The p-n Junction — Question 10

Question 10

A critical-field model estimates reverse avalanche onset

For a one-sided $p^+n$ junction, $E_{\max}=eN_DW/\varepsilon$ and $V_j=E_{\max}W/2$. Assume avalanche begins at a specified field $E_{\mathrm{crit}}=3.00\times10^7\,\mathrm{V/m}$. Use $N_D=10^{22}\,\mathrm{m^{-3}}$, $\varepsilon=10^{-10}\,\mathrm{F/m}$, $e=1.60\times10^{-19}\,\mathrm C$, and $V_{bi}=.800\,\mathrm V$.

1. Find the depletion width and total junction potential at onset.

2. Find the applied reverse voltage and its approximate scaling with doping if $E_{\mathrm{crit}}$ is held fixed.

Question 10 - Solution

A critical-field model estimates reverse avalanche onset

(a) Method and calculation

$$\boxed{W_B=\varepsilon E_{\mathrm{crit}}/(eN_D)=1.875\,\mu\mathrm m}.$$$$\boxed{V_{jB}=\varepsilon E_{\mathrm{crit}}^2/(2eN_D)=28.125\,\mathrm V}.$$

(b) Interpretation and further calculation

$$\boxed{V_{RB}=V_{jB}-V_{bi}=27.325\,\mathrm V}.$$$$V_{jB}\gg V_{bi}\Rightarrow\boxed{V_{RB}\simeq\varepsilon E_{\mathrm{crit}}^2/(2eN_D)\propto N_D^{-1}}.$$

Physical check

The critical-field assumption is an idealized avalanche model. Real critical fields depend on material and doping; tunneling breakdown and edge curvature are excluded.