Design space for low sensitivity to size variations in [110] PMOS nanowire devices: The implications of anisotropy in the quantization mass

A 20-band sp3d5s* spin-orbit-coupled, semi-empirical, atomistic tight-binding model is used with a semi-classical, ballistic, field-effect-transistor (FET) model, to examine the ON-current variations to size variations of [110] oriented PMOS nanowire devices. Infinitely long, uniform, rectangular nanowires of side dimensions from 3nm to 12nm are examined and significantly different behavior in width vs. height variations are identified and explained. Design regions are identified, which show minor ON-current variations to significant width variations that might occur due to lack of line width control. Regions which show large ON-current variations to small height variations are also identified. The considerations of the full band model here show that ON-current doubling can be observed in the ON-state at the onset of volume inversion to surface inversion transport caused by structural side size variations. Strain engineering can smooth out or tune such sensitivities to size variations. The cause of variations described is the structural quantization behavior of the nanowires, which provide an additional variation mechanism to any other ON-current variations such as surface roughness, phonon scattering etc.Comment: 24 pages, 5 figure

On the interplay between electrical conductivity and Seebeck coefficient in ultra-narrow silicon nanowires

We analyze the effect of low dimensionality on the electrical conductivity ({\sigma}) and Seebeck coefficient (S) in ultra-narrow Si nanowires (NWs) by employing atomistic considerations for the electronic structures and linearized Boltzmann transport theory. We show that changes in the geometrical features of the NWs such as diameter and orientation, mostly affect {\sigma} and S in two ways: i) the distance of the band edges from the Fermi level ({\eta}F) changes, and ii) quantum confinement in some cases strongly affect the effective mass of the subbands, which influences the conductivity of the NWs and {\eta}F. Changes in eta_F cause exponential changes in {\sigma}, but linear changes in S. S seems to be only weakly dependent on the curvature of the bands, the strength of the scattering mechanisms, and the shape of the DOS(E) function, contrary to current view. Our results indicate that low dimensionality has a stronger influence on {\sigma} than on S due to the stronger sensitivity of {\sigma} on {\eta}F. We identify cases where bandstructure engineering through confinement can improve {\sigma} without significantly affecting S, which can result in power factor improvements.Comment: 19 pages, 5 figure

Band alignment and scattering considerations for enhancing the thermoelectric power factor of complex materials: The case of Co-based half-Heuslers

Half-Heuslers, an emerging thermoelectric material group, has complex bandstructures with multiple bands that can be aligned through band engineering approaches, giving us an opportunity to improve their power factor. In this work, going beyond the constant relaxation time approximation, we perform an investigation of the benefits of band alignment in improving the thermoelectric power factor under different density of states dependent scattering scenarios. As a test case we consider the Co-based p-type half-Heuslers TiCoSb, NbCoSn and ZrCoSb. First, using simplified effective mass models combined with Boltzmann transport, we investigate the conditions of band alignment that are beneficial to the thermoelectric power factor under three different carrier scattering scenarios: i) the usual constant relaxation time approximation, ii) intra-band scattering restricted to the current valley with the scattering rates proportional to the density of states as dictated by Fermi's Golden Rule, and iii) both intra- and inter-band scattering across all available valleys, with the rates determined by the total density of states at the relevant energies. We demonstrate that the band-alignment outcome differs significantly depending on the scattering details. Next, using the density functional theory calculated bandstructures of the half-Heuslers we study their power factor behavior under strain induced band alignment. We show that strain can improve the power factor of half-Heuslers, but the outcome heavily depends on the curvatures of the bands involved, the specifics of the carrier scattering mechanisms, and the initial band separation. Importantly, we also demonstrate that band alignment is not always beneficial to the power factor.Comment: 18 pages, 15 figure

Prospects of low-dimensional and nanostructured silicon-based thermoelectric materials : findings from theory and simulation

Silicon based low-dimensional materials receive significant attention as new generation thermoelectric materials after they have demonstrated record low thermal conductivities. Very few works to-date, however, report significant advances with regards to the power factor. In this review we examine possibilities of power factor enhancement in: (i) low-dimensional Si channels and (ii) nanocrystalline Si materials. For low-dimensional channels we use atomistic simulations and consider ultra-narrow Si nanowires and ultra-thin Si layers of feature sizes below 15 nm. Room temperature is exclusively considered. We show that, in general, low-dimensionality does not offer possibilities for power factor improvement, because although the Seebeck coefficient could slightly increase, the conductivity inevitably degrades at a much larger extend. The power factor in these channels, however, can be optimized by proper choice of geometrical parameters such as the transport orientation, confinement orientation, and confinement length scale. Our simulations show that in the case where room temperature thermal conductivities as low as κ l = 2 W/mK are achieved, the ZT figure of merit of an optimized Si low-dimensional channel could reach values around unity. For the second case of materials, we show that by making effective use of energy filtering, and taking advantage of the inhomogeneity within the nanocrystalline geometry, the underlying potential profile and dopant distribution large improvements in the thermoelectric power factor can be achieved. The paper is intended to be a review of the main findings with regards to the thermoelectric performance of nanoscale Si through our simulation work as well as through recent experimental observations

