A new simplified two-dimensional model for the threshold voltage of MOSFET's with nonuniformly doped substrate

• Published in: IEEE transactions on electron devices Vol. 38; no. 6; pp. 1376 - 1383
• Main Authors: Pole-Shang Lin, Ching-Yuan Wu
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.06.1991; Institute of Electrical and Electronics Engineers
• Subjects: Analytical models; Applied sciences; Boundary conditions; Dielectric substrates; Doping; Electronics; Exact sciences and technology; Green function; MOSFET circuits; Numerical analysis; Poisson equations; Semiconductor electronics. Microelectronics. Optoelectronics. Solid state devices; Semiconductor process modeling; Threshold voltage; Transistors; Voltage threshold; Field effect transistor; MOS transistor; Voltage current curve; Modeling
• ISSN: 0018-9383; 1557-9646
• DOI: 10.1109/16.81629

A new simplified two-dimensional model for the threshold voltage of MOSFETs is derived in terms of simple characteristic functions. These characteristic functions are transformed from the exact series solution of the two-dimensional Poisson's equation, in which the effects of a nonuniformly doped substrate and a finite graded source-drain junction depth are included. In this model, charge-screening effects are proposed to account for the weak dependence of the threshold voltage on the substrate bias for short-channel MOSFETs, and exact source and drain boundary potentials can be approximated by their equivalent power functions. The accuracy of the simplified 2-D model is verified by 2-D numerical analysis. Moreover, comparisons between the simplified 2-D model and the experimental results are made, and good agreement is obtained for wide ranges of channel lengths, applied substrate, and drain biases.< >