Ab initio model of amorphous zinc oxide (a-ZnO) and a-X_0.375 Z_0.625 O (X=Al, Ga and In)
aa r X i v : . [ c ond - m a t . m t r l - s c i ] O c t Ab initio model of amorphous zinc oxide (a-ZnO) and a-X . Z . O (X = Al,Ga and In)
Anup Pandey
Department of Physics and Astronomy, Condensed Matter and Surface Science Program, Ohio University, Athens OH 45701, USA
Heath Scherich
Department of Physics and Astronomy, Ohio University, Athens OH 45701, USA
D. A. Drabold
Department of Physics and Astronomy, Ohio University, Athens OH 45701, USA
Abstract
Density functional theory (DFT) calculations are carried out to study the structure and electronic structure of amor-phous zinc oxide (a-ZnO). The models were prepared by the ”melt-quench” method. The models are chemicallyordered with some coordination defects. The e ff ect of trivalent dopants in the structure and electronic properties of a-ZnO is investigated. Models of a-X . Z . O (X = Al, Ga and In) were also prepared by the ”melt-quench” method.The trivalent dopants reduce the four-fold Zn and O, thereby introducing some coordination defects in the network.The dopants prefer to bond with O atom. The network topology is discussed in detail. Dopants reduce the gap inEDOS by producing defect states minimum while maintaining the extended nature of the conduction band edge.
Keywords: amorphous Zinc Oxide, doping, EDOS, DFT
1. Introduction
Crystalline ZnO has important application as a piezo-electric material and due to its property of being trans-parent in visible light [1]. It has a wide direct band gap( ∼ ∼ / V s) compared to the covalentamorphous semiconductor like a-Si ( ∼ / V s)whichmake them a better candidate for the device applicationsuch as thin film transistors (TFTs) [4]. Experimentally,various techniques such as pulse laser deposition [5],molecular beam epitaxy [6], radio-frequency magnetron sputtering [7] etc. have been used to make a-ZnO andthe structure obtained is highly dependent on the sub-strate material and temperature. There are advantagesof a-ZnO over its crystalline counterpart. First, it is eas-ier and cost e ffi cient to produce a large amorphous sheetcompared to a large single crystal. Also, the a-ZnO hasbeen prepared at low temperature ( ∼
300 K) comparedto crystalline ZnO ( ∼
800 K - 1100 K) and its opticalproperties over the wide spectral range has been inves-tigated [1]. On doping trivalent elements such as Al, Gaand In on a-ZnO mobility can be increased significantly[8].In this work, we report the structure and electronicproperties of amorphous phases of ZnO and a-ZnOdoped with trivalent dopant atoms such as Indium (In),Gallium (Ga) and Aluminium (Al) using a plane wavebasis density functional theory (DFT) and comparisonswith the experiments and other molecular dynamics(MD) simulations are made when possible. For the firsttime, accurate methods are used to compute the topolog-ical and chemical order of the materials and determine
Preprint submitted to Journal of Non-Crystalline Solids October 4, 2016
Model 1 Model 2 g (r) r (¯) Figure 1: (color online) The total radial distribution function (RDF)for four a-ZnO models. Model 1 and Model 2 corresponds to themodels obtained by two di ff erent quenching rates as described in themethod section. Blue is for Model 1 and green is for Model 2. electronic characteristics.The paper is arranged as follows. In Section II, weprovide details about the computational technique usedin modeling various models. In Section III, we presentthe simulation results for a-ZnO and a-X . Z . O(X = Al, Ga and In) and make comparisons with experi-ments and other MD methods.
2. Computational Methods
Ab initio calculations are performed using the DFTcode VASP [10, 11, 12] using projected augmentedplane waves (PAW) [13] with Perdew-Burke-Ernzerhof(PBE) exchange-correlation functional [14] and a plane-wave cuto ff o ff energy of 300 eV. All calculations werecarried out at Γ point. We have prepared a model byusing the melt-quench method. For a-ZnO, the sys-tem consists of 128 atoms in a cubic box of length12.34 Å corresponding to the experimental density of4.6 g / cm [2]. The random starting configuration isequilibrated at 5000 K is cooled to 3000 K at 100 K / psfollowed by an equilibration of 5 ps. The structure at3000 K is cooled in steps to temperatures 2300 K, 1600K and 300 K at the rate of 50 K / ps followed by 5 psequilibration in each temperature. Finally, the structureat 300 K is quenched to 0 K at the rate of 25 K / ps whichis again followed by equilibration of 5 ps. The struc-ture is then relaxed using the conjugate gradient (CG)method. This model is termed as Model 1. To contrastdi ff erent quench rates, the configuration at 3000 K wasalso cooled to 300 K at a rate of 180 K / ps followed bythe equilibration of 5 ps. The model is relaxed using CG g (r) r (¯) Figure 2: (color online) Partial pair correlation functions for 128-atom model a-ZnO. Blue is for Model 1 and red is for Model 2 asdescribed in the method section. method. Finally, the equilibrated structure is quenchedto 0 K at a rate of 50 K / ps and then equilibrated for an-other 5 ps. We call this model as Model 2.For a-X . Z . O (X = Al, Ga and In), a randomstarting configuration of 128 atoms was melted at 5000K followed by cooling to 3000 K at 100 K / ps and thenequilibrated for 5 ps. A schedule of cooling is carriedout at temperatures 2300 K, 1600 K and 300 K at a rateof 25 K / ps followed by the equilibration of 5 ps in eachtemperature. Finally, the structures are cooled to 0 Kat the rate of 40 K / ps followed by the equilibration of 5ps. The final structures are volume relaxed to estimatethe density. The cubical box lengths for Al-, Ga- andIn-doped models after volume relaxations are 12.26 Å,12.28 Å and 12.31 Å respectively. We find no strongdependence on the quenching processes.
