Mobility of Carriers in Strong Inversion Layers Associated with Threshold Voltage for Gated Transistors

Hsin-Chia Yang; Sung-Ching Chi; Bo-Hao Huang; Tung-Cheng Lai; Han-Ya Yang

doi:10.3390/mi16121393

Mobility of Carriers in Strong Inversion Layers Associated with Threshold Voltage for Gated Transistors

Micromachines (Basel). 2025 Dec 9;16(12):1393. doi: 10.3390/mi16121393.

Authors

Hsin-Chia Yang¹, Sung-Ching Chi¹, Bo-Hao Huang¹, Tung-Cheng Lai¹, Han-Ya Yang²

Affiliations

¹ Department of Electronic Engineering, Ming Hsin University of Science and Technology, Hsinchu County 30401, Taiwan.
² Department of Electronic Physics, National Yang-Ming Chiao-Tung University, Hsinchu City 300, Taiwan.

Abstract

NMOSFET, whose gate is on the top of the n-p-n junction with gate oxide in between, is called the n-channel transistor. This bipolar junction underneath the gate oxide may provide an n-n-n-conductive channel as the gate is applied with a positive bias over the threshold voltage (V_th). Conceptually, the definition of an n-type or p-type semiconductor depends on whether the corresponding Fermi energy is higher or lower than the intrinsic Fermi energy, respectively. The positive bias applied to the gate would bend down the intrinsic Fermi energy until it is lower than the original p-type Fermi energy, which means that the p-type becomes strongly inverted to become an n-type. First, the thickness of the inversion layer is derived and presented in a planar 40 nm MOSFET, a 3D 240 nm FinFET, and a power discrete IGBT, with the help of the p (1/m³) of the p-type semiconductor. Different ways of finding p (1/m³) are, thus, proposed to resolve the strong inversion layers. Secondly, the conventional formulas, including the triode region and saturation region, are already modified, especially in the triode region from a continuity point of view. The modified formulas then become necessary and available for fitting the measured characteristic curves at different applied gate voltages. Nevertheless, they work well but not well enough. Thirdly, the electromagnetic wave (EM wave) generated from accelerating carriers (radiation by accelerated charges, such as synchrotron radiation) is proposed to demonstrate phonon scattering, which is responsible for the Source-Drain current reduction at the adjoining of the triode region and saturation region. This consideration of reduction makes the fitting more perfect. Fourthly, the strongly inverted layer may be formed but not conductive. The existing trapping would stop carriers from moving (nearly no mobility, μ) unless the applied gate bias is over the threshold voltage. The quantum confinement addressing the quantum well, which traps the carriers, is to be estimated.

Keywords: FinFET; IGBT; MOSFET; kink effects; quantum confinement; radiation by accelerated charges; strong inversion layer; threshold voltage.