Analysis of the interaction of a laser pulse with a silicon wafer - Determination of bulk lifetime and surface recombination velocity

The decay of excess minority carriers produced in a silicon wafer of thickness d by a laser pulse is analyzed. A comprehensive theory based on this analysis is presented for the determination of bulk lifetime Tau(b) and surface recombination velocity S. It is shown that, starting with an exponential spatial profile, the carrier profile assumes a spatially symmetrical form after approximately one time constant of the fundamental mode of decay. Expressions for the spatial average of the carrier density as a function of time are derived for three temporal laser pulse shapes: impulse, square, and Gaussian. Particular attention is paid to the time constants of the fundamental and higher modes of decay. The ratios of the time constants of the higher modes to the fundamental mode, as well as the time constant of the fundamental mode, are presented over wide ranges of values of S and d. For Sd less than about 40 sq cm/s, a two-wafer method is developed to determine Tau(b) and S; it is also shown that the requirement of d/Tau(b) greater than about 20S is sufficient to adequately guarantee that the asymptotic value of the instantaneous observed lifetime differs from the bulk lifetime by no more than 10 percent.