Competition between recombination and electron transfer the steady state case

7 COMPETITION BETWEEN RECOMBINATION AND ELECTRON TRANSFER (THE STEADY STATE CASE) 

This section considers the competition between electron transfer and surface recombination under steady state conditions, and shows that no kinetic information can be obtained from the measured photocurrent. 

In the presence of surface recombination, the minority carrier density at the surface is determined by the rate of their arrival from the collection region W + LP and the rate of their removal by the routes illustrated in Fig. 8.5. The concentration of holes accumulating at the surface can be expressed in terms of the equivalent surface concentration, ps (cm-2) = (Px=o since this allows a convenient formulation of the kinetic equations. Further simplification is achieved by considering the concentrations of redox species and majority carriers to be time invariant. This simplified scheme is illustrated for the case of an n-type semiconductor in Fig. 8.5. 

Consideration of the rates of arrival, charge transfer, trapping and recombination of minority carriers leads to expressions for the time dependent surface concentrations (cm-2) of free ps,(Tee and trapped pJ trap holes  

Here g is the Gartner flux of holes into the surface generated by illumination, [Red] is the bulk concentration of reduced species in solution and nxm.o is the electron density at x = 0. The rate constants, kET, for electron transfer involving free and trapped holes, and the recombination rate constant, kr, are shown in Fig. 8.5. They have units cm3 s-1 and can be converted to conventional heterogeneous rate constants (units cm4 s l) by multiplying by S. 

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