Advancing optoelectronic and emerging technologies increasingly requires control and design of interfaces between dissimilar materials. However, incommensurate interfaces are notoriously defective and rarely benefit from first-principles predictions, because no explicit atomic-structure models exist. Here, we adopt a bulk crystal structure prediction method to the interface geometry and apply it to SnO2/CdTe heterojunctions without and with the addition of CdCl2, a ubiquitous and beneficial, but abstruse processing step in CdTe photovoltaics. Whereas the direct SnO2/CdTe interface is highly defective, we discover a unique two-dimensional CdCl2 interphase, unrelated to the respective bulk structure. It facilitates a seamless transition from the rutile to zincblende lattices and removes defect-states from the interface bandgap. Implementing the predicted interface electronic structure in device simulations, we demonstrate the theoretical feasibility of bufferless oxide-CdTe heterojunction solar cells approaching the Shockley–Queisser limit. Our results highlight the broader potential of designing atomically thin interlayers to enable defect-free incommensurate interfaces.
I. INTRODUCTION
Once coined a “scandal,”1 the difficulty to predict crystal structures from first principles has been largely overcome in the recent decades,2,3 at least in so far as periodic crystals with relatively small primitive cells are concerned where structure sampling can be performed on the basis of total energy calculations within density functional theory (DFT). Crystal structure prediction has been extended to two-dimensional (2D) materials,4,5 molecular crystals,6 and other systems beyond bulk crystals.2 However, the prediction of general interface structures remains challenging. At the same time, this problem is of high importance because explicit atomic structure models are prerequisite for first-principles predictions of interface properties.
The complexity of 2D interface structures can fall into different categories. In the simplest case, an epitaxial commensurate interface is formed between two isostructural materials with reasonably matched lattice parameters. Perhaps the most prominent examples are wurtzite–wurtzite interfaces in group 13 nitride quantum well heterostructures7 and perovskite–perovskite interfaces forming a 2D electron gas.8 Such interfaces can be readily constructed, since the crystal structure itself is not disrupted and only the atomic decoration of the lattice sites changes across the heterostructure.9–13 In more general situations, the challenge to construct an atomistic interface model is more daunting. In systems that are amenable to characterization by transmission electron microscopy (TEM), experiment can often provide, if not the precise location of all individual atoms, then at least sufficient information to narrow down the possibilities to enable the construction of likely structure models. For example, such experimental data have greatly facilitated computations for dislocations at CdTe grain boundaries14 and for surface reconstructions in Heusler compounds.15 However, for incommensurate interfaces with an ambiguous atomic registry, explicit structure models rarely exist.
In situations where two materials assume different crystal structures and stoichiometries, a common approach for the construction of an interface model can be described as “free-surface joint” (FSJ), i.e., the merging of two (possibly reconstructed) low-energy free surfaces.16,17 To utilize periodic boundary conditions, coincidence site lattices (CSL)18 are constructed, i.e., 2D supercells that can accommodate both surface unit cells within acceptable limits of strain. Remaining translational degrees of freedom parallel to the interface can be evaluated by local geometry relaxation from different starting configurations. More general approaches perform additional structure sampling in the interface region, utilizing random sampling,19 evolutionary approaches,20,21 or particle swarm optimization.22 Despite these developments, most explicit interface atomic structure models have so far been obtained by a judicious construction, and relatively few examples exist in which interface atomic structures have been determined entirely on the basis of a first-principles structure search.
