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QuantumATK: An integrated platform of electronic and atomic-scale modelling tools

Søren Smidstrup, Troels Markussen, Pieter Vancraeyveld, Jess Wellendorff, Julian Schneider, Tue Gunst, Brecht Verstichel, Daniele Stradi, Petr A. Khomyakov, Ulrik G. Vej-Hansen, Maeng-Eun Lee, Samuel T. Chill, Filip Rasmussen, Gabriele Penazzi, Fabiano Corsetti, Ari Ojanperä, Kristian Jensen, Mattias L. N. Palsgaard, Umberto Martinez, Anders Blom, Mads Brandbyge, Kurt Stokbro

arXiv:1905.02794v2cond-mat.mtrl-scicond-mat.mes-hall

TL;DR

Atomic-scale modelling spans methods with different accuracy, applicability, and computational cost, motivating an integrated platform that avoids fragmented workflows. This paper presents QuantumATK as a unified environment combining multiple simulation engines and modules, and demonstrates that integration through application examples including transport, ion drift, and alloy electronic structure.

  • Problem

    Atomic-scale modelling requires complementary methods across applications, but separate tools create substantial installation, learning, and interoperability burdens.

  • Method

    The paper provides a general overview of QuantumATK, an integrated platform combining force fields, semi-empirical methods, DFT engines, and advanced modules through a common workflow environment.

  • Results

    The platform demonstrates combined simulation workflows through applications including electron transport, lithium-ion drift under an electric field, and composition-dependent SiGe electronic structure.

  • Takeaways & Limitations

    QuantumATK supports integrated atomic-scale modelling across semiconductor devices, batteries, materials science, and other application areas.

Abstract

from arXiv · show

QuantumATK is an integrated set of atomic-scale modelling tools developed since 2003 by professional software engineers in collaboration with academic researchers. While different aspects and individual modules of the platform have been previously presented, the purpose of this paper is to give a general overview of the platform. The QuantumATK simulation engines enable electronic-structure calculations using density functional theory or tight-binding model Hamiltonians, and also offers bonded or reactive empirical force fields in many different parametrizations. Density functional theory is implemented using either a plane-wave basis or expansion of electronic states in a linear combination of atomic orbitals. The platform includes a long list of advanced modules, including Green's-function methods for electron transport simulations and surface calculations, first-principles electron-phonon and electron-photon couplings, simulation of atomic-scale heat transport, ion dynamics, spintronics, optical properties of materials, static polarization, and more. Seamless integration of the different simulation engines into a common platform allows for easy combination of different simulation methods into complex workflows. Besides giving a general overview and presenting a number of implementation details not previously published, we also present four different application examples. These are calculations of the phonon-limited mobility of Cu, Ag and Au, electron transport in a gated 2D device, multi-model simulation of lithium ion drift through a battery cathode in an external electric field, and electronic-structure calculations of the composition-dependent band gap of SiGe alloys.

I. INTRODUCTION

QuantumATK addresses the fragmentation and scale range of atomic-scale modelling by integrating force fields, semi-empirical methods, and several DFT approaches into one platform. The paper introduces this unified toolbox, its scripting and parallel-computing infrastructure, and application-oriented workflows.

  • Motivation: Atomic-scale modelling supports research across semiconductors, batteries, catalysis, renewable energy, pharmaceuticals, and advanced materials, with a reported typical return on investment of around 5:1.The authors expect economic benefits to increase with more advanced algorithms and powerful computers.
  • Motivation: Atomic-scale simulations and materials screening reduce experimental trial-and-error by focusing investigations on promising designs and material systems.Simulations expose underlying atomic-scale processes, while screening evaluates properties across large material pools.
  • Platform scope: QuantumATK covers force fields, semi-empirical methods, and several DFT flavors across the range of atomic-scale simulation methodologies relevant to semiconductor and materials research.The platform includes both LCAO and plane-wave DFT representations.
  • Platform scope: The platform aims to make complementary simulation methods easy to access and combine, avoiding the installation, learning, and interoperability burdens of separate tools.QuantumATK is presented as a commercially developed platform intended to circumvent these integration issues.
  • Platform implementation: QuantumATK provides a GUI and Python scripting frontend within a unified framework supporting multiphysics and multiscale problems in devices and materials.Its C++ modules with Python bindings expose simulation engines through ATK-Python, while computationally demanding modules support parallel execution.
  • Paper scope: The paper gives a general platform overview and application examples showing how different simulation engines can complement one another in complex workflows.The examples span transport, phonon properties, ion dynamics, polarization, magnetic anisotropy, and related modules.

