A kinetic equation for minority carriers at the surface of semiconductor electrodes

Abstract

Mmorlty carrier relaxation and surface state relaxation are the two time dependent coupled processes that occur at semiconductor interfaces [1,2] Surface state relaxation 1s usually viewed as purely temporal with no spatial extension mto the bulk and hence 1s modelled as a first order kmetlc equation [31 However, mmorlty carrier relaxation 1s a volume process and Its time behavlour at the surface needs to be derived from the transport equation usmg appropriate boundary condltlons In the presence of a space-charge layer, whether it 1s possible to derive a kinetic form or not for the minority carriers 1s a question that has not been addressed so far Such kmetlc forms have been assumed previously, but as they were not rigorously derived, the order of magnitude of the length parameter needed to project a volume process at the surface has remained speculative [1,4] In this note, we report some of the results concerning minority carrier relaxation at the surface, whose general form 1s given by an integral equation which can be reduced to a simple kinetic form under certain condltlons From this kinetic equation we obtain the exact form of the earlier mentioned length parameter and more importantly the potential dependent rate constant for the mmorlty carrier relaxation, as we have included space-charge effects The rate of relaxation of the integral of the mmorlty carners m the semiconductor electrode can be shown to be approximately the same as that of the minority carriers at the surface [5] As a result the potential dependence of transient photomduced microwave conductlvlty [61 and the time resolved fluorescence signals [71, which are proportional to the total mmorlty carrier concentration, can be understood from the rate constant of the kinetic equation of mmorlty carriers at the surface