Understanding the impact of impurities in solar absorbers is critical to engineering high-performance in devices, particularly over extended periods of time. Here, we use hybrid functional calculations to explore the role of hydrogen interstitial (Hi) defects in the electronic properties of a number of attractive solar absorbers within the chalcopyrite and kesterite families to identify how this common impurity may influence device performance. Our results identify that Hi can inhibit the highly p-type conditions desirable for several higher-band gap absorbers and that H incorporation could detrimentally affect the open-circuit voltage (Voc) and limit device efficiencies. Additionally, we find that Hi can drive the Fermi level away from the valence band edge enough to lead to n-type conductivity in a number of chalcopyrite and kesterite absorbers, particularly those containing Ag rather than Cu. We find that these effects can lead to interfacial Fermi-level pinning that can qualitatively explain the observed performance in high-Ga content CIGSe solar cells that exhibit saturation in the Voc with increasing band gap. Our results suggest that compositional grading rather than bulk alloying, such as by creating In-rich surfaces, may be a better strategy to favorably engineering improved thin-film photovoltaics with larger-band gap absorbers.
I. INTRODUCTION
Photovoltaics provide an attractive source of renewable energy by directly converting solar energy into usable electricity, yet transforming to energy in other forms is also desirable. One approach is by storing solar energy in chemical bonds, e.g., via the production of hydrogen (H2) or other fuels though catalytic reactions. Solar-driven photoelectrochemical (PEC) water splitting remains one of the most intensely studied options and may provide an economically viable route to produce H2, which could offer an attractive renewable and carbon-free replacement for fossil fuels.1 Recent studies have identified that solar-to-hydrogen conversion efficiencies exceeding 20% may be possible with PEC cells that integrate tandem stacked absorber combinations with known highly active catalysts for the hydrogen and oxygen evolution reactions.2 The lower optimal band gap identified in this study, ∼1.2 eV, favorably matches that of chalcopyrite Cu(In,Ga)Se2 (CIGSe) alloys that have already established themselves as reliable and technologically mature solar absorbers that are currently being commercially produced in thin-film modules at the gigawatt scale. Other I-III-VI2 chalcopyrites (I = Ag,Cu; III = B,Al,Ga,In; VI = S,Se) can lead to alloys that achieve the optimal top cell band gap (∼1.9 eV)2 and suggest that solar absorbers within the chalcopyrite material family may be a promising platform for realizing highly efficient PEC devices.
A largely underexplored aspect of these or other light-absorbing materials subjected to hydrogen-rich environments is how H incorporation, primarily during thin films processing under non absolute vacuum conditions, may influence the underlying material and the resulting device properties. This knowledge may also help in understanding degradation of conventional solar absorbers or photovoltaic materials that may incorporate ambient hydrogen and/or water under operation.3,4 Interstitial hydrogen (Hi) is known to be electronically active in a number of materials5,6 and may lead to unexpected changes in the electrical conductivity that must be considered for engineering long-term performance. Hydrogen is also expected to be present in typical buffer layers like CdS that are commonly deposited on solar absorbers via a chemical bath7,8 and can act as a reservoir that may exchange with the other layers. Hi may additionally interact with other defects with a variety of consequences ranging from enhanced stability of point-defect complexes to the passivation of electrically active defects.9–11 Lastly, knowledge of the electronic transition levels of Hi, , has been strongly correlated with the energies of dangling bond states in a number of semiconductors and may act as a proxy for interface states that can influence Fermi-level pinning and band offsets.6,12 Owing to all these factors, knowledge of the behavior of Hi is necessary for the design of robust electronic, photovoltaic, and PEC devices.
