Article pubs.acs.org/JPCC
Electronic and Photon Absorber Properties of Cr-Doped Cu2ZnSnS4 C. Tablero Instituto de Energía Solar, E.T.S.I. de Telecomunicación, Universidad Politécnica de Madrid, Ciudad Universitaria s/n, 28040 Madrid, Spain ABSTRACT: The Cu2ZnSnS4 (CZTS) semiconductor is a potential photovoltaic material due to its optoelectronic properties. These optoelectronic properties can be potentially improved by the insertion of intermediate states into the energy bandgap. We explore this possibility using Cr as an impurity. We carried out first-principles calculations within the density functional theory analyzing three substitutions: Cu, Sn, or Zn by Cr. In all cases, the Cr introduces a deeper band into the host energy bandgap. Depending on the substitution, this band is full, empty, or partially full. The absorption coefficients in the independent-particle approximation have also been obtained. Comparison between the pure and doped host’s absorption coefficients shows that this deeper band opens more photon absorption channels and could therefore increase the solar-light absorption with respect to the host.
nides39−41 have been used as broadly tunable continuous wave lasers. The Cr-doped laser materials are characterized by high gain and an intrinsically low-lasing threshold, as well as by such remarkable spectroscopic features as the absence of excited state absorption and negligible nonradiative decay at room temperature. Because of the technological importance of CZTS as an absorbent material for low-cost thin-film solar cells and in order to further improve the conversion efficiency for the application to photovoltaic devices, it is important to explore the effect of Cr doping on the electronic properties of CZTS. In this work, we present first principles calculations of the electronic properties of CZTS:Cr in the most common kesterite structure.
I. INTRODUCTION The quaternary Cu2ZnSnS4 (CZTS) semiconductor is a potential photovoltaic material for low-cost thin-film solar cells due to its promising optical properties (1.4−1.6 eV bandgap energy), high absorption coefficient (α ≃ 104 cm−1), and abundant, low-cost, and nontoxic constituents. This semiconductor film can be obtained by replacing half of the indium atoms in the chalcopyrite CuInS2 with zinc and replacing the other half with tin. CZTS has been prepared by several methods, such as sulfurization of sputtered1−3 or evaporated4 stacked films, the spray method,5,6 the sol−gel method,7 hydrazine deposition,8 and electrode deposition.9 The structure and transport properties of CZTS have been extensively studied experimentally10−17 and theoretically.18−21 Experimentally, samples of CZTS and CZTSe are observed to crystallize in either kesterite or stannite structures, the first being the most common. When the ratios of the constituents in the CZTS thin films are close to stoichiometric, the single stannite type phase structure CZTS can be formed by a twostep process. Furthermore, by optimizing the precursor preparation conditions, a low resistivity and high absorption coefficient can be achieved.22 The insertion of intermediate states into the bandgap of a semiconductor material provides additional paths for optical transitions and corresponding absorption bands. Solar cell devices based on these materials offer a potential route to high efficiency (>60%),23 using a material with three defined absorption bands in a simplified one-junction structure. Some materials have attracted attention in the realization of an appropriate intermediate band using doped chalcopyrites,24−27 II−VI compound semiconductors doped with isoelectronic oxygen impurities, and Cr-doped zinc chalogenides.28,29 The isoelectronic doping of II−VI compounds with oxygen has shown that oxygen gives rise to deep traps30−33 at which carriers recombine radiatively.34−38 Cr-doped zinc chaloge© 2012 American Chemical Society
II. CALCULATIONS Regardless of the first principles procedure chosen, there is a fundamental problem in studying defects. In order to analyze smaller defect concentrations, it is necessary to use bigger supercells periodically repeated spatially (see below the relationship between the supercell size and the concentration). Therefore, care must be taken with a small amount of supercell atoms. It will correspond to a degenerate doping. The defect, instead of being surrounded by a large region of perfect host semiconductor as it would be under nondegenerate doping, is now surrounded by symmetry representations of itself. Due to this incorrectly high defect concentration, artificial interactions are introduced such as image charges, spurious electrostatic interactions, and spurious hybridization. Conventional implementations of density-functional theory (DFT)42−45 utilize (semi)local exchange-correlation functionals. Because of spurious electron self-interactions, these Received: June 26, 2012 Revised: October 16, 2012 Published: October 17, 2012 23224
