Consider a solid in the sc (simple cubic) crystal lattice configuration with the conventional lattice spacing a = 1. Within the tight-binding approximation for 3s orbitals with energy En = 10 eV, assuming only nearest-neighbour interaction with y R =-J dr q*(r)v(r)(r-R -1 eV, and neglecting the atomic self-energy orbital correction , (a) Determine the dispersion relation E
[5 marks]
(b) The Fermi energy for the solid is EF = 11 eV. Is the solid a conductor or an insulator? Motivate your answer.
[5 marks]
(c) Assuming a = 1 nm, determine the effective mass of an electron occupying the energy level (kx,ky,kz)=(,0,); [5 marks]
(d) For an electric field constant along the axis E = (Eo,0, 0), determine the acceleration of the electron occupying the state in question (c), i.e., k = (, 0, ); [5 marks]
(e) State the approximations leading to the tight-binding model and provide a short, one sen- tence brief description of each of them.
[5 marks]