20111ee2_1_2011_EE2_HW3_Solution - Physics for Electrical...

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Physics for Electrical Engineers Prof. B. Jalali EE 2 Winter 2011 Homework #3 solution 1 a) Si can emit photon energy 1.12 g E Ee V ≥= Photon Energy is given as hc Eh v λ == So the emission wavelength is 34 8 19 6.626 10 3 10 1109.2 1.12 1.6 10 g hc mn m E ×× × ≤= = Figure 1. Band diagram of Si and GaAs. b) Figure 1 (or figure 3-10 in the textbook) shows the band structure of Si and GaAs. As you can see, Si is an indirect bandgap material, therefore, it is not a good choice for LED. When emitting a photon from Si, an electron in the conduction band has to jump down to the valence band. Also, this emitting process has to obey both energy conservation and momentum conservation: E photon = Δ E electron =E c -E v =E g p photon = Δ p electron The energy conservation is easily satisfied, however, the momentum is not easily conserved,
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since the photon momentum is usually much smaller than the change in electron momentum. Therefore, usually a phonon with the right momentum is needed to assist this process, which makes it very slow (not as efficient as in direct bandgap material).
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This note was uploaded on 10/07/2011 for the course EE 2 taught by Professor Vis during the Spring '07 term at UCLA.

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20111ee2_1_2011_EE2_HW3_Solution - Physics for Electrical...

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