Rate Equations for the Phonon Peak in Resonant-Tunneling Structures

Roger Lake, Purdue University - Main Campus
Gerhard Klimeck, Purdue University - Main Campus
J. P. Anantram, Purdue University - Main Campus
Supriyo Datta, Purdue University - Main Campus

Date of this Version



Phys Rev. B, Vol. 48, Number 20 (1993) 15132.


This is the published version of Roger Lake, Gerhard Klimeck, M. P. Anantram, and Supriyo Datta. (15 November 1993). "Rate equations for the phonon peak in resonant-tunneling structures". First published in the Physical Review B and is available online at: https://doi.org/10.1103/PhysRevB.48.15132


The ratio of the phonon peak current to the main peak current in double-barrier resonant-tunneling structures is significantly enhanced by barrier asymmetry. Previously, using the Keldysh formalism, we derived analytical expressions, valid in the zero-temperature, high-bias regime, which explained this eftect. We now provide analytical expressions valid for finite temperature and bias obtained from (i) an intuitive derivation using a rate equation approach and (ii) a more general derivation using the Keldysh formalism. The results of the two difFerent approaches are shown to be essentially identical for the ex- perimental device parameters. The finite temperature expressions shed light on the e8'ect of the Pauli ex- clusion factors in the contacts on the current. In particular, we show that in a transmission formulation, the transmission coefficients, T(c,c, ), are themselves functions of the Fermi factors in the contacts.


Nanoscience and Nanotechnology