Assessing the Use of BiCuOS for Photovoltaic Application: From DFT

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Assessing the Use of BiCuOS for Photovoltaic Application: From DFT to Macroscopic Simulation. Tangui Le Bahers, Servane Haller, Thierry Le Mercier, and Philippe Barboux J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.5b05551 • Publication Date (Web): 08 Jul 2015 Downloaded from http://pubs.acs.org on July 10, 2015

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The Journal of Physical Chemistry

Assessing the Use of BiCuOS for Photovoltaic Application: From DFT to Macroscopic Simulation. Tangui Le Bahers1*, Servane Haller2,3, Thierry Le Mercier2 and Philippe Barboux3 1

Université de Lyon, Université Claude Bernard Lyon1, ENS Lyon, Centre Nationale de Recherche Scientifique, 46 allée d’Italie, 69007 Lyon Cedex 07, France 2 Solvay, Research and Innovation Center Paris, 52 rue de La Haie Coq 93308 Aubervillier Cedex, France. 3 PSL Research University, Chimie Paristech-CNRS, Institut de Recherche de Chimie Paris, 75005 Paris, France

*Corresponding author: Dr. Tangui Le Bahers, [email protected], +33472728846

ACS Paragon Plus Environment


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Abstract The objectives of the work presented in this article are two folds. First it presents computed properties of the semiconductor BiCuOS at the HSE06+spin-orbit coupling level and these properties are interpreted from the composition of the material point of view and are analyzed from a photovoltaic perspective. The calculated properties (Eg = 1.22 eV, εr = 36.2, 𝑚𝑒∗ =0.42, 𝑚ℎ∗ =0.33, Eb = 2 meV) illustrate that BiCuOS is a promising material for photovoltaic application. The second objective is to presents a multi-scale approach whose objective is to simulate photovoltaic macroscopic characteristics (Jsc, Voc, FF…) from microscopic properties computed at the DFT level. The approach is first tested in the CuInS2 solar cell, that has several similarities with BiCuOS, allowing to determine the strengths and limits of this approach. Then, this protocol is applied to BiCuOS solar cells in order to determine the best n-type semiconductor to put in contact with BiCuOS to achieve high photoconversion efficiencies. The results allow to dress the list of the drawbacks that must be overcome to use this material for photovoltaic application. Beyond BiCuOS, this protocol can be used by the community wanting to use modeling to design and characterize new semiconductors beyond the bandgap calculation.

Keywords: BiCuOS, photovoltaic, DFT, dielectric constant, exciton, effective masses.


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Introduction

The research of new semiconductors having photovoltaic properties has never ceased to grow since the establishment of the second photovoltaic generation, which has proven that other materials than silicon can be used for photovoltaic application with good efficiencies.1 An impressive expansion of research in that field happened in the early of the 2000s because of the development of new solar cell architectures mainly guided by the Dye-Sensitized Solar Cells2 and Bulk-heterojunction organic solar cells3 technologies. In parallel, the development of the research on photocatalysis, principally for water splitting, has lead to the design of new semiconductors also having the capacity to generate charge carrier upon sunlight absorption.4 These two research areas, photovoltaic and photocatalysis, generally take benefit from the advance made by the other one. The very recent high photoconversion efficiencies obtained with perovskite based materials5–7 proves that the research of new materials and new cell architectures for photovoltaic and photocatalytic applications can lead to new breaking technologies. Theoretical chemists take part in this research effort. Whether in the field of materials, of dyes (for DSSC) or polymers, they developed series of tools dedicated to determine the photovoltaic performances of these systems. For the case of semiconductors, in general, when studying a new material, theoretical calculations are performed only to compute the bandgap, the density of states and the band structure while several other properties can be obtained, without an important increase of the computational effort. For instance, the effective masses, that gives interesting information on the anisotropy of conductivity, is rarely computed when a new semiconductor is characterized (both experimentally and theoretically) while this quantity can be extracted from all quantum chemical codes dealing with periodic systems. Recently, some of us pointed out some fundamental properties that govern the ability of a semiconductor to generate a photocurrent that can be computed at the DFT level.18 These properties are the bandgap, Eg, governing the absorption of light, the dielectric constant, εr, that influences the exciton binding energy (Eb) and the effective mass, m*, involved in the charge carrier’s mobility . Required ranges of values for these quantities are presented in Table 1. A detailed explanation of how these requirements were derived is available in ref 8.



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Solar spectrum absorption

Exciton dissociation Eb < 25 meV

1.1 eV < Eg < 1.4 eV

εr > 10

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Charge carrier diffusion m* < 0.5 me

Table 1: Requirements on the semiconductors properties for photovoltaic application.

