4.18 In a material where ND > NA but NA 0, the Fermi level EF will lie above Ę; for any sys- tem temperature in the freeze-out and extrinsic ranges-i.e., the material will always appear to be n-type. Suppose that to be specific we consider a nondegenerate Si sample where ND NA but NA 0. Further assume that the system temperature is restricted to the freeze-out and extrinsic ranges. (a) Present arguments leading to the conclusion that NA NA in the Si sample at any T in the cited temperature ranges. (b) Show that one can also write n = N - NA in the given n-type (n>p) sample. (c) Paralleling the text n = N development, derive an expression for No in the N₁ = 0 material. (d) (i) From the part (b) expression, what is the value of N₁ if T→ 0 K? (ii) According to your part (c) result, what is No if T→0 K? Record your reasoning. (Are your answers here consistent?) (iii) What is the limiting position of EF when 70 K? Explain. 4.18 In a material where No > NA but NA 0, the Fermi level E, will lie above E, for any sys- tem temperature in the freeze-out and extrinsic ranges-i.e., the material will always appear to be n-type. Suppose that to be specific we consider a nondegenerate Si sample where ND > NA but NA 0. Further assume that the system temperature is restricted to the freeze-out and extrinsic ranges. (c) Paralleling the text n = N development, derive an expression for N in the N₁ = 0 material. (d) (i) From the part (b) expression, what is the value of ND if T→ OK? (ii) According to your part (c) result, what is N if 70K? Record your reasoning. (Are your answers here consistent?) (iii) What is the limiting position of E, when T→ 0 K? Explain.