First-Principles Design and Analysis of an Efficient ... - ACS Publications

Page 1 of 14

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Chemistry of Materials

First-principles design and analysis of an efficient, Pb-free ferroelectric photovoltaic absorber derived from ZnSnO3 Brian Kolb∗ and Alexie M. Kolpak∗ Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA, 02139 E-mail: [email protected]; [email protected]

Abstract

hibiting strong solar absorption, and may enable the development of solar cells with both high photovoltage and photocurrent.

Ferroelectric oxides, which exhibit a spontaneous and reversible electric polarization, have recently gained interest for photovoltaic applications because this polarization can potentially facilitate exciton separation and carrier extraction while also generating open-circuit voltages orders-of-magnitude larger than the band gap. However, photovoltaic efficiencies in these materials are often limited by large band gaps and high hole effective masses. Developing a means to simultaneously reduce both without destroying the ferroelectric polarization could revolutionize photovoltaic technologies. In this work, we use first-principles computations to describe how chemical substitution of oxygen in the recently characterized ferroelectric ZnSnO3 with sulfur to form ZnSnS3 reduces the band gap to a near-optimal 1.3 eV while leaving the polarization virtually unchanged. Further, we show that other key photovoltaic materials characteristics, such as hole effective mass, dielectric constant, and absorption coefficient, are also dramatically improved by sulfur substitution. Finally, we demonstrate that the wellknown semiconductor GaN provides an excellent substrate on which to grow ZnSnS3 , forming a strongly bound interface that is free of intrinsic mid-gap states and exhibits an ideal band alignment for efficient carrier extraction. This work advances the search for an earthabundant, nontoxic, ferroelectric material ex-

Introduction Converting free and abundant solar light energy to electricity would allow cheap production of substantial amounts of sustainable energy. Such conversion requires a system in which excitons are efficiently generated from absorbed photons and separated into charge carriers (electrons and holes) that can be extracted with minimal loss due to recombination. Many designs have been implemented to achieve this, including p-n junctions, bulk heterojunctions, and organic-inorganic interfaces. Recently, the use of ferroelectric materials as efficient alternatives for maximizing charge separation and carrier collection has gained considerable interest. 1–3 The lack of centro-symmetry in ferroelectric materials can provide a driving force for exciton separation throughout the absorber rather than just at an interface, in principle reducing recombination. 3,4 Even more promising, ferroelectric absorber materials have been used to drive open circuit voltages into the double digits, well in excess of their band gap. For example, photovoltages well over 10 V have been measured for BiFeO3 5,6 and near 10 V for lanthanide-doped lead zirconate titanate. 7 Although the attainable photovoltages of these

ACS Paragon Plus Environment

1


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

materials are impressive, their large band gaps make them inefficient solar absorbers, yielding poor photocurrents and overall efficiencies. 3,8 Compounding the problem is the observation that, for many ferroelectric materials, transitioning from the paraelectric phase to the ferroelectric phase itself creates a band gap widening effect with a magnitude proportional to the square of the polarization. 9,10 Doping and strain can sometimes be used to modulate the band gap of these materials (for example, the band gap of BiFeO3 can be lowered by 0.1– 0.2 eV with cation-doping 11,12 ) but such approaches cannot generally lower the gap enough to turn a wide band gap ferroelectric material into a good solar absorber. To realize the potential of ferroelectric photovoltaics—a large open-circuit voltage coupled with a useful photocurrent—a material with a band gap low enough to allow strong visible light absorption while retaining a significant polarization is required. Much effort has gone into finding such a material, especially within the perovskite oxides and halides. 13 Unfortunately, some of the more successful materials include either toxic elements such as lead and cadmium or expensive rare elements such as indium. For example, methyl-ammonium lead iodide has been shown to have strong absorption and good electronic characteristics, 14,15 but the requirement of sophisticated charge extraction layers 16–19 and the presence of lead makes it less appealing as a practical functional material. An interesting ferroelectric material is the recently characterized LiNbO3 -structured ZnSnO3 (LN-ZnSnO3 ). 20,21 This material has a strong remnant polarization of 59 µC/cm2 and has been used successfully in piezoelectric nanogenerators, 22–24 strain sensors, 23,25 and gas sensors. 26–29 However, like most ferroelectric oxides, its promise as a solar absorber material is limited by a relatively large band gap (3.0 eV, calculated here using the GW method 30 ), which places its absorption onset near the ultra-violet. Nevertheless, with relatively cheap, abundant, and non-toxic constituents, as well as a substantial polarization, ZnSnO3 would be an ideal material if its band gap could be lowered to op-

Page 2 of 14

timize solar absorption. In this paper, we demonstrate that substituting the oxygen in LN-ZnSnO3 with sulfur to form LN-ZnSnS3 dramatically reduces the band gap from 3.0 eV to a near-optimal 1.3 eV (similar to results found in other oxides, including ZnO 31 ). This phenomenal improvement is achieved without reducing the remnant polarization, and does not require strain, complex doping schemes, or the formation of intricate nanostructure. Further, we demonstrate that other key photovoltaic properties such as carrier effective mass and dielectric constant are also substantially improved by the O→S substitution. Finally, we show that ZnSnS3 forms a stable interface with a GaN, with which it has a lattice mismatch of only 0.5%. In addition to providing a substrate for epitaxial growth of ZnSnS3 films, the band alignment across the GaN/ZnSnS3 interface naturally allows electron flow in only one direction, facilitating exciton separation and reducing recombination without the need for additional charge blocking layers. The large 3.4 eV bandgap of GaN means it can be used even as a top contact within a solar device, without meaningfully interfering with the absorption in the ZnSnS3 layer. This heterojunction represents a substantial step forward in the search for an efficient, economical, and environmentally friendly ferroelectric photovoltaic absorber material.

