Refined Conformal Mapping Model for MOSFET Parasitic Capacitances Based on Elliptic Integrals

Abstract

In this paper, the main MOSFET parasitic capacitances of planar devices (i.e., bulk, Fully depleted silicon-on-insulator (FDSOI), and planar double gate) are computed using two successive conformal mapping transforms. First, the structure is mapped to the real axis of the complex plane, and then the second transform, deduced directly from the Schwarz-Christoffel theorem, reduces the capacitance to the trivial parallel electrodes case. This second step involves elliptic integrals, which provide a generic expression for all parasitic capacitances. This method is later compared against other models based on conformal mapping. Finally, the results are validated with finite-element method simulations of the inner and outer fringe capacitances in different architectures, including metallic contacts and raised and faceted junctions.Index Terms-CMOS, compact model, conformal mapping, electrostatic, elliptic integrals, Model for Assessment of CMOS Technologies and Roadmaps (MASTAR), MOSFET, parasitic capacitance, roadmap.

Impact of short-channel effects on velocity overshoot in MOSFET

“…The same approach could be applied to Single-Gate MOSFETs. The parasitic capacitances are evaluated with the conformal mapping model reported in [21].…”

Compact Modeling of Parasitic Capacitances in GAAFETs for Advanced Technology Nodes

“…In this work, an accurate analytical parasitic capacitance model is proposed using the conformal mapping as well as Schwarz Christoffel transform [21], [28], [29], [32]. The proposed model is then verified with the 3D TCAD simulation, and the effect of important device parameters on the parasitic capacitance is investigated as well.…”

Traps induced Greens function based mathematical modeling for BaTiO3–SrTiO3 gate stack dual metal GAA MOSFET

“…Charge sheet position values are varied [15][16][17][18] to provide for better outcome. It has been found that an epitaxial [8] oxide layer of BaTiO 3 -SrTiO 3 [19] as gate stack is way better than the other two and provides high accuracy of results [20][21][22][23] despite the presence of trap Charges [24] along the charge sheet position. Also, Conformal Mapping [17,18] is used in which Schwarz-Christoffel Transformation [20,21] has been employed for conversion of function to imaginary plane.…”

“…It has been found that an epitaxial [8] oxide layer of BaTiO 3 -SrTiO 3 [19] as gate stack is way better than the other two and provides high accuracy of results [20][21][22][23] despite the presence of trap Charges [24] along the charge sheet position. Also, Conformal Mapping [17,18] is used in which Schwarz-Christoffel Transformation [20,21] has been employed for conversion of function to imaginary plane. These concepts are applied to solve for surface potential due to trap charges and their influence on the Barium Titanate, a very high-k dielectric material.…”