2-D Quantum Confined Threshold Voltage Shift Model for Asymmetric Short-Channel Junctionless Quadruple-Gate FETs

This article presents a compact quantum threshold voltage ( ${V}_{\text {th}}$ ) shift model for a junctionless (JL) quadruple-gate (QG) FET in subthreshold region. Starting from our previous compact model for JL QG FET, the potential and the classical electron density are calculated. Considering 2-D quantum confinement, four types of quantum systems are modeled as a combination of quantum harmonic oscillator (QHO) and quantum well with bottom perturbation potential, depending on the device dimensions. Electron subband energy level for each quantum system is analytically derived to get quantum electron density. The quantum ${V}_{\text {th}}$ shift model is obtained by the ratio of quantum and classical electron line density. The modeling results are validated by 3-D numerical device simulation. It is shown that the proposed model can accurately capture the quantum ${V}_{\text {th}}$ shift in JL QG FET where both fin width and height are 3 nm. Therefore, the proposed ${V}_{\text {th}}$ shift model can be used for quantum corrections for circuit simulation of JL QG FETs.