Absorber composition: A critical parameter for the effectiveness of heat treatments in chalcopyrite solar cells

Post‐device heat treatment (HT) in chalcopyrite [Cu (In,Ga)(S,Se)2] solar cells is known to improve the performance of the devices. However, this HT is only beneficial for devices made with absorbers grown under Cu‐poor conditions but not under Cu excess. We present a systematic study to understand the effects of HT on CuInSe2 and CuInS2 solar cells. The study is performed for CuInSe2 solar cells grown under Cu‐rich and Cu‐poor chemical potential prepared with both CdS and Zn(O,S) buffer layers. In addition, we also study Cu‐rich CuInS2 solar cells prepared with the suitable Zn(O,S) buffer layer. For Cu‐poor selenide device, low‐temperature HT leads to passivation of bulk, whereas in Cu‐rich devices, no such passivation was observed. The Cu‐rich devices are hampered by a large shunt. The HT decreases shunt resistance in Cu‐rich selenides, whereas it increases shunt resistance in Cu‐rich sulfides. The origin of these changes in device performance was investigated with capacitance–voltage measurement, which shows the considerable decrease in carrier concentration with HT in Cu‐poor CuInSe2, and temperature‐dependent current–voltage measurements show the presence of barrier for minority carriers. Together with numerical simulations, these findings support a highly doped interfacial p+ layer device model in Cu‐rich selenide absorbers and explain the discrepancy between Cu‐poor and Cu‐rich device performance. Our findings provide insights into how the same treatment can have a completely different effect on the device depending on the composition of the absorber.

such as light soaking (LS), 4 heat treatment (HT) with 5 or without wet treatment, 6 combined heat LS (HLS) at different optimum temperatures, 7,8 and combined effect of heat and voltage bias soaking. 9 The optimum treatment and treatment conditions in each work are different and could be related either to the absorber composition or to the absorber/buffer (A/B) 7,10 interface.
The present work highlights the effect of absorber composition on the effectiveness of the post-device treatment. This was assessed by performing HT on both Cu-rich and Cu-poor absorbers with very different surface properties. Cu poor implies absorbers with a Cu/In ratio <1, and Cu rich implies absorbers grown under Cu excess, which consists of a stoichiometric CuInSe 2 phase and Cu selenide secondary phases. 11 The integral composition of the film shows a Cu/In ratio >1.
It has been reported that absorbers grown under Cu excess are characterized by larger grain size, lower potential fluctuation, better mobility, and lower defect density compared with Cu-poor absorbers. 12,13 However, solar cells based on absorbers grown under Cu excess suffer from lower efficiency compared with Cu-poor devices. This is mostly because they are dominated by interface recombination, 14 which can be traced to a Se-related defect, caused by the necessary etching process. 15 Therefore, to the present date, all the high-efficiency devices are realized by growing the absorbers with a final Cu-poor composition. 1,16,17 In all these Cu-poor devices, the dominant recombination path is in the bulk, rather than in the interface. 14 Therefore, it is worth performing an HT study using both Cupoor and Cu-rich chalcopyrite absorbers, which have different dominant recombination paths and allow us to study the effect of annealing on the interface versus the bulk. Moreover, some of the best devices deploy sulfur to achieve favorable band bending at the front surface. 1,18 Therefore, it is important to also study the sulfide chalcopyrite.
In this contribution, we investigate the effects of HT on highefficiency one-stage co-evaporated Cu-rich and Cu-poor CuInSe 2 and on Cu-rich CuInS 2 devices. Single-stage preparation of CuInSe 2 absorbers does not give us the best efficiencies, but we are aiming at comparable absorbers prepared by a similar process. Gallium-free absorbers are used to exclude any effects related to the Ga gradient.
The devices were prepared with two different buffer layers: cadmium sulfide (CdS) and zinc oxysulfide [Zn(O,S)], to rule out buffer-related changes in device performance because of HT. We measure the effect of HT on the performance of these devices. The origin of the changes in device performance is investigated with capacitance-voltage (CV) measurement together with external quantum efficiency (EQE) and temperature-dependent current-voltage (JVT) measurements.