Atomistic simulations of low-field mobility in Si nanowires: Influence of confinement and orientation

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 12nm in diameter. The sp3d5s*-spin-orbit-coupled atomistic tight-binding (TB) 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=12nm (electronically almost bulk-like) down to D=3nm (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 (of the order of ~4X) can be achieved as the diameter scales down to D=3nm. 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.Comment: 45 pages, 8 figure

Doping optimization for the power factor of bipolar thermoelectric materials

Bipolar carrier transport is often a limiting factor in the thermoelectric efficiency of narrow bandgap materials at high temperatures due to the reduction in the Seebeck coefficient and the introduction of an additional term to the thermal conductivity. Using the Boltzmann transport formalism and a two-band model, we simulate transport through bipolar systems and calculate their thermoelectric transport properties: the electrical conductivity, the Seebeck coefficient and the thermoelectric power factor. We present an investigation into the doping optimisation of such materials, showing the detrimental impact that rising temperatures have if the doping (and the Fermi level) is not optimised for each operating temperature. We also show that the doping levels for optimized power factors at a given operating temperature differ in bipolar systems compared to unipolar ones. We show finally that at 600 K, in a bipolar material with bandgap approximately that of Bi2Te3, the optimal doping required can reside between 10% and 30% larger than that required for an optimal unipolar material depending on the electronic scattering details of the material

On the channel width-dependence of the thermal conductivity in ultra-narrow graphene nanoribbons

The thermal conductivity of low-dimensional materials and graphene nanoribbons, in particular, is limited by the strength of line-edge-roughness scattering. One way to characterize the roughness strength is the dependency of the thermal conductivity on the channel's width in the form Wβ. Although in the case of electronic transport, this dependency is very well studied, resulting in W 6 for nanowires and quantum wells and W 4 for nanoribbons, in the case of phonon transport it is not yet clear what this dependence is. In this work, using lattice dynamics and Non-Equilibrium Green's Function simulations, we examine the width dependence of the thermal conductivity of ultra-narrow graphene nanoribbons under the influence of line edge-roughness. We show that the exponent β is in fact not a single well-defined number, but it is different for different parts of the phonon spectrum depending on whether phonon transport is ballistic, diffusive, or localized. The exponent β takes values β < 1 for semi-ballistic phonon transport, values β ≫ 1 for sub-diffusive or localized phonons, and β = 1 only in the case where the transport is diffusive. The overall Wβ dependence of the thermal conductivity is determined by the width-dependence of the dominant phonon modes (usually the acoustic ones). We show that due to the long phonon mean-free-paths, the width-dependence of thermal conductivity becomes a channel length dependent property, because the channel length determines whether transport is ballistic, diffusive, or localized

Analysis of Thermoelectric Properties of Scaled Silicon Nanowires Using an Atomistic Tight-Binding Model

Low dimensional materials provide the possibility of improved thermoelectric performance due to the additional length scale degree of freedom for engineering their electronic and thermal properties. As a result of suppressed phonon conduction, large improvements on the thermoelectric figure of merit, ZT, have been recently reported in nanostructures, compared to the raw materials' ZT values. In addition, low dimensionality can improve a device's power factor, offering an additional enhancement in ZT. In this work the atomistic sp3d5s*-spin-orbit-coupled tight-binding model is used to calculate the electronic structure of silicon nanowires (NWs). The Landauer formalism is applied to calculate an upper limit for the electrical conductivity, the Seebeck coefficient, and the power factor. We examine n-type and p-type nanowires of diameters from 3nm to 12nm, in [100], [110], and [111] transport orientations at different doping concentrations. Using experimental values for the lattice thermal conductivity in nanowires, an upper limit for ZT is computed. We find that at room temperature, scaling the diameter below 7nm can at most double the power factor and enhance ZT. In some cases, however, scaling does not enhance the performance at all. Orientations, geometries, and subband engineering techniques for optimized designs are discussed.Comment: 19 pages, 4 figure

Monte Carlo simulations for phonon transport in silicon nanomaterials

In nanostructures phonon transport behaviour is distinctly different to transport in bulk materials such that materials with ultra low thermal conductivities and enhanced thermoelectric performance can be realized. Low thermal conductivities have been achieved in nanocrystalline materials that include hierarchical sizes of inclusions and pores. Nanoporous structures present a promising set of material properties and structures which allow for ultra-low thermal conductivity, even below the amorphous limit. In this paper we outline a semiclassical Monte Carlo code for the study of phonon transport and present an investigation of the thermal conductivity in nanoporous and nanocrystalline silicon. Different disordered geometry configurations are incorporated to investigate the effects of pores and grain boundaries on the phonon flux and the thermal conductivity, including the effects of boundary roughness, pore position and pore diameter. At constant porosity, thermal conductivity reduction is maximized by having a large number of smaller diameter pores as compared to a small number of larger diameter pores. Furthermore, we show that porosity has a greater impact on thermal conductivity than the degree of boundary roughness. Our simulator is validated across multiple simulation and experimental works for both pristine silicon channels and nanoporous structures.Comment: 10 pages, 8 figure