Empirical Pseudopotentials Research Articles

Theoretical study of MgNa+ ionic system: potential energy curve, vibrational levels, dipole moments, radiative lifetimes and laser-cooling analysis

An extensive ab-initio quantum chemistry study and a discussion of the possible laser cooling and formation of the heteronuclear ionic MgNa+ molecule is presented in this paper. Our work is based on the use of non–empirical pseudo-potentials for the Mg2+ and Na+ cores, large Gaussian basis sets, parametrized l–dependent polarization potentials, and full valence configuration interaction calculations. We present here adiabatic potential energy curves of the ground and 44 low-lying excited electronic states of 1,3Σ+, 1,3Π, 1,3Δ symmetries, and their spectroscopic parameters (Re, De, Te, ωe, ωexe, and Be). Furthermore, numerous ionic – neutral avoided crossings, specially between higher adjacent electronic states of 1,3Σ+, 1,3Π symmetries, are identified and interpreted. The energy separations between these avoided crossings are also calculated. The electric dipole moment curves have been computed for a wide range of inter-nuclear distances. The vibrational energies are obtained by solving the nuclear Schrodinger equation, using the calculated potential energy curves. Thereafter, spontaneous and black-body radiation induced transition rates are calculated to obtain the ground and excited states vibrational level lifetimes. It has been observed that the lifetimes of the ground state vibrational levels are of the order of a second, while those of the excited states, mainly the 21Σ+ state, have the order of a nanosecond.

Full-Band Quantum Transport of Heterojunction Electron Devices With Empirical Pseudopotentials

This article presents the methodology, implementation, and application of a full-band quantum transport model based on the nonequilibrium Green’s function formalism and the empirical pseudopotentials. In particular, this article reports the treatment of heterojunctions between lattice-matched semiconductors, comprising a gradual transition region described according to a virtual crystal approximation. Our approach entails several numerical techniques to make the full-band quantum transport method computationally affordable and thus enable robust and efficient self-consistent device simulations. Then, we employ our simulation scheme for the analysis of some exemplary devices based on quantum tunneling, such as an Esaki tunneling diode, as well as n- and p-type heterojunction tunnel FETs. In particular, we investigate the influence on the current–voltage characteristics of the width of the heterojunction transition region. We observe that a gradual transition region mainly affects the device characteristics by lengthening the tunneling path at the heterojunction, which has a different impact on device current depending on the external bias conditions.

Quantum transport simulation of graphene-nanoribbon field-effect transistors with defects

We present a theoretical study of the effect of defects on the charge-transport properties of gate-all-around graphene nanoribbons field-effect transistors. Electronic transport is treated atomistically using an efficient method we have recently proposed that makes use of a Bloch-wave basis obtained from empirical pseudopotentials and solves the Schrodinger equation with open boundary conditions using the quantum transmitting boundary method. The defects considered here consist in single vacancies at different locations in the ribbon (center and edge of the ribbon; in the source or drain regions or along the channel). We have found that vacancies located at different locations along the ribbon width alter differently the Kekule patterns: Defects at the edge reduce the $$I_{\mathrm{on}}/I_{\mathrm{off}}$$ more than defects located near the center of the ribbon, and the effect is stronger in narrow ribbons. These results show that any proposed technology based on graphene nanoribbons must be able to control the quality of the material down to a single atom.

Generation of empirical pseudopotentials for transport applications and their application to group IV materials

Empirical pseudopotentials (EPs) allow for accurate and efficient modeling of atomistic electron transport. Unfortunately, EPs are available only for a few materials and atomic configurations. Furthermore, EPs for nanostructures have historically been described using a variety of different parameterized forms. To compete with more general first-principles methods, we propose an automated workflow to generate EPs of a general form for any material and atomistic configuration. In particular, we focus on the generation of EPs for electron transport calculations, i.e., we provide an EP that accurately reproduces a reference band structure. To demonstrate the applicability of the proposed method, we generate the EPs to reproduce the band structure for bulk Si, Ge, 3C–SiC (zinc-blende polytype), 4H–SiC (hexagonal polytype), diamond, and hydrogen terminated ⟨100⟩ oriented Si and Ge thin films, calculated using first principles. In addition, using the generated EPs, along with the virtual crystal approximation, we demonstrate that our method reproduces accurately the band structure related properties of Si1−xGex alloy as a function of Ge mole fraction, x. As an application of our generated EPs, we perform ballistic quantum transport simulations of extremely scaled (≈0.6 nm wide), hydrogen terminated, ⟨100⟩ oriented Ge and Si gate-all-around nanowire field-effect transistors and compare their transfer characteristics.