Methods All structure, energy, phonon, polarization, densities-of-states, and effective mass calculations in this work were carried out using density functional theory (DFT) performed in the Vienna Ab-Initio Simulation Package 32,33 (VASP) and the Quantum Espresso 34 (QE) suite of programs. Both of these are plane-wave pseudopotential (PAW 35,36 in the case of VASP and ultrasoft 37 in the case of QE) codes in which we employed the PBEsol 38,39 functional for exchange and correlation. Relaxations took forces to less than 0.01 eV/˚ A and stresses to within 0.5 kbar, and all convergence parameters were carefully tested for convergence. Polarizations


2

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


were calculated using the Berry Phase approach within the Modern Theory of Polarization. 40 Phonon calculations used a 6 × 6 × 6 grid of q-points within the Brilluoin zone, followed by Fourier interpolation. 34 Dielectric tensors and Born effective charges were calculated using density functional perturbation theory. 41 Interface calculations included 13 formula units of the GaN substrate (plus an addition layer of nitrogen to form the symmetric slab that minimizes the internal field), the bottom 9 of which were fixed at bulk geometry during relaxations. The overlying ZnSnS3 thin film contained 12 formula units plus a top layer of passivating hydrogens, all of which were fully relaxed. To minimize the unphysical interaction between periodic images in the z -direction, 15 ˚ Aof vacuum and slab dipole corrections were included. Crystal Orbital Hamilton Population (COHP) analysis was performed post-DFT using the Lobster program. 42,43 All band gaps, band structures, and absorption spectra were calculated within the G0 W0 approximation, starting from PBEsol wavefunctions and eigenvalues. Band structures were computed from GW calculations by way of Wannier interpolation, using the Wannier90 code. 44 Absorption spectra were calculated by computing the complex frequency-dependent dielectric function via sums over allowed transitions using G0 W0 eigenvalues, and including local field effects in the RPA. The absorption coefficient is then given by

2ω α(ω) = c

s

|1 (ω) + 2 (ω)| − 1 (ω) 2

Zn S n S

Pol a r i z a t i on

Page 3 of 14

a 3 a 2

a 1

Figure 1: Structure of LN-ZnSnS3 highlighting the sulfur octahedra surrounding an atom each of zinc and tin. We define here the crystal basis of {~ai }. The polarization in this hexagonal conventional unit cell is along the ~a3 direction. The representation of Zn, Sn, and S atoms will be used throughout. remnant polarization (59 µC/cm2 ) it is unsuitable as a solar absorber material due to a large, 3.0 eV band gap (as calculated here within the GW approximation), similar to those of prototypical ferroelectric oxides such as PbTiO3 (3.8 eV) and BaTiO3 (3.4 eV). We find, however, that the bandgap of ZnSnO3 is more sensitive to strain, decreasing, for example, by 0.44 eV with an epitaxial tensile strain of 3%. The band gaps of PbTiO3 and BaTiO3 , by contrast, change by only +0.03 eV and -0.26 eV, respectively, under similar strain. The difference arises form the nature of the conduction band edge, which is made up largely of tin s-states in ZnSnO3 in contrast to the relatively localized Ti d -states in PbTiO3 , BaTiO3 , and other ABO3 perovskite oxides with a transition metal B -site cation. The more diffuse s-states form strongly anti-bonding interactions with oxygen p-states, and are affected more dramatically by volume changes than those constructed from the localized d -states.

(1)

with 1 and 2 being the real and imaginary parts of the dielectric function, respectively.

Results and Discussion Band gap Lithium niobate structured zinc-tin-oxide (LNZnSnO3 ) exhibits a strong ferroelectric polarization and is the stable phase at high pressure. 45 Despite its direct band gap and strong


3


Although the band gap of ZnSnO3 can be tuned by strain, it cannot be lowered to . 1.5 eV within practical limits (see Figure S1 in the supporting information). Substitution of oxygen with a larger cation such as sulfur, however, will result in a substantial expansion of the lattice, potentially reducing the band gap by much more than can be realized with epitaxial strain alone. Indeed, the complete substitution of sulfur for oxygen (forming LN-ZnSnS3 ) expands the lattice constant of the material by about 20%, resulting in a reduction of the band gap to 1.3 eV, near the theoretical ideal value. In terms of the Shockley-Queisser limit, this band gap may allow ZnSnS3 to outperform the more common perovskite materials such as BFO and LZTO, and to directly compete with all known perovskite materials, including methyl-ammonium lead iodide and heavily engineered and finely tuned materials like [KNbO3 ]0.9 [BaNi1/2 Nb1/2 O3−δ ]0.1 (KBNNO 2 ). It should be pointed out that no external strain on the LN-ZnSnS3 is required to reach this band gap, as the anion substitution increases the equilibrium volume naturally. To understand the origin of the lowered band gap in the sulfide relative to the oxide, we examine the nature of the low-lying conduction states in ZnSnS3 and ZnSnO3 . 2 shows the projected densities of states for the two materials. It is immediately apparent from the figure that the substitution of sulfur for oxygen shifts states above the fermi level to lower energy. Since these conduction states have different character, their energies shift by different amounts, resulting in a resolved peak in what was the oxide gap. A crystal orbital Hamilton population (COHP) analysis is also shown in 2. COHP splits the band energy into contributions from pairwise interaction of atomic orbitals, with the sign indicating bonding or antibonding character, and the magnitude related to the strength of the interaction. As mentioned above, the conduction band edge is comprised largely of anti-bonding combinations of metalchalcogen states. In the oxide, these form a relatively diffuse set of bands at high energy. With the increased volume in the sulfide, the energy of these anti-bonding states decreases as

