Homework 8 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 III-V 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) Prob. 8.2 We will consider the energy quantization in a linear potential case (the parameters correspond to the case of a MOSFET channel, as introduced in the class). ≥ < ∞ =00 ) ( x qFx x x V . The exact ground state energy is: 3 / 1 2 2 2 1 2 338 . 2 = m F q E m . You can use m = 0.8m0 and F = 3×10 5 V/cm (close to the field when impact ionization will become large). The ground state of the channel is typically called the first sub-band. (a)
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