In a one-dimensional model of an intrinsic semiconductor the energy measured from the bottom of the valence band is
uploaded imageThis is an approximate formula accurate only in the vicinity of the minimum of the conduction band,, which occurs when k=k1 =pi/a, where a the lattice spacing is 0.314nm. The Fermi energy is at 2.17eV.
Calculate the energy gap between the valence and the conduction bands and the effective mass of electrons at the bottom of the conduction band. Assume that the Fermi level is halfway between the valence and conduction band.