European Journal of Applied Mathematics


Nano-scale MOSFET device modelling with quantum mechanical effects

a1 School of Mathematical Sciences, Claremont Graduate University, Claremont, CA 91711, USA
a2 USC Information Sciences Institute, MOSIS Service, 4676 Admiralty Way, Marina del Rey, CA 90292, USA email:

Article author query
cumberbatch e   [Google Scholar] 
uno s   [Google Scholar] 
abebe h   [Google Scholar] 


The continuing down-scaling trend of CMOS technology has brought serious deterioration in the accuracy of the SPICE (Simulation Program with Integrated Circuit Emphasis) device models used in the design of chip functions. This is due to in part to hot electron and quantum effects that occur in modern nano-scale MOSFET devices [13, 25, 28, 33, 34]. The focus of this paper is on modeling quantum confinement effects based on the Density-Gradient (DG) model [6, 9, 14], for application in SPICE. Analytic 1-D quantum mechanical (QM) effects correction formulae for the MOSFET inversion charge and electrostatic potential are derived from the DG model using matched asymptotic expansion techniques. Comparison of these new models with numerical data shows good results.

(Published Online November 1 2006)
(Received July 19 2005)
(Revised June 14 2006)