Hierarchical simulation of transport in silicon nanowire transistors (original) (raw)
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Three-dimensional simulation of one-dimensional transport in silicon nanowire transistors
IEEE Transactions on Nanotechnology, 2007
We present a simulation study of silicon nanowire transistors, based on an in-house code providing the self-consistent solution of Poisson, Schrödinger, and continuity equations on a generic three-dimensional domain. The main assumption, based on the very small nanowire cross section considered, is that an adiabatic approximation can be applied to the Schrödinger equation, so that transport occurs along one-dimensional subbands. Different subband transport models are considered, such as ballistic transport, either including quantum tunneling or not, and drift-diffusion. We show that nanowire transistors exhibit good control of short channel effects, and that barrier tunneling is significant in the strong inversion regime even for longer devices, while it is significant in subthreshold only for the shortest channel lengths. Finally, we show that a subband-based transport model allows to reach a very good trade off between physical accuracy of the simulation and computing time.
Simulation of one-dimensional subband transport in ultra-short silicon nanowire transistors
6th International Conference on the Ultimate Integration of Silicon, 2005
In this paper we present three-dimensional (3D) simulations of nanowire transistors (SNWTs), based on the self-consistent solution of the Poisson and Schrödinger equations, in which two dimensional confinement and one-dimensional (1D) transport of electrons in the channel have been considered. In particular, the continuity equation has been solved in 1D subbands for both the semiclassical and quantum ballistic regime, and in the drift-diffusion regime, in order to consider both limiting cases.
Physical Review B, 2009
An atomistic full-band quantum transport simulator has been developed to study three-dimensional Si nanowire field-effect transistors in the presence of electron-phonon scattering. The nonequilibrium Green's function ͑NEGF͒ formalism is solved in a nearest-neighbor sp 3 d 5 s ء tight-binding basis. The scattering selfenergies are derived in the self-consistent Born approximation to inelastically couple the full electron and phonon energy spectra. The band dispersion and the eigenmodes of the confined phonons are calculated using a dynamical matrix that includes the bond and the angle deformations of the nanowires. The optimization of the numerical algorithms and the parallelization of the NEGF scheme enable the investigation of nanowire structures with diameters up to 3 nm and lengths over 40 nm. It is found that the reduction in the device drain current, caused by electron-phonon scattering, is more important in the ON state than in the OFF state of the transistor. Ballistic transport simulations considerably overestimate the device ON currents by artificially increasing the charge injection mechanism at the source contact.
One-dimensional multi-subband Monte Carlo simulation of charge transport in Si nanowire transistors
2016 International Conference on Simulation of Semiconductor Processes and Devices (SISPAD), 2016
In this paper, we employ a newly-developed one-dimensional multi-subband Monte Carlo (1DMSMC) simulation module to study electron transport in nanowire structures. The 1DMSMC simulation module is integrated into the GSS TCAD simulator GARAND coupling a MC electron trajectory simulation with a 3D Poisson-2D Schrödinger solver, and accounting for the modified acoustic phonon, optical phonon, and surface roughness scattering mechanisms. We apply the simulator to investigate the effect of the overlap factor, scattering mechanisms, material and geometrical properties on the mobility in silicon nanowire field-effect transistors (NWTs). This paper emphasizes the importance of using 1D models that include correctly quantum confinement and allow for a reliable prediction of the performance of NWTs at the scaling limits. Our simulator is a valuable tool for providing optimal designs for ultra-scaled NWTs, in terms of performance and reliability.
IEEE Transactions on Electron Devices, 2000
An efficient approach for the simulation of electronic transport in nanoscale transistors is presented based on the multisubband Boltzmann transport equation under the relaxation time approximation, which takes into account the effects of quantum confinement and quasi-ballistic transport. This approach is applied to the study of electronic transport in circular gate-all-around silicon nanowire transistors. Comparison with the nonequilibrium Green's function method shows that the new method gives reasonably accurate terminal characteristics. We study the influence of silicon body diameter and gate length on the terminal current and subthreshold slope (SS). We have found that the calculated ON current is inversely proportional to the gate length to the power 1/2, and that the silicon body diameter should be smaller than roughly 2/3 of the channel length in order to maintain the SS within 80 mV/dec.
