Carl L. Gardner

The quantum hydrodynamic model for semiconductor devices

The classical hydrodynamic equations can be extended to include quantum effects by incorporating the first quantum corrections. These quantum corrections are

The dynamics of bubble growth for Rayleigh-Taylor unstable interfaces

O( {\hbar ^2 } )

Numerical methods for the hydrodynamic device model: subsonic flow

. The full three-dimensional quantum hydrodynamic (QHD) model is derived for the first time by a moment expansion of the Wigner–Boltzmann equation. The QHD conservation laws have the same form as the classical hydrodynamic equations, but the energy density and stress tensor have additional quantum terms. These quantum terms allow particles to tunnel through potential barriers and to build up in potential wells.The three-dimensional QHD transport equations are mathematically classified as having two Schrodinger modes, two hyperbolic modes, and one parabolic mode. The one-dimensional steady-state QHD equations are discretized in conservation form using the second upwind method.Simulations of a resonant tunneling diode are presented that show charge buildup in the quantum well and negative differential resistance (NDR) in the current-v...

Numerical simulation of a steady-state electron shock wave in a submicrometer semiconductor device

A statistical model is analyzed for the growth of bubbles in a Rayleigh–Taylor unstable interface. The model is compared to solutions of the full Euler equations for compressible two phase flow, using numerical solutions based on the method of front tracking. The front tracking method has the distinguishing feature of being a predominantly Eulerian method in which sharp interfaces are preserved with zero numerical diffusion. Various regimes in the statistical model exhibiting qualitatively distinct behavior are explored.

Smooth Quantum Hydrodynamic Model Simulation of the Resonant Tunneling Diode

An introduction to the hydrodynamic model for semiconductor devices is presented. Special attention is paid to classifying the hydrodynamic PDEs (partial differential equations) and analyzing their nonlinear wave structure. Numerical simulations of the ballistic diode using the hydrodynamical device model are presented, as an illustrative elliptic problem. The importance of nonlinear block iterative methods is emphasized. Arguments for existence of solutions and convergence of numerical methods are given for the case of subsonic electron flow. >

Approximation of thermal equilibrium for quantum gases with discontinuous potentials and application to semiconductor devices

Appropriate numerical methods for steady-state simulations (including shock waves) when the electron flow is both subsonic and supersonic are addressed. The one-dimensional steady-state hydrodynamic equations will then be elliptic in the subsonic regions and hyperbolic/elliptic in the supersonic regions. A second upwind method is used for both elliptic and hyperbolic/elliptic regions. In the elliptic regions, the second upwind method is related to the Scharfetter-Gummell exponential fitting method. The hydrodynamic model consists of a set of nonlinear conservation laws for particle number, momentum, and energy, coupled to Poissons equation for the electric potential. The nonlinear conservation laws are just the Euler equations of gas dynamics for a gas of charged particles in an electric field, with the addition of a heat conduction term. Thus the hydrodynamic model partial differential equations (PDEs) have hyperbolic, parabolic, and elliptic modes. The nonlinear hyperbolic modes support shock waves. The first numerical simulations of a steady-state electron shock wave in a semiconductor device are presented, using the hydrodynamic model. For the ballistic diode (which models the channel of a MOSFET), the shock wave is fully developed in Si (with 1-V bias) at 300 K for a 0.1- mu m channel and at 77 K for a 1.0- mu m channel. >

A multi-epoch HST study of the herbig-haro flow from XZ Tauri

Smooth quantum hydrodynamic (QHD) model simulations of the resonant tunneling diode are presented which exhibit enhanced negative differential resistance (NDR) when compared to simulations using the original O() QHD model. At both 300K and 77 K, the smooth QHD simulations predict significant NDR even when the original QHD model simulations predict no NDR.

Numerical Simulation of High Mach Number Astrophysical Jets with Radiative Cooling

We derive an approximate solution valid toall orders of

Hydrodynamic and Monte Carlo simulation of an electron shock wave in a 1- mu m n/sup +/-n-n/sup +/ diode

\hbar

Resonant Tunneling in the Quantum Hydrodynamic Model

to the Bloch equation for quantum mechanical thermal equilibrium distribution functions via asymptotic analysis for high temperatures and small external potentials. This approximation can be used as initial data for transient solutions of the quantum Liouville equation, to derive quantum mechanical correction terms to the classical hydrodynamic model, or to construct an effective partition function in statistical mechanics. The validity of the asymptotic solution is investigated analytically and numerically and compared with Wigners