Analytical calculation of the surface potential and the band profile within the i region of a semi-infinite p/i semiconductor junction with arbitrary thickness and surface charge coverage of the intrinsic top layer

Abstract

An analytical calculation scheme for the band profile in the i region of a semi-infinite p/i or n/i junction with arbitrary thickness of the intrinsic top layer is presented. Using this algorithm the surface potential as a function of i-layer thickness as well as the band profile within the top layer can be calculated without mathematical approximations as long as the surface potential is held a few kT away from its intrinsic position by the doped sublayer, i.e., up to a critical thickness. Above that thickness the band profile can be approximated with sufficient accuracy by that of the corresponding infinite junction for which the exact solution will be also given in analytical terms. In a second step an arbitrary surface charge layer is incorporated into the algorithm which can modify the band profile considerably. The method whose mathematical derivation is presented in detail in this article was motivated by experiments on the surface-near passivation of dopants in silicon by hydrogen but should be generally useful for the discussion of p/i or n/i junctions.