovoids nd line grins defines the structure of the mteril. The size nd distriution of voids nd nnolites control the electronic density of sttes in the mteril, nd, therefore, the opticl nd electricl properties. Well ordered lites define voids with nrrow size distriution. In such configurtions the doping of the mteril is possile ecuse the flexiility of the network is lower. Non-uniform distriution of the strined sp 3 onds is useful for the ppernce of n or p type centres, especilly when doping toms re dded [4]. A generl concept of nno-heteromorphism for complex glsses hs een developed y Minev [5]. This concept could e extended to elementl glsses: the glss consists of nnostructurl units formed y group of toms with low men distortion of the inter-tomic onds. This seems to e lso the cse of the morphous silicon.. Conclusions The void morphology, size distriution nd sptil configurtion hve een nlyzed in model for morphous silicon derived from the perfect line lttice of silicon y introducting in it lrge numer of deforming sttes. The voids seem to e ordered t the intermedite scle. The void structure is relevnt to the physicl properties of the mteril. Work is in progress for compring the void configurtion in this model with the continuous rndom network models for morphous silicon.

6 8 F. Sv Acknowledgement The uthor is indeted to the "Hori Huluei" foundtion for finncil support. He wishes to thnk Prof. Dr. Mihi Popescu for continuous interest nd help with this pper. References [] S. R. Elliott, Physics of Amorphous Mterils, Longmn, 984. [] I. Solomon, J. Optoelectron. Adv. Mter. 4(3), 49 (). [3] K. Kds, S. Kugler, J. Optoelectron. Adv. Mter. 4(3), 455 (). [4] C. Longeud, J. Optoelectron. Adv. Mter. 4(3), 4 (). [5] A. Popov, J. Optoelectron. Adv. Mter. 4(3), 48 (). [] A. F. Kokhlov, A. I. Mshin, J. Optoelectron. Adv. Mter. 4(3), 53 (). [7] F. Yonezw, K. Nishio, J. Kog, T. Ymguchi, J. Optoelectron. Adv. Mter. 4(3), 59 (). [8] F. H. Stillinger, T. A. Weer, Science 5, 983 (984). [9] G. Etherington, A. C. Wright, J. T. Wentel, J. C. Dore, J. H. Clrke, R. N. Sinclir, J. Non-Cryst. Solids 48, 5 (98). [] D. E. Polk, J. Non-Cryst. Solids 5, 35 (97). [] F. Wooten, K. Winer, D. Weire, Phys. Rev. Lett. 54, 39 (985). [] F. Wooten, G. A. Fuller, K. Winer, D. Weire, J. Non-Cryst. Solids 75, 45 (985). [3] S. R. Elliott, Nture 354, 445 (99). [4] K. O. Jensen, P. S. Slmon, I. T. Penfold, P. G. Colemn, J. Non-Cryst. Solids 7, 57 (994). [5] R. Grigorovici, J. Non-Cryst. Solids 35&3, 7 (98). [] I. Kn, Th. Hlm, W. Hoyer, J. Non-Cryst. Solids 88, 9 (). [7] P. H. Gskell, J. Non-Cryst. Solids 93-95, 4 (). [8] Th. Hlm, J. Nomssi Nzli, W. Hoyer, R. P. My, M. Bionducci, J. Non-Cryst. Solids 93-95, 8 (). [9] M. Popescu, Rev. Roum. Phys. 3(), 97 (99). [] P. N. Keting, Phys. Rev. 45, 39 (9). [] R. M. Mrtin, Solid Ste Comm. 8, 799 (97). [] M. Popescu, J. Non-Cryst. Solids 35-3, 549 (98). [3] S. Nkhmnson, Ph. D. Thesis, Ohio University, USA,. [4] S. T. Pntelides, Phys. Rev. Lett. 57, 979 (98). [5] V. S. Minev, J. Optoelectron. Adv. Mter. 4(4), 843 ().