Here, we investigate the stability and electronic effects of Hi in the I-III-VI2 chalcopyrites using first-principles calculations based on hybrid functionals. We also consider emerging earth-abundant absorbers such as the kesterites Cu2ZnSnS4 (CZTS) and Cu2ZnSnSe4 (CZTSe), and their Ag-containing analogs, AZTS and AZTSe. We consider how likely isolated Hi is expected to incorporate into the conditions often targeted for good photovoltaic performance, namely, in highly p-type absorber materials grown in anion-rich (e.g., Cu-poor and Se- or S-rich) conditions, and identify possible Fermi-level pinning values with sufficient Hi concentrations. These Hi-induced Fermi-level pinning values are found to fall within the band gap for virtually all of the chalcopyrites studied and would expectedly limit the band-bending achievable at the heterointerface with n-type buffer layers. Exceptions include several In- and Ag-containing materials that exhibit pinning levels within the conduction band that should facilitate improved band bending in these absorbers that could beneficially impact performance. We corroborate these findings with device-level simulations on a model CIGSe solar cell and show good agreement with the device performance typically observed with increasing Ga content. Our results also identify that Hi could limit the effectiveness of several candidate larger-gap top cell absorbers by strongly inhibiting the degree of p-type conductivity that may be obtained, in addition to limiting the amount of band-bending that could be expected at the absorber-buffer heterojunction. An understanding of these effects by considering the band edge positions of the chalcopyrites and kesterites on an absolute energy scale is also discussed.
II. COMPUTATIONAL METHODS
The calculations are based on density functional theory with the Heyd-Scuseria-Ernzerhof (HSE06) screened hybrid functional13 and projector-augmented wave (PAW) approach14 as implemented in the VASP code.15 To model the Hi defects, we use supercells with a 64-atom representation of the chalcopyrite and kesterite lattices. We modify the fraction of non-local Hartree-Fock exchange for each material to match with the experimental band gaps (see Table I) and summarize the chosen mixing values and the resulting lattice constants in the supplementary material. The plane-wave expansion of Kohn-Sham states uses an energy cutoff of 400 eV for all calculations, and integrations over the Brillouin zone are sampled by 2 × 2 × 2 mesh of Monkhorst-Pack k-points and spin-polarization effects were explicitly included. All calculations with Ga and In treated their filled d-shells as core electrons, and the 3p (4p) electrons were treated within the core for Cu (Ag). Spin-orbit effects were added as a post-correction to the valence band position from the calculated spin-orbit splitting. Surface calculations were performed using the nonpolar (110) chalcopyrite slab models with 11 layers, where 2 layers on each side were allowed to relax.16 The calculated ionization potentials are included with other tabulated data in the supplementary material. Ionization potentials of the kesterite materials were not computed, as different values are expected for different surface terminations of the (110) surface. Device-level models were performed using the SCAPS simulation software using their standard CIGSe-CdS-ZnO solar cell included in version 3.3.02.17 Additional details of the calculations and device model are included in the Supporting Information.
Summary of the calculated band gaps, formation energies (Ef), Hi charge-state transition levels , and the resulting valence and conduction band offsets (VBO and CBO) relative to CISe as defined by the . To assess the likelihood that Hi could act as charge-compensating defects, the Ef of are evaluated at the VBM for the case of p-type material, while the are evaluated at the CBM for the case of n-type material. All Ef are reported in the anion-rich limit as described in the text. All values are corrected for spin-orbit effects and reported in eV.
Material . | Eg . | Ef[] . | Ef[] . | . | VBO . | CBO . |
---|---|---|---|---|---|---|
