Ab-initio Prediction of Ultra-Wide Band Gap B xAl1xN Mate- rials Cody Milne Tathagata Biswas Arunima K. Singh

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Ab-initio Prediction of Ultra-Wide Band Gap BxAl1−xN Mate-

rials

Cody Milne* Tathagata Biswas Arunima K. Singh*

Cody Milne, Tathagata Biswas, Arunima K. Singh

Arizona State University

975 S Myrtle Ave

Tempe, AZ 85281

Email: clmilne@asu.edu, arunimasingh@asu.edu, tbiswas3@asu.edu

Keywords: Ultra wide bandgap, DFT, boron aluminum nitride, cluster expansion, high-throughput, power

electronics

Ultra-wide bandgap (UWBG) materials are poised to play an important role in the future of power electronics. Devices made from

UWBG materials are expected to operate at higher voltages, frequencies, and temperatures than current silicon and silicon carbide

based devices; and can even lead to signiﬁcant miniaturization of such devices. In the UWBG ﬁeld, aluminum nitride and boron nitride

have attracted great interest, however, the BxAl1−xN alloys are much less studied. In this article, using ﬁrst-principles simulations

combining density-functional theory and the cluster expansion method we predict the crystal structure of BxAl1−xN alloys. We ﬁnd

17 ground state structures of BxAl1−xN with formation energies between 0.11 and 0.25 eV/atom. All of these structures are found to

be dynamically stable. The BxAl1−xN structures are found to have predominantly a tetrahedral bonding environment, however, some

structures exhibit sp2bonds similar to hexagonal BN. This work expands our knowledge of the structures, energies, and bonding in

BxAl1−xN which aids their synthesis, the innovation of lateral or vertical devices, and discovery of compatible dielectric and Ohmic

contact materials.

arXiv:2210.14375v4 [cond-mat.mtrl-sci] 18 Jan 2023

1 Introduction

Ultra-wide bandgap (UWBG) semiconductors have

recently emerged as an exciting class of materials

due to their potential applications in power elec-

tronics, optoelectronics, and radio frequency devices.

UWBG materials are deﬁned as materials that have

a bandgap larger than that of GaN (3.4 eV)[1]. The

large bandgap of materials impacts many device per-

formance parameters, such as thinner drift layers

and lower speciﬁc on resistance, allowing signiﬁcant

miniaturization of devices like switches and transis-

tors. Furthermore, UWBG materials are generally

characterized by high bandgap, very large break-

down ﬁelds (>106V/cm), high thermal conduc-

tivity, and reduced impact ionization rates and tun-

nelling due their high bandgaps and high mechanical

strengths. AlN and BN are the largest gap group-

III nitrides, and AlN has already been explored for

application in the ﬁeld of power electronics and in

UV device applications[2–4]. AlGaN alloys have also

been used extensively in power electronics due to the

tunability of their bandgaps between the bandgap of

AlN (6.2 eV) and that of GaN (3.4 eV).

Realization of BxAl1−xN alloys could allow fur-

ther tunability of bandgaps beyond what is avail-

able via AlGaN alloys. Figure 1 shows the crys-

tal structures of the wurtzite AlN and BN, as well

as the ground state phase of BN, the hexagonal

phase. The predicted bandgap of w-BN ranges from

5.44 to 7.70 eV[5], much larger than that of GaN

(3.4 eV). Additionally, BxAl1−xN alloys are expected

to display high dielectric constants[6]. Therefore,

BxAl1−xN may have tunable dielectric constants and

high bandgaps without losing the other excellent me-

chanical and thermal properties. However, there are

several challenges in the realization of BxAl1−xN al-

loys. For example, the lattice mismatch between

AlN and BN is very large, 18%. Moreover, BN has a

preference for existing in the hexagonal phase rather

than the metastable wurtzite phase, which makes

introduction of boron into the wurtzite AlN lattice

challenging. Consequently, it leads to the formation

of polycrystalline BN phases in BxAl1−xN alloys and

a high density of grain boundaries that can be detri-

mental to device design and performance[7].

Despite these challenges, thin-ﬁlms of w-BxAl1−xN

have been successfully grown on AlN and sapphire

substrates in very recent years with thicknesses of up

to 300 nm and B-fractions up to x= 0.30[2,6,7,11–15].

Figure 1: The crystal structures of (a) wurtzite phase of alu-

minum nitride as well as (b) hexagonal, (c) cubic and (d)

wurtzite phase of boron nitride.

In addition, experimental eﬀorts have been made to-

wards understanding their crystal growth and struc-

tural properties[7,11,14].

Theory and simulations have been used to study

the structure of a broader range of B-fractions of

BxAl1−xN alloys. Mainly two classes of methods

have been used. The ﬁrst is the method of cation

substitution in the w-AlN host lattice[15–17]. The B-

fractions that can be studied using this method are

dependent on the size of the supercell used to gen-

erate the possible BxAl1−xN structures. Also, as the

BxAl1−xN alloys are highly mismatched alloys, the

restriction of the lattice to the wurtzite phase may

preclude other structures that could be formed in

BxAl1−xN . Another class of methods is the one used

by Ahmed et al that uses density-functional theory

(DFT) based evolutionary structure searches. This

method overcomes the limitations associated with

supercell size and constraints set on the symmetry

of the crystal to predict the structures. However,

due to the high computational resource and time

requirement of this method, only three B-fractions,

x= 0.25,0.5,0.75, were studied by Ahmed et al [18].

