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Unformatted text preview: Homework 8 Solution Prob. 8.1 For an electron is localized in a finite quantum well with a homogeneous electric field F : We will use the parameters from a quantum well photodiode implemented by the IIIV materials for the WKB estimate. The potential well height is 0.3eV, the effective mass is m* = 0.067 m 0 and the quantum well is 10nm wide. The kinetic energy is 0.026eV (for room temperature). Estimate the electric field that will give the electron a life time of 1ns. (10 pts) The electron will tunnel out the triangular barrier, as shown below. The tunneling distance is W = 0.3eV/ F , or V(x) = 0.3eV – Fx . Notice that we have taken x = 0 at the right wall. We will use the WKB function of the evanescent wave to do the calculation. ( 29 ( 29  =  2245 ∫ qF kT V m dx kT x V m T W 2 / 3 2 2 2 3 4 exp ) ( 2 2 exp F F The impinging frequency can be computed as: Hz d m kT f 12 10 8 . 4 2 / 2 × = = ns f T 1 1 = ⋅ ; T = 2.1×104 . We need to be careful in taking the unit in transforming everything to Joule so that the exponent for T and its exponent are unitless. 1eV = 1.6×1019 Joule. 1 Joule = kg m 2 /s 2 ( 29 [ ] × × ⋅ × × × × = 5 . 8 / 10 6 . 1 026 . 3 . 10 06 . 1 10 11 . 9 067 . 2 3 4 2 / 3 19 34 31 eV J eV eV Js kg qF F = 2.98×10 7 V/m = 2.98×10 5 V/cm. This is not a significant field, and the electrons in such as shallow well can be easily erased....
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 '05
 TANG
 pts, WKB

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