Electrostatic potential fluctuations and light‐soaking effects in Cu(In,Ga)Se2 solar cells

In Cu(In,Ga)Se2 (CIGS) thin‐film solar cells, laterally inhomogeneous distributions of point defects may induce electrostatic potential fluctuations and thus reduce the open‐circuit voltage (Voc). In the present work, we investigate possible origins of fluctuating potentials and estimate the amplitude of fluctuations and Voc losses in solar cells with various [Ga] in the CIGS absorber, with different buffer layers and with different durations of an RbF postdeposition treatment (PDT). Electron‐beam‐induced current measurements were employed to study the local difference in the width of the space‐charge region (wSCR). It is shown that the amplitude of fluctuations in the wSCR depends significantly on the choice of buffer system and on the duration of the RbF PDT. In addition, energy‐dispersive X‐ray spectroscopy and cathodoluminescence measurements reveal that band‐gap fluctuations do not have substantial impact on the device performance. Finally, some of the investigated cells were exposed to light soaking, which was found to be a means to reduce the detected electrostatic potential fluctuations and also to increase the effective electron diffusion length in the CIGS absorber for a part of the investigated cells.

doping (ii) and lifetime fluctuations (iii) due to inhomogeneous distributions of (charged) point defects and corresponding redistribution of free charge carriers. 11 While compositional inhomogeneities have already been studied extensively, 9,12 only a few reports are discussing possible origins of net doping and lifetime fluctuations in CIGS solar cells. In particular, it was suggested that the choice of a buffer layer 13 has an impact on electrostatic potential fluctuations, assuming a high density of defects at the CIGS/buffer interface. It was also proposed that the increase in V oc after PDT is due to reduction of electronic potential fluctuations. 14 In the course of the present work, electron-beam-induced cur-   These absorbers were covered with either 50-nm-thick CBD-CdS or CdIn 2 S 4 by physical vapor deposition (PVD). 19 This latter buffer layer was grown in a sulfide dedicated chamber coevaporating CdS, elemental In, and sulfur; the temperature of the SLG/Mo/CIGS stack was set to 200 C during CdIn 2 S 4 coevaporation. The total thickness of the buffer layer is about 25 nm. All devices were completed with 50-nm-thick i-ZnO and 200-nm-thick conductive ZnO:Al. The solar-cell parameters for these samples (Nos. 5 and 6) are provided in Table 1.

| Fabrication of CIGS solar cells with RbF-PDT
The samples for the experiment regarding the RbF-PDT were prepared at HZB on 2-mm-thick glass substrates coated with 800-nmthick molybdenum (deposited by DC-sputtering). On top of this back contact, the CIGS absorber was deposited using an adapted static three-stage coevaporation process as described in detail in Heinemann et al. 20 The maximum substrate temperature during growth was kept at 530 C. The final layers exhibited a Cu-poor (CGI < 1) composition with molar fraction ratios of CGI = 0.9 and GGI = 0.3.
In case of samples with an RbF-PDT, the substrates were cooled down to 280 C after the deposition of the absorber layer and kept at this temperature for the PDT. The PDT was performed for 1 min in one run and 10 min in a separate run. Since all other parameters of the PDT were kept constant, this variation of the duration equals a variation of the amount of RbF deposited on the CIGS. More details on the RbF-PDT can be found in Kodalle et al. 21 After cool-down, the absorber layers were transferred to our chemical lab in air. Subsequently, they were rinsed in NH 3 (aq), and an approximately 50-nm-thick CdS buffer layer was deposited by CBD. Finally, a bilayer of approximately 180-nm-thick i-ZnO/ZnO:Al was deposited by radio-frequency sputtering before Ni/Al/Ni finger grids were evaporated onto this window layer. The solar-cell parameters for these samples (Nos. 7-9) are given in Table 1.

| Cross-sectional specimen preparation
The cross-sectional samples for the SEM measurements were prepared by gluing two stripes of CIGS solar cells face-to-face together, in a way that one stripe was shorter than the other, which provided areas to contact the back and front contacts of one cell for EBIC measurements. Flat cross-sectional surfaces were obtained by mechanical polishing. On top of the cross section, a 4to 5-nm-thick carbon layer was evaporated in order to protect the surface and reduce charging of specimens during irradiation by the electron beam.

