Influence of band structure on electron ballistic transport in silicon (original) (raw)
Related papers
2006
This work investigates the conduction band structure of silicon nanowires, its dependence with the wire width and its influences on the electrical performances of Si nanowire-based MOSFET's working in the ballistic regime. The energy dispersions relations for Si nanowires have been calculated using a sp 3 tight-binding model and the ballistic response of n-channel devices with a 3D Poisson-Schrö dinger solver considering a mode-space approach and open boundary conditions (NEGF formalism). Results are compared with data obtained considering the parabolic bulk effective mass approximation, highlighting in this last case the overestimation of the I on current, up to 60% for the smallest (1.36 nm • 1.36 nm Si wire) devices.
Bandstructure effects in silicon nanowire electron transport
Electron Devices, IEEE …, 2008
Bandstructure effects in the electronic transport of strongly quantized silicon nanowire field-effect-transistors (FET) in various transport orientations are examined. A 10-band sp 3 d 5 s* semi-empirical atomistic tight-binding model coupled to a self consistent Poisson solver is used for the dispersion calculation. A semi-classical, ballistic FET model is used to evaluate the current-voltage characteristics. It is found that the total gate capacitance is degraded from the oxide capacitance value by 30% for wires in all the considered transport orientations ([100], [110], [111]). Different wire directions primarily influence the carrier velocities, which mainly determine the relative performance differences, while the total charge difference is weakly affected. The velocities depend on the effective mass and degeneracy of the dispersions. The [110] and secondly the [100] oriented 3nm thick nanowires examined, indicate the best ON-current performance compared to [111] wires. The dispersion features are strong functions of quantization. Effects such as valley splitting can lift the degeneracies especially for wires with cross section sides below 3nm. The effective masses also change significantly with quantization, and change differently for different transport orientations. For the cases of [100] and [111] wires the masses increase with quantization, however, in the [110] case, the mass decreases. The mass variations can be explained from the non-parabolicities and anisotropies that reside in the first Brillouin zone of silicon. Index terms -nanowire, bandstructure, tight binding, transistors, MOSFETs, nonparabolicity, effective mass, injection velocity, quantum capacitance, anisotropy. carrier velocities, closely followed by the [100] devices with a little higher masses. [111]
Journal of Applied …, 2010
A 20 band sp 3 d 5 s* spin-orbit-coupled, semi-empirical, atomistic tight-binding (TB) model is used with a semi-classical, ballistic, field-effect-transistor (FET) model, to theoretically examine the bandstructure carrier velocity and ballistic current in silicon nanowire (NW) transistors. Infinitely long, uniform, cylindrical and rectangular NWs, of cross sectional diameters/sides ranging from 3nm to 12nm are considered. For a comprehensive analysis, n-type and p-type metal-oxide-semiconductor (NMOS and PMOS) NWs in [100], [110] and [111] transport orientations are examined. In general, physical cross section reduction increases velocities, either by lifting the heavy mass valleys, or significantly changing the curvature of the bands. The carrier velocities of PMOS [110] and [111] NWs are a strong function of diameter, with the narrower D=3nm wires having twice the velocities of the D=12nm NWs. The velocity in the rest of the NW categories shows only minor diameter dependence. This behavior is explained through features in the electronic structure of the silicon host material. The ballistic current, on the other hand, shows the least sensitivity with cross section in the cases where the velocity has large variations. Since the carrier velocity is a measure of the effective mass and reflects on the channel mobility, these results can provide insight into the design of NW devices with enhanced performance and performance tolerant to structure geometry variations. In the case of ballistic transport in high performance devices, the [110] NWs are the ones with both high NMOS and PMOS performance, as well as low on-current variations with cross section geometry variations.
Applied Physics …, 2005
In this letter, we explore the bandstructure effects on the performance of ballistic silicon nanowire transistors (SNWTs). The energy dispersion relations for silicon nanowires are evaluated with an sp 3 d 5 s * tight binding model. Based on the calculated dispersion relations, the ballistic currents for both n-type and p-type SNWTs are evaluated by using a semi-numerical ballistic model. For large diameter nanowires, we find that the ballistic p-SNWT delivers half the ON-current of a ballistic n-SNWT. For small diameters, however, the ON-current of the p-type SNWT approaches that of its n-type counterpart. Finally, the carrier injection velocity for SNWTs is compared with those for planar metal-oxide-semiconductor field-effect transistors, clearly demonstrating the impact of quantum confinement on the performance limits of SNWTs. PACS numbers: 85.35.Be and 73.63.Nm
Bandstructure and mobility variations in p-type silicon nanowires under electrostatic gate field
Solid-State Electronics, 2013
The sp 3 d 5 s * -spin-orbit-coupled atomistic tight-binding (TB) model is used for the electronic structure calculation of Si nanowires (NWs), self consistently coupled to a 2D Poisson equation, solved in the cross section of the NW. Upon convergence, the linearized Boltzmann transport theory is employed for the mobility calculation, including carrier scattering by phonons and surface roughness. As the channel is driven into inversion, for [111] and [110] NW devices of diameters D>10nm the curvature of the bandstructure increases and the hole effective mass becomes lighter, resulting in a ~50% mobility increase. Such improvement is large enough to compensate for the detrimental effect of surface roughness scattering. The effect is very similar to the bandstructure variations and mobility improvement observed under geometric confinement, however, in this case confinement is caused by electrostatic gating. We provide explanations for this behavior based on features of the heavy-hole band. This effect could be exploited in the design of p-type NW devices. We note, finally, that the "apparent" mobility of low dimensional short channel transistors is always lower than the intrinsic channel diffusive mobility due to the detrimental influence of the so called "ballistic" mobility.
