r + 4. (10 points) An hole (charge e) tunnels along a chain of molecules in an electric field Ex) that is given as the gradient of an electrical potential 6. The drift-diffusion equation is given by e ; ao at 2.2 k r ( where p is the density of holes. (a) By pulling out an overall derivative and combining terms on the right hand side, show that the drift-diffusion equation can be re-written in the form, a ot ac where the particle-current density, Da J= -HC is proportional to the gradient of the chemical potential, H. (x) = -KT In p() - (). I KTP 1 (b) Show that the electrical-current density J = e) can be written in a form referred to as Ohm's law, J=-62 r where o = Pp is the electrical conductivity and the voltage V = Me /e is the chemical potential per charge