Short Notes K115 phys. stat. sol. ( a ) g , K115 (1985) Subject classification: 1 . 5 and 3; 11; 22 . 1 . 2 SeMion Physik der Priedrich-Schiller-UniversitP Jena Theoretical Evidence for Opposite Moving Phase Fronts during Ultrafast Solidification Processes BY D. STOCK, H. -D. GEILER, and K . HEHL 1 ) Rapid solidification processes of thin liquid layers of semiconductors produced by short laser pulses a re the subject of many experimental investigations / l / , and there is a lot of experimental evidence for crystallization velocities of about 1 0 m9-l /2/. It is impossible to understand this dynamics from the view-point of the heat flow control (HFC) of the moving phase front /3/, rather the kinetic interface control (KIC) has to be taken into account /4/. As can be expected from earlier model calculations /5/ of moving boundary problems with constant externally imprinted velocity of the phase front, the temperature peaks up at the moving interface due to the high rate of the re- lease of latent heat. To study this problem of transport of both energy and matter durhg melting and resolidification induced by short laser pulses, the Frenkel-Wilson law determining the velocity i of melting and crystallization of silicon as a function of the interface temperature Ti was used follawing latent heat Lc = 0.495 eV, melting temperature Tmc = 1685 K, activation energy E = 1 .22 eV, and vo = 6xlO ms governed by the heat conductivity K(T) and the energy deposition function Y /8/, which depends on the laser intensity I, the temperature T, and explicitly on the depth x, because of the layered structure of samples with a melting surface 5 -1 /6/. The energy transport is The specific enthalpy h(T) includes the latent heat. The coupled nonlinear equations (l), (2) were solved numerically using the boundary values = 0 , T(d, t) = T o , T(x, O ) = T = 1 5 0 K 0 1 ) Max-Wien-Platz 1, DDR-6900 Jena. GDR. K116 t 1750 - Y L I- physica status solidi (a) 8 7 Fig. 1. Temporal development of the temperature profile taking into account one interface (arrows indicate the ac- tual position of the interface); 0 .53pm pulse, 0.3 J/cm2, 0.5 ns, 150 K; (1) 0.4125 ns, (2) 1.1625 ns, (5) 1.4875 ns, (6) 1.9250 ns, (7) 2.411s 7 700 (3) 1.175Onm) (4)1.2750ns9 T I C 1650 and taking into account the energy de- position by a Q-switched frequency doubled neodymium laser (X = 532 nm, pulse length 0.5 ns, energy density 0.3 J ~ r n - ~ ) . In Fig. 1 the resulting tem- perature profiles at different times a re 1600 0 20 4.0 60 80 shown. The arrows indicate the actual 1550 position of the solid-liquid interface. Starting from the superheated solid (curve 1) the interface moves into the depth, and the molten layer obtains its greatest thickness, i f the superheating vanishes at the interface (curve 2). Then the strong temperature gradient produces an undercooling (curves 4 to 6) connected with the crystallization controlled by the actual interface temperature via (1). As expected, the tem- perature peaks up at the interface due to the released latent heat during the rapid solidification (curve 7). Therefore, the maximum temperature is established at the moving interface and the minimum temperature in the melt x (nm) - is realized at the surface. Hence, the most probable region for nucleation events in the undercooled melt should be the surface. To investigate the influence of nucleation followed by rapid growth, a heteronucleation at the surface was assumed at the moment - - - - Fig. 2. Temporal development of the tem- perature profile in the case of two op- posite mo2ing interfaces; 0.53 p m pulse, 0.3 J/cmL, 0.25 ns, 150 K; (1) 1.32 ns, - ' x(nd- (2) 3.60 ns Short Notes K117 Fig. 3. Position of the liquid- solid interfaces versus time. F o r comparison the path of one inter- face alone (without nucleation at the surface) is drawn 0 4 6 8 10 t (n5) - of minimum surface temperature. If the crystallization starts from one nucleus at the surface, a temperature profile results as it is shown in Fig. 2 (curve 1). The released latent heat from two opposite moving interfaces quickly changes this temper- a ture profile (curve 2). Fig. 3 shows the temporal development of both interfaces. Melting starts from the surface after 0.8 ns, the recrystallization begins from the depth and after about 1 . 3 ns the heteronucleation at the surface initiates the second crystallization front. After about 1 0 ns both interfaces impinge on each other in a depth of about 15 nm. faces could help to understand some experimental results recently published by Campisano /9/. The resulting two crystallized regions produced by opposite moving inter- References /1/ J . NARAYAN and C.W. WHITE, Appl. Phys. Letters - 44, 35 (1984). /2 /M. 0. THOMPSON, J .W. MAYER, A.G. CULLIS, H.C. WEBBER, N.G. CHEW, J .M. POATE, and D.C. JACOBSON, Phys. Rev. Letters 50, 896 (1980). /3/ P. BAERI, in: Laser and Electron-Beam Interactions with Solids, Ed. B.R. /4/ D. STOCK, H. -D. GEILER, and K. HEHL, Proc. Internat. Conf. EPM 84, /5/ R.W. HOPPER and D. R. UHLMA”, J. CrystalGrowthle, 177 (1973). /6/ G . ANDR& H. -D. GEILER, G. GOTZ, K.H. HEINIG, and H. WOITTEN- /7/ K. A. JACKSON, in: Proc. NATO Advanced Study Inst. on Surface Modifi- APPLETON and G.K. CELLER, North-Holland, New York 1982 (p. 151). Dresden 1984. NEK, phys. stat. sol. (a) 74 511 (1982). cation and Alloying, Trevi 1981, Ed. J .M. POATE, G. FOTI, and D.C. JACOBSON, Plenum Press, New York 1983 (Chap. 3). -’ K118 /8/ H. -D. GEILER, K. HEHL, and D. STOCK, phys. stat. sol . (a) z, 193 /9/ S. U. CAMPISANO, Proc. 1984 Fall Meeting of the MRS, Boston (USA) physica status solidi (a) 87 (1 983). 26. to 30.11. , 1984. (Received November 26, 1984)































































































































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