Quantum tunneling through a rectangular barrier
Compute the exact transmission probability T(E) for an electron crossing a barrier. Vary height, width and effective mass.
About this applet
The applet evaluates the exact transfer-matrix result for a single rectangular potential barrier of height $V_0$ and width $a$ in the effective-mass approximation:
\[T(E)=\left[1+\frac{V_0^2\,\sinh^2(\kappa a)}{4E(V_0-E)}\right]^{-1},\qquad \kappa=\frac{\sqrt{2m^*(V_0-E)}}{\hbar}\quad (E<V_0),\]with the corresponding oscillatory form above the barrier. It is a starting point for understanding tunneling in the band-to-band and Schottky-barrier transport that limits nanoscale FETs.