Quantum transport models based on NEGF and empirical pseudopotentials for accurate modeling of nanoscale electron devices

This paper presents significant new developments concerning the full-band, quantum simulation of nanostructured systems and nanoscale electron devices based on an empirical pseudopotential Hamiltonian. We demonstrate that the method is of general applicability, in fact, we show results for planar, ultrathin-body FETs and also for three-dimensional, nanowire FETs, and we deal with different crystal orientations and account for possible stress/strain conditions in the simulated systems. Some of the simulations reported in this paper have been made computationally viable by the substantial improvements of the numerical efficiency compared to our previous pseudopotentials based methodology. Most of the methods and algorithms discussed in this paper are not specific to an empirical pseudopotential Hamiltonian; on the contrary, they can also be applied to different Hamiltonians described with a plane-wave basis, which is frequently employed for ab initio, Density Functional Theory based calculations. The application of the methodologies described in this work may thus be more far reaching than it is illustrated by the case studies explicitly addressed in the present paper.

Extraction of eight-band k⋅p parameters from empirical pseudopotentials for GeSn

We extract the parameters for the eight-band k⋅p model for Ge1−xSnx (x≤0.15) from the calculation of the nonlocal empirical pseudopotential method with the modified virtual crystal approximation. The atomic pseudopotential form factors of Ge are improved such that the calculated Ge band structure has the commonly accepted bandgap and effective masses. The improved Ge parameters are used in proper interpolation to derive the parameters of GeSn for empirical pseudopotential calculation. The calculated band structures suggest that the Ge1−xSnx alloys exhibit a transition between an indirect bandgap semiconductor and a direct one at Sn composition xc=0.071. From the calculation, we extract the bandgap, the split-off energy, the interband momentum matrix element, and the effective masses of Ge1−xSnx (x≤0.15) as functions of x. From these results, we further derive the parameters used in the eight-band k⋅p model. These parameters are well expressed in quadratic form. The k⋅p model with the extracted parameters can give an interband tunneling current in a “pin” diode that is consistent with the current calculated by the empirical pseudopotential method.

“Hot electrons in Si lose energy mostly to optical phonons”: Truth or myth?

Theoretical studies of heat generation and diffusion in Si devices generally assume that hot electrons in Si lose their energy mainly to optical phonons. Here, we briefly review the history of this assumption, and using full-band Monte Carlo simulations—with electron-phonon scattering rates calculated using the rigid-ion approximation and both empirical pseudopotentials and Harris potentials—we show that, instead, electrons lose as much as 2/3 of their energy to acoustic phonons. The scattering rates that we have calculated have been used to study hot-electron effects, such as impact ionization and injection into SiO2, and are in rough agreement with those obtained using density functional theory. Moreover, direct subpicosecond pump-probe experimental results, some of them dating back to 1994, are consistent with the predictions of our model. We conclude that the study of heat generation and dissipation in nanometer-scale Si devices may require a substantial revision of the assumptions that have been considered “common wisdom” so far.

Theoretical Study of Ballistic Transport in Silicon Nanowire and Graphene Nanoribbon Field-Effect Transistors Using Empirical Pseudopotentials

