Bulk trapping effect on carrier diffusion length as determined by the surface photovoltage method: Theory

Abstract

The theory underlying a method for measuring carrier diffusion length based on the surface photovoltage is extended to include bulk trapping effects at low injection levels. This is done through recognizing that even in the presence of trapping when their lifetimes may differ, excess electrons and holes both diffuse in the bulk with the same characteristic length. The theory has been examined in terms of quasi-equilibrium conditions across the surface space charge layer; however, the method is expected to work under less restrictive conditions. As with no trapping, the method should yield the minority carrier diffusion length in extrinsic material for majority carrier trapping in general, but in the case of minority carrier trapping, only for moderate trapping. When strong minority carrier trapping occurs in slightly extrinsic material, the effective diffusion length, owing to trap-modified ambipolar diffusion in a Dember field, may be greater than the usual minority carrier diffusion length which obtains in the absence of trapping. A treatment of recombination statistics is included to illustrate how trapping effects may arise from the presence of deep-lying impurities such as gold in solicon. It also provides a basis for a detailed examination of the low injection-level assumptions used in simplifying the problem of trap-modified carrier diffusion in the bulk. It is shown, for example, that in extrinsic semiconductor, the usual assumptions that the excess carrier densities be much smaller than their equilibrium values need apply to majority carriers only. For minority carriers, the limitations are far less severe in most cases of practical interest, and depend on the characteristics of the trapping centers involved. © 1970.