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**Assignment #4Please submit all problems. Show ALL WORK for full credit. **

**Do problems 3.1 and 3.12 in “Semiconductor Fundamentals” from Pierret. For problem 3.12, (g) Determine for each energy band diagram where the material is intrinsic or degenerate.****A silicon crystal having a cross-sectional area of 0.001 cm2 and a length of 10-3 cm is connected at its ends to a 10-V battery. At T=300K, we want a current of 100mA in the silicon. Calculate (a) the required resistance R, (b) the required conductivity, (c) the density of donor atoms to be added to achieve this conductivity, and (d) the concentration of acceptor atoms to be added to form a compensated p-type material with the conductivity given from part (b) if the initial concentration of donor atoms is Nd = 1015cm-3.****Consider an infinitely large, homogeneous n-type Si at T = 300K doped to Nd = 5 x 1016cm-3. Assume that, for t < 0, the semiconductor is in thermal equilibrium and that, for t ≥ 0, a uniform generation rate exists in the crystal. (a) Determine the excess minority carrier concentration as a function of time assuming the condition of low-level injection. (b) Assume a generation rate of 5 x 1021 cm-3 s-1. And let τpo = 10-7 s. Determine the excess minority carrier concentration at (i) t = 0, (ii) t = 10-7 s, (iii) t = 5 x 10-7 s, and (iv) t → ∞. (c) Using Excel or Matlab, Plot the excess carrier concentration for t ≥ 0.****Consider silicon at T = 300K that is doped with donor impurity atoms to a concentration of Nd = 5 x 1015 cm-3. The excess carrier lifetime is 2 x 10- 7 s. (a) Determine the thermal equilibrium recombination rate of holes. (b) Excess carriers are generated such that ∆n = ∆p = 1014cm-3. What is the recombination rate of holes for this condition?**