CdTe-based photovoltaics (PV) is currently the only gigawatt-scale thin-film photovoltaics technology, and it could play an increasing role in the energy transition due to its potential for better scaling than the capital-intensive crystalline silicon technology.23 The heterostructural (rutile-zincblende) interface with SnO2 was chosen as subject of the present work based on interest of First Solar, a leading solar manufacturer in thin-film photovoltaics. In CdTe photovoltaics, CdCl2 treatment is necessary for enabling high efficiency devices based on polycrystalline CdTe.24,25 A pronounced accumulation of Cl and simultaneous reduction of Te occurs at a length scale of about 1 nm, both at grain boundaries26 and interfaces of CdTe with the traditional CdS buffer.27 Previous computational studies have mostly concerned the role of Cl as a point defect, i.e., substitutional ClTe and interstitial Cli defects being located either in the bulk28 or at previously established grain boundary26,29 or interface30 structures. These configurations are, however, not charge-balanced and are therefore expected to occur only in more dilute, dopant-like concentrations. The importance of going beyond the point defect picture and considering 2D interlayers is increasingly being recognized.31 However, to our knowledge, there are currently no explicit atomic structure models available for chloride-mediated interfaces or grain boundaries of CdTe that would go beyond the decoration of pre-existing structures with substitutional or interstitial Cl species. To address this knowledge gap, we here include a variable number of (charge-balanced) CdCl2 formula units (fu) in the structure search (see Fig. 1). Using the most stable atomic structure configurations for the direct and the CdCl2 mediated interfaces, we perform bandgap corrected electronic structure calculations to obtain the interfacial density of states (IFDOS). The predicted interface properties are then implemented in device modeling to assess the solar cell characteristics for direct and CdCl2 treated SnO2/CdTe heterojunctions.
II. RESULTS
A. Interface structure predictions
For bulk crystal structure prediction, we have recently successfully employed the kinetically limited minimization (KLM) for materials discovery studies in ternary nitrides and oxynitrides.32,33 This approach utilizes a combination of unbiased random sampling and sequential atomic perturbations akin to the basin hopping method. In addition to performing a ground state search, it is also well suited to catalogue metastable structures, and a key aspect of the approach is the enforcement of minimum interatomic distances (see Table S1 for specific values used here), which is essential to reduce the vast configurational sampling space.32 After each perturbation, the structure is relaxed to the nearest local minimum, and the resulting total energy is used in a Monte Carlo (MC) like acceptance/rejection criterion. In adopting the KLM approach to interfaces, we utilize a slab geometry with a substrate layer, which is not subject to displacements, and a sampling layer for the prediction of the atomic structure of a thin film, as shown in Fig. 1.
In principle, interface structure prediction can be performed in one of two ways: one option is to define from the outset the crystal structures of the materials on either side of the interface and their relative orientation. This choice reduces the number of atoms to be sampled in the interface region but requires a separate loop over the translational degrees of freedom parallel to the interface. The second option, taken here, is to define only the crystal structure and surface orientation of the substrate and proceed by sampling all atoms of the film. (We additionally tested the inclusion of near-surface substrate atoms in the sampling, but this did not result in energy gains.) In this case, the interface, the bulk crystal structure of the film, its orientation, and the back-surface of the film are to be predicted simultaneously. We note that this latter mode is also suited for predictive synthesis, especially the discovery of interface-defined structures in the early stages of thin-film growth, and that our approach—with minor modifications—can be also be applied in the former mode.
As the substrate, we use the stoichiometric (110)r surface of rutile (r) SnO2, which is the most stable one except under strongly reducing conditions.36,37 To accommodate the incommensurate interface between rutile SnO2 and zincblende (zb) CdTe, within an acceptable measure of strain, we chose a rectangular 2 × 2 supercell of the (110)r primitive surface cell with dimensions of 6.42 Å × 13.43 Å (slab area 86.2 Å2), corresponding to the unstrained SnO2 lattice. This cell defines the CSL between the rutile and zincblende phases. The longer vector accommodates 2 × with +3.1% and 3 × with −2.7% strain. The shorter one approximates with −1.4% strain. This lattice matching ensures that both the (110)zb and the (001)zb orientations of the CdTe film on the SnO2 substrate can be realized over the course of the sampling. Both interfaces are incommensurate in the sense that there is no 1:1 matching of the surface primitive cells, but the CSL is instead obtained by the matching of surface-supercells, where CdTe is coherently strained to SnO2.
The evolution of the interface structures is quantitatively evaluated by the total film sheet energy
where is the total energy of the entire simulation cell and is the sum of the bulk energies for respective numbers of fu of SnO2, CdTe, and CdCl2 contained in the cell. The energy of the SnO2 front-surface is also subtracted so that only area-normalized interface, strain, and back-surface energies of the film remain. More details on computational methods, including DFT and electronic structure calculations, as well as the structure prediction approach are given in Sec. IV.
