100%(1)1 out of 1 people found this document helpful
This preview shows page 2 out of 2 pages.
c.Make another sketch of the first few periods of the nearly free electron band in theperiodic zone scheme, for both the 1stand 2ndenergy 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 massm∗for an electron in a one-dimensional lattice. Plot the massm∗versusk, and show that the mass is independent ofkonly near the zone edge.b.Calculate for a simple cubic lattice the effective mass (i) at the zone center, and (ii) zonecorner along the  direction.6.Oscillations induced by a static force. (15 pts)A 1D electron band has the following dispersion𝜖(𝑘) =𝜖0𝑐𝑜𝑠(𝑘𝑎), where𝑎is the latticeconstant. Under the influence of static force𝐹, the momentum of the electron𝑝=ℏ𝑘increases according to the Newton’s lawℏ𝑑𝑘𝑑𝑡=𝐹. Assume that at time𝑡= 0, the electron isat𝑥= 0and has zero velocity𝑣= 0. Find the position of electron at time𝑡.