Ionization Levels of Doped Copper Indium Sulfide Chalcopyrites - The

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Ionization Levels of Doped Copper Indium Sulfide Chalcopyrites C. Tablero Instituto de Energía Solar, ETSI de Telecomunicación, Universidad Politécnica de Madrid, Ciudad Universitaria s/n, 28040 Madrid, Spain ABSTRACT: The electronic structure of modified chalcopyrite CuInS2 has been analyzed from first principles within the density functional theory. The host chalcopyrite has been modified by introducing atomic impurities M at substitutional sites in the lattice host with M = C, Si, Ge, Sn, Ti, V, Cr, Fe, Co, Ni, Rh, and Ir. Both substitutions M for In and M for Cu have been analyzed. The gap and ionization energies are obtained as a function of the M−S displacements. It is interesting for both spintronic and optoelectronic applications because it can provide significant information with respect to the pressure effect and the nonradiative recombination. theoretical limiting efficiency of 63.2%,8 in contrast to the 40.7% of conventional single-gap solar cells. There are two ways of avoiding the nonradiative recombination: an increase in the density of the impurities responsible for the midgap levels in order to form an intermediate band instead of a deep level and an increase in the impurity-host interaction. The former is related to the Mott transition,9 while the latter is associated with the modification of the contribution from the impurity to the midgap levels and to the host semiconductor bands.10 Experimentally, the energy band gap of the copper indium sulfide (CuInS2), known as roquesite, increases with the temperature from 10 to 120 K and starts to decrease as the temperature goes beyond 120 K. This temperature dependence of the energy gap is anomalous for semiconductors and has been observed in several chalcopyrite semiconductors.11,12 For the Fe-doped CuInS2 crystals the experimental optical absorption spectra present a subgap absorption band with a threshold at 0.8 eV13 associated with the photoionization transition from the VB to the acceptor-related Fe deep level. This compound has been analyzed from first principles14 using a methodology similar to that used in this work. The results place the d-Fe band in agreement with the experimental results. The cation site where the impurity is substituted is diverse in the chalcopyrite family. For example, experimental results in CuAlS25 suggest that Cr supposedly substitutes for both the Cu and Al sites, V and Mn for the Cu sites, Ti for the Al sites, and Fe for both the Cu and Al sites. In CuGaS2 the experiments suggest that Fe and Mn substitutes both cation sites. To address the modifications that occur in the electronic properties of doped CuInS2 chalcopyrite, we have carried out first-principles theoretical calculations of the ionization energy levels for a series of impurities in CuInS2 for both cation sites.

I. INTRODUCTION In recent years, ternary compounds with a chalcopyrite-type crystal structure have attracted a lot of interest among researchers into compound semiconductors as candidates for materials for new optoelectronic devices. In particular, thin film chalcopyrite solar cells are of considerable interest for photovoltaics due to their low cost, potential for upscaling, radiation hardness, long-term stability, high flexibility, low weight, and high conversion efficiencies. The I−III−VI (I = Cu; III = In, Ga; VI = Se,S) chalcopyrite family of compounds is the ternary analogue to II−VI binary semiconductors. The I−III−VI chalcopyrite tetragonal structure is obtained from the cubic II−VI structure by occupying the group II atom sites alternatively with group I (Cu) and group III (In, Ga) atoms. Despite the structural similarities, the band gap energies of the I−III−VI chalcopyrites are substantially smaller than those of their binary analogues.1 The valence band maximum in chalcopyrites is dominated by the hybridization of Cu 3d and anion sp orbitals. The CB edge also has a high contribution of sp anion orbitals. Although Cu(In,Ga,Al)Se2 alloys have been studied in some detail in recent years,2−5 much less is known about the modifications that occur in the electronic properties of doped CuInS2 chalcopyrite by impurity-doping. Some impurities have been known to introduce deep levels into the band gaps of semiconductors, which not only control the concentration and type of conducting carriers but also influence the radiative and nonradiative processes. The deep impurities could have a negative effect because these deep levels act as very effective Shockley, Read, and Hall recombination centers6 via a lattice relaxation multiphonon emission (MPE) mechanism.7 However, if the charge density around the impurity is equilibrated in response to the electronic capture of the MPE mechanism, then the negative nonradiative recombination is suppressed. Additionally, these solar cell devices with an intermediate band partially full have a © 2012 American Chemical Society

