TITLE:

TRANSISTOR MODELING FOR THE SEMI-CONDUCTOR INDUSTRY (No. 147)

DATE:

Friday, March 2nd, 2007

TIME:

3:30 PM

LOCATION:

GMCS 214

SPEAKER:

Ellis Cumberbatch, Department of Mathematics, Claremont Graduate University

ABSTRACT:

Software packages, under the generic name SPICE, simulate C-MOS integrated circuits. Since there may be up to 106 transistors on a chip, each transistor must have a simple representation in SPICE.

The current/voltage characteristics of a single transistor are derived from the flow of electrons and holes, governed by non-linear partial differential equations, the so-called drift-diffusion equations (in the classical limit). Simple approximations were found suitable in early models, and as device sizes reduced these have been adapted empirically to fit data so much so that now there can be as many as 400 fitting parameters needed. This is expensive it requires lots of measurements and parameter extraction. We have been re-visiting the physics, obtaining better approximations.
After a brief introduction to the physics of semi-conductors, I shall describe an approach to the basic equations using asymptotic analysis that, for some transistor characteristics including the current/voltage relationship, yields accurate formulae needing much fewer parameters. In particular work done for our industrial sponsor has involved modeling the dependence of junction capacitance on voltage. Also I shall describe enhanced equations that have been introduced to model quantum effects that are present in the ultra-small devices.

Our results are compared with exact numerical solutions and with data.

HOST:

Jose Castillo

DOWNLOAD: