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Many materials have been used in nanostructured devices; the goal of attaining high-efficiency thin-film solar cells in such a way has yet to be achieved. Heterojunctions based on ZnO/Cu
_{2}O oxides have recently emerged as promising materials for high-efficiency nanostructured devices. In this work, we are interested in the characterization of the surface and interface through nano-scale modeling based on ab initio (Density Functional Theory (DFT), Local Density Approximation (LDA), Generalized Gradient Approximation (GGA-PBE), and Pseudopotential (PP)). This study aims also to build a supercell containing a ZnO/Cu
_{2}O heterojunction and study the structural properties and the discontinuity of the valence band (band offset) from a semiconductor to an-other. We investigate crystal terminations of ZnO (0001) and Cu
_{2}O (0001). We calculate the energies of the polar surfaces and the work function in the c-axis for both oxides. We built a zinc oxide layer in the wurtzite structure along the [0001] direction, on which we placed a copper oxide layer in the hexagonal structure (CdI
_{2}-type). We choose the method of Van de Walle and Martin to calcu-late the energy offset. This approach fits well with the DFT. Our calculations give us a value that corresponds to other experimental and theoretical values.

Many different photovoltaic technologies are being developed for large-scale solar energy conversion [

Photovoltaic cell requires two semiconductor slabs (n-type and p-type). Zinc oxide (ZnO) attracted researchers’ attention for a long time, owing to its potential applications in many scientific and industrial areas [_{2}O) is also a potential material for the fabrication of low cost solar cells [_{2}O-based solar cell was manufactured at the end of 1920. However, at that time, and until the first space explorations, the energy production from the sunlight by the photovoltaic effect was just a curiosity. Cu_{2}O is a p-type semiconductor with a direct band gap of about 2 eV, which is suitable for photovoltaic conversion.

The ZnO/Cu_{2}O heterojunction has been fabricated and studied for a long time [_{2}O is cubic (cuprite). An epitaxial growth of (111)- oriented Cu_{2}O film on the (0001) surface of ZnO is thus possible as it has been reported in several papers [_{2}O under pressure [_{2} structure. This suggests that a growth of Cu_{2}O films according to the CdI_{2} structure on a ZnO substrate is also possible. This kind of growth would have the advantage of giving superlattices preserving the stoichiometry. In the present work, we will investigate this kind of growth.

Surface and interface physics has in recent decades become an ever more important sub-discipline within the physics of condensed matter. Many phenomena and experimental techniques cannot be treated without a pro- found knowledge of surface and interface effects [_{2}O, surface energy represents a non-negligible contribution for the overall energetic balance [_{2}O possess preferred directions [_{2}O is polar, and has a positively charged Zn- or Cu-terminated (0001) surface and negatively charged O-terminated (000-1) surface [_{2}O [_{2}O bulk, polar surfaces, and interactions among surfaces forming the heterojunction have to be considered.

Many important properties of semiconductors are not solely determined by the band gap. For instance, the relative band bending near two different semiconductors and the corresponding band offsets are of fundamental interest in solid state physics, and are indispensable for the design of heterojunction devices [

where_{2}O heterojunction. Previous experimental studies of this heterojonction can be found in Refs. [

In this paper, we are interested first to build a supercell containing a heterojunction formed by [_{2}-type), and second to calculate the band alignments in ZnO/Cu_{2}O heterojunction and compare it with any other new experimental and theoretical results. There is a need for more fundamental studies on the polar ZnO and Cu_{2}O surfaces in order to get a better understanding of the physical properties of the heterojunction, which plays an important role in determining the properties of the interface. This theoretical calculation was performed in the framework of the DFT using pseudopotentials and a planewave basis implemented in the Abinit package.

The calculations have been performed in the framework of the Density Functional Theory [_{cut}, of 50 Hartree. Troullier-Martins pseudopotentials [^{10}4s^{2}, 3d^{10}4s^{1} and 2s^{2}2p^{4} atomic configurations of zinc, copper and oxygen, respectively. Exchange-correlation energy and potential have been taken into account at the local density approximation (LDA) level by mean of the Perdew-Wang [_{2}O. For the ZnO/Cu_{2}O interface and the polar surfaces ZnO (0001) and Cu_{2}O (0001), a mesh of 8 × 8 × 2 was sufficient to reach convergence. The standard procedure for calculating interface and surface energies is the slab supercell technique, in which one needs to subtract bulk energy from total energy of slab supercell. Interface structure is modeled in a supercell geometry employing 8 layers (_{2}O, respectively. A vacuum region of 3c (~12Å) ensures the decoupling of repeated slabs.