For some absorbers, we include an in-depth study by photoluminescence (PL) quantum yield and lifetime measurements. Our findings provide insights into how the same treatment can have a completely different effect on the device depending on the composition of the absorber. Furthermore, while low-temperature HT (maximum 150 C) may slightly alter buffer layer properties, we do show that the HT has similar effects on the device properties independent of the buffer layer, as long as an appropriate band alignment 19 is ensured.
In this work, we first present the analysis of the effects of HT in the Cu-poor CuInSe 2 device prepared with the CdS and the Zn(O,S) buffer layers. We inspect and analyze the improvement in device performance and associate it to interface passivation and change in buffer composition. In the same section, we discuss the effects of the HT on Cu-rich CuInSe 2 and CuInS 2 solar cells. Further work is divided into four parts, always comparing Cu-poor to Cu-rich CuInSe 2 devices with a CdS buffer layer, plus CuInS 2 device with the better suited Zn(O,S) buffer layer. First, a direct comparison of the CV analysis of Cu-poor and Cu-rich devices is done. Whereas for Cu-poor devices, the apparent doping decreases with HT, for Cu-rich devices, it remains unchanged. Next, using PL as a tool, we discuss the impact of HT on the optical properties of Cu-poor and Cu-rich selenides. In Section 4, we discuss the JVT analysis of these devices, especially comparing Cu-poor and Cu-rich CuInSe 2 with Cu-rich CuInS 2 , which provides insight into the observed differences and provides evidence for a surface with high defect density in the Cu-rich devices. Finally, in Section 5, to validate our assertions, numerical simulations are presented with a highly defective surface for Cu-rich CuInSe 2 , which provides correspondence with our experimental results.

| PREPARATION AND TREATMENT OF SOLAR CELLS AND CHARACTERIZATION METHODS
Polycrystalline thin films of both CuInSe 2 and CuInS 2 absorbers were grown on a molybdenum-coated glass substrate. The CuInSe 2 absorbers were grown using a molecular beam epitaxy system, with a base pressure of 2 × 10 −8 Torr in the chamber. Absorbers were made by a one-stage process by simultaneous co-evaporation of copper and indium metals on the substrates kept at a fixed temperature of 540 C in a selenium atmosphere. Different copper and indium fluxes were used to obtain "Cu-rich" and "Cu-poor" absorbers. The selenium flux was controlled using a valve cracker effusion cell. The growth of the Cu-rich CuInS 2 absorbers was done in a similar one-stage coevaporation process at a constant process temperature of 590 C on molybdenum-coated high-temperature glass. It is to be noted that for CuInSe 2 , we used soda-lime glass (SLG), whereas for CuInS 2 , a hightemperature glass was used to avoid the temperature constraints posed by SLG due to its low melting point. The Na atomic % content in high-temperature glass is less than half the one in SLG, and the K atomic % content is more than an order of magnitude lower than SLG.
We have to use higher temperatures for the sulfide absorbers because it was shown that temperature is a critical parameter for sulfide absorbers. 2,20 Otherwise, we try to keep the processes as similar as possible, in particular by using one-stage processes for all absorbers investigated. It must be noted that the CuInS 2 device grown on SLG also shows same trends in performance before and after HT as will be presented here with the high-temperature glass.
The elemental composition of unetched absorbers was measured using energy-dispersive x-ray spectroscopy (EDX) at 20 kV and is reported in Table 1. The values given represent an integral composition, including the Cu chalcogenide phases for Cu-rich films.
After the absorber growth, the Cu 2-x S/Se secondary phases 11 21 On top of the buffer layer, undoped zinc oxide (ZnO) and highly conductive aluminum-doped zinc oxide (Al: ZnO) window layers were sputtered before depositing Ni-Al contact grids using an electron beam evaporation. Finally, devices with an area of 0.4-0.5 cm 2 were identified using mechanical scribing. A list of all the devices investigated is reported in Table 2.
