Stochastic analysis of surface roughness models in quantum wires

Abstract

We present a signed particle computational approach for the Wigner transport model and use it to analyze the electron state dynamics in quantum wires focusing on the effect of surface roughness. Usually surface roughness is considered as a scattering model, accounted for by the Fermi Golden Rule, which relies on approximations like statistical averaging and in the case of quantum wires incorporates quantum corrections based on the mode space approach. We provide a novel computational approach to enable physical analysis of these assumptions in terms of phase space and particles. Utilized is the signed particles model of Wigner evolution, which, besides providing a full quantum description of the electron dynamics, enables intuitive insights into the processes of tunneling, which govern the physical evolution. It is shown that the basic assumptions of the quantum-corrected scattering model correspond to the quantum behavior of the electron system. Of particular importance is the distribution of the density: Due to the quantum confinement, electrons are kept away from the walls, which

Simulation of the Impact of Ionized Impurity Scattering on the Total Mobility in Si Nanowire Transistors

“…In the first step, we use the coupled 3D Poisson–2D Schrödinger solver in GARAND to evaluate the electric potential and field distributions at the cross section area of a gated (long channel) NWT, and to calculate the electron densities and the details of the electronic subbands (eigenfunctions and eigenvalues) in the NWT cross section normal to the transport direction. In the second step, we utilize the potential distribution, and the corresponding eigenfunctions (and relevant subband details) to calculate the 1D transition rates for the dominant scattering mechanisms in silicon, including the modified acoustic phonon, optical phonon, ionized impurity [18] and surface roughness scattering [20]. In the final step, we use the set of multi-subband scattering mechanism rates to calculate the scattering-limited mobilities of interesting NWT structures, by adopting the KG formalism solving for the (semi-classical) BTE within the relaxation time approximation [10,11].…”

“…Surface roughness scattering is most pronounced when confinement keeps electrons close to non-ideal interfaces. The extent of the interaction with surface imperfections is dependent on the force normal to the interface, and the statistical description of the interface roughness [20]. Assuming x is the direction of transport along the nanowire, the perturbation Hamiltonian can be written as:H′=eEy(s,x)Δy(x)+eEz(s,x)Δz(x), where Δ(y) and Δ(z) are the corresponding deviations of the silicon nanowire surface from the ideal surface, and boldEy and boldEz are the electric field components in the cross section normal to the direction of transport.…”

Nanowire FETs

“…For surface roughness scattering, we assume that the root mean square (RMS) roughness and correlation length are 0.48 and 1.3nm, respectively. The assumptions of the SR scattering model have been recently verified in [14]. A constant effective ionized impurity concentration n0 = 10 18 cm -3 has been considered.…”

Wigner Ensemble Monte Carlo Simulation Without Discretization Error of a GaAs Resonant Tunneling Diode

“…We have to wait until the beginning of 2000, to have particle Monte Carlo (MC) solvers for the Wigner equation [21,15]. From that period up to now, several papers have been published on this subject (see [23] for a review) and, recently, very interesting device simulations have been provided [3,14,17].…”