Sn( s ) S( s )

COHP

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 4 of 14

t ot al

( a)

Sn( s ) S( p)

E-EF ( eV)

Zn Sn O/ S

( b) ( c)

( d)

Figure 2: (a) Crystal orbital Hamilton population (COHP) analysis of the low-lying conduction states, showing that the states are antibonding and dominated by tin s-orbital and sulfur p-orbital contributions, as illustrated in the spatially resolved the density of these states (b). Also shown is a comparison of the density of states of ZnSnS3 (c) and ZnSnO3 (d). a result of relaxed confinement. Unlike many transition-metal perovskites, in which the lowlying conduction states have localized metal d character, the lowest energy conduction states here are comprised mainly of extended antibonding combinations of Sn-s and S-p states. These strongly interacting states are lowered substantially in energy as the volume increases and split out from the rest of the conduction states (made largely of anti-bonding combinations of O p- and Zn d -states), forming an isolated set of bands in what was the gap in the oxide. It is important to note that these are lower-energy versions of the same states that exist in the oxide; i.e. they are not localized defect states but typical Bloch states that extend throughout the crystal, as illustrated in the spatially resolved density of low-lying conduction band states shown in 2.


4

Page 5 of 14


Solar Absorption (%)

100

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

80

Strong absorption is paramount to realizing the potential of a ferroelectric photovoltaic material, because the depolarization field and the efficiency of carrier extraction decrease with film thickness. As the efficiency of ferroelectric photovoltaic cells is typically limited by poor photocurrents, it is beneficial to use the thinnest films possible to maximize current density. Given the wavelength-dependent absorption coefficient (αλ ) and film thickness (d), the total fractional absorption (A) of incident solar radiation can be approximated as

ZnSnS3 Si

60 40 20 0 0.001

0.01

0.1

1

10

100

Thickness (µm)

Figure 3: Total fractional absorption of solar radiation as a function of film thickness (on a log scale) for ZnSnS3 and crystalline Si. The effects of reflection are neglected here. The difference in absorption at saturation is due to the different band gaps of the two materials.

R∞ A=1−

e−αλ d Sλ dλ

λEg

R∞

(2) Sλ dλ

0

where Sλ is the incident solar spectral irradiance 48,49 and λEg is the wavelength corresponding to the band gap. For simplicity, reflection is neglected since it is not an intrinsic material property but depends on the details of the dielectric function on both sides of an interface. 3 shows the calculated fraction of incident solar flux that is absorbed by a thin film of ZnSnS3 as a function of film thickness. For comparison, the same quantity is shown for silicon. The larger optical-wavelength absorption of ZnSnS3 relative to silicon results in greater overall absorption given the same cell thickness, for thicknesses below 7 µm. Above this thickness both materials start to saturate, and silicon absorbs a larger fraction (≈ 10%) of the solar spectrum due to its lower band gap. The figure also indicates that the saturation of ZnSnS3 absorption nears completion at a thickness around 8 µm, whereas silicon doesn’t approach saturation until almost 50 µm. Silicon is by no means an optimum solar absorber, and typical absorber layer thicknesses in commercial cells are on the order of 100-200 µm, where efficiencies can reach 25%. 50 Nevertheless, reasonably efficient (≈ 10%) crystalline silicon solar cells have been made with films as thin as 1.4 µm, 51 and respectable efficiencies (≈ 15%) have been achieved for films as thin as 14 µm. 52 Since the efficiency of these ultra-thin cells is mainly limited by their ability to ab-

Absorption coefficient The band gap determines which photons can be absorbed by a material, but it does not predict how strongly that material will absorb them. For this, one needs to calculate the frequency-dependent, complex dielectric function (see Reference 46 for a thorough review of current approaches). Here, we compute the dielectric function by summing over the allowed transitions as determined by a G0 W0 calculation including local field effects within the RPA. For comparison, and as a check on the approach, the absorption curve of pure silicon was calculated in a similar manner. We first note that our values for silicon are in reasonable agreement with experiment, 47 especially for visible wavelengths and above. The surprising result is that ZnSnS3 is predicted to absorb more strongly than Si for wavelengths above 380 nm. For example, at 650 nm the calculated absorption coefficient of ZnSnS3 is 2.4 × 104 cm−1 , whereas it is 4 × 103 cm−1 for silicon. Both materials absorb equally well near 380 nm, with an absorption coefficient of 5 × 105 cm−1 . Silicon is the stronger absorber of photons with wavelengths less than 380 nm, although both materials are excellent absorbers in this region of the spectrum, which constitutes only about 3.3% of the solar flux.


5


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 6 of 14

Table 1: Effective masses in the x, y, and z directions for electrons (m∗e ), heavy holes (m∗hh ) and light holes (m∗lh ) at Γ in ZnSnO 3 , and elec ¯ trons (at Γ) and holes (at δ δ0 ) in ZnSnS3 . All values are in electron masses.

sorb incident light, the stronger absorption in ZnSnS3 suggests that films thin enough to support reasonable current densities can still absorb effectively enough to be useful. This fact is critical to achieve improved currents over most of the ferroelectric materials studied to date.