Device annealing at 100 C and 150 C was performed on a hot plate in the air on the same device sequentially. These two annealing steps will be referred to as HT1 and HT2. The HT was performed for 30 min in each case. After annealing, the sample was allowed to cool down to room temperature for 2 h.
Time-resolved PL (TRPL) measurements were performed to investigate the PL lifetime of the minority charge carriers in the Mo/CuInSe 2 /CdS stack before and after the HTs. The excitation was performed with a pulsed laser of 638-nm wavelength at a repetition rate of 200 kHz. The injection level was moderately high for the Cupoor CuInSe 2 absorber, being on the same order as the estimated carrier concentration. However, for the Cu-rich CuInSe 2 absorber, the injection level was somewhat lower than the estimated carrier concentration. Although under high injection condition, the PL signal is proportional to Δn 2 , contrary to Δn in the low injection condition, the excess carriers can still be monitored by the transient PL signal after low injection conditions have been established. 22 The integral PL signal near the band edge was measured. The lifetimes were extracted from the final slow long decay after the initial fast decay with a single exponential fit within one order of magnitude. The quasi-Fermi level splitting (qFls) is extracted from intensity calibrated and spectrally corrected PL spectra. Details can be found in the supporting information (data in SI) and in Babbe et al. 23 The current-voltage (JV) characteristics of the produced solar

| Device performance
We start by discussing the HT effects on Cu-poor selenide devices with different buffers. Figure 1A,B shows the summary of the device performance before and after the two HTs for devices with the CdS and Zn(O,S) buffer layers. 14  To understand the origin of these improvements after the HT, the JV curve is fitted ( Figure S1) with one diode model to extract the ideality factor (A) and the saturation current (J o ). Fitting was done by the JV fit method 25 using a Python script developed in our lab, based on orthogonal distance fitting. The fit results along with the device JV parameters for the dark curve are presented in Table 3.
We will start by discussing the impact of HTs on the device V oc .
After HT1 the saturation current (J o ) decreases in both devices (Table 3), as a consequence, we see an improvement in V oc by increases the series resistance of the device (Table 3), which reduces the FF.
To understand the increase in J sc in both devices after HT2, we investigate the EQE of both devices. Figure 2A shows the EQE spectrum of the CuInSe 2 /CdS device before and after HT1 + HT2; there is an improvement in EQE of the device in the long-wavelength region.
This is a direct result of increased carrier collection of the carriers generated far from the junction, as the space charge region (SCR) width increases after HT due to reduced doping of the absorber. This change of SCR width is observable in capacitance measurements and will be discussed later. The CuInSe 2 /Zn(O,S) device also shows an improvement in the EQE after HT1 + HT2 ( Figure 2B), unlike the CuInSe 2 /CdS the improvement in this case is in the entire wavelength spectrum. Even though the SCR width also increases in this device after HT, it is not enough to improve the EQE. The increase in the EQE is completely dominated by the decreased reflectance of the light in the structure (see inset Figure 2B).
We now discuss the results for the Cu-rich CuInSe 2   T A B L E 3 Device parameters of best Cu-poor CuInSe 2 device prepared with CdS and ZnOS buffer layer before and after the HTs, extracted from the current-voltage characteristics, from fit to dark current-voltage characteristics  (Table 4 and Figure  Unlike Cu-poor CuInSe 2 devices, the Cu-rich CuInSe 2 device performance decreased slightly after HT1 ( Figure 3A). This is mostly due to a loss in FF, which is at least partly due to the decrease in the already low R sh ( Table 4). The device shunt became even worse after HT2, leading to further deterioration of the FF. In addition, the V oc also decreases substantially, much more than the qFls, as we will T A B L E 4 Device parameters of best Cu-rich CuInSe 2 device prepared with CdS and best Cu-rich CuInS 2 device prepared with ZnOS before and after the HTs  30 which depends upon the chemical potential of constituents and final composition, even though the absorbers were grown by a similar deposition process. Furthermore, the necessary etching process for the Cu-rich absorbers leads to a p + layer near the junction, as we will discuss later, which influences the reaction to the HT. This confirms the crucial role of the absorber composition on the electronic properties and defect formation energy.
