Determining interface properties limiting open-circuit voltage in heterojunction solar cells

As a competitor to conventional c-Si based solar cells, thin-film photovoltaic (PV) absorbers offer advantages such as lower capital equipment costs and reduced materials usage.^1,2 In particular, thin-film PV formed from Earth-abundant elements could offer a compelling path towards achieving low cost PV power at terawatt scales.^3–5 However, emerging thin-film PV technologies lag behind c-Si in performance and reliability, and these areas have attracted significant research interest on materials platforms such as Cu(In,Ga)Se₂ (CIGS),^6,7 CdTe,⁸ CuZnSn(S,Se)₄,⁹ and the lead halide (APbX₃) perovskite family.¹⁰ 

In addition to these well-studied materials families, dozens of other Earth-abundant PV absorbers have captured research attention, including SnS,^11,12 CuSb(S,Se)₂,¹³ Sb₂(S,Se)₃,¹⁴ and cuprous oxide (Cu₂O),^15,16 which is the focus of the present work. Despite decades of research on these materials, or a century in the case of Cu₂O, performance improvements have been slow and device efficiencies still sit in the range of 3%–8%.¹⁷ In the past four years, significant advances were made in Cu₂O performance by focusing not only on the bulk material properties but more critically on the interfaces with contact materials—in particular improving the conduction-band offset^15,18,19 and reducing interface recombination with the electron selective contact (ESC).^20–22 This improvement largely rests in the open circuit voltage (V_OC); Fig. 1 shows the extent of recent progress in Cu₂O by comparing the V_OC to the bandgap for several prominent thin-film PV materials. The V_OC deficit, or the energy difference between the absorber bandgap (E_G) and qV_OC, now approaches that of copper zinc tin selenide (CZTS) and a-Si, with a V_OC of 1.2 V.

For well-established PV absorbers, the importance of electronic band offsets to reach high performance in heterojunctions has been well established.^30,31 Despite this, the process of discovering optimal contacts for new materials is slow and occasionally controversial. New contacts are predominantly evaluated through ultraviolet and X-ray photoelectron spectroscopy (UPS and XPS), which can probe the valence-band energy offsets between an absorber and a contact layer. Direct measurements of the conduction-band offset can also be performed by inverse photoemission spectroscopy (IPES). These spectroscopy techniques can offer accurate offsets but only when performed very carefully—even then, the precision is on the order of one tenth the absorber bandgap (error bars between 0.1 and 0.2 eV) (Ref. 32), and the sample preparation and experiments may take several weeks or months to perform.

An alternative strategy to evaluate the performance of contact materials is to observe their impact on the electrical performance of a completed device and, in doing so, infer the energy level alignments. The use of temperature to electrically probe the energetics of a heterojunction PV device has been applied to a number of different PV absorbers.^6,33–39 Recently, there have been several efforts to incorporate illumination intensity as well to provide a more complete understanding of the kinetics of recombination in heterojunction PV devices.^40–42 

In the present work, we apply current-voltage measurements as a function of temperature and illumination intensity (termed JVTi) to a test-case PV absorber, cuprous oxide (Cu₂O). We develop a model for the V_OC as a function of bulk and interface recombination rates and cell operating conditions and use this model to infer the conduction band alignment between Cu₂O and its respective electron selective contacts. We compare these results to those obtained by photoelectron spectroscopy and discuss when these electrical measurements may be substituted for conventional spectroscopy techniques. Through faster feedback, higher energetic resolution, and a more accurate representation of the final device architecture, JVTi may improve the characterization of new contact materials on PV absorbers.

We fabricate thin-film Cu₂O heterojunction solar cells with the device stack: Au/Cu₂O/ESC/Al:ZnO, where ESC represents one of the three different electron selective contacts (often referred to as “buffer layers” in thin-film PV cells): zinc oxide (ZnO), zinc tin oxide (ZTO), and gallium oxide (Ga₂O₃). Both the ESC and transparent conducting oxide (Al:ZnO) are both deposited by atomic layer deposition, while the Cu₂O is deposited by electrochemical deposition. The ZnO and Al:ZnO are microcrystalline, while the ZTO and Ga₂O₃ are amorphous. Deposition conditions are detailed elsewhere;¹⁹ the cell stacks are identical in thickness and deposition conditions, with the only exception being the differing ESCs. This suggests that all variations in electrical performance between these devices may be prescribed to the ESC properties and heterojunction interface.

