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 Ek 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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 '09
 Condensed matter physics, intrinsic carrier concentration, energy Eg,Ge=0.67 eV

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