scholarly journals Hot Electron Modelling of HEMTs

VLSI Design ◽  
2001 ◽  
Vol 13 (1-4) ◽  
pp. 287-293 ◽  
Author(s):  
Eric A. B. Cole ◽  
Christopher M. Snowden ◽  
Shahzad Hussain
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Quantum Wells ◽  
Numerical Solution ◽  
Conduction Band ◽  
Finite Difference Scheme ◽  
Energy Transport ◽  
Two Dimensional ◽  
Hot Electron ◽  
Recessed Gate

The hot-electron two-dimensional HEMT with recessed gate is modelled by solving the Poisson, current continuity and energy transport equations consistently with the Schrödinger equation using a finite difference scheme. New expressions are used for the energy densities inside and outside the quantum wells. A method is described for pinning the conduction band at the contact edge to produce an extremely stable numerical solution. Results are presented for an eight layer GaAs-ALGaAs-InGaAs device.

scholarly journals ENERGY-CONSERVING AND RECIPROCAL SOLUTIONS FOR HIGHER-ORDER PARABOLIC EQUATIONS

2001 ◽  
Vol 09 (01) ◽  
pp. 183-203 ◽  
Author(s):  
DMITRY MIKHIN
Keyword(s):  
Finite Difference ◽  
Energy Conservation ◽  
Difference Scheme ◽  
Numerical Solution ◽  
Finite Difference Scheme ◽  
Flow Reversal ◽  
Difference Operators ◽  
Energy Conserving ◽  
The One ◽  
Moving Media

The energy conservation law and the flow reversal theorem are valid for underwater acoustic fields. In media at rest the theorem transforms into well-known reciprocity principle. The presented parabolic equation (PE) model strictly preserves these important physical properties in the numerical solution. The new PE is obtained from the one-way wave equation by Godin12 via Padé approximation of the square root operator and generalized to the case of moving media. The PE is range-dependent and explicitly includes range derivatives of the medium parameters. Implicit finite difference scheme solves the PE written in terms of energy flux. Such formalism inherently provides simple and exact energy-conserving boundary condition at vertical interfaces. The finite-difference operators, the discreet boundary conditions, and the self-starter are derived by discretization of the differential PE. Discreet energy conservation and flow reversal theorem are rigorously proved as mathematical properties of the finite-difference scheme and confirmed by numerical modeling. Numerical solution is shown to be reciprocal with accuracy of 10–12 decimal digits, which is the accuracy of round-off errors. Energy conservation and wide-angle capabilities of the model are illustrated by comparison with two-way normal mode solutions including the ASA benchmark wedge.

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