Fig. 2 displays the room temperature, one-sun J-V scans for all three devices, and the V_OC of each device plotted as a function of temperature at AM1.5 illumination. Each cell (0.15 cm² in area) is selected from a substrate of 18 identical devices, chosen for having a high shunt resistance (>2000 Ω cm²) and median J-V characteristics on its substrate (excluding shunted outliers). Cell data are taken over five orders of magnitude in light intensity (10⁻⁵–10⁰ suns or 0.01–100 mW/cm² in incident light flux) and over the temperature range of 100–320 K. This full dataset is presented in Fig. 3 for one particular cell, the Cu₂O/ZnO heterojunction. Surface plots of J_SC indicate a linear response with respect to illumination intensity.

The first noticeable feature in Fig. 2(b) is that, while each device shows a similar slope of V_OC vs. T, the extrapolation of the V_OC to 0 K results in a different intercept for each device. In Secs. III and IV, we seek to develop an analytical approach to interpret this result and compare the results to alternative measurements of the interface properties. Second, the V_OC flattens out below 200 K. This may be attributed to the freeze-out in the acceptors doping the Cu₂O. As the Cu₂O becomes intrinsic and insulating, the work functions of the contacts start to influence the quasi-Fermi level separation, and furthermore, the fill factor gradually drops to 25%, suggesting that the cells no longer act as a solar cell or as a photodiode.

Focusing on the V_OC offers several advantages. First, mathematically, the recombination currents are the easiest to calculate as they balance equally with the forward photocurrent. Second, the effects of series resistance are negated as no net current flows in the open-circuit: ΔV = IR_series = 0. Modeling the V_OC as a function of temperature and illumination requires the functional forms of different recombination mechanisms, allowing us to identify their presence in the observed data above.

To begin, we hypothesize that recombination at the heterojunction interface limits the performance of thin-film Cu₂O cells measured here (and will test this hypothesis). Interface recombination is exponentially activated with temperature, corresponding to the barrier height for holes and electrons to recombine at the interface; therefore, T- and i-dependent measurements of V_OC, which probe this recombination current, should be sufficient to determine the interface barrier height and the kinetics of recombination.

The modeling of the dominant recombination mechanisms is done using a formalism adapted from Grover and Li.^40,41 The open-circuit voltage of a cell can be expressed as the separation in quasi-Fermi levels, which in turn are related to the product of electron and hole concentrations (np). This allows us to define a quantity, β = (np/n_i²)^1/2. The V_OC can therefore be written as

Here, q is the charge on an electron and k_B is the Boltzmann constant.

At the V_OC point, generation is perfectly balanced by recombination currents coming from each region of Cu₂O: the depletion region, the quasi-neutral region, and at the two contact interfaces. If the internal quantum efficiency were 100%, this generation rate G, integrated over the full thickness of the absorber, would equal the photocurrent J_ph. In many non-ideal materials, not all photogenerated carriers produce a forward photocurrent before they recombine, the effect of which is discussed in Sec. V C. Thus, the balance between photocurrent and recombination may be expressed as

where J^b, J^d, and Jⁱ represent the bulk quasi-neutral region, depletion region, and heterojunction interface recombination rates, respectively, with units of [A/cm²]. Note that these current densities have the opposite sign of J_ph, as illustrated schematically in Fig. 4. We ignore back contact recombination in the present work given that the device thickness is over five times greater than the diffusion length in Cu₂O;¹⁹ thus, very few minority carriers are expected to reach the back contact.

Beginning with depletion region recombination, Shockley-Read-Hall recombination statistics posit that the recombination rate is of the form

where τ_h and τ_e are hole and electron lifetimes, respectively, and n₁ and p₁ represent the electron and hole occupancies of the defects, respectively. Assuming that recombination occurs through the worst-case scenario of a midgap trap, the hole and electron occupancies match the intrinsic carrier concentration (n_i) and the recombination rate can be greatly simplified. Integrating this recombination over the depletion width thickness W_d gives the following recombination current density:

This current can be expressed with a voltage independent term (J₀^d) as the pre-factor and an exponential voltage term (β). Integrating instead over the quasi-neutral region, for a p-type absorber, the bulk quasi-neutral region recombination current may be modeled as

Recombination at the interface may be more similar to the depletion region or quasi-neutral recombination depending upon where the Fermi level sits at the interface. If the Fermi level is near a band edge (as in the case of an inverted interface), the recombination rate is relatively simple. In the case of a mid-gap Fermi level, or a non-inverted interface, the recombination rate is more complicated as it relies on the supply of both holes and electrons. For the former case, the inverted heterojunction is gives as follows:

Here, S_p is the hole surface recombination velocity at the heterojunction, N_V^a is the valence band density of states in the Cu₂O absorber, and E_G^IF is the interface bandgap. For the non-inverted case, fewer simplifying assumptions can be made. The recombination at the interface is limited by the concentration of both holes from the absorber (p^abs) and electrons in the ESC (n^ESC). Expressions for both may be found in Ref. 7, p. 66. Combining the voltage-dependent expressions for electrons and holes and their respective surface recombination velocities, we get

Together, these recombination rates reveal an important distinction. For some mechanisms, the recombination rate is dependent upon the supply of the minority carrier, where the majority carrier type is in abundant supply and occupies all of the traps. The resulting recombination rates are proportional to β² and have an ideality factor of 1. For other mechanisms, the recombination rate is instead proportional to β and has an ideality factor of 2, where the defects sit directly between the hole and electron quasi-Fermi levels and both carriers are readily available. This dichotomy offers a convenient grouping of recombination rates with ideality factor 1 (J_0,1) and those with ideality factor 2 (J_0,2). The resulting current balance at open-circuit conditions can therefore be expressed as

This is a quadratic equation for β; solving for β and plugging it into Eq. (1) give

Given this expression, we can determine the functional form for the temperature- and illumination-dependence of V_OC. In particular, the local slope of the V_OC at room temperature T_R provides information about the activation energy of the dominant recombination mechanism,

Here, the extrapolation of V_OC to 0 K is termed the activation energy, E_A. With this expression, we can numerically determine and plot the activation energy as a function of fundamental underlying properties like the bulk minority carrier lifetime and the interface SRV, to explore the behavior under different limiting cases. To visualize the transition between bulk and interface recombination-dominated regions, the activation energy is plotted in Fig. 5. For the purposes of modeling, the following properties of Cu₂O are assumed based on a previous work:^19,43 a bulk bandgap of 2 eV, N_A = 10¹⁴cm⁻³, a depletion width of 2 μm, a quasi-neutral region width of 500 nm, and an interface gap of 1.6 eV. The bulk lifetime τ_e and interface recombination velocity S_h are varied over several orders of magnitude. The activation energy transitions between 1.6 eV and 2.0 eV for interface- and bulk-limited regimes, respectively. In this analysis, we assume that the interface is not inverted. Previous work has assumed an inverted interface,⁴⁰ and in general, this analysis requires making a binary assumption about which interface condition applies. In Sec. IV, we address the case of an intermediate scenario and correspondingly intermediate ideality factor.

The transition region between interface- and bulk-dominated recombination is not fixed; in fact, it changes with illumination intensity (generation rate). For different interface energy gaps, increasing the size of the conduction band offset or decreasing the interface energy gap increases the region of interface-limited activation energy substantially, and for large cliff-type offsets, it is nearly impossible to find a bulk-dominated recombination regime. For smaller interface conduction band offsets, increasing light intensity can increase the region of parameter space in which bulk recombination dominates. If a cell sits in between these limits in parameter space, sweeping the light intensity should show a change in activation energy. Similarly, a device limited by recombination currents of different ideality factors should show a transition in the ideality factor as a function of light intensity. Table I offers an overview of the expected transition behavior under different limiting regimes.

To fit the V_OC and activation energy of these cells, several additional assumptions can be made about these Cu₂O devices. We will apply one set of assumptions in the following text, as a simplified case. First, we assume that the depletion region and interface recombination dominate over quasi-neutral region recombination, given that the depletion width in Cu₂O is larger than the minority carrier diffusion length.¹⁹ Similarly, the heterojunction interface is not inverted; thus, recombination currents in these cells would be expected to have an ideality factor closer to 2. Finally, the cells are in low injection due to the low minority-carrier lifetime. Given those assumptions, the V_OC model (Eq. (9)) would reduce to

Again taking the derivative of V_OC with respect to T and extrapolating to 0 K yield the activation energy,

Thus, the activation energy may be expressed as a weighted average of the depletion region and interface recombination activation energies, weighted by their respective exponential pre-factors. If the interface recombination dominates over the bulk or depletion region, then this reduces simply to a constant activation energy equal to the interface gap,

When different recombination pathways in Eq. (13) are characterized by different ideality factors, or in other words scale differently with the light intensity or injection level, then the activation energy itself is expected to vary as a function of light intensity. If we revise our assumptions at the interface to assume complete inversion and ideality factor n = 1, the activation energy expression in Equations (12) and (13) reduces to the same form, suggesting that this analysis is independent of the ideality factor of interface recombination. The array of possible limiting scenarios is detailed in Table I and described in more detail in the supplementary material. In particular, we note that the only case where the ideality factor can take any value between 1 and 2, and the activation energy takes a constant value less than the absorber band-gap, is when interface recombination dominates across the entire illumination range.