The objective of the work presented here is to show that another step can be crossed at the theoretical level. The philosophy is to integrate the microscopic properties computed at the quantum chemical level into softwares that are able to simulate the electronic structure of a solar cell, solving the classical equations of semiconductors with a finite element method, to extract macroscopic properties such as the open circuit voltage (Voc) or the short-circuit photocurrent (Jsc) of the solar cell. CuInS2 was selected as test system to check the reliability, the strength but also the limit of this theoretical procedure. This sulfide has the advantage that its structure (presented in Table 2) and electronic properties (presented in Table 3) are relatively well known and tabulated and because of its importance in the field of photovoltaic and photocatalysis. Furthermore, its use for photovoltaic application was intensively explored leading to high quality photovoltaic cells whose J-V characteristics are reliable. In a second step, we show that this method can be used to propose new materials as potential absorber in photovoltaic devices through the case of BiCuOS. This oxysulfide of copper and bismuth seems to possess attractive properties. It was first synthesized in 1994 by Kusainova et al.9 using solid state reactions and received a renewed interest when Sheets et al.10 proposed an alternative low temperature route through hydrothermal synthesis. However, the first works made on the BiCuOCh family (Ch = S, Se and Te) were focused on their thermoelectric behavior.11,12 For that application, BiCuOSe and BiCuOTe are more interesting than BiCuOS. Although its bandgap of 1.1 eV lies in the optimal region and therefore suggests its potentiality for photovoltaic application13, no previous study has shown interest for this application to the best of our knowledge and there are still several properties that have to be determined for this compound. For these reasons, determining the theoretical solar cell efficiency from the material structure of this oxysulfide is an interesting test case to highlight the potentiality of our theoretical procedure.

This manuscript is organized as follows. In the first part, the methodology of our approach is presented in order to explain what properties can be computed or estimated at the DFT level and how the J-V simulation will be performed. The second part is dedicated to computational details that give all numerical and very technical issues. Then, the procedure is applied to


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CuInS2 in the third part. This section will confirm that our DFT protocol is reliable for computing microscopic properties for this type of semiconductor (mixed sulfide) and will compare the simulated J-V characteristics to the experimental one on a realistic cell architecture. The final part will focus on BiCuOS. The objective of this section is two folds. First the full characterization of BiCuOS properties at the HSE06+spin-orbit coupling level will be presented, that is the state of the art of DFT calculation for semiconductors. Then the best n-type semiconductor in junction of the p-type BiCuOS will be determined in a list of seven semiconductors frequently used in the field of photovoltaic and photocatalysis.



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Methodology It is interesting to note that the fundamental equations developed to compute the properties presented in this work, such as the electronic contribution to the dielectric constant (noted ε∞) or the vibrational contribution to the dielectric constant (noted εvib), are known from several decades ago (from the 60’s for ε∞14 and from the 90’s for εvib15,16). But the implementation of these equations in quantum mechanical codes dealing with periodic systems is much more recent (less than 10 years ago).17–19 Moreover, these implementations have been mainly used to compute properties of materials whose experimental values are well tabulated in order to check the validity of the computational protocols. The use of these recently implemented equations for predicting properties’ values unknown experimentally on newly synthesized materials is still at the beginning. One aim of this work is to push the community in the way of a larger theoretical characterization of newly synthesized semiconductors. The way to compute the properties such as the bandgap (Eg), the electronic contribution to the dielectric constant (ε∞), the vibrational contribution to the dielectric constant (εvib), the effective masses (m*) and the exciton binding energies (Eb) were presented in the following article8 and used to compute properties of representative of the PbX3CH3NH3 (X=Cl, Br, I) family of semiconductor20. It can just be reminded that first the total dielectric constant (εr) is the sum of the electronic (ε∞) and the vibrational contribution (εvib) and then the exciton binding energy is computed in the framework of the Wannier’s model using the average values of m* and εr. This model is well adapted for delocalized exciton (large dielectric constant and low effective masses) that is the case for CuInS2 and BiCuOS, as it will be shown after. The electron affinity (EA) was computed using the protocol proposed by Stevanović et al.21 According to this protocol, the EA is obtained from the position of the conduction band of a surface of the semiconductor. In the case of CuInS2 and BiCuOS, the non-polar surfaces (110) and (100) were selected respectively. Stevanović et al. suggested to optimize the geometries of the surface with the PBE functional and to perform GW calculation on top of the PBE geometries to obtain a reliable conduction band position. In the present work, we decided to optimize the geometries with the hybrid functional PBE0 and to perform single point calculation with the range separated hybrid HSE06. The choice is motivated by the fact that PBE0 and HSE06 reproduce accurately the crystal structure and the bandgap of bulk semiconductors respectively. The results presented after will confirm this computational protocol.


