Four-Fold Multi-Modal X-ray Microscopy Measurements of a Cu(In,Ga)Se2 Solar Cell

Inhomogeneities and defects often limit the overall performance of thin-film solar cells. Therefore, sophisticated microscopy approaches are sought to characterize performance and defects at the nanoscale. Here, we demonstrate, for the first time, the simultaneous assessment of composition, structure, and performance in four-fold multi-modality. Using scanning X-ray microscopy of a Cu(In,Ga)Se2 (CIGS) solar cell, we measured the elemental distribution of the key absorber elements, the electrical and optical response, and the phase shift of the coherent X-rays with nanoscale resolution. We found structural features in the absorber layer—interpreted as voids—that correlate with poor electrical performance and point towards defects that limit the overall solar cell efficiency.


S.1 X-Ray Fluorescence
The X-ray fluorescence data have been fitted with PyMca version 5.5.3 [1]. To correct for the background radiation, we subtracted an average background-gained from a fit of the spectra integrated over the scanned area-of each single spectrum and did not use further background stripping routines, as justified and detailed in [2]. To extract the mass fraction of the elements, we used PyMca's built-in routine, which is based on the fundamental parameter method [3,4]. For the application of self-absorption correction, the nominal values for the sample structure and for the measurement geometry as described in sections 2.1 and 2.2 were considered as a priori information. We used Se as reference element to scale the mass fraction, as Se is the absorber element with highest signal-to-noise ratio and most homogeneous stoichiometric distribution. Based on the measured fluorescence count rate f i and the unscaled mass fraction w * i obtained through PyMca for each element i, the effective molar area density ρ i A was calculated as follows.
First, the mass fraction was scaled for each element such that the sum equals 1 at each scanned spot: By multiplying the scaled mass fraction w i with the nominal thickness d nom and mass density ρ mass,tot nom of the layer, the nominal mass area density ρ mass,i A,nom = w * i · d nom · ρ mass,tot nom (S.2) Figure S1: Effective molar area density ρ A of Se, Cu, Ga, In, Rb and Zn extracted from scanning X-ray fluorescence measurements.
in [g/cm 2 ] was calculated for each element and converted into the nominal molar area density in [mol/cm 2 ] with the molar mass M i : To obtain the effective molar area density map for each element i, the count rate f i was scaled to ρ mol,i A,nom averaged over all scan points: For completeness, the resulting maps of all main absorber elements as well as Rb and Zn are shown in Figure S1.

S.2 X-ray Beam-Induced Current
To regain the measured current I XBIC from the acquired count rate f XBIC , the factors along the signal processing chain are considered in with W ff = √ 2 taking into account the sine-shape of the modulated signal, p = 10 6 V/A the sensitivity of the pre-amplifier, k = 10 6 Hz/V from the voltage-to-frequency conversion, and l = 10 the scaling of the lock-in amplifier. The factor 2 takes into account the oscillation between the positive and negative amplitude [5].

S.3 X-ray Excited Optical Luminescence
As the interaction point between the sample and the X-ray beam was aligned to the focus spot of the confocal XEOL setup, the luminescence photons were projected to a reasonably narrow point on the CCD detector. For maximum signal-to-noise ratio, the photon count rate of the camera pixels were first integrated in the vertical direction of the detector and second fitted in horizontal direction by a Gaussian on top of a linear background.

S.4 Ptychography
The reconstruction of the phase shift Φ via ptychography was done with an in-house developed code [6]. Lacking of an absolute reference for the phase shift in this measurement, we have offset Φ such, that the minimal phase shift (maximal value of Φ) is zero; the resulting relative phase shift is denoted ∆Φ. The reconstructed image has a pixel size of 17 nm and is displayed in Fig. S2a.
The phase shift Φ is related to δ from Equation (2) through where λ is the wavelength and x the direction of X-ray beam propagation [7]. With Equation (2) and the conversion of the electron density to the area electron density via the relative phase shift can be converted into the relative area electron density: As introduced in Equation (2), r e is the classical electron radius. Figure S2b shows the resulting relative area electron density map.

S.5 Position Correction and Normalization
Within the ptychographic reconstruction, the position of the sample-beam interaction could be refined beyond the accuracy of the scanning system. Therefore, we have applied this position correction to the measurements from all modalities which required, however, the re-alignment of the reconstructed ptychographic image with the results obtained from the other modalities. The alignment was achieved through registration of the phaseshift image and the Se area density image using the enhanced correlation coefficient image alignment algorithm [8] from the OpenCV library [9]. All measurands except the ptychographic phase shift were interpolated on the supergrid given by the ptychographic reconstruction with the nearest neighbor method.
To compensate for the oversampling during the measurement, a Gaussian filter from the OpenCV library was applied. With a beam size of 105 nm × 108 nm (FWHM), a filter size with a standard deviation of σ = 54 nm was appropriate. For statistical correlation, the maps were cropped by half filter width on all sides to avoid artifacts from the filter at the border corrupting the correlation.
Furthermore, all measurements were normalized to the dwell time and incident photon flux.

S.6 k-Means Clustering
Given a set of n measurands spanning an n-dimensional space, the k-means clustering algorithm aims to separate the data into k groups of similar size and small variance by minimizing the sum of squared Euklidian distances between each data point and the center of the cluster it belongs to [10]. The k-means implementation of the scikit-learn library [11] in Python was employed in this study. The optimal number of groups k was determined using the so-called elbow and silhouette methods, both of which we implemented in Python using scikit-learn. The elbow refers to a kink in the plot of the minimized sum of squared Euklidian distances as a function of k. Details on the silhouette score can be found elsewhere [12]. In general, a silhouette score of 1 means that a perfect cluster structure has been found and a score of −1 translates to poor clustering. In Figure S3 it can be seen, that both methods indicate a group size of k = 2 to be ideal. Figure S4: Correlation coefficient of Se (ρ Se A ), In (ρ In A ), Ga (ρ Ga A ), Cu (ρ Cu A ), Rb (ρ Rb A ) and Zn (ρ Zn A ), of the X-ray beam-induced current (I XBIC ), of the XEOL photon count rate (f XEOL ) and of the relative electron area density (∆ρ e A ) for the total data set as well as the two sub-sets with data from the k-means groups 1 and 2, respectively.

S.7 Correlation Coefficients
The correlation coefficient ρ that is shown in the manuscript only for a subset of measurands is shown in Figure S4 for all measurands, with Figure S4a including the data from the entire maps and Figure S4b-c including only the data for the k-means groups 1 and 2, respectively.