ZnSnO3

Polarization The strong remnant polarization of ferroelectric ZnSnO3 (59 µC/cm2 ) is one of its most interesting properties, so it is important to investigate the effects of sulfur substitution on this characteristic. The polarization of LN-ZnSnS3 was computed using the Berry Phase formalism within the modern theory of polarization. 40 Despite the large change in volume upon sulfur substitution, as well as considerable rearrangement of atoms, the magnitude of the polarization is nearly unchanged in the sulfide from its value in the oxide. In the oxide, the polarization arises from off-center displacements of both cations along the z-direction. The cations possess different Born effective charges (Zn= 2.8e, Sn= 4.1e) and displace in opposite directions, with Zn displacing more than Sn. Thus, the contributions to the polarizations from Zn and Sn are in opposite directions, with the net polarization coming from Zn. Interestingly, the reverse is true in the sulfide, where the Born effective charges are slightly larger (Zn= 3.0e, Sn= 4.6e) and tin displaces more than zinc. It is also interesting to note that most (≈ 32 ) of the polarization in ZnSnO3 can be attributed to the electronic contribution, whereas the bulk of the polarization in ZnSnS3 comes from the classical ionic contribution. Thus, although the magnitude of the polarization is virtually unchanged upon sulfur substitution, the microscopic origin is different. The substitution of sulfur for oxygen has ramifications on other properties as well. The electronic component of the dielectric constant is critical for aiding in exciton separation by reducing the effective binding energy. The relatively low dielectric constant of 4.3 in the oxide increases significantly to 10.3 in the sulfide. This increase is due to the increased polarizability of the sulfur atoms. Similarly, the com-

ZnSnS3

direction

m∗e

m∗hh

m∗lh

m∗e

m∗h

x

0.18

4.50

0.92

0.12

0.35

y

0.18

4.54

0.92

0.12

0.79

z

0.17

33.5

30.2 0.13

1.42

ponents of the piezoelectric tensor increase by a factor of 2.5 in the sulfide, indicating a stronger piezoelectric response. This is significant since LN-ZnSnO3 has already been successfully fabricated into a piezoelectric generator, microbelts of which are capable of producing electrical energy with up to 6.6% power conversion efficiency. 22–24 A stronger piezoelectric response would likely increase this figure.

Effective mass Because the valence bands of ferroelectric oxides are often comprised of weakly hybridized oxygen p-states, their hole effective masses tend to be relatively large. The resulting poor hole mobility makes carrier extraction difficult, and is one of the reasons for the low photocurrents seen in these materials. The calculated effective masses of electrons, and the heavy and light holes, which result from the degeneracy at the valence band maximum of LN-ZnSnO3 , are shown in the left side of 1. The electron effective mass is quite low and isotropic, while hole masses show a large anisotropy, being considerably higher in the polarization (ˆ z ) direction. At the Γ point, the band structure for LN-ZnSnS3 looks quite similar, still possessing heavy and light holes, but with all effective masses reduced from their values in the oxide (see supporting information Table S3). For example, the light hole effective mass is 0.64 m0 in the xˆ direction and 12.3 in the zˆ-direction, only 67% and 41% of their respective values in the oxide. This is an important result, as it suggests substitu-


6

Page 7 of 14

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


tion of sulfur for oxygen as a possible route to improving hole mobility in ferroelectric oxides. However, although the conduction band minimum remains at the Γ point in the sulfide, the valence band maximum does not, but shifts by a small amount, δ ≈ 81 , in the [1¯10] direction. The right side of the table shows the effective mass of electrons and holes at the proper band edges in ZnSnS3 . The hole effective masses at the valence band edge in LN-ZnSnS3 are substantially lower than those in the oxide.

m*h

f r ontv i ew

for that direction. The results show that the hole effective mass is a minimum (0.27 m0 ) in the ~a2 −~a1 direction and a maximum (2.23 m0 ) in the ~a1 + ~a2 direction. The effective mass for propagation in the ~a3 direction, the one most relevant if a solar cell is to take advantage of the remnant polarization, is intermediate between these extremes at 1.42 m0 . These values directly correlate with the nearest-neighbor sulfur-sulfur distances in each direction, hinting that hole conduction occurs within sulfur planes through covalent interaction. Although the effective mass for direct propagation along ~a3 is larger than the ideal, the large anisotropy suggests that reasonably low values can be achieved by propagation in a direction with a modest component along ~a2 −~a1 . For example, the hole effective mass drops to less than 0.5 m0 at an angle of 39◦ down from the posˆ3 + 3√2 3 (ˆ a2 − a ˆ1 )). The itive z -axis (e.g. ≈ 43 a results also highlight the potential dangers of assuming isotropic effective mass values (as is done implicitly when they are calculated from a 1-dimensional band structure), or of choosing an otherwise arbitrary set of cartesian vectors along which to calculate them. It may be worth investigating whether a similar phenomenon exists in other LN-structured materials, such as BiFeO3 , and whether it may be important for understanding the often complex directional dependence of the photocurrents observed within these materials.

2. 23 1. 84 1. 45 1. 05 0. 66 0. 27

t opv i ew

Figure 4: Spherical plot of the hole effective mass (m∗h ) of ZnSnS3 as a function of propagation direction through the lattice. The surface is embedded in the unit cell for reference. For the surface, the origin is the center of the xy-plane and the distance from that point to the surface in some direction gives the effective mass for hole propagation in that direction. Only the surface for z > 0 is shown, as the lower half is equivalent by symmetry.