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The simulation of the properties of a p-n junction involves also the valence and conduction bands effective density of states, noted NV and NC respectively. These parameters can be calculated using the following formula derived from the free electron gas model and involving the knowledge of the effective masses (that are computed at the DFT level). 3/2

𝑁𝑉(𝐶)

∗ 2𝜋𝑚𝑒(ℎ) 𝑘𝐵 𝑇 = 2( ) ℎ2

(1)

Finally, the simulations of the electronic structure of the p-n junction and the properties derived from these simulations were performed by solving numerically the semiconductor equations (i.e. the holes and electrons continuity equations and the Poisson equation). This can be performed for a one-dimensional system by the software SCAPS developed in ELIS (Gent, Belgium).22–26 This code was designed to model photovoltaic systems involving CdTe and CuInSe2 semiconductors, for that reason, it will be also adapted to study CuInS2 and BiCuOS. Only the charge carrier mobility, noted μ, needed by SCAPS, cannot be computed at the DFT level. This property is obtained from the m* and the collision time (τ) of the charge carriers using the following formula (equation 2). While m* can be computed at the DFT level, the collision time is very dependent on the quality of the material and cannot be estimated at the DFT level. For that reason, the μ experimental values, when available, were used. When no experimental values are reported, μ values of semiconductor having a similar structure and composition were employed. 𝜇=𝑒

𝜏 𝑚∗


(2)


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Computational details. For bulk semiconductors, geometry optimizations and frequency calculations were performed with the global hybrid functional PBE027 along with the ab initio CRYSTAL14 code28,29, using localized (Gaussian) basis sets and solving self-consistently the Hartree-Fock and Kohn-Sham equations thus allowing the efficient use of hybrid functionals. For the O, S, Cu and In atoms, the all-electron triple zeta valence basis set 8-411G(d)30, 6-311G(d)31 and 86411G(2d)32 and 976-311G(2d)33 were used respectively. For the Bi atom, a modified version of the Hay and Wadt pseudopotential was used along with the 31G(d) basis set for the valence electrons (5 valence electrons).34 The reciprocal space was sampled according to a sublattice with a 12x12x12 k-points mesh for both geometry optimization and vibrations calculations. The convergence criterion for the SCF cycle was fixed at 10-10 Ha per unit cell for geometry optimization and frequencies calculations. The calculation of frequencies has been performed within the harmonic approximation to the lattice potential and infrared intensities are obtained through the Berry Phase method35. Finally, the vibrational contribution to the dielectric constant (εvib) was computed with PBE0 using CRYSTAL14 code. All electronic properties were computed using the HSE0636,37 functional on top of the PBE0 geometries. In the case of BiCuOS, to take into account relativistic effects involved by the bismuth atom, the electronic properties calculations were performed with VASP (5.2 version)38–41 along with relativistic pseudopotentials and the non-collinear formalism42 to take into account the spin-orbit coupling since CRYSTAL14 cannot take into account this relativistic effect. For the dielectric constants and effective masses calculations, a 9x9x9 kpoints mesh was used while a 12x12x12 k-points mesh was used for bandgap calculations both with a 400 eV energy cutoff. The core electrons for each atom were described with the projector augmented plane wave (PAW) approach. For CuInS2, all calculations involving HSE06 were performed with CRYSTAL14 except ε∞ that was done with VASP with a 400 eV and a 9x9x9 k-point mesh. For surface calculations, a similar protocol was used but with a 8x8 k-point mesh. The surface thickness was taken with 10 atomic planes for BiCuOS(100) and 12 atomic planes for CuInS2(110), based on surface energy convergence. The geometries were fully relaxed at the PBE0 level and single point calculations were performed with HSE06. In the case of BiCuOS(100), the size of the large system doesn’t allow to compute the band position at the HSE06+spin orbit coupling level. To overcome this difficulty, the shift of the bands induced by the spin-orbit coupling on this surface was evaluated on a 4 layers surface and this shift


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was added to the conduction band position obtained for the 10 layers surface without spinorbit coupling. The optimized structures of the surfaces and their cartesian coordinates are given in supporting information. The band structure and the density of states were computed with the HSE06 functional using the CRYSTAL14 code with the same basis set as the one used for geometry optimization. The reason for this splitting between PBE0 (for geometry optimization) and HSE06 (for electronic properties calculations) comes from a benchmark made by some of us on several semiconductors8. This previous work showed that PBE0 gives a better agreement for the cell parameters than HSE06, while this latter functional was more adapted for electronic properties simulation. This distribution (PBE0 for the geometry and HSE06 for the electronic structure) was applied to properties’ calculations of representatives of the family PbX3CH3NH3 and of wurtzite CuGaS2 doped by Zn.20,43 For p-n junction simulation with SCAPS22–26, all the parameters used to define semiconductor properties are gathered in supporting information.



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CuInS2 Fundamental Properties CuInS2 has been widely studied for photovoltaic application since the end of the 70s.44 It was first investigated for thin film solar cells, also called second photovoltaic generation,45 but was replaced by Cu(In,Ga)Se2 (known as CIGS) because this latter compound has a lower bandgap and larger charge carrier mobilities, more adapted for photovoltaic application.46 Nevertheless, the study of this material saw a renew of interest during the 2000’s pushed by the development of new photovoltaic technologies and by the research of non-toxic absorbing material for photovoltaic device.47 Furthermore, the possibility to tune the bandgap by substitution of In by Ga offers the possibility to adapt the bandgap for several photocatalytic reaction such as the water splitting.46 For these reasons, CuInS2 is an interesting system for testing our theoretical protocol. Furthermore, the electronic properties of CuInS2 semiconductor are well tabulated. CuInS2 was used as absorber in efficient thin film solar cells and its nature (structure and composition) has lot of similarities with BiCuOS that will be analyzed in the next section and for which we have less data. Experimental and DFT optimized cell parameters of the chalcopyrite form of CuInS2 (space group I-42d) are presented in table 2, while the cell representation is depicted in Figure 1. The DFT error is around 1.0% for the cell parameters that is in the standard deviation for this level of theory. The only one degree of freedom for atomic position is the x position of the S atom that is computed by DFT in agreement with the experiment. a/Å

c/Å

Exp48 5.552 11.133 DFT

xS 0.23

5.593 11.286 0.229

Table 2: Experimental and computed (PBE0) cell parameters of CuInS2.


