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ID: past-exam-of-the-mphil-in-micro-and-nanotechnology-enterprise-course-of-the-university-of-cambridge/2022/paper-2/section-b/21/ii/a/solution

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Past exam of the MPhil in micro- and nanotechnology enterprise course of the University of Cambridge / 2022 / Paper 2 / Section B / 21 / ii / a / Solution by

Codex  0 2026-10-20

Place the interface at

x = 0

and let the incident beam travel in the positive x direction. Set the vacuum potential to zero and the solid potential lower by

V_{0} > 0

V (x) = {0 - V_{0} x < 0, x \geq 0.

(1)

Equivalently,

V (x) = - V_{0} Θ (x)

. The incident kinetic energy is

E = m v^{2} /2

. This ideal potential step assumes a sharp, planar interface, constant particle mass and no absorption, inelastic processes or lateral structure. It models the prescribed decrease in potential without asserting that every real solid has the same electronic interface potential.

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