FIRST-PRINCIPLE STUDY OF THE STRUCTURAL, ELECTRONIC, AND THERMODYNAMIC PROPERTIES OF CUPROUS OXIDE
UNDER PRESSURE
M. Zemzemia* N. Elghoula, K. Khirounia, S. Alayaa'h
"Laboratoire de Physique des Matériaux et des Nanomatériaux appliquée à l'Environnement, Université de Gabès, Faculté des Sciences de Gabès, Cité Erriadh Zrig 6072. Gabès, Tunisie
h King Faisal University, College of Science, Physics Department 31982, Hofuf, Saudi Arabia
Received March 18, 2013
Cuprous oxide is selected as a promising material for photovoltaic applications. Density functional theory is used to study the structural, electronic, and thermodynamic properties of cuprous oxide by using the local density approximation and generalized-gradient approximation. The effect of pressure on the structural and electronic properties of CuîO is investigated. This study confirms and characterizes the existence of new phases. Hexagonal and tetragonal phases are not completely indentified. We focus on the phase transition of the cuprous oxide under hydrostatic pressure to tetragonal and hexagonal (Cdli) structures. Variation of enthalpy with pressure is used to calculate the pressure of the phase transition.
DOI: 10.7868/S0044451014020084
1. INTRODUCTION
Metal oxides are widely used in various applications such as electronic components, building materials and refractories in drastic conditions of pressure and/or temperature. Studies of metal oxides are thus of great importance for obtaining a better understanding of corrosion of metals, heterogeneous catalysis, gas sensors, and transparent conductive oxides. The cuprous oxide (Cu20) was the first substance known to behave as a semiconductor, together with selenium [1]. Most of the semiconductor theories were developed using the data on Cu20. This oxide remains an attractive alternative material to silicon and other semiconductors, being favored at present for many applications due to its many advantages. It is nontoxic, its starting material (which is copper) is very abundant, and its production process is simple [2]. The most important methods for the production of Cu20 are thermal oxidation, electrode-position, and sputtering technique [3 5].
Cuprous oxide is a potential material for fabrication of low-cost solar cells [6,7]. The first real solar
E-mail: mzemzemi'fflgmail.com
cell with Cu20 was fabricated in the late 1920s. But at that time, and until the first space explorations, the energy production from the sun by photovoltaic effect was just a curiosity. High-efficiency Cu20-based solar cells require a good understanding of the crystallinity of this oxide and a judicious choice of the structural orientation. C112O is a />type semiconductor; it crystallizes in the cubic structure (Pn — Sin) and has a direct band gap of about 2 eV [8], which is suitable for photovoltaic conversion [9,10].
Cuprous oxide has been the subject of numerous theoretical and experimental studies, but still its electronic and atomic structures continue to puzzle the researchers. New applications of Cu20 in nanoelectron-ics, spintronics, superconductivity, and photovoltaics are emerging [11,12]. A better understanding of the atomic structure and electronic levels of cuprous oxide may be useful for predicting and controlling the phase transition under hydrostatic pressure, which will in turn allow a better understanding of the growth mechanism. Metal oxides present many polymorphs. The stability and mechanism of phase transitions represent an active field of investigation to discover a new stable phase or improve an existent one [13]. In ambient conditions, Cu20 stabilizes in a simple cubic Bra-
vais lattice, with the space group Pn — 3m(223) [14]. Under high pressure, the cubic phase has a number of low-pressure phases. These phase transitions have been studied both theoretically and experimentally [15,16]. Experimental studies have shown that cuprous oxide grows preferntially along the (111) direction [17,18]. Atomic stacking along this direction coincides well with the hexagonal structure [19].
The present work is focused on clarifying some fundamental aspects of C112O that can be important for both device fabrication and a better understanding of the physical phenomena observed in C112O. The aim of this work is to characterize hexagonal and tetragonal structure of cuprous oxide. We focus on the effect of pressure in the structural and electronic properties of C112O polymorphs. A relation is established between the electronic structure and the phase transition mechanism in C112O.
2. COMPUTATIONAL DETAILS
Theoretical calculations are performed in the framework of the density functional theory (DFT) [20,21] using pseudopotentials and a plane-wave basis implemented in the ABINIT package [22]. This package is available under a free software licence and allows computing a large set of useful properties for solid state studies [23]. The valence electron wavefunctions are expanded in plane waves with the kinetic energy cutoff Ecut equal to 50 Hartree. The pseudopotentials are generated with the respective 3ii104.s1 and 2.s22/>4 atomic configurations of copper and oxygen. Norm-conserving pseudopotentials [24] of Troullier Martins (TM) scheme [25], generated from the FritzHaber-Institute package [26], are used. The exchange-correlation terms were depicted, first, with the local density approximation of Ceperly and Adler [27] by the parameterization of Perdew and Zunger [28]; on the other hand, we used the generalized-gradient approximation (GGA) proposed by Perdew, Burke, and Ernzerhof (PBE) [29]. For the Brillouin zone sampling, the 8x8x8 ¿-points distributed on a shifted Monkhorst Pack grid was used [30]. The numerical results given below correspond to zero temperature. A judicious choice of the EcuL value and the ¿-point number is very important because if we increase these numbers, the CPU time and memory space also increase.
