Abstract: NFinFET transistors with fin channel length 90nm and a planar MOSFET transistor with channel length 180nm and 90nm are presented with characteristic curves at various gate biases. A finalized algorithm with kink effects is effectively responsible for addressing the field effect transistors. The algorithm includes the modified conventional current-voltage formula and a nonlinear heat-associated kink solution which is simplified as a Gaussian form. Three parameters in modified model includes kN (related with channel width, channel length, and gate oxide capacitor, and proportional to the mobility of carriers)Vth(Threshold Voltage), and (the inverse of Early Voltage). Those parameters are determined to minimize the discrepancies between the measured data and the fitting values, but leave kinks located at around (VGS－Vth), which are deliberately eliminated by the Gaussian form because of the agitation of thermal kink effects. The whole fitting is made to be as close as the as-measured IDS-VDS. In the mean time, those determined parameters are physically meaningful after the analysis has been done.

Insulated Gate Bipolar Transistor (IGBT) may convey high current and sustain high breakdown voltages; it may provide high power control. In a sense, how IGBT demonstrates the capability of power control was not specifically described, and the equivalent bipolar junction transistors (BJT) activated by an applied bias to the insulated gate is intriguing. As seen in Figure 1, IGBT shows an equivalent circuit structure containing two types of BJT, (NPN-type Bipolar transistor and PNP-type Bipolar transistor), which can be modeled as diode-associated transistor. Apparently, as a bias applies to the controlling gate, the channel beneath the gate oxide gets strongly inversed and turns out to be conductive just like what happens on metal-oxide-silicon field effect transistor (MOSFET), which provides necessary igniting currents to both BJTs and thus causes high current gain flowing through them-selves from the bottom. A proposed and renewed formula provides addressing the above scenario and successfully fitting the measured data that forms the characteristic curves. Some parameters in the proposed formula, which includes size and mobility associated constant, threshold voltage, and Early-Voltage-related lambda for MOSFET, explain and explore the underlying physics. IGBT thus enjoy high input impedance and high current gain due to MOSFET (Insulated Gate) and BJT, respectively. This formula combines both merits of MOSFET and BJT in order to fit the measured data. Indeed, the formula intimately fits IGBT electrical characteristic curves, and thus may be qualified and served as a model. The new model is then advisable for designing power integrated circuit to exactly achieve power saving, power control, and power efficiency.

Current-voltage characteristics curves of NFinFET are presented and are fitted with the modi-fied current-voltage (I-V) formulas, where the modified term in the triode region is demon-strated to be indispensable. In the as-known I-V formula, important parameters need determin-ing to make both the measured data and the fitting data as close as possible. Those parameters include kN (associated with the sizes of the transistor and mobility), (associated with Early Voltage), and Vth (the threshold voltage). The differences between the measured data and the fit-ting data vary as the applied source-drain bias, proving that the mobility of the carriers is not consistently constant. On the other hand, a modified formula, called kink effect factor, is nega-tively or positively added simulating solitary heat waves, which disturb the propagation of car-riers and thus influence the Source-Drain current (IDS). The new statistical standard deviations () are then found to be effectively suppressed as the kink effect is taken into account.