Abstract: The Wigner-Liouville equation is reformulated using a spectral decomposition of the classical force field instead of the potential energy. The latter is shown to simplify the Wigner-Liouville kernel both conceptually and numerically as the spectral force Wigner-Liouville equation avoids the numerical evaluation of the highly oscillatory Wigner kernel which is nonlocal in both position and momentum. The quantum mechanical evolution is instead governed by a term local in space and non-local in momentum, where the non locality in momentum has only a limited range. An interpretation of the time evolution in terms of two processes is presented; a classical evolution under the influence of the averaged driving field, and a probability-preserving quantum-mechanical generation and annihilation term. Using the inherent stability and reduced complexity, a direct deterministic numerical implementation using Chebyshev and Fourier pseudo-spectral methods is detailed. For the purpose of illustration, we present results for the time evolution of a one-dimensional resonant tunneling diode driven out of equilibrium. (C) 2017 Elsevier Inc. All rights reserved.

Abstract: For many decades the Boltzmann distribution function has been used to calculate the non-equilibrium properties of mobile particles undergoing the combined action of various scattering mechanisms and externally applied force fields. When the latter give rise to the occurrence of inhomogeneous potential profiles across the region through which the particles are moving, the numerical solution of the Boltzmann equation becomes a highly complicated task. In this work we highlight a particular algorithm that can be used to solve the time dependent Boltzmann equation as well as its quantum mechanical extension, the WignerBoltzmann equation. As an illustration, we show the calculated distribution function describing electrons propagating under the action of both a uniform and a pronouncedly non-uniform electric field.

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: In the quantum mechanical simulation of exploratory semiconductor devices, continuum methods based on a k.p/envelope function model have the potential to significantly reduce the computational burden compared to prevalent atomistic methods. However, full-zone k.p/envelope function simulation approaches are scarce and existing implementations are not self-consistent with the calculation of the electrostatic potential due to the lack of a stable procedure and a proper normalization of the multi-band envelope functions. Here, we therefore present a self-consistent procedure based on a full-zone spectral k.p/envelope function band structure model. First, we develop a proper normalization for the multi-band envelope functions in the presence of transmitting boundary conditions. This enables the calculation of the free carrier densities. Next, we construct a procedure to obtain self-consistency of the carrier densities with the electrostatic potential. This procedure is stabilized with an adaptive scheme that relies on the solution of Poisson's equation in the Gummel form, combined with successive underrelaxation. Finally, we apply our procedure to homostructure In0.53Ga0.47As tunnel field-effect transistors (TFETs) and staggered heterostructure GaAs0.5Sb0.5/In0.53Ga0.47As TFETs and show the importance of self-consistency on the device predictions for scaled dimensions. Published by AIP Publishing.

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: 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: 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: Promising predictions are made for III-V tunnel-field-effect transistor (FET), but there is still uncertainty on the parameters used in the band-to-band tunneling models. Therefore, two simulators are calibrated in this paper; the first one uses a semi-classical tunneling model based on Kane's formalism, and the second one is a quantum mechanical simulator implemented with an envelope function formalism. The calibration is done for In0.53Ga0.47As using several p+/intrinsic/n+ diodes with different intrinsic region thicknesses. The dopant profile is determined by SIMS and capacitance-voltage measurements. Error bars are used based on statistical and systematic uncertainties in the measurement techniques. The obtained parameters are in close agreement with theoretically predicted values and validate the semi-classical and quantum mechanical models. Finally, the models are applied to predict the input characteristics of In0.53Ga0.47As n- and p-lineTFET, with the n-lineTFET showing competitive performance compared to MOSFET.

Abstract: Group IV based tunnel field-effect transistors generally show lower on-current than III-V based devices because of the weaker phonon-assisted tunneling transitions in the group IV indirect bandgap materials. Direct tunneling in Ge, however, can be enhanced by strain engineering. In this work, we use a 30-band k.p method to calculate the band structure of biaxial tensile strained Ge and then extract the bandgaps and effective masses at Gamma and L symmetry points in k-space, from which the parameters for the direct and indirect band-to-band tunneling (BTBT) models are determined. While transitions from the heavy and light hole valence bands to the conduction band edge at the L point are always bridged by phonon scattering, we highlight a new finding that only the light-holelike valence band is strongly coupling to the conduction band at the Gamma point even in the presence of strain based on the 30-band k.p analysis. By utilizing a Technology Computer Aided Design simulator equipped with the calculated band-to-band tunneling BTBT models, the electrical characteristics of tensile strained Ge point and line tunneling devices are self-consistently computed considering multiple dynamic nonlocal tunnel paths. The influence of field-induced quantum confinement on the tunneling onset is included. Our simulation predicts that an on-current up to 160 (260) mu A/mu m can be achieved along with on/off ratio > 10(6) for V-DD = 0.5V by the n-type (p-type) line tunneling device made of 2.5% biaxial tensile strained Ge. (C) 2014 AIP Publishing LLC.

