Special Problem (20) Consider a Si $p^+$-$n$ diode at 300 K with $N_a = 5 \times 10^{17} cm^{-3}$ on the p-side and $N_d = 1 \times 10^{16} cm^{-3}$. The cross-sectional area of the diode is 1 $cm^2$. Assume both the n and p-side widths are 'long' compared to the minority carrier diffusion lengths. Assume $\tau_p = \tau_n = 5 \times 10^{-6}$ s, and the diffusion coefficients for holes and electrons are $D_p = 10 \frac{cm^2}{s}$; $D_n = 25 \frac{cm^2}{s}$. The series resistance due to the bulk and contacts is 2 $\Omega$. Using Excel, Matlab, Python, or your other favorite package, calculate and plot on a semi-log plot the forward bias current including recombination current and series resistance effects up to 1.0 V forward bias (applied to the terminals of the diode, not across the junction). Neglect high-level injection effects on the I-V characteristics, but indicate on the plot where high-level inject will start to occur.
