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First-principle investigation of monoclinic(AlxInyGa1−x−y)2O3 quaternary alloys

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First-principle investigation of monoclinic(AlxInyGa1−x−y)2O3 quaternary alloys

Xiaoli Liu and Chee-Keong Tan

Department of Electrical and Computer Engineering, Clarkson University, Potsdam, NY 13699, UnitedStates of America

E-mail: liux8@clarkson.edu and ctan@clarkson.edu

Received 26 July 2019, revised 15 October 2019Accepted for publication 10 December 2019Published 17 January 2020

AbstractFirst-principle density functional theory calculations were performed to explore electronic andstructural properties of β-(AlxInyGa1−x−y)2O3 quaternary alloys with both Al-content (x) and In-content (y) ranging from 0% to 18.75%. The β-(AlxInyGa1−x−y)2O3 quaternary alloys exhibitindirect band gap property with the bandgap energy varying from 4.432 to 5.171 eV. Electroneffective masses are also presented for β-(AlxInyGa1−x−y)2O3 quaternary alloys, showing ageneral reduction with In-content increases but a general increment with Al-content increases inthe material. Further analysis indicates the possibility of achieving lattice-matched or near-lattice-matched β-(AlxInyGa1−x−y)2O3/β-Ga2O3 structures system, which is critical for highperformance field effect transistor and deep ultraviolet photodetector applications. Our workshows that the β-(AlInGa)2O3 alloys with proper tuning of Al- and In-content have strongpotential to be used as part of the epitaxial layers for β-Ga2O3-based material system.

Supplementary material for this article is available online

Keywords: gallium oxide, quaternary alloy, density functional theory, electronic properties,lattice constants, band structure, band gap

(Some figures may appear in colour only in the online journal)

Introduction

Gallium oxide material class has emerged as one of the mostpromising semiconductors for electronic device applicationswithin the last decade. Among all the five confirmed poly-types of gallium oxide (α, β, γ, κ and ε), monoclinic galliumoxide (β-Ga2O3) has drawn much attention in numeroustechnological applications fields such as high-power fieldeffect transistors (FETs) and deep ultraviolet (DUV) photo-detectors. One of the unique properties of β-Ga2O3 is thepossession of ultrawide bandgap of 4.6–4.9 eV [1], whichenables β-Ga2O3-based devices to exhibit excellent advan-tages including large critical breakdown field voltage andhigh electrical conductivity [2]. Nonetheless, devices includ-ing FETs and DUV photodetectors involve multi-layer het-erostructure design aiming for enhanced carrier confinementor transport, with the goal of attaining performance thatotherwise could not be achieved with one single bulk mat-erial. In the case of β-Ga2O3, there emerges a strong need of

constructing such multi-layer structure and accessing the useof aluminum (Al) and indium (In) to form ternary and qua-ternary III-Oxide alloys would satisfy the need in a relativelysimilar fashion to the III-Nitride-based materials in the formof InGaN and AlGaN alloys [3–7].

Extensive research work on III-Oxide binary and ternaryalloys (Al2O3, Ga2O3 and In2O3) have been reported [1, 2,8–31], but the understanding on the properties ofβ-Ga2O3-based quaternary materials (i.e.β-(AlxInyGa1−x−y)2O3 alloys) is non-existent in literature byfar. It is important to point out that quaternary alloy layer hasbeen implanted in well-established III-Nitride and III–Vmaterials class to achieve desirable device performance [4, 6,31–43]. Quaternary alloys typically allow large tuning rangeof structural, electronic and optical properties that are differ-ent from the host material. In certain cases, quaternary alloyalso provides lattice-matching condition with the host mat-erial, allowing greater flexibility in the structure design indevices. In addition, lattice-matched structures will lead to

Semiconductor Science and Technology

Semicond. Sci. Technol. 35 (2020) 025023 (10pp) https://doi.org/10.1088/1361-6641/ab607c

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lower defect densities in materials, enabling higher perfor-mance in the devices. Notable use of quaternary alloyincludes the AlInGaN electron blocking layer for III-Nitridelight emitting diodes [4, 6], dilute-nitride AlGaAsN for highefficiency solar cell [40] and AlInGaAs/InGaAs for strainedquantum well laser [43]. Interestingly, there has been noheterostucture design of (AlxInyGa1−x−y)2O3/Ga2O3, eventhough the quaternary alloy would potentially provide prop-erties tuning flexibility in Ga2O3 based devices. In fact, therehas been no literature on (AlxInyGa1−x−y)2O3 quaternary alloyup to present. To achieve such design purpose forβ-Ga2O3-based devices, the least understanding of the elec-tronic and structural properties of (AlxInyGa1−x−y)2O3 alloyswill be required. Thus, investigating the electronic propertiesof the β-Ga2O3-based quaternary materials is a critical step inthe pathway towards implementing the semiconductors fordevices in the field of electronics and optoelectronics.

In this work, the β-(AlxInyGa1−x−y)2O3 alloys with bothAl-content (x) and In-content (y) up to 18.75% are investi-gated using density function theory (DFT) calculations. Theeffect of aluminum and indium atoms on the electronic bandstructures of β-Ga2O3 quaternary alloys are analyzed. Inaddition, the lattice constants of β-(AlxInyGa1−x−y)2O3 alloysare analyzed, and the electron effective masses of the alloysare also presented. Our analysis indicates the possibility toachieve lattice-matching condition betweenβ-(AlxInyGa1−x−y)2O3 and β-Ga2O3 alloys with proper tuningof Al- and In-content, which is an important criteria for lowstrain and small interface roughness within device structure.Our analysis presents the first-time findings on III-Oxidequaternary alloys and our work indicate the strong potential ofusing (AlxInyGa1−x−y)2O3 alloys as part of the gallium oxide-based structures including two-dimensional gas electrons(2DEG) structure for electronic devices [5]. For simplicitysake, we also define β-(AlxInyGa1−x−y)2O3 as AlInGaO alloysin this study.