| Characterization of the solar cells
Chemical composition and thickness of CIGS absorbers were determined by means of X-ray fluorescence and glow-discharge optical emission spectroscopy. Current-voltage (I-V) measurements for solar cells were measured with a simulated AM1.5G spectrum at standard testing conditions in the as-grown state, that is, without additional LS or postannealing procedures. EBIC and energy-dispersive X-ray spectrometry (EDX) data were acquired using a Zeiss UltraPlus SEM, equipped with a beam blanker, an EBIC amplifier by point electronic GmbH, and an Oxford Instruments XMax 80 X-ray detector. EBIC measurements were performed at low beam current in order to avoid high injection conditions and varying beam energies from 5 to 15 keV. The frequency of the beam blanker was 5 kHz. EDX elemental distribution maps were acquired at 10-keV beam energy and 1.5-nA beam current.
CL measurements were performed in a Zeiss Merlin SEM at room temperature using a DELMIC SPARC CL system equipped with an iDus InGaAs array as detector. A monochromator grating of 300 L/mm blazed at 1200 nm and IR spectrometer were used. For good spatial resolution, the CL images were acquired using 1-nA beam current, 8-keV beam energy, and with pixel size of 50 nm.
Capacitance-voltage (C-V) measurements were conducted at room temperature using an HP4284 LCR-Meter and frequencies of 100 kHz. The capacitance values were calculated assuming a simple parallel RC circuit. LS was performed for 30 min in air with an AM1.5 spectrum at 100 mW/cm. 2 The stage was cooled down to 300 K. Samples were exposed to light through the transparent conductive oxide (TCO) front contact. Red and blue illumination were performed using band pass filters with the center wavelength of (950 ± 2) nm and (450 ± 2) nm, respectively. The full width at half maximum (FWHM) for both filters is (10 ± 2) nm. I-V measurements were carried out before and after LS in order to detect corresponding changes of the photovoltaic parameters.

| Estimation of electrostatic fluctuations by means of EBIC
EBIC measurements are used to characterize local electrical properties of solar cells on a microscopic scale. By applying EBIC in cross section configuration and extracting current profiles from EBIC images perpendicular to the p-n junction, the width of the spacecharge region (w SCR ) and the diffusion length of minority charge carriers (L D ) in the quasineutral region can be extracted. 22,23 The simulations of the EBIC profiles were carried out based on a onedimensional, analytical model proposed by Donolato. 24 The detailed description of the model and evaluation of EBIC data can be found in Nichterwitz and Unold. 25 As the w SCR is influenced by the redistribution of the free charge carriers, the net-doping densities in the p-type and n-type parts of the p-n junction (expressed by N A and N D ) and the charge density at the CIGS/buffer interface, N IF , can be calculated. For a heterojunction, the width of the SCR is given by the following equation 26 : where Ω = ε a N A +ε w N D . Here, N A and N D are the net-doping densities for the p-type absorber layer, and for the n-type buffer/window stack, ε a and ε w are the corresponding dielectric susceptibilities, V bi is the built-in potential, and q the elemental charge. The interface charge N IF is the charge density of defects at the CIGS/buffer interface, which T A B L E 1 GGI ratios, buffer systems layers, and photovoltaic parameters of studied CIGS thin-film solar cells   Figure 1A,D is the corresponding SEM images, Figure 1B,E the CL intensity, and Figure 1C,F the peak-wavelength distributions. It can be seen that the CL intensity is substantially decreased at grain boundaries owing to a higher density of defects than in the grain interiors, leading to enhanced nonradiative recombination. 28 The panchromatic images ( Figure  suggests that fluctuations of the product Δ 0 Δ Δ are negligible. In addition, when applied on a cross section, CL measurements feature the peak emission wavelength, which can be taken as a rough estimate of the local band-gap energy (the real band-gap energy may deviate substantially from this CL peak energy, since the CL maximum may exhibit contributions mainly by transition between defect states in the band gap, instead of band-band transitions). 30 From Figure 1C, F, it is apparent that the CL peak shifts perpendicular to the substrate from 840 to 900 nm, which corresponds to a shift in the band-gap energy ranging from 1.38 to 1.48 eV. Extracted CL line scans are in a good agreement with the corresponding GGI distribution obtained from EDX measurements ( Figure 2).
Lateral variations in composition within the CIGS alloy need to be in the order of 1 at.% to be relevant for the device performance, 11 which has not been detected in the cells studied in the present work device simulation. 31 Therefore, in the course of the present work, we will concentrate on electrostatic potential fluctuations. in Table 3. The order of magnitude of the average values of w SCR were confirmed by C-V measurements (not shown here).

