Dynamical Modeling of Laser ablation Processes
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Mat. Res. Soc. Symp. Proc. Vol. 388 01995 Materials Research Society
The laser energy input is specified at each instant of time and each point in space through the source term S related to the intensity of the laser pulse D: S(x,t)= [I
-
R(x,t)]F(t) ae-x .
For silicon, the absorption coefficient o: is taken to be a =1 x 106 cm-1 in both the solid and liquid phases; the reflectivity R is set at 0.58 for the solid phase and 0.69 for the liquid phase; and the profile of the thermal conductivity Kis as in Ref. 5. Phase transitions, which may be timedelayed, are handled through the state array concept that determines the state of each cell in space and time according to the appropriate (enthalpy h, temperature T) state diagram. In addition to the solid-liquid transition appropriate for laser annealing, we have extended the process to include the liquid-vapor transition necessary to model the initial stages of laser ablation. The extended thermal model also includes the effect of the pressure at the liquid surface P, on the vaporization temperature through the Clausius-Clapeyron equation:
T =[ 1
ln(p,/P,/1) AH
To
where To is the vaporization temperature at atmospheric pressure P0 and AH is the latent heat. Results from calculations with the I -D version of the Laser8 computer program are displayed in Fig. 1. The depth of vaporization and maximum recession speed at atmospheric pressure as a function of laser energy density are displayed on the right. Both are linear with energy density and indicate that the vaporization threshold is around 4 J/cm 2 . The vaporization temperature and threshold laser energy density for onset of vaporization as a function of pressure at the liquid surface Ps are displayed on the left. Both go like log(Ps) and indicate that a lower vaporization temperature and a lower threshold laser energy density are obtained in near-vacuum than at atmospheric pressure in accordance with the Clausius-Clapeyron equation. In particular, the predicted threshold laser energy density decreases from -4 J/cm 2 at atmospheric pressure to -1.5 J/cm 2 at a pressure of 1 mTorr. 3500
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Fig. I Results from 1-D Laser8 for silicon: vaporization temperature and laser energy density threshold for vaporization as a function of surface pressure (left) and vaporization depth and maximum recession speed as a function of laser fluence at a liquid surface pressure of 1 atm (right).
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The thermal model allows us to specify the initial conditions for the plume transport models to be described next. III. PLUME FORMATION AND TRANSPORT Plasma formation Before considering gas dynamic and collisional models of plume transport from the target to the deposition substr
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