Near surface defects: Cause of deficit between internal and external open-circuit voltage in solar cells

The presence of interface recombination in a complex multilayered thin-film solar structure causes a disparity between the internal open-circuit voltage (VOC,in), measured by photoluminescence, and the external open-circuit voltage (VOC,ex) i.e. an additional VOC deficit. Higher VOC,ex value aim require a comprehensive understanding of connection between VOC deficit and interface recombination. Here, a deep near-surface defect model at the absorber/buffer interface is developed for copper indium di-selenide solar cells grown under Cu excess conditions to explain the disparity between VOC,in and VOC,ex.. The model is based on experimental analysis of admittance spectroscopy and deep-level transient spectroscopy, which show the signature of deep acceptor defect. Further, temperature-dependent current-voltage measurements confirm the presence of near surface defects as the cause of interface recombination. The numerical simulations show strong decrease in the local VOC,in near the absorber/buffer interface leading to a VOC deficit in the device. This loss mechanism leads to interface recombination without a reduced interface bandgap or Fermi level pinning. Further, these findings demonstrate that the VOC,in measurements alone can be inconclusive and might conceal the information on interface recombination pathways, establishing the need for complementary techniques like temperature dependent current voltage measurements to identify the cause of interface recombination in the devices.


Introduction
Open-circuit voltage (VOC), a key factor for the efficiency of a solar cell, is measured by either electrical or optical techniques. Electrical measurements, particularly current-voltage measurements give the measure of external open-circuit voltage (VOC,ex) of a device, whereas, optical measurements particularly calibrated photoluminescence (PL) provide the measure of the internal open-circuit voltage (VOC,in) or quasi-Fermi level splitting (qFLs). The VOC,in (qFLs) is calculated from the ratio of total radiative recombination flux of the device to the flux of injected photons. It is generally measured via one sun calibrated PL measurement (in order to compare it to AM 1.5 G illuminated solar cell VOC,ex), and translates to the energetic difference between the hole quasi-Fermi level (Fh) and electron quasi-Fermi level (Fe) in the bulk. 1 Moreover, VOC,in provides a direct measure of the bulk quality of an absorber. While, the VOC,ex measured in a current-voltage (I-V) measurement under one sun illumination is the energetic difference between the Fh at the hole contact and the Fe at the electron contact. The VOC,ex takes into account the interfaces and contacts as well, and is a device related parameter. Hence, VOC,ex is a metric that represent the overall quality of the device. In order to translate optical quality of the absorber into electrical efficiency i.e. VOC,ex it is essential to have a constant qFLs throughout the device structure. [2][3][4] Thin films solar cells comprise of a complex multilayer structure consisting of absorber, charge transport layer etc., each of which individually affect the qFLs and could be a source of a gradient in qFLs. This often leads to a deficit between internal and external VOC i.e. VOC,in -VOC,ex. The deficit can be observed in thin film solar cells such as Cu(In,Ga)(Se,S)2, 5,6 CdTe, 7 perovskite, 4,8,9 and is associated to interface recombination in the device. 4,[9][10][11][12][13] Identifying the source of interface recombination and the underlying qFLs gradient is crucial for achieving higher efficiency in these devices and enabling better understanding of device physics. The mismatch of the energy bands at interface between absorber and charge transport layer, 4,14,15 and Fermi-level pinning are the two commonly evoked models to explain why and more so, in which case interface recombination dominates. [16][17][18][19] Researchers employ qFLs measurements for quantifying interface recombination and determining the quality of surface passivation after charge transport layer deposition or post deposition treatment. 4,20 Though qFLs measurements provide significant information regarding non-radiative recombination in the bulk, it fails to capture the details of interface processes especially in devices dominated by IF recombination. 21 The photoluminescence intensity increases exponentially with the qFLs. Thus in the case of a qFLs gradient, photoluminescence will always detect the highest qFLs and will not indicate the gradient. 15 Therefore, temperature dependent VOC,ex measurements are required to unravel the presence of interface recombination in the device and thus provide necessary information to understand the full extent of the non-radiative interface recombination losses in the device. 22 Here, with the help of copper indium diselenide (CISe), a chalcogenide photovoltaic absorber material, we develop a comprehensive model for understanding the interface VOC deficit by probing the effect of near-surface defects on VOC,in and VOC,ex of the CISe device. We choose CISe for studying the interface VOC deficit, since CISe absorbers grown under Cu-excess conditions (addressed as Cu-rich throughout this work with as grown [Cu]/[In] > 1) and under In-excess (addressed as Cu-poor with as grown [Cu]/[In] < 1) growth conditions result in similar VOC,in with completely different VOC,ex, and therefore different interface VOC deficit. 10,23,24 Moreover, instead of the commonly used Cu(In,Ga)Se2 compounds that have bandgap graded absorber layers, 25 the ternary CISe compound allows to reduce the amount of free variables and redundant complexity in our model. This makes CISe an ideal case study to investigate the cause of the interface VOC deficit in thin film solar cells.
