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Black phosphorus has been revisited recently as a new two-dimensional material showing potential applications in electronics and optoelectronics. Here we report the anisotropic in-plane thermal conductivity of suspended few-layer black phosphorus measured by micro-Raman spectroscopy. The armchair and zigzag thermal conductivities are ~20 and ~40 W m$^{-1}$ K$^{-1}$ for black phosphorus films thicker than 15 nm, respectively, and decrease to ~10 and ~20 W m$^{-1}$ K$^{-1}$ as the film thickness is reduced, exhibiting significant anisotropy. The thermal conductivity anisotropic ratio is found to be ~2 for thick black phosphorus films and drops to ~1.5 for the thinnest 9.5-nm-thick film. Theoretical modeling reveals that the observed anisotropy is primarily related to the anisotropic phonon dispersion, whereas the intrinsic phonon scattering rates are found to be similar along the armchair and zigzag directions. Surface scattering in the black phosphorus films is shown to strongly suppress the contribution of long-mean-free-path acoustic phonons., Comment: Accepted by Nature Communications

A formalism for incorporating electron-phonon scattering into the nonequilibrium Green's function (NEGF) framework that is applicable to planar MOSFETs is presented. Restructuring the NEGF equations in terms of approximate summation of transverse momentum modes leads to a rigorous and efficient method of solution. This helps to drastically reduce the computational complexity, allowing treatment of both quantum mechanics and dissipative electron-phonon scattering processes for device sizes from nanometers to microns. The formalism is systematically benchmarked against Monte Carlo solutions of the classical Boltzmann transport for model potential profiles. Results show a remarkably close agreement between the two methods for variety of channel lengths and bias conditions, both for elastic and inelastic scattering processes., Comment: 30 pages, 10 figures

A numerical simulation of spin-dependent quantum transport for a spin field effect transistor (spinFET) is implemented in a widely used simulator nanoMOS. This method includes the effect of both spin relaxation in the channel and the tunneling barrier between the source/drain and the channel. Account for these factors permits setting more realistic performance limits for the transistor, especially the magnetoresistance, which is found to be lower compared to earlier predictions. The interplay between tunneling and spin relaxation is elucidated by numerical simulation. Insertion of the tunneling barrier leads to an increased magnetoresistance. Numerical simulations are used to explore the tunneling barrier design issues., Comment: 31 pages, 14 figures, submitted to Journal of Applied Physics

The band-to-band tunneling transistors have some performance advantages over the conventional MOSFETs due to the <60mV/dec sub-threshold slope. In this paper, carbon nanotubes are used as a model channel material to address issues that we believe will apply to BTBT FETs vs. MOSFETs more generally. We use pz-orbital tight-binding Hamiltonian and the non-equilibrium Green function (NEGF) formalism for rigorous treatment of dissipative quantum transport. A device level comparison of p-i-n TFETs and n-i-n MOSFETs in both ballistic and dissipative cases has been performed previously. In this paper, the possibility of using p-i-n TFETs in ultra-low power sub-threshold logic circuits is investigated using a rigorous numerical simulator. The results show that, in sub-threshold circuit operation, the p-i-n TFETs have better DC characteristics, and can deliver ~15x higher performance at the iso-P_LEAKAGE, iso-VDD conditions. Because p-i-n TFETs can operate at lower VDD than n-i-n MOSFETs, they can deliver ~3x higher performance at the same power (P_OPERATION). This results in ~3x energy reduction under iso-delay conditions. Therefore the p-i-n TFETs are more suitable for sub-threshold logic operation., Comment: This work was presented in TECHCON 2009 Austin, TX

The question of whether relaxing momentum conservation can increase the performance of thermionic cooling device is examined. Both homojunctions and heterojunctions are considered. It is shown that for many cases, a non-conserved lateral momentum model overestimates the current. For the case of heterojunctions with a much heavier effective mass in the barrier and with a low barrier height, however, non-conservation of lateral momentum may increase the current. These results may be simply understood from the general principle that the current is limited by the location, well or barrier, with the smallest number of conducting channels. These results also show that within thermionic emission framework, the possibilities of increasing thermionic cooling by relaxing momentum conservation are limited. More generally, however, when the connection to the source is weak or in the presence of scattering, the situation may be different. Issues that deserve further study are identified., Comment: 36 pages, 1 table, 9 figures

