Elucidating the Origin of External Quantum Efficiency Losses in Cuprous Oxide Solar Cells through Defect Analysis

: Heterojunction Cu 2 O solar cells are an important class of earth-abundant photovoltaics that can be synthesized by a variety of techniques, including electrochemical deposition (ECD) and thermal oxidation (TO). The latter gives the most efficient solar cells of up to 8.1 %, but is limited by low external quantum efficiencies (EQE) in the long wavelength region. By contrast, ECD Cu 2 O gives higher short wavelength EQEs of up to 90 %. We elucidate the cause of this difference by characterizing and comparing ECD and TO films using impedance spectroscopy and fitting with a lumped circuit model to determine the trap density, followed by simulations. The data indicates that TO Cu 2 O has a higher density of interface defects, located approximately 0.5 eV above the valence band maximum ( N V ) , and lower bulk defect density thus explaining the lower short wavelength EQEs and higher long wavelength EQEs. This work shows that a route to further efficiency increases of TO Cu 2 O is to reduce the density of interface defect states.

To study the differences in EQE, Cu2O/Zn0.8Mg0.2Oheterojunction (HJ) solar cells were made.The Cu2O was fabricated by both TO and ECD, while the Zn0.8Mg0.2Obuffer layer was deposited on top by AP-CVD using previously reported conditions.[6,9] In AP-CVD, the metal precursor and oxidant gas channels are separated with inert gas barriers, enabling the two half-reactions in ALD to occur under atmospheric pressure, with an order of magnitude higher growth rate than standard ALD.[3] We have found AP-CVD to be highly advantageous for rapidly depositing pinhole-free, thin (10-200 nm) oxide buffer layers for both ECD and TO Cu2O solar cells.[6,9] We characterized these devices by impedance spectroscopy and developed an equivalent lumped circuit model to analyze and compare differences in interfacial and bulk traps.In the model, a pair of resistors and capacitors were used in series to simulate the electrical response of active defects located both in the bulk and at the interface, and the differential capacitance ω•dC/dω was used to determine the trap density from frequency sweeps in impedance spectroscopy.By comparing the traps in ECD Cu2O to TO Cu2O, we conclude that TO Cu2O exhibits a higher density of interface traps.Through SCAPS simulations, we confirmed that this correlates with a reduced short wavelength EQE.We determine that further efficiency improvements to ECD Cu2O heterojunctional solar cells could come about by improve interface with less interface defect recombination.