dx.doi.org/10.1021/jp306283v | J. Phys. Chem. C 2012, 116, 23224−23230
The Journal of Physical Chemistry C
Article
CZTS structure without cation disorder (I4̅ symmetry) has been predicted to be the most stable,19,54 possible cation disorder within the Cu/Zn layer cannot be excluded.19 CZTS:Cr alloys ((CrxCu2−x)ZnSnS4, Cu2(CrxZn1−x)SnS4, and Cu 2 Zn(Cr x Sn 1−x )S 4 for the Cr Cu , Cr Zn , and Cr Sn substitutions, respectively) are studied using 64-, 96-, 144-, and 216-atom supercells (x = 1/8, 1/12, 1/18, and 1/27, respectively). For all of these structures, we start from a unit cell in which the Cu, Sn, or Zn atoms are replaced by Cr. In all of the results presented in this work, a double-ζ with polarization functions basis set has been used with periodic boundary conditions. Between 32 and 18 special k-points are used depending on the supercell size in order to keep a constant k-point density in the irreducible Brillouin zone (BZ). The calculations of the electronic structure are carried out preserving the experimental atomic positions of the reference compound for the larger supercells and relaxing the host atoms for the smallest. For this purpose, the conjugate gradient algorithm is used, in accordance with the calculated quantum mechanical forces. Relaxation into the configuration of absolute energy minimum is considered accomplished when the forces on the atoms fall below 0.004 eV·Å−1. To determine the optical properties, the complex dielectric function is calculated as a function of the photon energy, the energy and occupations of the bands at k⃗ points of the BZ, and the momentum matrix elements. The other optical properties are obtained using the Kramers−Kronig relations.
approximations lead to the band gap underestimation, bandwidth overestimation, bond-length of weakly bound molecules and solids underestimation, binding energy overestimation, etc. Other methods such as DFT+U and hybrid DFT studies incorporate a U parameter or a fraction of exact exchange in order to avoid partially the self-interaction problem. In many cases, the U parameter and the fraction of exact exchange are adjusted a posteriori for obtaining the correct band gap or other properties. It does not satisfactorily resolve the problem. In theory, this problem may be avoided using many-body methods such as self-consistent GW, quantum Monte Carlo (QMC) calculations, etc. Nevertheless, some non-self-consistent GW and QMC calculations presently involve ad hoc assumptions. The main problem of these more sophisticated methods is that they are not practical today for the large supercells required in point-defect studies: they are very expensive and present delicate convergence issues. From the previous discussion, density functional theory (DFT) is the method used in this work for studying the electronic structure of defects in semiconductors. It is the approach currently tractable for large supercell calculations in order to explore isolated defects (at least on the order of hundreds of atoms). Of course, calculations of the electronic structure are affected by the well-known band gap underestimation characteristic of the GGA-DFT method. However, this underestimation does not severely affect the main results of the general screening carried out in this work regarding the presence or absence of IBs upon substitution of Cr at the cation sublattices. Although the absolute position of the eventual IB is thus not accurately calculated without further corrections, we can, nonetheless, conclude on the existence or absence of IBs, while avoiding certain arbitrariness related with the proportionality of the shifts to be introduced to correct the band gaps. The electronic properties are investigated using firstprinciples within the density functional formalism. The standard Kohn−Sham46 equations are solved self-consistently with a private modification of the SIESTA code47 using a confined pseudoatomic orbitals48 basis set. For the exchangecorrelation potential, we use the generalized gradient approximation (GGA) of Perdew, Burke, and Ernzerhof.49 The standard Troullier−Martins50 pseudopotential is adopted and expressed in the Kleinman−Bylander51 factorized form. All calculations were performed considering spin polarization. The kesterite type structure is characterized by alternating cation layers of CuSn, CuZn, CuSn, and CuZn at z = 0, 1/4, 1/ 2, and 3/4. The space group is I4̅ and the primitive cell is basecentered-tetragonal with 8 atoms/cell. The experimental52 lattice parameters of the natural CZTS (HLP) are aH = 5.427 (1) Å and cH/2aH = 1.002. However, natural CZTS often contains Fe. Experimental analyses of the synthetic (iron-free) CZTS53 reports different cell parameters (SLP) aS = 5.485 (
