We address a linearized KdV equation on metric star graphs with one incoming finite bond and two outgoing semi-infinite bonds. Using the theory of potentials, we reduce the problem to systems of linear integral equations and show that they are uniquely solvable under conditions of the uniqueness theorem.

In this work we study the self-heating effect (SHE) in nanoscale Silicon on Insulator Junctionless (SOI JL) FinFET transistor with fin cross section in rectangular, trapeze and triangle form. The lattice temperature dependence on the channel length as well as on buried oxide thickness is considered. It is shown that for considered transistor structure the lattice temperature in the middle of the channel is lower than at lateral sides, near source and drain. Also, we have found at the same conditions the lattice temperature depends on shape of channel cross section too.

The dependence of random telegraph noise (RTN) amplitude on the gate overdrive in a junctionless field-effect transistor (FinFET) with rectangular and trapezoidal channel (fin) cross sections manufactured using silicon-on-insulator technology has been numerically simulated. It is established that the RTN amplitude in the subthreshold region of gate voltages for a FinFET with a trapezoidal cross section of channel is significantly lower than that for the transistor with rectangular cross section of a channel. In addition, under the same conditions, the RTN amplitude at the threshold gate voltage in a junctionless FinFET is significantly lower than that in planar fully depleted and in usual FinFET.

The self-heating effect is simulated in a nanoscale junctionless fin field-effect transistor fabricated on the basis of silicon-on-insulator structures with a transistor base cross section of a rectangular, trapezoidal, or triangular shape. It is shown that, for the structures under consideration, the temperature in the middle of the transistor is lower than along its lateral edges near the source and drain.