In the case of Cu-rich CuInS 2 , we observed degradation in the device performance from 5.3% to 4.6% after HT1. This decrease is due to lower V oc , which is a result of a reduction in R sh . However, the HT2 results in an increase of R sh , and consequently, both V oc and FF improve ( Table 4). As a net result of this, we get an improved device efficiency from 4.6% to 6.4%. This trend is opposite to Cu-rich Although in this section, we looked at the impact of HT1 and a combination of HT1 + HT2 on device efficiency, it must be noted that the impact of HT2 alone on the device without HT1 results in similar device efficiency trends as for HT1 + HT2 (Table S1).

| Effect of HT on doping density
To ascertain the change in apparent doping and SCR width after annealing in the CuInSe 2 devices, the CV measurements were performed before and after annealing. The SCR width in Table 5 is extracted from capacitance at $0.2 V at 100 kHz by where C is the capacitance, w is the SCR width, ɛ is the relative dielectric permittivity of absorber, and ɛ o is the dielectric permittivity of free space. For calculations, we have used a value of ɛ equal to 10, as is often used in literature. 31,32 This SCR width does contain contributions from the buffer layer. 33,34 We therefore discuss only changes and not the absolute values. For the same reason, we use the label "apparent" for the doping density and the depth inside the absorber.
The apparent carrier concentration for Cu-poor device is calculated using the local derivative in forward bias $0.2 V in the Mott-Schottky plot. The detailed methodology is described in the supporting information. Figure 4A shows the doping profile before and after the two the "U" shape. This shape is due to high apparent doping towards the front and back part of the junction. The increase in apparent doping towards the front is attributed to minority carrier injection at high forward bias, whereas the increase towards the back could be due to a contribution from the deep defects 40,43 or the bulk doping at the back of the absorber, unaffected by buffer (i.e., Cd or Zn) diffusion. 41 The CV analysis of Cu-rich CuInSe 2 shows higher apparent doping compared with Cu-poor CuInSe 2 ( Figure 4B). This has been observed previously. 12 A similar observation is made for Cu-rich CuInS 2 solar cells (see Figure S4). In CuInS 2 also, HT has no significant effect on the doping profile of the absorber. The most probable cause for this in Cu-rich devices might be the low concentration of Cu vacancies in the absorber. As a result, the Cd or Zn does not have enough sites to diffuse into the absorber. 45 Another reason may be the highly defective surface layer in Cu-rich absorbers, 15 which can also reduce the diffusion of Cd and Zn. We will discuss the nature of this layer later. In summary, whereas in Cu-poor devices, the diffusion of Cd or Zn chemical species results in the decrease of the absorber carrier concentration after HT2, in Cu-rich CuInSe 2 or CuInS 2 device, we do not see any major change in the doping concentration.

| Impact on optical properties
To understand the effects of HT on Cu-poor and Cu-rich selenides, in this section, we will examine their optical properties using PL spectroscopy. Due to poor PL signal, the Cu-rich sulfides will not be presented in Figure 5A. The entire procedure of extracting qFls can be found in the supporting information and in Figure S5. Before the HTs, the qFls was evaluated to be 454 meV. After HT1, the qFls was increased to 473 meV (+19 meV). In contrast, after HT2, the value reduced back to 455 meV (unchanged with respect to the untreated absorber). These changes in qFls could originate from the change in carrier concentration as 46 where k is Boltzmann constant, T is the temperature, N A is the net majority carrier concentration after either of the HTs, and N Ao is the majority carrier concentration before HT. The calculated ΔqFls from Equation 2 using the apparent majority carrier concentration from Table 5, before and after HT1 and before and after HT2, comes out to be −3 and −75 meV, respectively. This predicted change is much smaller than the measured qFls change after HT1 and more negative than the measured qFls change after HT2 with respect to the untreated case. Hence, changes in qFls cannot be explained by the change in N A alone, and therefore, the lifetime (τ) must also change. Figure 5C depicts the measured TRPL decay of Cu-poor CuInSe 2 before and after the HTs. The lifetime increases continuously with every HT, reaching a nearly double value after HT2 compared with the untreated absorber.
