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NASA NTRS2009

A theoretical analysis of steady-state charge collection in simple diodes under high-injection conditions

A previous rigorous mathematical analysis of drift-diffusion equations was used to investigate collected charge in a simple reverse-biased p-n junction diode exposed to an ionization source that liberates carriers (electron-hole pairs) in a quasi-neutral region within the diode. Each of two simple models was found to agree with the more rigorous analysis when carrier liberation is sufficiently intense. One is the sensitive volume (SV) model, and the other was called “ambipolar diffusion with a cutoff” (ADC). The earlier rigorous analysis was worked out in detail only for a localized source, i.e., a point source of carrier liberation, so it was able to validate the applicability of each simple model only for that case. The present paper treats an arbitrary spatial distribution of carrier generation and concludes that the ADC model remains valid for this more general case, but the SV model does

Edmonds, Larry D.↗

NASA NTRS1996

Comparison of Non-Parabolic Hydrodynamic Simulations for Semiconductor Devices

Parabolic drift-diffusion simulators are common engineering level design tools for semiconductor devices. Hydrodynamic simulators, based on the parabolic band approximation, are becoming more prevalent as device dimensions shrink and energy transport effects begin to dominate device characteristic. However, band structure effects present in state-of-the-art devices necessitate relaxing the parabolic band approximation. This paper presents simulations of ballistic diodes, a benchmark device, of Si and GaAs using two different non-parabolic hydrodynamic formulations. The first formulation uses the Kane dispersion relationship in the derivation of the conservation equations. The second model uses a power law dispersion relation {(hk)(exp 2)/2m = xW(exp Y)}. Current-voltage relations show that for the ballistic diodes considered. the non-parabolic formulations predict less current than the parabolic case. Explanations of this will be provided by examination of velocity and energy profiles. At low bias, the simulations based on the Kane formulation predict greater current flow than the power law formulation. As the bias is increased this trend changes and the power law predicts greater current than the Kane formulation. It will be shown that the non-parabolicity and energy range of the hydrodynamic model based on the Kane dispersion relation are limited due to the binomial approximation which was utilized in the derivation.

Smith, A. W.↗

NASA NTRS2001

2-D Modeling of Nanoscale MOSFETs: Non-Equilibrium Green's Function Approach

We have developed physical approximations and computer code capable of realistically simulating 2-D nanoscale transistors, using the non-equilibrium Green's function (NEGF) method. This is the most accurate full quantum model yet applied to 2-D device simulation. Open boundary conditions and oxide tunneling are treated on an equal footing. Electrons in the ellipsoids of the conduction band are treated within the anisotropic effective mass approximation. Electron-electron interaction is treated within Hartree approximation by solving NEGF and Poisson equations self-consistently. For the calculations presented here, parallelization is performed by distributing the solution of NEGF equations to various processors, energy wise. We present simulation of the "benchmark" MIT 25nm and 90nm MOSFETs and compare our results to those from the drift-diffusion simulator and the quantum-corrected results available. In the 25nm MOSFET, the channel length is less than ten times the electron wavelength, and the electron scattering time is comparable to its transit time. Our main results are: (1) Simulated drain subthreshold current characteristics are shown, where the potential profiles are calculated self-consistently by the corresponding simulation methods. The current predicted by our quantum simulation has smaller subthreshold slope of the Vg dependence which results in higher threshold voltage. (2) When gate oxide thickness is less than 2 nm, gate oxide leakage is a primary factor which determines off-current of a MOSFET (3) Using our 2-D NEGF simulator, we found several ways to drastically decrease oxide leakage current without compromising drive current. (4) Quantum mechanically calculated electron density is much smaller than the background doping density in the poly silicon gate region near oxide interface. This creates an additional effective gate voltage. Different ways to. include this effect approximately will be discussed.

Svizhenko, Alexei↗