Question

6) Determine the number of energy states per cubic c m in (a) Silicon between E, and Ec + 0.56 eV at T-300K (b) GaAs between Ee and Ee + 0.65 eV at T- 300K Note: the effective mass of an electron in Silicon is 1.08 times its normal mass; the effective mass of an electron in GaAs is 0.067 times its normal mass. Your final answer will be in cubic meters so you will need to multiply by 10 to convert to cubic centimeters. Hint: solve the integral for the general case of states between Ec and Ee + x and then substitute the values in the problem for x after you have completed the integration

Answer 1

N(E) = 4pi (2 m n/h^2)^3/2 squareroot E - E_c where N(E) = density of states in conduction band. mn = effective mass of electron a) No of energy states between E_c f E_c + 0.56 ev at T = 300k silicon n = integral^E_c + 0.56_E_c 4pi (2mn/h^2)^3/2 (E - E_c)^1/2 dE let E - E_c = x rightarrow dE = dx integral^0.56 ev_x = 0 4pi (2mn/h^2)^3/2 middot 1/2 x dx = 8pi/3 (2mn/h^2)^3/2 (x^3/2)^0.56_0 mn = 1.08 m = 6.526 times 10^19 (mn/m0)^3/2 (0.56)^3/2 cm^3 = 6.526 times 10^19 (1.08)^7/2 (0.56)^3/2 = 3.07 times 10^19 /cm^3 \r\n (b) n = 6.526 times 10^19 (0.067)^3/2 (0.65)^3/2 [e_c & e_c + 0.65] = 5.93 times 10^17 1cm^3