Received: October 5, 2011 Revised: December 14, 2011 Published: January 12, 2012 1390

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II. CALCULATIONS The ionization energies of the system S with N electrons (SN) are calculated from total-energy differences15 such as eD = E(N) − E(N−1) and eA = E(N+1) − E(N). These energies + correspond to the processes SN ⇌ SN−1 + e and SN + e ⇌ − , where e represents an electron just outside the material, SN+1 i.e., at the vacuum level. Similarly, the acceptor and donor energies of the host semiconductor, with NH electrons, correspond to the energy of the CB (eC) and VB (eV), respectively. Then, the gap of the host semiconductor obtained from total energies is as follows: Eg = eC −eV = [EH(NH+1) − EH(NH)] − [EH(NH) − EH(NH−1)]. The ionization energies are usually referred to the bottom of the CB (eD(CB) = eC −eD) or to the top of the VB (eA(VB) = eA −eV). These ionization energies describe the transition of an electron from the valence continuum (eVB) to a defect acceptor level (SN + eVB ⇌ − ) or from a donor level to the conduction continuum of SN+1 + states (SN ⇌ SN−1 + eCB). The ionization energies calculated from total-energy differences are in general different from the respective single-particle Kohn−Sham (KS) eigenvalue energies. The latter is equivalent to using Koopman’s theorem. The habitual gap underestimation using single-particle Kohn−Sham eigenvalues differences is around 30−50%. The calculated band gap and the donor and acceptor levels calculated from total-energy differences are much closer to the experiment than that obtained from the single-particle eigenvalues. In our calculations, one In or Cu atom was replaced with one impurity atom M, i.e. CuIn1−xMxS2 (MIn substitution) and Cu1−xMxInS2 (MCu substitution), with M = C, Si, Ge, Sn, Ti, V, Cr, Fe, Co, Ni, Rh, and Ir. To obtain the total energies, we have used the density-functional theory (DFT).16 The standard KS17 equations are solved self-consistently using the SIESTA code.18 For the exchange and correlation term, the local-spin density approximation (LDA) has been used with the Perdew−Zunger parametrization to the Ceperley−Alder numerical data19 and the generalized gradient approximation (GGA) in the form of Perdew, Burke, and Ernzerhof.20 The standard Troullier− Martins21 pseudopotential is adopted and expressed in the Kleinman−Bylander22 factorization. The KS orbitals are represented using a linear combination of confined pseudoatomic orbitals.23 An analysis of the basis set has been carried out using from single-ζ to triple-ζ with polarization basis sets for all atoms and by varying the number of the special k points in the irreducible Brillouin zone. Supercells containing from 16 to 216 atoms (x from 0.25 to 0.018) have been used. The bigger supercells have only been used in a few cases in order to compare them with 64 atom supercells. In all of the results presented in this work a double-ζ with polarization localized basis set has been used with periodic boundary conditions and 18 special k points in the irreducible Brillouin zone for a 64-atom cell (x = 0.06). Several further corrections to the calculated energies24 were applied: potential alignment between a charged defect calculation and the perfect host crystal, and spurious interaction of periodic image charges.

