Question

Problem 4: An intrinsic Si sample is doped with donors from one side such that NdNo eTaa (a) Find an expression for the built-in electric field @ equilibrium over the range for which Nd » nj (use equations 4-23 and 4-26 from textbook). (b) Evaluate the field when a -1 (um) (c) Sketch the energy band diagram (like the one in fig 4.15) and indicate the direction of the field -ax

Answer 1

N_d = N_0 e^-ax a) find an expression for the Built - in electric field at equilibrium over range for which N_d > > n_i E_0 = -a/E [N_d dx = -a/E]^x_N_0 N_o e^-ax_dx E_0 = -a/E N_0 middot e^-ax/-a Vertical-bar ^x_n_0 x_n rightarrow with region E_0 = -a/E N_0/a [1 - e^-ax_N] Implies -a N_0/E_a [1 - e^-ax_N] N_d > > n_i x_N is very small (B) field at a = 1 mu m^-1 E_0 = -a N_0/E 1 times 50^6 [1 - e^-a x_N] (c) Ef_N - Ef_i = k T ln[ND/NI] EC - Ef = k T ln [NC/ND]