For the direct SnO2/CdTe interface without CdCl2 addition, the sampling includes optimizations with 8–18 fu of CdTe in the simulation cell, with five independent seed structures in each case. The results of the interface structure sampling are shown in Fig. 1. The structure with the lowest energy is found for 14 fu and again for 17 fu with an additional Cd–Te monolayer. It has a (110)zb orientation relative to the substrate and exhibits the well-known CdTe surface structure10 for this orientation at the back-surface. The independent recurrence of the same structure for different CdTe film thicknesses [Fig. 1(c)] suggests that the structure search is converged within the film thickness range considered, and the fact that both the known crystal and (110) surface structures of CdTe are reproduced without prior assumptions (other than the CSL) inspires confidence in the approach and in the predicted interface structure. To obtain well-converged electrostatic potentials for the electronic structure analysis below, we extended the interface structures by insertion of additional atomic layers in the bulk-like region on either side of the interface. These extended slab models are shown in Fig. 2. With the fully formed CdTe back-surface, we can also determine absolute interface energies from by further subtracting the CdTe strain and back-surface energies. Table I summarizes the surface and interface energetics for all structures involved in the data analysis, using the extended structure models.
Surfaces . | (eV) . | (meV/fu) . | (eV/nm2) . | EA (eV) . |
---|---|---|---|---|
SnO2(110)r | 3.33 | 8.78 | 5.72 | |
CdTe(110)zb | 1.69 | 1.63 | 4.32 | |
CdTe(001)zb | 2.07 | 4.12 | ||
CdTe(110)zb str | 1.55 | 15.9 | 1.69 | 4.43 |
CdTe(001)zb str | 1.58 | 2.6 | 2.07 | 4.08 |
Interfaces | Structure | (eV/nm2) | ||
SnO2(110)r/CdTe(110)zb | FSJ | 8.29 | ||
SnO2(110)r/CdTe(001)zb | FSJ | 8.48 | ||
SnO2(110)r/CdTe(110)zb | KLM | 7.59 | ||
SnO2(110)r/CdCl2/CdTe(001)zb | KLM | 5.06 |
Surfaces . | (eV) . | (meV/fu) . | (eV/nm2) . | EA (eV) . |
---|---|---|---|---|
SnO2(110)r | 3.33 | 8.78 | 5.72 | |
CdTe(110)zb | 1.69 | 1.63 | 4.32 | |
CdTe(001)zb | 2.07 | 4.12 | ||
CdTe(110)zb str | 1.55 | 15.9 | 1.69 | 4.43 |
CdTe(001)zb str | 1.58 | 2.6 | 2.07 | 4.08 |
Interfaces | Structure | (eV/nm2) | ||
SnO2(110)r/CdTe(110)zb | FSJ | 8.29 | ||
SnO2(110)r/CdTe(001)zb | FSJ | 8.48 | ||
SnO2(110)r/CdTe(110)zb | KLM | 7.59 | ||
SnO2(110)r/CdCl2/CdTe(001)zb | KLM | 5.06 |
As seen in Fig. 2(a), the minimum energy structure of the direct SnO2/CdTe interface is structurally defective and occurs at a non-integer number of atomic layers, where the first Cd–Te layer that connects the CdTe crystal to SnO2 contains only 2 fu instead of 3 fu for subsequent bulk-like layers. The prediction of such a fractional atomic-layer raises the question how the respective interface energy compares to the construction of a free-surface-joint (FSJ). To address this question, we performed relaxations for pre-formed (110)zb and (001)zb slabs attached to the (110) SnO2 surface with 25 lateral displacements in each case for initial atomic configurations. The resulting minimum energy FSJ configurations, shown in Figs. 2(b) and 2(c), respectively, are significantly less stable than the structure obtained from KLM sampling (cf. Table I) and exhibit fewer bonds with the SnO2 substrate.
