A numerical approach to quasi-ballistic transport and plasma oscillations in junctionless nanowire transistors

Abstract

A numerical framework for DC and RF small-signal simulations of nanowire transistors is presented, which is based on the self-consistent solution of the Poisson, Schrödinger, and Boltzmann transport equations and is stable for the entire range from weak to strong particle scattering. The proposed approach does not suffer from the deficiencies due to the transformation of the Boltzmann transport equation into the energy space and can handle the quasi-ballistic case. This is a key requirement for the investigation of plasma resonances and other high-mobility phenomena. The in-house solver is validated with results of a previously developed simulator based on the H-transformation for a conventional N + NN + silicon transistor with strong scattering. Then, its results are compared with those of moments-based models and it is shown that these do not provide a satisfactory description of the electron dynamics in the quasi-ballistic transport regime. Furthermore, the internal boundary conditions of the transport models at the contacts are found to have a significant impact on plasma resonances and the physics-based thermal-bath boundary condition strongly suppresses them.

Numerical aspects of a Godunov-type stabilization scheme for the Boltzmann transport equation

“…In the case of a nanowire MOSFET, we solve the PE, SE and BE self-consistently as explained in Refs. [12,20]. The quasi-stationary SE yields the subband structure with the total energy tot (z, k) of the th subband and the wave function Ψ (x, y;z, k) for a cross section of the wire at position z in real space and wave number k. The cross section is parallel to the x, y-plane.…”

“…In order to apply Godunov's stabilization scheme to the BE the drift operator is moved into the interface between two adjacent cells by assuming that the subband structure is constant within a cell and changes abruptly between cells (Fig. 2) [20,22,30,31]. Within a finite volume in real space, the force is now zero and i = 1, … , N z .…”

“…With the Bose-Einstein distribution (20), this equality can be shown to hold, because the energy transfer of the scattering processes was aligned with the energy grid (h = m ) , and the principle of detailed balance also holds in the discrete case.…”

“…This degrades the stability. However, by choosing a different set of functions that are nonnegative themselves for projection, this problem can be avoided [12,13,[16][17][18][19][20]. Such functions are directly defined in the phase space and are piecewise constant with a value of either zero or one.…”

Nano Device Simulator—A Practical Subband-BTE Solver for Path-Finding and DTCO

“…This approach is comparably straightforward in its implementation and enables the use of perturbative methods, such as smallsignal ac-analysis, on the SBTE. However, its major drawback is the artificial carrier heating (ACH) phenomenon, arising due to numerical diffusion in phase-space [10], which broadens the distribution function on the source side causing an increase in subthreshold-slope as if the device was heated.…”