The figure below is a part of the energy band diagram of a P-type semiconductor bar under equilibrium conditions (i.e., EF is constant). The valence band edge is sloped because doping is nonuniform along the bar. Assume that Ey rises with a slope of A/L. 0 L EF Ev (a) Write an expression for the electric field inside this semiconductor bar. (b) Within the Boltzmann approximation, what is the electron concentration n(x) along the bar? Assume that n(x = 0) is no. Express your answer in terms of no, A, and L. (c) Given that the semiconductor bar is under equilibrium, the total electron and hole currents are individually zero. Use this fact and your answers to parts (a) and (b) to derive the Einstein relation (Dn/un= kT/q) relating electron mobility and diffusion constant.

The figure below is a part of the energy band diagram of a P-type semiconductor bar under equilibrium conditions (i.e., EF is constant). The valence band edge is sloped because doping is nonuniform along the bar. Assume that Ey rises with a slope of A/L. 0 L EF Ev (a) Write an expression for the electric field inside this semiconductor bar. (b) Within the Boltzmann approximation, what is the electron concentration n(x) along the bar? Assume that n(x = 0) is no. Express your answer in terms of no, A, and L. (c) Given that the semiconductor bar is under equilibrium, the total electron and hole currents are individually zero. Use this fact and your answers to parts (a) and (b) to derive the Einstein relation (Dn/un= kT/q) relating electron mobility and diffusion constant.