Evaluation of photovoltaic materials within the Cu-Sn-S family
Pawel Zawadzki,1 Lauryn L. Baranowski,1, 2 Haowei Peng,1 Eric S. Toberer,1, 2 David
S. Ginley,1 W. Tumas,1 Andriy Zakutayev,1, a) and Stephan Lany1, b)
1National Renewable Energy Laboratory, Golden, CO, USA
2Physics Department, Colorado School of Mines, Golden, CO, USA
The radio-frequency (RF) sputtering depositions were performed from 50 mm diameter
Cu2S and SnS2 targets in 3x10−3 torr of Ar in a chamber with a base pressure of less than
10−7 torr. Films were deposited onto 50x50 mm Eagle-XG glass substrates heated to
475-500 °C, located 10 cm from the targets. The gun powers between 25-50 W and the
gun angle of ~25 degrees with respect to the normal to the substrate were used to provide
the desired chemical compositional spread across the substrates.
X-ray fluorescence spectra were collected using a System-SMX instrument and analyzed
using MTF-FP software to obtain both the Cu/Sn ratios and the thickness of the films.
The X-ray diffraction (XRD) spectra were collected using Cu K-alpha radiation and a
proportional 2D detector. The peaks in the spectra were compared with reference patterns
for SnS (orthorhombic), Cu2SnS3 (cubic), Cu4SnS4 (orthorhombic), and Cu2S
(monoclinic) obtained from the Inorganic Crystal Structure Database (ICSD), and
matched to the cubic Cu2SnS3. Optical transmittance and reflectance were mapped from
300-2000 nm using a fiber-optics-based spectrometer with deuterium and
tungsten/halogen light sources and Si and InGaAs detector arrays. The absorption
coefficient was calculated from the measured reflectance (R) and transmittance (T)
spectra, and the measured film thickness (d) from the X-ray fluorescence (XRF), using
the relationship α = -ln[T/(1-R)]/d. The sheet resistance was mapped using a collinear
four point probe with 1 mm distance between probes.
Density functional theory with onsite Coulomb potential (DFT+U) calculations were
performed in a plane wave basis set with the expansion cutoff of 320 eV. The Brillouin
zone was sampled with density of at least 430 k-points/(number of atoms in the unit cell)
that was found sufficient to converge total energies to 1 meV/atom. All structures were
relaxed until a convergence criterion of 0.02 eV/Å for the maximal force component in
each direction on each atom is achieved.
We have modeled disordered structures of Cu4Sn7S16 and Cu3SnS4 using the following
ordered structures: The crystallographic 81 atom cell of Cu4Sn7S16 (𝑅3̅𝑚) exhibit
disorder on tetrahedral Cu sites: the Cu1 site is six-fold degenerated and has fractional
occupation of 0.5; the Cu2 and Cu3 site are three-fold degenerated and have fractional
occupations of 0.6 and 0.4, respectively. Cu sites are arranged in three layers. We find
that the ordered structure with the lowest formation energy has one Cu1 site vacant per
layer. Occupation of either the Cu2 site or the Cu3 site leads to the same formation
energy because these sites are closely degenerated. Such ordered structure of Cu4Sn7S16
was used for the calculation of phase diagram (Fig. 1). Since the 81 atom
crystallographic cell of Cu4Sn7S16 is too large for computationally expensive GW
calculations we constructed also a smaller model for the Cu4Sn7S16 structure based on the
rhombohedral 28 atom cell of spinel structure. In this cell we arrange Cu and Sn atoms
such that the distance between the empty tetrahedral site and the Cu on the octahedral
site is the same as in the crystallographic cell and equals to 6.7 Å. The thus constructed
27 atom cell has formation energy that is only 2 meV/atom higher that that of the 81 atom
ordered structure of Cu4Sn7S16. Cu3SnS4 structure exhibits disorder on cationic sites of
underlying zinc blend structure. For the calculation of phase diagram (Fig. 1) we
constructed an order structure built from tetrahedral S-Cu3Sn motifs. Presence of other
motives, such as S-Cu2Sn2 and S-Cu4, leads to higher formation energies.