A. LCAO Representation

QuantumATK represents Kohn–Sham electronic states with either localized atomic orbitals or plane waves, then obtains densities through matrix-based or Green’s-function procedures. The comparison highlights a system-size-dependent performance trade-off between the two representations.

  • LCAO Representation: DFT-LCAO expands Kohn–Sham eigenfunctions in finite-range atomic-like basis functions, producing a localized matrix representation of the Kohn–Sham Hamiltonian.This representation supports molecules, bulk materials, interfaces, and nanoscaled devices.
  • LCAO Representation: For molecules and bulk systems, diagonalizing the Hamiltonian yields the density matrix, while device and surface densities are calculated with NEGF.The electron density is then computed from the density matrix on a regular real-space grid.
  • PW Representation: The plane-wave method expands Kohn–Sham eigenfunctions in reciprocal-lattice basis functions, with the included wave vectors controlled by the kinetic-energy cutoff Ecut.The cutoff determines the upper threshold for reciprocal-lattice-vector lengths.
  • PW Representation: Plane waves are efficient for relatively small bulk systems but inefficient for low-dimensional systems with large vacuum regions and incompatible with DFT-NEGF transport calculations.LCAO is more suitable for open boundaries and large systems.
  • PW Representation: For gold melts, plane waves are efficient for smaller systems, whereas LCAO can be more than an order of magnitude faster above 100 atoms.The comparison measures CPU time for 10 self-consistent-field iterations using different LCAO basis sets.

C. Pseudopotentials and LCAO Basis Sets

QuantumATK combines pseudopotentials and systematically constructed LCAO basis sets with multiple exchange-correlation approaches to balance accuracy, computational cost, and semiconductor band-gap performance.

  • QuantumATK supports scalar-relativistic and fully relativistic norm-conserving pseudopotentials, with PAW potentials available in ATK-PlaneWave.
  • Built-in pseudopotential databases cover elements up to Z = 83, excluding lanthanides, using SG15 and PseudoDojo sets.
  • QuantumATK constructs Ultra, High, and Medium LCAO basis sets by progressively reducing orbital range or number while controlling energy or overlap changes.
  • High and Ultra LCAO calculations have accuracy close to plane-wave calculations, while Medium reduces computational cost by factors of 2–4 or 10–20 relative to larger basis sets.
  • QuantumATK provides LDA, GGA, meta-GGA, HSE06, DFT-1/2, TB09, and PPS approaches for electronic-structure calculations and band-gap improvement.
  • DFT-1/2 can improve band gaps at almost no extra computational cost but contains empirical parameters, has limitations for some antiferromagnetic oxides, and does not provide reliable forces or stresses.

E. Boundary Conditions and Poisson Solvers

QuantumATK solves electrostatics with configurable boundary conditions and Poisson solvers matched to system geometry, periodicity, and material regions.

  • Boundary conditions: QuantumATK implements multipole, periodic, Dirichlet, and Neumann boundary conditions, including mixed combinations on simulation-cell facets.
  • Boundary conditions: Dirichlet conditions fix the boundary potential, whereas Neumann conditions fix its normal derivative.
  • Boundary conditions: Multipole conditions suit molecules, periodic conditions suit bulk materials, and mixed conditions support slab and surface calculations.
  • Boundary conditions: Two-probe device simulations use Dirichlet conditions at electrode boundaries and may use periodic conditions perpendicular to transport.
  • Poisson solvers: For periodic or all-Neumann systems, QuantumATK sets the average Hartree potential to zero to remove the additive-constant ambiguity.
  • Poisson solvers: FFT solvers handle fully periodic systems efficiently, while mixed-dimensional cases use 2D FFT combined with 1D finite differences.