The Van de Walle and Martin model [

where S represents the area of a unit cell in the xy-plane (

where a is the period length in the direction perpendicular to the interface. The macroscopic average potential shows a discontinuity at the interface, indicating that electrons should overcome a potential barrier to cross from ZnO section to Cu_{2}O section. This value is given by,

The band offset can be determined by aligning the average electrostatic potential across the interface between two segments when the average of the electrostatic potential converges to the values of their infinite materials, using the following equation,

where the first and second terms represent the positions of the valence/conduction band (E_{v/c}) relative to those of the average electrostatic potentials for the ZnO and Cu_{2}O, respectively. The third term indicates the difference between the two macroscopic average potential from ZnO to Cu_{2}O (

The first step in the calculation of the interface properties is the construction of the supercell. The supercell has to be periodic in the three dimensions and must be large enough in order to describe both ZnO and Cu_{2}O bulk and interface regions. In order to simulate the ZnO/Cu_{2}O heterojunction, we have built the supercell formed by 8 layers shown in _{2}O and of the ZnO/Cu_{2}O superlattice have been fully determined. The resulting lattice parameters are reported in

ZnO crystals generally grow along the c-axis by alternating layers of Zn^{2+} and O^{2−}. This atomic arrangement along the c-axis leads to a polar crystal along the hexagonal longitudinal c-axis. This polarity imposes a growth direction for Cu_{2}O. Several experimental and theoretical studies [_{2}O grows on the ZnO substrate according to the hexagonal symmetry. As under standard thermodynamic

ZnO | Cu_{2}O | ZnO/Cu_{2}O | ||||||
---|---|---|---|---|---|---|---|---|

LDA | GGA-PBE | Expt. [ | LDA | GGA-PBE | Expt. [ | LDA | GGA-PBE | |

a[A] | 3.192 | 3.316 | 3.250 | 2.802 | 2.904 | 2.900 | 3.085 | 3.198 |

c[A] | 5.190 | 5.336 | 5.207 | 4.393 | 4.496 | 3.862 | 9.479 | 9.701 |

B[GPa] | 158.61 | 127.22 | 142.6 | 137.91 | 103.11 | - | - | - |

B’ | 4.48 | 4.73 | 3.6 | 4.45 | 4.34 | - | - | - |

conditions Cu_{2}O has the cuprite structure, it is usually accepted that the growth is made in the hexagonal structure (CdI_{2}-type) of the cubic lattice. In this study, we consider the possibility of a Cu_{2}O growth CdI_{2}-type, which differs from the cubic one for the stacking of the Cu and O planes. As in the CdI_{2}-type, each O plane is between two Cu planes, this arrangement gives rise to a stoichiometric superlattice. As already noticed in the introduction, Cu_{2}O transforms to a CdI_{2}-type phase under pressure, as it was shown both experimentally [

The atomic arrangements in the Cu_{2}O and ZnO (0001) suggest that it is energetically favorable for Cu_{2}O to grow on the ZnO (0001) substrate [_{2}O heterojunction, the inﬂuences may be more obvious because of the large mismatch between cubic Cu_{2}O (a = 4.27 Å) and wurtzite ZnO (a = 3.25 Å and c = 5.21 Å) [_{2}O thin ﬁlms deposited on ZnO substrate (_{2}O (CdI_{2}-type) and the ZnO (0001). In this case, the Cu_{2}O lattice would be compressed and the Cu-O bond length is decreased which explains the choice of the high pressure phase of Cu_{2}O.

Under normal conditions, ZnO in the wurtzite structure (P6_{3}mc) is the most stable polymorph. This is a hexagonal lattice belonging to the space group P6_{3}mc and is characterized by two interconnected sublattices of Zn^{2+} and O^{2−} in such a way that each Zn ion is surrounded by tetrahedra of O ions, and vice-versa. This tetrahedral coordination gives rise to a polar symmetry along the hexagonal axis. This polarity is responsible for a number of ZnO properties including piezoelectricity and spontaneous polarization. It is also a key factor in crystal growth. Wurtzite structure is characterized by three parameters including the lattice constant a, the c/a ratio, and the internal parameter u [_{2}O crystallizes in a simple cubic structure, which belongs to space group Pn-3m. Under hydrostatic pressure, cuprous oxide transforms into tetragonal or hexagonal structure [_{2}O in the (111) direction. The Cu_{2}O structure in this direction coincides well with the hexagonal structure [_{2}O structure that meets the growth of ZnO, is hexagonal type CdI_{2} with space group P-3m (164) [

The lattice parameters and bulk modulus are determined by ﬁtting a set of data points to the Murnaghan equation of state [

The structural and electrical properties of nanostructures based on different semiconductors are governed by the interfaces. A microscopic understanding of physics properties (conductivity, transparency, growth processes, etc.) requires the investigation of the surface processes at an atomic level [

crystalline thin film and some vacuum layers.

