半导体物理-Threshold Voltage Model for FinFET

The threshold voltage (Vth) of the virgin FinFET device is given by[1][2]

where VFB is flat-band voltage, Ψs(inv) is the surface potential at threshold voltage, Cox=(εox/tox) is the gate oxide capacitance, tox is gate oxide thickness, Na is the acceptor concentration, k is the Boltzmann's constant, T is the temperature, ni is the intrinsic carrier concentration, Tfin is the fin thickness and q is the electronic charge. The charge in threshold voltage due to quantum mechanical effects is given by[3]

where mx/mL is the ratio of the carrier effective mass in the direction of confinement to the free electron mass. The analytical evaluated subthreshold swing factor (S) is given by[4]

The results obtained for the variation in threshold voltage with Fin thickness (TFIN) are illustrated in the figure below. Threshold voltage increase in thinner device suggests that the sub-band energy level increases due to quantum mechanical confinement effects in ultrathin channels. 

Ref. 

S. S. Rathod, et.al., Modeling of threshold voltage, mobility, drain current and subthreshold leakage current in virgin and irradiated silicon-on-insulator fin-shaped field effect transistor device. Journal of Applied Physics 109, 084504 (2011)