tetrahedron. This distortion is described by the anion displacement parameter u, which is 0.25 for an ideal tetrahedron in cubic binary systems. The anion displacement parameter u is related to Cu−S and In−S bond lengths (rCu−S and rIn−S, respectively) as u = 0.25 + (rCu−S2 − rIn−S2)/a2. Theoretical calculations based on the LDA or GGA underestimate the u parameter25 (0.213 ≤ u ≤ 0.220) with respect to other more sophisticated schemes such as hybrid functionals, LDA+U, and GW methods (0.22626 ≤ u ≤ 0.22927). Unfortunately, experimentally measured values (0.213 ≤ u ≤ 0.229)28−30 also have numerous uncertainties. It is possibly a result of crystalline imperfection, partial disordering, the presence of defects, and nonuniformity in the composition of the samples. The main limitation of these more sophisticated methods is the very high computational cost. For this reason, to analyze the electronic structure of the modified chalcopyrite with many M substitutional impurities at Cu and In sites, we have used the DFT with LDA and GGA. CuInS2 has experimental lattice parameters a = 5.52 Å, c/2a = 1.006,28−30 and u = 0.229.29 In the substituted MIn chalcopyrite (CuIn1−xMxS2) the distribution of the first shells of the neighbors around M is as follows: 2.46 (4S), 3.90 (4Cu), 3.91 (4Cu + 4In), 4.49 (4S), 4.57 (4S), and 4.61 Å (4S), etc. For MCu the distribution of the first shells of the neighbors is as follows: 2.34 (4S), 3.90 (4In), 3.91 (4Cu + 4In), 4.55 (4S), 4.63 (4S), and 4.67 Å (4S), etc. The first shell of anions around the M atom is distributed with tetrahedral symmetry. The s and p atomic orbitals of M have a and t2 tetrahedral symmetry, respectively, i.e., as and t2p, whereas the d orbitals are split by the crystalline field into doubly degenerate ed states (dz2 and dx2−y2) and 3-fold degenerate t2d states (dxy, dxz, and dyz). The crystal wave functions with t2 symmetry are formed by the combination of the t2d and the t2p states of M, and by the states with t2 symmetry of the host, mainly with the p-S states of the first shell of anions. Some of these functions are those that lead to the donor and acceptor levels within the gap for the substituted chalcopyrites. The host gap and the donor and acceptor ionization energies for the MIn- and MCu-doped chalcopyrites have been obtained in accordance with Calculations. To analyze the dependence of the energy gap and the ionization energy levels with the impurity atomic environment, these ionization energies have been obtained as a function of the inward and outward displacement of the nearest S neighbors to the M atom. The distances M−S have been chosen as a generalized coordinate Q. These distances are proportional to the distances of the energy minimum, labeled Q0. The changes in these ionization energies with the configuration coordinate Q−Q0 are shown in Figures 1 and 2 for the MIn and MCu substitutions with M = C, Si, Ge, Sn, Ti, V, Cr, Fe, Co, Ni, Rh, and Ir. The vertical line in the Q−Q0 axis indicates the equilibrium position of the In−S distance in the host chalcopyrite CuInS2 (Q0 = 2.461 Å with LDA and 2.463 Å with GGA). These distances will be equivalent to an anion displacement parameter of 0.229 in the first shells of the neighbors around M. From Figures 1 and 2, the gap for the equilibrium distance (Eg = eC − eV = 1.4 eV) is comparable with the experimental results in the literature (1.48−1.55 eV31). Note that the usual gap subestimation using single-particle differences with DFT in the chalcopyrites is more than 50%. For example, the gaps for the chalcopyrite CuInS2 in ref 30 is −0.14 eV, 0.01 eV in ref 32, 0.812 eV in ref 33, approximately zero in ref 34, and 0.02 eV in

III. RESULTS AND DISCUSSION The chalcopyrite structure is derived from the zinc-blend structure by replacing the Zn cations alternatively with Cu and In. These substitutions lead to a ratio c/2a ≠ 1 (=1 for the ideal zinc-blend structure), and to a deformation of the anion 1391

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Figure 1. Donor (eD), acceptor (eA), and CB edge (eC) energies with respect to the VB edge (eV) energy as a function of Q −Q0, for the MIn substitution in CuInS2 with M = C (a), Si (b), Ge(c), Sn (d), Ti (e), V (f), Cr (g), Fe (h), Co (i), Ni (j), Rh (k), and Ir (l). Q is the generalized coordinate (M−S distance) and Q0 is its value for the energy minimum. The vertical line in the panels indicates the equilibrium position of the host semiconductor CuInS2.