Simulation methods

A crystal model of AlInGaO quaternary alloy is constructedfor the band structure calculations using the supercellapproach implemented in atomistic simulation packageMedeA-VASP software [44–46]. As shown in figure 1, the80-atom β-Ga2O3 1×2×2 supercell contains 32 galliumatoms and 48 oxygen atoms in total. Theβ-(AlxInyGa1−x−y)2O3 alloys are obtained via replacing Gaatoms in a certain proportion using Al and In atoms. Note thatall the substituted gallium atoms are located at the octahedralsites of the β-Ga2O3 crystal structure, since the formationenergy required to substitute Ga atom at tetrahedral site ishigher compared to octahedral site [11].β-(AlxInyGa1−x−y)2O3 alloys with In-content higher than18.75% are not considered in this study, since the phaseseparation issue is known in the β-Ga2O3 alloys with morethan 20%-In [12, 13]. For consistency purpose, Al-content iskept at maximum of 18.75% for β-(AlxInyGa1−x−y)2O3 alloys,even though the upper limit for incorporation of Al-content in

β-Ga2O3 alloys can be much higher [19]. Note that clusterexpansion approach can be implemented to find out variousthermodynamically stable configurations of AlInGaO alloys.Cluster expansion method is a widely used technique to cal-culate thermodynamic properties of solids [47, 48]. Furtherwork implementing cluster expansion method will be con-ducted to determine the maximum Al and In content in thequaternary AlInGaO alloys that can remain thermo-dynamically stable.

The band structure calculations for β-(AlxInyGa1−x−y)2O3

alloys were performed by using the projector augmentedwave method. The semilocal generalized gradient approx-imation Perdew–Burke–Ernzerhof (GGA-PBE) functional isapplied to treat the exchange-correlation potential in the DFTcalculations. Electronic wave functions are described in aplane wave basis with a cut-off energy of 400 eV and thegeometric structure optimization was performed by relaxingthe atom positions with the Hellmann–Feynman force set to0.02 eV Å−1. External stress is not applied to the supercell,and the energy convergence tolerance was set to 1×10−5

eV/atom. The Monkhorst–Pack grid is Gamma-centered andhigh symmetry k-points in x, y and z-directions were used forband structure calculations. For all the structures, the k-spa-cing is 0.25/Angstrom, which leads to a 3×5×3 mesh.This corresponds to actual k-spacings of0.177×0.207×0.186 per Angstrom.

In general, DFT methods can be categorized into threedifferent functionals: (a) local density approximation (LDA),(b) GGA, and (c) meta-generalized gradient approximation(M-GGA). A Hartree–Fock exchange can be included in thesefunctionals to form hybrid functional. In general, hybridfunctionals provide closer agreement with experimentalresults, at the expense of high computational costs. On theother hand, LDA and GGA based functionals offer muchfaster calculations, at the expense of result accuracies espe-cially on the prediction of energy band gaps of materials.However, for semiconductor materials, the band gap errorsfrom the LDA and GGA functionals can be corrected byapplying the scissor operator, allowing the result to be inclose agreement with the experimental results. Besides, GGAfunctional provides a reasonable estimation of the structural

Figure 1. Supercell structure β-Ga2O3 crystal in which the Ga atomscan be substituted by Al and In atom to obtain β-(AlxInyGa1−x−y)2O3

quaternary alloy with different Al and In-content.

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Semicond. Sci. Technol. 35 (2020) 025023 X Liu and C-K Tan

properties as compared to that of hybrid functional [49]. Thus,as the first study in the quaternary AlInGaO alloy, GGAfunctional is implemented. Future studies of AlInGaO alloywill be conducted using hybrid functional. Results compar-ison using GGA and hybrid functionals will be made todetermine the advantages and disadvantages for III-Oxidematerials.

Results and discussions

Scissor operator has been applied to correct the error origi-nated from the GGA exchange correlation functional in theDFT calculations [50]. The dielectric constant ε required forscissor operator calculation for the β-(AlxInyGa1−x−y)2O3

alloys is calculated using interpolation as following,

( ) ( )( ) ( ) ( )

e e ee

= ++ - -

x y

x y

Al O In O

1 Ga O , 12 3 2 3

2 3

* **

in which the dielectric constant parameters for the Al2O3,Ga2O3 and In2O3 binary alloys are obtained from literature[8, 16, 24].

Figure 2 presents the corrected DFT-calculated bandstructures of β-(AlxInyGa1−x−y)2O3 alloys with (a)

x=y=0%, (b) x=18.75%, y=0%, (c) x=0%,y=18.75% and (d) x=y=6.25%. According to the bandstructures of β-(AlxInyGa1−x−y)2O3 alloys with different Al/In-content obtained through DFT calculations, all the alloysexhibit indirect band gap property, which is similar to that ofβ-Ga2O3. Here the symmetry points included the F (0, 0.5, 0),B (0.5, 0, 0), N (0, 0, 0.5), Γ (0, 0, 0) and A (0.5, 0.5, 0.5). Theconduction band minimum of the alloys is always located atthe Г point in the brillouin zone, while the valance bandmaximum location is off the Г point. Further analysis revealedthat when the content of indium is equal or higher than that ofaluminum, the valance band maximum tends to move from Г–N (0, 0, 0.5) direction to Г–F (0, 0.5, 0) direction, whichimplies the addition of impurity has effect on not only theconduction band, but also the valance band dispersion.

