Atomistic Tight Binding Research Articles

Bounds to electron spin qubit variability for scalable CMOS architectures

Spins of electrons in silicon MOS quantum dots combine exquisite quantum properties and scalable fabrication. In the age of quantum technology, however, the metrics that crowned Si/SiO2 as the microelectronics standard need to be reassessed with respect to their impact upon qubit performance. We chart spin qubit variability due to the unavoidable atomic-scale roughness of the Si/SiO2 interface, compiling experiments across 12 devices, and develop theoretical tools to analyse these results. Atomistic tight binding and path integral Monte Carlo methods are adapted to describe fluctuations in devices with millions of atoms by directly analysing their wavefunctions and electron paths instead of their energy spectra. We correlate the effect of roughness with the variability in qubit position, deformation, valley splitting, valley phase, spin-orbit coupling and exchange coupling. These variabilities are found to be bounded, and they lie within the tolerances for scalable architectures for quantum computing as long as robust control methods are incorporated.

Impact of Channel Thickness on the Performance of GaAs and GaSb DG-JLMOSFETs: An Atomistic Tight Binding Based Evaluation

In this paper, the performance of GaAs and GaSb based sub-10 nm double-gate junctionless metal-oxide-semiconductor field-effect transistors (DG-JLMOSFETs) have been studied for high-performance switching applications. The quantum transmitting boundary method (QTBM) has been considered for electron transport, and the band structures are accounted for sp3d5s* tight-binding modeling. The channel thickness, t <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ch</sub> is varied from 1.7 to 4.7 nm to evaluate the device figure of merits (FOMs). The thinner channel’s device shows a lower OFF-state current, while the ticker channel device allows a higher ON-state current. The threshold voltage is approximately 0.4 V for GaAs DG-JLMOSFETs with t <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ch</sub> = 1.7 nm, whereas it reduces to ~0.05 V for that of t <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ch</sub> = 4.7 nm. Similar characteristics have been shown in GaSb devices. Besides, a significant impact of t <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ch</sub> on the subthreshold swing (SS) and drain-induced barrier lowering (DIBL) is found in GaSb DG-JLMOSFETs compared with those of GaAs devices. The devices show a higher leakage-power dissipation in both channel materials and low-intrinsic delay for thicker t <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ch</sub> due to a substantial amount of energy drop. The above results indicate that III-V-based DG-JLMOSFETs are very promising for next-generation high-performance switching technology.

Simulating random alloy effects in III-nitride light emitting diodes

Statistical fluctuations in the alloy composition on the atomic scale can have important effects on electronic and optical properties of bulk materials and devices. In particular, carrier localization induced by alloy disorder has been a much discussed topic during the last decade with regard to III-nitride light emitting diodes (LEDs). Much experimental and theoretical work has been dedicated to the study of the effects of alloy disorder on carrier localization and finally on the efficiency and transport properties in such devices. Modeling approaches range from empirical analytical models down to atomistic ab initio ones, each with its advantages and disadvantages. In this tutorial, we discuss the simulation of alloy fluctuations in nitride quantum well LEDs by combining continuum device models and an atomistic empirical tight binding model, which provides a suitable compromise between atomic precision and computational effort.

Electrostatic quantum dot confinement in phosphorene

We consider states localized by electrostatic potentials in phosphorene using an atomistic tight binding approach. From the results of the tight-binding calculations of the confined states we extract effective masses for the conduction band electrons in the armchair and zigzag directions. The masses derived in this way are used for a simple single-band effective mass model which, as we find, reproduces very well the tight-binding energy spectrum in external magnetic field, the probability densities and the interaction effects. Both methods produce Wigner crystallization for the ground-state of the electron pair with the single-electron islands separated in the armchair direction already for small quantum dots.

Band-tail Formation and Band-gap Narrowing Driven by Polar Optical Phonons and Charged Impurities in Atomically Resolved III-V Semiconductors and Nanodevices

High-doping induced Urbach tails and band gap narrowing play a significant role in determining the performance of tunneling devices and optoelectronic devices such as tunnel field-effect transistors (TFETs), Esaki diodes and light-emitting diodes. In this work, Urbach tails and band gap narrowing values are calculated explicitly for GaAs, InAs, GaSb and GaN as well as ultra-thin bodies and nanowires of the same. Electrons are solved in the non-equilibrium Green's function method in multi-band atomistic tight binding. Scattering on polar optical phonons and charged impurities is solved in the self-consistent Born approximation. The corresponding nonlocal scattering self-energies as well as their numerically efficient formulations are introduced for ultra-thin bodies and nanowires. Predicted Urbach band tails and conduction band gap narrowing agree well with experimental literature for a range of temperatures and doping concentrations. Polynomial fits of the Urbach tail and band gap narrowing as a function of doping are tabulated for quick reference.