We present a theoretical study of the ballistic performance of gate-all-around field-effect transistors (FETs) with channels consisting of armchair-edge graphene nanoribbons (aGNRs) of various widths and silicon nanowires (SiNWs) with square cross sections. We apply an atomistic quantum transport formalism based on empirical pseudopotentials. Our results show that the turn-OFF behavior of aGNRFETs is seriously affected by source-to-drain tunneling at short channel lengths (e.g., below 10 nm for 3-aGNRs). Defining the threshold voltage ${\textit V}_{\textsf {th}}$ as the gate bias at which the current reaches a given $I_{ \mathrm{\scriptscriptstyle OFF}} = 0.4~\mu \text{A}/\mu \text{m}$ , devices with a 5-nm channel length can reach a maximum current of only $400~\mu \text{A}/\mu \text{m}$ at a gate overdrive ${\textit V}_{\textit {GS}}-{\textit V}_{\textsf {th}} = 0.25$ V (corresponding to an assumed ${V}_{\textsf DD}$ of about 0.4 V). In contrast, SiNWFETs remain immune from source-to-drain tunneling even at 5 nm and show an almost ideal subthreshold swing, a satisfactory current of $1000~\mu \text{A}/\mu \text{m}$ at the same gate overdrive of 0.25 V, and a reasonable ${\textit I}_{ \mathrm{\scriptscriptstyle ON}}/I_{ \mathrm{\scriptscriptstyle OFF}}$ ratio around $2\times 10^{3}$ .

Effective passivant pseudopotentials for semiconductors: Beyond the spherical approximation

A new type of atomic pseudopotential for passivation of semiconductors surfaces is presented. These pseudopotentials are intended to be used with empirical or effective pseudopotentials methods, where the main goal is to address nanostructures composed of thousands of atoms, but at low computational costs in comparison to density functional theory (DFT). It is shown that the spherical approximation, which is currently used for these potentials, is not suitable for describing passivants and that, instead, they have to be regarded as complex quantities in reciprocal space. A methodology to extract and implement the new pseudopotentials are described here based on an analytic formulation. Passivants for six different semiconductor compounds (GaAs, AlAs, Si, Ge, CdSe and ZnO) are generated, and their accuracy and high transferability are demonstrated by the calculation of the electronic states of different kinds of surfaces and structures and comparison to DFT calculations. The results show that the DFT results can be reproduced with high fidelity with the passivant potentials here presented.

Microscopic dielectric permittivities of graphene nanoribbons and graphene

We derive a microscopic Poisson equation using the density-density response function. This equation is valid for any realistic potential perturbation and permits the study of dielectric response in nanostructures, especially in one-dimensional nanostructures and quantum dots. We apply this equation to simulate a nanoscale parallel-plate capacitor (nanocapacitor) with graphene as dielectric and two nanocapacitors with a graphene nanoribbon (GNR) as dielectric. The density-density response function is calculated using first-order perturbation theory and empirical pseudopotentials. From the microscopic electric field of the graphene nanocapacitor, we calculate the out-of-plane microscopic dielectric constant of graphene and from the electric field of GNR nanocapacitors, we calculate the full microscopic dielectric tensor of several GNRs with different widths. We find that the out-of-plane microscopic dielectric constants of GNRs and graphene do not depend on their energy band gap. We also study the effect of a surrounding dielectric on the dielectric permittivity of graphene and we conclude that the surrounding dielectric barely affects the dielectric permittivity of graphene.

Inter-ribbon tunneling in graphene: An atomistic Bardeen approach

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.

(Invited) Physics of Electronic Transport in Low-Dimensionality Materials for Future FETs

The scaling of electronic devices has continued unabated for the past 5 decades, despite repeated predictions of the "end of scaling". The "more than Moore" slogan has been, and still is, viewed by industry as a need to explore realistic low-to-medium-risk avenues, some already in production -- such as strained Si/Ge or high-κ dielectrics, some yet to be translated to products in the near future or never -- such III-V semiconductors or tunnel-FETs. On the contrary, Academia has looked far ahead, even beyond carbon-based electronics (carbon nanotubes, graphene, nanoribbons). Now that the ULSI technology is looking at a feature size of 5 nm by 2026, even more “improbable” alternatives are considered, including transition metal dichalcogenides (TMDs), silicene/ane, germanene/ane (together with other *enes and *anes), topological insulators, Weyl semimetals, and other strongly correlated fermion systems. Here I will first discuss the fact that, if we really wish to scale to 5 nm, simple electrostatic scaling laws demand that we take two-dimensional materials very seriously, despite their thermodynamic instability (Mermin-Wagner theorem) and the related technological difficulties. I will first consider how electronic transport in non mirror-symmetric 2D crystals (e.g., silicene, germanene, stanene, TMDs of the 1T/T’ crystal structure) may be severely affected by coupling of the electrons with the acoustic flexural modes (ZA-phonons). I will then consider whether graphene has any chance of replacing Si by looking at how the extremely promising electronic properties it exhibits in its ideal form become much less interesting when it becomes a component of some non-ideal structure (such when supported and gated and/or in nanoribbon form). Finally, I will discuss a couple of very interesting admittedly improbable but fun ideas: 1. The Bose-Einstein condensation in bilayer systems (motivating UT-Austin’s BiSFETs) as an example of how issues of practical implementation may regrettably transform an excellent idea into a pure academic exercise; and 2. Monolayer tin (“stannanane”) as a 2D topological insulator with potential applications in spintronics and low-power high-performance devices (… assuming we can make it, of course…). For the entire discussion I will keep density functional theory (DFT), empirical pseudopotentials, and transport equations in the background. This work qas done in collaboration with Shela Aboud, Bo Fu, Jiseok Kim, Sudarshan Narayanan, Ana Suarez Negreira, Zhun-Yong Ong, Cathy Sachs, and William Vandenberghe.

