( 112 ) Surface of CuInSe 2 Thin Films with Doped Cd Atoms

The doping behavior of Cd atoms in the CuInSe 2 thin films and their influences on electronic structures are investigated.The doped Cd atoms replace Cu atoms and prefer to stay at the (112) surface of the thin films. They combine with Cu vacancies to form defect pairs due to low formation energy. The Cd atom does not by itself modify significantly the electronic structure of the surface, but the defect pairs have important influences. They result in a down shift of valence band maximum and form a hole barrier at the surface, which can prevent holes from reaching the surface and reduce the recombination of carriers.


Introduction
Chalcopyrite semiconductors such as CuInSe 2 (CIS) and CuInGaSe 2 (CIGS) are important photovoltaic materials. They are used as the absorber of the polycrystalline thin film solar cells which reached a high conversion efficiency record of 20.3% [1]. In this kind of solar cells, the surface of the chalcopyrite thin films plays a significant role because its atomic structure and the chemical composition have effects on the heterojunction of the solar cells and consequently influence their performance [2][3][4][5][6].
In past decades, the surface of the polycrystalline chalcopyrite thin film was investigated extensively [7][8][9][10][11][12][13]. Their stable surface is a polar (112) plane with defect-induced reconstruction [8]. Theoretical and experimental studies have found that the polar surface (112) is popular in the CuInSe 2 thin films due to their low surface energy [7,9]. It has also been revealed that the surface layer of the films usually has Cu vacancies (V Cu ) which modify the electronic structure of the materials [3,4,14].
For the surface of the chalcopyrite thin films inside the CIS/CdS heterojunction, the situation becomes more complicated. According to previous works [15], the (112) surface inside the heterojunction will become more Cu deficient. Furthermore, the n-type CdS film which is on the (112) surface of the CIS films has chances to diffuse Cd atoms into the chalcopyrite thin films. So it is worthy to investigate how the doped Cd atoms influence the surface of the chalcopyrite thin films because it will improve our understanding about the mechanism of carrier transportation inside the chalcopyrite thin film solar cells.
In this paper, the model of surface of the CIS thin films with doped Cd atoms is built. By comparing the defect formation energies, the locations of Cd atoms are investigated. We have also calculated the influences of Cd doping on the electronic structures and the transportation of carriers.

Methodology
A defect-free (112) surface model is built, as shown in Figure 1. This is the basis of the next studies about the Cd doping. The crystal lattice parameters are set according to experimental values = 5.784Å, = 11.616Å, and / = 2.0083 [16]. These values are close to the first-determined experimental values ( = 5.781Å, = 11.642Å, and / = 2.0138) [17]. Table 1 shows the calculated lattice parameters , , and / of CIS unit cell after the relaxation and the experimental values. The experimental values are also shown for comparison (the changes between the theoretical and experimental values are also shown in parentheses). The calculated lattice parameters of CIS ( = 5.719Å, = 11.492Å, and / = 2.0094) have satisfactory agreement with the experimental values.
To investigate the locations of the Cd atoms, the complete model including seven atomic layers and 56 atoms is built, as shown in Figure 2. To prevent the charge-transfer  between the top layer and bottom layer of the slab, we use pseudohydrogen to passivate the bottom layer. The surface structure was optimized by atomic relaxation. The formation energies are calculated to determine the possible locations of the doping Cd atoms in the slab. We also investigated the influences of Cd doping on the electronic structure by calculating the density of state (DOS). All calculations, including geometry optimization and total energy calculation, are based on the density-functional theory [18,19]. We used the functional CA-PZ [20,21] (the Perdew and Zunger parameterization of the numerical results of Ceperley and Alder) of local density approximation (LDA) [22] and the ultrasoft pseudopotential [23] plane-wave method [24]. The cutoff energy for the plane-wave basis is set as 310 eV, and for the first Brillion zone, 3 × 4 × 1 k-point grids are used for all structures. During the geometry optimization, the two bottom atomic layers of the slab were fixed, and the atoms in the top five layers are relaxed until the forces are less than 0.03 eV/Å.