Energetics Like its parent oxide, LN-ZnSnS3 is metastable (∆G = 0.66 eV/formula unit) with respect to phase separation into the endpoint chalcogenides (SnS2 and ZnS) at low temperature and pressure. Elevated temperature and pressure lower ∆G with respect to phase separation, but, unlike the oxide, phase separation remains thermodynamically favorable under all reasonable conditions. Thus, formation of the bulk is not likely a viable route to production of the material. Nevertheless, calculation of the phonon band structure throughout the Brillouin zone reveals that there are no dynamic instabilities in LN-ZnSnS3 , raising the possibility that this

An interesting aspect of 1 is the obvious directional anisotropy in the hole effective masses for both the oxide and sulfide. We explore this anisotropy further by calculating the hole effective mass at the valence band edge in ZnSnS3 as a function of cartesian direction. 4 shows the results in the form of a spherical plot where the origin lies at the center of the xy-plane and the distance from that point to the surface in a particular direction gives the effective mass


7

a n t i b o n d i n g

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 8 of 14

b o n d i n g


Zn( s ) N( p) S n( p) N( s ) S n( p) N( p)

Figure 6: The energy of deposition for each formula unit layer as a function of film thickness, as defined in 3. The energies are referenced to bulk Zn, Sn, and S in their standard states.

Figure 5: COHP analysis of the interface between GaN and ZnSnS3 . Shown are contributions from zinc s and nitrogen p-states (blue), tin p and nitrogen s-states (red) and tin p and nitrogen p-states (green). The inset shows a closeup of the interface under investigation.

subsequent formula unit as layers are deposited on the substrate. The layer formation energy is computed as

metastable material can be epitaxially grown on a suitable substrate.

∆EN = EN − (EN −1 + EZn + ESn + 3ES ) (3)

GaN Substrate

where EN is the total energy of the substrate with N layers of ZnSnS3 deposited on it, and the energies of the elements are those of their bulk standard states. The first layer binds strongly—partially a result of the excellent passivation of GaN due to the chemistry discussed above—with the deposition energy of subsequent layers quickly saturating to a constant value of −2.18 eV. The favorability of growth and the confirmed metastability of LN-ZnSnS3 make it likely that it can be grown effectively. Insight into possible deposition techniques for ZnSnS3 can be obtained by looking at methods already used to grow films of related Zn/Sn-based sulfides (e.g. Cu2 ZnSnS4 , ZnS, and SnS). For example, high-quality films might be grown on a GaN substrate by molecular beam epitaxy using elemental Zn and Sn sources and a sulfur cracker, 53,54 by atomic layer deposition using various established precursors for ZnS and SnS deposition, 55,56 or by solution synthesis using solvents developed for Cu2 ZnSnS4 . 57 There is

Energetics The wide band gap semiconductor GaN makes such a substrate. A 2 × 2 unit cell of the [0001] surface of hexagonal GaN is an excellent lattice match for LN-ZnSnS3 , with around half a percent lattice mismatch. In addition, when the GaN is N-terminated and the ZnSnS3 is terminated with a Zn/Sn plane (as shown in the inset to 5), the chemistry is favorable across the interface. The tin remains octahedrally coordinated with three sulfur atoms and three nitrogen atoms forming the vertices. The interface zinc atom is now tetrahedrally coordinated with one nitrogen and three sulfurs. Charge transfer requirements are satisfied across the interface, with the cation layer donating 3 electrons to the nitrogen layer. 5 shows a COHP analysis of the bonding at the interface between GaN and ZnSnS3 . The bonding between the two cations and surface nitrogen is quite strong, being dominated by the nitrogen p-states located near the Fermi level interacting with Zn s-states and Sn p-states. 6 shows the deposition energy for each


8

Page 9 of 14

states of the GaN and those of the ZnSnS3 . Free photogenerated electrons created in the ZnSnS3 will not be able to pass across the interface and will be forced to migrate toward the surface. Also evident in the figure is a slight field within the ZnSnS3 that aids this direction of carrier transport. This field also produces a slight tendency for holes to move into the GaN, although there is no substantial barrier to movement of holes in either direction. The favorable electronic structure of the interface suggests that LN-ZnSnS3 could be grown on GaN, and used directly within a photovoltaic device, without the need to remove the ZnSnS3 or transfer it to a different substrate for practical usage.

E-E ( eV) F

1. 3eV

Dens i t yofs t a t es

3. 4eV

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Conclusion Figure 7: Projected density of states of the GaN/ZnSnS3 heterojunction layer-by-layer through the interface. The extreme left panel represents the center of the GaN substrate while the extreme right corresponds to the center of the ZnSnS3 thin film. For visualization purposes, the scissor operator has been applied to the conduction states to be consistent with the GW-computed band gaps.

With the objective of creating a better photovoltaic absorber material, we have investigated the substitution of sulfur atoms for oxygen in ferroelectric ZnSnO3 . This change expands the lattice by 25%, lowering the conduction band energies significantly and resulting in a nearly ideal band gap of 1.3 eV. This change occurs without a noticeable change in the magnitude of the remnant polarization. Also important are a concomitant increase in the dielectric constant and a large reduction in the hole effective mass at the valence band edge. As is true with the oxide, phase separation is thermodynamically favorable at low temperature and pressure, but LN-ZnSnS3 shows no dynamic instabilities, indicating that it can be kinetically trapped. With its lattice match and favorable chemistry, GaN makes an ideal substrate on which to grow ZnSnS3 . Further, the electronic structure of the GaN/ZnSnS3 system is amenable to direct use as a photovoltaic, since the band alignment at the interface blocks electron transfer into the GaN. It is hoped that this work inspires experimental efforts to grow LN-ZnSnS3 films and verify their properties, as this system may represent a significant step forward in the search for the next generation of efficient solar materials.

