# First Principles Assessment of ZnTe and CdSe as Prospective Tunnel Barriers at the InAs/Al Interface

Malcolm J A Jardine, Derek Dardzinski, Zefeng Cai, Vladimir N Strocov, Moïra Hocevar, Chris Palmstrøm, Sergey Frolov, Noa Marom

► To cite this version:

Malcolm J A Jardine, Derek Dardzinski, Zefeng Cai, Vladimir N Strocov, Moïra Hocevar, et al. First Principles Assessment of ZnTe and CdSe as Prospective Tunnel Barriers at the InAs/Al Interface. ACS Applied Materials & Interfaces, 2025, 17 (3), pp.5462-5474. 10.1021/acsami.4c17957. [https://doi.org/10.1021/acsami.4c17957](https://doi.org/10.1021/acsami.4c17957)

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# First Principles Assessment of ZnTe and CdSe as Prospective Tunnel Barriers at the InAs/Al Interface

Malcolm J. A. Jardine,† Derek Dardzinski,† Zefeng Cai,† Vladimir N. Strocov,‡

Moïra Hocevar,¶ Chris Palmstrøm,§,|| and Noa Marom*,†,⊥,#

†Department of Materials Science and Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA

‡Paul Scherrer Institut, Swiss Light Source, CH-5232 Villigen PSI, Switzerland

¶Univ. Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, 38000 Grenoble, France

§Materials Department, University of California-Santa Barbara, Santa Barbara, CA 93106, USA

‖Department of Electrical and Computer Engineering, University of California-Santa Barbara, Santa Barbara, CA 93106, USA

⊥Department of Physics, Carnegie Mellon University, Pittsburgh, PA 15213, USA

#Department of Chemistry, Carnegie Mellon University, Pittsburgh, PA 15213, USA

E-mail: nmarom@andrew.cmu.edu
Abstract

Majorana zero modes are predicted to emerge in superconductor/semiconductor interfaces, such as Al/InAs. Majorana modes could be utilized for fault tolerant topological qubits. However, their realization is hindered by materials challenges. The coupling between the superconductor and the semiconductor may be too strong for Majorana modes to emerge, due to effective doping of the semiconductor by the metallic contact. This could be mediated by adding a tunnel barrier of controlled thickness. We use density functional theory (DFT) with Hubbard U corrections, whose values are machine-learned via Bayesian optimization (BO) to assess ZnTe and CdSe as prospective tunnel barriers for the InAs/Al interface. The results of DFT+U(BO) for ZnTe are validated by comparison to angle resolved photoemission spectroscopy (ARPES). We then study bilayer interfaces of the three semiconductors with each other and with Al, as well as tri-layer interfaces with a varying number of ZnTe or CdSe layers inserted between InAs and Al. We find that 16 atomic layers of either material completely insulate the InAs from metal induced gap states (MIGS). However, ZnTe and CdSe differ significantly in their band alignment, such that ZnTe forms an effective barrier for electrons, whereas CdSe forms a barrier for holes. Because of Fermi level pinning in the conduction band at the surface, only electron transport is possible in InAs-based devices. Therefore, ZnTe is the better choice. Based on the results of our simulations, we suggest conducting experiments with ZnTe barriers in the thickness range of 6-18 atomic layers.

Keywords: density functional theory, electronic structure, metal-semiconductor interface,
tunnel barrier, InAs, ZnTe, CdSe, Al
Introduction

Majorana Zero Modes (MZMs) are an active area of research into potentially non-Abelian
quantum states which some authors suggested could offer a degree of protection for de-
coherence in specially designed quantum computing architectures. ¹⁻³ MZMs manifest as
zero-energy mid-gap states localized at boundaries and topological defects within one- and
two-dimensional topological superconductors. ⁴ One heavily researched platform for realiz-
ing MZMs involves proximity coupling a conventional superconductor, most commonly Al
and Nb-based alloys, with a semiconductor nanowire with strong spin-orbit coupling (SOC),
such as InAs or InSb. The realization of MZMs typically requires external magnetic field or
another form of broken symmetry. ⁵⁻⁸ Recently, advancements have been made in material
selection and experimental techniques in such semiconductor-nanowire/superconductor sys-
tems, addressing challenges identified during initial experimental efforts that did not yield
a clear evidence of MZMs. ⁹⁻¹¹ Approaches include investigating different combinations of
semiconductors such as InAs and InSb and superconductors, such as Pb, Sn, Nb, which aim
to improve electron mobility and harness larger superconducting gaps and higher critical
magnetic fields. ¹²⁻¹⁶

A challenge of the semiconductor/superconductor hybrid nanowire configuration is that excessive coupling between the superconducting metal and semiconductor can lead to the “metallization” of the semiconductor, which could hinder achieving the desired topological phase in experimental setups. Theoretical investigations, utilizing the Poisson-Schrödinger equation to model the semiconducting and superconducting properties of the system, have shown that excessive coupling leads to the renormalization of critical semiconductor properties, such as the Landé g-factor and spin-orbit-coupling (SOC), towards values of the metal. Furthermore, undesired band shifts may be induced. ¹³,¹⁷⁻²⁴ The incorporation of a tunnel barrier could serve to modulate the strength of the superconductor-semiconductor coupling, thereby influencing the induced proximity effect, a critical factor in experimental control. Another benefit of a tunnel barrier is that it may act as a passivation layer on top
of the semiconductor nanowire, protecting it from environmental effects.²⁵⁻²⁸ Previously, we have explored this idea by using density functional theory (DFT) to investigate CdTe as a prospective tunnel barrier at the InSb/α-Sn interface.²⁹ It was found that 16 atomic layers (3.5 nm) of CdTe completely shield the InSb from metal induced gap states (MIGS) from the α-Sn, effectively decoupling the semiconductor from the metal. We therefore concluded that the thickness range most likely to be of interest for experimental exploration is 6-10 atomic layers, where some MIGS are still present, indicating coupling between the metal and semiconductor.

InAs and Al are prominent materials that are frequently used to fabricate nanowire based devices in search of MZMs.¹²,¹⁷,³⁰⁻³⁶ InAs is one semiconductor of choice in such setups thanks to its strong spin-orbit coupling and large Landé g-factor. Al, despite its relatively low transition temperature of 1.2K, is compatible with established fabrication methods and has yielded devices with clear signatures of induced effective superconductivity. Al has been epitaxially grown on InAs nanowires producing well-ordered, high-quality interfaces with low mismatch, in which the crystallinity of both the InAs and Al components was maintained though the Al layer is typically granular. This enabled the experimental observation of a hard superconducting gap induced in InAs.¹⁴ To date, there have been no theoretical or experimental investigations of a tunnel barrier at the InAs/Al interface. It is presently unknown what material(s) could serve as a barrier and what would be the optimal thickness range.