It is important to point out that this work assumes lineardependence of dielectric constant with the Al/Ga/In com-positions to estimate the energy band gaps of AlInGaO alloys,as can be seen in equation (1). In general, band bowing existsin most compound alloy systems [11, 51, 52]. For quaternaryAlInGaO system, bowing parameters for correspondingternary alloys (AlGaO, InGaO and AlInO) will be required.The literature in III-Oxide system is still limited, and furtherstudies will be required to find out the bowing parameters.

Figure 2. First principle DFT-calculated band structures of β-(AlxInyGa1−x−y)2O3 alloy with (a) x=y=0%, (b) x=18.75%, y=0%, (c)x=0%, y=18.75% and (d) x=y=6.25%.

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Semicond. Sci. Technol. 35 (2020) 025023 X Liu and C-K Tan

Further investigation will be conducted using hybrid func-tional or meta-GGA approach to understand the compositiondependence of bowing parameters in the III-Oxide materialsystems. The conclusion based on this work however shouldremain valid, with the fact that the addition of Indium andAluminum will shrink and enlarge the band gaps of galliumoxide respectively.

To further explain the band structure change, thecorresponding density of states (DOS) of AlInGaO alloys arepresented in figure 3 below. Figures 3(a) and (b) presents thetotal and partial DOS for Ga2O3 and AlInGaO alloys with6.25%-Al and 6.25%-In respectively. As shown in figure 1(a),the valence band of the intrinsic Ga2O3 is composed of Ga 4s,4p and 3d states, as well as O 2s and 2p states. The uppervalence subbands consist primarily of O 2p states and thecontributions of the other states are relatively small. For thelower conduction bands, the primary contributions originatefrom Ga 4s and 4p states, which are consistent with previousliterature [53]. For AlInGaO alloy, the O 2p states play thedominant role in the upper valence subbands, even though In4d states also contribute considerably onto the bands. Moresubstantial contributions from In and Al states occur in theconduction bands. Interestingly, the In 5s states and Ga 4sstates contribute almost equally in the lower conductionbands, which might explain the reduction of electron effectivemass as In content increases in the alloy. It is known thatIn2O3 alloy has a lower electron effective mass than that ofGa2O3 alloy [54]. In general, the hybridization between O 2pstates with the In and Al orbital states would likely result inthe band structure changes. Note that scissor operator has notbeen applied on the DOS, as our goal is to provide a quali-tative picture on the contribution of each orbital state on theband structures.

Figure 4(a) presents the direct and indirect energybandgap as a function of Al-content and In-content for

β-(AlxInyGa1−x−y)2O3 alloys with x and y ranging from 0% to18.75%. The direct and indirect bandgap of the oxide alloysare represented by the solid lines and dotted lines respec-tively. The direct band gap value is obtained by taking theminimum value of conduction band and maximum value ofvalence band energy at the Gamma-point (Г) in the brillouinzone, while the indirect band gap value is obtained by takingthe minimum conduction band and maximum valence band inthe brillouin zone. As shown in figure 4(a), it shows a generallinear relation between the bandgap change ofβ-(AlxInyGa1−x−y)2O3 alloys and the impurity content when xand y is below 12.5%, while a slight distortion appears when xand y go beyond 12.5%. This is expected to be related withthe crystal structure deformation in the relative high impuritycontent situation. As illustrated by the intercepts of solid linesin the y-axis, the direct bandgap of β-(AlxGa1−x)2O3 increasesfrom 4.835 to 5.171 eV when the Al-content increases from0% to 18.75%, while the direct bandgap of β-(InxGa1−x)2O3

alloys decreases from 4.835 to 4.432 eV when the In-contentgo up to 18.75%. This can be explained by the band prop-erties of Al2O3 and In2O3, which possess bandgaps of ∼7.5eV and ∼3 eV, respectively [10]. The incorporation of alu-minum tends to enlarge the bandgap and the indium contrarilypromotes bandgap to shrink. With the capability of tuning theenergy band gap through flexibility in tuning Al/In-content inthe β-(AlxInyGa1−x−y)2O3 alloys, the ultrawide bandgap gal-lium oxide-based material is expected to be applicable in theultraviolet (UV) photodetector and transistor devices.

The energy band gap can also be viewed in the form ofbulk transition wavelength. Here the transition wavelength iscalculated based on the indirect band gap energy of the oxidequaternary alloys. As shown in figure 4(b), the calculatedtransition wavelength of β-(AlxInyGa1−x−y)2O3 alloys coversa range of 240–280 nm, which implies that theβ-(AlxInyGa1−x−y)2O3 alloys can be applied for devices

Figure 3. The total and partial DOS of (a) Ga2O3 and (b) (AlxInyGa1−x−y)2O3 alloys with x=y=6.25%.

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Semicond. Sci. Technol. 35 (2020) 025023 X Liu and C-K Tan

operating in the deep UV regime. It is important to point outthat the energy difference between indirect and direct energyband gap values for the oxide quaternary alloy remain small(<0.03 eV) across all the contents under consideration in thiswork. In addition, the indirect-direct energy gap difference isshown to be smaller as the In-content reaches 18.75% in theβ-(AlxInyGa1−x−y)2O3 alloys. It is possible that a crossover ofindirect-direct band gap property could occur, but furtherstudy on the band structure evolution will be required tounderstand the effect of In-content and Al-content in the III-Oxide quaternary alloys. In addition, complex dielectricfunction will be taken into account in future work to obtainthe absorption coefficients for the AlInGaO alloys, which canthen be used to provide a more accurate determination oftransition wavelength where the actual transition occurs.

