Abstract
A general analytical description of the depletion-layer problem in nonuniformly doped semiconductors is a valuable tool because it permits analytical manipulation of critical quantities for the purpose of establishing criteria and relating measurable quantities. A formulation is presented here which retains the dopant profile as an arbitrary function and defines integrals over this profile together with functions of the potential that uniquely specify the problem. An example of a such a criterion, which is presented, is the threshold voltage of a metal-oxide semiconductor field-effect transistor with a highly nonuniform substrate dopant profile.
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