3. Results
Structural properties are investigated by the radialdistribution functions (RDFs) and partial radial distribu-tion functions. The total RDFs for Model 1 and Model2 are shown in Fig.1. The partial pair correlation func-tions for Zn-Zn, Zn-O and O-O are shown in Fig.2. Thepartials for both models show similar features. For bothZn-Zn and O-O partials, the first peak is around 3.40 Å2 able 1: The coordination number for Zn and O expressed in per-centage, average coordination number and the DFT-GGA energy fora-ZnO model. The coordination number for Zn are compared with theother MD model [2]. As expected there are a few more coordinationdefects in the more rapidly quenched model 2.
Model 1 Model 2 MD(Ref.([2])Zn-Zn (%) 0 0 -O-O (%) 0 0 -Zn (%) 15.63 23.44 32.00Zn (%) 81.25 75.00 60.00Zn (%) 3.12 1.56 7.00O (%) 15.63 25.00 -O (%) 81.25 71.88 -O (%) 3.12 3.12 - n Zn n O / atom) -4.36 -4.34 -while for Zn-O the first peak position is at 2.00 Å asshown in Table 2.The network is chemically ordered. We calculatedthe coordination number for Zn and O given by the aver-age first neighbour atoms around Zn or O as a referenceatom. Most of the atoms are four-fold coordinated withabove 75% of four-fold coordinated Zn and O in all fourmodels. Our models exhibit a higher percentage of four-fold Zn compared to the model obtained from empiri-cal molecular dynamics simulation model ( ∼ n Zn ) and O( n O ) and the 3-, 4- and 5-fold coordinated Zn and O, de-noted by the respective subscript (Zn , O ,...) is shown -20 -15 -10 -5 0 5 10Energy (eV)0100200300400500 E DO S ( s t a t e s / e V ) EDOS 00.20.40.60.81 I P R IPR
Figure 3: (color online) (black) Electronic density of states of the128-atom model a-ZnO at 300 K (Model I) obtained using GGA-PBEdensity functional theory calculation. The green vertical lines rep-resent the inverse participation ratio (IPR) used to measure the elec-tronic state localization. Longer IPR implies strong localization. TheFermi level is at 0.28 eV. The PBE gap is 1.36 eV. g (r) r (¯) a)
012 In-In 1357 In-O012 g (r) O-O 13579 Zn-O2 4 60123 r (¯)
Zn-Zn 2 4 6In-Zn b)Figure 4: (color online)(a) Total pair correlation functions for 128-atom model a-IZO at 300 K. (b) Partial pair correlation function ofa-IZO at 300 K. E DO S ( s t a t e s / e V ) a-ZnOAl-doped a-ZnO0100200300400500 E DO S ( s t a t e s / e V ) Ga-doped a-ZnO-20 -15 -10 -5 0 5 10Energy (eV)0100200300400500 E DO S ( s t a t e s / e V ) In-doped a-ZnO0.28 eV 2.72 eV1.67 eV3.28 eV
Figure 5: (color online) Electronic density of states for a-X . Z . O (X = Al, Ga and In) models compared to that of a-ZnOat 300 K. The Fermi levels are shown by vertical broken lines. in Table 1. The DFT energy per atom for Model 1 is-4.36 eV / atom and for Model 2 is -4.34 eV / atom (Table1). This suggest that Model 1 is energetically favorablecompared to Model 2.The electronic structure is analysed by calculating theelectronic density of states (EDOS) and inverse partic-ipation ratio (IPR) of the individual states. The EDOSis shown in Fig.3 (black) and the green vertical linesrepresents the electronic state localization measured byIPR [15, 16]. The value of IPR is 1 for highly localizedstate and 1 / N for extended state, where N is the numberof atoms. The IPR in Fig.3 shows that the localizationof valence tail states much larger than the conductiontail states. Thus, the mobility of n -type of carrier is ex-pected to be much higher than the p -type. This featuresupports the asymmetry in the localization of valenceand conduction band tail states in amorphous metal ox-ide by Robertson [4]. Similar asymmetrical behaviorin amorphous gallium nitride was shown by Cai andDrabold [17].The band gap (gap between the highest occupiedelectronic state and the lowest unoccupied electronicstate), in the model is 1.36 eV which is slightly lessthan the experimental band gap of 1.60 eV between thevalence band edge and Zn4s4p states [18]. The under-estimate of the band gap is of course expected in theDFT-GGA calculation. Table 2: First peak position for Zn-Zn, Zn-O and O-O partial paircorrelation functions of a-ZnO (Model 1) and a-X . Z . O (X = Al, Ga and In) models.
