- Email: [email protected]
Phase-field modelling of excimer laser lateral crystallization of silicon thin films
Thin Solid Films 427 (2003) 309–313
Phase-field modelling of excimer laser lateral crystallization of silicon thin films A. Burtseva,*, M. Apelb, R. Ishiharaa, C.I.M. Beenakkera a
Laboratory of Electronic Components, Technology and Materials (ECTM), Delft University of Technology, Feldmannweg 17, 2628 CT Delft, The Netherlands b Access e.V., Intzestr. 5, D-52072 Aachen, Germany
Abstract A 2D phase-field model was applied to simulate the phase-transition kinetics and the thermal field distribution during the lateral crystallization of a-Si induced by single pulse excimer laser. The higher tilt of solidyliquid interface increases the supercooling temperature in the melt due to the fast latent heat extraction at the solidyliquid interface. The lateral growth velocity is in average four times faster than the vertical one. When the lateral growth velocity exceeds the critical value of 19 mys, amorphization of Si can be initiated because of unstable growth front. Therefore, thickness of Si film and the thermal properties of underlying layer play a crucial role not only in ultra-large grain fabrication but also in defect-free crystal growth. 䊚 2002 Elsevier Science B.V. All rights reserved. Keywords: Excimer-laser; Lateral growth; Phase-field model; Supercooling; Spontaneous nucleation
1. Introduction Mathematically, the growth of crystals in pure melt is modeled by a moving free boundary problem (FBP), often referred to as the modified Stefan problem. In thermal models, the phase transformations are governed by thermal balance at the equilibrium transition temperature Tm w1,2x. In capillary w3x and kinetic w4–6x models the temperature fields in each phase satisfy a heat diffusion equation and are coupled at the unknown crystalymelt interface. Pure thermal or kinetic models, utilizing only solidification rate temperature gradient arguments, cannot solve the selection of interface morphology in the case of solidification into supercooled melts, because the interfacial energies are neglected. However, taking curvature effects into account is in general a non-trivial problem, which has not been extended with perhaps one exception w7x into 3D. The phase-field approach w8,9x is an alternative method to solve the FBP, which circumvents the problems of front tracking, since it is a continuum description leading to a set of partial differential equations. The interfaces are not sharp but of finite thickness which allows a straight*Corresponding author. Tel.: q31-15-278-7061; fax: q31-15-2622163. E-mail address: [email protected] (A. Burtsev).
forward calculation of the curvature and easy extension into 3D. This work presents an adequate 2D modelling tool for simulation of the phase-transition kinetics and the thermal field distribution of the lateral growth in Si melt pool from unmelted residual Si fraction after pulsed laser irradiation. The spontaneous nucleation process is also taken into account. The solution of the FBP, which includes curvature supercooling and latent heat recalescence is obtained by utilizing the phase-field method. The influence of a-Si layer thickness and underlying oxide thickness on grain size has been investigated numerically and experimentally. 2. Experimental The first step in the preparation of the samples involved deposition of a SiO2 layer with thickness varying from 100 to 1000 nm onto a 4-inch c-Si (1 0 0)oriented wafer by LPCVD at a temperature of 425 8C. Subsequently, an a-Si layer with thickness varying from 50 to 200 nm was deposited on the planar oxide by LPCVD using SiH4 decomposition at 545 8C. The resulting oxide and a-Si layer thickness variations are summarized in Table 1. Finally, the laser beam of the XeCl excimer-laser (308 nm, XMR 7100) was directed to the top of the structure with single pulse duration of
0040-6090/03/$ - see front matter 䊚 2002 Elsevier Science B.V. All rights reserved. PII: S 0 0 4 0 - 6 0 9 0 Ž 0 2 . 0 1 1 6 0 - 4
A. Burtsev et al. / Thin Solid Films 427 (2003) 309–313
310 Table 1 Oxide and a-Si layer thickness variations SiO2 thickness (nm) a-Si thickness (nm)
100 100
150 100
200 100
1000 50
1000 100
1000 200
