Question

4. (2 points) An electron in a semiconductor material's conduction band is initially at the electronic state corresponding to wavevector k = (kx, ky,k,), where kz = 3 x 10'm-7, and ky = k, = 0. The effective mass of the semiconductor conduction band is m = 0.1mo. At some moment, this electron absorbed an acoustic phonon with a wavevector of a = (92,9y, 92), where 9x = -5 X 107m 1,4y = 2.5 X 107m 1,9, = 0. (1) What is the energy of the electron with respect to the conduction band edge before it absorbs the phonon? (2) What is the wavevector of the electron after it absorbs the phonon? (Hint: wavevector conservation) (3) What does the energy of the phonon need to be for this absorption process to occur? (Hint: energy conservation)

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Answer 1

Answer: What is the energy of the clection with respect to the Conduc bion band edge before it absorbs the phonon? Energy of the election with respect to the Conduction band Ex= £22² where, &= R + R + R² } ame me = 0.1 Thereforer (6.636 * 9x104 Ex = (6.636 x1034)2 x 2 x019.11 21039 172 4712 = 0.55 X1D-92 E2-065 X101 of the elechon after it absorb the phonon! ♡ What is the wave vector We know that Behr hence K is conserved a kä, ky, k3 be the Component of maven ment mave Vector of the Election ofter absorption 9 the photon. 2) Lave reactor before absorption - Weve. Vector offer absorption Kx + 2x = ka Similarly, typ + ay = Ky and 'ky + qy = ky and kz tqz - Kz.

Therefore, Kå= -axlom" ky'e 25 xrom, KŽ-0 Thus, R1² khart kint Kit [446.26] x10 m2 i. IR 1- 10.25 x104m2 con Rl: 3.2x104mm 3 What does the energy of the phonon need to be for this absorption process to occur? from the Energy conserva bion the Energy of the phonon is the difference is Energy of the final. electoon and the initial elechon Eph= hk2 hk² 2me 2me 14 T10-95-9] X10 < (6.636 x10 342 40?x2x0.1x9.481631 = 0.076 x10 Eph = 0.076X10"?