Peak position for 300 K (slow) models (Å)Firstpeak ZnO Al . Z . O Ga . Z . O In . Z . OZn-Zn 3.40 2.46 2.90 3.20O-O 2.00 1.90 2.00 2.00O-O 3.40 3.00 3.10 3.20 . Z . O (X = Al, Ga and In)
To investigate the e ff ect of trivalent dopants on localcoordination and electronic structure of a-ZnO, 37.5%of Zn is replaced by group III elements X (X = Al, Gaand In) to model a-X . Z . O. The atomic percent-age of dopants in all the models is 18.75%. The e ff ectof dopants in the structure and electronic properties areinvestigated by RDFs, partial pair correlation functionsand electronic density of states.The total RDFs for In-doped a-ZnO is shown inFig.4a. The Zn-O correlation is not a ff ected by thepresence of dopants while there is a slight decrease inthe correlation peaks for Zn-Zn and O-O which is illus-trated in Table 2. The peak positions are obtained fromthe partial pair correlation functions shown in Fig.4b forIn-doped a-ZnO and similar plots for Al-, and Ga-dopeda-ZnO which is not shown here. The 4-fold Zn and Oare reduced significantly in all three doped models. TheAl and In bond only with O. In Al-doped model, 95.83%and 4.17% Al forms 4-fold and 3-fold bond with O. InIn-doped model, 20.83%, 25.00%, 8.33%, 37.5% and8.34% In form 6-, 5-, 4-, 3- and 2-fold bond with Oatom. In Ga-doped model, 58.33% and 33.33% Ga form4-fold and 3-fold bond with O while 8.34% Ga form 3-fold with O and 1-fold with Zn. This suggest that thegroup III elements are more likely to form a bond withO while doped in a-ZnO.The Zn-Zn and In-In distances in our model arearound 3.20 Å and 3.50 Å which is close to 3.20-3.40Å for Zn-Zn and 3.30-3.6 Å for In-In of classical MDmodel [19]. This compares well with the average metal-metal peak in x-ray di ff raction measurements of IZOthin layers [20]. Also, the Zn-O and In-O distances inour model are around 2.00 Å and 2.20 Å compared tothe 1.95 Å— and 2.20 Å respectively of the classicalMD model [19]. These peak positions are consistent4ith the metal-oxygen peaks at 2.12-2-14 Å in the ex-periment [20].The electronic density of states (EDOS) for a-X . Z . O (X = Al, Ga and In) models compared tothat of a-ZnO at 0 K is shown in Fig.5. The introduc-tion of dopants clearly reduces the gap by introducingthe defect states. The localized states near the valenceband edge induced by doping can be inferred to the in-crease in undercoordinated O atoms in the network in-troduced by doping. The conduction band edge is unal-tered by the addition of dopant elements. The extendednature of the conduction band is preserved by the addi-tion of dopants which is in accordance to the conclusionby Hosono [8]. On the other hand, in crystalline ZnOdoped by group III elements Al, Ga and In, the dopantsform extra localized level in the conduction band, whichmodifies the conduction band and reduces the opticalband gap [9].
4. Conclusions
In conclusion, we have created models of amor-phous zinc oxide (a-ZnO) using melt-quench methodand studied their structural and electronic properties indetail. The electronic band gap of our model is 1.36eV which is in reasonable agreement with the experi-mental band gap 1.60 eV. We have calculated the DFTenergies for the two models of a-ZnO obtained by dif-ferent quenching rate for comparison. The e ff ect oftrivalent dopants in the local structure and the electronicstructure of a-ZnO is investigated in detail by prepar-ing a-X . Z . O (X = Al, Ga and In) models by melt-quench method. The dopants reduce the number of 4-fold coordinated Zn and O in the network and most ofthem prefer to bond with oxygen. The electronic gap isreduced by the presence of defect states by forming un-dercoordinated O states in the valence band edge whilethe conduction band edge is still extended. Coordinatesare available upon request.
5. Acknowledgements
We thank the US NSF under the grants DMR 150683,1507166 and 1507670 for supporting this work, and theOhio Supercomputer Center for computer time. We ac-knowledge the financial support of Condensed Matterand Surface Science program of Ohio University.
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