V. SEMI-EMPIRICAL MODELS

ATK-SE provides computationally efficient tight-binding models with optional self-consistent charge and spin corrections, while sharing workflows with force-field and DFT engines.

  • Model framework: ATK-SE uses semi-empirical tight-binding Hamiltonians that can include self-consistent corrections for charge fluctuations and spin polarization.
  • Model framework: Supported models include Slater–Koster and environment-dependent parameterizations, with orthogonal or non-orthogonal Hamiltonians and different interaction ranges.
  • Self-consistent corrections: Self-consistent corrections assign Gaussian orbital charges from changes in Mulliken populations relative to a reference system.
  • Self-consistent corrections: ATK-SE supports spin polarization through spin-dependent Mulliken populations and database-provided shell-dependent splitting parameters.
  • Computational role: Tight-binding methods reduce computational expense through smaller Hamiltonians, provided the semi-empirical parametrization is appropriate for the simulation.
  • Integrated workflows: QuantumATK also integrates force-field models, including more than 300 predefined literature parameter sets and customizable subsystem combinations.

B. Global Structural Optimization

QuantumATK combines structural optimization, molecular dynamics, rare-event methods, and vibrational analysis to model equilibrium structures and dynamic atomic processes.

  • Global Structural Optimization: A genetic algorithm searches for globally stable crystal structures by evolving randomly generated configurations through genetic operators.
  • Global Structural Optimization: The NEB method finds minimum-energy paths between stable configurations, with climbing-image optimization and IDPP-generated initial images available.
  • Molecular Dynamics: QuantumATK supports NVE, NVT, and NPT molecular dynamics using velocity-Verlet integration and thermostat or barostat controls.
  • Molecular Dynamics: Pre-step and post-step Python hooks can modify configurations, forces, or stresses during molecular dynamics for constraints and custom analyses.
  • Molecular Dynamics: Metadynamics and RNEMD are available through predefined hooks, with PLUMED integration extending metadynamics functionality.
  • Adaptive Kinetic Monte Carlo: Adaptive kinetic Monte Carlo locates product states with high-temperature MD, determines saddle points with NEB, and selects reactions using KMC.
  • Vibrational Analysis: Vibrational modes and phonon densities of states are obtained from dynamical matrices computed using finite-difference force constants.
  • Vibrational Analysis: ATK-LCAO and ATK-ForceField produce closely agreeing vibrational properties for Cu, Ag, and Au, with dispersions following the same trends.

D. Electron-Phonon Coupling

QuantumATK computes electron-phonon coupling and uses it to obtain transport properties, including phonon-limited mobilities and metallic resistivity. Its workflow combines calculated scattering rates with efficient k- and q-point integration strategies.

  • Electron-Phonon Coupling: Electron-phonon coupling is used to calculate bulk transport coefficients and inelastic electron scattering in two-probe devices.QuantumATK obtains the coupling from Hamiltonian derivatives with respect to atomic positions and transforms the result into electron and phonon states.
  • Transport Coefficients: QuantumATK supports Gaussian and tetrahedron methods for q-integration, with the tetrahedron method especially efficient for metals.The Gaussian approach broadens delta functions, whereas the tetrahedron method treats the integral similarly to a density-of-states calculation.
  • Transport Coefficients: A two-step sampling procedure reduces transport calculations by reusing an energy-dependent isotropic scattering rate on a dense k-point grid.The initial calculation identifies relevant states and generates the scattering rate; the second evaluates velocities and effective masses on the finer grid.
  • Transport Coefficients: The approximation is suitable when scattering rates vary slowly across the Fermi surface, particularly for metals.For semiconductors and semimetals, QuantumATK uses direct integration, while metals can use tetrahedron integration.
  • Transport Coefficients: Predefined energy-dependent scattering rates can add mechanisms such as impurity scattering to electron-phonon scattering.The framework also supports constant-relaxation-time calculations, although more accurate relaxation-time models are needed for quantitative predictions.