CuBS2 | 2.86 | 0.51 | 0.06 | 1.20 | –0.15 | 1.67 |
CuAlS2 | 3.34 | 0.05 | –0.38 | 1.45 | –0.40 | 1.90 |
CuGaS2 | 2.43 | 0.12 | 0.79 | 1.55 | –0.49 | 0.90 |
CuInS2 | 1.53 | –0.01 | 1.28 | 1.41 | –0.36 | 0.13 |
CuBSe2 | 2.29 | 0.84 | –0.55 | 0.45 | 0.61 | 1.85 |
CuAlSe2 | 2.65 | 0.18 | –0.23 | 1.12 | –0.07 | 1.54 |
CuGaSe2 | 1.68 | 0.34 | 0.95 | 1.15 | –0.09 | 0.55 |
CuInSe2 | 1.04 | 0.27 | 1.34 | 1.05 | 0.00 | 0.00 |
AgAlS2 | 3.18 | –0.62 | 0.35 | 2.08 | –1.03 | 1.12 |
AgGaS2 | 2.65 | –0.62 | 1.04 | 2.16 | –1.10 | 0.51 |
AgInS2 | 1.88 | –0.65 | 1.41 | 1.97 | –0.92 | –0.08 |
AgAlSe2 | 2.55 | –0.33 | 0.45 | 1.66 | –0.61 | 0.90 |
AgGaSe2 | 1.81 | –0.21 | 1.05 | 1.54 | –0.49 | 0.29 |
AgInSe2 | 1.25 | –0.23 | 1.49 | 1.48 | –0.43 | –0.23 |
Cu2ZnSnS4 | 1.49 | 0.24 | 1.09 | 1.17 | –0.12 | 0.33 |
Cu2ZnSnSe4 | 1.00 | 0.34 | 1.18 | 0.92 | 0.13 | 0.09 |
Ag2ZnSnS4 | 2.01 | –0.54 | 1.17 | 1.86 | –0.81 | 0.16 |
Ag2ZnSnSe4 | 1.34 | –0.15 | 1.22 | 1.35 | –0.30 | 0.00 |
CdS (wz) | 2.54 | –0.82 | 1.50 | 2.43 | –1.38 | 0.12 |
CdS (zb) | 2.45 | –0.69 | 1.51 | 2.33 | –1.28 | 0.13 |
ZnO (wz) | 3.46 | –1.02 | 3.28 | 3.88 | –2.82 | –0.41 |
Material . | Eg . | Ef[] . | Ef[] . | . | VBO . | CBO . |
---|---|---|---|---|---|---|
CuBS2 | 2.86 | 0.51 | 0.06 | 1.20 | –0.15 | 1.67 |
CuAlS2 | 3.34 | 0.05 | –0.38 | 1.45 | –0.40 | 1.90 |
CuGaS2 | 2.43 | 0.12 | 0.79 | 1.55 | –0.49 | 0.90 |
CuInS2 | 1.53 | –0.01 | 1.28 | 1.41 | –0.36 | 0.13 |
CuBSe2 | 2.29 | 0.84 | –0.55 | 0.45 | 0.61 | 1.85 |
CuAlSe2 | 2.65 | 0.18 | –0.23 | 1.12 | –0.07 | 1.54 |
CuGaSe2 | 1.68 | 0.34 | 0.95 | 1.15 | –0.09 | 0.55 |
CuInSe2 | 1.04 | 0.27 | 1.34 | 1.05 | 0.00 | 0.00 |
AgAlS2 | 3.18 | –0.62 | 0.35 | 2.08 | –1.03 | 1.12 |
AgGaS2 | 2.65 | –0.62 | 1.04 | 2.16 | –1.10 | 0.51 |
AgInS2 | 1.88 | –0.65 | 1.41 | 1.97 | –0.92 | –0.08 |
AgAlSe2 | 2.55 | –0.33 | 0.45 | 1.66 | –0.61 | 0.90 |
AgGaSe2 | 1.81 | –0.21 | 1.05 | 1.54 | –0.49 | 0.29 |
AgInSe2 | 1.25 | –0.23 | 1.49 | 1.48 | –0.43 | –0.23 |
Cu2ZnSnS4 | 1.49 | 0.24 | 1.09 | 1.17 | –0.12 | 0.33 |
Cu2ZnSnSe4 | 1.00 | 0.34 | 1.18 | 0.92 | 0.13 | 0.09 |
Ag2ZnSnS4 | 2.01 | –0.54 | 1.17 | 1.86 | –0.81 | 0.16 |
Ag2ZnSnSe4 | 1.34 | –0.15 | 1.22 | 1.35 | –0.30 | 0.00 |
CdS (wz) | 2.54 | –0.82 | 1.50 | 2.43 | –1.38 | 0.12 |
CdS (zb) | 2.45 | –0.69 | 1.51 | 2.33 | –1.28 | 0.13 |
ZnO (wz) | 3.46 | –1.02 | 3.28 | 3.88 | –2.82 | –0.41 |
To assess the stability and electronic behavior of the Hi, we calculate their defect formation energies (Ef) to determine the relative equilibrium concentrations and favorability of different charge states (q) for different conditions.18 For example, the formation energy of Hi in CuInSe2 (CISe) is given by
where represents the total energy of the CISe supercell containing the Hi defect in charge state q, and that of a CISe bulk crystal in the same supercell. We report all formation energies assuming a chemical potential for Hi (μH) that is referenced to the 0 K electronic energy per hydrogen atom of the H2 molecule. In principle, μH may also be limited by the formation of H2Se and H2S molecules, e.g., via the relationship for the case of H2S, where the free energy is equivalent to the formation enthalpy at 0 K. Our for H2Se is 0.15 eV calculated with the standard HSE06 values, indicating no dependence of μH on , while the value of –0.32 eV for H2S would lead to an additional contribution of –0.16 eV to μH in sulfide compounds grown in the S-rich limit. These values compare well with experimental values (0.31 eV and –0.21 eV, respectively)19 and identify that the chemical potential of H should weakly depend on the growth conditions in the selenides but have stronger dependence in the sulfides, particularly in the limit of anion-rich (Cu- or Ag-poor) growth conditions. Because of this additional dependence and that anion-rich conditions generally yield better-performing material,20,21 we report all Ef in the limit of anion-rich conditions. The electrons are exchanged with a reservoir whose chemical potential is the Fermi level ϵF, which we reference to the energy of the valence-band maximum (VBM) of each material. The ϵF at which one charge state becomes more or less favorable