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%.

On the c-Si/SiO2 interface recombination parameters from photo-conductance decay measurements

“…Similarly, carriers generated at the surface may recombine instantaneously or diffuse to the bulk. To account for this dependence, Luke and Cheng 73 developed a formalism and found a solution that indicates that the effective SRV is a function of an infinite sum of decaying exponential terms of effective lifetime. The first mode is dominant and it is written as…”

Optical Measurement Techniques of Recombination Lifetime Based on the Free Carriers Absorption Effect

“…The simulations reported in [55] show that in practice the influence of can be neglected for > 120 cm 2 /s.…”

“…The experimental Transient Pump and Probe scheme to measure the recombination lifetime was well settled by Ling et al in 1987 [1], but only with subsequent works [51][52][53][54], based on the analytical analysis of the interaction of a pulse laser beam with a semiconductor wafer performed by Luke and Cheng [55], the potentialities of the technique were clear. These consist in the capability to discriminate between the surface contribution to the recombination and the bulk one with only one measurement, or, in other words, to measure simultaneously the bulk recombination lifetime and the surface recombination velocity.…”

“…We report in the following the analysis as presented in [52], where the study of Luke and Cheng [55] is extended to the case of different SRV on the two surfaces of the wafer.…”

“…Let be the minority carriers diffusion coefficient in the material, 1 and 2 the surface recombination velocity on the surfaces 1 and 2, respectively, and let us consider the same coordinate system as reported in the cited figure. If the duration of the pump pulse is much shorter than the expected recombination lifetime, the analysis can be carried out for an ideal delta-pulse ( ) = 0 ( ) ( 0 is the number of photons and ( ) the unitary Dirac distribution) and then it can be easily extended to the other cases [52,55]. Moreover, let us consider a pulse beam with a uniform spot size impinging on the sample surface along the propagation direction of the probe beam and similarly a probe spot size on the sample thickness.…”