The Atomic
Relaxation of (112) Surface. For the defect-free (112) surface, after the relaxation, the atomic arrangement at the top surface layer is changed to reduce the total energy. Figure 1(b) shows the atomic structures after the relaxation. The two Cu atoms at the surface are denoted as "Cu1" and "Cu2, " and the two In atoms are denoted as "In1" and "In2. The atoms Cu1 and Cu2 move down from the original positions, almost on the same plane with the Se atoms of the surface. However, the two In atoms have contradictory behaviors: the atom In1 moves up to become a top atom, and the atom In2 moves down, nearly in the plane of Cu1 and Cu2. The reconstruction of the atomic structure can be explained by the crystal field theory and the valence-bond theory [25][26][27]. In CIS bulk materials, the Cu atom is the center of the tetrahedral structure which consists of the Cu atom and its four neighboring Se atoms. However, at the (112) surface, the Cu atom loses one neighboring Se atom, and the tetrahedral structure cannot be kept. In order to redistribute the electrons around Cu-Se bonds, the Cu atom and its three neighboring Se atoms form a new triangular structure and reach a stable state. This can be seen from the values of bond angle between Cu and Se atoms, as listed in Table 2.
In CIS the bonding between the atoms In and Se is mainly consisted of s and p orbital electrons of In and p orbital electrons of Se [27,28]. The tetrahedral structure is formed by sp 3 hybridization, like the diamond cubic structure. After the relaxation, for the In atoms located at the surface, their positions are changed likely due to degenerated sp 3 hybridization according to the valence-bond theory [29,30]. The degenerated hybridization of sp 3 has two directions: sp 3 → p 3 + s 1 and sp 3 → sp 2 + p 1 . Correspondingly, the bond angles become 90 ∘ (p 3 ) and 120 ∘ (sp 2 ) from 109 ∘ (sp 3 ), respectively. From the data in Table 2, we can deduce that the rising In1 atom corresponds to sp 3 → p 3 + s 1 , and the lower In2 atom results from the degeneration sp 3 → sp 2 + p 1 .
To prove the relaxed results in Figure 1(b), we also built a 12-layer model. The optimization of geometry gives similar results. (112) Surface. When the Cd atom enters into the CIS films, it may locate at the surface or migrate into a deeper position. Some experiments [31] reveal that the Cd atoms will replace the Cu and In atoms in the form of defects Cd Cu and Cd In . Because there exist many Cu vacancies in the CIS thin films, especially at the surface [4,5], it is more possible that the Cd atom substitutes Cu instead of In. Here we consider only the defect Cd Cu .