Atomistic Full-Band Simulations of Si Nanowire Transistors: Effects of Electron-Phonon Scattering
An atomistic full-band quantum transport simulator has been developed to study threedimensional Si nanowire field-effect transistors (FETs) in the presence of electron-phonon scattering. The Non-equilibrium Green’s Function (NEGF) formalism is solved in a nearest-neighbor sp3d5s∗ tight-binding basis. The scattering self-energies are derived in the self-consistent Born approximation to inelastically couple the full electron and phonon energy spectra. The band dispersion and the eigenmodes of the confined phonons are calculated using a dynamical matrix that includes the bond and the angle deformations of the nanowires. The optimization of the numerical algorithms and the parallelization of the NEGF scheme enable the investigation of nanowire structures with diameters up to 3 nm and lengths over 40 nm. It is found that the reduction of the device drain current, caused by electron-phonon scattering, is more important in the ON-state than in the OFF-state of the transistor. Ballistic transport simulations considerably overestimate the device ON-currents by artificially increasing the charge injection mechanism at the source contact. 1
Phys Rev B, 2011
A simulation framework that couples atomistic electronic structures to Boltzmann transport formalism is developed and applied to calculate the transport characteristics of thin silicon nanowires (NWs) up to 12 nm in diameter. The sp3d5s*-spin-orbit-coupled atomistic tight-binding model is used for the electronic structure calculation. Linearized Boltzmann transport theory is applied, including carrier scattering by phonons, surface roughness (SRS), and impurities. We present a comprehensive investigation of the low-field mobility in silicon NWs considering i) n- and p-type NWs, ii) [100], [110], and [111] transport orientations, and iii) diameters from D = 12 nm (electronically almost bulk-like) down to D = 3 nm (ultra-scaled). The simulation results display strong variations in the characteristics of the different NW types. For n-type NWs, phonon scattering and SRS become stronger as the diameter is reduced and drastically degrade the mobility by up to an order of magnitude depending on the orientation. For the [111] and [110] p-type NWs, on the other hand, large mobility enhancements (on the order of ˜4×) can be achieved as the diameter scales down to D = 3 nm. This enhancement originates from the increase in the subband curvatures as the diameter is scaled. It overcompensates for the mobility reduction caused by SRS in narrow NWs and offers an advantage with diameter scaling. Our results may provide understanding of recent experimental measurements, as well as guidance in the design of NW channel devices with improved transport properties.
IEEE Transactions on Electron Devices, 2000
We study electronic transport in silicon nanowire transistors at room temperature based on the self-consistent numerical solution of the multisubband Boltzmann transport equation and Poisson equation. The Schrödinger equation with nonparabolic corrections is solved in order to obtain the multisubband structure. Relevant microscopic scattering mechanisms due to acoustic and intervalley phonons, surface roughness, and ionized impurities are included in the simulation. A fluxconserving discretization scheme based on the uniform total energy grid is employed to avoid excessive numerical diffusion originating from the conventional kinetic-energy-based upwind scheme. We report an interesting kink behavior in the output characteristics and study the electron energy distribution inside the transistor as a function of bias conditions and scattering mechanisms.
IEEE Transactions on Electron Devices, 2008
We investigate the transport properties of siliconnanowire FETs by using two different approaches to the solution of the Boltzmann equation for the quasi-1-D electron gas, namely, the Monte Carlo method and a deterministic numerical solver. In both cases, we first solve the coupled Schrödinger-Poisson equations to extract the profiles of the 1-D subbands along the channel; next, the coupled multisubband Boltzmann equations are tackled with the two different procedures. A very good agreement is achieved between the two approaches to the transport problem in terms of mobility, drain-current, and internal physical quantities, such as carrier-distribution functions and average velocities. Some peculiar features of the low-field mobility as a function of the wire diameter and gate bias are discussed and justified based on the subband energy and wave-function behavior within the cylindrical geometry of the nanowire, as well as the heavy degeneracy of the electron gas at large gate biases.