Question

Band structure Consider a one-dimensional semiconductor crystal consisting of 11 atoms with nearest- neighbor atoms separated by a 5 . The band structure for electrons in the conduction band is given by Ec(k) = 101(k-0.2n)2-A(k-02n)"] + 2.25 [eV] and the band structure for holes in the valence band is given by where the wavevector k s in units ofA-1. The allowed wavevectors are--< k 즈 al (a) Is this a direct or indirect gap semiconductor? What is the energy gap of this semiconductor crystal? (b) Determine the value of the constants B and C. (Note that the slope of the bands must be zero at x = 0 and k =-) Cl. (c) Determine the effective masses for electrons and holes in this semiconductor (d) Since there is an odd number of atoms in the crystal, the allowed wavevectors are given Rn Na n = 0, ±1, ±2, t- Determine the allowed wavevectors for this one-dimensional crystal and calculate the corresponding conduction and valence band energy levels. Sketch the band structure for this crystal showing the discrete energy levels for each band. (e) Using the band diagram in part (d), sketch the electron occupancy of the energy levels in the band for case of 11 electrons. Can the semiconductor conduct for this case? If, so what type of charge carriers (electron or hole) wll carry this current? Repeat this question for 22 electrons and 33 electrons.