The role of dimensionality on the electronic performance of thermoelectric devices is clarified using the Landauer formalism, which shows that the thermoelectric coefficients are related to the transmission, T(E), and how the conducing channels, M(E), are distributed in energy. The Landauer formalism applies from the ballistic to diffusive limits and provides a clear way to compare performance in different dimensions. It also provides a physical interpretation of the "transport distribution," a quantity that arises in the Boltzmann transport equation approach. Quantitative comparison of thermoelectric coefficients in one, two, and three dimension shows that the channels may be utilized more effectively in lower-dimensions. To realize the advantage of lower dimensionality, however, the packing density must be very high, so the thicknesses of the quantum wells or wires must be small. The potential benefits of engineering M(E) into a delta-function are also investigated. When compared to a bulk semiconductor, we find the potential for ~50 % improvement in performance. The shape of M(E) improves as dimensionality decreases, but lower dimensionality itself does not guarantee better performance because it is controlled by both the shape and the magnitude of M(E). The benefits of engineering the shape of M(E) appear to be modest, but approaches to increase the magnitude of M(E) could pay large dividends., Comment: 23 pages, 5 figures

An analysis of recent experimental data for high-performance In0.7Ga0.3As high electron mobility transistors (HEMTs) is presented. Using a fully quantum mechanical, ballistic model, we simulate In0.7Ga0.3As HEMTs with gate lengths of LG = 60nm, 85, and 135 nm and compare the result to the measured I-V characteristics including draininduced barrier lowering, sub-threshold swing, and threshold voltage variation with gate insulator thickness, as well as on-current performance. To first order, devices with three different oxide thicknesses and channel lengths can all be described by our ballistic model with appropriate values of parasitic series resistance. For high gate voltages, however, the ballistic simulations consistently overestimate the measured on-current, and they do not show the experimentally observed decrease in on-current with increasing gate length. With no parasitic series resistance at all, the simulated on-current of the LG = 60 nm device is about twice the measured current. According to the simulation, the estimated ballistic carrier injection velocity for this device is about 2.7 x 10^7 cm/s. Because of the importance of the semiconductor capacitance, the simulated gate capacitance is about 2.5 times less than the insulator capacitance. Possible causes of the transconductance degradation observed under high gate voltages in these devices are also explored. In addition to a possible gate-voltage dependent scattering mechanism, the limited ability of the source to supply carriers to the channel, and the effect of nonparabolicity are likely to play a role. The drop in on-current with increasing gate length is an indication that the devices operate below the ballistic limit., Comment: 35 pages, 11 figures, submitted to IEEE Transactions on Electron Devices, 2008

A spin metal-oxide-semiconductor field-effect-transistor (spin MOSFET), which combines a Schottky-barrier MOSFET with ferromagnetic source and drain contacts, is a promising device for spintronic logic. Previous simulation studies predict that this device should display a very high magnetoresistance (MR) ratio (between the cases of parallel and anti-parallel magnetizations) for the case of half-metal ferromagnets (HMF). We use the non-equilibrium Green's function (NEGF) formalism to describe tunneling and carrier transport in this device and to incorporate spin relaxation at the HMF-semiconductor interfaces. Spin relaxation at interfaces results in non-ideal spin injection. Minority spin currents arise and dominate the leakage current for anti-parallel magnetizations. This reduces the MR ratio and sets a practical limit for spin MOSFET performance. We found that MR saturates at a lower value for smaller source-to-drain bias. In addition, spin relaxation at the detector side is found to be more detrimental to MR than that at the injector side, for drain bias less than the energy difference of the minority spin edge and the Fermi level., Comment: 11 pages, 11 figures, To be published in Journal of Applied Physics