Developing a lumped circuit model of Cu2O-Zn1-xMgxO solar cells
A lumped resistor-capacitor (RC) circuit (Figure 1a) can be established to describe the electrical response of a complete p-n junction (including metal-semiconductor junctions).[29,30] For the Cu2O/Zn0.8Mg0.2OHJ in the current study, the circuit is comprised of two types of junctions: (1) the p-n junction (between Cu2O/Zn0.8Mg0.2O)and ( 2) two metal-semiconductor junctions, Ag/ITO/Al doped ZnO (AZO)/Zn0.8Mg0.2Oand Cu2O/Au (or Cu2O/ITO for the anode of ECD Cu2O).In Figure 1a, Rnc and Rpc are the contact resistances for Ag/ITO/(AZO)/Zn0.8Mg0.2Oand Cu2O/Au (or Cu2O/ITO) junctions, respectively.Dynamic resistance and capacitance associated with surface states at the metal-semiconductor interface are denoted by Rns and Cns for Ag/ITO/(AZO)/Zn0.8Mg0.2O,Rps and Cps for Au/Cu2O (or Cu2O/ITO).In order to analyze the depletion region of the HJ, the circuit was divided into an infinite number of small segments by geometry and each segment (i.e. the ith segment) consists of resistors and capacitors connected in parallel (ΔCi and ΔRi) and series (ΔCti and ΔRti).In the Cu2O/Zn0.8Mg0.2OHJ, Cu2O (p-type, NA ≈ 10 14 -10 15 cm -3 ) [17] is usually ~2-4 orders of magnitude lower than Zn0.8Mg0.2O(n-type, ND =~10 17-10 19 cm -3 ), [9,17] forming an abrupt heterojunction, see Figure 1b.As a result, ΔCi and ΔRi in Figure 1a are geometry related elements and can be expressed by Equations 1a&b, [29] while ΔCti and ΔRti are dynamic (or defect) related elements and can be expressed by Equations 1a&d: [31] (1a) In Equations 1a&b, ε and σ are the dielectric constants and conductivity of Cu2O respectively.Δx is the thickness of the ith segment.In Equation 1c, Nt is denoted as the trap density, q the electron charge and ΔCti the capacitance associated with a certain trap, which models the capture and emission of carriers from the trap.The conductance of the trap, ΔGti, can be related to ΔCti by Equation 1d, where τt is the time constant of a trap and the reciprocal of its angular frequency, ω.As a result, elements associated with traps are frequency dependent.The relation between frequency and energy levels can be expressed by Equation 2a: [17] (2a) (2b) In Equations 2a&b, σj is the capture cross-section of a trap, vth the thermal velocity, NV the density of states at the Cu2O valence band, Eω the corresponding energy position at xω (Figure 1a).ω(Eω) in Equation 2a has an inverse exponential relationship with Eω.The angular frequency, ω, can therefore be expressed as the corresponding trap frequency, ωo, when the energy level, Eω, is equal to Eo for a bulk defect level at the location xo (Equation 2b).In Equations 2a&b, σj is the capture cross-section of a trap, vth the thermal velocity, NV the density of states at the Cu2O valence band, Eω the corresponding energy position at xω (Figure 1a).ω(Eω) in Equation 2a has an inverse exponential relationship with Eω.The angular frequency, ω, can therefore be expressed as the corresponding trap frequency, ωo, when the energy level, Eω, is equal to Eo for a bulk defect level at the location xo (Equation 2b).
Before establishing the theoretical model, three approximations were made: (1) Contact resistances (Rnc, Rpc) were neglected here even if a small Schottky barrier exists for both types of solar cells, with the one in the ECD Cu2O sample being more significant (Nyquist plots in Figure S1).This approximation is valid because, in the model, these two parameters are associated in the circuit in a parallel fashion, which makes it constant in the differential capacitance measurement; (2) For simplicity, surface states at the metal-semiconductor junctions (Rns and Cns for Ag/ITO/AZO/Zn0.8Mg0.2O,Rps and Cps for Au/Cu2O) were neglected.[29] These parameters are slow reacting in comparison to that from the bulk and interface of the device, reflected by the distance from the hetero-interface.In the measurement, the lowest frequency was ~10 2 rad/s, making it less possible for detecting the influence of two slow reacting regions; (3) The dimension-related elements for ZnO, Rn and Cn, were ignored.This is valid because Cu2O/Zn0.8Mg0.2O is an abrupt heterojunction.[17,29] In the equivalent circuit model (Figure 1a), the frequency response of traps to carriers affects whether a group of electrical elements should be incorporated in parallel to the previous circuit, i.e., whether ΔRi and ΔCi are connected in parallel to ΔRti and ΔCti.