Abstract: The tunneling current has been computed for a cylindrical nanowire tunneling field-effect transistor (TFET) with an all-round gate that covers the source region. Being the underlying mechanism, band-to-band tunneling, mediated by electron-phonon interaction, is pronouncedly affected by carrier confinement in the radial direction and, therefore, involves the self-consistent solution of the Schrodinger and Poisson equations. The latter has been accomplished by exploiting a non-linear variational principle within the framework of the modified local density approximation taking into account the nonparabolicity of both the valence band and conduction band in relatively thick wires. Moreover, while the effective-mass approximation might still provide a reasonable description of the conduction band in relatively thick wires, we have found that the nonparabolicity of the valence band needs to be included. As a major conclusion, it is observed that confinement effects in nanowire tunneling field-effect transistors have a stronger impact on the onset voltage of the tunneling current in comparison with planar TFETs. On the other hand, the value of the onset voltage is found to be overestimated when the valence band nonparabolicity is ignored. (C) 2013 AIP Publishing LLC.

Abstract: A general framework to calculate the Zener current in an indirect semiconductor with an externally applied potential is provided. Assuming a parabolic valence and conduction band dispersion, the semiconductor is in equilibrium in the presence of the external field as long as the electron-phonon interaction is absent. The linear response to the electron-phonon interaction results in a non-equilibrium system. The Zener tunneling current is calculated from the number of electrons making the transition from valence to conduction band per unit time. A convenient expression based on the single particle spectral functions is provided, enabling the evaluation of the Zener tunneling current under any three-dimensional potential profile. For a one-dimensional potential profile an analytical expression is obtained for the current in a bulk semiconductor, a semiconductor under uniform field, and a semiconductor under a non-uniform field using the WKB (Wentzel-Kramers-Brillouin) approximation. The obtained results agree with the Kane result in the low field limit. A numerical example for abrupt p-n diodes with different doping concentrations is given, from which it can be seen that the uniform field model is a better approximation than the WKB model, but a direct numerical treatment is required for low bias conditions.

Abstract: Tunnel field-effect transistors (TFETs) are potential successors of metal-oxide-semiconductor FETs because scaling the supply voltage below 1 V is possible due to the absence of a subthreshold-swing limit of 60 mV/decade. The modeling of the TFET performance, however, is still preliminary. We have developed models allowing a direct comparison between the single-gate, double-gate, and gate-all-around configuration at high drain voltage, when the drain-voltage dependence is negligible, and we provide improved insight in the TFET physics. The dependence of the tunnel current on device parameters is analyzed, in particular, the scaling with gate-dielectric thickness, channel thickness, and dielectric constants of gate dielectric and channel material. We show that scaling the gate-dielectric thickness improves the TFET performance more than scaling the channel thickness and that improvements are often overestimated. There is qualitative agreement between our model and our experimental data.

Abstract: Recently, a renewed interest in Zener tunneling has arisen because of its increasing impact on semiconductor device performance at nanometer dimensions. In this paper we evaluate the tunnel probability under the action of a nonuniform electric field using a two-band model and arrive at significant deviations from the commonly used Kanes model, valid for weak uniform fields only. A threshold on the junction bias where Kanes model for Zener tunneling breaks down is determined. Comparison with Kanes model particularly shows that our calculation yields a higher tunnel probability for intermediate electric fields and a lower tunnel probability for high electric fields. When performing a current calculation comparing to the WKB approximation for the case of an abrupt p-n junction significant differences concerning the shape of the I-V curve are demonstrated.

Abstract: We present comprehensive calculations of the low-field hole mobility in Ge p-channel inversion layers with SiO2 insulator using a six-band k·p band-structure model. The cases of relaxed, biaxially, and uniaxially (both tensily and compressively) strained Ge are studied employing an efficient self-consistent methodmaking use of a nonuniform spatial mesh and of the Broyden second methodto solve the coupled envelope-wave function k·p and Poisson equations. The hole mobility is computed using the KuboGreenwood formalism accounting for nonpolar hole-phonon scattering and scattering with interfacial roughness. Different approximations to handle dielectric screening are also investigated. As our main result, we find a large enhancement (up to a factor of 10 with respect to Si) of the mobility in the case of uniaxial compressive stress similarly to the well-known case of Si. Comparison with experimental data shows overall qualitative agreement but with significant deviations due mainly to the unknown morphology of the rough Ge-insulator interface, to additional scattering with surface optical phonon from the high- insulator, to Coulomb scattering interface traps or oxide chargesignored in our calculationsand to different channel structures employed.