The V_OC extrapolation to below the bulk bandgap energy levels in Fig. 2 would appear to indicate an interface-limited V_OC and, as a result, the interface bandgap. To verify this, the cells are measured over a range of light intensities. Over two orders of magnitude in light intensity below AM1.5, the activation energy of each cell is found to be roughly constant, as shown in Fig. 6. There is no evidence of a transition in activation energy toward the bandgap energy at lower light intensity. This may imply one of the two things: either that the cells tested are interface recombination-limited and that Jⁱ limits the V_OC in these Cu₂O cells or that both dominant recombination mechanisms have similar ideality factors, thereby preventing intensity-dependent changes in activation energy.

To study this further, the interface energy gap extracted may be compared to that measured through photoelectron spectroscopy. In Fig. 6, the measured band offsets for the three ESCs employed here are plotted next to one another. These band offsets are determined through X-ray photoelectron spectroscopy of thin Cu₂O/ESC heterojunction samples to determine the valence band offset. Then, the optical bandgap is added to infer the conduction band offset. Details and calculations for this may be found in previous works.^15,19 Comparing the interface energy gap extracted from these photoelectron spectroscopy measurements to that measured from JVTi in Table II suggests a very strong agreement. JVTi measurements of the interface energy gap on these particular cells offer similar accuracy but higher precision than comparable photoelectron spectroscopy measurements. The above-referenced photoelectron spectroscopy measurements took three months to perform, from fabrication, measurement, and data analysis, while the JVTi measurements took approximately one week from sample fabrication to data analysis. This implies that JVTi as a technique may be able to substitute for XPS and UPS measurements and offer a significantly faster rate of materials screening in pursuit of the optimal contact material.

In cases like this, where interface recombination strongly limits the V_OC, bulk recombination may not be detected at the V_OC point over several orders of magnitude in the injection level. In the limiting case of ideality factor of 1 or 2, we could use this to determine the properties of the interface (such as the surface recombination velocity) and set a lower bound for bulk minority-carrier lifetime, through Equations (4)–(7). The ideality factor of these cells may be inferred from the illumination-dependent V_OC as

The ideality factor is plotted in Fig. 7 and is found to behave differently for different ESC materials. For Cu₂O/ZnO, it transitions from approximately 1 at full light intensity to greater than 2 at weak light intensities. The Cu₂O/Ga₂O₃ device exhibits a similar behavior, beginning at an ideality factor of 1.4. Finally, the Cu₂O/ZTO device exhibits a relatively constant ideality factor of 1.4. These results suggest that the Fermi level and defect occupation at the interface are not either of the limiting cases proposed earlier (i.e., n = 1 or n = 2). In the previous work, transitions in the ideality factor from 1 to 2 would have been modeled as transitions between two diode currents (e.g., bulk and interface recombination), whereas here we believe that the interface recombination is always dominant. In that case, we have chosen not to fit the ideality factor using the Li and Grover method.^40,41 What this implies is that the interface recombination current itself has an ideality factor between 1 and 2, set by the carrier concentrations on either side of the interface and the fractional defect occupation at the interface.

Illumination will change both the carrier concentrations and defect occupations of the ESC,⁴⁴ which may explain the variation in the ideality factor with light intensity in our devices. Unfortunately, this variation is impossible to capture with simple analytical expressions. Fortunately, regardless of the ideality factor, we find that dominant interface recombination will indeed still lead to an extrapolated V_OC equal to the interface energy gap. This adds to the theory of Li and Grover and presents the difficulties in applying n = 1 and n = 2 analytical models to (especially less efficient or less ideal) solar cells.

The models expressed above are built for an ideal solar cell, but Cu₂O and other cells may be subject to a number of experimental artifacts that violate the assumptions made. These pitfalls include the effects of conductivity freeze-out, shunt conductance, and voltage-dependent photocurrent. It is important to understand each of these artifacts, as they may lead to below-bandgap activation energies and may therefore be misinterpreted as evidence of interface recombination or other physical mechanisms.

