# Showing the transmission coefficient is valid

In a semiconductor device, electrons accelerated through a potential difference of 7V attempts to tunnel through a barrier of width 0.5nm and height 10V. Assume the potential is zero outside the barrier. The barrier is on the domain $0\leq x\leq a$

Verify that the transmission coefficient $T=\frac{16\bar{h^{2}\kappa^{2}p_{0}^{2}}}{\left ( \bar{h^{2}}\kappa^{2}+p_{0}^{2} \right )^{2}}e^{-2ka}$ is valid.

The solution gives $\kappa=\frac{\sqrt{2m\left ( v_{0}-E \right )}}{\bar{h}}$

$\kappa a=8.9\times 10^{-0}m^{-1}\left ( 0.5\times 10^{-9}m \right )$

Since $e^{-\kappa a}=0.012\ll 1$, the transmission coefficient is valid.

Could someone explain to me how should I begin with this question? I do not understand the solution simply because I cannot recall any related theory to this question. This is an application of quantum tunnelling. I've gone through my notes for quite a while in hopes of finding something related to this question but to no avail. Could someone fill me in on the theory or point me in the right direction so that I can read up more about it?

• a transmition coefficient $T$ is valid iff $0\le T\le 1$. – AccidentalFourierTransform Apr 12 '16 at 13:38
• @AccidentalFourierTransform Thank you. I will take it from here. – Physkid Apr 12 '16 at 13:40