A Silicon Junction
Consider an abrupt Si p-n junction which has 2 x 10^5 donors per cm on the n-side and 5 x 10^7 acceptors on the p-side. The minority carrier recombination times are Th ~ 400 ns for holes in the n-side and ~ 50 ns for electrons in the p+-side. The cross-sectional area is 0.1 mm^2. Assume a long diode. The thermal generation time in the depletion region is 2 ns. Assume that the reverse current is dominated by the thermal generation rate in the depletion region.
(a) Calculate the forward current at 27 °C when the voltage across the diode is 0.6 V.
(b) Estimate the forward current at 57 °C when the voltage across the diode is still 0.6 V.
(c) Calculate the voltage across the diode at 57 °C if the forward current in (a) at 27 °C is kept constant.
What is the reverse current at 27 °C when the diode voltage is -5 V?
(e) Estimate the reverse current at 57 °C when the diode voltage is V.
Note: Assume that the forward current is determined by the Shockley equation (minority carrier diffusion).