Defect properties of Sb- and Bi-doped CuInSe 2 : The effect of the deep lone-pair s states

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1 Defect properties of Sb- and Bi-doped CuInSe 2 : The effect of the deep lone-pair s states Ji-Sang Park, Ji-Hui Yang, Kannan Ramanathan, and Su-Huai Wei a National Renewable Energy Laboratory, Golden, Colorado, 80401, USA ABSTRACT Bi or Sb doping has been used to make better material properties of polycrystalline Cu 2 (In,Ga)Se 2 (CIGS) as solar cell absorbers, including the experimentally observed improved electrical properties. However, the mechanism is still not clear. Using firstprinciples method, we investigate the stability and electronic structure of Bi- and Sb-related defects in CuInSe 2 and study their effects on the doping efficiency. Contrary to previous thinking that Bi or Sb substituted on the anion site, we find that under anion-rich conditions the impurities can substitute on cation sites and are isovalent to In because of the formation of the impurity lone pair s states. When the impurities substitute for Cu, the defects act as shallow double donors and help remove the deep In Cu level, thus resulting in the improved carrier life time. On the other hand, under anion-poor conditions, impurities at the Se site create amphoteric deep levels, therefore, is detrimental to the device performance. PACS Number: jn, J-, S-, i a Electronic mail: Suhuai.Wei@nrel.gov 1

2 Thin-film photovoltaic devices based on Cu(In,Ga)Se 2 (CIGS) absorber layers have attracted much attention because of their high absorption coefficient and high energy conversion efficiency, which exceeds 20% among thin-film solar cells. 1,2 To improve the conversion efficiency of the device, dopants are often introduced to the CIGS absorber layer to improve its material properties. One of the most widely used dopants in CIGS is sodium (Na), which plays an important role in enhancing hole concentration and carrier collection. 3,4 Recently, potassium (K) doping has also been shown to act similarly to Na and can further improve the conversion efficiency in CIGS. 2 Antimony (Sb) and bismuth (Bi) are other dopants that have been found to be beneficial to the material properties and enhance the conversion efficiency of CIGS based solar cells However, the detailed mechanism is still not clear because the defect properties of Sb and Bi have not yet been studied comprehensively. Previous studies often assume that group-15 elements Sb and Bi have five valence electrons, thus when they dope CIGS, the dopants should substitute on group-16 elements Se (or S) sites. 12 As we will show, through firstprinciples density functional theory (DFT) calculations, this assumption is not correct. The preferred doping sites actually strongly depend on growth conditions. Because of the high electronegativity and large relativistic effects, heavy dopants such as Sb and Bi show multivalence feature and are isovalent to the group-13 element, In, when it substitutes on cation sites of CuInSe 2 (CIS). In this case, the dopants at the In site do not act as donors despite the dopants having two more valence electrons than In, because Bi 6s and Sb 5s form semicore lone-pair states deep inside the valence band. These dopants at Cu sites form shallow donors and are beneficial to the performance of the solar cell because they can remove the deep gap state of In Cu. They act as group-15 elements, contributing five valence electrons only when they substitute on an anion site. In this case, they create amphoteric deep levels that are detrimental to the solar cell performance. Our theoretical studies on the 2

3 stability and electronic structure of Bi and Sb doping in CIS, therefore, provide a better understanding of the defect physics of the dopants with high atomic numbers and guidelines for further improvement of the CIGS-based solar cell efficiency. Our calculations are performed within the density functional framework by using the hybrid density functional proposed by Heyd, Scuseria, and Ernzerhof (HSE) for the exchange correlation potential 13 and the projector augmented wave (PAW) method to describe corevalence electron interactions, 14 as implemented in the Vienna ab-initio Simulation Package (VASP) code. 15 The screening parameter of ω = 0.2 A -1 and the optimized parameter of α = 0.3 in the HSE functional are used. The wavefunctions are expanded in plane waves with an energy cutoff of 295 ev. The optimized lattice constants of chalcopyrite-type CIS are a = Å and c = Å, close to experiment values of a = Å and c = Å. 16 The bandgap calculated using this hybrid density functional is 1.11 ev, similar to the experiment bandgap of 1.04 ev. For defect calculations, we use a supercell approach containing 64 host atoms. For Brillouin zone integration, only a single Γ-point is used. Our test calculations on a larger supercell containing 144 atoms give similar results. The ionic coordinates are fully relaxed until the residual forces are less than 0.05 ev/å. The formation energy (E f ) of a defect X (Bi or Sb) in the charge state q is given by 17 E f (X,q) = E tot (X,q) E(host) + n Cu μ Cu + n In μ In + n Se μ Se + n X μ X + q (E F +E V ), where E tot (X,q) is the total energy of a supercell, including the defect X, and E(host) is the total energy of the same supercell without the defect. The variables n i and μ i are the number of species i (i = Cu, In, Se, Bi, and Sb) removed from the supercell in forming the defect and the corresponding chemical potential, respectively. E F is the Fermi energy with respect to the valence band maximum (VBM, E V ) of the CIS host. In CIS, the chemical potentials of Cu, In, and Se satisfy the relation, μ Cu + μ In + 2μ Se = μ CIS = ev, and the maximum chemical potential of Cu, In, and Se should be lower than that of face-centered cubic Cu, tetragonal In, 3