66 ns. Morphological characterization of the obtained large grains was performed using SEM microscopy after the samples were defect-etched (Schimmel etching). 3. Results and discussion 3.1. Effect of Si film and underlying SiO2 film thicknesses Fig. 1 illustrates maximum diameter of the grain as a function of the Si film thickness. The underlying oxide thickness was fixed at 1000 nm. As can be seen in Fig. 1 the grain size increases almost linearly with Si film thickness, reaching an average size of 2.3 mm for 200nm thick Si film. Fig. 2 illustrates the maximum diameter of the grain as a function of the underlying oxide film thickness. The top Si layer thickness was fixed at 100 nm. The grain size increases significantly with oxide film thickness, reaching an average size of 1.6 mm for 1000-nm thick oxide. As can be seen in Figs. 1 and 2, the final crystallized structure represents typical SLG pattern which consists of: (1) a large disk-shaped structure with diameter varying between 0.5 and 2.2 mm in the center; (2) a small grained poly-crystal ring attached around the disk; (3) a fine grain region, surrounding the entire structure. 4. Numerical simulation 4.1. Overview of solidification dynamics We simulated only the 2D solidification process i.e. the lateral growth in Si melt pool from unmelted residual Si fraction, taking into account curvature supercooling, latent heat recalescence and spontaneous nucleation. Details about the applied phase-field model, which is able to describe such lateral solidification, were presented elsewhere w10x. Fig. 3a shows the evolution of the crystalline silicon area in the liquid 100-nm thick Si layer on 200-nm thick underlying oxide as a function of time t. The simulation starts with a small initial nucleus of solid silicon (light grey colour) in the lower left corner of liquid Si (dark grey colour). The black line marks the solidyliquid interface. As can be directly seen from the parabolic shape of the solidyliquid interface, solidification rate is larger in lateral direction parallel to the SiySiO2 than normal to the interface. The position of the solidyliquid boundary along and perpendicular to the SiySiO2 interface is shown in Fig. 3b. The lateral growth rate RL, which is the slope of the
Fig. 1. Maximum diameter of grain as a function of Si film thickness. The underlying oxide thickness was fixed at 1000 nm.
curve, increases with time, reaching the value of 44 my s, while that in the vertical direction RV decreases with square root behavior, reaching the value of 9.4 mys. Fig. 3c illustrates detailed 2D temperature profile near the solidyliquid interface in the Si film for various time steps. Thin curves show isothermal temperature profiles at temperatures between 1675 and 1575 K. As it can be seen, the temperature along the SiySiO2 interface is always lower than that in the direction of Si surface due to the thermal diffusion towards the underlying oxide. As a result, the stronger supercooling near the SiySiO2 interface provides faster growth rate there, while the less supercooled surface region of molten Si film near the surface results in a slow growth rate there (Fig. 3b). The tilted solidyliquid interface is convenient for the fast growth rate, because of the efficiently fast release of the excess latent heat from the solidyliquid interface tip in the supercooled melt. However, in simulations of Aichmayr et al. w5x the solidyliquid interface is sharp at the center of the Si thin film, while Gupta et al. w4x reported that the solidyliquid interface is vertical to the Si–underlayer interface. In both cases the interfacial energies are neglected, due to the utilized model types,
Fig. 2. Maximum diameter of grain as a function of underlying SiO2 film thickness. The top Si layer thickness was fixed at 100 nm.
A. Burtsev et al. / Thin Solid Films 427 (2003) 309–313
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Fig. 3. Dynamics of Si solidyliquid interface for 100-nm thick Si layer on 200-nm thick SiO2. (a) Shape of Si solidyliquid interface at ts1, 6, 6.7, 8, 12, 24 and 32 ns. The domain size shown is 1.5=0.1 mm in x and y direction. (b) Interface position perpendicular and parallel to the substrate vs. time. (c) Si temperature profiles around Si solidyliquid interface at ts1, 6, 6.7, 8, 12 and 24 ns. Thin curves indicate isothermal temperature profiles from left to right, at following temperatures: 1675, 1670, 1665, 1650, 1625, 1600 and 1575 K. The domain size shown is 1.5=0.1 mm in x and y direction. (d) Temperature profiles at SiySiO2 interface at ts1, 6, 6.7, 8, 12 and 24 ns. Arrows indicate the position of solidyliquid interface. Note that Tm is not the equilibrium melting temperature but reduced approximately 7 K due to the capillarity effect to 1673 K.
