MOSFET Analytical Inversion Charge Model with Quantum Effects using a Triangular Potential Well Approximation
H. Abebe, E.C. Cumberbatch, V. Tyree and H.C. Morris
USC/ISI MOSIS, US
device modeling, MOSFET, quantum effects, SPICE
The eigenfunctions from solutions of the Schrödinger equation for a triangular potential well are the Airy functions. The triangular potential approximation has been shown to be a good approximation for the charge density when the MOS device is in depletion or weak inversion. However, the approach has not had comparable success in approximating the inversion charge density when the device is at strong inversion (see Stern  and Moglestue ). In this paper we continue to use the triangular potential to estimate the inversion charge, but we use asymptotic solutions of the Poisson equation for the MOS device at strong inversion. The electrostatic potential asymptotic expression is given in , which was improved in . Our analytical Schrödinger-Poisson (SP) result is compared with the Bohm potential  or Density-Gradient (DG) solutions [6, 7] and Hansch quantum models . Our SP analytical model gives a close approximation to the full numerical inversion charge density simulation results of the DG model (see Figure 1).
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Nanotech 2005 Conference Program Abstract