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ECE230A_Homework-3 - a k k k a z y x π ≤ ≤ −(b Using...

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ECE230A Homework #3 Homework due: November 10, 2009 1. The intrinsic carrier concentration at room temperature (300K) for Ge and Si is 2.3x10 13 cm -3 and 1.1x10 10 cm -3 , respectively. The bandgap energy Eg, Ge =0.67 eV, Eg, Si = 1.1 eV. (a) Find the intrinsic concentrations of Ge and Si at 400K. (b) If Si is doped with shallow acceptors and shallow donors: N A =2x10 15 cm -3 and N D =1x10 15 cm -3 . Calculate the Fermi energy above the valence band edge. (c) If N d > N a , derive ] exp[ ) ( 2 kT E E N n N N n N n d c c a d a = + where E d is the energy of the donor state. 2. Aluminum has a simple cubic structure with an atomic mass “M” and spring constant β ”, (a) Find the dispersion relation ω (k) for phonons in the 1st BZ
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Unformatted text preview: a k k k a z y x π ≤ ≤ − , , . (b) Using the relation β /M=Y/ ρ a 2 (Y: Young’s modulus = 1.14x10 11 Nt/m 2 , a=4.03Å, and ρ =2.73 g/cm 3 ), calculate the maximum phonon energy in electron volt (eV). (c) Calculate the speed of the sound in aluminum. 3. This is a problem created by your classmate: Assuming an E-k relation: ߝ ൌ ߝ ௖ ൅ ԰ మ ௠௔ మ ൤1 െ ܿ݋ݏ ቂቀ݇ െ గ ସ௔ ቁ ܽቃ൨ . Plot the band diagram, the group velocity, and the effective mass over the first Brillouin Zone. 4. Create your own question related to the density of states, phonons, Fermi function, or carrier concentrations....
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