An ideal tunnel barrier should be a wide band gap semiconductor with a lattice constant that closely matches that of InAs to enable the growth of a high-quality epitaxial interface. In general, it is desirable for the band gap of a tunnel barrier to straddle the gap of the semiconductor in order to provide a barrier for both electrons and holes. However, in the case of InAs, because the Fermi level is pinned in the conduction band at the surface, only electron transport is relevant and hence a tunnel barrier for electrons is needed. ZnTe and CdSe have wide band gaps of 2.26 eV and 1.75 eV, respectively. The cubic (Zinc Blende)
phases of InAs, ZnTe, and CdSe have similar lattice parameters with lattice mismatches
of approximately 0.5% for InAs/ZnTe, 0.3% for InAs/CdSe, and 0.2% for ZnTe/CdSe. ³⁷⁻⁴²
Based on their bulk band edge positions, the band gaps of both ZnTe and CdSe are expected
to straddle the gap of InAs. ⁴³,⁴⁴ Epitaxial growth of ZnTe and CdSe on InAs{100} and
on each other, has been investigated in the context of visible wavelength semiconductor
electronics, ⁴⁰,⁴⁵⁻⁴⁸ mid-IR lasers, spin-related phenomena, ⁴⁹⁻⁵¹ and as barriers in InAs-based
heterostructures. ⁵²⁻⁵⁵ Studies of the ZnTe/Al and CdSe/Al interfaces have aimed to elucidate
the physics of metal-semiconductor interfaces in the context of devices such as light emitting
diodes (LEDs) and Schottky diodes, where the Fermi level position and interface structure
are of importance. ⁵⁶⁻⁶² Therefore, it should be feasible to grow epitaxial InAs/Al interfaces
with ZnTe or CdSe as a tunnel barrier.

Here, we use DFT with machine-learned Hubbard U corrections<sup>63</sup> to assess ZnTe and
CdSe as prospective tunnel barriers for the InAs/Al interface. We conduct simulations
of bulk ZnTe and CdSe, bilayer (110) interfaces of InAs/ZnTe, InAs/CdSe, CdSe/ZnTe,
and (InAs,ZnTe,CdSe)/Al, as well as tri-layer (110) interfaces of InAs/Al with a ZnTe or
CdSe tunnel barrier of varying thickness. For ZnTe, the PBE+U(BO) results are verified
by comparison with published angle-resolved photoemission spectroscopy (ARPES) data.
We note that describing proximity-induced superconductivity at a semiconductor interface
remains beyond the capabilities of current DFT methods, despite recent advances in pre-
dicting phonon-mediated superconductivity. <sup>64</sup> Nevertheless, DFT offers valuable insights
into interface properties, including the band alignment, the extent of band bending, and the
penetration depth of metal-induced gap states (MIGS) into the semiconductor. <sup>29</sup> We find
that 16 atomic layers of either ZnTe or CdSe are sufficient to completely insulate the InAs
from MIGS emanating from the Al. However, the two materials significantly differ in their
band edge positions affecting their band alignment with InAs and Al. As a result, only ZnTe
provides an effective barrier for electrons and therefore it would be the better candidate to
pursue experimentally.
# Methods

## Computational Details

DFT calculations were conducted using the Vienna Ab Initio Simulation Package (VASP)⁶⁵ with the projector augmented wave method (PAW).⁶⁶,⁶⁷ The generalized gradient approximation (GGA) of Perdew, Burke, and Ernzerhof (PBE)⁶⁸ was employed to describe the exchange-correlation interactions among electrons with a Hubbard *U* correction.⁶⁹ The *U* values were machine learned using Bayesian optimization (BO).⁶³ An updated version of the “BayesianOpt4dftu” code is available at:

https://github.com/caizefeng/BayesianOpt4dftu. Briefly, the BO objective function is formulated to reproduce as closely as possible the band structure obtained from the Heyd-Scuseria-Ernzerhof (HSE)⁷⁰ hybrid functional. The reference HSE calculations were conducted using the experimental lattice parameters of 6.101 Å for ZnTe³⁷,³⁸,⁷¹⁻⁷³ and 6.077 Å for CdSe.⁴²,⁷⁴ For ZnTe, a comparison to the results obtained with the lattice constant of InAs, 6.0584 Å, which was used for interface models, is provided in the SI. It was verified that using the lattice constant of InAs does not have an appreciable effect on the electronic properties of ZnTe (the lattice parameter of CdSe is so close to that of InAs that such a comparison was deemed unnecessary).

The hyperparameters of our BO implementation are the coefficients $\alpha_1$ and $\alpha_2$, which assign different weights to the band gap vs. the band structure in the objective function, the number of valence and conduction bands used for the calculation of the objective function, $N_b$, and the parameter $\kappa$ that controls the balance between exploration and exploitation in the upper confidence bound acquisition function. The hyperparameters $\kappa = 5$, $N_b = (5, 5)$, $\alpha_1 = 0.25$ and $\alpha_2 = 0.75$ were used here to find optimal *U* values for the Zn and Cd *d*-states, which dominate the top of the valence band and the bottom of the conduction band (see orbital decomposition provided in the SI). The latter two parameters were chosen to assign more weight to the band shape rather than the band gap. *U* values of 9.4 eV and 8.3
eV were obtained for ZnTe and CdSe, respectively. For InAs, the *U* values of -0.5 eV and -7.5 eV were applied to the *p*-orbitals of In and As, respectively, following Ref. ⁶³,⁷⁵ It has been shown previously that with these parameters PBE+U(BO) produces a band structure in good agreement with ARPES for InAs.⁷⁵ For structural relaxation at interfaces, the Tkatchenko-Scheffler (TS) method was used to account for dispersion interactions using tags IVDW=20 and LVDW EWALD=True.⁷⁶

Spin-orbit coupling (SOC) was used in all calculations and dipole corrections were applied to slab models.⁷⁷ The tags used for convergence of calculations are BMIX = 3, AMIN = 0.01, ALGO = Fast, and EDIFF = 1·10⁻⁵. The kinetic energy cutoff was set to 400 eV for all bulk calculations and 350 eV for surface and interface slab models. A 7 × 7 × 7 k-point mesh was used for bulk calculations. For 1 × 1 slab models a k-point mesh of 7 × 7 × 1 was used for SCF calculations and a k-point mesh of 13 × 13 × 1 was used for density of states (DOS) calculations. For supercell slab models (2 × 2 for the semiconductor and 3 × 3 for Al) a k-point mesh of 5 × 5 × 1 was used for SCF calculations and a 9 × 9 × 1 k-point mesh was used for DOS calculations. Interface optimization calculations were conducted using a *k*-point grid of 3 × 3 × 1. The recommended POTCAR provided by VASP was used for all materials except In, for which POTCAR\_In was used.

