## Haynes-Shockley Experiment

The diffusion equation for minority electrons in a semiconductor is,

$\large \frac{\partial n}{\partial t}= D\nabla^2n +G+\frac{n-n_0}{\tau}$.

If the generation term $G$ is pulsed on for a short time at $t=0$ and $x=0$, the solution is,

$\large n-n_0=\frac{\exp\left(\frac{-(r-\mu Et)^2}{4Dt}\right)\exp\left(\frac{-t}{\tau}\right)}{\sqrt{4\pi Dt}}$.

The form below plots a cross section of the minority electron concentration for various parameters. This is what is measured in a Haynes-Shockley experiment.

 $n-n_0$ $x$ at $t=0.01$
 τ = [s] E = [V/cm] μ = [cm²/V s]

• Haynes, J. R. and Shockley, W. (1948). "Investigation of Hole Injection in Transistor Action". Physical Review 75: 691.
• Shockley, W. and Pearson, G. L., and Haynes, J. R. (1949). "Hole injection in germanium – Quantitative studies and filamentary transistors". Bell System Technical Journal 28: 344–366.
• Wikipedia: Haynes-Shockley Experiment