FEMAG晶体生长建模软件--Numerical_Prediction_of_Bulk_Crystal_Defects

FEMAG晶体生长建模软件Optimization of Silicon I n go t Q u al it yby the Numerical P r e d i c ti on of Bulk Crystal D e f ec t sF. Loix2*, F. D upr e t1,2*, A. de Potter2, R. R ol i n s ky2, W. L i a ng2, N. Van den B oga e rt21CESAME R e s e a r ch C e nt e r, Uni v e r s i téc at ho li que de L ouva i n,Bât i m e nt EULER, 4 av. Georges L e m aît r e,B-1348 Louva i n-l a-N e uv e,B e l g i um2FEMAGSoft S.A. Company, 7 Rue André Dumont, A x i s Parc, B-1435 Mont-Saint-Guibert, B e l g i umThe growth of S ili c on(Si) i ngot s by the Cz oc hra l s ki(Cz) technique for e l e c t roni c (IC) a ppl i c a t i ons has been governed for more than 50 years by two, somewhat c ont ra di c t ory, t e c hnol ogi c a l obj e c t i ve s.First, the c rys t a l diameter has to be nearly constant and the l a rge s t pos s i bl e according to current market requirements. Second, the product quality has to be pe rfe c t l y c ont rol l e d in terms of c rys t a l defects and composition. On the other hand, grow i ng Cz S i c rys t a l s for phot o-volt a i c(PV) a ppl i c a t i ons requires to m i ni m i z e both the energy c ons umpt i on and the growth dura t i on without, however, gene ra t i ng a too l a rge content of m i c ro-voi ds in the c rys t a l.A c hi e vi ng these goa l s i s by no means easy s i nc e i nc re a s i ng the c rys t a l diameter re qui re s a l a rge r m e l t volume and hence results in a much more complex m e l t flow regime with c om pl i c a t e d heat, momentum and s pe c i e s transport effects, a very s e ns i t i ve s ol i d-li qui d i nt e rfa c e shape (with a l e ss uniform t he rm a l gradient), and in gene ra l an enhanced dynamic s ys t e m behavior. A s i m il a r enhancement of the system dyna m i c behavior can result from the use of a high pull rate to i nc re a s e the growth speed. Therefore, in gene ra l,de s i gni ng the furnace hot zonewill require to i nt roduc e appropriate heat s hi e l ds in order to w e ll-c ont rol the ra di a t i on he a t transfer whi l e a s a t i s fa c t ory m e l t flow pattern can only be obt a i ne d for l a rge diameter c rys t a l s by the a c t i on of transverse or configured m a gne t i c fi e l ds.Moreover the s e l e c t i on of opt i m a l proc e ss parameters (heater power, c rys t a l pulling rate, c rys t a l and c ruc i bl e rot a t i on rates, m a gne t i c fi e l d i nt e ns i ty if any, ambient gas flow rate, etc.) becomes much more difficult in vi e w of the i nc re a s e d system nonl i ne a ri ty and t i m e-depe nde nc y,e s pe c i a ll y during the c ri t i c a l process stages (necking, shouldering, t a il-e nd stage, c rys t a l detachment, …).N one t he l e ss,compared to the high difficulty to address these different t e c hnol ogi c a l i ss ue s,it i s worth observing that huge progress has been achieved in the l a s t decades in s e ve ra l s c i e nt i fi c dom a i ns.F i r s t, the phys i c s of ra di a t i on and c onve c t i on in Cz furnaces, and of defect form a t i on and transport in growing S i c rys t a l s,i s much better known, and hence the m a t he m a t i c a l m ode l s governing Cz S i c ry s t a l growth are better and better e s t a bl i s he d.In spite of the i mport a nt i m prove m e n t s that re m a i n necessary in the m ode li ng of turbulence in the m e l t a nd the ambient gas (i nc l udi ng the m ode li ng of m e l t turbulence under the effect of a m a gne t i c fi e l d) and of the s t ill i ns uffi c i e nt kno w l e dge of the m a t e ri a l parameters governing point-and micro-defect e vol ut i on in S i s i ngl e c rys t a l s,an a l m os t complete picture of the phy s i c s of S i growth today i s a va il a bl e.Secondly, num e ri c a l methods and computers have a l s o quickly progre ss e d s i nc e the de ve l opm e n t of the first m ode l s of Cz growth achieved in the 1980’s. Nowadays the qua s i-s t ea dy or t i m e-depe nde nt s i m ul a t i on of the Cz process hasbecome po ss i bl e in an a cc e pt a b l e c om put i ng t i m e,with s uffi c i e nt l y refined meshes to resolve the key de t a il s of the problem, and with appropriate num e ri c a l techniques to handle the system de form i ng ge om e try (which comprises s e ve ra l moving components together with free boundaries such as the m e l t-c rys t a l and m e l t-ga s i nt e rfa c e s).Therefore, having at one’s di s pos a l the appropriate phys i c a l m ode l s, num e ri c a l tools a nd computer hardware, the route i s directly opened to process opt i m i z a t i on by means of num e ri c a l s i m ul a t i on.The obj e c t i ve of the present paper i s to ill us t ra t e how this strategy can be a ppl i e d by use of the FEMAG-CZ software as today co-de ve l ope d by FEMAG Soft S.A. Company and the CESAME research center of the Uni ve rs i téde L ouva i n (Belgium).We will here focus on the S i ingot quality pre di c t i on and i t s opt i m i z a t i on.We present a fully t i m e-depe nde nt m ode l devoted to predict the gl oba l heat transfer in the furnace, the s ol i d-liquid i nt e rfa c e shape, and the re s ult i ng di s t ri but i ons of point-and m i c ro-de fe c t s as c a l c ul a t e d from the S i nno-D ornbe rge r (S-D) model together with an e xt e ns i on of the l um pe d model of Voronkov and Kulkarni. All the t ra ns i e nt s are c ons i de re d including the effects of c rys t a l a nd c ruc i bl e lift, of the heat c a pa c i t i e s of the furnace c ons t i t ue nt s, of the t he rm a l i ne rt i a of the s ol i di fi c a t i on front, and of the dyna m i c defect governing l a w s.We hence show that dynamic effects deeply affect the defect di s t ri but i on in the c rys t a l(fig 1.). In a ddi t i on to the c l a ss i c a l point-defect e vol ut i on mechanisms, a new l um pe d m ode l i s de ve l ope d to c a l c ul a t e theform a t i on a nd growth of m i c ro-de fe c t s in order to predict their dens i t i e s and s i z e di s t ri but i ons anywhere in the c rys t a l.Another key i ss ue in Cz S i growth i s to control the dens i ty of oxygen and any other s pe c i e s(i nc l udi ng dopants and i m puri t i e s) i ns i de the c rys t a l.M ode li ng i ss ue s will be here a ga i n de t a il e d.Finally, off-line process control pri nc i pl e s will be addressed. Results will ill us t ra t e how this tool can he l p in opt i m i z i ng c rys t a l shape and quality.P r e di c t e d defect de l t a C i-C v di s t r i bu t i on (C i, C v be i ng the c onc e nt r at i on of i n t e r s t i t i al s , v acan c i e re s p e c t i v e l y) with a quas i-s t e ady (a) and a t i m e-d e pendent （b）simulation. The OSF ring is located at the position where delta~= 0. This picture highlights the strong impact on the point defect of the transient effects in the growing crystal.。