The longer lifetime after the HT indicates that there is a reduction in non-radiative recombination loss, 22 as recombination centers reduce minority carrier lifetime. These results together with device characteristics (Table 3) suggest that HT1 leads to qFls increase and, as a consequence, an equivalent increase in V oc , suggesting the passivation of recombination centers in the absorber. This passivation is most probably caused by the diffusion of chemical species from the buffer into the absorber. After HT2, the lifetime increases further; this explains the lower decrease in qFls compared with the one calculated just by carrier concentration changes (72 meV expected due to decrease in doping). In addition, there is also a lower deficit between the qFls and V oc after HT2 (Table 3); this observation indicates the passivation of the interface/contacts in addition to the absorber. We now discuss the impact of HT on the qFls and TRPL values for Cu-rich CuInSe 2 . Figure 5B shows the qFls values after HT1 and HT2. Only HT2 results in a significant decrease in the qFls, from 473 meV before HT to 454 meV after HT2. This value is very close to the ΔqFls, calculated from Equation 2 (10 meV) using majority carrier concentrations (from Table 5) for the device before and after HT2. For HT1, the calculated ΔqFls is 2 meV, nearly equal to the difference of the qFls measured by calibrated PL. In contrast to the Cu-poor device, the minority carrier lifetime evaluated (15 ± 2 ns) does not change for Cu-rich device ( Figure 5D). This explains why the Cu-rich device performance does not improve after HT1 or HT2, as neither qFls nor lifetime improves. The higher difference between the V oc and qFls after HT indicates a degradation of the B/W layers, leading to an additional gradient in the electron quasi-Fermi level and hence lower V oc in the device.

| JVT ANALYSIS
JVT analysis is an important characterization technique that can help to understand the carrier transport and recombination dynamics in the device. In this section, we will discuss the JVT curves of the Cupoor and Cu-rich CuInSe 2 device with the CdS buffer layer and Curich CuInS 2 device with the Zn(O,S) buffer layer, before and after HT.
In all the JV curves, we observe that the superposition principle is not valid: the dark and light JV curves cross each other. The crossing becomes more prominent after HT as seen in Figure 6. Under ideal circumstances (i.e., device has a similar behavior under dark and illumination), a moderate conduction band (CB) barrier (<0.4 eV) 19 should not result in JV crossover. However, in the buffer layer, a phenomenon known as "photodoping" has been observed. 47,48 This is mostly explained by an increase in the free carrier concentration in the material upon illumination and the release of free electrons from the deep acceptor levels in CdS 49 or from a thin ordered defective layer near the interface 32 (the latter is not observed in our case; see Raman spectra, Figure S6). Thus, the photodoping of the buffer, together with the CB spike at the A/B interface and CB cliff at the B/W interface, 48,50,51 can explain the JV crossover. In the following, we discuss first the cause of the crossover for the example of the standard Cu-poor CuInSe 2 device.
To investigate the origin of the photodoping in our case, we performed JV measurement under illumination with the red light at  Figure S7). This measurement reveals that it is not the direct generation of the carriers in the CdS buffer under illumination that causes this photodoping, rather it is the injection of carriers from the absorber into the buffer. Hence, the crossover is most likely due to carriers generated in the absorber close to the interface and not due to the carrier generation in the buffer itself.
