Abstract
We introduce charge accumulation in quantum wells through the use of the nonlinear Schrodinger equation: where the symbols here have their usual meanings and ξ is a measure of the strength of the charge-accumulation effect. Letting V(x) be an infinite square well allows us to calulate the new energy spectrum, including the effects of charge accumulation (ξ|Φ(x)|2). This gives us insight into the new resonant tunneling energies that arise because of the quasibound states being shifted by the reaction field built up through the accumulation of charge. Using a normal quantum well potential between two finite square barriers, we calculate the transmission coefficient and contrast it with the transmission coefficient without charge accumulation. To simplify the results we also go to the limit of two delta-function barriers. Finally, we compare these results to the same cases when there is an external biasing field present by using the exact Airy function solutions of the linear Schrodinger equation with an applied field.
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