(
) Therefore, the admittance relation between Ypn(x + Δx) and Ypn(x) can be formulated as Equation 3. [32] (3) In Equation 3, Zpn(x + Δx) is the impedance of the p-n junction.Inserting Equations 1a-d into Equation 3 yields Equation 4a.The calculation details can be found in Figure S2 of the supporting information (SI): (4a) By inserting Equations S3-S7 into Equation 4a from Figure S3: where λ is an attenuation factor (λ = -kTLo/ΔEω).The admittance consists of real and imaginary components, namely, Ypn = Gpn + jBpn and thus can be projected for the two components for the p-n junction.
(5a) (5b) Further, replacing Bpn with ωCpn in Equation 5a, and by rearranging Equation 5a so that Nt(C) is the subject the trap density, Nt(C), can be obtained.At the same time, the subscript p-n for G, B and C are removed for convenience and Equations 6 are obtained: Nt(C) is related to the differential capacitance, ω•dC/dω, by the second term in Equation 6a.Nt(G) can be related to the differential conductance G in Equation 6b, but further discussion is beyond the scope of this paper.
In Figure 1b, the Fermi level (EF) intersects with both interface defects and the bulk trap level (ET), numbered 1 and 2 respectively.Both types of defects can affect the results of admittance spectroscopy.In order to differentiate interface defects from bulk defects, admittance measurements should be performed at different biases to ) ( determine how the differential capacitance, ω•dC/dω, is affected.[33] In Figure 1b, the bulk defect level (ET) is in general energetically discrete and the energy difference (ΔEo) is bias independent.Conversely, the interface defects are continuous and the energy difference (Efpi) is bias dependent, [33] which is defined as: (7) Consequently, the peak of ω•dC/dω from admittance measurements will shift under different biases for interface defect states.Equation 6a describes Nt for bulk defects.In order to calculate the trap density for interface defects, Equation 8 from the literature can alternatively be used as a simple approach: [33] (8) In Equation 8, the differential capacitance, ω•dC/dω, is also used for trap density calculations in a similar way to Equation 6a.
To determine the trap density for bulk defects, Nt, of the heterojunction, Equation 6a can be solved numerically.In the current study, the Ordinary Differential Equation (ODE) function in MATLAB ® was used.Before solving Equation 6a, some important parameters needed to be estimated or calculated from the literature, i.e., Debye length, thermal velocity, trap capture cross-section, thickness distribution of the depletion region at each side of the HJ.Initial conditions, such as Nt and trap energy level, are also needed to numerically solve the differential equations.Here, the first term in Equation 6a according to the above mentioned numerical analysis does not obviously change the capacitance of the p-n junction and thus can be removed from the equation, at the same time C in the second term is removed for the same reason, resulting in a reduced form as Equation 9: [30,33] (9) Below is an example of the result from the numerical analysis.In the bias dependent measurements (Figures 2a-b), the peaks of the differential capacitance ω•dC/dω are plotted against the angular frequency under different applied biases (from -0.5 to 0.5 V).For bulk traps (Figure 2a), the peaks at each bias are plotted in such a way that they align at one frequency (ω = 1.7×10 4 rad•s -1 ) depending on the bulk trap energy level above EV.The intensity of peaks increases from reverse to forward bias.The exception is for 0.5 V forward bias, where the ω•dC/dω peak is absent because the probing energy, Eω, would otherwise be smaller than EVF at the highest frequency (Figure 1b), which is physically impossible.The increase in peak intensity from reverse to forward bias indicates a higher bulk trap density at larger bias as a result of the trap density being proportional to ω•dC/dω (Equation 9).This is reasonable because the capture cross-section between the trap level and Fermi level is larger with the lower band bending under forward bias (Figure 1b).By contrast, for interface defects (Figure 2b), the peaks shift evenly from low to high frequencies for applied ( ) biases between -0.1 V and 0.1 V.This peak shift is due to ΔEω is being highly influenced by the external applied voltage for interface defects, as reflected by the voltage dependence of Efpi (Eq.7).Whereas for the bulk defects, ΔEω remains constant because the applied bias does not change the bulk trap energy level.
In Figure S1c, the differential capacitance ω•dC/dω shifts its peak position in angular frequency, ω, (from 1.2×10 5 to 1.7×10 4 rad•s -1 ) with increasing temperature (from 22 ºC to 72 ºC).The main reason for the shifts can be explained by Equation 2b, where the angular frequency of a trap (ωo) is dependent on the thermal energy, kT.In order to extract ΔEo (bulk trap energy level above NV) from Figure S1c, the results of ln(ωo) and (kT) -1 are obtained and summarized in Table 1.Rewriting Equation 2b, Equation 10 can be obtained: (10) As a result, the Arrhenius plot can be made based on the temperature-dependent measurements (Figure 2d), with ΔEo as the slope of the ln(ωo) and (kT) -1 plot.
In order to determine ΔEo, Equation 6a can again be solved numerically with an initial value of trap energy, 0.45 eV from the valance band, as obtained from the literature, [17] so that under different temperatures (22-72 ℃), the differential capacitance can be plotted with frequency in Figure 2c.Further, values of ln (ω o ) and -1/kT are extracted from Figure 2c, and are listed in Table 1 and displayed in Figure 2d, so that ΔEo can be extracted.The extracted ΔEo is ~0.43±0.01eV and agrees well with the initial value.This actually further indicates the validity of Equation 6a for trap density determination.The difference of 0.02 eV between the value obtained by fitting the measurements and the literature value can be considered as numerical errors in the simulation (given that kT is 0.025 eV).The measurements at different temperatures is also complicated by the heating of the Cu2O and possible formation of CuO at the heterojunction at above 50 ºC during the growth of the Zn0.8Mg0.2Olayer.[10] As a result, we will focus on the bias-dependent measurements in this work.We have therefore developed the necessary analytical techniques and methodology for measuring the defect states present in our Cu2O/Zn1-xMgxO HJs.