For slab calculations, a vacuum region of around 60 Å was added to prevent spurious interactions between periodic replicas. Semiconductor surfaces were passivated by pseudo-hydrogen atoms to avoid surface states from dangling bonds.⁷⁸ The pseudo-hydrogen fractional charges utilized to passivate each atom were 1.25 for In and 0.75 for As in InAs, 1.5 for Zn and 0.5 for Te in ZnTe, 1.5 for Cd and 0.5 for Se in CdSe. Structural relaxation of the pseudo-hydrogen atoms was performed until the maximal force was below 0.001 eV/Å. All band structure and density of states plots were generated using the open-source Python package, VaspVis,⁷⁹ which is freely available from The Python Package Index (PyPI) via the command: *pip install vaspvis*, or on GitHub at: https://github.com/DerekDardzinski/vaspvis
Interface Model Construction

All interface models were constructed with a (110) orientation using the experimental InAs
lattice constant value of 6.0584 Å,<sup>41,80</sup> based on the assumption that the epitaxial films would
become coincident to the substrate. When constructing slab models, it is necessary to con-
verge the number of layers to avoid quantum size effects and approach the bulk properties.<sup>79</sup>
For InAs it has previously been shown that 50 atomic layers are sufficiently converged.<sup>75</sup>
Figure 1a shows the Γ-point band gap obtained with PBE+U(BO) vs. the number of atomic
layers for ZnTe(110) and CdSe(110) slabs. The band gap is considered converged when the
band-gap changes by less than 5 × 10<sup>-2</sup> eV when more layers are added. ZnTe and CdSe
are deemed converged with 40 atomic layers with gap values of 1.52 eV and 1.00 eV respec-
tively, which are close to their bulk PBE+U(BO) values. For metal slabs, convergence is
determined based on the DOS.<sup>79</sup> Figure 1b shows the local DOS at the center of a slab
with a varying number of Al layers compared to the bulk DOS (obtained for a unit cell
with the same orientation), calculated using the experimental lattice parameter of 4.0389 Å.
With 4 atomic layers the DOS deviates very significantly from the bulk DOS. With 8 layers
the DOS at the center of the slab starts to resemble the bulk DOS, and with 16 layers the
DOS is close to converged relative to the bulk DOS, in particular around the Fermi level.
We note that even with 4 layers the Al slab is already metallic and the fluctuations in the
DOS around the Fermi level with an increasing number of layers are small. In this sense,
metals are less sensitive to thickness convergence than semiconductors, semi-metals,<sup>29</sup> and
topological materials.<sup>81</sup>

Interface models were constructed using the Ogre code.<sup>79,82</sup> For semiconductor/Al inter-
faces, lattice matching was performed, resulting in a domain-matched interface comprising
a 2×2 supercell of the semiconductor and a 3×3 supercell of Al with a mismatch of less
than 0.1%, as shown in Figure 2a. To determine the optimal position of the film on top of
the substrate and the bonding configuration across the interface, a potential energy surface
(PES) was calculated by shifting the film on top of the substrate parallel to the plane of
<figure><img src="image_2.png" /></figure>

Figure 1: Thickness convergence: (a) The Γ-point band gap of ZnTe(110) and CdTe(110), using the InAs lattice constant, as a function of number of atomic-layers. Dashed lines denote the PBE+U(BO) bulk limit of 1.484 eV for ZnTe and 0.967 eV for CdSe. (b) Thickness convergence of Al(110): The local density of states for the middle layer of the slab is given as a function of number of atomic layers (L). The thick black line denotes PBE+U(BO) bulk density of states. Gaussian broadening with σ = 0.3 was applied to the data.

the interface. This is done at an interfacial distance of the average interlayer distance of the
film and substrate structures which is given by $(a_{sub} + a_{film})/(\sqrt{2} * 4)$, which is 1.784 Å for
InAs,CdSe,ZnTe/Al interfaces and 2.142 Å for the semiconductor/semiconductor interfaces.
Figure 2b shows an example for InAs/Al and plots for the remaining bilayer interfaces
are provided in the SI. The most stable configuration of the InAs/(ZnTe,CdSe) interfaces
is found to be with In-Te,Se and As-Zn,Cd bonding.<sup>40,83</sup> In the same vein, the ZnTe/CdSe
interface has Zn-Se and Te-Cd bonding.<sup>84</sup> For the most stable bonding configuration, a bind-
ing energy curve was calculated perpendicular to the plane to find the optimal interfacial
distance. A value of 2.337 Å was obtained for the InAs/Al interface, as shown in Figure 2c.
The optimal interfacial distance found for the other interfaces are 2.465 Å for ZnTe/Al, 2.5
Å for CdSe/Al, 2.11 Å for InAs/ZnTe, 2.1875 Å for InAs/CdSe, and 2.163 Å for ZnTe/CdSe.
For computational efficiency, the PES and binding energy curves were calculated without
SOC, using 4 atomic layers of each material.

<figure><img src="image_3.png" /></figure>

Figure 2: Interface construction for the InAs/Al interface. (a) Domain-matched supercells constructed of a 2×2 supercell of InAs (A,green) and a 3×3 supercell (B,orange). The arrows indicate the surface parallel crystallographic directions along **x** and **y** of the film and substrate. (b) Potential energy change as a function of the registry between the film and substrate with the minimum set to zero. Only one symmetry-unique tile is shown with the location of the minimum indicated by a cross. (c) Binding energy curve as function of interfacial distance. (d) Top-view of the structure of the optimized interface configuration with Al atoms colored in red, In atoms colored in dark blue, and As atoms colored in light blue.