The crossover and its temperature dependence can be understood by assuming thermionic emission transport across the barrier at the A/B interface. According to thermionic transport model, the current across the barrier is given by 52 φ is the barrier height, which in this case, φ = E c − E fn , as shown in Figure 7, where E c is the minimum of the CB edge at the buffer absorber interface and E fn is the electron quasi-Fermi level at the interface, and A * = (4πqm * k 2 /h 3 ) is the modified Richardson constant and T is the temperature. Now under dark conditions at sufficient forward bias >V oc, the barrier is active and has a certain value ( Figure 7A) that an electron has to overcome to travel across the interface into the absorber. As a result, there is a small potential drop across the interface. However, due to the increase of electron concentration in the buffer under illumination, the barrier is reduced ( Figure 7B), and as a result, the potential drop across the interface is less than in the dark. This leads to the crossover of light and dark JV curves as can be seen in Figure 6. This effect is demonstrated by device simulations in Section 5.
The temperature dependence of the crossover can be understood by the following: considering a constant barrier, the thermionic current is smaller at a lower temperature. Therefore, the current at which the effect of the different barriers in dark and light matters becomes lower. This shifts the crossover points to lower currents and higher voltages.The crossover effect is more pronounced in the device with HT2 as observed in Figure 6B, that is, the current at the crossover point is lower. This can be due to the increase of Cu diffusion into the CdS causing the dark carrier concentration of the CdS to decrease even more and eventually resulting in an even higher barrier in the dark.The behavior of the JVT characteristics ( Figure S8) for the Curich CuInSe 2 device before any HT and after HT2 is similar to the one in the Cu-poor CuInSe 2 devices: it also shows pronounced crossover between JV under dark and illumination at all temperatures in HT device and at lower temperatures in untreated device. In addition to this, the JVT curves show a peculiar feature that is not observed for the Cu-poor CuInSe 2 device. At lower temperatures, around 150 K, the forward dark current of the untreated device tends to flatten at moderate voltages $0.4 V ( Figure S8a). A rollover is observed for the same device under illumination ( Figure 8A) at lower temperatures (<150 K). After HT2, however, the forward dark current becomes more exponential with voltage compared with the unannealed device ( Figure S8b). Furthermore, no rollover is observed for the HT2 device under illumination. This can be most clearly seen in Figure 8B where we compare the illuminated JV characteristics at low temperature for annealed and unannealed devices. In the following, we trace back this behavior to the reduction of a p + layer in the Cu-rich devices.
We have recently shown that in Cu-rich CuInSe 2 , after strong KCN etching, we form deep defects near the interface. 15 Plus, it has been argued that this defect is an acceptor defect and causes the carrier concentration gradient in the CuInSe 2 absorber layer with high doping (p + ) towards the front surface. As a result, we form a p-p + -n device structure, and in the energy band diagram under equilibrium conditions, an additional barrier forms near the surface of the absorber (see Figure 9). The impact of the properties of the p + layer on device JV rollover has been studied in detail by Maciaszek. 53 In this report, for simulations, a carrier concentration of 3 × 10 17 cm −3 was used for the p + layer, which is much higher than the calculated values (2 × 10 16 to 4 × 10 16 cm −3 , Table S2) for the Cu-rich CuInSe 2 devices discussed here. In addition, for simplicity, no CB offset (CBO) at any of the interfaces was considered in their work. But in a realistic scenario, in the device structure, there are band offsets at the different interfaces, namely, A/B and B/W interface. [54][55][56] The energy band diagram in such a case is depicted in Figure 9. It is evident that in addition to the p + layer for the photogenerated electrons, there is an additional barrier at the A/B interface due to the CB spike. Similarly, for injected electrons at high forward voltage, that is, above V oc , there are again two active barriers: one due to p + layer as considered in the report by Maciaszek 53 and the other one due to CBO at B/W interface. This combination of two barriers causes the rollover as observed in Figure 8A in our case with much lower doping in the p + layer, than assumed by Maciaszek. It is known that even in Cu-rich Cu (In,Ga)Se 2 , annealing causes cadmium diffusion into the absorber (albeit significantly lower than in Cu-poor ones). 39 Another potential effect is the outdiffusion of sodium (Na) from the bulk to the surface 57 after annealing. We speculate that either of these species (Cd or Na) partially removes or compensates the acceptor-like defect near the absorber surface. The reduction in p-type doping is evident from the CV measurements ( Figure 4B) where the equilibrium apparent doping decreases from 4 × 10 16 to 3 × 10 16 cm −3 after HT2 due to partial passivation or compensation of the acceptor defect (see discussion supplement and Figure S9). Furthermore, the strong increase of the apparent doping near the surface of the absorber (low apparent depth in Figure 4B) is reduced after HT2. This reduction in doping concentration lowers the barrier due to the p-p + layer at the front, and consequently, one no longer sees the double diode or the rollover effect ( Figure 8B) at lower temperatures for HT2 device. We must emphasize here that even though the p + layer is partially passivated by HT2, the device performance becomes worse. This can be understood by two observations, discussed above: (i) the lifetime does not increase, indicating that the observed lifetime depends mostly on recombination centers in the bulk, outside the p + layer, and (ii) the difference between qFls and V oc increases dramatically, due to contact layer degradation, which overcompensates any positive effect of the passivation of the p + layer. In the case of CuInS 2 device , unlike CuInSe 2 , neither the flattening of dark JVT curve nor the rollover effect in illuminated JVT curve at forward bias is observed for the device in Figure 10.