Performance of Cu2O/Zn0.8Mg0.2O solar cells
We made test on devices from both TO and ECD Cu2O.The J-V curves measured under 1 sun AM 1.5G illumination is shown in Figure 3a.From these, the performance parameters were calculated and shown in Table 2.We have previously found the optimal deposition temperature for Zn0.8Mg0.2O is with thermally oxidized Cu2O underlayer being held at 150 °C, [6] which we used here.For comparison, we also deposited Zn0.8Mg0.2Owith ECD Cu2O (ECD05) at 150 °C.On the other hand, we have previously found the device performance to be improved at lower deposition temperatures (80 °C).[9] Hence, we also used this lower deposition temperature for the fabrication of a further ECD sample, ECD03.Irrespective of Cu2O deposition ( ) ( ) methods using TO or ECD, we have obtained a final PCE of approximately 1% in both of the Cu2O devices.But their contributions are quite different.For ECD03 Cu2O sample, it has a higher FF (53%) but it has a lower JSC (4.4 mA•cm -2 ), in comparison with those of 35% and 8.5 mA•cm -2 in the TO Cu2O sample.Typically, the difference of the contributions to the PCEs for the ECD and TO Cu2O samples suggests that the recombination mechanisms are not the same, which we will further compared the wavelength dependent measurement setup.
Despite the comparable efficiencies, the TO and ECD Cu2O devices had different EQEs (Figure 3b).Whereas the TO Cu2O had a higher EQE in the long wavelength range (490-600 nm), its EQE dips by approximately 20 % at wavelengths between 400 nm and 490 nm, consistent with previous reports.[6,12] By contrast, the EQE of the ECD Cu2O reached ~90% in the short wavelength range, even for ECD05 (Figure 3b).In order to clarify the differences in the EQE results, the drift-diffusion model by Musselman et al. [18] was used to model the charge transport length in both types of devices.The results showed than the diffusion length of minority carriers in the TO sample is 310 nm, three times of that of the ECD sample.Consequently, this leads to a large EQE at long wavelengths.Our results agree well with the diffusion lengths obtained from earlier studies.However, the efficiency of the TO sample is still limited by a poor hetero-interface, [6] even though it has a longer drift length of minority charge carriers (2790 nm) than the ECD sample (110 nm drift length).[18] Musselman et al. [18] was successful in using the drift-diffusion model to determine the charge transport diffusion for TO and ECD samples.On the other hand, the underlying mechanisms and the fundamental reasons for the difference between the two samples were not explored.On the other hand, Marin et al. [33] introduced admittance spectroscopy as a means to determine the trap density of hetero-interfaces in Cu2O based PV solar cells.But they did not differentiate between the two major recombination pathways.In particular, the reason for the low short wavelength EQE in thermally oxidized Cu2O device was not determined.To answer these questions, in this work, we established a lumped circuit model to differentiate the effects of interface and bulk detects on efficiency losses in these two samples.