Atomistic tight binding study of quantum confined Stark effect in GaBixAs1−x/GaAs quantum wells

Recently, there has been tremendous research interest in novel bismide semiconductor materials (such as GaBixAs1−x) for wavelength-engineered, low-loss optoelectronic devices. We report a study of the quantum confined Stark effect (QCSE) computed for GaBixAs1−x/GaAs quantum well (QW) structures based on large-scale atomistic tight-binding calculations. A comprehensive investigation of the QCSE as a function of the applied electric field orientations and the QW Bi fractions reveals unconventional character of the Stark shift at low Bi compositions (). This atypical QCSE is attributed to a strong confinement of the ground-state hole wave functions due to the presence of Bi clusters. At technologically-relevant large Bi fractions (10%), the impact of Bi clustering on the electronic structure is found to be weak, leading to a quadratic Stark shift of the ground-state transition wavelength, similar to previously observed in other conventional III–V materials. Our results provide useful insights for the understanding of the electric field dependence of the electronic and optical properties of GaBixAs1−x/GaAs QWs, and will be important for the design of devices in the optoelectronics and spintronics areas of research.

Atomistic Tight-Binding Study of Contact Resistivity in Si/SiGe PMOS Schottky Contacts

The metal-semiconductor contact resistivity has started to play a critical role for the overall device performance as Si is reaching 10-nm size ranges. The International Technology Roadmap for Semiconductors (ITRS) target predicts a requirement of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-9</sup> Ω·cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> by 2023 which has been a challenging target to achieve. This paper explores the impact of doping concentration, Schottky barrier height, strain, and SiGe mole fraction on the resistivity of Si/SiGe p-type metal-oxide semiconductor (PMOS) contacts with 20-band atomistic tight binding quantum transport simulations. Commonly used simple effective mass approximation models are shown to overestimate the resistivity values. The predicted model results are compared with experimental data and the device parameters needed to achieve 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-9</sup> Ω·cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> are identified.

Resonant photoluminescence studies of carrier localisation in c-plane InGaN/GaN quantum well structures

In this paper we report on changes in the form of the low temperature (12 K) photoluminescence spectra of an InGaN/GaN quantum well structure as a function of excitation photon energy. As the photon energy is progressively reduced we observe at a critical energy a change in the form of the spectra from one which is determined by the occupation of the complete distribution of hole localisation centres to one which is determined by the resonant excitation of specific localisation sites. This change is governed by an effective mobility edge whereby the photo-excited holes remain localised at their initial energy and are prevented from scattering to other localisation sites. This assignment is confirmed by the results of atomistic tight binding calculations which show that the wave function overlap of the lowest lying localised holes with other hole states is low compared with the overlap of higher lying hole states with other higher lying hole states.

Grain-Boundary Resistance in Copper Interconnects: From an Atomistic Model to a Neural Network

Orientation effects on the resistivity of copper grain boundaries are studied systematically with two different atomistic tight binding methods. A methodology is developed to model the resistivity of grain boundaries using the Embedded Atom Model, tight binding methods and non-equilibrum Green's functions (NEGF). The methodology is validated against first principles calculations for small, ultra-thin body grain boundaries (<5nm) with 6.4% deviation in the resistivity. A statistical ensemble of 600 large, random structures with grains is studied. For structures with three grains, it is found that the distribution of resistivities is close to normal. Finally, a compact model for grain boundary resistivity is constructed based on a neural network.

Imaging backscattering in graphene quantum point contacts

We study graphene quantum point contacts (QPC) and imaging of the backscattering of the Fermi level wave function by potential introduced by a scanning probe. We consider both etched single-layer QPCs as well as the ones formed by bilayer patches deposited at the sides of the monolayer conducting channel using an atomistic tight binding approach. A computational method is developed to effectively simulate an infinite graphene plane outside the QPC using a computational box of a finite size. We demonstrate that in spite of the Klein phenomenon interference due to the backscattering at a circular n-p junction induced by the probe potential is visible in spatial maps of conductance as functions of the probe position.

