Modeling of electron mobility in gated silicon nanowires at room temperature: Surface roughness scattering, dielectric screening, and band nonparabolicity

Abstract

We present a theoretical study of electron mobility in cylindrical gated silicon nanowires at 300 K based on the Kubo-Greenwood formula and the self-consistent solution of the Schrödinger and Poisson equations. A rigorous surface roughness scattering model is derived, which takes into account the roughness-induced fluctuation of the subband wave function, of the electron charge, and of the interface polarization charge. Dielectric screening of the scattering potential is modeled within the random phase approximation, wherein a generalized dielectric function for a multi-subband quasi-one-dimensional electron gas system is derived accounting for the presence of the gate electrode and the mismatch of the dielectric constant between the semiconductor and gate insulator. A nonparabolic correction method is also presented, which is applied to the calculation of the density of states, the matrix element of the scattering potential, and the generalized Lindhard function. The Coulomb scattering due to the fixed interface charge and the intra- and intervalley phonon scattering are included in the mobility calculation in addition to the surface roughness scattering. Using these models, we study the low-field electron mobility and its dependence on the silicon body diameter, effective field, dielectric constant, and gate insulator thickness.

Bandstructure and mobility variations in p-type silicon nanowires under electrostatic gate field

“…There we employ the linearized Boltzmann formalism in NWs with flat electrostatic potential in the cross section, and consider the band edge shift as the dominant influence of the SRS. That 7 mechanism is the dominant for ultra-narrow NWs, of diameters D<8nm, and is responsible for the µ~D 6 mobility behavior observed in ultra thin-layers and NWs is [14,45]. For the diameters of interest in this new work, i.e.…”

“…In those works the electronic structure was calculated using approaches varying from continuum effective mass descriptions [13,14], to k·p [15,16,17] and atomistic tight-binding (TB) [11,12,18,19,20,21,22], or even DFT [23]. Transport methodologies from semiclassical to fully quantum mechanical were also utilized.…”

Charged impurity scattering and mobility in gated silicon nanowires

“…This work showed, in particular, that minority carriers are blocked by the impurities, but did not consider screening by the environment or free carriers, which is known to be essential from bulk 28,29 , to nanowires. 22 There is, therefore, a clear need for a better assessment of the effects of impurities in nanowires with more realistic potentials.…”

“…In this case the impurity potential is efficiently screened by the gate, the binding energy remains close to its bulk value, and most of the donor impurities are ionized at room temperature (acceptors being usually charged negatively in the inversion regime). 30,31 Only a few theoretical works have addressed the effect of charged impurities on the transport in gated SiNWs, with either the (perturbative) Kubo-Greenwood formula 22 or a (non-perturbative) Green function approach, [23][24][25][26] but using the effective mass approximation for the electronic structure. Our objective is to go beyond these approximations and to perform a systematic study as function of the type of impurity (donor or acceptor), its radial position in the wire, the diameter of the SiNWs and the nature of the oxide.…”

“…Recent theoretical works have therefore addressed the scattering of free carriers by phonons, 13,14 and by bulk and surface disorder in SiNWs. [15][16][17] The scattering by dopants has also been studied with either density functional theory (DFT) [18][19][20][21] or the semi-empirical effective mass [22][23][24][25][26] approximation. Most DFT calculations reported so far [18][19][20] have, however, considered neutral dopants.…”