Finally, a few layers near the interface were relaxed, with SOC applied and a slab with 8 atomic layers of each material. For semiconductor/semiconductor interfaces, two atomic layers were relaxed on either side, and for semiconductor/Al interfaces four atomic layers were relaxed on either side. A representative example of the relaxed InAs/Al interface is shown in Figure 2d. The relaxed geometries of the bilayer interfaces were used to construct tri-layer interfaces. For tri-layer interfaces with fewer than 8 barrier layers, the entire interface region was relaxed. The bilayer semiconductor interfaces, which do not necessitate supercells in the plane of the interface, comprised 40 atomic layers of each material. Owing to the increased computational cost of the supercells used to construct the interfaces with Al, the bilayer interfaces contained 30 layers of the semiconductor and 16 layers of Al. The tri-layer
interface models comprised 20 layers of InAs, 8 layers of Al and up to 24 atomic layers of ZnTe or CdSe, amounting to a total slab thickness of around 9 nm (not including vacuum) with barrier of up to 5 nm. The smaller number of semiconductor layers in these interfaces results in a somewhat wider gap, owing to the quantum size effect (see Figure 1 and Ref. 75). Ideal abrupt interfaces were considered, with no intermixing.

# Results and Discussion

## Bulk ZnTe and CdSe

<figure><img src="image_4.png" /><figcaption>Figure 3: Comparison between the band structures obtained using PBE, HSE, and PBE+U(BO) for (a) ZnTe and (b) CdSe.</figcaption></figure>

Figure 3 shows the bulk band structures of ZnTe and CdSe obtained with different exchange-correlation functionals. The magnitude of the band gap is the main difference between the results of different functionals. For both compounds, the transition metal *d*
states contribute significantly to the top of the valence band and the bottom of the conduc-
tion band at the Γ point, as shown in the SI. The PBE functional significantly underestimates
the band gap of both compounds, yielding 1.07 eV for ZnTe compared to the experimental
values of 2.26 at ambient temperature<sup>53,85,86</sup> and 2.38 eV at 0K<sup>71,87,88</sup> and 0.51 eV for CdSe,
compared to the experimental value of 1.75 eV.<sup>37,39,74</sup> The band gap underestimation of
(semi-)local functionals <sup>89</sup> has been attributed to the self-interaction error (SIE), a spurious
repulsion of an electron from its own charge density.<sup>90</sup> Highly localized states, such as *d* orbitals, are typically affected more strongly by SIE.

Hybrid functionals, which include a fraction of exact (Fock) exchange, mitigate the effect
of SIE and yield band gaps in better agreement with experiment.<sup>89,91</sup> The HSE functional
yields improved band gaps of 1.86 eV for ZnTe and 1.46 eV for CdSe. However, the compu-
tational cost of hybrid functionals is too high for simulations of large interface systems, such
as the InAs/ZnTe,CdSe/Al tri-layer systems studied here. The DFT+U approach, whereby
a Hubbard U correction is added to certain atomic orbitals, provides a good balance between
accuracy and computational cost.<sup>89,91</sup> *U* parameters determined by Bayesian optimization<sup>63</sup>
are applied to the *d*-states of Zn and Cd, as described in the Computational Details section.
The PBE+U(BO) band gaps of 1.48 eV for ZnTe and 0.96 eV for CdSe are a significant
improvement over PBE but still lower than the HSE and experimental values. For ZnTe,
it has been reported previously that even with very large *U* values the band gap is still
considerably narrower than the experimental value.<sup>92</sup>

Comparison to ARPES for ZnTe

The most powerful experimental tool for verifying the validity of electronic structure models
is ARPES. This technique is able to resolve the electronic structure in three-dimensional
momentum, **k**. The surface-parallel momentum, **k**<sub>xy</sub>, is varied through the photoelectron
emission angle (ϑ), whereas the surface-perpendicular component, **k**<sub>z</sub>, is varied through the
photon energy (*hv*) (see, for example, <sup>93,94</sup>). The PBE+U(BO) results for ZnTe are verified
by comparison with the ARPES data for ZnTe (110) reported in Ref.⁹⁵ Often, ARPES experiments are compared to bulk band structure calculations. However, bulk band structures cannot capture surface and interface phenomena, which require technically more demanding slab calculations. Here, the ZnTe (110) surface is simulated using a slab model, shown in Figure 4a. The supercell extends over 50 unit layers in the surface-perpendicular direction and includes an additional vacuum region. Such supercell models produce band structures that appear as a dense manifold ("spaghetti") of bands as a function of $k_{xy}$, shown in the SI. Each band within this manifold is characterized by a certain, albeit smeared, value of $k_z$ in the Fourier expansion of the corresponding wave-function.⁹⁶ The relation between such band structure calculations and ARPES spectra, which is far from obvious, can be recovered using so-called "band unfolding". In this approach, the band structure generated from supercell calculations is projected, or unfolded, onto the appropriate smaller unit cell.⁹⁷ The band manifolds in the small Brillouin zone of the supercell then split into the separate bands in the larger Brillouin zone of the smaller unit cell, untangling the spaghetti. This can help resolve e.g., the contributions of surface states vs. the bulk bands of the material.²⁹,⁷⁵

In the bulk Brillouin zone, the surface-perpendicular $\Gamma - K|U' - X'$ direction is symmetry equivalent to the surface-parallel $\Gamma - K|U' - X'$ directions, as shown in Figure 4b via the blue and red arrows respectively. However, the finite length of the slab in the surface-perpendicular direction breaks this symmetry and produces a Brillouin zone that is very thin in the surface-perpendicular direction. This manifests in the differences between the unfolded band structures along the surface-parallel vs. the surface-perpendicular paths, shown in Figure 4c,d. Along the surface-parallel path, in which full periodicity is retained, a bulk-like band structure is obtained. Confinement in the surface-perpendicular direction (between the vacuum regions of the supercell) leads to discretization of $k_z$, as well as its broadening, owing to the Heisenberg uncertainty principle. This manifests as ladder-like horizontal stripes in the unfolded band structure (further plots of the dependence of the unfolded surface perpendicular band structure on the slab thickness, confirming the quantum-confinement
<figure><img src="image_5.png" /></figure>

Figure 4: Electronic structure of ZnTe: (a) Illustration of the 50 layer ZnTe slab (with vacuum). (b) Illustration of the Brillouin zone (BZ) of bulk FCC (gray), the (110) 2D surface BZ (red), and the BZ of a slab model with a finite thickness (blue). The surface parallel and surface perpendicular $\Gamma - K|U - X$ paths are indicated by the red and blue arrows, respectively. Bulk-unfolded band structures along the (c) surface-perpendicular and (d) surface-parallel paths. The corresponding bands of bulk ZnTe are shown in red in both panels. (e) Bulk-unfolded band structure of the surface perpendicular $\Gamma - K|U - X$ path (cyan) compared to the ARPES data adapted with permission from "Angle-resolved photoelectron spectroscopy study of the surface electronic structure of ZnTe(110)" by H. Qu et al., Phys. Rev. B, 43, 9843 (1991); Copyright (1991) by the American Physical Society.⁹⁵ The bands colored in green are shifted by a $|\Gamma X'|$ lattice vector to reproduce the Umklapp bands in the ARPES.

origin of the discrete broadened energy levels, is provided in the SI).

