Question

Case Study (Read Carefully): Assume you have a typical piece of Silicon Wafer, it is doped by N-type carriers (electrons) and it operated at an elevated temperature. Assume, Na = 1e8 cm. We will use Short-hand (assumption) approach to calculate the n, p, and E--E; then use recalculate using first principal equation while making minimal assumptions. We want to know the range in which the Short-hand approach gives the same answer as the first principal approach. Part 1, Short-Hand Approach: • Assume: n = 1e10cm", Eş = 1.1eV, n N • For N-Type: o Ex-E = KTIn(n/n) o np = n^ Output: 3 Contour Plots, Solve for n and A = Er-E o Z/Color Axis #1: n = electron concentration o Z/Color Axis #2: A = Fermi Level o Z/Color Axis #3: Degeneracy = 1 (degenerate) or 0 (non-degenerate) o X-axis: Temperature (range = 250K - 1200K) o Y-axis: N-type Doping (range = 1e8-1e20 cm]) D

Answer 1

Solution of Given NA = 1x100 / cm3 hi = 1x100 cm3 lilev NA Zp np-hi? ņa 2 ni NA २ (ixolo , 12 1x10² 1cm² 108 Er - Ei KT In h ni 1x 10 0.00259 In 1x1000 Er - Ei 0.1192 er Therefore h = 1x102 cm3 1X100 1 m3 EF - Ei= 0.1192 ev Any