leading to inaccurate growth rate estimations and elimination of the influence of Si–underlayer interface properties. Different inclination angles of the isothermal lines to the SiySiO2 interface indicate the removal of the latent heat in all directions: (a) lateral energy removal mechanism near the solidyliquid interface indicated by the isothermal lines normal to the SiySiO2 interface; (b) vertical heat removal mechanism is observed during the first 3 ns for temperature of 1575 K, shown by outward tilted isothermal lines. Fig. 3d shows temperature profiles at the SiySiO2 interface parallel to the substrate for several t values after end of laser pulse. The solidy liquid interface is located at the right edge of the temperature peak (as shown by arrows), immediately followed by supercooling region. The solid Si fraction is located at the left edge of the temperature pike. This peculiar temperature profile is always present during the
complete solidification process of growing crystal fraction; either initially set nuclei or spontaneously nucleated one. As it can be seen, melt supercooling reaches the critical undercooling temperature of Tm—250 K within 6.7 ns after the end of laser pulse. Immediately triggered nucleation event raises the temperature at the peripheral area significantly due to the latent heat recalescence, and competitive grain growth starts. At ts8 ns numerous amount of nuclei is generated spontaneously, decreasing the supercooling temperature to Tm—30 K. The temperature peaks at the right side of the plot represent solidyliquid interface for newly formed grains. At ts24 ns the initial grain collides with the neighboring one at the SiySiO2 interface. At ts32 ns the solidification process is completed, resulting in a 1-mm large grain that is in a very good agreement with experimental data from Fig. 2.
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A. Burtsev et al. / Thin Solid Films 427 (2003) 309–313
Fig. 4. Simulated grain radius as a function of time for various Si film thicknesses. The thickness of underlying oxide was kept at 1000 nm.
4.2. Effect of the Si film thickness Fig. 4 shows the simulated grain radius as a function of time for various Si film thicknesses. The thickness of underlying oxide was kept at 1000 nm. As one can see, the grain size increases with Si film thickness. On the other hand, the thinner Si film has the fastest growth rate, which can be estimated from the slope of the respective curve. However, when the crystal growth is driven at critically high velocity of 19 mys, the growth front can breakdown completely with the formation of a disordered amorphous solid fraction w11x, which can be seen from SEM photo in Fig. 1 for 50-nm thick Si film. The black ring pattern around the central grain disk depicts the remnants of amorphous fraction, removed with Schimmel etching. The faster growth rate in 50-nm thick Si film is due to stronger supercooling near the solidyliquid interface, which is determined by the thermal flow to the underlying oxide. Despite the faster crystal growth rate for the thinner film, the temperature in the supercooled melt drops more quickly, reaching the critical temperature of spontaneous nucleation already at 11.4 ns after the end of the laser pulse for 50-nm Si film, compared to that at 33.2 ns for 200nm thick Si film. As a consequence, the crystal growth time is reduced, resulting in a smaller grain size.