Defect analysis of Cu2O/Zn0.8Mg0.2O heterojunctions
A lumped circuit model with impedance spectroscopy was used to analyze TO and ECD samples (ECD03 and ECD05, respectively, with more details on impedance analysis of ECD05 shown in Figure S4).In the Nyquist plots for the two types of samples, the imaginary component of the impedance (-Z") is plotted against the real component (Z') under an applied D.C. bias of -0.5 V to 0.5 V.The Nyquist plots are depressed semicircles at each D.C. bias, in which the center is below the Z' axis (i.e., -Z" < Z' at the maximum for -Z"), which indicates that a defect-related impedance component should be added to the model.[33] A separate small semicircle was also present in the low impedance region for both types of samples.But for the TO Cu2O, the smaller semicircle merged into the larger semicircle (Figure S1b'), indicating that Schottky contacts have less of an influence than for ECD03 (Figure S1a').
Analyzing the differential capacitance plots gives an indication of the defect states present.For ECD03 (Figure 4a), there is only one differential capacitance peak at each D.C. bias and the peak intensity showed a slight increase with applied biases from -0.5 V to 0.3 V, but then reduced to a lower intensity at a bias of 0.5 V.At the same time, the peak position shifted from 3.7×10 4 rad•s -1 to 2.7×10 5 rad•s -1 with increasing D.C. bias.In a first approximation, the bias dependent differential capacitance for the ECD sample may seem to have followed the trend of interface defects.However, the magnitude of the bias dependent peak indicated in Figure 2b for interface defects shows a strong shift in frequency within a voltage range of -0.1 V to 0.1 V. Hence, the experimental peak shift in the ECD sample does not seem to match the characteristics of interface defects.Because a small shift in these peaks means little variation of trap energy, formulated by Equation 2a, where frequency is related to the energy, contradicting the nature of continuous energy distribution of the interface traps (0.4-0.8 eV above valance band).[17] Using this equation, however, the peak shift in the ECD sample indicated a bias dependent trap energy (Eo) of ~0.44-0.48eV, with trap energy of 0.46 eV for zero bias.If bulk defects are allowed to vary within a certain range, e.g., due to its density distribution with energy, or formation of bulk defects in band, with external bias, then it is reasonable to attribute these peaks to bulk defects.Indeed, a defect band was observed in as-deposited Cu2O film and was claimed as the main reason for difference in optical absorption.[34] Therefore, it is surmised that the peak shifting in the ECD sample is caused by a band defect and the bulk defects are located 0.46 ±0.02 eV above EV.This agrees with early observation of trap density at 0.475 eV for Cu2O from deep level transient spectroscopy (DLTS).[35] Further, assignment of the peaks to bulk defects hinges on observation of long wavelength EQE loss in ECD sample.
From the differential capacitance plots for the thermally oxidized Cu2O device (Figure 4b), the angular frequency (ωo, aligned at 1.2×10 4 rad•s -1 ) was unchanged with applied bias.In contrast, the peak intensity increased with applied biases of -0.5 V to 0.3 V, before dropping at 0.5 V. Again, according to the bias dependent feature of the differential peaks, the alignment of peaks for frequency can thus be tentatively assigned to bulk defects.However, the peak intensity in the thermally oxidized sample does not increase by the same magnitude as it does from the bulk defects (in Figure 2a), thus not reflecting the effect of band bending in defect activity with external biases.In fact, both the J-V and EQE measurements (Figure 3) suggest that interface defects played important roles for the thermally oxidized Cu2O device.If so, one possibility for the absence of peak shifts with external bias in this device is that a large density of interface defects can pin the Fermi level and prevent the shift of the differential capacitance peaks under applied bias.[33] At interfaces, traps can be generated as a result of, e.g., dangling bonds or strain induced formation of CuO.[21] Fermi level pinning occurs when a particular vacancy or interstitial accumulates at the surface, resulting in the localization of these defects in energy.[33] The pinning of the Fermi level may result in lower band-bending at the heterojunction, resulting in a smaller built-in voltage, which may contribute to the lower VOC of the thermally oxidized Cu2O device (Table 2), and further the observed dip in EQEs at the short wavelength.We note that the thermally oxidized sample, which a VOC of 0.336 V is much lower than that (0.43 V) of the ECD sample.At this moment, therefore, the peaks at ωo~10 4 rad•s -1 for the thermally oxidized Cu2O is assigned to pinned interface defects with Efpi ≈ 0.5 eV above EV.[17] Further information is discussed in Sec.2.4.
We also note that, in the thermally oxidized sample, there is a differential capacitance shoulder located at ωo~10 6 rad•s -1 (Figure 4b) with lower intensity, and its intensity becomes larger at forward biases.Using Equation 2a, the corresponding energy level of the shoulders is ~0.27 eV above the NV.This shoulder is mostly probably related to the inhomogeneity at the heterojunction, rather than a perturbation by a Schottky barrier.[17,33] The inhomogeneity can cause varying profiles of energy level for defects.The appearance of such a shoulder is a characteristic feature of interface defects.In addition, as stated in Sec.2.1, items (1) and ( 2) resistances at the metal/semiconductor contact are ignored for simplicity and thus in the simulation results, Fig. 2b&c, there is no trace of such small peaks.In addition, surface defects will affect both the simulation and experimental results at low frequencies because they are further away from the hetero-interface.
The trap density, calculated from Equation 8(interface defects) and 9 (bulk defects) with our measurements, is shown in Figure S5.The thermally oxidized Cu2O has interface defects with a peak in trap density at ~0.5 eV above EV (Figure 6a).At the same time, the interface defect shows a variation in energy level to 0.27 eV due to inhomogeneity in the Cu2O films.On the other hand, the ECD Cu2O has a band of bulk defects located 0.46 ± 0.02 eV above EV (Figure S5b).The distributed bulk defects in the ECD Cu2O may arise from the higher density of grain boundaries than in the thermally oxidized Cu2O, which can act as bulk recombination centers.[6,9,18] The trap density in the ECD Cu2O is also an order of magnitude higher than the interface trap density in the thermally oxidized sample, which could be another reason why the ECD Cu2O samples have lower long wavelength EQEs (Figure 3b).For sample ECD05, the differential capacitance peaks align at 6.1×10 4 rad/s for bias voltages varying from -0.5 V to 0.5 V (Figure S4c).This fits well with the simulated results, see Figure 2a, in terms of the alignment of peaks with external biases.Thus, this indicates that the defects are located at a fixed energy level, rather than an energy band for the ECD03 sample.On the other hand, the intensity of these peaks does not change with bias, indicating a uniform trap density.As a result, in comparison with the ECD03 sample, the ECD05 sample shows bulk defects with single energy level at 0.31 eV above NV.

