solidifies to a critical depth having order of where p eff is the effective pressure order of 10 bar taking into account the surface tension u03bc is the viscosity and u03c4 is the melting duration u02dc 100 ns at the propagating plug front that depends on the thermal diffusivity d u03ba u03c1cp with u03ba as thermal conductivity cp as specific heat and u03c1 as density and the laser pulse duration tp due to the low viscosity of liquid cu and si that is comparable to that of water the theoretical filling depth l c1 is calculated to be several u03bcm one order higher than the hole depth in the experiment similarly the effect of inertial force which decides how fast the steady flow develops can be estimated by assuming an inviscid liquid u03bc 0 the corresponding critical filling depth has order of l c2 is estimated to be several u03bcm the same range as l c1 therefore both the viscous and the inertial force is important in determining the maximum filling depth as for substrate heating an upper limit of the maximum temperature experienced at the supposed dielectric semiconductor interface can be estimated as following for a homogeneous material the maximum temperature reached at depth equal to its characteristic heat diffusion length u03b4 2 u221a dtp is roughly u2155 that of the maximum temperature experienced at the top surface now suppose that the dielectric material below depth u03b4 is replaced by a semiconductor i e assume dielectric thickness equal to u03b4 or 260 nm for sio 2 that conducts.