RATE-EQUATIONS FOR THE PHONON PEAK IN RESONANT-TUNNELING STRUCTURES

The ratio of the phonon peak current to the main peak current in doubl e-barrier resonant-tunneling structures is significantly enhanced by b arrier asymmetry. Previously, using the Keldysh formalism, we derived analytical expressions, valid in the zero-temperature, high-bias regim e, which explained this effect. We now provide analytical expressions valid for finite temperature and bias obtained from (i) an intuitive d erivation using a rate equation approach and (ii) a more general deriv ation using the Keldysh formalism. The results of the two different ap proaches are shown to be essentially identical for the experimental de vice parameters. The finite temperature expressions shed light on the effect of the Pauli exclusion factors in the contacts on the current. In particular, we show that in a transmission formulation, the transmi ssion coefficients, T(epsilon,epsilon'), are themselves functions of t he Fermi factors in the contacts.