Optical emission from carbon nanotube transistors (CNTFETs) has recently attracted significant attention due to its potential applications. In this paper, we use a self-consistent numerical solution of the Boltzmann transport equation in the presence of both phonon and exciton scattering to present a detailed study of the operation of a partially suspended CNTFET light emitter, which has been discussed in a recent experiment. We determine the energy distribution of hot carriers in the CNTFET, and, as reported in the experiment, observe localized generation of excitons near the trench-substrate junction and an exponential increase in emission intensity with a linear increase in current versus gate voltage. We further provide detailed insight into device operation, and propose optimization schemes for efficient exciton generation; a deeper trench increases the generation efficiency, and use of high-k substrate oxides could lead to even larger enhancements., Comment: 17 pages, 5 figures

Field-effect transistors based on band-to-band tunneling (BTBT) have gained a lot of recent interest due to their potential for reducing power dissipation in integrated circuits. In this paper we present a detailed performance comparison between conventional n-i-n MOSFET transistors, and BTBT transistors based on the p-i-n geometry (p-i-n TFET), using semiconducting carbon nanotubes as the model channel material. Quantum transport simulations are performed using the nonequilibrium Green's function formalism including realistic phonon scattering. We find that the TFET can indeed produce subthreshold swings below the conventional MOSFET limit of 60mV/decade at room temperature leading to smaller off-currents and standby power dissipation. Phonon assisted tunneling, however, limits the off-state performance benefits that could have been achieved otherwise. Under on-state conditions the drive current and the intrinsic device delay of the TFET are mainly governed by the tunneling barrier properties. On the other hand, the switching energy for the TFET is observed to be fundamentally smaller than that for the MOSFET, reducing the dynamic power dissipation. Aforementioned reasons make the p-i-n geometry well suited for low power applications., Comment: 37 pages, 12 figures

The ballistic performance of electron transport in nanowire transistors is examined using a 10 orbital sp3d5s* atomistic tight-binding model for the description of the electronic structure, and the top-of-the-barrier semiclassical ballistic model for calculation of the transport properties of the transistors. The dispersion is self consistently computed with a 2D Poisson solution for the electrostatic potential in the cross section of the wire. The effective mass of the nanowire changes significantly from the bulk value under strong quantization, and effects such as valley splitting strongly lift the degeneracies of the valleys. These effects are pronounced even further under filling of the lattice with charge. The effective mass approximation is in good agreement with the tight binding model in terms of current-voltage characteristics only in certain cases. In general, for small diameter wires, the effective mass approximation fails., Comment: 6 pages, 6 figures, appeared in Journal of Computational Electronics, 2008, presented in IWCE-12

Power dissipation has become a major obstacle in performance scaling of modern integrated circuits, and has spurred the search for devices operating at lower voltage swing. In this letter, we study p-i-n band-to-band tunneling field effect transistors (TFET) taking semiconducting carbon nanotubes as the channel material. The on-current of these devices is mainly limited by the tunneling barrier properties, and phonon scattering has only a moderate effect. We show, however, that the off-current is limited by phonon absorption assisted tunneling, and thus is strongly temperature-dependent. Subthreshold swings below the 60mV/decade conventional limit can be readily achieved even at room temperature. Interestingly, although subthreshold swing degrades due to the effects of phonon scattering, it remains low under practical biasing conditions., Comment: 14 pages, 3 figures

A real-space quantum transport simulator for carbon nanoribbon (CNR) MOSFETs has been developed. Using this simulator, the performance of carbon nanoribbon (CNR) MOSFETs is examined in the ballistic limit. The impact of quantum effects on device performance of CNR MOSFETs is also studied. We found that 2D semi-infinite graphene contacts provide metal-induced-gap-states (MIGS) in the CNR channel. These states would provide quantum tunneling in the short channel device and cause Fermi level pining. These effects cause device performance degradation both on the ON-state and the OFF-state. Pure 1D devices (infinite contacts), however, show no MIGS. Quantum tunneling effects are still playing an important role in the device characteristics. Conduction due to band-to-band tunneling is accurately captured in our simulations. It is important in these devices, and found to dominate the off-state current. Based on our simulations, both a 1.4nm wide and a 1.8nm wide CNR with channel length of 12.5nm can outperform ultra scaled Si devices in terms of drive current capabilities and electrostatic control. Although subthreshold slopes in the forward-bias conduction are better than in Si transistors, tunneling currents are important and prevent the achievement of the theoretical limit of 60mV/dec.