In Fig. 4e, the unfolded band structure along the surface-perpendicular path $\Gamma - K|U' - X'$ is compared to the ARPES data reported in Ref.⁹⁵. Figure 1 therein presents the ARPES spectra collected at normal emission (corresponding to $k_{xy}=0$) under variation of $h\nu$ over the range 19-95 eV, whereby $k$ is varied along the out-of-plane direction $\Gamma - K|U' - X$ (the $\Sigma$ line) of the bulk Brillouin zone of ZnTe. Figure 4e shows the spectra digitized from the original figure and plotted in the binding energy ($E_b$) vs $h\nu$ coordinates as the negative second derivative of the ARPES intensity ($-d²I/dE_b²$) represented by the heat color scale. The $E_b$ scale here is referenced to the VBM. For the comparison, the $k_z$ coordinates of calculated points were converted to $h\nu$ coordinates assuming free-electron final states as $h\nu = (\hbar^2/2m_0)*(k_z+G_z)^2 - V_{000} + E_b$. Here, $m_0$ is the free-electron mass, $G_z$ runs through surface-perpendicular bulk reciprocal vectors, and the inner potential $V_{000}$ is chosen as 5 eV
The unfolded band structure is in good agreement with the ARPES data. The discrete, broadened energy levels hardly affect the comparison because their energy separation is less than the energy broadening of the experimental dispersions due to the finite hole lifetime and the experimental energy resolution. The broadening effects in the experiment also explain why the splitting of the calculated bands around the K—U' point is not resolved. In the lower left region of panel (e) there are ARPES peaks that do not correspond to any of the DFT bands. Their dispersion can be described, however, with the same theoretical valence bands but with the final states shifted by a certain $\Delta k_z$ from the free-electron ones. The theoretical dispersion in the $(hv, E_b)$ coordinates then becomes $hv = (\hbar^2/2m_0)*(k_z+\Delta k_z+G_z)^2 - V_{000} + E_b$. Therefore, in this $hv$ range, the ARPES final state incorporates two bands, one having the free-electron $k_z$ and another having $k_z+\Delta k_z$ shifted from the free-electron dispersion, with the ARPES intensity distribution between these bands defined by the energy- and k-dependent photoemission matrix elements. In our case, we find $\Delta k_z \approx 1.0371 A^{-1}$, equal to $|\Gamma X'|$. Conventionally, such final-state bands are called Umklapp bands, implying an Umklapp scattering process of the photoelectrons,⁹⁵ although the corresponding momentum transfer is not necessarily an integer reciprocal-lattice vector. A rigorous description of such multi-band final states based on the one-step theory of photoemission, where they are treated as the time-reversed low-energy electron diffraction (LEED) states, can be found in Refs.,⁹⁸⁻¹⁰⁰ and the references therein.

## Semiconductor Interfaces

Determining the band alignment in semiconductor/semiconductor hetero-junctions is important for understanding and improving the performance of semiconductor devices such as lasers, photovoltaic cells, and transistors.¹⁰¹⁻¹⁰³ The band edge positions of the two separate materials may be considered as a zero-order approximation for the band alignment at an interface. The bonding configuration and orientation between the two materials and the
<figure><img src="image_6.png" /><figcaption>Figure 5: Electronic structure of semiconductor-semiconductor bilayer interfaces: Density of states as a function of position across the (a) ZnTe/CdSe, (b) InAs/ZnTe and (c) InAs/CdSe interfaces. The atomic layers are numbered based on distance from the interface, which is located at zero. Illustrations of the interface structures are also shown.</figcaption></figure>

presence of an interface dipole, as well as the presence of defects can lead to significant differences.⁴⁰,⁵³,¹⁰⁴⁻¹⁰⁶ This may explain some of the variation between experimentally reported values.

Simulations can help interpret experiments, as well as predict the band alignment produced by different combinations of semiconductors.¹⁰⁷ The underestimation of band gaps by (semi-)local DFT functionals can lead to errors in the computed band alignment. In principle, the interface band alignment could be calculated using the GW approximation within the framework of many-body perturbation theory. However, owing to the high computational cost, simulations of sufficiently large interface models with enough layers to approach the bulk band gaps are not currently feasible using GW or even hybrid DFT functionals. To circumnavigate this problem, corrections based on the shift of the electrostatic potential can be applied to the bulk band edge positions. The electrostatic potential lineup is relatively insensitive to the method used and converges fast with the number of layers.¹⁰⁸,¹⁰⁹ Therefore, the electrostatic potential correction can be calculated using a more computationally efficient method (e.g., semi-local DFT), while the bulk band structure is calculated using a more accurate and expensive method (e.g., GW or hybrid DFT).⁴³,¹⁰⁸⁻¹¹⁰ The electrostatic potential correction may be performed for separate surface slabs of each material or for periodic heterostructures with a relatively small number of layers of each material.¹¹¹ Additional
corrections may be performed at the semi-local DFT level e.g., to account for the effect of interface strain,¹⁰⁸ and the formation of a dipole in polar interfaces¹⁰⁴,¹⁰⁶ Thus, expensive calculations of large interface models are avoided.

A limitation of approaches that avoid direct modeling of the interface is that they cannot describe phenomena, such as band bending and the penetration of states from one material into the gap of the other in the vicinity of the interface. Modeling these phenomena requires a sufficient number of layers to span their length-scale. We also note that it has been shown that structural relaxation at the interface can have a significant effect on the band alignment,¹⁰⁴ and this is indeed the case for the interfaces studied here, as discussed below. Therefore, if periodic interface models with a small number of layers are used to calculate electrostatic potential corrections, care should be taken to include and relax a sufficient number of layers around the interface. In our case, the main drawback of approaches that avoid direct simulations of large interface models is that they cannot be used to assess the effectiveness of a tunnel barrier, which is the goal of this work.