We vary the interface defect density by treating Cu-rich absorbers with different solutions namely, aqueous KCN, aqueous bromine (Braq.), aqueous zinc (Znaq.), sulfur (S) and cadmium (Cd) solution, as well as by depositing a Zn(O,S) buffer. With the help of admittance spectroscopy (AS), deep-level transient spectroscopy (DLTS) and temperature-dependent current-voltage (I-V-T) measurements we probe the impact of these treatments. The study identifies the role of defects near (not at) the interface, which was hitherto not discussed. Furthermore, we scrutinize the limitations of VOC,in (qFLs) measurements alone in characterizing interface recombination and the necessity of temperature-dependent VOC,ex measurements. Using numerical modelling, we establish a model based on strong sub-surface defects, which demonstrates an interface VOC deficit for an interface with favorable band alignment and no Fermi level pinning. The model is experimentally endorsed and provides insights on the origin and nature of these sub-surface defects in CISe solar cells.

Experimental observations Cu-rich vs Cu-poor CISe solar cell
Before building a comprehensive model, it is necessary to look at the optical and electrical characteristics of CISe solar cells prepared using absorbers grown under Cu-rich and Cu-poor growth conditions. Throughout this work VOC,in will be used to define the qFLs, and the deficit between VOC,in and VOC,ex will be referred to as interface VOC deficit, unless stated otherwise. Figure 1a shows typical I-V characteristics of Cu-rich and Cu-poor devices. Both devices are processed in a similar manner i.e. with same buffer (CdS) and window layer (i-ZnO+AZO), deposited with identical process parameters. The Cu-rich device exhibits a lower VOC,ex compared to Cu-poor device, even though both absorbers have almost the same VOC,in values [table in Figure 1b]. The VOC,in is measured with the help of calibrated PL measurements which were performed using our own lab-built system with continuous wave 663 nm diode laser as an excitation source. For extracting VOC,in, samples covered with buffer layer on top are illuminated with laser and PL is measured. Intensity and spectral corrections is then applied to the raw data to determine VOC,in, the entire procedure details can be found in reports 23,26 . An exemplary PL spectra is presented in Figure S1. As a consequence, Cu-rich devices suffer from a high interface VOC deficit (~130 mV), similar to previous data on Cu(In,Ga)Se2. 23 This is significantly higher than the one in Cu-poor device (~20 mV) or in fully optimized devices (~10 mV). 27 This IF VOC deficit is clearly associated to IF recombination being the dominant recombination path in the device as revealed from VOC,ex measurements at different temperatures [ Figure 1c]. The activation energy (Ea) of the saturation current density is obtained from extrapolation of VOC,ex to 0 K. 19 For Cu-rich devices, Ea is always lower than the bulk bandgap (EG) and is associated to the presence of deep defects. 28,29 Whereas, in Cu-poor devices Ea extrapolates to the EG and hence, IF recombination does not limit VOC,ex. Furthermore, an 'S shape' in the first quadrant is observed at lower temperatures in Cu-rich devices, which is not present in Cu-poor device [ Figure 1d]. This roll-over in the first quadrant indicates a barrier for the forward current. 30 Problematic interface properties often lead to an S-shape in the fourth quadrant, which indicates an extraction barrier for the photocurrent. 31 Thus, a model will be valid only if it can successfully reproduce the three observations made for Cu-rich devices: (i) a large interface VOC deficit, (ii) an Ea of the saturation current smaller than the EG and (iii) a 'S shape' in the first quadrant. However, to build a reliable model, we will first probe the characteristics of the deep defect that has been speculated to be the cause of all these issues in Cu-rich CuInSe2. 32 Although AS provides the defect activation energy, it does not yield the defect nature. Therefore, to investigate whether the defect is acceptor or donor in nature, DLTS is measured on KCN etched

(d)
CISe Schottky-devices ( Figure 2c). For the measurement, the device was kept at -1V bias followed by a +1V voltage pulse and the capacitance transient was measured. Figure 2d shows the DLTS results for a chosen rate window alongside with the corresponding Arrhenius plot in Figure 2c.
