Past exam of the MPhil in micro- and nanotechnology enterprise course of the University of Cambridge / 2021 / Paper 1 / 9 / ii

With conventional electric current defined into the positive terminal, an ideal junction hasThe reverse-bias branch tends to $-I_0$ before breakdown. In forward bias the electric current rises exponentially; a visibly sharp “turn-on” is a convenient operating description rather than a discontinuity in the equation. A powered LED emits in quadrant I, where $V>0$, $I>0$ and the device absorbs electrical power $VI$. Strong reverse breakdown lies outside the ideal curve below.

forward bias opposes the built-in electric field and lowers the junction barrier from approximately $V_{\mathrm{bi}}$ to $V_{\mathrm{bi}}-V$. In the abrupt-junction depletion approximation,Thus the depletion region narrows and carriers cross the reduced barrier more readily. electron injection into the p side and hole injection into the n side increase strongly, allowing radiative recombination in an LED.

The injected minority-carrier concentrations, and therefore the ideal diffusion electric current, vary approximately as $\exp (qV/k_{B}T)$. This produces the steep forward branch of the electric current–voltage curve. One should not extrapolate the depletion-width formula to claim that the junction must lose its entire depletion region before conducting; appreciable electric current flows while a barrier remains, and high injection and series resistance eventually invalidate the simple formulas.

Taking room temperature as $300\mathrm{K}$, the thermal voltage is $V_T=k_{B}T/q=0.025852\mathrm{V}$. For the stated ideal diode, $n=1$, soThe $-1$ term is negligible here. A different precise interpretation of room temperature changes the result noticeably because of the exponential; the calculation above states its temperature explicitly.

For a lower-bandgap material, the intrinsic carrier concentration generally rises, increasing the reverse saturation current density, approximately through $J_0\propto n_i^2$ with $n_i^2\propto \exp (-E_g/k_{B}T)$ when other parameters are held comparable. Thus the forward electric current at the same voltage would normally increase. If $J_0$ were artificially held fixed at the supplied numerical value, however, the ideal-diode equation would give the same electric current: the band gap dependence enters through the material parameters rather than as a separate term in that equation.