A Si p-n junction at room temperature is doped with 10^16 donor atoms/cm^3 on the n-side and 6 x 10^15 acceptor atoms/cm^3 on the p-side. The cross-sectional area of the device is 10^-3 cm^2 and the electron and hole lifetimes are both 10^-7 s.
a) For this device, determine the built-in potential at the p-n junction.
b) Calculate the width of the space charge region and the maximum electric field at the junction under the following conditions: (i) thermal equilibrium, (ii) forward bias of 0.6V, and (iii) reverse bias of 10V.
c) Calculate the reverse saturation current in this p-n junction.
d) Determine the excess electron density at the edge of the space charge region on the p-side and the excess hole density at the edge of the depletion region on the n-side if the junction is biased with the following forward voltages: (i) 0.60V, (ii) 0.62V, and (iii) 0.65V.
e) Calculate the hole current injected into the quasi-neutral n-region at x_n = 0 and the electron injected current into the quasi-neutral p-region at x_p = 0 for the three forward bias voltages of part c).
f) Calculate the minority carrier currents 10 um into the quasi-neutral regions (as measured from the edges of the space charge region) on both the n- and p-sides of the junction for an applied forward bias of 0.65V.
g) Assuming no recombination in the space charge region, calculate the majority carrier currents at the same locations in part e) at a forward bias of 0.65V.
h) Determine the positions of the electron and hole quasi-Fermi levels with respect to the bottom of the conduction band at both the edge of the space charge region and 10 um into the quasi-neutral regions on both sides of the junction at a forward bias of 0.65V. Sketch these on a band diagram of the p-n junction.
i) Using a computer, plot the current-voltage characteristics of this device for applied forward biases between 0 and 0.67V. Also plot ln (current) vs. voltage over the same range of forward biases.