Question

Find barrier height, built-in voltage, maximum E- field, and the depletion layer width at equilibrium for W-Si (n-type) contact (tungsten silicide) Given: Φ,-4.55eV for WX(Si)-4.01 eV: Si doping - 1016 cm-3 Draw the band diagram at equilibrium. Required Constants: for silicon at T-300°K, ni-1010/cm3. The Boltzmann constant kg-k-8.61x10-eV/K. Silicon bandgap energy Ev-1.12 eV

Answer 1

Given, phi_M = 4.55 ev, x(si) = 4.01 ev, Eg = 1.12 ev Barrier height, phi_BP = Eg - x - phi_M = 1.12 - 4.01 - 4.55 = -7.44 ev Built in potential, V_bi = KT/q ln N_A N_D/n^-2_l, K/q = 8.61 times 10^-5 ev/K Given, N_D = 10^16/cm^3 = N_A V_bi = 8.61 times 10^-5 times 300 ln {(10^16)^2/(10^10)^2} = 0.714 ev Max^m Electric field, epsilon (x = 0) = -q N_D x_n/epsilon_s and x_n = W N_A/N_A + N_D = W/2 Depletion layer, W = squareroot 4 epsilon_r epsilon_0 K T ln (N_A/)/q^2 N_A, epsilon_r = 11.7 W = squareroot 4 times 11.7 times 8.85 times 10^-12 times 8.61 times 10^-5 times 300 ln (10^6)/1.6 times 10^-19 times 10^16 = 0.298 mu m therefore E_max = -1.6 times 10^-19 times 10616 times 0.298 times 10^-6/ .85 times 10^-12 times 2 = -26.938 v/m