Analytical Compact Model of Ballistic Cylindrical Nanowire Metal–Oxide–Semiconductor Field-Effect Transistor

Abstract

We propose a compact model of drain current in the ballistic mode in a cylindrical gate-all-around metal–oxide–semiconductor field-effect transistor (MOSFET). Wave functions of electrons in a channel are represented by a linear combination of wave functions in a cylindrical infinite quantum well. With these wave functions, the energy levels of electrons in a channel are analytically derived by approximately solving the Schrödinger equation. Drain current is obtained using a coupled equation of electron energy levels and a current equation for ballistic transport. Electron energy levels are compared with numerical simulation results. The electron energy levels obtained using our compact model demonstrate excellent agreement with numerical simulation results. With our compact model, surface potential, potential shape in the confinement plane, total charge density, electron energy level, and drain current are calculated self-consistently with only two fitting parameters and one transcendental equation.

Simplified calculation method of electron subband profile in ballistic nanowire MOSFET

“…These parameters are treated as the fitting parameters as shown in [10]. We assume that electric fields in the oxide are uniform along the direction perpendicular to z-axis in Fig.…”

“…From (3) and (4), the surface potential is written in terms of ∆U G and ∆U SD (z). The Schrödinger equation in the wire cross section with (1) is solved analytically to derive the subband profiles E ν nx,ny , where n x and n y (= 0, 1, 2...) are quantum numbers in the x-and y-directions, respectively, and ν represents the specific valley of the energy band structure of the channel material [10]. Electron wave functions in the xy-plane are decomposed into the two components along the x-and y-axes, respectively.…”

“…The wave functions in each axis are expanded by those in the infinite square well potential. The Schrödinger equation with (1) can then be solved by considering only main terms of the expansion to obtain an analytic expression for E ν nx,ny as a function of ∆U G and ∆U SD (z) [10]. Assuming the top value of each subband profiles, E ν nx,ny,top , is taken at z max , charge density per unit length at z max , Q q , is derived from the Fermi-Dirac distribution F (E F , E Total ) and the onedimensional density of states D(E z ) with the above subband profiles:…”

“…As ∆U G is determined by the long channel condition [10], we can determine the ∆U SD (z) from (8), and E ν nx,ny are calculated with the obtained ∆U G and ∆U SD (z). This method requires the subband values at the source and drain edges for the lowest subband profile under each gate and drain bias condition as boundary conditions.…”

ANALYTIC COMPACT MODEL of BALLISTIC and QUASI-BALLISTIC CYLINDRICAL GATE-ALL-AROUND MOSFET INCLUDING TWO SUBBANDS

“…Until now, some fully analytic compact models have been reported, but only the lowest subband is considered [1,2,3] . More than one subband must be considered to maintain good accuracy, when wire radius becomes larger than 1.5nm [4] . In this work, we propose a compact model incorporating two subbands for the first time, which provides one analytic formula of drain current for all operating regions.…”