Simulation of Transport over Heterojunctions

The use of thermionic emission theory versus drift-diffusion in two-dimensional finite difference simulations of carrier transport over heterojunctions is discussed. We show the advantages of a two-dimensional mesh which is double-valued with respect to quasi-Fermi levels at heterojunctions. A heterojunction diode is then simulated using both drift-diffusion and thermionic emission at the heterojunction, and the results are compared. Thermionic emission at hetero-interfaces is also used to simulate current confinement by a wide bandgap blocking region in a p-n diode. We find that the use of thermionic emission theory always improves the results and sometimes provides the conditions necessary for convergence. Heterojunctions are proving to be very important in the design of many classes of semiconductor devices. They are the key to the high performance of transistor structures such as t h e HEMT and the HBT [1, 2, 3] and have improved the efficiencies of semiconductor solar cells [4]. They have also made possible novel device structures such as the charge injection transistor (CHINT) and the negative resistance field-effect transistor (NERFET) [5, 6]. And i t is, of course, the heterojunction that has made the semiconductor laser a practical, coherent light source suitable for commercial applications [7]. Because the use of heterostructures is so pervasive, the accurate simulation of carrier t ransport in these structures is of vital interest. Most numerical models assume continuous quasi-Fermi levels at the heterojunction interfaces and use drift-diffusion to describe transport throughout the entire device [8, 9, 10, 11, 12, 13], however, it has been shown in one dimension that quasi-Fermi levels need not be continuous at hetero-interfaces [14]. In this paper, the use of thermionic emission and drift-diffusion at heterojunctions is compared, and a new twodimensional discretization technique is introduced to more efficiently account for heterojunction points in numerical simulations. 1 Treatment of Transport over Heterojunctions I n conventional drift-diffusion models, the assumption of continuous quasi-Fermi levels can be made in two ways. The first way is to avoid determining carrier transport at a heterojunction and instead set the quasi-Fermi levels at points on either side of the junction equal to one another. Drift-diffusion theory can be used between points away from the heterojunction, and current continuity can be maintained [14]. The second way uses drift-diffusion theory to calculate carrier transport over a heterojunction. In drift-diffusion theory, carrier flux densities can be expressed as J n = ixnnVFn (1) 'Currently employed at BellCore, Redbank, N3.