than another defines the thermodynamic charge-state transition levels (ϵ). A correction of 0.1 eV was added to the formation energies of both the and singly charged defects to account for the finite-size effects and the periodic defect-defect interactions based on the corrections obtained for these defects in CISe assuming an effective dielectric constant of 12.18 This assumption may lead to errors on the order of 0.1–0.2 eV for the defect formation energies in the other materials, but the error is expected to be much smaller (<0.1 eV) for the reported thermodynamic charge-state transition levels. Equilibrium defect concentrations for the Hi (n) can be derived from a Boltzmann-like expression
where N is a site density, T is the temperature, and kB is Boltzmann's constant.
III. RESULTS AND DISCUSSION
In Fig. 1, we include a typical plot of the formation energy of Hi defects in CISe and CGSe as a function of the ϵF, which is varied from the VBM to the conduction band minimum (CBM) for each material. In typical thin-film photovoltaics adopting CISe, CGSe, and CIGSe absorbers, the best performance for conventional device designs results from a highly p-type material that is interfaced with a series of n-type layers that help extract the photo-generated carriers [see Fig. 2(a) for a schematic band diagram of a typical thin-film solar cell]. This means that the region of interest is for Fermi levels in the close vicinity of the VBM, where we find that Hi is most favorable as a shallow donor for both materials, with quite low formation energies of ∼0.2–0.3 eV (see Table I). These values correspond to equilibrium bulk defect concentrations on the order of 1017 cm–3 at room temperature assuming a possible site density of one H per formula unit. While this estimated concentration is likely less than the dominant acceptor concentrations like grown in Cu-poor/Se-rich growth conditions and higher temperatures,21 the concentration of Hi may be significant enough to act as compensating donors that shift the Fermi level away from the VBM in certain growth conditions (e.g., Cu-rich or lower growth temperatures) in which native defect concentrations or other impurities are suppressed to comparable or lower relative amounts.20,21 We note that these estimates are for equilibrium bulk defect concentrations, and growth processes that probe more non-equilibrium conditions may also lead to different bulk, surface, and/or interfacial defect populations.
Formation energies of Hi defects in (a) CuInSe2 and (b) CuGaSe2. Only the lowest energy charge states are included; Hi acts exclusively as a shallow donor in CISe but is amphoteric in CGSe, having a transition level at 1.15 eV above the VBM (∼0.5 eV below the CBM). Schematic representations of the and configurations are included in (c)–(e) as described in the text. Group I atoms are blue, Group VI atoms are orange, and Group III are green.
Formation energies of Hi defects in (a) CuInSe2 and (b) CuGaSe2. Only the lowest energy charge states are included; Hi acts exclusively as a shallow donor in CISe but is amphoteric in CGSe, having a transition level at 1.15 eV above the VBM (∼0.5 eV below the CBM). Schematic representations of the and configurations are included in (c)–(e) as described in the text. Group I atoms are blue, Group VI atoms are orange, and Group III are green.
(a) Schematic band diagram with band-bending partially mediated by Fermi-pinning defects at the absorber-buffer interface in a typical low-Ga CIGSe thin-film solar cell. The green box highlights the interfacial region which we confine the amphoteric Hi defects in the device model. The blue (red) lines are the quasi-Fermi levels of electrons (holes) under illumination at open-circuit conditions. (b) The simulated open-circuit voltage (Voc) of the model device in (a) plotted as a function of the absorber band gap (Ga-content in the CIGSe). The rollover in Voc is shown for a range of interfacial defect concentrations that correspond to different values of the interfacial recombination velocity (Si), whereas no interfacial recombination results in a linear increase in Voc with the band gap.