suppresses efficiently the vertical thermal flow from molten Si film towards the substrate. In this way the molten Si film can keep its temperature above the critical temperature of nucleation for a long time, which also results in the high solidyliquid interface temperature, providing the slow crystal growth rate. However, the influence of underlying substrate (i.e. Si wafer or glass wafer) on cooling rate and solidification velocity is significant when intermediate oxide thickness is comparable with diffusion length of thermal wave. One micrometer thick oxide is already near the limit of infinite SiO2 thickness, when the properties of underlying substrate do not play any role. As was mentioned before, the breakdown of growth front can occur at high crystallization velocities, followed by film amorphization. Such behavior is depicted in SEM photo from Fig. 2 for 100 nm thick SiO2 film. The value of critical velocity was estimated to be 19 mys by comparing the position of amorphization onset of SEM image in Fig. 2 and simulation results. This value lies close to observed velocity of 15 mys reported in w11x. Therefore, thicker SiO2 underlayers are desirable for defect-free ultra-large grain growth. 5. Conclusions A 2D phase-field modelling tool for simulation of the phase-transition kinetics and the thermal field distribution of the lateral growth in Si melt pool from unmelted residual Si fraction after laser irradiation was developed. The maximum lateral and vertical growth velocities for 100-nm thick Si film on 200-nm thick SiO2 layer differ by nearly four times, i.e. RLs44 mys and RVs9.4 my s. The solidyliquid interface is non-planar: RV decreases in vertical direction governed by the propagation of the
4.3. Effect of the underlying SiO2 film thickness Fig. 5 shows the simulated grain radius as a function of time for various underlying SiO2 film thicknesses. The thickness of top Si film was kept at 100 nm. As one can see, the grain size increases with underlying SiO2 film thickness. It stems from the fact that the spontaneous nucleation is delayed for thicker underlying SiO2 film, therefore leading to longer crystal growth, and subsequently larger grain size, which is consistent with our experimental results. The thicker SiO2 layer
Fig. 5. Simulated grain radius as a function of time for various underlying SiO2 film thicknesses. The thickness of top Si film was kept at 100 nm.
A. Burtsev et al. / Thin Solid Films 427 (2003) 309–313
thermal wave into the SiO2 layer; RL accelerates as a consequence of the increasing melt supercooling in front of the interface in lateral direction. The supercooling temperatures approximately 250 K far away from the solidifying Si melt were achieved within 6.7 ns. The grain size enlargement with thicker Si and underlying SiO2 film was explained by the reduced cooling rate in the supercooled Si melt and subsequently delayed spontaneous nucleation. The growth front breakdown (i.e. film amorphization) for thinnest Si and underlying SiO2 films occurred at RLs19 mys. Therefore, the thermal properties and thickness of underlying SiO2 layer, as well as Si layer thickness play an important role in grain size enlargement and defect-free crystal growth. Acknowledgments The authors are grateful to Dr J.W. Metselaar for warm encouragement and motivation. This work was supported in part by the Dutch Technology Foundation
313
STW Project No. DEL.4542 and XMR Inc. Santa Clara, CA. References w1x H. Kuriyama, S. Kiyama, S. Noguchi, T. Kuwahara, S. Ishida, T. Nohda, K. Sano, H. Iwata, H. Kawata, M. Osumi, S. Tsuda, S. Nakano, Y. Kuwano, Jpn. J. Appl. Phys. 30 (1991) 3700. w2x T. Sameshima, S. Usui, Jpn. J. Appl. Phys. 74 (1993) 6592. w3x A.B. Limanov, J. Rus. Microelectr. 26 (1997) 113. w4x V.V. Gupta, H.J. Song, J.S. Im, Appl. Phys. Lett. 71 (1997) 99. w5x G. Aichmayr, D. Toet, M. Mulato, P.V. Santos, A. Spangenberg, S. Christiansen, M. Albrecht, H.P. Strunk, J. Appl. Phys. 85 (1999) 4010. w6x J.P. Leonardo, J.S. Im, Mat. Res. Sci. Proc. 580 (1999). w7x A.R. Roosen, J.E. Taylor, J. Comput. Phys. 114 (1994) 113. w8x G.J. Fix, Theory Appl. 2 (1983) 580. w9x I. Steinbach, F. Pezzolla, B. Nestler, M. Seesselberg, R. Prieler, G.J. Schmitz, J.L. Rezende, Physica D 94 (1996) 135–147. w10x A. Burtsev, M. Apel, R. Ishihara, Proceedings of the Fourth SAFE Workshop Veldhoven, The Netherlands, November 25– 28, 2001, pp. 9–10. w11x A.G. Cullis, N.G. Chew, H.C. Webber, D.J. Smith, J. Cryst. Growth 68 (1984) 634.