Therefore, JVT does not provide sufficient evidence for the presence of the p + layer in the sulfide absorber in this device. However, there can still be a p + layer in the Cu-rich CuInS 2 device. As our numerical simulations (Section 5) prove, the rollover in the JVT depends not only on the presence of the p + layer but also on the CBO at the B/W interface. We do find evidence for a p + layer in Cu-rich sulfide absorbers: we investigate a similar one-stage CuInS 2 absorber but equipped with an alternative Zn(O,S) buffer. This alternative Zn(O,S) is deposited by a different CBD recipe and has lower oxygen to sulfur ratio (see supporting information), leading to a higher CB minimum. 58 In this device, the rollover effect is observed in illuminated JVT curves ( Figure S10) absorber does contain a p + layer. However, the effect is only visible with the alternative buffer, which likely has a higher CBO at the B/W interface. This is a necessary condition for the rollover, as discussed in the following section.

| DEVICE SIMULATIONS
To check our explanations and to understand the observed JVT characteristics before and after HT, we perform numerical simulations using SCAPS-1D software. 59 The simulation parameters used for the device structure are given in Table 6. Where a range is given, the results of the parameter variation are discussed in the following. The parameters were optimized to match the unannealed Cu-poor    The above model works very well for explaining the crossover in Cu-rich CuInSe 2, but to explain the rollover effect at lower temperatures, we need an additional barrier of some sort, which we introduce by adding a highly doped layer at the front in our Cu-poor device (the p + layer). The defect parameters of this layer were fixed by taking the experimental CV and admittance results (see supporting information) of Cu-rich devices into consideration. Figure 11B shows the simulations done with a p + at the front near the A/B interface. The parameters for this defective layer are reported in Table 6. For the blue curve, we can see a rollover at moderate voltage $0.6 V. To ascertain the p + layer as the origin of the strong rollover, a device without the p + layer was simulated. Figure 12A shows the JVT curves of the device without the p + layer. The rollover that was observable for the device with the p + layer is not that obvious in this case. Finally, the JVT of the device with the p + layer but without the B/W offset is simulated.
Unlike the first case, no rollover for this device was observed ( Figure 12B). These simulations show that to explain the JVT curves as observed in our Cu-rich device (Figure 8), a p + layer in combination with B/W offset is needed.
There can be other causes of this kind of JVT behavior. For example, a back contact barrier or a difference in front contact barrier can also cause this rollover in the JV curve. However, we speculate that these might not be the main cause as both the Cu-rich and Cu-poor devices were made in the same deposition run for the buffer and the window. And if it is the back contact barrier, then one should also observe it in both Cu-rich and Cu-poor devices, because both types of absorbers were prepared at the same deposition temperature. Also, we do not think mild annealing such as in our case can change the back contact barrier so much, as the absorber processing temperatures are much higher than our annealing temperature. Hence, in our case, the model of the defective p + layer surface gives a more convincing explanation for our observations.