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c

a

b

Figure 1: Scheme of the conventional cell of chalcopyrite CuInS2. The blue, brown and yellow atoms correspond to In, Cu and S respectively. a, b and c are the crystallographic axis.

The HSE06 computed electronic properties are presented in the Table 3 along with experimental values. The computed bandgap is close to the one experimentally extrapolated at 0 K, but at room temperature the bandgap reduces of around 0.1 eV. It is interesting to note that the vibrational contribution to the dielectric is rather low (εvib ~ 2.4) both experimentally and theoretically. This is a consequence of the strong covalent nature of the bonds that leads to a low variation of the polarizability of the crystal upon vibration of the atoms. The total dielectric constant, εr, is relatively low for photovoltaic application. Values higher than 10 are generally preferred (see Table 1). Only the hole effective mass is not particularly well reproduced. It is known that the effective mass is a quantity difficult to reproduce and sometime, a discrepancy can appear between theory and experiment. Furthermore, only one hole effective mass has been reported in the literature, it could be interesting to determine this property by different method to confirm this value. Nevertheless, the exciton binding is well reproduced by the Wannier’s model confirming that the exciton is delocalized in the compound and feels only a homogenous dielectric medium. Finally, the computed electron affinity of the (110) non-polar surface, which corresponds in our model to the position of the conduction level, is also in nice agreement with the experiment. HSE06 proves its reliability to compute the electronic properties mixed metal sulfides.



Exp

DFT

1.54(d) (T=300K)49

Eg / eV

1.69(d)

1.62(d) (T=0K)49

ε∞

6.2(⊥)50 6.0(∥)50

6.6(⊥) 6.5(∥)

εr

8.6(⊥)50 8.4(∥)50

8.6(⊥) 9.1(∥)

𝑚𝑒∗ / me

0.1651

0.21(⊥) 0.19(∥)

𝑚ℎ∗ / me

1.3051

0.90(⊥) 0.25(∥)

Eb / meV

2052

25

EA / eV

4.053

4.1

Table 3. Computed and experimental properties of CuInS2 using the HSE06 functional. The symbols ⊥ and ∥ mean along the {110} and the {001} directions respectively. The (d) indication means direct bandgap.

Photovoltaic simulation The next step of our theoretical procedure is to use the computed electronic properties to model the J-V characteristic of a solar cell by solving the semiconductor equations of a p-n junction. The scheme of the simulated solar cell is presented on Figure 2. It corresponds to a standard architecture of a CIGS solar cell where CuInS2, that is p-type semiconductor, is in contact with a layer of n-type CdS and a layer of n-type ZnO.45 The electrodes are a

0.1 µm

0.1 µm

FTO

n-ZnO

light

n-CdS

p-CuInS2

3 µm

conductive glass (FTO) and molybdenum (Mo) and the sunlight enters from the FTO side.

Mo

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Figure 2: Architecture of the simulated CuInS2 based solar cell.

The simulated J-V characteristics with an AM1.5 solar spectrum are depicted in the Table 4 along with the best published photoconversion efficiency with this cell architecture. It appears clearly that the junction model used for this work over-estimates the open-circuit voltage (Voc) and the fill factor (FF). But this discrepancy is well-known in the field of solar cell modeling.


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To reproduce the experimental Voc and FF, the models need to include both the presence of isolated defects such as copper vacancies for CuInS2 and the existence of a layer called OVC for Ordered Vacancy Compound.54–56 This latter appears at the interface between CuInS2 and CdS and is made of compounds having various Cu/In/S ratios giving compositions such as CuIn5S8 or CuIn3S5. Models including the presence of these defects have proven that they are the main reason of the Voc and FF decrease, and finally explaining the photoconversion efficiency drop.26,57 Nevertheless, it is interesting to state that the short-circuit current (Jsc) is much less affected by these defects and can be modeled with a nice agreement with the experiment using our approach.

Voc / V Jsc / mA.cm2 FF / % η / % Exp45

0.73

21.8

72

11.4

Simulated

1.15

23.0

88

23.0

Table 4. Experimental and computed J-V characteristics.

