Field-effect transistor structures with a quasi–1D channel

A theory of drift–diffusion transport in a low–dimensional field effect transistor is developed. Two cases of a semiconductor nanowire and a single–wall nanotube are considered using self-consistent electrostatics to obtain a general expression for transconductance. This quantum wire channel device description is shown to differ from classical device theory because of the specific nanowire charge density distribution. In the present work we consider carrier distributions and parameters of a field effect transistor (FET) with a quantum wire channel, which may be a semiconductor nanowire or a carbon nanotube. The structure includes source and drain electrodes connected by a nanowire/nanotube −L/2 < x < L/2, and a gate electrode separated by a thin dielectric layer of the thickness d. We assume the wire to be uniformly doped with 1D density N = const(x). When the structure is in operation, the source-drain voltage Vd causes a current j along the channel and a re-distribution of carrier concentration as compared with the initial specific density. A voltage Vg is applied to the gate and changes the concentration, which controls the FET transport. All potentials are measured from the middle point of the wire (x = 0) so that the source and drain potentials are −Vd/2 andVd/2. In this case the potentials along the wire and concentration changes caused by Vg together with the contact potentials, and byVd are, respectively, symmetric and antisymmetric functions of x and are given the subscripts s and a: φs,a(x) and ns,a(x). The potentials φs,a(x) can be divided into two parts: the components φ0 s,a(x) created by electrodes and contact potentials, which should be found from the Laplace equation containing no channel charge density and the components φ1 s,a(x) caused by the electron charge in the channel −ens,a(x). We assume that the characteristic lengths L and d determining the potential and density distribution along the channel, noticeably exceed the nanowire/nanotube radius a. In this case the relationship between φ1 s,a(x) and ns,a(x) is approximately linear [1–4] and for a nanowire with non-degenerate carriers, the current j can be written as: