Abstract: In tunnel field-effect transistors, trap-assisted tunneling (TAT) is one of the probable causes for degraded subthreshold swing. The accurate quantum-mechanical (QM) assessment of TAT currents also requires a QM treatment of phonon-assisted tunneling (PAT) currents. Therefore, we present a multi-band PAT current formalism within the framework of the quantum transmitting boundary method. An envelope function approximation is used to construct the electron-phonon coupling terms corresponding to local Frohlich-based phonon-assisted inter-band tunneling in direct-bandgap III-V semiconductors. The PAT current density is studied in up to 100 nm long and 20 nm wide p-n diodes with the 2- and 15-band material description of our formalism. We observe an inefficient electron-phonon coupling across the tunneling junction. We further demonstrate the dependence of PAT currents on the device length, for our non-self-consistent formalism which neglects changes in the electron distribution function caused by the electron-phonon coupling. Finally, we discuss the differences in doping dependence between direct band-to-band tunneling and PAT current. Published under license by AIP Publishing.

Abstract: Employing the quantum transmitting boundary (QTB) method, we have developed a two-dimensional Schrödinger-Poisson solver in order to investigate quantum transport in nano-scale CMOS transistors subjected to open boundary conditions. In this paper we briefly describe the building blocks of the solver that was originally written to model silicon devices. Next, we explain how to extend the code to semiconducting materials such as germanium, having conduction bands with energy ellipsoids that are neither parallel nor perpendicular to the channel interfaces or even to each other. The latter introduces mixed derivatives in the 2D effective mass equation, thereby heavily complicating the implementation of open boundary conditions. We present a generalized quantum transmitting boundary method that mainly leans on the completeness of the eigenstates of the effective mass equation. Finally, we propose a new algorithm to calculate the chemical potentials of the source and drain reservoirs, taking into account their mutual interaction at high drain voltages. As an illustration, we present the potential and carrier density profiles obtained for a (111) Ge NMOS transistor as well as the ballistic current characteristics.

Abstract: This paper investigates energy filtering in silicon nanowires and nanosheets by resonant electron tunneling through a geometric superlattice. A geometric superlattice is any kind of periodic geometric feature along the transport direction of the nanowire or nanosheet. Multivalley quantum-transport simulations are used to demonstrate the manifestation of minibands and minibandgaps in the transmission spectra of such a superlattice. We find that the presence of different valleys in the conduction band of silicon favors a nanowire with a rectangular cross section for effective energy filtering. The obtained energy filter can consequently be used in the source extension of a field-effect transistor to prevent high-energy electrons from contributing to the leakage current. Self-consistent Schrodinger-Poisson simulations in the ballistic limit show minimum subthreshold swings of 6 mV/decade for geometric superlattices with indentations. The obtained theoretical performance metrics for the simulated devices are compared with conventional III-V superlatticeFETs and TunnelFETs. The adaptation of the quantum transmitting boundary method to the finite-element simulation of 3-D structures with anisotropic effective mass is presented in Appendixes A and B. Our results bare relevance in the search for steep-slope transistor alternatives which are compatible with the silicon industry and can overcome the power-consumption bottleneck inherent to standard CMOS technologies. Published by AIP Publishing.

Abstract: The dynamics of electrons and holes propagating through the nano-scaled channels of modern semiconductor devices can be seen as a widespread manifestation of non-equilibrium statistical physics and its ruling principles. In this respect both the devices that are pushing conventional CMOS technology towards the final frontiers of Moores law and the upcoming set of alternative, novel nanostructures grounded on entirely new concepts and working principles, provide an almost unlimited playground for assessing physical models and numerical techniques emerging from classical and quantum mechanical non-equilibrium theory. In this paper we revisit the Boltzmann as well as the WignerBoltzmann equation which offers a valuable platform to study transport of charge carriers taking part in drive currents. We focus on a numerical procedure that regained attention recently as an alternative tool to solve the time-dependent Boltzmann equation for inhomogeneous systems, such as the channel regions of field-effect transistors, and we discuss its extension to the WignerBoltzmann equation. Furthermore, we pay attention to the calculation of tunneling leakage currents. The latter typically occurs in nano-scaled transistors when part of the carrier distribution sustaining the drive current is found to tunnel into the gate due the presence of an ultra-thin insulating barrier separating the gate from the channel region. In particular, we discuss the paradox related to the very existence of leakage currents established by electrons occupying quasi-bound states, while the (real) wave functions of the latter cannot carry net currents. Finally, we describe a simple model to resolve the paradox as well as to estimate gate currents provided the local carrier generation rates largely exceed the tunneling rates.

Abstract: We investigate the diffusive electron-transport properties of charge-doped graphene ribbons and nanoribbons with imperfect edges. We consider different regimes of edge scattering, ranging from wide graphene ribbons with (partially) diffusive edge scattering to ribbons with large width variations and nanoribbons with atomistic edge roughness. For the latter, we introduce an approach based on pseudopotentials, allowing for an atomistic treatment of the band structure and the scattering potential, on the self-consistent solution of the Boltzmann transport equation within the relaxation-time approximation and taking into account the edge-roughness properties and statistics. The resulting resistivity depends strongly on the ribbon orientation, with zigzag (armchair) ribbons showing the smallest (largest) resistivity and intermediate ribbon orientations exhibiting intermediate resistivity values. The results also show clear resistivity peaks, corresponding to peaks in the density of states due to the confinement-induced subband quantization, except for armchair-edge ribbons that show a very strong width dependence because of their claromatic behavior. Furthermore, we identify a strong interplay between the relative position of the two valleys of graphene along the transport direction, the correlation profile of the atomistic edge roughness, and the chiral valley modes, leading to a peculiar strongly suppressed resistivity regime, most pronounced for the zigzag orientation.

Abstract: The envelope function method traditionally employs a single basis set which, in practice, relates to a single material because the k.p matrix elements are generally only known in a particular basis. In this work, we defined a basis function transformation to alleviate this restriction. The transformation is completely described by the known inter-band momentum matrix elements. The resulting envelope function equation can solve the electronic structure in lattice matched heterostructures without resorting to boundary conditions at the interface between materials, while all unit-cell averaged observables can be calculated as with the standard envelope function formalism. In the case of two coupled bands, this heterostructure formalism is equivalent to the standard formalism while taking position dependent matrix elements. (C) 2015 Elsevier B.V. All rights reserved

Abstract: Discrepancies exist between the theoretically predicted and experimentally measured performance of band-to-band tunneling devices, such as Esaki diodes and tunnel field-effect transistors (TFETs). We resolve this discrepancy for highly-doped, direct-bandgap Esaki diodes by successfully calibrating a semi-classical model for high-doping-induced ballistic band-tails tunneling currents at multiple temperatures with two In0.53Ga0.47As Esaki diodes using their SIMS doping profiles, C-V characteristics and their forward-bias current density in the negative differential resistance (NDR) regime. The current swing in the NDR regime is shown not to be linked to the band-tails Urbach energy. We further demonstrate theoretically that the calibrated band-tails contribution is also the dominant band-tails contribution to the subthreshold swing of the corresponding TFETs. Lastly, we verify that the presented procedure is applicable to all direct-bandgap semiconductors by successfully applying it to InAs Esaki diodes in literature.

Abstract: A weakly coupled system of two crossed graphene nanoribbons exhibits direct tunneling due to the overlap of the wavefunctions of both ribbons. We apply the Bardeen transfer Hamiltonian formalism, using atomistic band structure calculations to account for the effect of the atomic structure on the tunneling process. The strong quantum-size confinement of the nanoribbons is mirrored by the one-dimensional character of the electronic structure, resulting in properties that differ significantly from the case of inter-layer tunneling, where tunneling occurs between bulk two-dimensional graphene sheets. The current-voltage characteristics of the inter-ribbon tunneling structures exhibit resonance, as well as stepwise increases in current. Both features are caused by the energetic alignment of one-dimensional peaks in the density-of-states of the ribbons. Resonant tunneling occurs if the sign of the curvature of the coupled energy bands is equal, whereas a step-like increase in the current occurs if the signs are opposite. Changing the doping modulates the onset-voltage of the effects as well as their magnitude. Doping through electrostatic gating makes these structures promising for application towards steep slope switching devices. Using the atomistic empirical pseudopotentials based Bardeen transfer Hamiltonian method, inter-ribbon tunneling can be studied for the whole range of two-dimensional materials, such as transition metal dichalcogenides. The effects of resonance and of step-like increases in the current we observe in graphene ribbons are also expected in ribbons made from these alternative two-dimensional materials, because these effects are manifestations of the one-dimensional character of the density-of-states. Published by AIP Publishing.

Abstract: The trap-assisted tunneling (TAT) current in tunnel field-effect transistors (TFETs) is one of the crucial factors degrading the sub-60 mV/dec sub-threshold swing. To correctly predict the TAT currents, an accurate description of the trap is required. Since electric fields in TFETs typically reach beyond 10(6) V/cm, there is a need to quantify the impact of such high field on the traps. We use a quantum mechanical implementation based on the modified transfer matrix method to obtain the trap energy level. We present the qualitative impact of electric field on different trap configurations, locations, and host materials, including both semiconductors and oxides. We determine that there is an electric-field related trap level shift and level broadening. We find that these electric-field induced quantum effects can enhance the trap emission rates. Published by AIP Publishing.

Abstract: The interaction between the surface of a 3D topological insulator and a skyrmion/anti-skyrmion structure is studied in order to investigate the possibility of electron confinement due to the skyrmion presence. Both hedgehog (Neel) and vortex (Bloch) skyrmions are considered. For the hedgehog skyrmion, the in-plane components cannot be disregarded and their interaction with the surface state of the topological insulator (TI) has to be taken into account. A semi-classical description of the skyrmion chiral angle is obtained using the variational principle. It is shown that both the hedgehog and the vortex skyrmion can induce bound states on the surface of the TI. However, the number and the properties of these states depend strongly on the skyrmion type and the skyrmion topological number N-Sk. The probability densities of the bound electrons are also derived where it is shown that they are localized within the skyrmion region. Published by AIP Publishing.

Abstract: Recent years have seen a tremendous rise of two-dimensional (2D) magnetic materials, several of which were verified experimentally. However, most of the theoretical predictions to date rely on ab initio methods, at zero temperature and fluctuation-free, while one certainly expects detrimental quantum fluctuations at finite temperatures. Here, we present the solution of the quantum Heisenberg model for honeycomb/hexagonal lattices with anisotropic exchange interaction up to third nearest neighbors and in an applied field in arbitrary direction, which answers the question whether long-range magnetization can indeed survive in the ultrathin limit of materials, up to which temperature, and what the characteristic excitation (magnon) frequencies are, all essential to envisaged applications of magnetic 2D materials. We find that long-range magnetic order persists at finite temperature for materials with overall easy-axis anisotropy. We validate the calculations on the examples of monolayers CrI3, CrBr3, and MnSe2. Moreover, we provide an easy-to-use tool to calculate Curie temperatures of new 2D computational materials.

Abstract: Efficient quantum mechanical simulation of tunnel field-effect transistors (TFETs) is indispensable to allow for an optimal configuration identification. We therefore present a full-zone 15-band quantum mechanical solver based on the envelope function formalism and employing a spectral method to reduce computational complexity and handle spurious solutions. We demonstrate the versatility of the solver by simulating a 40 nm wide In0.53Ga0.47As lineTFET and comparing it to p-n-i-n configurations with various pocket and body thicknesses. We find that the lineTFET performance is not degraded compared to semi-classical simulations. Furthermore, we show that a suitably optimized p-n-i-n TFET can obtain similar performance to the lineTFET. (C) 2015 AIP Publishing LLC.

Abstract: Strongly confined nano-systems, such as one-dimensional nanowires, feature deviations in their structural, electronic and optical properties from the corresponding bulk. In this work, we investigate the behavior of long-wavelength, optical phonons in vertical arrays of InAs nanowires by Raman spectroscopy. We attribute the main changes in the spectral features to thermal anharmonicity, due to temperature effects, and rule out the contribution of quantum confinement and Fano resonances. We also observe the appearance of surface optical modes, whose details allow for a quantitative, independent estimation of the nanowire diameter. The results shed light onto the mechanisms of lineshape change in low-dimensional InAs nanostructures, and are useful to help tailoring their electronic and vibrational properties for novel functionalities.

Abstract: In this work we investigate quantum ballistic transport in ultrasmall junctionless and inversion mode semiconducting nanowire transistors within the framework of the self-consistent Schrödinger-Poisson problem. The quantum transmitting boundary method is used to generate open boundary conditions between the active region and the electron reservoirs. We adopt a subband decomposition approach to make the problem numerically tractable and make a comparison of four different numerical approaches to solve the self-consistent Schrödinger-Poisson problem. Finally we discuss the IV-characteristics for small (r≤5 nm) GaAs nanowire transistors. The novel junctionless pinch-off FET or junctionless nanowire transistor is extensively compared with the gate-all-around (GAA) nanowire MOSFET.