The peak in the DLTS spectrum is negative, which is a fingerprint of emission of majority carriers from a trap. Further, the activation energy of the corresponding signal is similar to the one observed in admittance spectroscopy. The DLTS data points in the Arrhenius plot continue the admittance data, suggesting that it is the same signal as the one observed in AS. These results are in accordance with our earlier observations, where a reduction in apparent doping was observed after passivation of the ~200 meV defect, 5,32 and confirm our speculation of the ~200 meV defect being acceptor in nature.
Earlier work has established the presence of deep defects in CISe solar cells, which can be passivated with mild surface chalcogen treatments and buffer layers with high sulfur concentration in the deposition process. 28  To summarize Zn treatment leads to a complete passivation of the defects, while S treatment leads to a partial passivation and Cd treatment alone leads to no passivation of the defect. In addition these chemical treatments, ultra-high vacuum (UHV) annealing, which is known to passivate near surface properties of Cu(In,Ga)Se2, also results in passivation of the 200 meV defect (see discussion in SI, Figure S4 and S5). [38][39][40] Thus, together with this and the PDT results it can be concluded that the 200 meV defect is actually a defect at or near the surface, consisting of two constituents, which can be passivated with proper surface treatment.  PDT CISe absorber in a Schottky device (c) corresponding dC/dplot, which at 124 K shows double peak structure, the high frequency peak is arbitrarily named primary peak and the low frequency peak as secondary peak.
(d) The plot of normalized frequency vs normalized dC/d with respect to frequency. The curve shows the appearance of a secondary peak particularly at low temperature.
To get an estimate of defect density capacitance steps consisting of overlapping defect contributions (see for instance Figure 3d) were fitted as described in 41 . In particular, the defect response from a discrete defect level is extended to Gaussian defect distributions. Here, two Gaussian distributions are used and are fitted simultaneously to the complete temperature and frequency range. A fit describing the two and overlapping capacitance steps of the spectra shown in Figure 3d is shown Figure S6. For untreated sample a defect density ~2x10 16 cm -3 and for S-PDT sample a defect density of ~4x10 15 cm -3 was obtained.
To summarize, the experimental findings: the 200 meV defect is an acceptor defect, has a defect density of around ~10 16-17 cm -3 , 32 and is present at or near the surface i.e. it is a sub-surface defect.
It is not clear how this defect can lead to the observed large interface VOC loss and to a saturation current activation energy lower than the band gap. In the next section, a numerical model is realized by introducing defects in CISe based on above discussed defect properties with the aim to describe the experimentally observed losses.

Numerical simulation with sub-surface defects
The results of the previous section indicate the near-surface and acceptor nature of the defect i.e.
an acceptor defect present close to or at the absorber/buffer (A/B) interface. Therefore, the defect could represent either a defective layer within the absorber, just below the surface, or a defective interface between the absorber and the buffer. In this section, using numerical modelling, the impact of both, a defective layer and a defective interface on the VOC,in and Voc,ex of the device will be investigated. The models will be assessed to reproduce the experimentally observed characteristics of Cu-rich CISe devices as discussed before: (i) >100 meV interface VOC deficit, (ii) an Ea of the saturation current density lower than the EG of CISe and (iii) an 'S shape' in the first quadrant at lower temperatures in the I-V curves.