Figure 4(c) illustrated the calculated average effectivemass of electrons of β-(AlxInyGa1−x−y)2O3 alloys in differentdirections. The electron effective masses are calculated based

on the DFT-calculated band structures. The average effectivemass values are obtained by taking the geometric mean ofeffective masses in four directions, i.e. Γ-(0.5, 0, 0), Γ-(0, 0.5,0), Γ-(0, 0, 0.5), Γ-(0.5,0.5,0.5). Our results for β-Ga2O3 arein good agreement with existing literature [9, 14], and theelectron effective mass value of β-(AlxInyGa1−x−y)2O3 alloysare generally within 0.22–0.28m0. Moreover, the addition ofaluminum and indium has an obvious effect on the effectivemass changing. The β-(AlxGa1−x)2O3 alloys appear to possesslarger effective mass value than the β-(InyGa1−y)2O3 alloys.In general, the effective mass of β-(AlxInyGa1−x−y)2O3 alloysshows reduction with the increasing of In-content, butincreases with the increasing of Al-content. This finding isvaluable for exploring devices sensitivity improvement inDUV photodetectors [15, 55] and further investigations needto be conducted to evaluate the importance of electroneffective mass tuning in the photodetector deviceperformance.

Figure 4. (a) Energy bandgap of β-(AlxInyGa1−x−y)2O3 alloy with Al-content and In-content up to 18.75%; (b) wavelength corresponding toindirect bandgap of β-(AlxInyGa1−x−y)2O3 alloy; (c) electron effective mass of β-(AlxInyGa1−x−y)2O3 alloy with Al-content and In-content upto 18.75%.

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Semicond. Sci. Technol. 35 (2020) 025023 X Liu and C-K Tan

The advantage of using AlInGaO quaternary alloycompared to the AlGaO or InGaO ternary alloys lies on thelattices. It is well known that unmatched lattice parametersbetween epitaxial layers and the supporting substrate or bufferlayer will cause strained or relaxed growth, leading to inter-facial defects or misfit dislocations. Such defects would likelylead to adverse changes in the electronic or optical propertiesof the films. Growth of AlGaO or InGaO ternary alloys on topof β-Ga2O3 alloy in c-direction is confronted with the lattice-mismatching problem as illustrated in the figure 5, causingtensile or compressive strain to the structure system. Nearlymatched lattices, as shown in figure 5(c) using(AlxInyGa1−x−y)2O3/β-Ga2O3 system, are desired to mini-mize defects and potentially increase electron mobility, whichis critical for high electron mobility transistor applicationsespecially in the case of 2DEG channels. The use of lattice-matched epitaxial layers has been widely sought after in theapplication of transistor or heterostructure-based devices, asevidenced in the field of III-Nitride, Si–Ge and III–V mate-rials system [33, 56–58]. As a prime example, the growth oflarge Al fraction III-Nitrides has been suffering from the lackof a lattice-matched substrate, and resultant lattice strain inAlGaN/GaN heterostructures degrades the critical thicknessof AlGaN barrier and causes uncontrolled local strainrelaxation at the heterointerface via generation of misfit dis-locations and cracks [33]. As a result, much work has beenconducted in using AlInN and AlInGaN epitaxial layers[5, 34, 59–61], and substrate engineering [62, 63] to reducethe lattice mismatch between the layers. From the perspectiveof ensuring higher material quality, achieving lattice-match-ing condition within a device structure is an important goal insemiconductor epitaxial growth.

Our analysis indicated that the AlInGaO quaternary alloysystem can be designed to be lattice-matching with β-Ga2O3

alloy, implying the possibility of adjusting the band propertiesof β-Ga2O3-based material without creating compressive ortensile strain within the material systems. The lattice para-meters of the AlInGaO alloys have been investigated andanalyzed. Figures 6(a)–(c) presents the lattice constants a, band c of β-(AlxInyGa1−x−y)2O3 quaternary alloys with x and ycontent ranging from 0% to 18.75%, respectively. As shown

in figure 6, when In-content increases in theβ-(AlxInyGa1−x−y)2O3 quaternary alloys at a fixed Al-content,all the lattice constants a, b and c increase generally. As anexample, the addition of 18.75%-In in theβ-(AlxInyGa1−x−y)2O3 quaternary alloys with 6.25%-Alresults in the increase of lattice constants a, b and c from12.239 to 12.409 Å, from 3.044 to 3.107 Å, and from 5.812 to5.885 Å, respectively. The lattices a, b and c show incrementof 0.925%, 1.492%, and 0.901% respectively, as compared tothe lattice constants of β-Ga2O3 alloys. The lattice incrementis similar for the β-(AlxInyGa1−x−y)2O3 quaternary alloys withdifferent fixed Al-content. On the other hand, when Al-con-tent increases in the β-(AlxInyGa1−x−y)2O3 quaternary alloysat a fixed In-content, the lattice constants a, b and c reducesgenerally. For example, when In-content is fixed at 6.25%,the addition of 18.75%-Al in the β-(AlxInyGa1−x−y)2O3 qua-ternary alloys leads to reduction of lattice constants a, b and cfrom 12.348 to 12.244 Å, from 3.08 to 3.05 Å and from 5.865to 5.827 Å, respectively. The lattices a, b and c showreduction of 0.416%, 0.389%, and 0.36% respectively, ascompared to the lattice constants of β-Ga2O3 alloys. Similarreduction is found in β-(AlxInyGa1−x−y)2O3 quaternary alloyswith different fixed In-contents as well. For the part of(AlGa)2O3 or (InGa)2O3 ternary alloys (i.e. either 0%-Al or0%-In), our results are consistent with previous work [18–20,64, 65]. The other results are first reported through this study.The effect of Aluminum and Indium addition on the lattices ofβ-Ga2O3 alloys are primarily attributed to the atomic sizedifference in the material, which is also consistent withobservations shown in III-Nitride-based quaternary materials[7, 35–38]. Specifically, aluminum atom is smaller thanGallium atom while Indium atom is larger than Gallium atom.To accommodate the atomic size difference, supercell willexpand or shrink accordingly to achieve equilibrium, whichdirectly results in the increase or reduction of lattice constantsof the materials.

