That would depend on the screening length. In metals the charge build-up on the edges decays very fast as you go into the sample, however in semiconductors the charge build-up penetrates further into the sample.
The simplest view is that charge will accumulate on the sample boundary, the question is about the charge profile. On one hand the charges want to be separated due to the Coulombic repulsion, and on the other hand there is a screening between the charges. Therefore i think that the screening length gives a rough estimate to the length over which the charges are smeared.
Can I understand in this way that screening of charge carriers are associated with the scattering phenomena? And screening length is about the mean free path?
Screening length is not the mean free path. Screening length depends on the density and mobility of free charge carriers. mean free path has to do with disorder etc.
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