4 and hexagonal gray Se, respectively, which are set to be zero. The chemical potentials are chosen to prevent the formation of secondary phases, such as cubic (F-43m) Cu 2 Se (μ Cu2Se = ev), hexagonal (P6 3 /mmc) CuSe (μ CuSe = ev), hexagonal (P6 1 ) In 2 Se 3 (μ In2Se3 = ev), and hexagonal (P6 3 /mmc) InSe (μ InSe = ev), as shown in Fig In Cu-poor conditions, a relatively In-poor condition is employed to prevent formation of In 2 Se 3. The maximum chemical potentials of Bi (μ Bi ) and Sb (μ Sb ) are bounded by avoiding the formation of trigonal (R-3m) Bi (μ Bi =0), trigonal Sb (μ Sb =0), trigonal (R-3m) Bi 2 Se 3 (μ Bi2Se3 = ev), cubic (F-43m) InSb (μ InSb = -0.6 ev), and orthorhombic (Pbnm) Sb 2 Se 3 (μ Sb2Se3 = -0.4 ev). Note that tetragonal (P4/nmm) InBi is found to be unstable (μ InBi > 0 ev). Figure 2 shows the formation energy of Bi- and Sb-related point defects under three different growth conditions, Cu-poor, In-poor, and Se-poor (see Figure 1). We considered three substitutional defects (X Cu, X In, and X Se ), and interstitial defects at cation and anion tetrahedral sites (X T,C and X T,A ). Interstitials at the anion tetrahedral sites in neutral charge state are found to be not stable because of large electrostatic repulsion, and they tend to form split interstitials with In (X split ). Previous studies assumed that Bi and Sb substitute for Se and act as acceptors; 6,12 however, as shown in Figure 2, it strongly depends on the chemical potentials. In Cu-poor condition [Figures 2(a) and (d)], the dopants have low energy when they substitute on cation sites. For p-type material, the dopant is most stable on the Cu site and becomes more stable at the In site when the Fermi energy increases. When the dopant substitutes on the Cu site, deep Bi 6s and Sb 5s states only weakly interact with Se 4s states, and both the levels are deep inside the valence band. The dopants 6p and 5p states interact with neighboring Se 4p orbitals and the p-p anti-bonding levels of the dopants and neighboring Se are higher than the conduction band minimum (CBM) by about 1 ev, thus the X Cu defects are always ionized at a 2+ charge state and the CBM is occupied by two excess 4

5 electrons of the dopants. It should be emphasized that the In Cu defect has a (2+/0) transition level in the band-gap, which becomes deep in CIGS when the Ga concentration increases; thus the defect acts as a Shockley-Read-Hall recombination center, resulting in the lower conversion efficiency. 19 Because the In Cu deep level can be removed by forming Bi Cu and Sb Cu defects, Bi or Sb doping can improve conversion efficiency under Cu-poor conditions, consistent with previous experiments. The formation of Bi Cu and Sb Cu has another beneficial role at the interface between the CIGS/CdS. The interface is usually more Cu-poor compared to bulk counterparts, thus the defects are more easily formed at the interface. Because X Cu is a shallow donor compared to In Cu, the n-type conversion can be more easily achieved at the interface, which can increase open-circuit voltage (V OC ). Therefore, we suggest that doping of Bi and Sb at the CdS/CIGS interface would be most beneficial to the solar cell performance. Note that in this case interstitial Bi has relatively high formation energy because the chemical potential of the dopant is restricted to prohibit the formation of Bi 2 Se 3. Under In-poor condition [Figs. 2(b) and (e)], the dopants predominantly substitute on the isovalent In site. The In-poor condition is characterized by high μ Cu and low μ In, thus the formation energies of Bi Cu and Sb Cu are higher than that of Bi In and Sb In, respectively. Also, formation of In Cu is less favorable compared to the other two growth conditions. The defects (Bi In and Sb In ) are always in the neutral state because of the formation of lone-pair s states deep inside the valence band. Therefore, no appreciable effect on the electronic structure is expected when the concentrations of Bi or Sb are low. We will discuss the alloying effect later in this paper. In Se-poor condition [Figures 2(c) and (f)], Sb substitutes for Se in a wide range of Fermi energies, whereas Bi substitutes for Se only when Fermi energy is rather close to the CBM. When the dopant substitutes for Se, the high energy dopant p states interact with Cu d states, 5