(a) Schematic band diagram with band-bending partially mediated by Fermi-pinning defects at the absorber-buffer interface in a typical low-Ga CIGSe thin-film solar cell. The green box highlights the interfacial region which we confine the amphoteric Hi defects in the device model. The blue (red) lines are the quasi-Fermi levels of electrons (holes) under illumination at open-circuit conditions. (b) The simulated open-circuit voltage (Voc) of the model device in (a) plotted as a function of the absorber band gap (Ga-content in the CIGSe). The rollover in Voc is shown for a range of interfacial defect concentrations that correspond to different values of the interfacial recombination velocity (Si), whereas no interfacial recombination results in a linear increase in Voc with the band gap.
Interestingly, we find that Hi acts exclusively as a donor in CISe, consistent with experimental observations of hydrogen-treated single crystals and the behavior of muonium in CISe,22,23 but in contrast to previous theoretical studies within the local density approximation.24 Similar to results in Ref. 24, our results indicate that prefers a bond-center position between the Cu-Se bond [Fig. 1(c)] and occupies a tetrahedral interstitial position bonded to neighboring In [Fig. 1(e)]. We find the neutral charge state is unstable for all Fermi levels and find this to be a general trend among the chalcopyrite and kesterite materials considered, i.e., Hi is a negative-U center that is only stable in electrically active donor or acceptor configurations analogous to those seen in Fig. 1. Our calculated Hi transition level is found to be 0.01 eV above the CBM in CISe, rather than within the band gap. This indicates that the incorporation of Hi will tend to drive CISe n-type, and that Hi incorporation can even drive Cu-depletion either directly via charge compensation with or indirectly by creating surface band-bending that drives the electromigration of Cui away from (or toward) the surface.22 This may further facilitate doping or chemical modification of the interface upon deposition of an n-type buffer layer like CdS, where CdCu shallow donors can favorably incorporate at vacant Cu sites,25,26 shifting the space-charge region deeper into the absorber and away from the absorber-buffer interface. The subsequent interaction of Hi with other defects to form defect complexes is also highly relevant to the long-term dynamics of H incorporation and depends sensitively on the chemical potentials of other defect constituents but will not be considered further in this publication.
Turning to CGSe, we find that Hi exhibits an within the band gap, 1.15 eV above the VBM. These results confirm that Hi acts an amphoteric impurity that can preferentially adopt either donor or acceptor configurations depending on the Fermi level. Therefore in typical low-Ga (∼20%) content CIGSe alloys, the Hi is expected to be very close to the CBM, but for higher Ga-content alloys it drops into the band gap as the electron affinity decreases with Ga content.7,21,27,28 With sufficient concentration, the Hi would pin the Fermi level within the band gap and limit the magnitude of the band bending at the heterointerface with the n-type buffer layer. The reduction in interfacial band-bending would also likely reduce the Cu depletion at the surface/interface as compared to CISe and Ga-poor CIGSe, owing both to a decrease in the electromigration of Cu from the surface and charge-compensation by defects in addition to or other acceptors. This would presumably adversely affect the extent of substitutional donor incorporation (e.g., ) on the vacant Cu sites upon deposition of the n-type buffer or contact layers.
To quantify these effects, we include device-level simulations of a CIGSe-CdS-ZnO thin-film solar cell in Fig. 2, where we summarize the calculated open-circuit voltage (Voc) obtained as a function of the absorber band gap. In these simulations, we model the increase in the absorber band gap with an equal decrease in the electron affinity as expected with higher Ga-incorporation in CIGSe and provide additional details of the model in the supplementary material.7 The effects of the Hi are included as an interfacial amphoteric defect density at the absorber-buffer interface with a level 1.2 eV above the absorber VBM. We also consider an equivalent amphoteric defect density at the buffer-TCO interface as highlighted in Fig. 2(a), using Fermi-pinning values associated with the Hi as reported previously for CdS and ZnO and included in Table I.7,29 The relevant property characterizing the interfacial defects is the surface recombination velocity (Si), which is the interfacial defect density divided by their capture cross section for a particular carrier type. Since we do not know explicit values for these quantities, we assume an equivalent surface recombination velocity for holes and electrons and consider a range of values for Si from 102 to 105 cm/s.
