c Make another sketch of the first few periods of the nearly free electron band

C make another sketch of the first few periods of the

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c. Make another sketch of the first few periods of the nearly free electron band in the periodic zone scheme, for both the 1 st and 2 nd energy bands. d. Is it more likely to be a metal or an insulator? 5. Electron Mass in Tight Binding Model. (25 pts) a. Using the tight-binding model, evaluate the effective mass m for an electron in a one- dimensional lattice. Plot the mass m versus k , and show that the mass is independent of k only near the zone edge. b. Calculate for a simple cubic lattice the effective mass (i) at the zone center, and (ii) zone corner along the [111] direction. 6. Oscillations induced by a static force. (15 pts) A 1D electron band has the following dispersion 𝜖 ( 𝑘 ) = 𝜖 0 𝑐𝑜𝑠 ( 𝑘𝑎 ) , where 𝑎 is the lattice constant. Under the influence of static force 𝐹 , the momentum of the electron 𝑝 = ℏ𝑘 increases according to the Newton’s law 𝑑𝑘 𝑑𝑡 = 𝐹 . Assume that at time 𝑡 = 0 , the electron is at 𝑥 = 0 and has zero velocity 𝑣 = 0 . Find the position of electron at time 𝑡 .
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  • Fall '08
  • Lei Duan
  • Electron, Energy, Condensed matter physics, Reciprocal lattice, Brillouin zone, energy bands, Fermi Sphere

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