| EBIC analysis
In order to elucidate the contribution of each variable from Equation 1 to the fluctuation of w SCR , the dependence of w SCR of the netdoping densities N A and N D as well as of the interface-charge density N IF (Equation 1) has to be considered. We estimated the standard deviations ΔN A , ΔN D , and ΔN IF by applying Gaussian error propagation to Equation 1.
where Δw SCR is the difference in the SCR width between two neighboring points. They are provided in Table 2. We note that these values may vary strongly for devices with different buffer layers and PDT treatment.
The net-doping density in the CdS buffer layer was reported to be lower than that of Zn(O,S) by at least one order of magnitude. 26,34 We  ε a 12 II. ΔN IF = 0: In this case, we estimate only fluctuations in N D : It is noteworthy that in real solar-cell devices, we have to assume that both, N IF and N D , contribute to the fluctuations in w SCR detected in the EBIC images. However, in the present work, we will consider and discuss cases I and II separately.
Electrostatic potential fluctuations may be considered to stem from deviations in charge densities, N 1 and N 2 , between two neighboring positions. The amplitudes of these fluctuations, Δφ, can be estimated using the expression 11 : In Werner et al. 7 electrostatic potential fluctuations are described by Gaussian distributions of the conduction and valence band energies.
The standard deviations of these Gaussian distributions, σ (in eV), can be related to V oc losses, V oc,loss , via the following equation 35 : The effect of the electrostatic potential fluctuations on the V oc is attributed to the fact 7,35 that they reduce the radiative limit of the V oc compared with the Shockley-Queisser limit. In our case, we approximate the quantity σ as the average of the determined amplitudes of fluctuations, Δφ, calculated using Equations 1-5.  Table 4.

| Characterization of CIGS solar cells with RbF PDT
To gain insight into the effect of an RbF PDT, an EBIC analysis on CIGS with short (1 min) and completed (10 min) RbF treatment was carried out, with an RbF-free sample as reference. All samples contain  Figure 8C). The average values of w SCR and Δw SCR are shown in Table 5.    Table 7. In addition to the reduction of fluctuations in w SCR , also, one further effect of the LS was detected in the studied solar cells. This decay length in an ideal model can be interpreted as an effective minority diffusion length, L eff , although it has also been shown to be influenced by artifacts, such as generation-dependent collection, and recombination at the cross-sectional surface. 25,37 Values for the effective diffusion lengths before and after LS are summarized in Table 8.
We note that L eff values obtained from EBIC analyses are always much smaller (typically one order of magnitude) than the real electron diffusion lengths, owing to a substantial influence of recombination of charge carriers at the cross-sectional surface and the limitation imposed by applying a simplified collection model.   Table 1) with blue light for 30 min. The blue-light illumination was conducted using a band-pass filter with a center wavelength of (450 ± 2) nm and an FWHM of (10 ± 2) nm.

| Effects of blue and red illumination
Indeed, from EBIC measurements performed before and after illumination with blue light, it can be seen that fluctuations in the SCR are reduced (Figure 13). The average difference in the SCR values between two neighboring positions Δw SCR decreases from 200 to 90 nm after blue LS.
Red-light illumination is mainly absorbed in the CIGS layer, absorption in the buffer/window layer can be neglected. We performed red LS for 30 min using a band filter with the center wavelength of (950 ± 2) nm and FWHM of (10 ± 2) nm. Figure 14 shows  This could originate from no or less amount of OH − ions compared with the CBD process.
Strong fluctuations in w SCR were also detected in CIGS solar cells with PVD-CdIn 2 S 4 buffer layer. The proposed scenario represented in Figure 15 can be applied to explain lower V oc values compared with CdS-buffered cells (Table 1) CdS-buffered cells ( Table 1). The presence of strong fluctuations exhibiting σ of 50 meV was detected in the RbF-treated sample with the short PDT (1 min). As can be seen in Table 1  after white LS, as determined from j-V measurements ( Table 6). In the following, we will discuss two possible scenarios (a and b) that can lead to this improvement.   (Table 10) and ΔN D (Table 11) as well as on the corresponding average amplitude of fluctuations σ. The calculations were based on the method described in the Section 3.1 assuming two cases and Δw SCR = 200 nm. Table 10 represents the Case I where ΔN D = 0, whereas Table 11