Fig. 5 shows the DOS as a function of position across the three semiconductor interfaces. ZnTe and CdSe differ significantly in their band edge positions with respect to each other and to InAs. Panel (a) shows that ZnTe and CdSe form a type-II interface with staggered band gaps. Close to the interface, there is significant penetration of states from the bands of one material into the gap of the other. Therefore, the band offsets are extracted from the asymptotic band edge positions. We find a valence band offset (VBO) of 0.5 eV and a conduction band offset (CBO) of 1.2 eV. These values are within the range of other first principles studies, which reported VBOs of 0.5-0.9 eV and CBOs of 1.0-1.4 eV.⁴³,¹⁰⁴,¹⁰⁷,¹¹² Prior to relaxation, we obtained a type-II band alignment, but with a VBO of 0.15 eV and a CBO of 0.85 eV, as shown in the SI. All the experimental band offset data available are for ZnTe/CdSe interfaces with a (001) orientation. Typically, only the VBO is measured directly and the CBO is deduced based on the bulk band gaps of the two materials. Yu et. al. have reported a VBO of 0.64 ± 0.07 eV using X-ray photoelectron spectroscopy (XPS).⁴⁷
Mourad *et. al.*<sup>46</sup> have reported a VBO of 0.75 ± 0.01 eV, based on photoluminescence (PL) measurements. Gleim *et. al.* and Sedova *et. al.* conducted experiments on trilayer junctions of CdSe/ZnTe/InAs.<sup>40,53</sup> Gleim *et. al.* conducted photoelectron spectroscopy (PES) measurements for both thin (three monolayer) and thick films of ZnTe. They reported a VBO of 0.6 ± 0.1 eV. Sedova *et. al.* conducted their experiments only with a three monolayer film of ZnTe and reported a significantly different VBO of 0.94 eV. Depending on what VBO was measured and what values were used for the band gaps of both materials, the CBO has been estimated as 1.09 eV,<sup>53</sup> 1.22 eV,<sup>47</sup> and 1.54 eV.<sup>40</sup> Despite the band gap underestimation by PBE+U(BO) the band offsets are in good agreement with experimental values.

Panel (b) shows that InAs and ZnTe form a type-I interface with the valence band maximum aligned to give a VBO of zero and a CBO of 1.1 eV. States penetrate from the InAs conduction band into the band gap of the ZnTe and decay within about 14 atomic layers from the interface. The band offsets obtained here are close to the VBO of 0.2 eV and CBO of 1.1 eV computed in Ref.<sup>43</sup> We note, however, that structural relaxation, which was not performed in Ref.,<sup>43</sup> significantly affects the resulting band alignment of the InAs/ZnTe interface. Prior to relaxation, we obtained a VBO of 0.35 eV and CBO of 0.6 eV, as shown in the SI. Experiments have been conducted only for InAs/ZnTe interfaces with a (001) orientation. VBO values of 0.2 eV to 0.3 eV have been reported.<sup>40,53</sup> The presence of a dipole at the (001) interface may cause some differences in the band offsets compared to the non-polar (110) orientation.

Pairing InAs with CdSe leads to an opposite band alignment to ZnTe, as shown in Panel (c). The InAs/CdSe interface is also type-I, but with the bottom of the InAs and CdSe conduction bands aligning to produce a CBO of zero. We find a VBO of 0.425 eV. States penetrate from the valence band of the InAs into the gap of the CdSe and decay within 14 atomic layers. In this case, geometry relaxation qualitatively changed the band alignment. Before relaxation, a type-II band alignment was found with a CBO of 0.1 and a VBO of
0.6 eV, as shown in the SI. Ref. ⁴³ has reported a type I interface with a small CBO of 0.16 eV, but a significantly larger VBO of 1.25 eV. Two experimental values have been reported for the VBO for (001) InAs/CdSe interfaces. Ref. ⁵³ has reported VBO of 0.86 ± 0.15 eV, whereas Ref. ⁴⁰ has reported a value of 1.05 eV (we note that Ref. ⁴⁰ appears to systematically report higher VBO values than Ref. ⁵³). The differences between the values obtained here and the values reported in other computational and experimental studies may be attributed to the significant underestimation of the band gap of CdSe by PBE+U(BO) and the different interface orientation.

## Semiconductor/Al Interfaces

<figure><img src="image_7.png" /><figcaption>Figure 6: Electronic structure of semiconductor/Al bilayer interfaces: Density of states in the (a) InAs/Al, (b) ZnTe/Al and (c) CdSe/Al interfaces as a function of position. The atomic layers are numbered based on distance from the interface, which is located at zero. The structure of each interface is illustrated on top.</figcaption></figure>

The band alignment at semiconductor/metal interfaces is a key parameter for device performance because it fundamentally affects charge transport through metal contacts and contact resistances.¹¹³,¹¹⁴ Depending on the semiconductor band edge positions with respect to the metal work function, either an Ohmic contact or a potential step, known as a Schottky barrier, may form.¹¹⁵,¹¹⁶ It has been established, both theoretically and experimentally, that the local properties of the interface, including the crystal lattice orientation, the bonding configuration, presence of defects, charge redistribution, and dipole formation, may further affect the band alignment and Schottky barrier height (SBH).¹¹⁴,¹¹⁷⁻¹²⁰ First principles simulations
can help interpret experiments and predict the band alignment at metal/semiconductor interfaces. To this end, the electrostatic potential alignment method, described in detail in the SI, is often used.<sup>109,121,122</sup> The idea is similar to the method described above for determining the band alignment at semiconductor interfaces. To avoid expensive calculations of large slab models, and to compensate for errors caused by the underestimation of band gaps by semi-local functionals, the SBH is evaluated by referencing the average electrostatic potential difference between the semiconductor and metal, calculated using a smaller slab model, to calibrate bulk values of the Fermi energy and band edges. Similar to the band alignment at semiconductor interfaces discussed above, the SBH results can also be sensitive to geometry relaxation in the interface region.<sup>119,121</sup> As explained above, we are ultimately interested in studying the spatial evolution of the electronic structure as a function of position across the interface. To describe local effects, such as the presence of MIGS, which manifest as a finite density of states in the gap of the semiconductor due to the penetration of exponentially decaying metallic Bloch states,<sup>123-126</sup> fully converged slab models are used. Below, the band alignment and SBH values extracted from the local DOS of large slab models. For completeness, we also provide values calculated using the potential alignment method. We note that the values obtained using the potential alignment method are highly sensitive to relaxation.