Cd Doping at the
In order to clarify the position of the Cd atom in CIS thin film, we place the defect Cd Cu at three different sites. (1) The defect Cd Cu is arranged at the top surface layer (denoted as "1st layer" in Figure 2). (2) The defect Cd Cu is located at the third layer. (3) The defect Cd Cu is located at the fifth layer. For convenience, the three sites are named as "site A, " "site B, " and "site C, " respectively. The formation energies of the defect at the three sites are calculated to clarify the distribution of Cd atom along the direction vertical to the surface (112).
In addition, considering that the Cu vacancies (denoted as V Cu ) are most likely located at the surface layer, it is possible that the defect Cd Cu forms a defect pair with V Cu , so we also calculate the formation energies of two kinds of defect pairs: (1) defects Cd Cu and V Cu are located closely to form defect pair Cd Cu + + V Cu − at the surface layer; (2) the defect Cd Cu is located at the surface layer, and the Cu vacancy is located at the second layer and not as close as the former. Both of them are shown in Figures 3(a) and 3(b). All the defective structures are based on the relaxed (112) surface structure discussed in Section 3.1.
To determine the favorite site of the defect Cd Cu , we calculate the defect formation energies. For uncharged defect , the formation energy is given by [15] Δ ( ) = defect − ideal + .
Here defect is the total energy of the defective system and ideal is the total energy of the ideal system (defect-free surface). is the number of the atoms which are added to/ removed from the ideal structure. If the atoms are added, is negative; if the atoms are removed, is positive. is the chemical potential of an atom which is removed or added.
For the defect Cd Cu , the expression of formation energy is rewritten as Here Cu and Cd are the chemical potentials of a Cu atom and a Cd atom, respectively. For the defect pair Cd Cu + + V Cu − , the defect formation energy is (3) Here p defect is the total energy of the defective system. To make the comparison easier, we defined a relative chemical potential Δ . For Cu and Cd atoms, the relative chemical potential can be written as Here solid Cu is the chemical potential of Cu atom in the solid Cu (fcc) and solid Cd is the chemical potential of Cd atom in solid Cd (primitive hexagonal), which can be determined by calculations.
So (2) and (3) can be rewritten as  According to (5), we can obtain the defect formation energies of Cd Cu and the defect pair, as listed in Table 3.
In order to compare clearly the formation energies of the defects, it is needed to determine the values of Δ Cu and Δ Cd . To simplify the calculation, we assume that the value of Δ Cd does not vary with the site of the Cd atom, so we just consider the variation of Δ Cu .
In order to maintain a stable CuInSe 2 compound and avoid the precipitation of elemental solids (elements Cu, In, and Se), the relative chemical potential of Cu can vary in the intervals [15] as where Δ (CuInSe 2 ) (−2.0 eV) is the formation energy of solid CuInSe 2 [15]. Δ Cu = 0 corresponds to Cu-rich conditions and Δ Cu = −2.0 corresponds to Cu-poor conditions. From the defect formation energies in Table 3 and (5)-(6), we can plot the curves of the formation energy versus the relative chemical potential Δ Cu , as shown in Figure 4. It can be seen that all formation energies of single defect and defect pair decrease when the relative chemical potential of Cu decreases, and this indicates that the defects are formed easier in Cu-poor environment than Cu-rich environment. The formation energy of the defect pair at the surface layer is the lowest.
For the single defect Cd Cu , the formation energy at the deeper site (site C) is lower than that at the surface (site A).  It means the Cd atoms may migrate into the deep layers of the CIS thin film. This agrees with the results [31][32][33] that Cd atoms diffuse approximately 100Å∼300Å from the heterojunction boundary.
However, the defect pair Cd Cu + +V Cu − at the surface layer has the lowest formation energy. The energy reduction can be attributed to the electrostatic interaction between Cd Cu and V Cu [15]. To clearly explain this, here we defined the interaction energy Here int is the energy change when two defects Cd Cu and V Cu are located closely to form a defect pair [15]. The term Δ (V Cu ) and Δ (Cd Cu ) are the formation energy of isolated defect V Cu and Cd Cu , respectively. For the defect pair in the surface layer, the interaction energy int can be calculated, and its value is −0.857 eV. When Cd Cu and V Cu are located at the different layers, the distance between them becomes longer, so their electrostatics interaction is weakened. The interaction energy becomes −0.422 eV when V Cu and Cd Cu are located at the surface and the second layer, respectively. Therefore, the Cd atoms prefer staying at the surface layer with the Cu vacancies to form the defect pair Cd Cu

Electronic Structure.
The electronic structures were also investigated by the calculations of density of states (DOS). Figure 5(a) shows the site projected density of states (PDOS) of the surface layer with the defect pair Cd Cu + + V Cu − and the third layer without the defect pair. The third layer has no defect, and it is considered as the bulk CIS to facilitate comparisons. The PDOS curve of the surface layer is aligned with that of bulk CIS, and the top of valence band of bulk CIS is set as an energy reference. In Figure 5(a), it can be seen that in the surface layer the valence band maximum (VBM) has a left shift (the calculation shows that the shift is about 0.1 eV). This is because of the lack of copper which weakens the repulsions between Cu-d and Se-p orbitals and depress the valence band. The introduction of the Cd atoms brings a strong repulsion between Cd-d and Se-p orbitals and results in a sharp peak at −9.29 eV. The position of the peak is located at lower energy levels and has little influence on the VBM. Figure 5(b) shows the PDOS of Cd, In, and Se atoms in the surface layer. The DOS of the third layer is also shown in the figure (marked by "CIS") for comparison. It can be seen that the density of states from the In atoms are higher than those of the Cd atoms in upper energy levels. It means that the In atoms have more important influences on the electronic structure of CIS than the Cd atoms. However, for perfect CIS or Cu-poor CIS, the Cu-Se bonds play the most important role in forming the electronic structure [7].