Here we assume that the β-(AlxInyGa1−x−y)2O3 qua-ternary alloys are to be grown on (001) β-Ga2O3 substrate, inwhich the growth direction is on the c-direction [21–24, 30].As the β-Ga2O3 related alloys exhibit monoclinic phase nat-ure, the in-plane direction constitutes dissimilar a and b latticeparameters which are different from that of III–V basedmaterials with wurtzite or zinc-blende crystal structures.Lattice constant c is less of a concern in this case. Thisimplies that there is a need to satisfy lattice-matching con-dition in both a and b directions for the β-(AlxInyGa1−x−y)2O3

quaternary alloys. Figure 7 presents the required Al-contentand In-content in the β-(AlxInyGa1−x−y)2O3 quaternary alloysto achieve lattice-matching condition with β-Ga2O3 alloys forlattice constant a and lattice constant b respectively. Asshown in figure 7, the lattice misfit in a and b of β-Ga2O3

alloys caused by addition of Al content can be compensatedby the addition of In-content in the material. The Al and In-content proportionality for lattice constant a and b is howeverdifferent. As an example, in the β-(AlxInyGa1−x−y)2O3 qua-ternary alloys with 6.25% Al-content, the required In-contentto match lattice parameters a and b are 5.8% and 4.5%respectively, but the required In-content for

Figure 5. Illustration of three different structure systems that can belattice-mismatched (tensile or compressive) or near-lattice-matchedby tuning Al and In-content in the oxide alloys.

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Semicond. Sci. Technol. 35 (2020) 025023 X Liu and C-K Tan

β-(AlxInyGa1−x−y)2O3 quaternary alloys with 18.75% Al-content are 12.8% and 9.0% respectively. The difference inthe required In-content for lattice-matching a and b increasesas Al-content increases in the quaternary alloys. This indi-cates the difficulty of satisfying both lattice-matching condi-tion simultaneously in the β-(AlxInyGa1−x−y)2O3 quaternaryalloys. Nonetheless, it is important to point out that it ispossible to compromise and achieve near-lattice-match con-dition in β-(AlxInyGa1−x−y)2O3/β-Ga2O3 alloys by taking theaverage of In-contents required for a and b (as shown indotted line of figure 7). Our analysis estimates that the latticemisfit in both a and b directions will be less than 1% whenAl-content increases from 0% to 18.75% in theβ-(AlxInyGa1−x−y)2O3 quaternary alloys.

It is important to point out that the ternary AlInO alloy ata certain Al:In proportion could also provide reasonable lat-tice-matching condition to Ga2O3 material, in addition to theAlInGaO material. However, the ground state Al2O3 andIn2O3 are corundum and cubic phases respectively. Theground state ternary AlInO alloys are likely to be either

Figure 6. (a) Lattice constant a, (b) lattice constant b, and (c) lattice constant c, of β-(AlxInyGa1−x−y)2O3 alloy with Al-content and In-contentup to 18.75%.

Figure 7. Lattice matching condition based on lattice constant a andb, assuming growth of β-(AlxInyGa1−x−y)2O3 quaternary alloys on(001) Ga2O3 substrate.

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Semicond. Sci. Technol. 35 (2020) 025023 X Liu and C-K Tan

corundum or cubic crystal phase, which will be different fromGa2O3 of monoclinic phase. Note that the III-Oxide system isdifferent from III-Nitride materials system. The ground stateAlN, GaN and InN possess wurtzite crystal structures,allowing the use of lattice-matched AlInN/GaN system.Further studies on AlInO alloys will be conducted to under-stand the properties of AlInO and to gauge its potential for III-Oxide devices use.

The work on β-(AlxInyGa1−x−y)2O3 quaternary alloys isunprecedented at present, and there is no analysis available inthe literature in regards on the properties of this alloy. There isalso no available growth data for β-(AlxInyGa1−x−y)2O3

quaternary alloys. It is expected that β-(AlxInyGa1−x−y)2O3

quaternary alloys can be grown via molecular beam epitaxyand metal-organic chemical vapor deposition epitaxial tech-niques [26–29]. Our work shows that β-(AlxInyGa1−x−y)2O3

quaternary alloys can be a promising material candidate to beused in conjunction with β-Ga2O3 material or other relevantIII-Oxide materials, if Al-content and In-content is properlytuned. Future work will be conducted to understand the otherproperties of β-(AlxInyGa1−x−y)2O3 quaternary alloys as wellas the band alignment of β-(AlxInyGa1−x−y)2O3/β-Ga2O3

structure system for further gauge of its potential as part ofIII-Oxide based devices.

