The maximum electric field occurs at the junction between the p- and n-type material. The integration constants C 1 and C 2 can be determined by using the depletion approximation, which states that the electric field must go to zero at the boundary of the depletion regions. The depletion region in the p- and n-type side respectively, measured from the physical junction between the two materials. Ε 0 is the permittivity in free space, and ε s is the permittivity in the semiconductor and -x p and x n are the edges of The only equation left to solve is Poisson’s Equation, with n(x) and p(x) =0, abrupt doping profile and ionized dopant atoms. All dopants are ionised ( N A += N A, N D + = N D).Abrupt or step doping profile ( N A +, N D + are constant in their respective regions).Similarly, J p is also constant across the depletion region. This means that J n is constant across the depletion region. No free carriers means (1) transport equations drop out and (2) no recombination or generation, so the continuity equation becomes We can assume no free carriers since the electric field sweeps them out of the depletion region quickly.No free carriers ( n(x), p(x) = 0 ) in depletion region.Depletion approximation: the electric field is confined to the junction region and there is no electric field in the quasi-neutral regions.Can solve for both the maximum electric field and the total depletion width.Īs stated on the previous page we need to make certain assumption to solve the diode equations analytically.Based on these assumptions, can use Poisson's Equation to develop a solution for the depletion region.Major assumptions: depletion approximation, no free carriers in this region, dopant concentration is constant.
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