A device model is designed in SCAPS-1D emulating the Cu-rich CISe devices (back contact/CISe/CdS/ZnO/Al:ZnO/front contact). Table S1 records the electrical and optical parameters used in the simulations, which were set constant, taking values from previous measurements, [42][43][44] and are the same as in our earlier simulations. 33   As demonstrated in Figure 4, both models are capable of reproducing the experimentally observed VOC,in and VOC,ex, and hence, the interface VOC deficit. However, the validation of either model as the appropriate description for Cu-rich CISe devices requires also fulfillment of criteria (ii) and (iii). All Cu-rich chalcopyrite devices are characterized by a saturation current, strongly dominated by interface recombination. This is indicated by the Ea obtained from extrapolating VOC,ex vs temperature is always lower than the EG. 10,19 As shown before, the Cu-rich CISe devices presented here also suffer from the same issue. Two possible explanations for an activation energy of the saturation current Ea lower than the bandgap are established in the literature: a cliff at the absorber buffer interface, i.e. conduction band minimum of CdS lower than that of CISe, or Fermi level pinning at this interface. 19,47 Thus, a straightforward origin of interface recombination could be an unfavorable band offset, i.e. a cliff at the interface. However, CdS is a perfectly suited buffer for Cu-poor Cu(InGa)Se2 absorbers, which have a higher conduction band minimum than pure CuInSe2. There is no indication that the band edges of Cu-rich CuInSe2 are different from those of Cu-poor material. Furthermore, the photoelectron study by Morkel et. al. reports a conduction band minimum of CdS aligned with the one of CISe, eliminating unfavorable band offset as the possible cause for interface recombination. 48 The other possible scenario could be the presence of a high concentration of defects (NIF) at the CISe/CdS interface, which pins the electron Fermilevel at the interface. In order to have a working solar cell like in Figure 1a, the pinning position must be above the middle of EG to obtain a decent VOC,ex. Thereby the electron concentration at the interface remains significantly higher than the hole concentration. Thus, making the interface recombination dependent on the interface hole concentration (pIF) and the hole surface recombination velocity (Sp) i.e. R ≈ pIF*Sp. 19 The reverse saturation current density (J0) then is Where, Nv,a is the effective valence band density of states in the absorber and q is the elementary charge, φb is the equilibrium hole barrier at the interface and is equal to the energy difference between the position of electron fermi level (Fe) and the valence band edge (Ev) i.e. φb = Fe -Ev.
Equation (1) Where Jph is the photogenerated current, n is the diode ideality factor. Thus, VOC,ex is dominated by φb. One should note that in a good device without interface recombination, the VOC,ex at 0K is equal to the bandgap of the absorber. Thus, in case of Cu-rich CISe device with spike-type band alignment, Fermi-level pinning could explain an Ea value smaller than the EG, namely φb obtained from VOC,ex vs temperature plot (assuming n, Sp and Jph are not or only weakly temperature dependent). We will therefore investigate further predictions from this model in the following.
For conceiving the appropriate defect model for CISe by numerical simulations, the device performance as displayed in Figure 1 will be simulated. Figure 5a shows the simulated Voc values at different temperatures obtained from the two models with defects at or near the interface and for a reference model without any near interface defects. The simulations go down to 210 K, at lower temperatures the numerical calculations would no longer converge. Remarkably, not only the model with electron Fermi-level pinning but, also the model with a defective layer leads to an Ea of the saturation current less than the absorber EG. It should be noted, that the main recombination in the device with defective layer occurs in that defective layer and not at the interface [ Figure S7a]. The Ea values obtained with this model are slightly higher than experimental values. Even a considerable increase in defect concentration does not result in an Ea value below 0.81 eV [ Figure S8a]. Also, above a certain value the defect concentration starts to limit the short-circuit current (Jsc) of the device meaning that the model would be no longer realistic ( Figure S8b). Thus, we kept the defect density at a value that still gives a realistic short circuit current density, although it cannot fully describe the reduction of Ea. This effect is also not unexpected, since we kept the model rather simple, to allow for temperature dependent simulations.
Thus, both models are capable of introducing a recombination pathway with an Ea lower than the EG. Another important observation comes from hole barrier simulation at different temperatures ( Figure 5b). Neither of the two model results in a temperature independent hole barrier (φb).
However, the φb exhibits a weak temperature dependence in the device with interface defect model, and the extrapolation of φb to 0 K equals the Ea obtained from VOC,ex measurements. This indicates that the simple model of Fermi-level pinning in eq. 1 is only an approximation, and Ea should be identified as φb at 0 K as the φb itself is weakly temperature dependent. It is noteworthy, that the NIF used here was 10 12 cm -2 and even NIF of 10 14 cm -2 results in a weakly temperature dependent φb. Even in the latter case Ea is not equal to the φb at 300 K. On the contrary, in the device with the defective layer the φb extrapolates to EG at 0 K and is strongly temperature dependent. In this case Ea of the recombination current is not determined by the hole barrier. Yet, a strongly defective layer can also lead to activation energies lower than EG -without Fermi-level pinning, and without a cliff in the conduction band alignment.