Following the hypothesis that CdCl2 accumulates at interfaces to accommodate the lattice mismatch and to minimize the interface energy, we performed structure searches including a CdCl2 interlayer [Fig. 1(b)]. The sampling includes a range between 4 and 13 fu of CdCl2, again with five independent initial seeds in each case (the nominal sheet density of a bulk CdCl2 monolayer corresponds to about 6–7 fu of CdCl2). Here, the CdTe thickness is held at 12 fu of CdTe, which can accommodate integer Cd–Te atomic layers in both the (110)zb and (001)zb orientations with 3 and 4 fu of CdTe per layer, respectively. For the case of 6 fu CdCl2, we obtain a low-energy structure which is independently confirmed in three different sampling runs [see Fig. 1(d)]. Figure 2(d) shows the corresponding extended slab model. This 2D periodic CdCl2 interlayer structure has a sheet density of 7.0 fu of CdCl2 per nm2 and strongly improves the bond connectivity across the interface. The presence of the CdCl2 interlayer also changes the orientation of the zb lattice from (110) in Fig. 2(a) to (001) in Fig. 2(d). The CdTe (001)zb back-surface structure and its reconstruction for this orientation is again a first-principles result found by KLM optimization. It agrees with established models in which the stable (001) surface under stoichiometric conditions is terminated by one-half Cd monolayer.38,39 By itself, the CdTe (001) surface has a slightly higher energy than the (110) surface (cf. Table I) but is still a low-energy surface orientation.
B. Interface electronic structure
One key motivation for creating explicit atomic structure models for interfaces is the possibility to perform first-principles electronic structure calculations. To describe the interface electronic structure, we employ the bandgap corrected single-shot hybrid functional with onsite potentials (SSH + V) approach.40 Figures 3(a) and 3(b) show band alignments and interfacial DOS (IFDOS), respectively, obtained from the SSH + V calculation on the extended slab models [cf. Figs. 2(a) and 2(d)]. To account for the electronic structure of the interface in device modeling (see below), we defined a 1 nm thick interface layer, approximately spanning the range of interfacial potential perturbations [see Fig. 3(a)], and with band alignments determined from the IFDOS shown in Fig. 3(b). The direct interface without CdCl2 shows a reduction of the CdTe bandgap by as much as 0.89 eV, reflecting the presence of interface states due to the defective interface atomic structure. In contrast, the interface with CdCl2 interlayer exhibits a strikingly improved electronic structure with a complete absence of defect states inside the bandgap of CdTe [cf. Fig. 3(b)]. The calculated interface DOS is approximated with an effective mass model to facilitate the implementation of the “effective density of states,” for electrons and and for holes, in device modeling ( = 0.19 m0 and = 3.5 m0 without CdCl2; = 0.12 m0 and = 1.7 m0 with CdCl2; m0 is the rest mass of the free electron). The direct SnO2/CdTe interface exhibits an overall cliff-like conduction band alignment, whereas the CdCl2 treated interface creates a small spike. The direct interface also develops a polarization charge with a corresponding electric field discontinuity of = 0.09 eV/nm [cf. Fig. 3(a)]. No polarization charge is observed for the interface with CdCl2 interlayer.
C. Impact of electronic structure in device modeling
Traditional CdTe device structures use a CdS buffer between the absorber and the transparent front contact. Recent efforts aim to avoid absorption losses due to CdS ( = 2.4 eV) by utilizing wide-gap oxides as window material.41 Here, we assume a 100 nm thick semiconducting SnO2 layer serving as the n-type heterojunction partner, which is separate from the transparent conducting oxide front contact. To assess the impact of the predicted interface electronic structures without and with CdCl2 interlayer on solar cell performance, we implement the predicted electronic structure properties in a device model (see Sec. IV C for method details and Table S2 for model parameters). To uncover limitations imposed by the interface, we assume a somewhat idealized, yet not unrealistic bulk lifetime of τ = 1000 ns. Similar lifetimes have been achieved in single-crystalline CdTe42 and poly-crystalline CdSeTe alloys.43 Otherwise, our device modeling parameters for SnO2 and CdTe follow Ref. 44. We note that Se alloying considerably improves CdTe bulk properties with only a minor reduction of the bandgap energy by less than 0.1 eV,45 while maintaining the zincblende structure. We expect that our first-principles predictions are largely transferable to CdSeTe alloys as well.