Summary

In summary, first-principle DFT calculations are carried outusing GGA-PBE exchange correlation functional to investi-gate the electronic properties of β-(AlxInyGa1−x−y)2O3 alloys.With Al-content and In-content changing from 0% to 18.75%,the band structures of β-(AlxInyGa1−x−y)2O3 alloys are foundto exhibit indirect bandgap property with the bandgap energyranging from 5.171 to 4.432 eV. The wavelength corresp-onding to the bandgap energy is extracted which covers aregion of 240–280 nm, indicating the potential use ofβ-(AlxInyGa1−x−y)2O3 alloys for deep UV photodetector.Electron effective masses of β-(AlxInyGa1−x−y)2O3 qua-ternary alloys are presented, as the effective mass reduceswith In-content increasing but increases with Al-contentincreasing in the alloys. In addition, the lattice properties ofβ-(AlxInyGa1−x−y)2O3 alloys are presented. Our results showthat the increase of In-content leads to increment of latticeconstants a and b, while the increase of Al-content leads toreduction of lattice constants a and b. With proper tuning ofAl/In-content, lattice-matching or near-lattice-matching con-ditions can be achieved for β-(AlxInyGa1−x−y)2O3/β-Ga2O3

structure, which are important for high speed electron mobi-lity transistor and optoelectronic devices applications. Ourstudies on the effect of Al/In content on the bandgap,effective masses and lattice parameters of the quaternaryβ-(AlxInyGa1−x−y)2O3 alloys are presented for the first time.Our results indicate the strong potential ofβ-(AlxInyGa1−x−y)2O3 quaternary alloys as a candidate forepitaxial layers for semiconductor devices, and our work areessential for future device modeling and simulations invol-ving the III-Oxide materials.

Acknowledgments

The work is supported by C K Tan startup grant that is kindlyprovided by Clarkson University, as well as grant provided byNSF-IUCRC Center for Metamaterials funded project.

ORCID iDs

Chee-Keong Tan https://orcid.org/0000-0002-1776-4491

References

[1] Razeghi M, Park J H, McClintock R, Pavlidis D, Teherani F H,Rogers D J and Dravid V P 2018 A review of the growth,doping, and applications of β-Ga2O3 thin films Oxide-basedMaterials And Devices IX 10533

[2] Stepanov S I, Nikolaev V I, Bougrov V E and Romanov A E2016 Gallium oxide: properties and applications-a reviewRev. Adv. Mater. Sci 44 63–86

[3] Nakamura S, Mukai T and Senoh M 2019 Candela-class high-brightness InGaN/AlGaN double-heterostructure blue-light-emitting diodes Appl. Phys. Lett. 64 1687

[4] Zhang J, Yang J, Simin G, Shatalov M, Khan M A,Shur M S and Gaska R 2000 Enhanced luminescence inInGaN multiple quantum wells with quaternary AlInGaNbarriers Appl. Phys. Lett. 77 2668

[5] Ambacher O et al 1999 Two-dimensional electron gasesinduced by spontaneous and piezoelectric polarizationcharges in N-and Ga-face AlGaN/GaN heterostructuresJ. Appl. Phys. 85 3222

[6] Liu G, Zhang J, Tan C K and Tansu N 2013 Efficiency-droopsuppression by using large-bandgap AlGaInN thin barrierlayers in InGaN quantum-well light-emitting diodes IEEEPhotonics J. 5 2201011

[7] Dridi Z, Bouhafs B and Ruterana P 2003 First-principlesinvestigation of lattice constants and bowing parameters inwurtzite AlxGa1−xN, InxGa1−xN and InxAl1−xN alloysSemicond. Sci. Technol. 18 850

[8] Harman A K, Ninomiya S and Adachi S 1994 Opticalconstantsof sapphire (α-Al2O3) single crystals J. Appl. Phys. 76 8032

[9] Yamaguchi K 2004 First principles study on electronicstructure of β-Ga2O3 Solid State Commun. 131 12

[10] King P D C, Veal T D, Fuchs F, Wang C Y, Payne D J,Bourlange A and Egdell R G 2009 Band gap, electronicstructure, and surface electron accumulation of cubic andrhombohedral In2O3 Phys. Rev. B 79 205211

[11] Peelaers H, Steiauf D, Varley J B, Janotti A andVan de Walle C G 2015 (InxGa1−x)2O3 alloys for transparentelectronics Phys. Rev. B 92 085206

[12] Maccioni M B and Fiorentini V 2016 Phase diagram andpolarization of stable phases of (Ga1−xInx)2O3 Appl. Phys.Express 9 041102

[13] Maccioni M B, Ricci F and Fiorentini V 2015 Low in solubilityand band offsets in the small-x β-Ga2O3/(Ga1−xInx)2O3

system Appl. Phys. Express 8 021102[14] Peelaers H and Van de Walle C G 2017 Lack of quantum

confinement in Ga2O3 nanolayers Phys. Rev. B 96 081409[15] Pratiyush A S, Krishnamoorthy S, Muralidharan R,

Rajan S and Nath D N 2019 Advances in Ga2O3 solar-blindUV photodetectors Gallium Oxide (Amsterdam: Elsevier)

[16] Krishnamoorthy S, Xia Z, Joishi C, Zhang Y, McGlone J,Johnson J and Rajan S 2017 Modulation-dopedβ-(Al0.2Ga0.8)2O3/Ga2O3 field-effect transistor Appl. Phys.Lett. 111 023502