Phase-field modelling of excimer laser lateral crystallization of silicon thin films A. Burtseva,*, M. Apelb, R. Ishiharaa, C.I.M. Beenakkera a
Laboratory of Electronic Components, Technology and Materials (ECTM), Delft University of Technology, Feldmannweg 17, 2628 CT Delft, The Netherlands b Access e.V., Intzestr. 5, D-52072 Aachen, Germany
Abstract A 2D phase-field model was applied to simulate the phase-transition kinetics and the thermal field distribution during the lateral crystallization of a-Si induced by single pulse excimer laser. The higher tilt of solidyliquid interface increases the supercooling temperature in the melt due to the fast latent heat extraction at the solidyliquid interface. The lateral growth velocity is in average four times faster than the vertical one. When the lateral growth velocity exceeds the critical value of 19 mys, amorphization of Si can be initiated because of unstable growth front. Therefore, thickness of Si film and the thermal properties of underlying layer play a crucial role not only in ultra-large grain fabrication but also in defect-free crystal growth. 䊚 2002 Elsevier Science B.V. All rights reserved. Keywords: Excimer-laser; Lateral growth; Phase-field model; Supercooling; Spontaneous nucleation
1. Introduction Mathematically, the growth of crystals in pure melt is modeled by a moving free boundary problem (FBP), often referred to as the modified Stefan problem. In thermal models, the phase transformations are governed by thermal balance at the equilibrium transition temperature Tm w1,2x. In capillary w3x and kinetic w4–6x models the temperature fields in each phase satisfy a heat diffusion equation and are coupled at the unknown crystalymelt interface. Pure thermal or kinetic models, utilizing only solidification rate temperature gradient arguments, cannot solve the selection of interface morphology in the case of solidification into supercooled melts, because the interfacial energies are neglected. However, taking curvature effects into account is in general a non-trivial problem, which has not been extended with perhaps one exception w7x into 3D. The phase-field approach w8,9x is an alternative method to solve the FBP, which circumvents the problems of front tracking, since it is a continuum description leading to a set of partial differential equations. The interfaces are not sharp but of finite thickness which allows a straight*Corresponding author. Tel.: q31-15-278-7061; fax: q31-15-2622163. E-mail address: [email protected] (A. Burtsev).
forward calculation of the curvature and easy extension into 3D. This work presents an adequate 2D modelling tool for simulation of the phase-transition kinetics and the thermal field distribution of the lateral growth in Si melt pool from unmelted residual Si fraction after pulsed laser irradiation. The spontaneous nucleation process is also taken into account. The solution of the FBP, which includes curvature supercooling and latent heat recalescence is obtained by utilizing the phase-field method. The influence of a-Si layer thickness and underlying oxide thickness on grain size has been investigated numerically and experimentally. 2. Experimental The first step in the preparation of the samples involved deposition of a SiO2 layer with thickness varying from 100 to 1000 nm onto a 4-inch c-Si (1 0 0)oriented wafer by LPCVD at a temperature of 425 8C. Subsequently, an a-Si layer with thickness varying from 50 to 200 nm was deposited on the planar oxide by LPCVD using SiH4 decomposition at 545 8C. The resulting oxide and a-Si layer thickness variations are summarized in Table 1. Finally, the laser beam of the XeCl excimer-laser (308 nm, XMR 7100) was directed to the top of the structure with single pulse duration of
0040-6090/03/$ - see front matter 䊚 2002 Elsevier Science B.V. All rights reserved. PII: S 0 0 4 0 - 6 0 9 0 Ž 0 2 . 0 1 1 6 0 - 4
A. Burtsev et al. / Thin Solid Films 427 (2003) 309–313
310 Table 1 Oxide and a-Si layer thickness variations SiO2 thickness (nm) a-Si thickness (nm)
100 100
150 100
200 100
1000 50
1000 100
1000 200