Discussion
For single defect Cd Cu , the Cd atoms might migrate into the deeper positions in the CIS thin film. However, because there are many Cu vacancies at the surface layer, Cd Cu is easier to form the defect pair Cd Cu + + V Cu − with Cu vacancies at the surface (112). They have the lowest formation energy due to the electrostatics interactions between the defect Cd Cu and V Cu . The interaction reduces the formation energy through two ways: (1) the transfer of one electron from the highenergy donor level to low-energy acceptor level and (2) a strong electrostatic attraction between the two charged defects [15]. So most of the Cd atoms from the CdS buffer layer prefer to stay at the (112) surface of CIS to form defect pairs. The diffusion of Cd atoms is localized in a narrow region, and the concentration of Cd at the surface layer is higher than that at deeper layers [31][32][33].
For the (112) surface of CIS, the formation energy of defect pair Cd Cu + +V Cu − is lower than that of the single defect Cd Cu . The existence of many Cu vacancies makes Cd Cu appear in the form of defect pair Cd Cu + + V Cu − and results in that the electrons from Cd Cu are accepted by V Cu . So there is no accumulation of electrons at the surface, and this has little influence on the band structure and the carrier transportation.
The electronic structure of CIS is mainly influenced by Cu-Se and In-Se bonds. Because of the lack of Cu atoms at the surface, the repulsions between Cu-d and Se-p orbitals is weakened, and the valence band is depressed. This results in the down shift of the VBM. The antibonding states of Cd-Se bonds are located at the lower energy levels far from the VBM (shown in Figure 5), so a doped Cd atom by itself does not significantly influence on the electronic structure, but the defect pair Cd Cu + + V Cu − plays an important role.
If we consider CuInSe 2 (112)/CdS as interface, the down shift (about 0.1 eV) of the VBM caused by the defect pair Cd Cu + + V Cu − will bring a hole barrier. The hole barrier can prevent the holes from approaching the interface and allow electrons to pass through it. This can reduce the recombination of carriers and is conducive to improve the performance of the thin film solar cells.
To explain the reason of the replacement of Cu by Cd, it is helpful to consider the electronegativities of Cu and Cd. The electronegativity of atom Cd ( = 1.69) is lower than that of atom Cu ( = 1.90), and so the chemical potential of its electron is higher than that of Cu atom [34]. Because the Se atom has higher electronegativity (lower chemical potential of electron) than Cu and Cd, the difference in chemical potential makes it easier to drive the electrons of Cd to transfer to Se and form Cd-Se bonds. This may be the reason why the atom Cd can substitute Cu in CIS films.
It should be pointed out that the substitution of Cu by Cd in the CIS films is different from the replacement of Cu by Zn [35]. In the latter case, Zn atoms bring additional electrons and form an n-type region near the surface of the CIS films. This results in a bent energy band and prevents the transportation of holes. For the single defect Cd Cu , it has similar effects on the band structure and the transportation of carriers. However, in CIS films, the defect Cd Cu prefers to form the defect pair Cd Cu + + V Cu − with Cu vacancy due to their low formation energy, and their concentration is much higher than that of the single defect Cd Cu . In this case, the additional electron of Cd atom is accepted by Cu vacancy, so the bent band and n-type region are not formed. Therefore, unlike the replacement of Cu by Zn, the substitution of Cu by Cd has little effect on the band structure and the transportation.

Conclusion
In this paper, we investigate the doping behaviors of Cd atoms in CuInSe 2 thin films. It is found that the Cd atoms prefer to stay at the surface in the form of defect pair Cd Cu + + V Cu − which has the lowest formation energy and is formed easily. The defect pair brings a down shift of valence band maximum about 0.1 eV, which form a hole barrier at the CuInSe 2 / CdS interface, which can prevent holes from arriving at the interface and reduce the carrier recombination.