8

Semicond. Sci. Technol. 35 (2020) 025023 X Liu and C-K Tan

[17] Feneberg M, Nixdorf J, Lidig C, Goldhahn R, Galazka Z,Bierwagen O and Speck J S 2016 Many-electron effects onthe dielectric function of cubic In2O3: effective electronmass, band nonparabolicity, band gap renormalization, andBurstein-Moss shift Phys. Rev. B 93 045203

[18] Marezio M 1966 Refinement of the crystal structure of In2O3 attwo wavelengths Acta Crystallogr. 20 6

[19] Peelaers H, Varley J B, Speck J S and Van de Walle C G 2018Structural and electronic properties of Ga2O3-Al2O3 alloysAppl. Phys. Lett. 112 242101

[20] Wang T, Li W, Ni C and Janotti A 2018 Band gap and bandoffset of Ga2O3 and (AlxGa1−x)2O3 alloys Phys. Rev. Appl.10 011003

[21] Higashiwaki M, Sasaki K, Murakami H, Kumagai Y,Koukitu A, Kuramata A, Masui T and Yamakoshi S 2016Recent progress in Ga2O3 power devices Semicond. Sci.Technol. 31 034001

[22] Oshima Y, Ahmadi E, Kaun S, Wu F and Speck J S 2017Growth and etching characteristics of (001) β-Ga2O3 byplasma-assisted molecular beam epitaxy Semicond. Sci.Technol. 33 015013

[23] Han S H, Mauze A, Ahmadi E, Mates T, Oshima Y andSpeck J S 2018 n-type dopants in (001) β-Ga2O3 grown on(001) β-Ga2O3 substrates by plasma-assisted molecularbeam epitaxy Semicond. Sci. Technol. 33 045001

[24] Goto K, Konishi K, Murakami H, Kumagai Y, Monemar B,Higashiwaki M, Kuramata A and Yamakoshi S 2018 Halidevapor phase epitaxy of Si doped β-Ga2O3 and its electricalproperties Thin Solid Films 666 182

[25] Pearton S J, Yang J, Cary P H IV, Ren F, Kim J,Tadjer M J and Mastro M A 2018 A review of Ga2O3

materials, processing, and devices Appl. Phys. Rev. 5011301

[26] Higashiwaki M, Sasaki K, Kuramata A, Masui T andYamakoshi S 2014 Development of gallium oxide powerdevices Phys. Status Solidi a 211 1

[27] Wang A, Edleman N L, Babcock J R, Marks T J, Lane M A,Brazis P R and Kannewurf C R 2002 Growth,microstructure, charge transport, and transparency ofrandom polycrystalline and heteroepitaxial metalorganicchemical vapor deposition-derived gallium–indium–oxidethin films J. Mater. Res. 17 3155–62

[28] Kaun S W, Wu F and Speck J S 2015 β-(AlxGa1−x)2O3/Ga2O3

(010) heterostructures grown on β-Ga2O3 (010) substratesby plasma-assisted molecular beam epitaxy J. Vac. Sci.Technol. A 33 4

[29] Yao Y, Okur S, Lyle L A, Tompa G S, Salagaj T, Sbrockey N,Davis R F and Porter L M 2018 Growth and characterizationof α-, β-, and ò-phases of Ga2O3 using MOCVD and HVPEtechniques Mater. Res. Lett. 6 268–75

[30] Rafique S, Karim M R, Johnson J M, Hwang J and Zhao H2018 LPCVD homoepitaxy of Si doped β-Ga2O3 thin filmson (010) and (001) substrates Appl. Phys. Lett. 112 052104

[31] Ketteniss N, Khoshroo L R, Eickelkamp M, Heuken M,Kalisch H, Jansen R H and Vescan A 2010 Study onquaternary AlInGaN/GaN HFETs grown on sapphiresubstrates Semicond. Sci. Technol. 25 075013

[32] Saïdi I, Neffati R, Ben Radhia S, Boujdaria K, Lemaître A,Bernardot F and Testelin C 2016 Optical properties of type-II AlInAs/AlGaAs quantum dots by photoluminescencestudies J. Appl. Phys. 120 035701

[33] Khan M A, Yang J W and Simin G 2000 Lattice and energyband engineering in AlInGaN/GaN heterostructures Appl.Phys. Lett. 76 1161

[34] Reuters B, Finken M, Wille A, Holländer B, Heuken M,Kalisch H and Vescan A 2012 Relaxation and critical strainfor maximum In incorporation in AlInGaN on GaN grownby metal organic vapour phase epitaxy J. Appl. Phys. 112093524

[35] Xu F, Chen P, Jiang F L, Liu Y Y, Xie Z L, Xiu X Q,Hua X M, Shi Y, Zhang R and Zheng Y L 2017 High-efficiency InGaN/AlInGaN multiple quantum wells withlattice-matched AlInGaN superlattices barrier Chin. Phys. B26 017803

[36] Quah H J, Lim W F, Hassan Z, Radzali R, Zainal N andYam F K 2019 Effects of ultraviolet-assistedelectrochemical etching current densities on structural andoptical characteristics of porous quaternary AlInGaN alloysArab. J. Chem. 12 3417

[37] Minj A, Skuridina D, Cavalcoli D, Cros A, Vogt P, Kneissl M,Giesen C and Heuken M 2016 Surface properties ofAlInGaN/GaN heterostructure Mater. Sci. Semicond.Process. 55 26–31

[38] Li Y, Zhang J, Xue J, Liu G, Quan R, Duan X, Zhang J andHao Y 2018 Electronic transport properties in AlInGaN/AlGaN heterostructures Phys. Status Solidi a 215 1700787