The first potential artifact to consider, which may lead to an underestimation of activation energy, is the role of freeze-out of bulk acceptors and its impact on cell performance. Cu₂O contains relatively deep bulk acceptors with a binding energy of 0.25 eV,⁴⁵ in part due to its low static dielectric constant and relatively high hole effective mass. This means that not all acceptors are ionized at room temperature, and at the lowest measurement temperatures, these acceptors would be expected to be completely frozen out. Reducing the effective doping density in Cu₂O will raise the hole quasi-Fermi level in the absorber and thereby reduce the V_OC; furthermore at complete freeze-out, the solar cell will begin to act like an insulator.

The hole concentration (p) as a function of temperature and acceptor binding energy can be expressed as⁴⁶ 

where E_b is the acceptor binding energy. The hole concentration equals the acceptor density in the limit of sufficiently high temperatures or low acceptor binding energies when the argument of the exponential is small. As the open circuit voltage scales with the natural logarithm of p, this freeze-out carries over into the V_OC. Fig. 8 plots both the effect of deep acceptor binding energies on the activation ratio (inset) and the open-circuit voltage and extrapolated V_OC.

The most important feature to note from these plots is the temperature at which the slope of V_OC vs. T changes. For a binding energy of 0.25 eV, this occurs around 200 K. Thus, for Cu₂O, extrapolating any information from the plot of dV_OC/dT must be done above 200 K. Indeed, in Fig. 2, it is clear that for all three devices, the V_OC stops increasing and flattens or rolls over between 180 and 200 K. The observation of this freeze-out from device characteristics corroborates earlier measurements and our own admittance spectroscopy measurements of a 0.25 eV bulk acceptor binding energy in Cu₂O.

At lower temperatures, the extrapolation of V_OC to 0 K is impacted by the deeper acceptor energy and in fact extrapolates to E_G − E_b/2 instead of the bandgap. For other materials with deep acceptors or donors, one may observe below-bandgap extrapolations of V_OC from this artifact; therefore, measurements should be performed above the appropriate transition temperature.

Shunting is a common artifact that can lead to underestimates of both the V_OC and the activation energy. In the equivalent-circuit model of a solar cell, voltage may be similarly lost due to reverse current traveling through recombination pathways and ohmic shunting pathways. The effect of a shunt on the open circuit voltage is negligible above a certain resistance; however, this threshold resistance depends strongly upon the V_OC itself. In Fig. 9, room temperature cell data are plotted for a random set of 16 solar cells from the same Cu₂O/Ga₂O₃ device library. For shunt resistances below 1000 Ω-cm², the V_OC drops precipitously. This is critical to avoid when measuring and modeling the V_OC, as such shunting will strongly mask any real trends in the V_OC with respect to temperature and illumination intensity.

To determine a lower bound on shunt resistance for performing JVTi measurements, its impact is confirmed through numerical device modeling in SCAPS, in which a baseline Cu₂O/Ga₂O₃ device is simulated over a range of shunt resistances and temperatures. At 300 K, the model of shunt resistance and open-circuit voltage closely matches the data. At higher temperatures (350 K), the lower V_OC makes the cell less sensitive to shunting, while at 250 K, the opposite occurs. Thus, a cell that does not appear to be negatively impacted by shunting at room temperature may become limited by the shunt resistance at lower temperatures. In order to properly measure and model Cu₂O devices down to 200 K, it is recommended to have a device shunt resistance greater than 2000 Ω-cm².

A final artifact commonly observed in V_OC measurements, which can readily lower the measured V_OC and activation energy, is voltage-dependent photocurrent. Earlier, we assumed that recombination currents at the V_OC point would perfectly balance the forward photocurrent, taken to be equal to the current at short-circuit conditions. However, in depleted absorbers with relatively low mobility-lifetime products, carriers are collected predominantly through drift rather than diffusion. As the bands flatten closer to the V_OC, this photocurrent will decrease, forcing the device to reach V_OC at a lower voltage than anticipated.

