Analytical Modeling of Threshold Voltage for Double-Gate MOSFET Fully Comprising Quantum Mechanical Effects

The analytical solutions to 1D Schrodinger equation (in depth direction) in douBle-gate (DG) MOSFETs are derived to calculate electron density and threshold voltage.The non-uniform potential in the channel is concerned with an arbitrary depth so that the analytical solutions agree well with numerical ones.Then,an implicit expression for electron density and a closed form of threshold voltage are presented fully comprising quantum mechanical (QM) effects.This model predicts an increased electron density with an increasing channel depth in subthreshold region or mild inversion region.However,it becomes independent on channel depth in strong inversion region,which is in accordance with numerical analysis.It is also concluded that the QM model,which barely considers a box-like potential in the channel,slightly overpredicts threshold voltage and underestimates electron density，and the error increases with an increasing channel depth or a decreasing gateoxide thickness.