Quantum Statistical Behaviors of Carriers in Strong Inversion Layers Associated with Mobility and Threshold Voltage in FinFET Transistors

Gated transistors in the form of MOSFET, FinFET, or IGBT are capable of controlling and transferring either signals or powers. These capabilities are closely associated with applied biases on Gates, which surpass the respective threshold voltages. Source/Drain bias, VDS, then establishes the electric field, EDS, driving carriers to flow with a speed which is proportional to EDS with the proportionality, termed mobility, μ. The mobility somewhat addresses the electrical performances of the specific transistor, and is VGS-dependent, where the generated electric field is perpendicular to the interface in between the Gate and the Gate oxide and is directed across the channel. The mobility may be treated as the collective quantum statistical behaviors of carriers, i.e., electrons or fermions. It is worth analyzing the electrical performances by way of quantum statistics. Nevertheless, the threshold voltages are surprisingly negative on FinFETs as the fitting is performed, which means that IDS would flow even without applied voltage on the Gate. IDS-VDS characteristic curves with negative threshold voltage intriguingly perform just like the other ones with positive threshold voltages. Therefore, there might exist some kind of mechanism enhancing strong inversion layers that is responsible for the characteristics. In this paper, characteristic curves of FinFETs may be well fitted by using both modified characteristic formulas and the proposed kink effects. The extracted parameters (kN, Vth, λ) thus provide information on mobility, concentration of p (1/cm3), or even leakage current. Also, the mobility, μ, here is analyzed by using Fermion statistics. Furthermore, trivial solutions for the specific boundary conditions, VGS = 0 V, surrounding the channel are presented, where one of the possibilities proposed is the mass plasma oscillation of electrons, which might be an option for addressing the negative threshold voltage.