In a previous work,³⁸ this effect has been accounted for by calculating the voltage-dependent photocurrent at the V_OC point, by subtracting the dark and light J-V curves. Unfortunately, this process is difficult for Cu₂O devices, which have an injection-dependent series resistance that influences the light and dark J-V curves differently near the V_OC point. Based on the voltage-dependent EQE measurements on the Cu₂O/ZTO device, the photocurrent is expected to be 40%–80% of the short-circuit value at V_OC, and the impact of this can be estimated through a simple ideal diode model

For a photocurrent ratio of 1.2 (80% of the short-circuit value), this corresponds to a δV_OC of 9 mV. The photocurrent ratio would have to reach 2.7 (37% of the short-circuit value) for δV_OC to be ∼ 50 meV (the error bars established herein). Therefore, we conclude that this effect is not significant in the present devices but should be tested for in every measurement, especially where the photocurrent is expected to drop by over a factor of three in forward bias.

In the previous analysis, we have assumed that many fundamental properties of each layer are independent of the illumination condition or light intensity. However, a common intensity-dependent property of semiconductors is their photoconductivity or, more specifically, the change in the effective carrier concentration under different light biases. In the previous work, we have found that lowly doped electron-selective contacts like ZnO or Zn(O,S) can exhibit a change in the carrier concentration up to three orders of magnitude upon illumination.⁴⁴ Such a change in the electron concentration (or effective donor density) can significantly change the built-in voltage (V_bi) of the junction and the carrier populations on either side of the heterojunction. For example, assuming a non-degenerately doped absorber/ESC heterojunction, we get

For example, a factor of 1000 change in the ESC carrier concentration under illumination would therefore increase the built-in voltage by 180 meV.

This increase in the effective built-in voltage with the increasing illumination intensity may affect recombination kinetics and may help explain the moderate drop in activation energy observed at low light intensities for the ZTO and Ga₂O₃ ESCs tested in the present study, as well as the change in the ideality factor.

A final non-ideality to consider in the present model is a changing depletion width as a function of applied bias. The model described above considers the recombination at open-circuit conditions, with a fixed quasi-neutral region and a depletion region width. However, the width of the depletion region in the absorber (W_d^abs) is voltage dependent. Considering the depletion width at the V_OC condition specifically, we get

It is difficult to quantify this effect with an accurate analytical expression, but it may be semi-quantitatively analyzed using Equations (4) and (18) together. As the temperature and light intensity change, and the V_OC changes, the depletion width will be different in the open-circuit. Increases in light intensity, for example, will shrink the depletion width at open-circuit conditions and potentially drive the device towards the interface or quasi-neutral region recombination dominating instead. This will have impacts on both the ideality factor and the activation energy extracted.

In the present work, we investigated the effect of varying electron-selective contacts or heterojunction partners on the interface recombination in cuprous oxide solar cells. To quantify interface recombination and the energetics of the heterojunction interface, we used temperature- and illumination-dependent J-V measurements, as well as simple analytical models of recombination currents. We extract the interface energy gap at the Cu₂O heterojunction through this JVTi technique and demonstrate that the values extracted are comparable to those extracted by X-ray photoelectron spectroscopy. This confirms that JVTi may be a faster, more precise technique for evaluating heterojunction selective contacts for PV, on complete devices. However, depending on the properties of absorber bulk defects and contact-layer carrier concentrations, JVTi outputs may be influenced by artifacts, which can lead to lower or higher activation energies than the “true” recombination-limited value. Given the complexity of these artifacts, it may not be possible to fully capture them through analytical expressions; this points towards the eventual use of numerical modeling to properly understand cell data. If these artifacts are considered, and proper care is taken to model the relevant device physics, JVTi measurements may offer the best combination of speed and accuracy for characterizing novel PV materials and their heterojunctions.

See supplementary material for further details on the light and dark J-V curves for the devices tested here and for deeper modeling of the ideality factor as a function of light intensity or temperature. This discussion offers more insights into transitions in the ideality factor and how they may be interpreted.

The authors acknowledge Danny Chua, Jaeyeong Heo, and Sang Woon Lee for assistance with atomic layer deposition. R.E.B. acknowledges the support of an NSF GRFP fellowship. This work was supported by NREL as a part of the Non-Proprietary Partnering Program under Contract No. DE-AC36-08-GO28308 with the U.S. Department of Energy and the Center for Next Generation Materials by Design (CMGMD), an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Basic Energy Sciences. This work made use of the Microsystems Technology Laboratories at MIT and the Center for Nanoscale Systems at Harvard University supported by NSF under Award Nos. DMR-0819762 and ECS-0335765, respectively. J.V.L. acknowledges the support by U.S. Department of Energy SunShot initiative through the PVRD program under Contract No. DE-EE-0007541.