Quantum and semi-classical transport in RTDs using NEMO 1-D

Gerhard Klimeck, Phillip Stout and R. Chris Bowen Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109 CFDRC, Huntsville, AL 35899 email: gekco@jpl.nasa.gov website: http://hpc.jpl.nasa.gov/PEP/gekco NEMO 1-D has been developed primarily for the simulation of resonant tunneling diodes (RTDs), and quantitative and predictive agreements with experimental high performance, high current density devices have been achieved in the past. There are four key ingredients to the success of these simulations: 1) the treatment of the extended contacts including quasi bound states and empirical relaxation time approximation scattering with a surface Green function, 2) accurate description of bandstructure using empirical tight binding models, 3) quantum charge self-consistency including a Hartree and exchange potential, and 4) the proper numerical integration over the transverse momentum. The treatment of the contacts assumes that the device is subdivided into three distinct regions: 1/2) a left/right reservoir in local equilibrium with the left/right contact with well established left/right quasi-Fermi levels, and 3) a central device region which is treated to be in non-equilibrium using the non-equilibrium Green function formalism (NEGF). The central device region is considered to be the current limiting element in the device. The left/right reservoirs are assumed to be in local equilibrium with a flat Fermi level and conductive enough to provide current without depletion of the reservoir. Despite the successful comparisons to experiments one question remained lingering in the treatment of the reservoirs: How good is the assumption of a local equilibrium? or How good is the assumption of a flat Fermi level? The expansion of the NEMO 1-D code to couple a drift-diffusion model in the reservoirs to the central non-equilibrium region addresses these questions. It can be shown that the drift diffusion equation can be formulated such that the current density in a particular device region is J ∝μ ini∇EF ,i , where μi, ni, and EF,i are the device site (i) dependent mobility, electron density and quasi Fermi level). The expression holds for an arbitrary density of states for arbitrary electron distributions. Continually assuming that the central quantum region dominates the current flow in the device the spatially dependent quasi Fermi level in the left/right contact is computed iteratively with a quantum mechanically computed electron density.