This simulation clearly highlights the strength and the limit of our approach to model J-V characteristics of a solar cell using DFT computed parameters. The main advantage of our protocol is on the semiconductor properties calculation. All the quantities presented in the table 3 are necessary to define the semiconductor for the macroscopic simulation. The first part of this section, dedicated to the DFT simulation of these properties, clearly reveals that the quantum chemical calculations are now very reliable to compute bulk semiconductor properties. The J-V simulation has shown that the Jsc value is mainly governed by the bulk semiconductors properties and the architecture of the cell. So this quantity can be obtained by our methodology. But this J-V simulation also has brought out that our approach needs also to include the defects because they govern principally the Voc and in less markedly way the FF. The study of the defects properties (whether punctual or organized) has been the subject of several theoretical works that have proven that some of their properties such as their energy positions and their relative stability can be modeled with a good agreement with the experiment.58–60 But some of the defect characteristics cannot be obtained at the DFT level such as their concentration. Consequently, experimental or ad-hoc inputs will be always needed to get closer to experimental results. The next section is an example based BiCuOS material that is little studied but was, in the literature, supposed to be interesting for photovoltaic application.



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BiCuOS Fundamental Properties BiCuOS was theoretically investigated by Sheets et al. and Zou et al.10,12 Although interesting because presenting the first theoretical insights on this material, the level of theory used (GGA functional) doesn’t correspond to the state of the art of DFT for semiconductors. It has been proven that hybrid functionals computes properties in better agreement with experimental results than GGAs. More precisely, a benchmark performed by some of us on the properties investigated here allows to conclude that the global hybrid functional PBE0 is particularly adapted to determine cell parameters of crystals whereas the range-separated hybrid HSE06 gives better results for electronic properties. This result is also confirmed by the previous section of this work on CuInS2. For this reason, the PBE0 functional was used to optimize the geometry of the crystal structure of BiCuOS and to perform the subsequent frequency calculation while HSE06 was employed to compute electronic properties on top of the PBE0 geometry. The Figure 3 presents the crystal structure of BiCuOS (space group P4/nmm). The cell parameters and the z fractional coordinates of Bi and S are gathered in the Table 5 (all other Wyckoff positions are presented in the Supporting Information). The mean absolute error obtained by DFT on the a and c parameters is 1.0% which is in the standard deviation expected from this method. It can be noted that the only degrees of freedom allowed by the crystal symmetry, zBi and zS, are particularly well reproduced by DFT calculations confirming the relevance of choosing PBE0 to optimize the geometry of the system.

BiO+ layer c CuS- layer a

b BiO+ layer

Figure 3: Scheme of the BiCuOS cell (supercell 2x2x1) presenting the layers packing along the c axis of the compound. The green, brown, yellow and red atoms correspond to Bi, Cu, S and O respectively. a, b and c are the crystallographic axis.


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a/Å 11

c/Å

zBi

zS

Exp

3.869 8.560 0.148 0.671

DFT

3.833 8.653 0.144 0.678

Table 5: Experimental and computed (PBE0) cell parameters of BiCuOS.

The computed physical properties of BiCuOS are gathered in Table 6. From the light absorption point of view, the computed bandgap of BiCuOS (Eg = 1.22 eV) is clearly in the optimum range for photovoltaic application, which is between 1.1 eV and 1.4 eV.13 Furthermore, this result is in agreement with the experimental bandgap (Eg(exp) = 1.1 eV) confirming the interest of the HSE06 functional with the spin-orbit coupling for the computation of electronic properties. Unfortunately, as it can be seen on the band structure (Figure 4) and in agreement with previous works10–12, this is an indirect bandgap, which is a major drawback compared to other materials such as CdTe61 or GaAs62. The first direct bandgap of BiCuOS is at 1.46 eV (at the Z-point of the Brillouin zone), which is very near the optimum interval. Exp

DFT

Eg / eV

1.163

1.22(i) 1.46(d)

ε∞

--

10.0(⊥) 7.5(∥)

εr

--

56.7(⊥) 23.5(∥)

𝑚𝑒∗ / me

--

0.42(⊥) 0.68(∥)

𝑚ℎ∗ / me

--

0.33(⊥) 1.36(∥)

Eb / meV

--

2

EA / eV

3.863

4.0

Table 6: Computed and experimental properties of BiCuOS using the HSE06 functional along with the spin-orbit coupling. The symbols ⊥ and ∥ mean along the {110} and the {001} directions respectively. The (d) and (i) indications mean direct and indirect bandgap respectively.



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Figure 4: Band structure computed at DFT level along with the HSE06 functionals. The red and blue bands correspond to full and empty states respectively. The dashed line corresponds to the top of valence band. The band structure were computed without spin-orbit coupling and the conduction bands were translated to give the bandgap with spin-orbit coupling (i.e. 1.22 eV)

The importance of the relativistic effects on the electronic structure of BiCuOS is well illustrated by the calculation of Eg. Without taking into account spin-orbit coupling, Eg is 1.52 eV, 0.3 eV larger than the one computed with this relativist effect. The large relativistic effects are induced by the heavy bismuth atom in the structure, as already pointed out by Zou et al.12 To go into more details in the setting of the absorption spectrum, the imaginary (ε2) and real (ε1) part of the frequency dependent dielectric constant were computed along with the spinorbit coupling. This allows determining the absorption spectrum depicted in Figure 5 using the equations (3)-(4). For this type of calculation, no electron-phonon interactions are taken into account, which means that only direct (i.e. at the same k vector of the reciprocal space) transitions are considered for frequency-dependent dielectric constant calculation. Thus, the curves presented in Figure 3 must be seen as a lower value of the real absorption of BiCuOS since all the indirect absorptions are lacking. In Figure 5, a first feature is observed around 1.5 eV that corresponds to the direct bandgap. Then, the absorption increases significantly above 1.75 eV and overpasses 105 cm-1 at 2.2 eV. This is ten times higher than the absorption of crystalline silicon at 2.2 eV. Note that the absorption in BiCuOS is also quite dependent on the light polarization since it is more intense for polarization along the a and b directions than along the c direction of the structure.


