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GaAs/AlAs (110) Valence Band Offset

1. Introduction

This tutorial calculates the valence band offset ΔE_v of the GaAs/AlAs (110) interface, reproducing the result of the following manuscript:

Manuscript

Yoyo Hinuma, Andreas Grüneis, Georg Kresse and Fumiyasu Oba, "Band alignment of semiconductors from density-functional theory and many-body perturbation theory", Physical Review B 90, 155405 (2014). DOI: 10.1103/PhysRevB.90.155405. 1

This tutorial builds upon the GaAs/AlAs (110) Strained Superlattice tutorial, where the superlattice and the two strained bulk cells are created. Here, the platform's valence band offset workflow runs Quantum ESPRESSO on all three, and the offset is assembled as in the manuscript: each bulk's valence band maximum E_VBM is measured from its own average potential V̄, and the superlattice gives the step in V̄ between the two materials,

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ΔE_v = (E_VBM − V̄)_GaAs − (E_VBM − V̄)_AlAs + (V̄_GaAs − V̄_AlAs)_superlattice

The manuscript gives ΔE_v = 0.45 eV at the Perdew–Burke–Ernzerhof (PBE) level, GaAs above AlAs (Table II).

2. Prerequisites

Before starting this tutorial, one of the following steps should be completed:

  1. Follow the GaAs/AlAs (110) Strained Superlattice tutorial, using the interface_3d_3d_gallium_arsenide_aluminum_arsenide.ipynb notebook embedded in its section 6, to create and save GaAs/AlAs (110) superlattice 12+12, GaAs (110) bulk strained and AlAs (110) bulk strained, OR
  2. Have the three materials saved in the uploads folder or in the account's materials collection

3. Workflow overview

The calculation consists of the following steps:

  1. Set up the environment and parameters: Configure the material names, the Density Functional Theory (DFT) model, and compute resources
  2. Authenticate and initialize API client: Connect to the platform
  3. Load materials: Import the superlattice and the two bulks, print their plane spacings
  4. Configure the model and k-grids: One DFT model, a k-grid per material from one k-point density
  5. Configure compute resources: Select the cluster, queue, and processor settings
  6. Configure the workflow: The model, a k-grid per material, and the band structures the valence band maxima are read from
  7. Run the job: One Valence Band Offset job, which runs a band structure and the electrostatic potential on each of the three materials
  8. Retrieve results: The valence band maxima and average potentials, the offset, and the potential across the superlattice
  9. Compare with the manuscript: Print the calculated values beside Hinuma et al.'s

4. Calculation parameters

this tutorial Hinuma et al.
Code Quantum ESPRESSO VASP
Functional PBE PBE
Pseudopotentials ultrasoft, Garrity–Bennett–Rabe–Vanderbilt (GBRV) library, Ga 3d in valence projector augmented-wave (PAW) potentials, Ga 3d frozen in the core
Cutoff 40 / 200 Ry 550 eV for the bulks, not stated for the interface
k-points 3.5 points per Å⁻¹: 6×4×1 for the 48-atom superlattice cell, 4×3×6 for the 8-atom (110) bulk cells 6×4×1 for the interface cell, 6×6×6 for the bulk cells
Bulk lattice constant 5.713 Å, the superlattice's, for both bulks experimental, GaAs 5.654 Å and AlAs 5.661 Å, related to the interface lattice through the vacuum level (Eq. 2)
Cell 12 + 12 planes, 48 atoms, a∥ = 5.713 Å, as built 11 + 11 layers, out-of-plane lattice and positions relaxed
Reference potential V̄ planar average of the electrostatic potential over one plane spacing at each block's centre local Kohn–Sham potential averaged in the PAW spheres at the atomic sites, middle third of each region
Spin–orbit not included included, as a Heyd–Scuseria–Ernzerhof (HSE) correction to each valence band maximum

5. Step-by-step instructions

5.1. Open the notebook

Navigate to the API examples repository and open the notebook:

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other/materials_designer/specific_examples/interface_3d_3d_gallium_arsenide_aluminum_arsenide_SIMULATION.ipynb

5.2. Configure parameters

Cells 1.2-1.4 set the material names, the compute resources, and the DFT model:

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# Names saved by interface_3d_3d_gallium_arsenide_aluminum_arsenide.ipynb.
SUPERLATTICE_NAME = "GaAs/AlAs (110) superlattice 12+12"
SUBSTRATE_BULK_NAME = "GaAs (110) bulk strained"
FILM_BULK_NAME = "AlAs (110) bulk strained"

CLUSTER_NAME = "001"  # specify full or partial name i.e. "cluster-001" to select
QUEUE_NAME = QueueName.OR
PPN = 16  # the OR queue allows at most 16 cores per node
TIME_LIMIT = "04:00:00"

