Modelling of Threshold Voltage with Non-uniform Substrate Doping

K. Y. Lim and X. Zhou

School of Electrical & Electronic Engineering, Nanyang Technological University
Nanyang Avenue, Singapore 639798
(Phone: 65-7991368, Fax: 65-7912687, Email:

Proc. of the 1998 IEEE International Conference on Semiconductor Electronics (ICSE’98)

Malaysia, November 24-26, 1998, pp. 27-31.

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A simple analytical threshold voltage equation for modelling non-uniform channel doping is derived, which takes the peak doping concentration and peak location as inputs with a single process-dependent fitting parameter. The model has been verified with extensive numerical simulation results and can be applied to real devices for a wide range of non-uniform doping profiles with a simple, empirical parameter extraction.



  1. [8] X. Zhou, K. Y. Lim, and D. Lim, "A simple and unambiguous definition of threshold voltage and its implications in deep-submicron MOS device modeling," IEEE Trans. Electron Devices, Vol. 46, No. 4, pp. 807-809, Apr. 1999.
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  3. [1] K. Y. Lim, X. Zhou, and Y. Wang, "Modeling of threshold voltage with reverse short channel effect," Proc. 3rd International Conference on Modeling and Simulation of Microsystems (MSM2000), San Diego, CA, Mar. 2000, pp. 317-320.
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  6. [1] K. Y. Lim, X. Zhou, and Y. Wang, "Physics-Based Threshold Voltage Modeling with Reverse Short Channel Effect," J. Modeling Simulation Microsystems (JMSM), Vol. 2, No. 1, pp. 51-55, 2001.