Simulations on the influence of interface recombination velocity on EQE
We performed simulations on the Cu2O/Zn0.8Mg0.2O/AZOstack using SCAPS.[36] Using these simulations, we were able to determine the correlation between the defect states we measured and the EQE.For thermally oxidized Cu2O, we modeled the defects as interface states with a Gaussian distribution centered 0.5 eV above EV.We compared the EQEs at different trap densities (Nt).When there are no interfacial traps, the EQE is 100% for wavelengths below 490 nm (Figure 7a).When the trap density increases to 2 × 10 12 eV -1 •cm -2 (the same as the Nt measured for ECD Cu2O), the EQE decreases in the short wavelength range.But with the trap density measured for thermally oxidized Cu2O (2 × 10 13 eV -1 •cm -2 ), the simulated EQE was 0%.Simulated EQEs are 0% for trap densities higher than 5.24 × 10 12 eV -1 •cm -2 .We modeled ECD Cu2O as having a Gaussian distribution of bulk defects centered 0.46 above EV and no interface defects.In this case, the long wavelength EQEs are lower than those for thermally oxidized Cu2O (Figure 5), and the short wavelength EQEs are 100 % for wavelengths below 490 nm.The trend in long wavelength EQEs is in agreement with our measurements (Figure 3b).We took the series resistance (20 Ω.cm 2 ) and shunt resistance (300 Ω•cm 2 ) of the device into account in our simulations, but our short wavelength EQEs for ECD Cu2O may not reach 100 % due to losses in the Zn0.8Mg0.2Olayer, [37] which we did not take to account for simplicity.We also considered the case where the 2 × 10 12 eV -1 •cm -2 density of bulk defect states in ECD Cu2O also occurred at the interface.This again resulted in a decrease in the short wavelength EQEs (Figure 5b).Our simulations are therefore consistent with our defect analysis that indicates that the lower short wavelength EQEs for thermally oxidized Cu2O are a result of interfacial defect states.

Conclusion
We have analyzed defects in Cu2O made by thermal oxidation (TO) and electrochemical deposition (ECD) by developing a lumped circuit model in impedance spectroscopy measurements.These show that TO Cu2O predominantly has interfacial defect states centered 0.5 eV above EV, whereas ECD Cu2O predominantly has bulk states centered between 0.46 ± 0.02 eV above EV.Through SCAPS simulations, we found that Cu2O with predominantly interfacial rather than bulk defect states has higher long wavelength EQEs but lower short wavelength EQEs.This strongly agrees with our EQE measurements of TO and ECD Cu2O heterojunction solar cells.This work indicates that the route to further improvements in Cu2O solar cells is by defect control with interface engineering of the TO Cu2O devices.

