Solution for Undoped Symmetric Double-Gate MOSFETs Considering Both Electrons
and Holes at Quasi Nonequilibrium
Xing Zhou, Senior Member, IEEE, Zhaomin Zhu, Subhash C.
Rustagi, Senior Member, IEEE, Guan Huei See, Student Member, IEEE, Guojun
Zhu, Shihuan Lin, Chengqing Wei, and Guan Hui Lim, Student Member, IEEE
IEEE Transactions on Electron Devices,
55, No. 2, pp.
616-623, Feb. 2008.
(Manuscript received May 22, 2007; revised
October 15, 2007.)
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This paper presents a rigorously-derived analytical solution of the
Poisson equation with both electrons and holes in pure silicon, which is
applied to the analysis of undoped symmetric double-gate transistors.
An implicit surface-potential equation is obtained that can be solved by
a second-order Newton–Raphson technique along with an appropriate initial
guess. Within the assumption of holes at equilibrium that is being
used in the existing literature, the new results, when compared with the
models based on one carrier, reveal that missing the other carrier in the
formulation results in a singularity in the gate capacitance exactly at
flatband, which may give trouble for high-frequency analysis, although
the errors in surface potentials are below the nano-volt range for all
gate voltages. However, the solution without assuming constant hole
imref, as presented in this paper for the first time, further pinpoints
the inadequacy in existing theories of surface-potential solutions in double-gate
MOSFETs with undoped thin bodies, although its application to transport
solutions of terminal current/charge models depends highly on the type
of source/drain structures and contacts.
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