Two-Dimensional Quantum Model of a Nanotransistor

Quantum effects that become important at the nanoscale are taken into account.

A mathematical model, and software to implement the model, have been devised to enable numerical simulation of the transport of electric charge in, and the resulting electrical performance characteristics of, a nanotransistor [in particular, a metal oxide/semiconductor field-effect transistor (MOSFET) having a channel length of the order of tens of nanometers] in which the overall device geometry, including the doping profiles and the injection of charge from the source, gate, and drain contacts, are approximated as being two-dimensional. The model and software constitute a computational framework for quantitatively exploring such device-physics issues as those of source-drain and gate leakage currents, drain-induced barrier lowering, and threshold voltage shift due to quantization. The model and software can also be used as means of studying the accuracy of quantum corrections to other semiclassical models.

Drain Current Versus Gate Potential in a conceptual 25-nm-gate-length MOSFET commonly used as an example for testing MOSFET-simulating software was calculated by means of a three-band and a one-band version of the present quantum-based model. For comparison, the plot also shows results from a classical diffusion-drift model and a quantum-corrected model embodied in a commercial MOSFET-simulation computer program. A drain bias of 1 V and a gate oxide thickness of 1.5 nm were used in the simulations.
The present model accounts for two quantum effects that become increasingly important as channel length decreases toward the nanometer range: quantization of the inversion layer and ballistic transport of electrons across the channel. Heretofore, some quantum effects in nanotransistors have been analyzed qualitatively by use of simple one- dimensional ballistic models, but two-dimensional models are necessary for obtaining quantitative results. Central to any quantum- mechanical approach to modeling of charge transport is the self-consistent solution of a wave equation to describe the quantum-mechanical aspect of the transport, Poisson’s equation, and equations for statistics of the particle ensemble.

Non-equilibrium Green’s function (NEGF) formalisms have been successful in modeling steady-state transport in a variety of one-dimensional semiconductor structures. The present model for the two-dimensional case includes the NEGF equations, which are solved self-consistently with Poisson’s equation. At the time of this work, this was the most accurate full quantum model yet applied to simulation of two-dimensional semiconductor devices. Open boundary conditions (in which the narrow channel region opens into broad source, gate, and drain regions) and tunneling through oxide are treated on an equal footing. Interactions between electrons and phonons are taken into account, causing the modeled transport to deviate from ballistic in a realistic manner. Electrons in the wave-vector-space ellipsoids of the conduction band are treated within the anisotropic-effective-mass approximation.

Self-consistent solution of the Poisson and NEGF equations is computation-intensive because of the number of spatial and energy coordinates involved. Therefore, parallel distributed computing is imperative: the software that implements the model distributes the computations, energy-wise, to the various processors. Initial simulations were performed using, variously, between 16 and 64 processors of an SGI Origin multiprocessor computer. The figure presents an example of results of one set of simulations.

This work was done by T. R. Govindan and B. Biegel of Ames Research Center and A. Svizhenko and M. P. Anantram of Computer Science Corp. ARC-15471-1

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