Effect of Van Hove singularities on high- Tc superconductivity in H3S

One of interesting open questions for the high transition temperature (Tc) superconductivity in sulfur hydrides is why high pressure phases of H3S have extremely high Tc's. Recently, it has been pointed out that the presence of the van Hove singularities (vHs) around the Fermi level is crucial. However, while there have been quantitative estimates of Tc based on the Migdal-Eliashberg theory, the energy dependence of the density of states (DOS) has been neglected to simplify the Eliashberg equation. In this study, we go beyond the constant DOS approximation and explicitly consider the electronic structure over 40eV around the Fermi level. In contrast with the previous conventional calculations, this approach with a sufficiently large number of Matsubara frequencies enables us to calculate Tc without introducing the empirical pseudo Coulomb potential. We show that while H3S has much higher Tc than H2S for which the vHs is absent, the constant DOS approximation employed so far seriously overestimates (underestimates) Tc by ~ 60K (~ 10K) for H3S (H2S). We then discuss the impact of the strong electron-phonon coupling on the electronic structure with and without the vHs and how it affects the superconductivity. Especially, we focus on (1) the feedback effect in the self-consistent calculation of the self-energy, (2) the effect of the energy shift due to the zero-point motion, and (3) the effect of the changes in the phonon frequencies due to strong anharmonicity. We show that the effect of (1)-(3) on Tc is about 10-30K for both H3S and H2S. Eventually, Tc is estimated to be 181K for H3S at 250GPa and 34K for H2S at 140GPa, which explains the pressure dependence of Tc observed in the experiment. In addition, we evaluate the lowest order vertex correction beyond the Migdal-Eliashberg theory and discuss the validity of the Migdal approximation for sulfur hydrides.

Strained band edge characteristics from hybrid density functional theory and empirical pseudopotentials: GaAs, GaSb, InAs and InSb

The properties of a semiconductor are drastically modified when the crystal point group symmetry is broken under an arbitrary strain. We investigate the family of semiconductors consisting of GaAs, GaSb, InAs and InSb, considering their electronic band structure and deformation potentials subject to various strains based on hybrid density functional theory. Guided by these first-principles results, we develop strain-compliant local pseudopotentials for use in the empirical pseudopotential method (EPM). We demonstrate that the newly proposed empirical pseudopotentials perform well close to band edges and under anisotropic crystal deformations. Using the EPM, we explore the heavy hole–light hole mixing characteristics under different stress directions, which may be useful in manipulating their transport properties and optical selection rules. The very low 5 Ry cutoff targeted in the generated pseudopotentials paves the way for large-scale EPM-based electronic structure computations involving these lattice mismatched constituents.

Pseudopotential-based electron quantum transport: Theoretical formulation and application to nanometer-scale silicon nanowire transistors

We present a formalism to treat quantum electronic transport at the nanometer scale based on empirical pseudopotentials. This formalism offers explicit atomistic wavefunctions and an accurate band structure, enabling a detailed study of the characteristics of devices with a nanometer-scale channel and body. Assuming externally applied potentials that change slowly along the electron-transport direction, we invoke the envelope-wavefunction approximation to apply the open boundary conditions and to develop the transport equations. We construct the full-band open boundary conditions (self-energies of device contacts) from the complex band structure of the contacts. We solve the transport equations and present the expressions required to calculate the device characteristics, such as device current and charge density. We apply this formalism to study ballistic transport in a gate-all-around (GAA) silicon nanowire field-effect transistor with a body-size of 0.39 nm, a gate length of 6.52 nm, and an effective oxide thickness of 0.43 nm. Simulation results show that this device exhibits a subthreshold slope (SS) of ∼66 mV/decade and a drain-induced barrier-lowering of ∼2.5 mV/V. Our theoretical calculations predict that low-dimensionality channels in a 3D GAA architecture are able to meet the performance requirements of future devices in terms of SS swing and electrostatic control.