Figure 2. Same legend as Figure 1, but for the MCu substitution.

position Q0 of the host CuInS2 (vertical line on the Q−Q0 axis), i.e., Q < Q0, the gap increases slightly close to the vertical line, and later decreases. Furthermore, from Figure 1, for the MIn substitution, almost all of the donor and acceptor ionization levels can increase their energy in the band gap through pressure. This behavior is not so general for the M Cu substitution (Figure 2). The experimental optical absorption spectra of the FeIn present a subgap absorption at 0.8 eV13 that is associated with the photoionization transition from the eV to the acceptorrelated d-Fe deep level eA. From Figure 1 (panel h) eA − eV ∼ 0.75 eV. This result is in agreement with experimental results13 and with other theoretical results.14

ref 35. Different methodologies, basis sets, and different exchange−correlation functionals are used in these references. As it has already been mentioned, the experimental band gap energy of CuInS2 shows a slight anomalous increase with the increase in temperature in the low-temperature range, while at higher temperatures the band gap decreases with an increase in the temperature.11 It is consistent with the results in Figure 1. For the inward displacement with respect to the equilibrium 1392

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LDA. This difference around the equilibrium Q0 position is lower than 0.15 eV and higher for Q < Q0 (the inward mode). In addition, the position of the donor and acceptor ionization energies has been checked with respect to the anion displacement parameter u in order to estimate the possible errors (Figure 3, panel c). From the figure, the energy differences are almost indiscernible, indicating that the modification of the ionization energies with u is small. For a few points we have also compared the ionization energies obtained with larger supercells (216 atoms) for comparison with the 64-atom supercells. The differences are of the order of the calculations (∼±0.02 eV) and lower than those obtained with different exchange-correlation potentials. Although the objective of this work is not to study the nonradiative recombination profoundly, the figures showing the VB and the CB edges (eV and eC) and those of the acceptor and the donor energy levels (eA and eD) with respect to Q −Q0 can provide important information. As the lattice vibrates, the ionization levels move up and down in the energy gap (Figure

The positions of the donor and acceptor ionization energies allow an easy characterization of the impurity as a donor (eD lies in the gap but eA does not) and acceptor (eA lies in the gap but eD does not) or with amphoteric behavior (both eD and eA are found within the gap). With this classification, Ge, Sn, Ir, Cr, and Rh will be amphoteric for the MIn substitution (Figure 1), and C, V, Cr, Fe, Co, Ni, Rh, and Ir, for the MCu substitution (Figure 2). For the substituted chalcopyrites, when the In atom is substituted by M (MIn substitution), the oxidation state is M3+, whereas if M substitutes Cu (MCu substitution) the oxidation state is M+. The energy range in which these oxidation states are stable depends on the Fermi energy. For example, for the MIn (MCu) substitution the oxidation state M3+ (M+) is stable when the Fermi energy is between eA and eD. In general, the stability of positive oxidation states decreases as the Fermi energy shifts from the VB to the CB. For this reason the ionization energies corresponding to the MIn substitution (Figure 1) are lower than the ionization energies corresponding to the MCu substitution (Figure 2). The ionization energies have been calculated with both LDA and GGA. To estimate the LDA and GGA differences, a comparison for the two substitutions GeIn and CrIn is shown in Figure 3. With GGA these energies are slightly larger than with

Figure 4. Schematic representation of the nonradiative recombination with respect to the configuration coordinate Q using total energy curves (upper panel) and ionization energies (lower panel). A quadratic representation of the total energies with respect to Q has been used. As a consequence, the evolution of the ionization levels with Q is linear.