We find that in the absence of the interfacial defects, the simple CIGSe solar cell model shows a linear increase in the Voc with the band gap, as expected for recombination limited in the absorber bulk or space-charge regions.30 When the interfacial amphoteric defects are included, the exhibits a clear rollover and saturation owing to the Fermi-level pinning resulting from these defects. While the quantitative details of this rollover are sensitive to the specific values of the pinning levels and the Si as evident in Fig. 2(b) and the supplementary material, the qualitative features are robust to the exact values chosen. The conclusions are also independent of other relevant material parameters in the device model, such as whether the CIGSe-CdS conduction band offset is a small spike like in Fig. 2(a), flat, or a small cliff, which we also include in the supplementary material.31 This rollover in the open-circuit voltage has been widely observed with increasing Ga content in CIGSe-based photovoltaics28,32 and supports that Hi defects or possibly unpassivated interfacial dangling-bond states likely contribute to this phenomenon along with other interfacial defects that may be present, such as GaCu and InCu at the absorber-buffer interface.20,21,33
Next we consider the behavior of Hi in a number of other I-III-VI2 chalcopyrites that are summarized in Table I. We first focus on the formation energies of in p-type conditions for each material, as this is the desired state for the absorber layer in a conventional thin-film photovoltaic device architecture. Our results identify several key features, namely, (1) can be readily incorporated into these conditions for a number of the materials, and (2) many of the transition levels fall deep within the band gap rather than near the valence or conduction band edges. As discussed previously, the latter point could lead to the Fermi-level pinning away from the band edges that would inhibit the theoretically achievable band-bending and type-inversion at the absorber-buffer heterointerface.
With regard to Hi incorporation, we find that the Cu-III-S2 (III = Al,In,Ga) exhibit lower formation energies than their selenide counterparts and all the Ag-containing compounds in Table I are found to have negative formation energies for defects in p-type conditions. The latter result represents an unphysical situation that must be thermodynamically prohibited, indicating a strong driving force to inhibiting the p-type material in these compounds in the presence of a H-containing environment. This would indicate that the minimum Fermi level achievable in these systems would be when the Ef[] > 0, which corresponds to 0.65 eV above the VBM for the example of AgInS2 based on the 0 K equilibrium bulk formation energies in Table I for the least-favorable limit of anion-rich conditions. This indicates that incorporation may severely impact the p-type dopability in the Cu-III-S2 (III = Al,In,Ga) compounds in certain growth conditions and may fundamentally limit the prospects of achieving a robust p-type material in the Ag-containing materials.
Considering the positions of the Hi levels, we find that they fall within the band gap for all the materials studied apart from CISe, AIS, AISe, CZTSe, and AZTSe. In these exceptions, the transition levels fall at or above the CBM, indicating that Hi defects act exclusively as shallow donors and that these materials should show n-type conductivity upon sufficient hydrogenation, as observed for CISe.22 As with CISe, this is likely beneficial for achieving maximal band-bending at the heterojunction with an n-type buffer in conventional thin-film photovoltaics and improving the carrier collection efficiency in the solar cell. The closer proximity of the Hi to the CBM in CIS compared to CGSe would suggest that CISSe alloys are a potentially more promising route for higher-band gap absorber alloys less likely to suffer from saturation in Voc with increasing band gap as shown in Fig. 2(b), although their band gaps are still too small for optimal tandem partners to CIGSe.2 More importantly, the results suggest that compositional grading rather than bulk alloying may be a more effective route to identifying larger band gap absorbers that exhibit favorable Fermi-level pinning characteristics at the absorber-buffer heterointerface, i.e., by creating more In-rich layers near the absorber-buffer interface.34 Grading or creating In-rich layers could preserve the large band gaps in the absorber bulk but ensure that any Fermi-level pinning at the absorber-buffer interface advantageously affects the device as discussed for CISe-CdS heterojunctions. Ag-rich surfaces would also be promising based on the data in Table I, but the stability of such surface/interfaces is questionable since the group-I atoms are far more mobile than the group-III atoms and group-I poor surfaces are desirable from the standpoint of intermixing with the buffer. Nonetheless, this approach has been recently pursued in CZTS-based devices and found to yield improved performance and suggests future promise.35