IX. POLARIZATION AND BERRY PHASE

QuantumATK calculates polarization and polarization-derived response properties using ionic and electronic contributions, with the electronic part obtained from Berry phases. The implementation supports piezoelectric and Born effective-charge calculations validated against reference results.

  • Polarization: Polarization is relevant to ferroelectric and piezoelectric materials because it responds to electric fields or mechanical strain.The paper distinguishes ionic and electronic contributions to the total polarization.
  • Polarization: The ionic polarization contribution is computed as a classical electrostatic sum over valence charges and ionic positions.The sum is normalized by the unit-cell volume.
  • Berry Phase: The electronic polarization contribution is obtained from Berry phases evaluated along reciprocal-space lines parallel to a lattice vector.The Berry-phase calculation uses k-points in planes perpendicular to the chosen lattice direction and overlap integrals along that direction.
  • Berry Phase: Because polarization is defined modulo a polarization quantum, measurable quantities depend on changes between values calculated on the same polarization branch.The polarization therefore forms a lattice of equivalent values rather than a single absolute value.
  • Derived Quantities: QuantumATK supports polarization, piezoelectric tensors, and Born effective charges, whose calculated values agree well with reference calculations for nitrides and GaAs.Table VIII reports Born effective charges and piezoelectric tensor components for III-V wurtzite nitrides and zincblende GaAs.

2. For each of the considered spin orientations

QuantumATK calculates magnetocrystalline anisotropy using force-theorem workflows and decomposes the result into atom- and orbital-projected contributions. It also provides an integrated device-simulation framework for bulk electrodes and two-probe systems.

  • MAE Workflow: The force-theorem workflow begins with a selfconsistent spin-polarized calculation followed by non-selfconsistent SOC calculations for specified spin directions.The resulting band-energy differences are used to calculate the total MAE and its projections.
  • MAE Projections: MAE projections use eigenstates, overlap matrices, and projection matrices to resolve contributions from selected atoms or orbitals.The projection matrix selects the orbitals of interest through diagonal entries equal to one or zero.
  • MAE Results: QuantumATK MAEs agree well across four codes for Fe-based L10 alloys, except FeAu, where LCAO values are smaller than plane-wave results.The paper attributes the FeAu discrepancy to insufficient accuracy of the LCAO basis representation.
  • MAE Results: 1.41 mJ/m2 is the calculated Fe/MgO interfacial anisotropy constant, compared with 1.40 mJ/m2 from a previous report.Interface Fe atoms favor perpendicular magnetization, and the interfacial MAE peak is attributed primarily to Fe d-orbital contributions.
  • Device Systems: QuantumATK is designed to simulate both bulk and device systems, including two-probe geometries with left and right electrodes surrounding a central region.The electrodes are treated as bulk systems, while their chemical potentials and potential alignment define the device boundary conditions.

A. NEGF Method

QuantumATK uses nonequilibrium Green’s functions to calculate the steady-state density matrix of a device central region coupled to left and right electrodes. The method combines electrode self-energies, Green’s functions, and equilibrium/non-equilibrium energy integration.

  • Density Matrix: QuantumATK uses NEGF instead of explicit scattering states to calculate the non-equilibrium electron density, with formally equivalent results.The density matrix is split into left and right electrode contributions.
  • Density Matrix: The left electrode contribution uses a spectral density matrix built from the retarded Green’s function and the electrode broadening function.The broadening function is determined by the left electrode self-energy, while the electrode distribution remains Fermi–Dirac.
  • Spintronics: The NEGF implementation supports noncollinear spin and spin-orbit coupling for spintronic device simulations.The paper identifies spin-transfer-torque device physics as an example application.
  • Green’s Function: The retarded Green’s function is calculated from the central-region Hamiltonian and overlap matrices after adding electrode self-energies.The self-energies describe how electrode states affect the central-region electronic structure.
  • Implementation: Sparse block diagonal inversion gives an O(N) operation in the number of diagonal blocks for calculating the density matrix.QuantumATK also exploits electrode sparsity through a recursion-based self-energy algorithm.
  • Energy Integration: The energy integral is divided into an equilibrium contour contribution and a real-axis non-equilibrium contribution restricted to the bias window.A double-contour scheme weights the equilibrium parts more heavily because contour integration is usually more accurate.
  • Bound States: Bound states below the lower chemical potential receive full equilibrium weight, while states inside the bias window receive position-dependent fractional weighting.The occupation of a bound state depends on its coupling to the electrodes and on physical occupation mechanisms such as electron-phonon scattering.

E. Spill-in Terms

QuantumATK accounts for electrode-boundary effects in device calculations through spill-in terms and extends transport workflows to electron-phonon scattering and thermal-displacement approximations.

  • Spill-in terms: Spill-in terms from electrode blocks are required to calculate electron density correctly near central-region boundaries.The terms involving DLL, DLC, DCR, and DRR supplement the central-region density matrix.
  • Spill-in terms: QuantumATK includes all spill-in terms for electron density and Hamiltonian integrals, improving stability and convergence in device simulations.
  • Device energetics: Two-probe devices are open systems whose left and right reservoirs can have different chemical potentials, requiring a grand canonical description.At finite bias, the particle terms in the grand potential affect forces, while current-induced forces are neglected in the simulations.
  • Transport calculations: Transmission spectra obtained from the retarded Green’s function provide current and differential conductance, with inelastic contributions calculated using the LOE method.The LOE approach uses first-Born perturbation theory and requires the dynamical matrix and Hamiltonian derivatives with respect to central-region atomic positions.
  • Special thermal displacement method: The STD method replaces thermal configuration averaging with one representative displaced configuration, reducing inelastic transport cost to that of ordinary elastic transmission.Opposite phonon phases make phonon-phonon correlations average to zero, producing a spectrum similar to thermal averaging of single-phonon excitations.
  • Special thermal displacement method: The STD method is formally accurate when the central region is a large unit cell generated by repeating a basic unit cell.

I. Thermoelectric Transport

QuantumATK computes thermoelectric transport coefficients from electron and phonon transmission spectra and supports efficient multi-model workflows. It also provides first-order electron-photon transport calculations, with phonon effects available through the STD method.

  • Thermoelectric coefficients: The thermoelectric figure of merit ZT measures conversion of a temperature difference into a voltage difference.
  • Thermoelectric coefficients: QuantumATK uses linear-response theory with electron and phonon transmission spectra to calculate thermoelectric coefficients and the Peltier coefficient.The thermal conductivity includes electronic and phononic contributions, κ = κe + κph.
  • Thermal transport: The electronic heat current is calculated similarly to the electronic current, with an additional energy factor ε − µ in the integral.Here µ is the average chemical potential, µ = (µL + µR)/2.
  • Thermoelectric workflows: Electron transmission can be computed with DFT or tight binding while phonon transmission uses a force field, forming a computationally efficient thermoelectric workflow.
  • Photocurrent: QuantumATK calculates photocurrent using first-order perturbation theory within the first Born approximation by adding electron-light coupling to the Hamiltonian.The interaction uses the electromagnetic vector potential of a monochromatic light source.
  • Photocurrent: Phonon effects can be included through the STD method, which is important for describing photocurrent in indirect-band-gap materials such as silicon.

A. Bulk DFT and Semi-Empirical Simulations

QuantumATK combines multiple simulation engines, parallel execution, scripting, and GUI workflows for bulk, device, and large-scale atomistic modelling. The supplied examples show performance trade-offs among representations and how atomistic device simulations connect electrostatics with transport behavior.

  • QuantumATK distributes bulk DFT work over k-points with MPI and can add shared-memory threading within each process.
  • LCAO is faster and uses less memory than plane waves for the 64-atom SiGe supercell, but its scaling degrades when cores exceed k-points.
  • NEGF speedup generally comes from parallelizing over contour points, whereas threading reduces memory with comparatively smaller computational speedup.
  • Python Scripting: Python scripting exposes developer-level functionality, including advanced workflows, analysis, new energy terms, and access to internal quantities.
  • Workflow Integration: Study objects coordinate complex task combinations, parallel execution, and resumption after interrupted calculations.
  • Workflow Integration: NanoLab connects geometry building, scripting, job submission, visualization, databases, and third-party codes through GUI tools and plugins.
  • 2D Device Transport: In a gated 2D TFET, asymmetric metallic contacts create an additional built-in field and alter local electrostatics and density of states.
  • 2D Device Transport: The resulting effective barrier changes explain why asymmetric contacts produce stronger gate dependence of reverse-bias current than symmetric contacts.

B. Phonon-limited Mobility of Metals

QuantumATK applies first-principles transport and multi-model dynamics to atomistic materials problems. The examples connect phonon scattering with metal resistivity and combine force fields, DFT, temperature, and electric fields to study lithium drift.

  • Phonon-limited Mobility: First-principles Boltzmann transport calculations evaluate phonon-limited resistivity in FCC Cu, Ag, and Au using electron-phonon coupling constants.
  • Phonon-limited Mobility: Tetrahedron integration makes the computationally demanding electron- and phonon-wave-vector integration efficient enough for materials screening.
  • Phonon-limited Mobility: Resistivity rises with temperature as phonon occupation increases and becomes linear above each metal’s Debye temperature.
  • Phonon-limited Mobility: The calculations reproduce the experimental ranking of Au, Cu, and Ag resistivities, while 1 nm nanowires show substantially increased resistivity.
  • Multi-model Dynamics: Without an applied field, lithium hopping is rare at both 300 K and 1000 K in the reported simulations.
  • Multi-model Dynamics: At 300 K, fields Dy ≥0.20 V/˚A increase displacement steadily, indicating predominantly field-induced drift.
  • Multi-model Dynamics: At 1000 K, stronger lattice perturbations increase ion-lattice collisions and reduce lithium motion relative to 300 K for comparable fields.
  • Multi-model Dynamics: The LiFePO4 study combines classical force-field molecular dynamics with DFT-derived time-dependent charges to model field-driven lithium drift.

D. Electronic Structure of Binary Alloys

The SiGe alloy example uses special quasi-random structures to model composition-dependent electronic structure with reduced configurational sampling. HSE06 and PPS-PBE provide complementary accuracy and efficiency across band-energy calculations.

  • Motivation: Traditional random-alloy simulations require multiple large supercells, making composition-dependent properties computationally challenging.
  • Method: The SQS method captures configurational averaging with one 64-atom supercell across the full Si1−xGex composition range.
  • Method: A genetic algorithm generates SQS configurations by fitting pair, triplet, and quadruplet correlation functions of the alloy.
  • Results: SQS band energies closely match the more expensive random-alloy approach, while the SiGe band-gap transition is predicted near x ∼0.88 with PPS-PBE and x ∼0.82 with HSE06.
  • Results: PPS-PBE band gaps agree with room-temperature experiments within ∼50 meV across the Ge-composition range, whereas HSE06 better matches low-temperature experiments.
  • Results: PPS-PBE and HSE06 produce broadly similar bulk Si and Ge band structures near the Fermi energy.
  • Results: HSE06 more accurately describes band-gap bowing, while PPS-PBE offers a computationally efficient alternative when only bands near the Fermi level matter.
  • Platform Context: The paper presents the alloy example as part of QuantumATK’s broader integrated platform and application range.

Appendix A: Computational Details

The appendix specifies the amorphous Al2O3 systems used to compare simulation-method speed across increasing system sizes. The structures span 5 to 30720 atoms and are generated by high-temperature randomization followed by quenching.

  • The amorphous Al2O3 benchmark contains systems ranging from 5 to 30720 atoms at a constant density of 2.81 g/cm3.
  • Structures were generated by randomizing at 5000 K and then quenching to 0 K.
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