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

Abstract

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 τb 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. Two complementary methods applicable for values of the product Sd≳40 cm2/s are proposed to determine τB and S, without having to invoke the usual stringent requirement of either S→∞ or d→∞, and thus permit the determination of τb and S for a greater variety of wafer characteristics. For Sd≲40 cm2/s, a two-wafer method is developed to determine τb and S; it is also shown that the requirement of d/τb ≳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%.