This information can be visualized in Fig. 3(a), where we align the conduction and valence bands of the chalcopyrites according to the position of their calculated ionization potentials for the (110) surface and include the positions of the Hi . The results in Fig. 3 identify that the origins for the difficulty in obtaining the p-type material for the Ag-containing compounds can at least partially be attributed to the low overall position of their valence bands on an absolute energy scale, particularly relative to those containing Cu. This stems from the fact that the valence bands in these materials are heavily comprised of group I d-orbitals (Cu 3d and Ag 4d states) that strongly hybridize with the anion p-orbitals. Additionally, the incorporation of In tends to push the conduction bands down on an absolute energy scale, resulting in an increased tendency for defect or impurity levels to act as shallow donors, as observed for Hi. Figure 3(a) also shows that the calculated do not align with the standard hydrogen electrode (SHE) potential 4.44 eV below the vacuum level for aqueous solutions.6,36–38 For the chalcopyrites, we find the level is 4.74 ± 0.14 eV relative to the vacuum level, which falls between the SHE potential and the “Fermi-stabilization energy” ∼4.9 eV below the vacuum level that has been discussed by Walukiewicz in the context of the charge-neutrality level.39,40
(a) Band edges of studied chalcopyrite materials aligned via the ionization potential of the (110) surfaces, also including the calculated Hi levels. The dashed red line indicates the SHE electrode potential –4.44 eV below the vacuum level. The alignment of all the materials band edges via their calculated Hi levels is in (b), which is set to 0.
(a) Band edges of studied chalcopyrite materials aligned via the ionization potential of the (110) surfaces, also including the calculated Hi levels. The dashed red line indicates the SHE electrode potential –4.44 eV below the vacuum level. The alignment of all the materials band edges via their calculated Hi levels is in (b), which is set to 0.
Alternatively, we include an alignment of the chalcopyrites via the calculated Hi in Fig. 3(b). We also summarize the valence band and conduction band offsets obtained via this alignment procedure in Table I, using the CISe band edge positions as a reference. These results are in good agreement with other predicted offsets calculated using a superlattice approach.27,41 The results also include values obtained for CdS and ZnO typically used as buffer and contact layers that can be used as inputs for interfacial pinning levels in device-level models. We note that these offsets can differ significantly from those identified from transitivity of ionization potentials, but point out that alignments based solely on surfaces do not capture the effects of interfacial dipoles that can drastically influence experimentally observed band offsets.42 While explicit band-offset calculations are the most direct route to simulating these effects, alignments based on the Hi or another metric of the charge-neutrality level provide a better representation of these effects than purely surface-based models.6,43
IV. CONCLUSIONS
In summary, we report on the energetics and electronic behavior of Hi impurities in a series of Cu and Ag-based chalcopyrite and kesterite solar absorbers. Our results suggest that these defects can fundamentally limit p-type dopability in Ag-containing and Cu-III-S2 (III = Al,Ga,In) absorber candidates, which we explain in terms of the lower positions of the valence bands of these materials on an absolute energy scale. Additionally Hi defects may lead to the Fermi-level pinning within the absorber or at the absorber-buffer interface that can strongly influence device performance depending on the location of this level relative to the absorber band edges. Our results show that these effects can beneficially affect low-Ga CIGSe-based photovoltaics and contribute to the open-circuit voltage deficits observed in higher Ga-content absorbers. These findings suggest the importance of tailoring the composition in larger band gap absorbers near the absorber-buffer interface, with In-rich surfaces suggested to be more robust to detrimental Fermi-level pinning that could limit performance metrics such as the open-circuit voltage.
V. SUPPLEMENTARY MATERIAL
See supplementary material for additional details of the calculations and device-level simulations.
ACKNOWLEDGMENTS
This project was supported by the U.S. Department of Energy, Office of Energy Efficiency and Renewable Energy, Fuel Cell Technologies Office. This work was performed under the auspices of the U.S. Department of Energy at Lawrence Livermore National Laboratory under Contract No. DE-AC52-07NA27344 and the University of Hawaii under Contract No. DE-EE0006670. The authors gratefully acknowledge research support from the HydroGEN Advanced Water Splitting Materials Consortium, established as part of the Energy Materials Network under the U.S. Department of Energy, Office of Energy Efficiency and Renewable Energy, Fuel Cell Technologies Office.
Note: The views and opinions of the authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, expressed or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights.