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HW3-Due_Nov-08 - interatomic distance(20 points Hint use...

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NNSE 618 Home assignment # 3 Due: November 8, 2011 1. Find a formula to calculate width of the emission line E in meV if width  and position are known in nm. What is the energetic FWHM ’s of the lines at 600, 1000 nm and 1.55 m with FWHM  = 1 nm. (5 points) 2. Estimate at what electron energy the piezoelectric acoustic phonon scattering becomes effective (not screened) in GaAs with N D =10 17 cm -3 . (10 points) 3. The optical phonon energies of GaAs and AlAs are 36 meV and 50 meV respectively at the zone center. What is the occupation probability of these phonons a 77K and 300K? (10 points) 4. Using graph in the Figure estimate momentum relaxation time on optical phonons responsible for carrier saturation velocity in GaAs, and optical phonon energy. (10 points) 5. Estimate the amplitude of atomic vibrations corresponding to long-wavelength longitudinal acoustical phonons at room temperature. Is the amplitude small or large as compared to
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Unformatted text preview: interatomic distance. (20 points) Hint: use the solution for a 1 m - long atomic chain. 6 Quasi-Fermi levels for electrons and holes in the undoped injection active region of GaAs LED at room temperature is 30 and 2 meV above and below respective band edges. Calculate radiative recombination rate and lifetime of carriers. Electron and hole nonradiative recombination coefficients: A =1x10 8 s-1 ; radiative recombination constant: B = 1.5x10-10 cm 3 s-1 ; electron and hole Auger recombination coefficients: C e = C h = 1.5x10-31 cm 6 s-1 . (20 points) 7. Calculate and plot a free exciton luminescence line (position and shape) in Si at 4 K and 20 K at low excitation intensity. (25 points) Hint: use exciton Rydberg and TA and TO phonon energies to find the positions of two exciton lines, and density of state and Maxwell distribution to find the shape....
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