Numerical simulation of vertical tunneling transistor with bilayer graphene as source and drain regions

In this paper, the electrical characteristics of vertical tunneling bilayer graphene field effect transistor (VTBGFET) are theoretically investigated. We evaluate the device behavior using nonequilibrium Green's function (NEGF) formalism combined with an atomistic tight binding model. By using this method, we extract the most significant figures of merit such as ON/OFF current ratio, subthreshold swing, and intrinsic gate‐delay time.The results indicate that using a bilayer graphene instead of a monolayer graphene as the base material for the source and drain regions leads to a larger ON/OFF current ratio due to the presence of an energy bandgap in biased bilayer graphene. Also, the subthreshold swing of VTBGFET can be much lower than that of vertical tunneling monolayer graphene field‐effect transistor (VTMGFET). We find that the increase of the number of hBN layers enhances the ON/OFF current ratio but degrades the intrinsic gate‐delay time.

A computational study of vertical tunneling transistors based on graphene-WS2 heterostructure

In this paper, for the first time, we present a computational study on electrical characteristics of field effect tunneling transistors based on a vertical graphene-WS2 heterostructure and vertical graphene nanoribbon (GNR)-WS2 heterostructure (VTGNRFET). Our model uses the nonequilibrium Green's function formalism along with an atomistic tight binding (TB) method. The TB parameters are extracted by fitting the bandstructure to first principles results. We show that, due to the advantage of switching between tunneling and thermionic transport regimes, an improvement can be achieved in the electrical characteristics of the device. We find that the increase of the number of WS2 layers enhances the on/off conductance ratio but degrades the intrinsic gate-delay time. The results indicate that the on/off conductance ratio of VTGNRFET increases with decreasing the GNR width.

Atomistic theory of excitonic fine structure in InAs/InP nanowire quantum dot molecules

Nanowire quantum dots have peculiar electronic and optical properties. In this work we use atomistic tight binding to study excitonic spectra of artificial molecules formed by a double nanowire quantum dot. We demonstrate a key role of atomistic symmetry and nanowire substrate orientation rather than cylindrical shape symmetry of a nanowire and a molecule. In particular for $[001]$ nanowire orientation we observe a nonvanishing bright exciton splitting for a quasimolecule formed by two cylindrical quantum dots of different heights. This effect is due to interdot coupling that effectively reduces the overall symmetry, whereas single uncoupled $[001]$ quantum dots have zero fine structure splitting. We found that the same double quantum dot system grown on $[111]$ nanowire reveals no excitonic fine structure for all considered quantum dot distances and individual quantum dot heights. Further we demonstrate a pronounced, by several orders of magnitude, increase of the dark exciton optical activity in a quantum dot molecule as compared to a single quantum dot. For $[111]$ systems we also show spontaneous localization of single particle states in one of nominally identical quantum dots forming a molecule, which is mediated by strain and origins from the lack of the vertical inversion symmetry in $[111]$ nanostructures of overall ${C}_{3v}$ symmetry. Finally, we study lowering of symmetry due to alloy randomness that triggers nonzero excitonic fine structure and the dark exciton optical activity in realistic nanowire quantum dot molecules of intermixed composition.

The effect of uniaxial strain on the optical properties of monolayer molybdenum disulfide

In this paper, we present our numerical studies on the optical properties of the monolayer molybdenum disulfide (MoS2). In order to calculate the Hamiltonian of the MoS2 structure, an atomistic tight binding (TB) model is employed, which includes the nearest neighbors. The tight binding model takes into account , and orbitals of the Mo atoms and orbitals of the S atoms. In addition, the dielectric function and the optical conductivity of a monolayer MoS2 is calculated based on the atomistic tight binding Hamiltonian. It is found that the absorption spectrum can be characterized by two peaks, associated with energies which provide optical applications in the range of the visible regime. Uniaxial tensile strain leads to a red shift of the peaks in the spectrum of the dielectric function. The amount of the shift varies with the tensile strain almost linearly. In contrast, an applied compressive strain along the direction of the zigzag edge gives rise to a blue shift of the dielectric function.

Electric gating induced bandgaps and enhanced Seebeck effect in zigzag bilayer graphene ribbons

We theoretically investigate the effect of a transverse electric field generated by side gates and a vertical electric field generated by top/back gates on energy bands and transport properties of zigzag bilayer graphene ribbons (Bernal stacking). Using atomistic tight binding calculations and Green’s function formalism we demonstrate that a bandgap is opened when either field is applied and even enlarged under simultaneous influence of the two fields. Interestingly, although vertical electric fields are widely used to control the bandgap in bilayer graphene, here we show that transverse fields exhibit a more positive effect in terms of modulating a larger range of bandgap and retaining good electrical conductance. The Seebeck effect is also demonstrated to be enhanced strongly—by about 13 times for a zigzag bilayer graphene ribbon with 16 chain lines. These results may motivate new designs of devices made of bilayer graphene ribbons using electric gates.