Band-to-band tunneling (BTBT) devices have recently gained a lot of interest due to their potential for reducing power dissipation in integrated circuits. We have performed extensive simulations for the BTBT operation of carbon nanotube metal-oxide-semiconductor field-effect transistors (CNT-MOSFETs) using the non-equilibrium Green's functions formalism for both ballistic and dissipative quantum transport. In comparison with recently reported experimental data (Y. Lu et al, J. Am. Chem. Soc., v. 128, p. 3518-3519, 2006), we have obtained strong evidence that BTBT in CNT-MOSFETs is dominated by optical phonon assisted inelastic transport, which can have important implications on the transistor characteristics. It is shown that under large biasing conditions two-phonon scattering may also become important., Comment: 20 pages, 5 figures

We present the detailed treatment of dissipative quantum transport in carbon nanotube field-effect transistors (CNTFETs) using the non-equilibrium Green's function formalism. The effect of phonon scattering on the device characteristics of CNTFETs is explored using extensive numerical simulation. Both intra-valley and inter-valley scattering mediated by acoustic (AP), optical (OP), and radial breathing mode (RBM) phonons are treated. Realistic phonon dispersion calculations are performed using force-constant methods, and electron-phonon coupling is determined through microscopic theory. Specific simulation results are presented for (16,0), (19,0), and (22,0) zigzag CNTFETs that are in the experimentally useful diameter range. We find that the effect of phonon scattering on device performance has a distinct bias dependence. Up to moderate gate biases the influence of high-energy OP scattering is suppressed, and the device current is reduced due to elastic back-scattering by AP and low-energy RBM phonons. At large gate biases the current degradation is mainly due to high-energy OP scattering. The influence of both AP and high-energy OP scattering is reduced for larger diameter tubes. The effect of RBM mode, however, is nearly independent of the diameter for the tubes studied here., Comment: 52 pages, 1 table, 9 figures

We investigate the role of electron-phonon scattering and gate bias in degrading the drive current of nanotube MOSFETs. Our central results are: (i) Optical phonon scattering significantly decreases the drive current only when gate voltage is higher than a well-defined threshold. It means that elastic scattering mechanisms are most detrimental to nanotube MOSFETs. (ii) For comparable mean free paths, a lower phonon energy leads to a larger degradation of drive current. Thus for semiconducting nanowire FETs, the drive current will be more sensitive than carbon nanotube FETs because of the smaller phonon energies in semiconductors. (iii) Radial breathing mode phonons cause an appreciable reduction in drive current., Comment: 16 pages, 1 table, 4 figures

Electronic transport in a carbon nanotube (CNT) metal-oxide-semiconductor field effect transistor (MOSFET) is simulated using the non-equilibrium Green's functions method with the account of electron-phonon scattering. For MOSFETs, ambipolar conduction is explained via phonon-assisted band-to-band (Landau-Zener) tunneling. In comparison to the ballistic case, we show that the phonon scattering shifts the onset of ambipolar conduction to more positive gate voltage (thereby increasing the off current). It is found that the subthreshold swing in ambipolar conduction can be made as steep as 40mV/decade despite the effect of phonon scattering., Comment: 13 pages, 4 figures

The general theory for quantum simulation of cubic semiconductor n-MOSFETs is presented within the effective mass equation approach. The full three-dimensional transport problem is described in terms of coupled transverse subband modes which arise due to quantum confinement along the body thickness direction. Couplings among the subbands are generated for two reasons: due to spatial variations of the confinement potential along the transport direction, and due to non-alignment of the device coordinate system with the principal axes of the constant energy conduction band ellipsoids. The problem simplifies considerably if the electrostatic potential is separable along transport and confinement directions, and further if the potential variations along the transport direction are slow enough to prevent dipolar coupling (Zener tunneling) between subbands. In this limit, the transport problem can be solved by employing two unitary operators to transform an arbitrarily oriented constant energy ellipsoid into a regular ellipsoid with principal axes along the transport, width and confinement directions of the device. The effective masses for several technologically important wafer orientations for silicon and germanium are calculated in this paper.