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(3) 2

2

√√𝜀1 (𝜔) + 𝜀2 (𝜔) − 𝜀1 (𝜔) 𝜅(𝜔) = 2 𝛼(𝜔) =

4𝜋 𝜅(𝜔) 𝜆

(4)

Figure 5: Simulated absorption spectrum of BiCuOS using HSE06 functional with spin-orbit coupling. The full line corresponds to a light polarization in the a and b directions and the dashed line corresponds to a light polarization in the c direction.

As presented in ref 8, the static dielectric constant is an important property for photovoltaic or photocatalytic applications. Indeed, a high dielectric constant will facilitate the exciton dissociation after light absorption. In the case of BiCuOS, the electronic contribution to the static dielectric constant (ε∞) is 8.7 in geometric average, which is comparable to what is found in standard materials such as GaAs, CdTe or Si.8 This large value has to be ascribed to the presence of the heavy Bi atom, which has, a very polarizable electron density. But, the potential originality of BiCuOS comes from its large global dielectric constant (εr) as compared to other materials used in photovoltaic. This value, around 36.5 in geometric average, is closer to what is found in oxides.8 For that reason, the large contribution of the vibrational part to the dielectric constant can be ascribed to the presence of the very electronegative oxygen atoms giving very large Born effective charges. All the computed vibration energies and IR intensities are presented in the Supporting Information. As can be expected from the electronic structure, the effective masses of electrons (𝑚𝑒∗ ) and holes (𝑚ℎ∗ ) are particularly anisotropic. Both particles are much more mobile in the {110} directions than along the {001} direction. This can be understood from the density of states



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drawn in Figure 6. For the electrons, the bottom of the conduction band is located on the Bi atoms, while for the holes, the top of the valence band is located on the Cu and S atoms. Since the {001} direction is perpendicular to the Cu-S planes and to the Bi-O planes, there is little dispersion of Cu-S bands and the Bi bands along this direction giving rise to a large effective mass. Nevertheless, the effective masses are comparable to what is found for TiO2-Anatase8. This means that BiCuOS is certainly a good electron or hole conductor (depending on the type of doping), to the condition that the defect concentration remains low enough. Experimentally, BiCuOS was characterized as a p-type semiconductor because of Cu vacancies, similarly to other materials containing Cu(I) ion like CuInS2 studied in the first section.64 Consequently, the low hole effective mass indicates that BiCuOS can be used as ptype conductor. From a theoretical point of view, the spin-orbit coupling does not modify significantly the effective masses contrary to what is computed for the lead-based perovskite.20,65 The exciton binding energy (Eb) has been computed using the Wannier’s model from the static dielectric constant and the effective masses of the charge carriers. The value is around 2 meV. This is clearly lower than the 25 meV of the thermal energy at room temperature. Consequently, there should be a rapid thermal dissociation of photo-generated excitons to form free charge carriers. This very low value, much lower than the one computed for CuInS2, comes from the very high dielectric constant of this material.

Figure 6: Projected Density of states computed at DFT level along with the HSE06 functionals. The green, yellow, red and blue lines correspond to the projections on copper, sulfur, oxygen an bismuth atoms respectively. The dashed lines represent the positions of the top of the valence band and the bottom of the conduction band. These DOS were computed without spin-orbit coupling and the conduction band was translated to give the bandgap with spin-orbit coupling (i.e. 1.22 eV)


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Finally, the electron affinity computed for the (100) non-polar surface is slightly higher (0.2 eV) than the measured one by Inverse Photoelectron Spectroscopy on a powder of BiCuOS.63 This discrepancy is in the standard deviation for this electron affinity computation method.21 Interestingly, the electron affinity of BiCuOS is relatively close to the one of CuInS2 (both theoretically and experimentally), giving another point of similarity between these two compounds. In conclusion, for the first time, all the electronic properties governing the photoresponse of a material were computed for BiCuOS at this level of theory (HSE06+spin-orbit coupling). This material theoretically fulfills all the specifications requested for a semiconductor to be used in photovoltaic devices. We have shown that BiCuOS can absorb efficiently the sunlight, that the exciton can be easily dissociated at room temperature and that free charge carriers can diffuse rapidly to the electrodes, giving a photocurrent in an external circuit. From the point of view of its intrinsic properties, the major drawback of BiCuOS comes from the indirect nature of its bandgap which is partially compensated by a direct bandgap low enough to allow a significant overlap between the absorption spectrum of BiCuOS and the solar spectrum. As a final remark on this part, it can be stated that higher level of calculation, such as GW/BSE, will probably improve the predictions of the properties since this latter method in its selfconsistent form is known to overpass the DFT.66 But we believe that the main conclusions on BiCuOS will be unchanged.