Fig. 6 shows the DOS as a function of position across interfaces of the three semiconductors with Al. In all three interfaces there is a significant presence of MIGS, which decay gradually with the distance from the interface, as also seen in the local DOS plots provided in the SI. In ZnTe, the MIGS decay more rapidly than in the CdSe and InAs, vanishing completely within 14 atomic layers. In the InAs and CdSe some MIGS persist about 18 layers (~ 4 nm) deep into the semiconductor. Deep MIGS are also seen in the structurally similar GaSb/Al interface, shown in the SI. Based on Fig. 6a, in the InAs/Al interface there is downward band bending with the conduction band minimum (CBM) lying ~0.1 eV below the Fermi level. SBH calculations using the potential alignment method yield a negative value of -0.05 eV, which also indicates an Ohmic contact. These results are consistent
with experimental observations in Ref.,¹²⁷ which measured a downward band bending of around 0.3 eV for InAs(100)/Al interfaces, and with the calculations reported in Ref. ¹²⁸ for InAs(100)/Al(111). Fig. 6b shows that in the ZnTe/Al interface there is no band bending and the Fermi level is located in the ZnTe gap with a SBH of ~0.8 eV. The potential alignment method yields a SBH of 0.9 eV. These results are consistent with reports of a Schottky barrier of 0.9 eV for ZnTe(111) ⁵⁶ and ZnTe(110) ⁵⁷,⁵⁸ interfaces with Al. Fig. 6c shows that in the CdSe/Al interface there is downward band bending, similar to InAs/Al, with the CBM positioned ~0.1 eV below the Fermi level. The potential alignment method yields a value of 0.01 eV. The similar band alignment in the CdSe/Al and InAs/Al is to be expected based on the similar conduction band edge positions of InAs and CdSe.⁴³ Our results are consistent with experimental reports of Ohmic contacts for CdSe(1010) interfaced with Al.

59,129,130

## Tri-layer Interfaces

<figure><img src="image_8.png" /><figcaption>Figure 7: Electronic structure of InAs/ZnTe/Al tri-layer interfaces: Density of states as a function of distance from the interface for (a) 8, (b) 16 and (c) 24 atomic layers of ZnTe. The atomic layers are numbered based on distance from the InAs interface, which is located at zero. The location of the InAs/ZnTe and ZnTe/Al interfaces is indicated by dashed lines. The structure of each interface is illustrated on top.</figcaption></figure>

Figures 7 and 8 show the DOS as a function of position across tri-layer interfaces, in which a ZnTe or CdSe tunnel barrier with varying thickness is inserted between InAs and Al. Results for Interfaces with 8, 16, and 24 layers of the tunnel barrier are shown
<figure><img src="image_9.png" /></figure>

Figure 8: Electronic structure of InAs/CdSe/Al tri-layer interfaces: Density of states as a function of distance from the interface for (a) 8, (b) 16 and (c) 24 atomic layers of CdSe. The atomic layers are numbered based on distance from the InAs interface, which is located at zero. The location of the InAs/CdSe and CdSe/Al interfaces is indicated by dashed lines. The structure of each interface is illustrated on top.

here and additional results are provided in the SI. In all cases, regardless of the barrier material and thickness, there is downward band bending and the Fermi level is in the InAs conduction band (as expected). With 8 atomic layers of either material, the MIGS from the Al penetrate through the tunnel barrier into the InAs. As the barrier thickness increases, the InAs becomes increasingly insulated from MIGS until with 16 barrier layers the InAs and Al are completely decoupled from each other. This is also evident from the local DOS in the second InAs layer from the interface, provided in the SI.

The evolution of the ZnTe and CdSe band gaps with the number of layers is similar to that of the CdTe tunnel barrier at the InSb/$\alpha$-Sn interface, reported previously.²⁹ On the one hand, for a thin layer of the barrier material the band gap is expected to be significantly larger than the bulk value because of the quantum size effect (see the gap convergence plot in Figure 1a). On the other hand, there are MIGS penetrating into the gap of the barrier from the Al side and InAs states penetrating from the other side (states from the InAs conduction band penetrate into the ZnTe and states from the InAs valence band penetrate into the CdSe, as seen in Figure 5b,c). For 8 atomic layers of barrier material the MIGS from the Al completely fill the ZnTe/CdSe band gap. With 16 atomic layers of barrier material the gap of the barrier remains smaller than its bulk value. For ZnTe the band gap reaches a maximum of 1.1 eV at a distance of 8 atomic layers from the Al interface. For CdSe the
band gap reaches a maximum of 0.5 eV at a distance of 8 atomic layers from the Al interface. With 24 barrier layers the gap of the barrier approaches the expected value of 1.58 eV for ZnTe and 1.06 eV for CdSe obtained for a slab of the same thickness (see Figure 1). For ZnTe the band gap reaches a maximum of 1.35 eV at a distance of 12 atomic layers from the Al interface. For CdSe the band gap reaches a maximum of 0.8 eV at a distance of 12 atomic layers from the Al interface.

Although ZnTe and CdSe exhibit similar characteristics in terms of the penetration of MIGS and the band gap evolution with barrier thickness, they significantly differ in their band edge positions. For the ZnTe barrier, the valence band maximum is aligned with that of the InAs, similar to the bilayer interface (Figure 5b). Once the ZnTe barrier becomes thick enough to fully develop a band gap (Figure 7c) the Fermi level is positioned approximately in the center of the gap, similar to the bilayer interface with Al (Figure 6b). This means that ZnTe forms an effective barrier for electrons. Owing to the slight downward band bending, a small barrier for holes is also present in Figure 7c. For the CdSe barrier, the conduction band minimum is aligned with that of the InAs, similar to the bilayer interface (Figure 5c). Regardless of the barrier thickness, the Fermi level is positioned in the CdSe conduction band, similar to the bilayer interface with Al (Figure 6c). As a result, CdSe forms an effective barrier for holes but no barrier for electrons. In InAs-based Majorana devices, there is only electron transport because of Fermi level pinning in the conduction band at the InAs surface. Therefore, of the two materials considered here, ZnTe is the better candidate. Similar to our previous study of CdTe as a prospective barrier material for the InSb/$\alpha$-Sn interface,²⁹ we consider the presence of MIGS as an indicator for coupling between the Al and InAs. Therefore, we suggest the thickness range between 6-18 atomic layers for experimental exploration.
Conclusion

In summary, we have used DFT with a Hubbard U correction machine-learned by Bayesian
optimization to study ZnTe and CdSe as prospective tunnel barriers at the InAs/Al interface.
The results of PBE+U(BO) were validated by comparing the band structure of a slab model
of ZnTe(110) with an ARPES experiment, in which the surface-perpendicular Γ − K|U −
X path was probed by varying the photon energy⁹⁵ (the PBE+U(BO) band structure of
InAs had been compared to ARPES experiments previously⁷⁵). We have elucidated the
manifestations of quantum confinement in the surface-perpendicular direction of the slab
in the unfolded band structure. Good agreement with experiment was obtained and the
Umklapp states observed in the experiment were reproduced by shifting the computed bands
by a |ΓX'| lattice vector.

