A general theory of an intensity-modulated beam method for determination of diffusion length, diffusion constant, lifetime, surface recombination velocity and absorption coefficient in a semiconductor material

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Using a modulated light (or electron) beam, some efforts, both theoretical and experimental, have been made to determine parameters such as minority carrier lifetime, τ, diffusion constant, D, and surface recombination velocity, S, in a semiconductor material. However, none of these workers considered a general space and frequency dependent response of the system. Moreover, the parameters were not determined independent of each other. Here we give a general theory of such a modulated-light (electron)-beam method. Space and frequency dependent expressions for the amplitude A( x, ω) and phase shift θ( x, ω) of modulated minority carrier concentration and current have been obtained. (These are the two basic quantities which are to be measured in a modulated beam experiment.) We have also obtained frequency dependent expressions for amplitude attenuation coefficient, α(ω) and phase shift per unit distance, ζ(ω). These can be determined experimentally from the slope of the measured space dependent amplitude and phase curves at different frequencies. It is shown that it is useful to construct quantities like 2 α( ω) ζ( ω)[= σ 2( ω)] and α 2( ω)− ζ 2( ω)(= k 0 2) which help in directly determining carrier lifetime, diffusion constant and diffusion length, L 0. The procedure for determining S and a, the optical absorption coefficient, knowing the measured values of A and θ at a certain distance, has been given. It may be pointed out that the present analysis enables us to determine all 5 parameters mentioned above simultaneously and independent of each other from the measurements in a modulated light beam experiment.