Excitonic optical properties of wurtzite ZnS quantum dots under pressure.

By means of atomistic empirical pseudopotentials combined with a configuration interaction approach, we have studied the optical properties of wurtzite ZnS quantum dots in the presence of strong quantum confinement effects as a function of pressure. We find the pressure coefficients of quantum dots to be highly size-dependent and reduced by as much as 23% in comparison to the bulk value of 63 meV/GPa obtained from density functional theory calculations. The many-body excitonic effects on the quantum dot pressure coefficients are found to be marginal. The absolute gap deformation potential of quantum dots originates mainly from the energy change of the lowest unoccupied molecular orbital state. Finally, we find that the exciton spin-splitting increases nearly linearly as a function of applied pressure.

Deriving k·p parameters from full-Brillouin-zone descriptions: A finite-element envelope function model for quantum-confined wurtzite nanostructures

We present a multiband envelope-function model for wurtzite nanostructures based on a rigorous numerical procedure to determine operator ordering and band parameters from nonlocal empirical pseudopotential calculations. The proposed approach, implemented within a finite-element scheme, leads to well-posed, numerically stable envelope equations that accurately reproduce full-Brillouin-zone subband dispersions of quantum systems. Although demonstrated here for III-nitride nonlocal empirical pseudopotentials, the model provides a general theoretical framework applicable to ab initio electronic structures of wurtzite semiconductors.

An efficient atomistic quantum mechanical simulation on InAs band-to-band tunneling field-effect transistors

We have presented a fully atomistic quantum mechanical simulation method on band-to-band tunneling (BTBT) field-effect transistors (FETs). Our simulation approach is based on the linear combination of bulk band method with empirical pseudopotentials, which is an atomist method beyond the effective-mass approximation or k.p perturbation method, and can be used to simulate real-size devices (∼105 atoms) efficiently (∼5 h on a few computational cores). Using this approach, we studied the InAs dual-gate BTBT FETs. The I-V characteristics from our approach agree very well with the tight-binding non-equilibrium Green's function results, yet our method costs much less computationally. In addition, we have studied ways to increase the tunneling current and analyzed the effects of different mechanisms for that purpose.

Theoretical Study of the Gate Leakage Current in Sub-10-nm Field-Effect Transistors

Scaling field-effect transistors (FETs) with conventional semiconductor channels requires a reduction of the body or fin thickness or of the diameter of the nanowire (NW) channel. We present a theoretical study showing that the increase of the ground-state sub-band energy induced by the quantum confinement associated with this scaling results in a dramatic reduction of the barrier at the channel/gate-insulator interface, which causes an increase of the leakage current across the gate insulator. We have studied the problem using scaling rules extracted from the 2011 International Technology Roadmap for Semiconductors (ITRS)-Roadmap (finding them excessively relaxed) and using more strict scaling rules from the literature confirmed by simulations of 5-nm gate-length III-V FETs. Employing local empirical pseudopotentials to calculate the electronic structure of Si and InAs thin bodies, the leakage gate current in the ON-state is shown to reach worrisome values at gate lengths of about 5 nm. This suggests that 1-D channels (i.e., NWs), but especially channels based on intrinsically 2-D (e.g., graphene/graphane or transition-metals dichalcogenides) or 1-D (e.g., carbon nanotubes) structures, are required to push scaling toward the 5-nm node.

(Invited) Pseudopotential-Based Study of Electron Transport in Low-Dimensionality Nanostructures

We argue that intrinsically low-dimensionality materials may be needed to scale VLSI devices beyond 10 nm. We present examples of the use of empirical pseudopotentials to study the electronic structure and transport materials such as thin semiconductor bodies used in scaled VLSI devices, graphene, and nanoribbons.