66 ns. Morphological characterization of the obtained large grains was performed using SEM microscopy after the samples were defect-etched (Schimmel etching). 3. Results and discussion 3.1. Effect of Si film and underlying SiO2 film thicknesses Fig. 1 illustrates maximum diameter of the grain as a function of the Si film thickness. The underlying oxide thickness was fixed at 1000 nm. As can be seen in Fig. 1 the grain size increases almost linearly with Si film thickness, reaching an average size of 2.3 mm for 200nm thick Si film. Fig. 2 illustrates the maximum diameter of the grain as a function of the underlying oxide film thickness. The top Si layer thickness was fixed at 100 nm. The grain size increases significantly with oxide film thickness, reaching an average size of 1.6 mm for 1000-nm thick oxide. As can be seen in Figs. 1 and 2, the final crystallized structure represents typical SLG pattern which consists of: (1) a large disk-shaped structure with diameter varying between 0.5 and 2.2 mm in the center; (2) a small grained poly-crystal ring attached around the disk; (3) a fine grain region, surrounding the entire structure. 4. Numerical simulation 4.1. Overview of solidification dynamics We simulated only the 2D solidification process i.e. the lateral growth in Si melt pool from unmelted residual Si fraction, taking into account curvature supercooling, latent heat recalescence and spontaneous nucleation. Details about the applied phase-field model, which is able to describe such lateral solidification, were presented elsewhere w10x. Fig. 3a shows the evolution of the crystalline silicon area in the liquid 100-nm thick Si layer on 200-nm thick underlying oxide as a function of time t. The simulation starts with a small initial nucleus of solid silicon (light grey colour) in the lower left corner of liquid Si (dark grey colour). The black line marks the solidyliquid interface. As can be directly seen from the parabolic shape of the solidyliquid interface, solidification rate is larger in lateral direction parallel to the SiySiO2 than normal to the interface. The position of the solidyliquid boundary along and perpendicular to the SiySiO2 interface is shown in Fig. 3b. The lateral growth rate RL, which is the slope of the
Fig. 1. Maximum diameter of grain as a function of Si film thickness. The underlying oxide thickness was fixed at 1000 nm.
curve, increases with time, reaching the value of 44 my s, while that in the vertical direction RV decreases with square root behavior, reaching the value of 9.4 mys. Fig. 3c illustrates detailed 2D temperature profile near the solidyliquid interface in the Si film for various time steps. Thin curves show isothermal temperature profiles at temperatures between 1675 and 1575 K. As it can be seen, the temperature along the SiySiO2 interface is always lower than that in the direction of Si surface due to the thermal diffusion towards the underlying oxide. As a result, the stronger supercooling near the SiySiO2 interface provides faster growth rate there, while the less supercooled surface region of molten Si film near the surface results in a slow growth rate there (Fig. 3b). The tilted solidyliquid interface is convenient for the fast growth rate, because of the efficiently fast release of the excess latent heat from the solidyliquid interface tip in the supercooled melt. However, in simulations of Aichmayr et al. w5x the solidyliquid interface is sharp at the center of the Si thin film, while Gupta et al. w4x reported that the solidyliquid interface is vertical to the Si–underlayer interface. In both cases the interfacial energies are neglected, due to the utilized model types,
Fig. 2. Maximum diameter of grain as a function of underlying SiO2 film thickness. The top Si layer thickness was fixed at 100 nm.
A. Burtsev et al. / Thin Solid Films 427 (2003) 309–313
311
Fig. 3. Dynamics of Si solidyliquid interface for 100-nm thick Si layer on 200-nm thick SiO2. (a) Shape of Si solidyliquid interface at ts1, 6, 6.7, 8, 12, 24 and 32 ns. The domain size shown is 1.5=0.1 mm in x and y direction. (b) Interface position perpendicular and parallel to the substrate vs. time. (c) Si temperature profiles around Si solidyliquid interface at ts1, 6, 6.7, 8, 12 and 24 ns. Thin curves indicate isothermal temperature profiles from left to right, at following temperatures: 1675, 1670, 1665, 1650, 1625, 1600 and 1575 K. The domain size shown is 1.5=0.1 mm in x and y direction. (d) Temperature profiles at SiySiO2 interface at ts1, 6, 6.7, 8, 12 and 24 ns. Arrows indicate the position of solidyliquid interface. Note that Tm is not the equilibrium melting temperature but reduced approximately 7 K due to the capillarity effect to 1673 K.