In this study, we investigate the structure and

bonding environment of BxAl1−xN over the entire

boron fraction range using the ab-initio cluster ex-

pansion (CE) method. In this method, special quasi-

random alloys structures are predicted based on a

Material Ef[eV atom−1]a[Å] c[Å]

w-AlN -1.584 3.128, 3.112[5] 5.016, 4.982[5]

w-GaN -0.657 3.247, 3.189[5] 5.284, 5.185[5]

w-BN -1.367 2.555, 2.54[5], 2.549[8] 4.226, 4.20[5], 4.223[8]

c-BN -1.384 3.626, 3.617[8] -

h-BN -1.461 2.500, 2.505[9] 6.426, 6.660[9]

Table 1: Comparison of the DFT computed formation energies, Efand lattice parameters of wurtzite group-III-nitrides and

polymorphs of BN. Formation energies are taken from the Materials Project database[10].

cluster expansion Hamiltonian that is ﬁt to DFT

calculated energies. We ﬁnd ground state phases

of BxAl1−xN at 17 B-compositions with formation

energy with respect to AlN and BN between 0.11

to 0.25 eV/atom. We found ﬁve metastable phases

at x= 0.333,0.4,0.5,0.6,and 0.667 that are likely

to be stabilized by high-temperature growth. We

show that the BxAl1−xN structures deviate from the

wurtzite symmetry due to the large lattice mismatch

between AlN and BN. Except one ground structure,

at x= 0.417, all ground structures have the cations

bonded in the sp3bonding environment with angles

of the tetrahedra 94◦to 141◦, and bond lengths be-

tween 1.46 and 1.99 Å. The x= 0.417 structure

displays sp2B bonds that are characteristic of the

hexagonal phase of BN. Dynamical stability of the

structures was established via phonon spectra simu-

lations. The phonon spectra of all the ground state

structures show that they have no imaginary phonon

modes and thus are dynamically stable.

2 Computational methods

We employed the cluster expansion methodology

as implemented in the Alloy Theoretic Automated

Toolkit (ATAT)[19–23] to predict the ground state

structures of BxAl1−xN alloys and compute their to-

tal energies. The energy of a system within the CE

method can be written as

E(σ) = J0+X

Jiˆ

Si(σ) + X

j<i

Jij ˆ

Si(σ)ˆ

Sj(σ)

k<j<i

Jijk ˆ

Si(σ)ˆ

Sj(σ)ˆ

Sk(σ) + ...

(1)

where Ji,Jij, and Jijk refer to the CE coeﬃcients

for the clusters consisting of one, two, and three

atoms, respectively. The value of ˆ

Si(σ)changes de-

pending on if the sites are occupied by Al, B, or

N atoms[24]. Together with the constant J0, these

CE coeﬃcients were determined from DFT ener-

gies of 224 diﬀerent BxAl1−xN compounds calcu-

lated with the Vienna Ab initio Simulation Package

(VASP) package[25–28]. Speciﬁcally, 97 clusters up to

quadruplets were used, the total number of atoms

per unit cell were unrestricted, and the wurtzite lat-

tice was used as the lattice system to generate the

alloy phases. We obtained a cross-validation (CV)

score, which is a measure of the diﬀerence between

the CE and DFT energies, of 0.012 eV/atom. The

CV score is deﬁned as

(CV )2=n−1

i=1

(Ei−ˆ

E(i))2,(2)

where Eiis the DFT calculated energy (per atom)

of structure i,ˆ

E(i)is the CE predicted energy of the

structure, and nis the number of structures included

in the ﬁt.

All the DFT calculations reported in this study

were performed using the Projector Augmented

Wave (PAW)[29] method and the Perdew–Burke–

Ernzerhof (PBE)[29–31] exchange-correlation func-

tional as implemented in the VASP package. We

have used a plane wave basis set with an energy cut-

oﬀ of 670 eV and a k-grid with 2000 k-points per re-

ciprocal atom for our calculations. The alloy struc-

tures are initialized from the AlN lattice and then

transformed to supercells using the CE formalism.

We then obtained the ﬁnal structures by relaxing

the atomic positions as well as the lattice parame-

ters such that the forces between the ions are less

than 0.01 eV/Å.

The phonon spectra of the ground state structures

were calculated using VASP and the phonopy pack-

age[32]. For all of the phonon calculations, we have

employed a 3×3×3supercell for each structure. An

energy cut-oﬀ of 500 eV was used and the atomic

positions were relaxed until the total free energy

change between steps was less than 10−8eV. For the

structures with fewer number of atoms per unit cell

(x= 0,0.167,0.25,0.333,0.5,0.667,0.75,0.833,1),

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Ab-initioPredictionofUltra-WideBandGapBxAl1xNMate-rialsCodyMilne*TathagataBiswasArunimaK.Singh*CodyMilne,TathagataBiswas,ArunimaK.SinghArizonaStateUniversity975SMyrtleAveTempe,AZ85281Email:clmilne@asu.edu,arunimasingh@asu.edu,tbiswas3@asu.eduKeywords:Ultrawidebandgap,DFT,boronaluminumnitride,cluster...

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