Abstract
A sigmoidal grading profile is proposed for the efficient study of the influence of material parameters and effective mass mismatch on the properties of graded heterojunctions. For the interest of accessing bound and scattering states, we have shown the exact solvability of the model on the entire real line. Focussing on transport across a compositionally graded heterojunction, we have discussed the effect of interface width and effective mass mismatch on the transmission probability.
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