Question

An electron is moving in a piece of lightly doped silicon under an applied electric field at 270C so that its drift velocity is one-tenth of its thermal velocity. Calculate the average number of collisions it will experience in traversing by drift a region 1 um wide. What is the voltage applied across this region? The mobility for electrons in Si is μ,-1500 cm3/V-sec and the effective mass is m 0.26m0.

Answer 1

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drift velocity = 1/10 thermal velocity = 1/10 squareroot 3kT/m^6_e V_2 = 1/10 squareroot 3 times 1.38 times 10^-23 times 300/0.26 times 3.1 times 10^-31 = 22.9 km/sec Transist time = t_r = Length of region/drift velocity = 10^-6/92.9 times 10^3 t_r = 43.4 n sec Collision time z_c = mu_n m^2_e/q = 1500 times 10^-4 times 0.26 times 9.1 times 10^-31/1.6 times 10^-19 z_c = 0.22 p sec = 0.22 times 10^-12 sec no.of collision = t_r/z_c = 198.49 almostequalto 198 electric field = V_alpha/mu_n = 22.9 times 10^3/0.1500 = 152.667 Kv/m therefore applied voltage = E times L = 0.153 V