no calculation that can adequately address the question of the lifetime of a metastable material, so experiments are needed to determine whether the LN phase is stable enough to be used for practical applications. Electronic Structure Apart from the energetic advantages of using GaN as a substrate on which to grow LNZnSnS3 there is a distinct benefit in terms of electronic structure. In any photovoltaic, some mechanism must be used to prevent recombination and get electrons to one side of the device and holes to the other. Polar materials have an innate asymmetry that helps accomplish this, but layers designed to prevent flow of carriers in the wrong direction are still useful. As shown in 7, the GaN/ZnSnS3 interface forms such a layer naturally, as the band alignment forms a near 2 eV difference in the energy of the conduction


9


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Associated Content

Page 10 of 14

Ager, J. W.; Martin, L. W.; Ramesh, R. Above-bandgap voltages from ferroelectric photovoltaic devices. Nat. Nanotechnol. 2010, 5, 143–147.

Supporting Information Available: Plots of the band gap and polarization of ZnSnO3 as a function of epitaxial strain; the atomic coordinates of ZnSnS3 ; a comparison of dielectric tensor, born effective charges, and band structures between ZnSnO3 and ZnSnS3 ; the effective masses of all carriers at the Γ-point in ZnSnS3 ; and a phonon band structure and density of states for ZnSnS3 . This material is available free of charge via the Internet at http://pubs.acs.org/.

(6) Alexe, M.; Hesse, D. Tip-enhanced photovoltaic effects in bismuth ferrite. Nat. Commun. 2011, 2, 256. (7) Zhang, J.; Su, X.; Shen, M.; Dai, Z.; Zhang, L.; He, X.; Cheng, W.; Cao, M.; Zou, G. Enlarging photovoltaic effect: combination of classic photoelectric and ferroelectric photovoltaic effects. Sci. Rep. 2013, 3, 2109.

Acknowledgement This work was supported as part of the Center for the Next Generation of Materials by Design, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Basic Energy Sciences under Contract No. DE-AC3608GO28308 to NREL.

(8) Fridkin, V. M. Bulk photovoltaic effect in noncentrosymmetric crystals. Crystallogr. Rep. 2001, 46, 654–658. (9) DiDomenico, M.; Wemple, S. H. Optical Properties of Perovskite Oxides in Their Paraelectric and Ferroelectric Phases. Phys. Rev. 1968, 166, 565–576.

References

(10) Wemple, S. H. Polarization Fluctuations and the Optical-Absorption Edge in BaTiO3 . Phys. Rev. B 1970, 2, 2679– 2689.

(1) Butler, K.; Frost, J. M.; Walsh, A. Ferroelectric Materials for Solar Energy Conversion: Photoferroics Revisited. Energy Environ. Sci. 2015, 8, 838–848.

(11) Kumar, N.; Kaushal, A.; Bhardwaj, C.; Kaur, D. Effect of La doping on structural, optical and magnetic properties of BiFeO3 thin films deposited by pulsed laser deposition technique. Optoelectron. Adv. Mater. Rapid Commun. 2010, 4, 1497–1502.

(2) Grinberg, I.; West, D. V.; Torres, M.; Gou, G.; Stein, D. M.; Wu, L.; Chen, G.; Gallo, E. M.; Akbashev, A. R.; Davies, P. K.; Spanier, J. E.; Rappe, A. M. Perovskite oxides for visible-lightabsorbing ferroelectric and photovoltaic materials. Nature 2013, 503, 509–12.

(12) Cai, W.; Fu, C.; Gao, R.; Jiang, W.; Deng, X.; Chen, G. Photovoltaic enhancement based on improvement of ferroelectric property and band gap in Tidoped bismuth ferrite thin films. J. Alloys Compd. 2014, 617, 240 – 246.

(3) Yuan, Y.; Xiao, Z.; Yang, B.; Huang, J. Arising applications of ferroelectric materials in photovoltaic devices. J. Mater. Chem. A 2014, 2, 6027. (4) Young, S. M.; Rappe, A. M. First Principles Calculation of the Shift Current Photovoltaic Effect in Ferroelectrics. Phys. Rev. Lett. 2012, 109, 116601.

(13) Green, M. A.; Ho-Baillie, A.; Snaith, H. J. The emergence of perovskite solar cells. Nat. Photon. 2014, 8, 506–514.

(5) Yang, S. Y.; Seidel, J.; Byrnes, S. J.; Shafer, P.; Yang, C.-H.; Rossell, M. D.; Yu, P.; Chu, Y.-H.; Scott, J. F.;

(14) Kim, H.-S.; Lee, C.-R.; Im, J.-H.; Lee, K.B.; Moehl, T.; Marchioro, A.; Moon, S.J.; Humphry-Baker, R.; Yum, J.-H.;


10

Page 11 of 14

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Moser, J. E.; Gratzel, M.; Park, N.-G. Lead iodide perovskite sensitized all-solidstate submicron thin film mesoscopic solar cell with efficiency exceeding 9%. Sci. Rep. 2012, 2, 591.

(21) Son, J.; Lee, G.; Jo, M.; Kim, H.; Jang, H. M.; Shin, Y.-H. Heteroepitaxial ferroelectric ZnSnO3 thin film. J. Am. Chem. Soc. 2009, 131, 8386–8387. (22) Wu, J. M.; Xu, C.; Zhang, Y.; Wang, Z. L. Lead-Free Nanogenerator Made from single ZnSnO3 microbelt. ACS Nano 2012, 6, 4335–4340.

