Semiconductor Infrared Nonlinear Optical Materials
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167 Mat. Res. Soc. Symp. Proc. Vol. 479 01997 Materials Research Society
interest not only to explain their current performance but also for guiding future applications. Some recent results of measurements of nonlinear absorption and a direct comparison of nonlinear behavior at different temperatures in some of these materials are also presented. THEORY A laser beam is assumed to be incident on a semiconductor sample (bandgap Eg, free electron density no, and free hole density P0) the thickness of which is small compared to the confocal parameter of the beam. The wavelength (X,)of the laser beam is assumed to lie between hc/Eg and 2hc/Eg (where h is the Planck's constant and c is the speed of light), so that two-photon absorption is the most significant band to band transition brought about by light absorption. The irradiance I of the beam propagating through the sample in the z direction is given by the equation: dldl=- (arno +flI +a,, N(I))I (1) dz Here aadenotes the free carrier absorption cross-section, N(I) is the density of excess carriers and 13denotes the two-photon absorption coefficient. For short enough laser pulses such that carrier diffusion can be ignored, the excess carrier density N(I) is governed by the rate equation dN(I) I3 1 2 ddt C noI + 2ý--(2) 2hv f(N, no,po) wherefis a function describing the decay of N. Expressions forf for two different decay mechanisms are given below. Optical limiting arises from the nonlinear absorption processes associated with both the second and the third terms in equation 1 and limiting is better if 3 is large as well as N(I) is large. It is not desirable to have aa to be too large because that would degrade the linear optical performance of the limiter. For a given semiconductor the value of P3 is usually determined by the value of Eg [5]. To have a large contribution from the third term in equation 1, it is desirable for the decay rate of N(I), denoted by the third term in equation 2, to be small. The decay of charge carriers occurs dominantly by recombination of electrons and holes. Two main recombination processes in the semiconductors of interest are band to band recombination and Auger recombination. The expressions relating the lifetimes for these two processes to fundamental material parameters have long been worked out [6]; they are presented here for their relevance to optical limiting. The goal is to obtain order of magnitude estimates of the decay times at different temperature ranges and for different dopant densities in the semiconductors. In the following, the standard semiconductor physics terminology will be adopted: no: conduction band electron density. Po valence band hole density. ni: conduction bandelectron density in an intrinsic semiconductor (for which no = Po = ni). Nr: Nr = no - Po , denotes the doping level. For both doped or intrinsic semiconductor, = ni 2 .
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N(I): density of excess electrons generatedby absorptionof radiationof intensity I N(I) denotes the modulation level. Radiative recombination [6]: When band-to-band radiative
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