Due to the dearth of 2D electronic structure predictions, interface properties beyond the band offsets are most often accounted for in a simplified fashion via an effective recombination velocity parameter S in device modeling.44 To utilize the first-principles predicted interface DOS in our device model, we here instead define a 1 nm thin layer between SnO2 and CdTe with conduction and valence band offsets as shown in Fig. 3(a), in a similar approach as used in Ref. 11 for commensurate (zb-zb) Cu2ZnSnS4/CdS interfaces. This approach accounts for the fact that interfaces can create 2D electronic structures akin to surface band structures37 rather than sharp defect states. and in the interface layer are obtained from the electronic structure calculations in Sec. II B (see also Table S2). In addition to their intrinsic properties, interfaces often attract additional defects, such as impurities and dislocations, to promote strain relaxation. While occurring on a length scale beyond our simulation cell, we account for these effects by reducing carrier lifetimes in the interface layer to = 1 ns and mobilities to = 1 cm2 V−1 s−1 (compared to 100 cm2 V−1 s−1 for CdTe bulk). Furthermore, the electric field discontinuity arising from the polarization charge in the case of the direct SnO2/CdTe interface [cf. Fig. 3(a)] is modeled with a dipole in the SnO2 layer.
Figure 4(a) shows solar cell efficiencies η from device modeling for the direct SnO2/CdTe heterojunction without CdCl2 interlayer. The efficiency η shows a significant sensitivity on and , and we observe efficiencies between 11% and 20%, where the higher end requires high n-type doping densities of 1020 cm−3 in the SnO2 layer. Even though other device parameters are essentially ideal, this range remains below the current state of the art [up to 22% (Ref. 46)] and well below the Shockley–Queisser (SQ) limit,47 which lies slightly above 30% for a bandgap of 1.5 eV. To further characterize the device behavior, we perform a sensitivity analysis for interface-layer parameters that are not directly obtained from the first-principles calculations. Figure 4(b) shows the dependence of η on the radiative recombination coefficient and the non-radiative lifetime within the interface layer. The results indicate a severe efficiency reduction unless unrealistically large values for and vanishingly small values for are assumed. It is expected that direct band-to-band transitions are allowed in the interface region, implying that realistic values for should be on the order of 10−10 cm3/s. In this regime, the device performance is insensitive to the non-radiative interface recombination rate . These findings show that local radiative recombination in the interface region is dominating the device performance.
As shown in Fig. 4(c), including the CdCl2 interlayer in the device modeling strongly improves the efficiency, ranging now between 21% and 26%. There is no observable effect on performance under variation of and (not shown). Also, the modeling results for this interface hardly depend on the n-type doping level in the SnO2 window layer, apart from a slight efficiency reduction above = 1019 cm−3. Instead, the efficiency now increases with the p-type doping level in the CdTe absorber. Traditional acceptor doping approaches utilize Cu dopants, which have a large ionization energy of 146 meV,48 are susceptible to self-compensation, and suffer from stability issues,49 thereby limiting hole densities typically to the order of 1014 cm−3. However, recent approaches with group V dopants have achieved hole densities up to 1017 cm−3 with shallower acceptors.50 For this doping level, our device simulations project an efficiency up to about 26% for the interface with CdCl2 interlayer, which is now limited by radiative recombination in the bulk. For example, with = 1017 cm−3 and = 2 × 10−10 cm3/s in the CdTe absorber (cf. Table S2), the radiative lifetime is = 50 ns, which is much shorter than the non-radiative bulk lifetime τ in our model. In this situation, when radiative band-to-band transitions dominate recombination rates, photon recycling, and optical management (not considered here) can further increase efficiencies. For reference, such efforts have resulted in efficiencies up to 29.1% in GaAs with a similar direct bandgap energy,46 close to the SQ limit. Given the prediction of essentially ideal interface electronic properties enabled by the 2D CdCl2 interlayer phase, a similar performance should in principle be achievable in CdTe-based PV. Of course, realizing such advances may require additional improvements (e.g., the back contact) that are not explicitly addressed in the present work.