(15) Frost, J.; Butler, K.; Brivio, F.; Hendon, C. H.; van Schilfgaarde, M.; Walsh, A. Atomistic origins of highperformance in hybrid halide perovskite solar cells. Nano lett. 2014, 14, 2584– 2590.

(23) Wu, J. M.; Chen, K.-H.; Zhang, Y.; Wang, Z. L. A self-powered piezotronic strain sensor based on single ZnSnO3 microbelts. RSC Adv. 2013, 3, 25184–25189.

(16) Bi, D.; Yang, L.; Boschloo, G.; Hagfeldt, A.; Johansson, E. M. J. Effect of Different Hole Transport Materials on Recombination in CH3 NH3 PbI3 Perovskite-Sensitized Mesoscopic Solar Cells. J. Phys. Chem. Lett. 2013, 4, 1532–1536.

(24) Lee, K. Y.; Kim, D.; Lee, J.-H.; Kim, T. Y.; Gupta, M. K.; Kim, S.W. Unidirectional High-Power Generation via Stress-Induced Dipole Alignment from ZnSnO3 Nanocubes/Polymer Hybrid Piezoelectric Nanogenerator. Adv. Func. Mater. 2014, 24, 37–43.

(17) Yella, A.; Heiniger, L.-P.; Gao, P.; Nazeeruddin, M. K.; Grätzel, M. Nanocrystalline Rutile Electron Extraction Layer Enables Low-Temperature Solution Processed Perovskite Photovoltaics with 13.7% Efficiency. Nano Lett. 2014, 14, 2591–2596.

(25) Wu, J.; Chen, C.; Zhang, Y.; Chen, K.; Yang, Y.; Hu, Y.; He, J.H.; Wang, Z. L. Ultrahigh sensitive piezotronic strain sensors based on a ZnSnO3 nanowire/microwire. ACS Nano 2012, 6, 4369–4374.

(18) Edri, E.; Kirmayer, S.; Henning, A.; Mukhopadhyay, S.; Gartsman, K.; Rosenwaks, Y.; Hodes, G.; Cahen, D. Why Lead Methylammonium Tri-Iodide PerovskiteBased Solar Cells Require a Mesoporous Electron Transporting Scaffold (but Not Necessarily a Hole Conductor). Nano Lett. 2014, 14, 1000–1004.

(26) Cao, Y.; Jia, D.; Zhou, J.; Sun, Y. Simple Solid-State Chemical Synthesis of ZnSnO3 Nanocubes and Their Application as Gas Sensors. Eur. J. Inorg. Chem. 2009, 2009, 4105–4109. (27) Zeng, Y.; Zhang, T.; Fan, H.; Lu, G.; Kang, M. Synthesis and gas-sensing properties of ZnSnO3 cubic nanocages and nanoskeletons. Sens. Actuators, B 2009, 143, 449–453.

(19) Christians, J. A.; Fung, R. C. M.; Kamat, P. V. An Inorganic Hole Conductor for Organo-Lead Halide Perovskite Solar Cells. Improved Hole Conductivity with Copper Iodide. J. Am. Chem. Soc. 2014, 136, 758–764.

(28) Men, H.; Gao, P.; Zhou, B.; Chen, Y.; Zhu, C.; Xiao, G.; Wang, L.; Zhang, M. Fast synthesis of ultra-thin ZnSnO3 nanorods with high ethanol sensing properties. Chem. Commun. 2010, 46, 7581– 7583.

(20) Inaguma, Y.; Yoshida, M.; Katsumata, T. A Polar Oxide ZnSnO3 with a LiNbO3 Type Structure. J. Am. Chem. Soc. 6704– 6705.

(29) Singh, R.; Yadav, A. K.; Gautam, C. Synthesis and Humidity Sensing Investiga-


11


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

tions of Nanostructured ZnSnO3 . J. Sensor Technol. 2011, 01, 116–124.

Page 12 of 14

Expansion for Exchange in Solids and Surfaces. Phys. Rev. Lett. 2008, 100, 136406.

(30) Hedin, L. New Method for Calculating the One-Particle Green’s Function with Application to the Electron-Gas Problem. Phys. Rev. 1965, 139, A796–A823.

(39) Perdew, J. P.; Ruzsinszky, A.; Csonka, G. I.; Vydrov, O. A.; Scuseria, G. E.; Constantin, L. A.; Zhou, X.; Burke, K. Erratum: Restoring the Density-Gradient Expansion for Exchange in Solids and Surfaces. Phys. Rev. Lett. 2009, 102, 039902.

(31) Lehr, D.; Luka, M.; Wagner, M. R.; B¨ ugler, M.; Hoffmann, A.; Polarz, S. Band-Gap Engineering of Zinc Oxide Colloids via Lattice Substitution with Sulfur Leading to Materials with Advanced Properties for Optical Applications Like Full Inorganic UV Protection. Chemistry of Materials 2012, 24, 1771–1778.

(40) Resta, R.; Vanderbilt, D. Physics of Ferroelectrics; Topics in Applied Physics; Springer Berlin Heidelberg, 2007; Vol. 105; pp 31–68.

(32) Kresse, G.; Furthm¨ uller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 1996, 54, 11169–11186.

(41) Gajdoˇs, M.; Hummer, K.; Kresse, G.; Furthm¨ uller, J.; Bechstedt, F. Linear optical properties in the projector-augmented wave methodology. Phys. Rev. B 2006, 73, 045112.

