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#2. Semiconductor Bands (35 points) Let's consider a semiconductor with an fcc lattice has an E-k diagram as below figure. 1) (5 points) How many conduction band minima are there in the first Brillouin zone? 2) (5 points) Which of the valence bands has the larger effective mass in the vicinity of T? 3) (5 points) Assume that the effective masses for the valence bands A and B are ma and mB, respectively. What is the total density of states for the valence band in the vicinity of the valence band maximum?
E Conduction band Valence band A Valence band B 4) (5 points) Write a simple functional form of the E(k) relation in the vicinity of the conduction band minimum. Take into account the symmetry of the crystal. 5) (7 points) If mi* = 0.9mo and mt* = 0.2mo, where mo is the mass of a free electron, find the density of states effective mass for the conduction band in the vicinity of the conduction band minima. 6) (8 points) Write the density of states for the conduction band.