[39] Kurtz S R, Allerman A A, Jones E D, Gee J M, Banas J J andHammons B E 1999 InGaAsN solar cells with 1.0 eV bandgap, lattice matched to GaAs Appl. Phys. Lett. 74 729–31

[40] Bellil W, Aissat A and Vilcot J P 2018 Performance of thestructure AlxGa1−xAs1−yNy/Ge for solar cell applicationsOptik 171 803

[41] Wang C A, Walpole J N, Missaggia L J, Donnelly J P andChoi H K 1991 AlInGaAs/AlGaAs separate-confinementheterostructure strained single quantum well diode lasersgrown by organometallic vapor phase epitaxy Appl. Phys.Lett. 58 2208

[42] Ohtani K, Beck M, Scalari G and Faist J 2013 Terahertzquantum cascade lasers based on quaternary AlInGaAsbarriers Appl. Phys. Lett. 103 041103

[43] Gu Y, Zhang Y G, Wang K, Li A Z and Li Y Y 2009Optimization of AlInGaAs/InGaAs/InAs straincompensated triangular quantum wells grown by gas sourcemolecular beam epitaxy for laser applications in 2.1–2.4 μmrange J. Cryst. Growth 311 1935

[44] Kresse G and Furthmüller J 1996 Efficiency of ab-initio totalenergy calculations for metals and semiconductors using aplane-wave basis set Comput. Mater. Sci. 6 1

[45] Perdew J P, Burke K and Ernzerhof M 1996 Generalizedgradient approximation made simple Phys. Rev. Lett.77 3865

[46] MedeA-VASP, Material Designs Inc (www.materialsdesign.com/medea/medea-vasp)

[47] Van De Walle A, Asta M and Ceder G 2002 The alloy theoreticautomated toolkit: a user guide Calphad 26 539–53

[48] Ghosh G, Van de Walle A and Asta M 2008 First-principlescalculations of the structural and thermodynamic propertiesof bcc, fcc and hcp solid solutions in the Al–TM (TM=Ti,Zr and Hf) systems: a comparison of cluster expansion andsupercell methods Acta Mater. 56 3202–21

[49] Haas P, Tran F and Blaha P 2009 Calculation of the latticeconstant of solids with semilocal functionals Phys. Rev. B 79085104

[50] Fiorentini V and Baldereschi A 1995 Dielectric scaling of theself-energy scissor operator in semiconductors and insulatorsPhys. Rev. B 51 17196

[51] Moses P G and Van de Walle C G 2010 Band bowing andband alignment in InGaN alloys Appl. Phys. Lett. 96 021908

[52] Khomyakov P A, Luisier M and Schenk A 2015Compositional bowing of band energies and theirdeformation potentials in strained InGaAs ternary alloys: afirst-principles study Appl. Phys. Lett. 107 062104

[53] Dong L, Jia R, Xin B, Peng B and Zhang Y 2017 Effects ofoxygen vacancies on the structural and optical properties ofβ-Ga2O3 Sci. Rep. 7 40160

[54] Liu X and Tan C K 2019 Electronic properties of monoclinic(InxGa1−x)2O3 alloys by first-principle AIP Adv. 9 035318

9

Semicond. Sci. Technol. 35 (2020) 025023 X Liu and C-K Tan

[55] Singh J 2007 Electronic and Optoelectronic Properties ofSemiconductor Structures (Cambridge: CambridgeUniversity Press)

[56] Lorenz K, Franco N, Alves E, Pereira S, Watson I M,Martin R W and O’Donnell K P 2008 Relaxation ofcompressively strained AlInN on GaN J. Cryst. Growth310 18

[57] Bakkers E P, Borgström M T and Verheijen M A 2007Epitaxial growth of III–V nanowires on group IV substratesMRS Bull. 32 2

[58] Van de Walle C G and Martin R M 1985 Theoretical study ofSi/Ge interfaces J. Vac. Sci. Technol. B 3 4

[59] Butté R, Carlin J F, Feltin E, Gonschorek M, Nicolay S,Christmann G and Christopoulos S 2007 Status of AlInNlayers lattice-matched to GaN for photonics and electronicsJ. Phys. D: Appl. Phys. 40 6328

[60] Liu G, Zhang J, Li X H, Huang G S, Paskova T,Evans K R and Tansu N 2012 Metalorganic vapor phase

epitaxy and characterizations of nearly-lattice-matchedAlInN alloys on GaN/sapphire templates and free-standingGaN substrates J. Cryst. Growth 340 1

[61] Lorenz K, Franco N, Alves E, Watson I M, Martin R W andO’donnell K P 2006 Anomalous ion channeling in AlInN/GaN bilayers:determination of the strain state Phys. Rev.Lett. 97 085501

[62] Ejeckam F E, Lo Y H, Subramanian S, Hou H Q andHammons B E 1997 Lattice engineered compliant substratefor defect-free heteroepitaxial growth Appl. Phys. Lett.70 1685

[63] Osinsky V and Dyachenko O 2010 Crystal lattice engineeringthe novel substrates for III-nitride-oxide heterostructuresSemicond. Phys. Quantum Electron. Optoelectron. 13 142–4

[64] Maccioni M B, Ricci F and Fiorentini V 2014 J. Phys.: Conf.Ser. 566 012016

[65] Åhman J, Svensson G and Albertsson J 1996 A reinvestigationof β-gallium oxide Acta Crystallogr. C 52 1336

10

Semicond. Sci. Technol. 35 (2020) 025023 X Liu and C-K Tan