(33) Kresse, G.; Furthm¨ uller, J. Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Comput. Mater. Sci. 1996, 6, 15 – 50.

(42) Dronskowski, R.; Bloechl, P. Crystal orbital Hamilton populations (COHP): energy-resolved visualization of chemical bonding in solids based on densityfunctional calculations. J. Phys. Chem. 1993, 97, 8617–8624.

(34) Giannozzi, P. et al. QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials. J. Phys. Condens. Matter 2009, 21, 395502.

(43) Maintz, S.; Deringer, V. L.; Tchougréeff, A. L.; Dronskowski, R. Analytic projection from plane-wave and PAW wavefunctions and application to chemical-bonding analysis in solids. J. Comput. Chem. 2013, 34, 2557–2567.

(35) Blöchl, P. E. Projector augmented-wave method. Phys. Rev. B 1994, 50, 17953– 17979. (36) Kresse, G.; Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B 1999, 59, 1758–1775.

(44) Mostofi, A. A.; Yates, J. R.; Lee, Y.-S.; Souza, I.; Vanderbilt, D.; Marzari, N. wannier90: A tool for obtaining maximallylocalised Wannier functions. Comput. Phys. Commun. 2008, 178, 685 – 699.

(37) Vanderbilt, D. Soft self-consistent pseudopotentials in a generalized eigenvalue formalism. Phys. Rev. B 1990, 41, 7892– 7895.

(45) Lee, J.; Lee, S.-C.; Hwang, C. S.; Choi, J.H. Thermodynamic stability of various phases of zinc tin oxides from ab initio calculations. J. Mater. Chem. 2013, 1, 6364.

(38) Perdew, J. P.; Ruzsinszky, A.; Csonka, G. I.; Vydrov, O. A.; Scuseria, G. E.; Constantin, L. A.; Zhou, X.; Burke, K. Restoring the Density-Gradient

(46) Onida, G.; Reining, L.; Rubio, A. Electronic excitations: density-functional


12

Page 13 of 14

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


versus many-body Green’s-function approaches. Rev. Mod. Phys. 2002, 74, 601– 659.

(54) Moutinho, H.; Young, M.; Harvey, S.; Jiang, C.-S.; Perkins, C.; Wilson, S.; AlJassim, M.; Repins, I.; Teeter, G. Epitaxial growth of CZTS on Si substrates investigated with electron backscatter diffraction. Photovoltaic Specialist Conference (PVSC), 2014 IEEE 40th. 2014; pp 2379– 2383.

(47) Green, M. A. Self-consistent optical parameters of intrinsic silicon at 300K including temperature coefficients. Sol. Energ. Mat. Sol. C. 2008, 92, 1305–1310. (48) Gueymard, C. A. Parameterized transmittance model for direct beam and circumsolar spectral irradiance. Sol. Energy 2001, 71, 325 – 346.

(55) Sinsermsuksakul, P.; Sun, L.; Lee, S. W.; Park, H. H.; Kim, S. B.; Yang, C.; Gordon, R. G. Overcoming Efficiency Limitations of SnS-Based Solar Cells. Adv. Energy Mater. 2014, 4, 1400496.

(49) Gueymard, C. A. The sun’s total and spectral irradiance for solar energy applications and solar radiation models. Sol. Energy 2004, 76, 423 – 453.

(56) Bakke, J.; King, J.; Jung, H.; Sinclair, R.; Bent, S. Atomic layer deposition of ZnS via in situ production of H2 S. Thin Solid Films 2010, 518, 5400 – 5408.

(50) Taguchi, M.; Yano, A.; Tohoda, S.; Matsuyama, K.; Nakamura, Y.; Nishiwaki, T.; Fujita, K.; Maruyama, E. 24.7% record efficiency HIT solar cell on thin silicon wafer. IEEE J. Photovoltaics 2014, 4, 96– 99.

(57) Todorov, T.; Gunawan, O.; Chey, S. J.; De Monsabert, T. G.; Prabhakar, A.; Mitzi, D. B. Progress towards marketable earth-abundant chalcogenide solar cells. Thin Solid Films 2011, 519, 7378–7381.

(51) Green, M.; Basore, P.; Chang, N.; Clugston, D.; Egan, R.; Evans, R.; Hogg, D.; Jarnason, S.; Keevers, M.; Lasswell, P.; O’Sullivan, J.; Schubert, U.; Turner, A.; Wenham, S.; Young, T. Crystalline silicon on glass (CSG) thin-film solar cell modules. Sol. Energy 2004, 77, 857 – 863. (52) Cruz-Campa, J. L.; Okandan, M.; Resnick, P. J.; Clews, P.; Pluym, T.; Grubbs, R. K.; Gupta, V. P.; Zubia, D.; Nielson, G. N. Microsystems enabled photovoltaics: 14.9% efficient 14 µm thick crystalline silicon solar cell. Sol. Energ. Mat. Sol. C. 2011, 95, 551 – 558. (53) Shin, B.; Gunawan, O.; Zhu, Y.; Bojarczuk, N. A.; Chey, S. J.; Guha, S. Thin film solar cell with 8.4% power conversion efficiency using an earth-abundant Cu2 ZnSnS4 absorber. Prog. Photovolt: Res. Appl. 2013, 21, 72–76.


13


Graphical TOC Entry ZnS nS  0. 5μm

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

 . eV

 . eV E CBM

E VBM


14

Page 14 of 14

First-Principles Design and Analysis of an Efficient ... - ACS Publications

Recommend Documents