MODEL_SUBTYPE = "gga"
FUNCTIONAL = "pbe"  # Hinuma et al. use PBE
PSEUDOPOTENTIAL_TYPE = "us"  # GBRV ultrasoft, the PBE family the platform publishes for Ga, Al and As
VALENCE_ELECTRONS_PER_ATOM = {"Ga": 19, "Al": 3, "As": 5}  # GBRV pseudopotentials, Ga with its 3p and 3d shells
BLOCK_LABEL = {SUBSTRATE_BULK_NAME: "GaAs", FILM_BULK_NAME: "AlAs"}
BLOCK_CATION = {SUBSTRATE_BULK_NAME: "Ga", FILM_BULK_NAME: "Al"}  # one cation per (110) plane marks each block
ECUTWFC = 40   # Ry, GBRV's recommended wavefunction cutoff
ECUTRHO = 200  # Ry, GBRV's recommended charge-density cutoff
ADDITIONAL_PARAMETERS = {"electrons": {"mixing_mode": "local-TF", "mixing_beta": 0.2, "electron_maxstep": 200}}  # the long cell needs local-TF mixing to converge
KPOINT_DENSITY = 3.5  # points per Å⁻¹: 6x4x1 on the superlattice as in the paper, an equivalent grid on the bulks

5.3. Run the notebook

Execute all cells by selecting Run > Run All from the menu.

The notebook first authenticates with the platform, then runs the steps listed in section 3.

5.4. Analyze results

Section 8.1 of the notebook prints each bulk's valence band maximum, its average potential and its gap, and the average potential of the GaAs and the AlAs block in the superlattice:

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GaAs (110) bulk strained: E_VBM = 6.8978 eV, V̄ = 9.3124 eV, E_VBM - V̄ = -2.4146 eV, gap +0.289 eV
  in the superlattice: V̄ = 8.4117 eV, averaged over 2.0198 Å centred at z = 0.0000 Å
AlAs (110) bulk strained: E_VBM = 4.6237 eV, V̄ = 7.6018 eV, E_VBM - V̄ = -2.9781 eV, gap +1.476 eV
  in the superlattice: V̄ = 8.5044 eV, averaged over 2.0198 Å centred at z = 24.2382 Å

The valence band maximum is the top of band N_electrons / 2 along each bulk's k-path, and the gap the bottom of the next band minus it. Each block is averaged over one plane spacing, one period of the potential, at its centre, away from both interfaces. Section 8.3 plots the potential across the superlattice with the bulk potentials overlaid.

The last cell prints the offset beside the manuscript's values:

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ΔE_v = 0.471 eV   paper 0.45 eV   deviation +4.6 %
GaAs valence band top above AlAs's   paper above
GaAs gap = 0.289 eV   paper 0.48 eV   deviation -39.8 %
AlAs gap = 1.476 eV   paper 1.32 eV   deviation +11.8 %
(E_VBM - V̄)_GaAs - (E_VBM - V̄)_AlAs = +0.56 eV
(V̄_GaAs - V̄_AlAs)_superlattice = -0.09 eV

6. Expected results

The manuscript's Table II lists ΔE_v = 0.45 eV for GaAs/AlAs at the PBE level, GaAs above AlAs, together with the HSE and GW values and the experimental values from 0.15 to 0.55 eV for this pair:

GaAs/AlAs in Table II of the manuscript

The manuscript's Table I lists the PBE bulk band gaps, 0.48 eV for GaAs and 1.32 eV for AlAs, at the experimental lattice constants (GaAs 5.654 Å, AlAs 5.661 Å). The bulk cells of this tutorial are at the mean of the two lattice constants of the platform's GaAs and AlAs structures, 5.713 Å.

6.1. Comparison with published results

ΔE_v (eV) GaAs gap (eV) AlAs gap (eV)
Hinuma et al. 0.45 0.48 1.32
This tutorial 0.471 (+4.6 %) 0.289 (−39.8 %) 1.476 (+11.8 %)

The offset splits into the bulk term (E_VBM − V̄)_GaAs − (E_VBM − V̄)_AlAs = +0.5635 eV and the lineup (V̄_GaAs − V̄_AlAs)_superlattice = −0.0928 eV. The manuscript does not list the two terms.

Section 8.3 of the notebook plots the electrostatic potential across one period of the superlattice, from the AlAs→GaAs interface: each bulk's own potential (dotted) shifted onto its block, and the two block averages (dashed). The bulk potentials coincide with the superlattice's inside both blocks and depart from it only at the interfaces:

Potential across the GaAs/AlAs (110) superlattice, this tutorial

7. Customization options

7.1. Adjust computational resources

CLUSTER_NAME selects the cluster by its full or partial name; a name that is not available makes the notebook stop and list the ones that are.

8. Troubleshooting

8.1. Material not found

If one of the three names is not found, run the GaAs/AlAs (110) Strained Superlattice tutorial first. In JupyterLite, save the three materials to the account from Materials Designer under those exact names; in a local Jupyter session, check that the uploads folder holds them.

8.2. No cluster available

If section 5.1 of the notebook prints an empty list of clusters, there is nothing to submit to. A cluster has to be available to the account before the notebook can run.

9. Interactive JupyterLite notebook

The following JupyterLite notebook calculates the valence band offset. Select Run > Run All Cells.

10. References

  1. Yoyo Hinuma, Andreas Grüneis, Georg Kresse, and Fumiyasu Oba. Band alignment of semiconductors from density-functional theory and many-body perturbation theory. Physical Review B, 90:155405, 2014. URL: https://link.aps.org/doi/10.1103/PhysRevB.90.155405. ↩