Question

draw all levels as well as the values of the energies

4. A Si sample is doped with 1016 As atoms/cm. What is the equilibrium hole concentration po at 300 K? Show the location of Er relative to Ei,. Ec, Ev in a band diagram at the same Ei, Ec, Ev in a band diagram at the same temperature (draw all the levels as well as the values of the energies).

Answer 1

Given S_i sample for s_i n_i rightarrow intrinsic carrier concentration n_i = 1.5 times 10^10 cm^-3 We know Band gap of silicon sample at 300 degree k is 0.72 ev i.e., E_c - E_v = 0.72 ev for intrinsic E_c - E_Fi = E_Fi - E_x = 0.36 ev E_Fi rightarrow Intrinsic Fermi level E_c rightarrow Energy of conduction band E_v rightarrow Energy of valance band Given Si sample doped with 10^16 as atoms/cm^3 As is n - type semico. Therefore N_D = 10^16 cm^-3 We know E_Fn - E_Fi = KT ln (N_D/n_i) KT at 300 degree k = 0.0258 ev E_Fn = Fermi level of n - type dopping E_Fn - E_Fi = 0.0258 ln (10^16/1.5 times 10^10) = 0.0258 ln (10^6/1.5) E_Fn - E_Fi = 0.346 ev Therefore E_Fn is 0.346 ev above E_i Fermi level Therefore E_F is below E_c by 0.014 ev E_F is above E_i by 0.346 ev E_F is above E_v