Experimental Section
Cu2O synthesis: For thermally oxidized cuprous oxide, Cu2O substrates were obtained by a 2 hour oxidation of 0.25 mm thick copper foil, finished by quenching of the substrates, as described in Ref. [6] The oxygen partial pressure was monitored throughout the heat treatment keep the substrates in the phase region where cuprous oxide is thermodynamically stable.[24] Cupric oxide (CuO) formed on the substrate surface during quenching was removed by etching.Substrates were then masked on one side with insulating black paint, defining the solar cell area to be approximately 0.1 cm 2 .
AP-CVD buffer layer deposition: Zn0.8Mg0.2Owas deposited on top of the Cu2O by atmospheric pressure chemical vapor deposition (AP-CVD).[2] Diethylzinc and bis (ethylcyclopentadienyl) magnesium were used as the Zn and Mg precursors respectively, and deionized water was used as the oxidant source.Nitrogen gas was used to bubble through the precursors at 6 mL•min -1 (Zn precursor), 200 mL•min -1 (Mg precursor) and 100 mL•min -1 (water).The metal precursors were diluted with nitrogen gas flowing at 100 mL•min -1 , and the oxidant diluted with nitrogen gas flowing at 200 mL•min -1 .These were fed to a gas manifold, along with nitrogen gas flowing at 500 mL•min -1 , to create separate channels of metal precursor and oxidant separated by channels of inert nitrogen gas.600 oscillations of the substrate beneath the gas manifold was used, giving films of approximately 60 nm in thickness.
Characterization: An Agilent 4294 Precision Impedance Analyzer was used to characterize the impedance spectra against the normal frequency in Hz.The measurement was performed at a certain applied bias voltage with AC signal (amplitude of 20 mV, sweeping from 40 Hz to 10 MHz).The temperature was controlled by using a hotplate and was monitored by a thermocouple.The samples were stored in the darkness for the same period of time (overnight) prior to the experiments in order to empty the traps that became occupied upon light soaking.Solar simulations were performed under AM 1.5G radiation using an Oriel 92250A solar simulator according to previous reports.[6,9] External quantum efficiency measurements were performed using a 100 W tungsten halogen lamp source and monochromator, according to previous reports.[6] Trust, the Rutherford Foundation of New Zealand, and the ERC Advanced Investigator Grant, Novox, ERC-2009-adG247276.

Figure 1 .
Figure 1.(a) An equivalent lumped resistor-capacitor (RC) circuit that represents the Cu2O/Zn0.8Mg0.2Op-n junction, including two metal-semiconductor junctions.ΔRi and ΔCi are the geometry related resistance and capacitance, while ΔRti and ΔCti are dynamic ones, which are related to the defects in Cu2O or at interface.(b) Schematic of band diagram for Zn0.8Mg0.2O/Cu2Oabrupt heterojunction.Numbers 1 and 2 in blue are used to denote the cross-section points of Fermi level (EF) with interface defects and bulk defect level (ET), respectively.Figure 1b is reproduced with permission.[17]Copyright 2013, American Institute of Physics.

Figure 2 .
Figure 2. (a) Differential capacitance ω•dC/dω with respect to angular frequency ω under different bias conditions from -0.5 V to 0.5 V from numerical results in Eq.6 to analyze bulk defects.The bias at 0.5 V did not give any result in the plot, the reason of the plot measured at forward 0.5 V is missing is because the probing energy Eω at the highest frequency is smaller than EVF).(b) Differential capacitance ω•dC/dω with respect to angular frequency ω under different bias conditions from -0.1 V to 0.1 V from simulation to analyze interface defects.(c) Differential capacitance ω•dC/dω with respect to angular frequency ω under different temperatures from 22 ºC to 72 ºC from simulation to analyze bulk defects (d) Extraction of the trap energy ΔEo from shifts of ω•dC/dω peaks with temperatures from Figure 2c.

Figure 3 .
Figure 3. (a) Plots of current density versus bias voltage (J-V) for both types of samples under illumination of AM 1.5G radiation.(b) Plots of external quantum efficiency (EQE) for both types of samples.

Figure 5 .
Figure5.External quantum efficiency (EQE) of (a) thermally oxidized and (b) ECD Cu2O devices calculated using SCAPS numerical simulation for different trap densities.The thermally oxidized Cu2O was modeled with only interfacial recombination, with the defects having a Gaussian distribution located 0.5 eV above EV.The ECD Cu2O was modeled with a Gaussian distribution of bulk defects located 0.46 eV above EV.The capture cross-section was taken as 4.5 × 10 -12 , based on previous measurements.[17]

Table 1 .
Results of the peak maximum (lnωo and kT ) at each temperature for bulk traps.

Table 2 .
Parameters extracted from the J-V measurements for the two types of Cu2O/Zn0.8Mg0.2Oheterojunction solar cells.