Perspective for photovoltaic application Now, we will discuss the development of new photovoltaic technologies involving BiCuOS. As a matter of fact, it can be wondered whether BiCuOS could be interesting for application in standard thin film solar cell technologies or in a perovskite type solar cell. The last section demonstrated that the absorption coefficient of BiCuOS is higher than 105 cm-1. With such a high absorption coefficient, a layer as thin as 460 nm is enough to absorb 99% of the incoming photons. This is largely compatible with applications in a thin film solar cell. Using the BiCuOS properties computed along with the DFT, the J-V simulations are used to determine what would be the best n-type semiconductor to put in junction with BiCuOS in thin film solar cell. The J-V and IPCE curves of BiCuOS in junction with ZnO, ZnS, TiO2Anatase, TiO2-Rutile, SnO2, CdS and CdO were simulated using SCAPS. These n-type semiconductors were selected since they are frequently proposed in the fields of photovoltaic and photocatalysis and therefore their integration in solar cell architecture is well controlled. The solar cell architecture simulated is inspired from the CuInS2 technology (see Figure 7)



because we have seen that BiCuOS and CuInS2 share several properties. All the parameters needed to perform these simulations are gathered in the Supporting Information. For BiCuOS, the only parameters that are unknown (both experimentally and theoretically) are the charge carrier mobilities which were set to 150 cm2.V-1.s-1 for the electrons and 20 cm2.V-1.s-1 for the holes by analogy to the electron mobility in ZnO (typical of an oxide conduction band) and the hole mobility in CuInS2 (characterizing a copper-sulfide valence band).61 The influence of the choice of the mobility values was checked by simulating the J-V curve of the BiCuOS/ZnO junction by multiplying and dividing by two the values chosen for BiCuOS. Only the Voc was affected, and very weakly (variation around 0.01 V), proving that a variation

0.5 µm FTO

light

n-SC

p-BiCuOS

1 µm

of the BiCuOS charge carrier mobilities would not affect the conclusions of this section.

Mo

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Figure 7. Architecture of the simulated BiCuOS based solar cell.

The solar cells characteristics (i.e. the open circuit voltage, Voc, the short circuit current, Jsc, the fill factor, FF, and the photoconversion efficiency, η) extracted from these simulations are presented in Table 7. The photoconversion efficiency of the junction is very dependent on the n-type semiconductor since it is high for ZnO and TiO2-Anatase and much lower for SnO2 and CdO. In the case of TiO2-Rutile and SnO2, the efficiency is low because the conduction band of these compounds is too low compared to that of BiCuOS. Indeed, by artificially lowering the conduction band level of ZnO, it was found that the efficiency dropped significantly when it was located below -4.4 eV. Although the conduction band of CdS (-4.0 eV) is at the right position to catch the photogenerated electrons from the conduction band of BiCuOS, it absorbs significantly the solar spectrum (Eg = 2.45 eV). This means that CdS competes with BiCuOS for absorption, reducing the final photocurrent, thus the photoconversion efficiency. CdO gathered all the drawbacks, the low conduction band level and the competing absorption of the solar spectrum explaining the very low η in that case.


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The case of ZnS is different. A band bending at the interface creates an energetic barrier for the electron transfer, reducing FF and finally η. ZnO Voc / V

TiO2 TiO2 CdO SnO2 ZnS CdS Anatase Rutile 0.74 0.74 0.75 0.79 0.75 0.74 0.74

Jsc / mA.cm-2 29.6

30.5

29.6

11.7

30.0

30.9 26.8

FF / %

82.3

82.6

66.3

20.8

57.0

69.3 83.2

η/%

18.3

18.8

14.7

1.9

12.8

15.9 16.6

Table 7: Simulated solar cells characteristics of BiCuOS in junction with several n-type semiconductors.

From now, the discussion will focus on the BiCuOS/ZnO junction, since this junction is simulated to be one the best and because ZnO is frequently used as n-type semiconductor in the CIGS solar cells. Figure 8 illustrates the simulated J-V and IPCE curves of BiCuOS in junction with ZnO. The drop of IPCE for wavelengths lower than 400 nm comes from the absorption of light by ZnO, which competes with the BiCuOS absorption. It should also be noted that for wavelengths beyond 900 nm, the IPCE is probably underestimated since the simulated absorption spectrum of BiCuOS (Figure 3) was used to model the IPCE curve. The indirect transitions occurring between 900 nm and 1000 nm (corresponding to, approximately, the indirect bandgap of BiCuOS) are not taken into account. Thus, the maximum short circuit current achievable with BiCuOS could be higher than that simulated in this study.

(a)

(b)

Figure 8: Simulated J-V (a) and IPCE (b) solar cell characteristics of the junction BiCuOS/ZnO.