PBE+U(BO) provides a balance between accuracy and computational cost that enables
calculations of very large interface models. We used PBE+U(BO) to calculate the electronic
structure of bilayer ZnTe/CdSe, InAs/ZnTe, and InAs/CdSe interfaces. For the ZnTe/CdSe
interface, we obtained a type-II interface with staggered band gaps. A type-I band alignment
was obtained for both the InAs/ZnTe and InAs/CdSe interfaces, such that for the ZnTe
interface the VBM is aligned, whereas for the CdSe interface the CBM is aligned with with
InAs. For the ZnTe/CdSe and InAs/ZnTe interfaces the band offsets obtained here are
within ~0.2 eV of experimental values and other computational studies. For the InAs/CdSe
interface the deviation in the VBO is somewhat larger, which may be attributed to the
underestimation of the CdSe band gap by PBE+U(BO). In all cases, the type of band
alignment predicted by PBE+U(BO) is qualitatively correct. All band offset measurements
have been conducted for the (001) interface, whereas we used a (110) orientation. This may
also explain some discrepancies, in particular for the more polar III-V/II-VI interfaces. We
also note that the computed band offset values were found to be highly sensitive to structural
relaxation at the interface.

We then proceeded to study bilayer interfaces of InAs, ZnTe, and CdSe with Al. In
all three interfaces, we have found significant penetration of MIGS into the semiconductor, which decay with distance from the interface. In InAs and CdSe, deep MIGS persist for about 18 atomic layers from the interface (~ 4 nm), whereas in ZnTe the MIGS vanish within about 14 atomic layers. InAs and CdSe were found to exhibit downward band bending at the interface, whereas for ZnTe the Fermi level was found to be located in the gap. For all three semiconductor/metal interfaces, our results are in agreement with experimental observations. PBE+U(BO) thus provides a correct description of the band alignment at semiconductor/metal interfaces.

Finally, we considered tri-layer interfaces with a varying number of atomic layers of the ZnTe or CdSe tunnel barrier between the InAs and Al. We have found that the band gap of the barrier evolves as function of distance from the InAs and Al interfaces in a similar manner to the Insb/CdTe/α-Sn interface we had studied previously.²⁹ Contrary to the expectation that the band gap of a very thin barrier would be wider than the bulk band gap because of the quantum size effect, in fact, it is narrowed owing to evanescent states penetrating from both the Al and InAs directions. Only with 24 atomic layers of either material the barrier band gap approaches the expected value about halfway between the Al and InAs. With 8 atomic layers of either ZnTe or CdSe, MIGS from the Al were found to penetrate through the entire width of the barrier into the InAs. 16 layers of either material were found to insulate the InAs from MIGS, which we interpret to mean that the InAs is effectively decoupled from the Al. Although ZnTe and CdSe behave similarly with respect to the barrier thickness, the two materials markedly differ in their band edge positions. As a result, we have found that ZnTe may provide an effective barrier mainly for electrons and to a lesser degree for holes, whereas CdSe only provides a barrier for holes.

In devices based on InAs, holes cannot be utilized because of Fermi level pinning in the conduction band at the surface. As a result, transport is based only on electrons. Therefore, of the two materials considered here, only ZnTe could serve as an effective tunnel barrier in InAs-based Majorana devices. We had previously postulated that in Majorana experiments
a barrier thick enough to completely insulate the semiconductor from the superconductor might also nearly eliminate transport.²⁹ We assume that the relevant regime for tuning the coupling at the interface would be in the thickness range where some MIGS are still present. In the case of a CdSe barrier, this may function as a spacer layer while allowing some current flow. Establishing a connection between parameters of the interface (such as the band alignment and presence MIGS) and proximity-induced superconductivity or other physical factors that affect the emergence of MZMs would require careful experimentation. Based on the results presented here, we would suggest conducting experiments in which the thickness of a ZnTe tunnel barrier is varied between 6-16 atomic layers and the induced superconducting gap in the InAs is measured. This would deepen our understanding of the physical relations between interface phenomena and the emergence of MZMs. Using this insight to design devices with optimal interface configurations could lead to advances in MZM experiments. Metal-semiconductor interfaces are ubiquitous in many types of devices. The results presented here demonstrate the prospects of DFT simulations as a powerful tool for optimizing interface configurations for semiconductor-based devices in general, including multi-layer stacks comprising multiple materials and interfaces.

## Acknowledgement

We thank Janusz Kanski from Chalmers University, Sweden for granting us permission to use the ZnTe ARPES data from Ref.⁹⁵ and for helpful discussions. Work at CMU, UCSB, and the University of Pittsburgh was supported by the Department of Energy through grant DE-SC-0019274. This research used computing resources of the National Energy Research Scientific Computing Center (NERSC), a U.S. Department of Energy Office of Science User Facility operated under Contract No. DE-AC02-05CH11231.
## Supporting Information Available

Effect of lattice parameter on the band structure of ZnTe; Orbital decomposition of the band structures of ZnTe and CdSe obtained with different DFT functionals; Effect of slab thickness on unfolded surface-parallel and surface-perpendicular band structures of ZnTe; Surface matching results for bilayer interfaces; Effect of relaxation on the band alignment at semiconductor interfaces; Element-resolved band structures of semiconductor interfaces; Local DOS for semiconductor/Al interfaces; DOS as a function of position and local DOS for the GaSb/Al interface; SBH calculations using the electrostatic potential alignment method; Local DOS for tri-layer interfaces; DOS as a function of position for tri-layer interfaces with additional barrier thickness values.

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