4). For sufficiently large vibrations the level can cross into the CB or VB and capture or emit an electron or a hole. After capture or emission the lattice near the impurity defect relaxes. During the damping, the localized energy propagates away from the impurity defect as lattice phonons, i.e., by multiphonon emission. This fact increases the nonradiative recombination.7 On the other hand, the lack of intersection greatly reduces the capture cross-sections and reduces the nonradiative recombination. This behavior can be very important in order to use these substituted chalcopyrites for solar cells and optoelectronic devices. Additionally, Figures 1−3 show that the evolution of the ionization levels with Q is not linear. It implies that the total energy curves are not quadratic with Q.7 Additionally, the cohesive energies of the modified chalcopyrite have been evaluated from the calculated energy of both the bare host and the corresponding elemental atomic reservoirs. The cohesive energies may be representative of the relative energy balance expected for growth processes that use gaseous phases rather than solids for the deposition, such as molecular beam epitaxy or physical vapor deposition. From the cohesive energy analyses, the substituted structures result in lower energies than the reference host chalcopyrite.

Figure 3. Comparison between LDA and GGA ionization energies as a function of Q − Q0 for the (a) GeIn and (b) CrIn substitutions. (c) Comparison between LDA ionization energies of the CrIn substitution for some values of the anion displacement parameter u.. 1393

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in chalcopyrite compounds of interest for thin-film photovoltaic applications. Even if some impurities do not have attractive photovoltaic conversion efficiencies, it could have potential applications in spintronic devices.

Nevertheless, the incorporation of atoms is governed more by kinetics than by thermodynamic requirements. The relative size of atoms, irrespective of the particular doping method, is the factor that limits the doping.36 To analyze this aspect, the differences among the equilibrium distances M−S in the substituted chalcopyrite (rM−In in the a panel and rM−Cu in the b panel) and the distances rhost in the chalcopyrite without substitution (In−S in the a panel and Cu−S in the b panel) are represented in Figure 5. For a comparison, the difference

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ACKNOWLEDGMENTS This work has been supported by the European Commission through the funding of Project IBPOWER (Ref. No.: Grant Agreement 211640), and by La Comunidad de Madrid through the funding of Project NUMANCIA-2 (Ref. No.: S-2009/ENE1477).

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REFERENCES

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Figure 5. Difference between the distance M−S (rM−In in panel a, and rM−Cu in panel b, for the MIn and MCu substitutions, respectively) and the distance (In,Cu)−S (rhost) for equilibrium positions of the host chalcopyrite. For comparison, the difference between the covalent radius of M (rM) and of In (rIn) or Cu (rCu) is represented in panels a and b.

between the covalent radius of M and In or Cu37 are also shown. The differences between the two curves (rM−In,Cu − rhost) and (rM − rIn,Cu) indicate approximately the distortion in the lattice when the M impurity substitutes the In or Cu host atom. From the figure, the distortions are, in general, larger for the MCu substitution.

IV. CONCLUSIONS In summary, we report the results for the donor and acceptor levels and gaps of the doped chalcopyrite CuInS2:M using firstprinciples total energy calculations. We have considered the two substitutions M for In and M for Cu, with a wide range of M impurities (M = C, Si, Ge, Sn, Ti, V, Cr, Fe, Co, Ni, Rh, and Ir) and with both LDA and GGA. We have also analyzed the evolution of the donor and acceptor energies and gaps as a function of the M−S distance. The results for the host chalcopyrite are good compared with experimental results in the literature, and it is in accordance with the anomalous gap increase with the increase in temperature in the low-temperature range. The position of the acceptor-related Fe deep level acceptor level is also in agreement with the experimental photoionization results. For the MIn substitution, the donors and acceptor ionization levels can increase their energy in the band gap through pressure. Some elements have been identified as interesting candidates to act as amphoteric impurities in the chalcopyrite hosts. It is expected that these results may guide future experimental work 1394

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