Finally, we test the model on criterion (iii), i.e. the 'S shape' in the first quadrant exhibited by Cu-rich CISe devices at lower temperatures. Figure 5c shows the I-V curves at low temperatures simulated for a device with a defective layer and a device with defective interface. For the first model 'S shape' in I-V at low temperatures in the first quadrant is observed, as established previously due to the presence of p + layer (defective layer) near the interface. 33 On the contrary, the presence of Fermi-level pinning at interface leads to an 'S shape' in the fourth quadrant, signifying that it rather acts as a barrier for extraction of photogenerated carriers. Thus, the I-V-T behavior of the device is best described by the model with a defective layer. weak Fermi-level pinning as evident from Figure 5b where the φb changes only weakly with temperature. The Ea is given by the value of φb at 0 K. Figure 5d shows simulated Ea and φb at 0 K (obtained by extrapolating simulated hole barrier values to 0 K), as in Figure 5 a and b as a function of interface defect density (Nd,IF). It is clear that in a certain range by varying the defect density one can have Ea anywhere between the EG and the defect position in the interface EG.
Further, there is a one-to-one correlation between Ea and φb at 0 K.
Even though the models presented here might be not fully accurate, as they do not include many factors such as surface EG widening or band offsets between absorber and buffer. Still, the models do a good job of reproducing the main experimental characteristics of Cu-rich CISe devices that indicate a problematic interface, and provide a suitable explanation. Out of the two models, the defective p+ layer explains better the observed I-V behavior at low temperatures. In addition, the simulations demonstrate that the commonly used model of eq. 1 is only an approximation, yet a useful one. Furthermore, we showed that the most critical parameters indicating interface recombination i.e. a significant difference between VOC,in and VOC,ex, and an Ea of saturation current lower than the EG can be reproduced by a model that contains neither a reduced interface bandgap, nor Fermi level pinning.
Moreover, these models, though applied and developed for Cu-rich CISe device, are equally applicable to any other device as well. Particularly, for heterojunction devices, which have optimum band-offset with the hole and electron transport layer, but are still dominated by interface recombination. Other than the conventional Fermi-level pinning, the interface recombination signature in this case could alternatively originate from the defective surface layer. The results of the simulations also demonstrate a way to differentiate between defective surface and defective interface. In both cases, the temperature dependent VOC,ex measurements will yield an Ea for saturation current lower than the EG. However, the two models can be distinguished looking at the I-V curves. While a defective interface results in 'S shape' in the first quadrant, the defective surface results in 'S shape' in the fourth quadrant. Once the root cause i.e. the presence of either defective interface or defective surface is identified, a dedicated passivation strategy can be used to improve the device performance.

Conclusions
In As a general point of view, calibrated PL measurements provide information regarding the ratio of non-radiative to radiative recombination in the bulk of the absorber. However, in these measurements near surface properties could be overlooked. To account for these there is the need of complimentary techniques such as temperature dependent I-V measurements to characterize the device and assign recombination channels in the device. We have provided two universal models which can also be applied to others photovoltaic technologies to explain and understand the cause of interface VOC deficit in the case where the band alignment does not impose a cliff situation.

Device preparation and characterization methods
For the experiments, we used polycrystalline CISe thin films grown on molybdenum coated soda lime glass in a 1-stage process. Comprehensive details of the deposition process can be found in our previous report. 32

Passivation of near surface defect by UHV annealing
The UHV annealing at 280 o C for 30mins at a base pressure < 2 x 10 -9 mbar, was performed on a Cu-rich CISe absorber to assess its ability to passivate sub-surface defects via measuring its impact on the ADM spectra, particularly on the deep defect signature. After UHV annealing the absorber along with a reference sample were finished into solar cell using the baseline process. Figure S3a displays the ADM spectra of reference device, where the highlighted capacitance step in the middle is the commonly observed ~200meV defect. The signature capacitance step disappears in the device prepared with UHV annealed absorber Figure S3b, thus leaving only a step with activation energy of ~86meV. Figure  As stated before the VOC,ex extrapolation at 0K of the devices dominated by sub-surface defects does not go to the band gap but rather to a value less than the bandgap determined from inflection point in external quantum efficiency measurements. For the UHV annealed device VOC,ex extrapolation goes almost to the bandgap ( Figure S4). Therefore, from ADM spectroscopy and VOC,ex extrapolation we conclude that the UHV annealing is an alternate passivation method for the 200meV defect.