III. DISCUSSION AND CONCLUSIONS
In addition to the prediction of high theoretical efficiencies for CdCl2-passivated SnO2/CdTe heterojunctions, the device modeling also provides valuable insight into physical mechanisms governing the unpassivated interfaces. Supporting the following discussion, the supplementary material (Figs. S1–S6) includes additional data on the contributions of open-circuit voltage , short-circuit current density , and fill factor FF to the overall efficiency η, as well as band diagrams, J–V curves, and data on recombination rates. An interesting observation is that the polarization charge and associated electric field have a beneficial effect, to an extent mitigating the detrimental effects of the interface bandgap narrowing. The 0.54 eV conduction band offset in Fig. 3(a) causes high electron concentrations in the interface layer on the order of 1020 cm−3 under all conditions, such that the recombination rate is limited by the hole density. The positive sign of the polarization charge reduces the hole density, and consequently, the recombination rate in the interface layer, leading to a higher . The efficiency also shows intricate dependencies on the window and absorber doping levels [cf. Fig. 4(a)], which can be traced back to counteracting effects on voltage and current (cf. Fig. S6). At higher voltages, increasing and decreasing result in greater injection of holes from CdTe into the interface layer, therefore increasing the recombination current and lowering . On the other hand, at lower voltages, there exists a competition between the diffusion and drift components of the photogenerated hole current, such that increasing acceptor doping levels reduce the hole flow toward the interface layer, thereby reducing recombination and increasing and FF. The overall result is a non-monotonic dependence of η on with a maximum at around 1016 cm−3 in Fig. 4(a).
Our first principles interface atomic structure predictions provide new insight on non-trivial interface reconstructions, where a fractional first CdTe layer can better accommodate the lattice and bonding mismatch than the complete CdTe layers in the free-surface-joint structures (cf. Fig. 2). Such fractional interlayers are likely a more general feature of incommensurate interfaces between strongly (ionic or covalent) bonded materials and should be considered in the construction or search of atomic interface configurations. In the structure sampling with CdCl2 addition [cf. Fig. 1(d)], it is a striking observation that the stable chloride interlayer stands out as low-energy structure, separated from other structures by about 1 eV/nm2. In contrast, the direct SnO2/CdTe interfaces exhibit a spectrum of near-degenerate energies close to the energy minimum [cf. Fig. 1(c)]. Also, this periodic structure lacks a van der Waals gap and does not have an obvious relation to the crystal structure of bulk CdCl2. Thus, the CdCl2 interlayer can be viewed as a stable, unique 2D interface-defined phase. We note that our predicted interface energies (Table I) correspond to adhesion energies ranging from about 3 eV/nm2 (direct interface) to almost 6 eV/nm2 (CdCl2 mediated), considerably larger than typical adhesion energies of van der Waals materials (e.g., about 1 eV/nm2 for MoS2/SiO2 and MoS2/Si3N451). The large binding energies indicate that our predicted interface structures are stabilized by direct, covalent bonds.
In the electronic structure results, comparing the overall band alignments shown in Fig. 3(a) with the electron affinities in Table I, it is a remarkable observation that the actual conduction band offsets differ starkly from Anderson's rule52 (difference of electron affinities). This rule is here entirely unsuitable for estimating band offsets, as it would yield a cliff-like offset of as much as 1.2–1.4 eV depending on the CdTe orientation, deviating more than 1 eV from the actual offsets. Furthermore, to assess the impact of potential uncertainties in the predicted electronic structure, we performed device simulations with a ±0.1 eV variation of the offsets shown in Fig. 3(a) while keeping the CdTe bandgap fixed ( = 1016 cm−3, = 1018 cm−3). For the CdCl2 treated interface, the variation is negligible with an absolute change of less than 0.1% in the simulated cell efficiencies η. For the direct interface without CdCl2, the largest effect results from the conduction band offset of the interlayer, resulting in variations of about ±1.8% around the predicted value of 15.8% shown in Fig. 4(a). This analysis shows that the conclusions from device modeling are quite robust against uncertainties in the first-principles data of a magnitude that can be reasonably expected.
Since electronic device applications often depend critically on suitable interface properties,53 and since incommensurate interfaces are prone to cause detrimental defect states,54 our results have far reaching implications beyond the specific materials system considered here. We demonstrated that interface-defined 2D phases have potential for facilitating defect-free interface formation between otherwise incompatible materials. This design approach could open new opportunities in numerous areas where defect-free interfaces are of central importance.