6 inducing an anti-bonding deep defect state inside the bandgap. In contrast to the previous studies, 6,12 we find that X Se exhibits an amphoteric nature; X Se can be either donors or acceptors, depending on the Fermi energy (Figure 2(c)). For Bi Se, the transition level of the defect is at about 0.8 ev above the VBM, i.e., relatively close to the CBM. For Sb Se, the transition level is at about 0.6 ev, which is relatively lower than that of Bi Se because the Sb 5p level is lower in energy than the Bi 6p state. Because the levels are in the middle of the bandgap, both n-type and p-type doping efficiencies are hindered in this Se-poor condition. Therefore, this condition should be avoided for better device performance. Another beneficial effect of doping with Sb and Bi is the reduction of the lattice mismatch between CIGS and CdS. Note that the lattice constant of CdS is about 1% larger than CIS and the lattice mismatch increases with the Ga composition ratio in CIGS. In the chalcopyrite phase, the calculated lattice constants of CuSbSe 2 (CAS) are a = Å and c = Å, and those of CuBiSe 2 (CBS) are a = Å and c = Å, larger than those of CIS (a = Å and c = Å) because of the larger atomic size of Sb and Bi. Therefore, we can compensate for the lattice mismatch by doping Sb and Bi, especially in the In-poor condition. It is worth noting that CAS has chalcostibite ground state structure and CBS is more stable in the emplectite structure, 20 thus alloy CAS and CBS with CIS can form different structures depending on the composition of In, Bi, and Sb. However, for a dilute alloy with X less than 10 % 6-9 as shown in the experiment, Cu(In,Bi)Se 2 and Cu(In,Sb)Se 2 are expected to be stable in the chalcopyrite phase. Figure 3 shows the band structure of CIS, CBS, and CAS in the chalcopyrite phase. Unlike with CIS, the VBMs of CBS and CAS are no longer located at the Γ point because of the coupling between the Se p and X lone pair s state. This coupling is weak at Γ because of the high symmetry at the Γ point and is larger at the N point. Calculating the natural band offsets, we find that the VBMs of CAS and CBS are higher than that of CIS by about 0.77 and

7 ev, respectively; the VBM of CAS is a little higher than that of CBS because of the higher Sb s orbital, which leads to stronger Sb s and Se p coupling. Therefore, the acceptors in CIS become shallow as Bi and Sb are incorporated, resulting in the increased hole concentration. Moreover, the conduction band edge states of CBS and CAS are derived from mostly Bi or Sb p orbitals, in contrast to that of CIS, because of deep lone pair s orbitals. In summary, our results show that for Bi and Sb doping in CIS, the dopants do not always substitute for Se, but it depends strongly on the chemical potential of Cu, In, and Se. Therefore, it is possible to control the defect type and concentration by changing the chemical potentials. Bi and Sb substitutions at the Cu site are double donors and have no defect level inside the band-gap, thus the substitutions can improve n-type conversion at the CIS/CdS interface and remove the recombination center of III Cu (III = Ga, In) in CIGS, which should be beneficial for the cell performance, The impurities at the In site are neutral because of the deep lone pair s state, even though they are group-15 elements. In contrast to the previous studies, the impurities at the Se site create deep amphoteric levels, and thus are detrimental to the device performance. This work at NREL is supported by the U.S. Department of Energy, EERE, under Contract No. DE-AC36-08GO

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10 Figure 1. (color online). Plot showing allowed chemical potentials (shaded region), which make CuInSe 2 stable, and the limiting secondary phases. Three different conditions, Cu-poor (μ Cu =-0.84 ev, μ In =-1.71 ev, μ Se =0 ev), In-poor (μ Cu =-0.39 ev, μ In =-2.17 ev, μ Se =0 ev), and Se-poor (μ Cu =0 ev, μ In =-0.17 ev, μ Se =-1.19 ev) conditions are shown. In Cu-poor and Inpoor conditions, μ Bi and μ Sb are restricted by Bi 2 Se 3 and Sb 2 Se 3 (μ Bi = ev, μ Sb = ev). In Se-poor condition, μ Sb is restricted by InSb (μ Sb = ev). 10

11 Figure 2. (color online). Formation energy of Bi-related (a-c) and Sb-related (d-f) defects as a function of Fermi Energy E F in Cu-poor, In-poor, and Se-poor conditions (see Figure 1). The slope represents the charge state of the defect. The defects are represented by the same color in these figures. 11

12 Figure 3. (color online). The electronic band structures of CuInSe 2, CuBiSe 2, and CuSbSe 2 in the chalcopyrite phase. Primitive lattice of body-centered tetragonal is given by a 1 = (-a/2, a/2, c/2), a 2 = (a/2, -a/2, c/2), and a 3 = (a/2, a/2, -c/2). The special k-points are given by Z = b 1 /2 + b 2 /2 b 3 /2, X = b 3 /2, P = b 1 /4 + b 2 /4 + b 3 /4, and N = b 2 /2, where b i (i = 1, 2, 3) is the reciprocal lattice vector. Red, blue, and green colors represent the percentage of s, p, and d orbitals of In, Bi, and Sb atoms. 12

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14 Formation energy (ev) Formation energy (ev) (a) Cu-poor Bi split Bi Cu Bi Se (d) Cu-poor Sb split Sb Cu Sb T,C E F (ev) (b) In-poor Bi In Bi T,C (e) In-poor Sb In Sb T,A E F (ev) (c) Se-poor Bi T,A (f) Se-poor Sb Se E F (ev)

15 (a) CuInSe 2 (b) CuBiSe 2 (c) CuSbSe Energy (ev) Z Γ X P N Γ k-point Z Γ X P N Γ k-point Z Γ X P N Γ k-point