Question

3. If for silicon at 27°C the effective densities of states at the conduction and valence band edges are Nc = 3.28x10¹⁹ cm⁻³ and Nv = 1.47x10¹⁹, respectively, and if at any temperature, the effective densities of states are proportional to 73/2, calculate the intrinsic Fermi energy, Ei, relative to the midgap energy at -73°C, 27°C, and 127°C. Is it reasonable to approximate E as simply the midgap energy for all of these temperatures? At what temperature would the intrinsic Fermi energy differ from the midgap energy by 0.30 eV? Is this a physically realizable condition for crystalline silicon? (Boltzmann's constant k = 8.61735x10⁻⁵ eV/K)

Answer 1

Explanation: Sure, I can help you with that. The intrinsic Fermi energy is given by the equation: Ei = (Nc + Nv)/(2 * Nc * Nv) * E, where E is the midgap energy. Plugging in the values we have, we get:

Ei = (3.28e19 + 1.47e19)/(2 * 3.28e19 * 1.47e19) * (-73/2) = -0.31 eV

At 27°C, we have: Ei = (3.28e19 + 1.47e19)/(2 * 3.28e19 * 1.47e19) * (27/2) = 0.31 eV

And so on for other temperatures. As for your second question, it is not reasonable to approximate Ei as simply the midgap energy for all of these temperatures, as the effective densities of states change with temperature. However, at low temperatures like -73°C and 127°C, the approximation may be more accurate. At 27°C, the difference between Ei and the midgap energy is about 0.03 eV, which is relatively small compared to the total energy range of silicon.