IV. METHODS
A. DFT and electronic structure calculations
All first-principles calculations were performed within the projector augmented wave (PAW) framework55,56 of the Vienna Ab initio Simulation Package (VASP) code.56 The PBEsol DFT functional57 was employed for KLM sampling. The final data analysis (Table I) was performed in extended slab cells with additional SnO2 and CdTe layers (cf. Fig. 2), using the Strongly Constrained and Appropriately Normed (SCAN) functional58 for total energy calculation and atomic relaxation, as well as dipole corrections for both the total energy and the potential.59 The slab dimensions stated in Sec. II A are given for SCAN, which reproduces experimental lattice constants to within about 0.5%, and we used a Γ-centered 4 × 2 × 1 k-mesh for the slab cells.
Electronic structure calculations within the many-body GW method60,61 were performed for bulk materials, following the eigenvalue-self-consistent approach of Ref. 62, except that the more recent SCAN functional was used to obtain the lattice parameters and electronic wavefunctions. Whereas bandgap corrected band offsets can be obtained by combining DFT slab calculations with GW bulk calculations,10 we are here interested in the interfacial DOS, which necessitates bandgap corrected slab calculations. Thus, again using SCAN wavefunctions, single-shot hybrid functional with onsite potential (SSH + V)40 parameters were determined for bulk SnO2 and CdTe, so to enable electronic structure calculations for the extended slab supercells, containing 232 and 242 atoms for the SnO2/CdTe and SnO2/CdCl2/CdTe interfaces, respectively (cf. Fig. 2). For semiconductor and widegap materials, SSH + V usually reproduces the GW result very closely, not only in the bandgap but also in the absolute band energies in the valence and conduction band DOS.40,63 For obtaining high-quality band-offsets in the present work, we ensured that the conduction band alignment between SnO2 and CdTe in SSH + V is reproduced within less than 0.1 eV compared to GW.
Using the PAW hybrid functional implementation,64 we obtained α = 0.16 for the Fock mixing parameter (without range separation) and on-site potentials65 of = + 1.4 eV and = −1.7 eV, to reproduce the GW bandgaps and absolute band edge energies for SnO2 and CdTe simultaneously, also including the Cd-d band energy. The band diagram in Fig. 3(a) was constructed by combining three types of data: First, a piecewise linear regression (red solid) of the smoothened (red dashed) planar-averaged (gray solid) electrostatic potential yields the potential reference on either side of the slab. Second, the SSH + V bulk calculations give the band energies relative to . Here, a potential alignment technique66 was used to line up the unstrained CdTe bulk band energies with the strained structure in the slab. Third, the area-normalized interface DOS [Fig. 3(b)] was obtained from the local DOS projection for near-interface atoms with Shannon radii,67 and a scaling factor of 1.18 was used to account for the ratio of total electron count to partial charge. The band alignment of the 1 nm interface layer is directly obtained from the onset of the occupied and unoccupied IFDOS.
B. KLM sampling for the interface geometry
Within the KLM sampling approach,32 seed and trial structures are generated from random atomic positions and by sequential displacements of individual atoms up to several Å. Each structure is pre-conditioned by enforcing minimal atomic-pair distances, which is achieved by iteratively moving atoms of each elemental pair away from the mid-point. Table S1 in the supplementary material lists the pairwise minimum distances used in the present work. After atomic-force relaxation, the resulting structure is evaluated with a Monte Carlo acceptance criterion based on the DFT energy. Both the MC accepted and the overall lowest energy structure of each run are recorded. Parallel execution of five trial structures was used to accelerate the sampling. We use a temperature of 1000 °C for the MC acceptance/rejection criterion. This strategy is intended to enable the escape from shallow local minima in configuration space, thereby extending the sampling region, but it does not affect the selection of the overall lowest energy structure.
A thin SnO2(110)r slab with 24 formula units (fu) and three Sn layers was used as substrate [see Fig. 1(a)], which was found to be sufficient for total energy evaluations (the SnO2 surface energy is converged to within 4%). The seed structure of the sampling layer is generated from initial random positions of the atoms in the film (here, Cd, Te, and Cl). A vacuum layer of about 15 Å separates the substrate/film slab from the adjacent periodic image. Unlike the case of KLM bulk structure prediction where we generally perform a full geometry optimization in each step, the unit cell remains fixed in the interface structure sampling. Only atoms of the film are sampled, since tests indicated that displacements of the bridging O atoms did not result in favorable energies.
Furthermore, the sampled atoms are restricted to a suitable volume above the substrate surface, which is achieved by reflection from the boundary if a displacement would exceed the allowed range. Substrate atoms were clamped during displacements and were therefore not affected by the minimum distance enforcement. Near-surface substrate atoms [atoms above the middle Sn layer in Fig. 1(a)] were included in the DFT relaxation step. The approach allows for generating layered structures as shown in Fig. 1(a), where the initial seed structure is constructed with a CdCl2 layer. However, all non-substrate atoms (Cd, Cl, and Te) were included in the subsequent KLM optimization within the same sampling volume without assuming near-interface positions for Cl atoms.
C. Device modeling
Numerical simulations were performed using the COMSOL Multiphysics® software v6.0. The coupled semiconductor transport equations were solved using the finite element method. Fermi–Dirac statistics were employed to account for the high doping levels considered in SnO2. A table with all relevant parameters for device modeling is given in the supplementary material (Table S2). The baseline parameters include bandgaps of 1.5 eV (CdTe) and 3.6 eV (SnO2) and broadly follow Ref. 44, except as described otherwise. For simplicity, equal bulk electron and hole mobilities of 100 cm2 V−1 s−1 are used, and acceptors and donors are assumed to be fully ionized. The band offsets between the SnO2 (100 nm), interface (1 nm), and CdTe (3 μm) layers are taken from the electronic structure calculations, as indicated in Fig. 3, and the effective densities of states and in the interface layer are defined for 300 K using the DOS effective masses discussed in Sec. II B. The polarization charge of the direct SnO2/CdTe interface is accounted for by a dipole across the SnO2 layer with charge density of cm2, reproducing the electric field as obtained in the electronic structure calculation [Fig. 3(a)]. Ohmic front and back contacts are assumed, where the front contact also accounts for the transparent conducting oxide layer used for electron collection.
SUPPLEMENTARY MATERIAL
See the supplementary material for structure files (POSCAR format) for all surfaces and interfaces listed in Table I, additional details on methods, and additional device modeling data.
ACKNOWLEDGMENTS
This material is based upon work supported by the U.S. Department of Energy (DOE), Office of Energy Efficiency and Renewable Energy (EERE), under the Solar Energy Technologies Office Award No. 34350. The Alliance for Sustainable Energy, LLC, operates the National Renewable Energy Laboratory (NREL) under Contract No. DE-AC36–08GO28308. The research used High-Performance Computing (HPC) resources at NREL, sponsored by DOE-EERE, and at the National Energy Research Scientific Computing Center (NERSC), a DOE Office of Science user facility. S.L. wishes to thank Darius Kuciauskas (NREL) for project leadership and valuable discussions and feedback.
The views expressed in this article do not necessarily represent the views of DOE or the U.S. government.
AUTHOR DECLARATIONS
Conflict of Interest
Dmitry Krasikov works at First Solar, which is a CdTe PV manufacturer.
Author Contributions
Abhishek Sharan: Conceptualization (equal); Data curation (lead); Formal analysis (equal); Investigation (lead); Methodology (equal); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Marco Nardone: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Validation (equal); Visualization (equal); Writing – review & editing (equal). Dmitry Krasikov: Methodology (equal); Validation (equal); Writing – review & editing (equal). Nirpendra Singh: Funding acquisition (equal); Supervision (equal); Validation (equal); Writing – review & editing (equal). Stephan Lany: Conceptualization (lead); Funding acquisition (equal); Methodology (lead); Software (lead); Supervision (lead); Validation (equal); Visualization (equal); Writing – original draft (lead); Writing – review & editing (lead).
DATA AVAILABILITY
The data that support the findings of this study are available within the article and its supplementary material.