3. RESULTS AND DISCUSSION
Under ambient conditions, C112O crystallizes in a simple cubic structure, which belongs to the space
J '-
0 0 0*0
0' r
o Copper ® Oxygen
Fig. 1. (a) Cubic, (b) hexagonal CdU-type, and (c) tetragonal conventional unit cell for copper oxide
group Pn — 3m. It can be described as a cubic unit cell where oxygen atoms are in the corners with a tetrahe-dral unit of C114O at the center (Fig. la). In the lattice, each copper atom coordinates with two oxygen atoms and each oxygen atom is surrounded by four copper atoms, which makes the stoichiometry 2:1. The atomic coordinates and space group of cuprous oxide are listed in Table 1. To obtain the equilibrium bulk structure, the total energy is minimized with respect to the unit cell volume. Figure 2 shows a parabolic dependence of the energy as a function of the volume. The volume corresponding to the minimum energy identifies the equilibrium lattice parameter. The lattice parameters and bulk modulus are determined by fitting a set of data points to the Murnaghan equation of state [31]. A fit of the resulting energy versus volume curve with the Murnaghan equation, shown in Fig. 2, gives the values of B0 and its pressure derivative B' = dB0/dP for cuprous oxide. Our calculated lattice parameters, the bulk moduli B0 and B' together with other theoretical and experimental values are listed in Table 2.
Our results are in good agreement with the published experimental and theoretical data [15,16,32,33]. For cuprous oxide, the local density approximation (LDA) calculations show the well-known overbinding effect value with a lattice parameter underestimated by —1.17% compared to the experimental results, and GGA-PBE calculation is overestimated by 2.10%.
Under hydrostatic pressure, in the range 0 10 GPa, cuprous oxide transforms into tetragonal or hexagonal structure (Fig. 1). It was confirmed in [16] that the cubic Cu20 becomes tetragonal under 5.7 GPa. On the other hand, as shown in [15], the oxide undergoes a phase transition toward an hexagonal structure under a pressure of 10 GPa. In this study, we have detailed the structural and electronic information of the tetragonal and hexagonal structures. We calculated and verified
6 >K9T<E>, Bbiii. 2
273
Table 1. Space group and atomic positions for copper oxide in the cuprous, hexagonal, and tetragonal structures [14]
Structure Space group Atomic positions
Cuprous Pn - 3m (223) Cu (1/4, 1/4, 1/4); (1/4, 3/4, 3/4) (3/4, 1/4, 3/4); (3/4, 3/4, 1/4) O (0, 0, 0); (1/2, 1/2, 1/2)
Hexagonal (Cdl2) P - 3 m (164) Cu (2/3, 1/3, 1/4); (1/3, 2/3, 1/4) O (0, 0, 0)
Tetragonal P42/nnni(VM) Cu (1/4, 3/4, 1/4); (3/4, 1/4, 3/4) (3/4, 3/4, 3/4); (1/4, 1/4, 3/4) O (0, 0, 0); (1/2, 1/2, 1/2)
E, oV/'atom E, oV/'atom
20 40 60 80 100
r. :
E, oV/'atom
20 40 60 80 100 120
r. :
v, A -
Fig.2. Total energies as a function of the unit cell volumes for the (•) cubic, (A) hexagonal (Cdla), and (o) tetragonal conventional unit cell for copper oxide with the (a,c) LDA and (b,d) PBE approximation. Figures c and d are a zoom of the area showing cubic (•) and tetragonal (o) energies versus volume curves
flic phase-transition pressure value. Table 1 summarizes the atomic positions and space group for the three structures. The atoms in the hexagonal and tetragonal structures are ordered in planes and form a lamellar
structure. In order to look for the structural phase transition, the total energies are obtained as a function of the cell volume in the three structures.
The total energy versus volume curves calculated
Table 2. Calculated and experimental lattice parameters, bulk modulus, and pressure derivative of the bulk modulus for copper oxide in the cuprous, hexagonal, and tetragonal structures
Structure u, À c, À Bo, GPa B' Reference
Cuprous 4.22 141.14 4.23 LDA This study
4.36 105.58 4.15 GGA
4.22 [15] 4.26 [32] 141.00 [15] 136.10 [32] 4.67 [36] Other calculations
4.27 114.10 Experiment [33]
Hexagonal (Cdl2) 2.48 3.90 137.91 4.45 LDA This study
2.52 3.86 103.1
Для дальнейшего прочтения статьи необходимо приобрести полный текст. Статьи высылаются в формате PDF на указанную при оплате почту. Время доставки составляет менее 10 минут. Стоимость одной статьи — 150 рублей.