A comprehensive atomistic analysis of bandstructure velocities in Si nanowires
2010
Abstract A 20 band sp 3 d 5 s* spin-orbit-coupled, semi-empirical, atomistic tight-binding (TB) model is used with a semi-classical, ballistic transport model, to theoretically examine the bandstructure carrier velocity under non-degenerate conditions in silicon nanowire (NW) transistors. Infinitely long, uniform, cylindrical and rectangular NWs, of cross sectional diameters/sides ranging from 3nm to 12nm are considered. For a comprehensive analysis, n-type and p-type NWs in [100],[110] and [111] transport orientations are examined.
Band-Structure Effects in Ultrascaled Silicon Nanowires
IEEE Transactions on Electron Devices, 2007
In this paper, we investigate band-structure effects on the transport properties of ultrascaled silicon nanowire FETs operating under quantum-ballistic conditions. More specifically, we expand the dispersion relationship ε(k) in a power series up to the third order in k 2 and generate the corresponding higher order operator to be used within the single-electron Hamiltonian for the solution of the Schrödinger equation. We work out a hierarchy of nonparabolic models accounting for the following: 1) the shift of the subband edges and the change in the transport effective masses; 2) the higher order Hamiltonian operator; and 3) the splitting of the fourfold unprimed subbands in nanometer-size FETs. We then compute the device turn-ON characteristics, the threshold shift versus diameter, and the subthreshold slope (SS) versus gate length. By compensating for the different threshold voltages, i.e., by reducing the turn-ON characteristics to the same leakage current at zero gate bias, it turns out that the current discrepancies between the most general model and the bulk-parabolic model are contained within 20%. Finally, it turns out that the nonparabolic band structure gives an improved SS at the lowest gate lengths due to a reduced source-drain tunneling, reaching up to 30% enhancement.
Full band calculations of low-field mobility in p-type silicon nanowire MOSFETs
2013 International Conference on Simulation of Semiconductor Processes and Devices (SISPAD), 2013
: Simulation procedure. (a) The NW bandstructure is calculated using the sp 3 d 5 s * TB model. (b) A semiclassical ballistic model is used to calculate the charge distribution in the gated NW. (c) The charge is selfconsistently coupled to a 2D Poisson equation for the electrostatic potential in the cross section of the wire. The oxide is assumed to be SiO2 of thickness tox=1.2nm (d) Upon convergence (and at VD=0V), Boltzmann transport theory, including all relevant scattering mechanisms, is used for mobility calculations.
Solid-State Electronics, 2013
In this paper, we address a physics based closed form model for the energy band gap (E g) and the transport electron effective mass in relaxed and strained [1 0 0] and [1 1 0] oriented rectangular Silicon Nanowire (SiNW). Our proposed analytical model along [1 0 0] and [1 1 0] directions are based on the k.p formalism of the conduction band energy dispersion relation through an appropriate rotation of the Hamiltonian of the electrons in the bulk crystal along [0 0 1] direction followed by the inclusion of a 4 Â 4 Lüttinger Hamiltonian for the description of the valance band structure. Using this, we demonstrate the variation in E g and the transport electron effective mass as function of the cross-sectional dimensions in a relaxed [1 0 0] and [1 1 0] oriented SiNW. The behaviour of these two parameters in [1 0 0] oriented SiNW has further been studied with the inclusion of a uniaxial strain along the transport direction and a biaxial strain, which is assumed to be decomposed from a hydrostatic deformation along [0 0 1] with the former one. In addition, the energy band gap and the effective mass of a strained [1 1 0] oriented SiNW has also been formulated. Using this, we compare our analytical model with that of the extracted data using the nearest neighbour empirical tight binding sp 3 d 5 s ⁄ method based simulations and has been found to agree well over a wide range of device dimensions and applied strain.
Bandstructure effects in silicon nanowire hole transport
… , IEEE Transactions on, 2008
Bandstructure effects in PMOS transport of strongly quantized silicon nanowire field-effect-transistors (FET) in various transport orientations are examined. A 20-band sp 3 d 5 s* spin-orbit-coupled (SO) atomistic tight-binding model coupled to a self consistent Poisson solver is used for the valence band dispersion calculation. A ballistic FET model is used to evaluate the capacitance and current-voltage characteristics. The dispersion shapes and curvatures are strong functions of device size, lattice orientation, and bias, and cannot be described within the effective mass approximation. The anisotropy of the confinement mass in the different quantization directions can cause the charge to preferably accumulate in the (110) and secondly on the (112) rather than (100) surfaces, leading to significant charge distributions for different wire orientations. The total gate capacitance of the nanowire FET devices is, however, very similar for all wires in all the transport orientations investigated ([100], [110], [111]), and is degraded from the oxide capacitance by ~30%. The [111] and secondly the [110] oriented nanowires indicate highest carrier velocities and better ON-current performance compared to [100] wires.