In the ab initio calculations and using a supercell model containing slabs with two equivalent surfaces, the surface energy, E_{surf} at T = 0 K of a clean surface can then be calculated as,

where E_{slab} and E_{bulk} are the total energy of the slab and the bulk, respectively. N is the number of atoms in the

slab, A is the surface unit area, and the factor

atoms were relaxed during calculations of E_{slab}. E_{Surf} is converged with respect to the vacuum thickness, in order to rule out undesired surface interactions either through the bulk material or through the separating vacuum.

ZnO crystallizes in the wurtzite structure. When the crystal is cleaved normal to the c-axis in a manner which breaks the interatomic bonds, two different polar surfaces are formed on opposite sides of the crystal, each hav-

ing only one type of ion in its outermost plane. The theoretical study of ZnO surfaces may hold the key to un-

derstanding the experimental results. The polar (0001) and (000-1) surface of ZnO has previously been studied using many methods and under various approximations [

Face | Surface energy (J/m^{2}) | Work function (eV) | Reference | |
---|---|---|---|---|

(0001)-Zn | 1.64 | 5.568 | LDA | This work |

2.08 | 5.713 | GGA-PBE | ||

5.1 | [ | |||

4.08 | [ | |||

3.7 | [ | |||

3.7 | [ | |||

3.15 | [ | |||

2.0 | [ | |||

2.25 | [ | |||

(000-1)-O | 1.68 | 5.60 | LDA | This work |

2.04 | 5.79 | GGA-PBE | ||

6.0 | [ | |||

4.85 | [ | |||

4.8 | [ | |||

4.5 | [ | |||

2.04 | [ | |||

(0001)-Cu | 0.69 | 5.74 | LDA | This work |

0.78 | 5.23 | GGA-PBE | ||

4.58 | [ | |||

4.84 | [ | |||

0.71 | [ | |||

(0001)-O | 1.35 | 6.43 | LDA | This work |

1.72 | 6.28 | GGA-PBE | ||

1.63 | [ |

energies calculated for the (0001)-Zn surface and (000-1)-O are 1.64 J/m^{2} and 1.68 J/m^{2}, respectively. These values are underestimated when compared with experimental values (

Cu_{2}O surface have been studied with great interest [_{2}O were performed recently [_{2}O (111) surface could be prepared as Cu-rich or O-rich (depending on the O exposure) and was found to exhibit various reconstruction patterns on the oxidation degree and annealing history [_{2}O in the structure CdI_{2}-type. Cu_{2}O (0001) surface consists of 2 copper layers sandwiched between one layer of oxygen. We are interested in the calculation of the surface energies of Cu_{2}O (0001)-Cu surface and Cu_{2}O (0001)-O surface. These surfaces are modeled using periodic supercells containing 8 atomic layers. A vacuum layer of 3c (~12Å) is sufficient to neglect interaction between the neighboring layers. The surface energies of the Cu_{2}O (0001)-Cu surface and Cu_{2}O (0001)-O surface are computed with the LDA and GGA-PBE approximations (_{2}O (0001)-Cu surface and Cu_{2}O (0001)-O surface are 1.78 J/m^{2} and 1.35 J/m^{2}, respectively. In our calculation, we observe a good agreement for the surface energies. For Cu_{2}O, it is not simple to compare our results with available experimental and theoretical results because our choice of hexagonal structure of this oxide while the others take a cubic structure along the [

Consider nanoscale constructions, such as self assembled monolayers, where the underlying oxide workfunctions (and Fermi energy) are crucial to determine interfacial phenomena [

where V_{vac} is the potential in the vacuum region and E_{f} is the Fermi energy. In practice, this is the energy required at 0 K to remove an electron from the Fermi level of the oxide to the vacuum level [

We used DFT method with LDA and GGA-PBE to investigate the workfunction of ZnO and Cu_{2}O. We investigated the workfunction values on different ZnO and Cu_{2}O surfaces. We calculated workfunctions of the surfaces in ZnO (0001). This orientation is characterized by two polar surfaces, Zn terminated and O terminated. While Cu_{2}O in the CdI_{2}-type structure has two polar surfaces, Cu terminated and O terminated. The calculated workfunctions of the ZnO and Cu_{2}O, in the different terminations, are presented in _{2}O surfaces vary widely from study to another, following experimental or theoretical methods adopted. Our results are in the range of previous results listed in _{2}O with the literature ones because we used in this work a CdI_{2}-type- structure while the other works used cubic Cu_{2}O (111).

