A Threshold Voltage Model of Silicon-Nanotube-Based Ultrathin Double Gate-All-Around (DGAA) MOSFETs Incorporating Quantum Confinement Effects

In this paper, a quantum-mechanical threshold voltage model for ultrathin double gate-all-around DGAA MOSFETs has been developed by solving three-dimensional (3-D) Poisson's and 2-D Schrödinger's equations in the channel region. The parabolic potential approximation is considered for Poisson's equation solution, whereas a hollow cylindrical potential well in the channel region is assumed to solve Schrödinger's equation. Simple equations for the wave function and energy quantization in the channel of DGAA MOSFET have been formulated. Discretized energy levels have been used for channel charge calculation in subthreshold regime of device operation. The calculated channel charge is compared with a threshold charge to formulate the threshold voltage model. The effects of the device parameters such as the channel thickness, oxide thickness, doping, etc. on threshold voltage and DIBL have been extensively studied. The proposed model results have been verified by comparing with the numerical simulation results obtained from the 3-D device simulator Visual TCAD of Cogenda Int.