While the simulated efficiency with ZnO is very high, it must be also interpreted looking at the results obtained on the CuInS2 test case. It was stated that the simulated Voc is too high



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because the defects are not taken into account in the simulation. If we assume that the efficiency decrease between the simulation and the experiment for CuInS2 will be the same for BiCuOS, the final Voc and η for the BiCuOS/ZnO junction will be probably around 0.5 V and 9% respectively. This makes BiCuOS less attractive for photovoltaic application. The simulation of J-V curve was also used to determine if the capacities of BiCuOS can be improved by tuning the acceptor concentration (i.e. Cu vacancies).64 The J-V curves simulated for acceptor concentration ranging from 1015 to 1018 cm-3 for the BiCuOS/ZnO junction are presented on Figure 9. The donor concentration of ZnO was fixed to 1018 cm-3, that is a standard value encountered for n-type semiconductors in excitonic solar cells.67,68 Going from 1015 cm-3 to 1018 cm-3, the Jsc decreases but seems to reach a plateau while the Voc increases continuously. This indicates that the performance of BiCuOS can be tuned by adapting the acceptor concentration.

Figure 9: Simulated J-V characteristics of the junction BiCuOS/ZnS. (a), (b), (c) and (d) curves correspond to 1018, 1017, 1016 and 1015 cm-3 donor concentrations in ZnS respectively.

The performance of these simulated p-n junctions revealed the weakness of BiCuOS for photovoltaic application. Nevertheless, these simulations also indicate what would bo the degree of freedom that could be used to improve the photoconversion efficiency. To use BiCuOS for photovoltaic application, the following issues must be addresses: 1- The development of a way to tune the acceptor concentration in the compound since this property influences the opto-electronic and the depletion region properties and finally the global efficiency of the device.


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2- The choice of the n-type semiconductor is important. The simulated J-V characteristics indicate very different results from n-type semiconductor to another. 3- The elaboration of a dense thin layer of BiCuOS. The deposition of thin layers of BiCuOS is challenging but some examples can be found in the literature. It is also possible to consider alternatives to the standard thin film stack of solar cells architectures such as perovskite-based architectures69 or bulk-heterojunctions70. 4- The design of the other components of the solar cell since the electrodes characteristics were not taken into account for the simulation of the J-V characteristics. While the junction of ZnO with the conductive glass FTO is known to efficiently collect electrons, some work must be done to choose an electrode in contact with BiCuOS to optimize the hole collection. By analogy to CIGS solar cells, molybdenum could be proposed.



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Conclusion Impressive progresses have been achieved by the DFT community to simulate semiconductor properties. These progresses are the consequences of new functional developments such as HSE06, new properties implementations such as dielectric constant calculation (both electronic and vibrational) and new computational tools such as the non-collinear formalism allowing to treat the spin-orbit coupling. The computed microscopic properties getting closer to the experimental ones, it is interesting to wonder if they can be used to simulate macroscopic properties. These approaches, going from quantum chemical simulation to macroscopic simulation, are called multi-scale approaches and they are the subjects of numerous works in the theoretical chemists community. They are under development in various research fields such as in catalysis71,72 and in dye-sensitized solar cell73,74 In the work presented in this article, we applied this methodology to the simulation of thin film p-n junctions. From the microscopic properties point of view, the test case of CuInS 2 confirmed that the DFT methodology used gives reliable results and can be applied for simulating less characterized semiconductors. This leads to the first interesting result of this work that is the prediction of several microscopic properties of BiCuOS at the HSE06+spin orbit coupling level. As it was supposed by other groups based only on the bandgap value, we confirm by the computation of a full series of index that BiCuOS possesses all the fundamental properties needed for photovoltaic application. But the simulation of J-V characteristics, made possible by the combination of the DFT results with a code solving the semiconductor equations, predicts that the BiCuOS photovoltaic capacities are not so evident. Indeed, by testing the protocol first on CuInS2, we can conclude that the global efficiency of a solar cell based on BiCuOS will difficultly exceed 10% of efficiency. This result highlights the fact that it is difficult to determine if a semiconductor will be efficient in a photovoltaic cell only from the value of its microscopic properties and a fortiori from only its bandgap. Of course, these properties must fulfill some requirements (presented in the introduction), but this is not enough for predicting the final efficiency. Nevertheless, from a more global point of view, the conclusion is more positive. It appears that a multi-scale approach can be used to help experimentalists in the design of a full solar cell junction for instance by helping in the choice of the appropriate n-type semiconducteur or by determining the influence of some properties such as the doping concentration.


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Acknowledgment We acknowledge the IDRIS and PSMN calculation centers for providing computational resources.

Supporting Information Description The supporting information includes: the crystal structure of BiCuOS, pictures and geometries of the surfaces considered for CuInS2 and BiCuOS, results of Infra-Red calculations for CuInS2 and BiCuOS, m* computed for BiCuOS in several crystallographic directions and complementary information about the J-V modeling. This material is available free of charge via Internet at http://pubs.acs.org.



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Assessing the Use of BiCuOS for Photovoltaic Application: From DFT

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