We will ﬁrst examine the atomic structures of ZnO and Cu_{2}O materials in the wurtzite and hexagonal CdI_{2}-type phases, respectively. We use Murnaghan equation to obtain the (a, c) lattice constants [

Supercell method was employed in the study of the ZnO/Cu_{2}O heterojunction. In _{2}O seen, respectively, along the [_{2}-type) is shown. In the ZnO structure, both Zn and O atoms are perfectly arranged in a hexagonal symmetry, while copper and oxygen retain the hexagonal symmetry in the Cu_{2}O structure. The interface region was modeled using a periodically repeated slab of 8 atomic layers; this is enough to reproduce a bulk-like character at both sides of the interface. The optimized lattice properties of the ZnO/Cu_{2}O heterojunction are tabulated in _{ZnO}, of the ZnO and dilating the lattice parameter, a_{Cu2O}, of the Cu_{2}O. The lattice parameter of the heterojunction in the z direction is the sum of the two lattice parameters of ZnO and Cu_{2}O.

The average potential _{LDA} = 5.66 eV and ∆V_{GGA} = 3.83 eV at the interface (_{v} = 1.51 eV in the LDA and ∆E_{v} = 1.23 eV in the GGA-PBE approximations. _{v} is 1.7 eV, and the theoretical values obtained by first principles calculation are 1.3 - 1.6 eV [_{v} = 2.2 eV is a large value found by Zhang et al. using electron affinity [_{LDA} = 5.66 eV and ∆V_{GGA} = 3.83 eV (

To calculate the conduction band alignment, we have used the experimental values of the bandgap energy because theoretical values in the LDA and GGA-PBE are under estimated and give incorrect values. In this work, we have used E_{g} equal to 3.37 eV and 2.1 eV for ZnO and Cu_{2}O, respectively [_{c}, is evaluated to 0.24 eV in the LDA and −0.04 eV in the GGA-PBE. Our values are in good agreement with other values, although other work has already chosen simplified structures while we choose a more realistic one [_{2}O, in the same zincblende structure. This choice is a first step to study this system with less complication in the calculation and in building the supercell, however this model is not too realistic.

We have investigated the electronic properties by calculating the density of states. The total DOS are shown in _{2} structures is clear, especially for the O 2s orbital. The valence band top of Cu_{2}O is mainly contributed by Cu 3d orbital, and that of ZnO is made up of the O 2p. We show in the _{2}O is higher than that of ZnO in the ZnO/Cu_{2}O system.

We have studied the surface energies and workfunction for the ZnO and Cu_{2}O. A supercell of 8 layers of ZnO and 6 layers Cu_{2}O is built. LDA and GGA-PBE are used. The polar (0001) surface of ZnO and Cu_{2}O, with zinc, copper and oxygen termination, show a significant difference in surface energies and in work function. Our results of the surface energies and workfunction of the cation and anion surface of the polar ZnO are in the range of the literature values (_{2}O because our choice of the crystal structure was different. The workfunction value of the Cu_{2}O (0001)-O is significantly large which can be explained by the instability of this surface.

We performed a first principle study of the ZnO/Cu_{2}O interface. These investigations have been carried out us-

ing the Density Functional Theory in the LDA and GGA-PBE approximations. This work was divided into three parts. The first part was devoted to the calculation of the bulk structural properties of ZnO and Cu_{2}O. The struc- ture, including equilibrium lattice constants, bulk modulus and pressure derivative are in good agreement with other theoretical and experimental results. In the second part, the band alignment analysis is performed using the average potential and density of states. We used the method of Van de Walle and Martin to calculate the energy offset. This approach fits well with the Density Functional Theory. We began this work by constructing a su- percell containing a junction formed by ZnO/Cu_{2}O. We selected from this work CdI_{2} structure of copper oxide deposited on the zinc oxide of wurtzite structure. Our calculations of the band offset gave us a value that corre- sponded to the experimental and theoretical values already published in the literature. In the third part, we investigated the surface energies and the workfunction on different ZnO and Cu_{2}O polar surfaces. Our results are in good agreement with experimental and theoretical values for ZnO. We found a difference between our results and other works in the case of Cu_{2}O because our choice of the crystal structure was different. This study can

5.66 | 1.04 | 5.20 | 1.51 | LDA | This work |

3.83 | 1.59 | 4.19 | 1.23 | PBE | |

1.3 - 1.6 | Others cal. [ | ||||

2.2 | Others cal. [ | ||||

1.7 | Exp. [ |

help to understand the effect of the surface and interface on the growth and electron transport in the heterojunctions.

MabroukZemzemi,SahbiAlaya, (2015) First Principles Study of the Structural and Electronic Properties of the ZnO/Cu_{2}O Heterojunction. Materials Sciences and Applications,06,661-675. doi: 10.4236/msa.2015.67068