Modified Dirac Hamiltonian for efficient quantum mechanical simulations of micron sized devices

Representing massless Dirac fermions on a spatial lattice poses a potential challenge known as the Fermion Doubling problem. Addition of a quadratic term to the Dirac Hamiltonian provides a possible way to circumvent this problem. We show that the modified Hamiltonian with the additional term results in a very small Hamiltonian matrix when discretized on a real space square lattice. The resulting Hamiltonian matrix is considerably more efficient for numerical simulations without sacrificing on accuracy and is several orders of magnitude faster than the atomistic tight binding model. Using this Hamiltonian and the non-equilibrium Green's function formalism, we show several transport phenomena in graphene, such as magnetic focusing, chiral tunneling in the ballistic limit, and conductivity in the diffusive limit in micron sized graphene devices. The modified Hamiltonian can be used for any system with massless Dirac fermions such as Topological Insulators, opening up a simulation domain that is not readily accessible otherwise.

Tunnel Field-Effect Transistors in 2-D Transition Metal Dichalcogenide Materials

In this work, the performance of Tunnel Field-Effect Transistors (TFETs) based on two-dimensional Transition Metal Dichalcogenide (TMD) materials is investigated by atomistic quantum transport simulations. One of the major challenges of TFETs is their low ON-currents. 2D material based TFETs can have tight gate control and high electric fields at the tunnel junction, and can in principle generate high ON-currents along with a sub-threshold swing smaller than 60 mV/dec. Our simulations reveal that high performance TMD TFETs, not only require good gate control, but also rely on the choice of the right channel material with optimum band gap, effective mass and source/drain doping level. Unlike previous works, a full band atomistic tight binding method is used self-consistently with 3D Poisson equation to simulate ballistic quantum transport in these devices. The effect of the choice of TMD material on the performance of the device and its transfer characteristics are discussed. Moreover, the criteria for high ON-currents are explained with a simple analytic model, showing the related fundamental factors. Finally, the subthreshold swing and energy-delay of these TFETs are compared with conventional CMOS devices.

Non-equilibrium Green's functions method: Non-trivial and disordered leads

The non-equilibrium Green's function algorithm requires contact self-energies to model charge injection and extraction. All existing approaches assume infinitely periodic leads attached to a possibly quite complex device. This contradicts today's realistic devices in which contacts are spatially inhomogeneous, chemically disordered, and impacting the overall device characteristics. This work extends the complex absorbing potentials method for arbitrary, ideal, or non-ideal leads in atomistic tight binding representation. The algorithm is demonstrated on a Si nanowire with periodic leads, a graphene nanoribbon with trumpet shape leads, and devices with leads of randomly alloyed Si0.5Ge0.5. It is found that alloy randomness in the leads can reduce the predicted ON-state current of Si0.5Ge0.5 transistors by 45% compared to conventional lead methods.

Large on/off current ratio in hybrid graphene/BN nanoribbons by transverse electric field-induced control of bandgap

We propose an approach to design efficient electronic switches based on Graphene/BN heterostructures. By means of atomistic Tight Binding simulations, we investigate heterostructures made of an armchair BN nanoribbon sided by two armchair graphene ribbons where a significant bandgap can be opened. In particular, we show that a bandgap of about 0.55 eV can be strongly suppressed by applying a relatively weak transverse electric field of 10 mV/A. Additionally, by using non-equilibrium Green's function simulation, we show that this effect can be used to control the current in electron devices even at small bias and small length. An on/off current ratio higher than 104 is achieved at room temperature.

Effects of interface disorder on valley splitting in SiGe/Si/SiGe quantum wells

A sharp potential barrier at the Si/SiGe interface introduces valley splitting (VS), which lifts the 2-fold valley degeneracy in strained SiGe/Si/SiGe quantum wells (QWs). This work examines in detail the effects of Si/SiGe interface disorder on the VS in an atomistic tight binding approach based on statistical sampling. VS is analyzed as a function of electric field, QW thickness, and simulation domain size. Strong electric fields push the electron wavefunctions into the SiGe buffer and introduce significant VS variations from device to device. A Gedankenexperiment with ordered alloys sheds light on the importance of different bonding configurations on VS. We conclude that a single SiGe band offset and effective mass cannot comprehend the complex Si/SiGe interface interactions that dominate VS.