leading to inaccurate growth rate estimations and elimination of the influence of Si–underlayer interface properties. Different inclination angles of the isothermal lines to the SiySiO2 interface indicate the removal of the latent heat in all directions: (a) lateral energy removal mechanism near the solidyliquid interface indicated by the isothermal lines normal to the SiySiO2 interface; (b) vertical heat removal mechanism is observed during the first 3 ns for temperature of 1575 K, shown by outward tilted isothermal lines. Fig. 3d shows temperature profiles at the SiySiO2 interface parallel to the substrate for several t values after end of laser pulse. The solidy liquid interface is located at the right edge of the temperature peak (as shown by arrows), immediately followed by supercooling region. The solid Si fraction is located at the left edge of the temperature pike. This peculiar temperature profile is always present during the
complete solidification process of growing crystal fraction; either initially set nuclei or spontaneously nucleated one. As it can be seen, melt supercooling reaches the critical undercooling temperature of Tm—250 K within 6.7 ns after the end of laser pulse. Immediately triggered nucleation event raises the temperature at the peripheral area significantly due to the latent heat recalescence, and competitive grain growth starts. At ts8 ns numerous amount of nuclei is generated spontaneously, decreasing the supercooling temperature to Tm—30 K. The temperature peaks at the right side of the plot represent solidyliquid interface for newly formed grains. At ts24 ns the initial grain collides with the neighboring one at the SiySiO2 interface. At ts32 ns the solidification process is completed, resulting in a 1-mm large grain that is in a very good agreement with experimental data from Fig. 2.
312
A. Burtsev et al. / Thin Solid Films 427 (2003) 309–313
Fig. 4. Simulated grain radius as a function of time for various Si film thicknesses. The thickness of underlying oxide was kept at 1000 nm.
4.2. Effect of the Si film thickness Fig. 4 shows the simulated grain radius as a function of time for various Si film thicknesses. The thickness of underlying oxide was kept at 1000 nm. As one can see, the grain size increases with Si film thickness. On the other hand, the thinner Si film has the fastest growth rate, which can be estimated from the slope of the respective curve. However, when the crystal growth is driven at critically high velocity of 19 mys, the growth front can breakdown completely with the formation of a disordered amorphous solid fraction w11x, which can be seen from SEM photo in Fig. 1 for 50-nm thick Si film. The black ring pattern around the central grain disk depicts the remnants of amorphous fraction, removed with Schimmel etching. The faster growth rate in 50-nm thick Si film is due to stronger supercooling near the solidyliquid interface, which is determined by the thermal flow to the underlying oxide. Despite the faster crystal growth rate for the thinner film, the temperature in the supercooled melt drops more quickly, reaching the critical temperature of spontaneous nucleation already at 11.4 ns after the end of the laser pulse for 50-nm Si film, compared to that at 33.2 ns for 200nm thick Si film. As a consequence, the crystal growth time is reduced, resulting in a smaller grain size.
