Optimized numerical models for semiconductor devices. I, II
Abstract
Systematic modeling procedures were developed for analytically making a trade-off between the two opposing considerations of efficiency of digital computation and accuracy in predicting semiconductor device responses. The use of nonuniform grids was chosen to improve the accuracy of the numerical model. This approach is a constrained optimization problem. A performance function is formed to measure the accuracy of the model relative to the 'exact' solution or device characteristics. Two types of performance functions were considered: (1) matching the computed response to the 'exact' response, using current density as the response, and (2) minimizing the truncation error made in the differencing approximations. Examples are presented showing the results obtained for applying the two types of performance functions. An interesting result is that when the truncation error is minimized, then all other desired features are optimized for the numerical models.
- Publication:
-
IEEE Transactions on Electron Devices
- Pub Date:
- April 1976
- DOI:
- 10.1109/T-ED.1976.18423
- Bibcode:
- 1976ITED...23..442M
- Keywords:
-
- Finite Difference Theory;
- Mathematical Models;
- Optimization;
- Semiconductor Devices;
- Volt-Ampere Characteristics;
- Algorithms;
- Current Density;
- Numerical Analysis;
- Partial Differential Equations;
- Truncation Errors;
- Electronics and Electrical Engineering