Pulsed Laser Induced Recrystallization of Amorphous Si
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PULSED LASER INDUCED RECRYSTALLIZATION OF AMORPHOUS Si
Sebastiano Tosto, ENEA Casaccia, via Anguillarese 301, 00060 Roma, Italy. e-mail: [email protected] ABSTRACT The paper introduces a 3D model to simulate the recrystallization microstructure of amorphous Si induced by pulsed laser irradiation. The computer simulation shows how the microstructure is modified when introducing into the model the assumption of rapid solidification quenching. INTRODUCTION. Laser processing of Si has been widely investigated in the recent literature from the experimental and [1] and theoretical point of view [2], in particular as concerns the surface melting and recrystallization [3]. A paper recently published [4] has introduced a 3D model, including the temperature dependence of the thermal and optical properties, to simulate the microstructure obtained by pulsed laser irradiation of amorphous Si (a-Si). Melting and solidification are described in this model by calculating the characteristic times of beginning of melting, end of melting and nucleation of a stable nucleus for each volume element of the heat affected zone. This kind of approach, deterministic as concerns the microstructure, can be made consistent with the random character of any solidification process by taking into account that the pulsed laser recrystallization is typically a non-equilibrium process characterized by rapid temperature transients. The paper shows how the deviation from the equilibrium condition affects the final microstructure. The simulation concerns in particular the recrystallization of a semi-infinite body of a-Si by laser irradiation at λ = 1.06 µ m with pulse lengths of the order of some tens ns . PHYSICAL BACKGROUND OF THE MODEL. This section summarizes for clarity the main results introduced in [4]. Let the irradiation conditions be such that in a proper region of heat affected zone the local temperature overcomes the thermodynamic melting point Tm of a-Si, so that surface melting is allowed to occur. A boundary condition of the problem is then the energy conservation at any point of the liquid-solid interface r K li ∇Tli − K si ∇Tsi = u ρ si H (1) The subscripts l and s stand for liquid and solid, i means that the various quantities refer to the r interface values; ρ and K are density and heat conductivity of the respective phases, u is the local r displacement rate of the interface, H the latent heat. Eq 1 gives the following expression of u = u 2
2
2
∂T ∂T ∂T ∂T ∂T ∂T u = ( ρ si H ) K si si − K li li + K si si − K li li + K si si − K li li (2) ∂xo ∂xo ∂yo ∂yo ∂zo ∂zo where x o = x o (t ) , y o = y o (t ) and z o = z o (t ) are the time dependent coordinates of any interface point. Then u can be calculated once knowing the thermal fields of the liquid and solid phases. The basic idea of the model is to include into the heat equations of both phases a source term taking into account the heat flow, additional to that of the laser source, due just to the latent heat involved during the state change. N
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