suppresses efficiently the vertical thermal flow from molten Si film towards the substrate. In this way the molten Si film can keep its temperature above the critical temperature of nucleation for a long time, which also results in the high solidyliquid interface temperature, providing the slow crystal growth rate. However, the influence of underlying substrate (i.e. Si wafer or glass wafer) on cooling rate and solidification velocity is significant when intermediate oxide thickness is comparable with diffusion length of thermal wave. One micrometer thick oxide is already near the limit of infinite SiO2 thickness, when the properties of underlying substrate do not play any role. As was mentioned before, the breakdown of growth front can occur at high crystallization velocities, followed by film amorphization. Such behavior is depicted in SEM photo from Fig. 2 for 100 nm thick SiO2 film. The value of critical velocity was estimated to be 19 mys by comparing the position of amorphization onset of SEM image in Fig. 2 and simulation results. This value lies close to observed velocity of 15 mys reported in w11x. Therefore, thicker SiO2 underlayers are desirable for defect-free ultra-large grain growth. 5. Conclusions A 2D phase-field modelling tool for simulation of the phase-transition kinetics and the thermal field distribution of the lateral growth in Si melt pool from unmelted residual Si fraction after laser irradiation was developed. The maximum lateral and vertical growth velocities for 100-nm thick Si film on 200-nm thick SiO2 layer differ by nearly four times, i.e. RLs44 mys and RVs9.4 my s. The solidyliquid interface is non-planar: RV decreases in vertical direction governed by the propagation of the
4.3. Effect of the underlying SiO2 film thickness Fig. 5 shows the simulated grain radius as a function of time for various underlying SiO2 film thicknesses. The thickness of top Si film was kept at 100 nm. As one can see, the grain size increases with underlying SiO2 film thickness. It stems from the fact that the spontaneous nucleation is delayed for thicker underlying SiO2 film, therefore leading to longer crystal growth, and subsequently larger grain size, which is consistent with our experimental results. The thicker SiO2 layer
Fig. 5. Simulated grain radius as a function of time for various underlying SiO2 film thicknesses. The thickness of top Si film was kept at 100 nm.
A. Burtsev et al. / Thin Solid Films 427 (2003) 309–313
thermal wave into the SiO2 layer; RL accelerates as a consequence of the increasing melt supercooling in front of the interface in lateral direction. The supercooling temperatures approximately 250 K far away from the solidifying Si melt were achieved within 6.7 ns. The grain size enlargement with thicker Si and underlying SiO2 film was explained by the reduced cooling rate in the supercooled Si melt and subsequently delayed spontaneous nucleation. The growth front breakdown (i.e. film amorphization) for thinnest Si and underlying SiO2 films occurred at RLs19 mys. Therefore, the thermal properties and thickness of underlying SiO2 layer, as well as Si layer thickness play an important role in grain size enlargement and defect-free crystal growth. Acknowledgments The authors are grateful to Dr J.W. Metselaar for warm encouragement and motivation. This work was supported in part by the Dutch Technology Foundation
313
STW Project No. DEL.4542 and XMR Inc. Santa Clara, CA. References w1x H. Kuriyama, S. Kiyama, S. Noguchi, T. Kuwahara, S. Ishida, T. Nohda, K. Sano, H. Iwata, H. Kawata, M. Osumi, S. Tsuda, S. Nakano, Y. Kuwano, Jpn. J. Appl. Phys. 30 (1991) 3700. w2x T. Sameshima, S. Usui, Jpn. J. Appl. Phys. 74 (1993) 6592. w3x A.B. Limanov, J. Rus. Microelectr. 26 (1997) 113. w4x V.V. Gupta, H.J. Song, J.S. Im, Appl. Phys. Lett. 71 (1997) 99. w5x G. Aichmayr, D. Toet, M. Mulato, P.V. Santos, A. Spangenberg, S. Christiansen, M. Albrecht, H.P. Strunk, J. Appl. Phys. 85 (1999) 4010. w6x J.P. Leonardo, J.S. Im, Mat. Res. Sci. Proc. 580 (1999). w7x A.R. Roosen, J.E. Taylor, J. Comput. Phys. 114 (1994) 113. w8x G.J. Fix, Theory Appl. 2 (1983) 580. w9x I. Steinbach, F. Pezzolla, B. Nestler, M. Seesselberg, R. Prieler, G.J. Schmitz, J.L. Rezende, Physica D 94 (1996) 135–147. w10x A. Burtsev, M. Apel, R. Ishihara, Proceedings of the Fourth SAFE Workshop Veldhoven, The Netherlands, November 25– 28, 2001, pp. 9–10. w11x A.G. Cullis, N.G. Chew, H.C. Webber, D.J. Smith, J. Cryst. Growth 68 (1984) 634.