Available online at ScienceDirect. Energy Procedia 92 (2016 ) 24 28

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1 Available online at ScienceDirect Energy Procedia 92 (2016 ) th International Conference on Silicon Photovoltaics, SiliconPV 2016 Laplacian PL image evaluation implying correction of photon scattering in the luminescence detector Felix Frühauf a*, Otwin Breitenstein a a Max Planck Institute of Microstructure Physics, Weinberg 2, Halle (Saale), Germany Abstract Photoluminescence (PL) imaging is an established characterization method for investigating local inhomogeneities in solar cells. Conventional evaluation methods are based on the model of independent diodes, leading to wrong results of the local saturation current density J 01. The Laplacian-based PL evaluation method does not rely on this model and has the potential to image J 01 correctly. First attempts for using this method to evaluate PL images failed. In this contribution it is shown that the main reason for this failure was due to the light scattering effect occurring in the luminescence detector. Implying an image deconvolution procedure to the PL images with the correct point spread function, the result of the Laplacian-based evaluation method nearly shows the correct J 01 distribution. It will be shown that the Laplacian-based method has also the potential to image the different dark current contributions (J 01, J 02 and ohmic) separately, as DLIT can do it already now The The Authors. Authors. Published Published by Elsevier by Elsevier Ltd. This Ltd. is an open access article under the CC BY-NC-ND license ( Keywords: Photoluminescence imaging; Lock-in thermography; Spatial deconvolution; Quantitative evaluation; Saturation current density imaging 1. Introduction In previous contributions PL was claimed to be a preferred evaluation method for imaging the local series resistance R s,i (i = position index) and the local saturation current density J 01,i of solar cells due to a high spatial resolution and fast data acquisition time [1-3]. Dark lock-in thermography (DLIT) is less suitable for imaging R s but is a reliable evaluation method for quantitative imaging of J 01 [4]. DLIT images suffer from inevitable thermal blurring, which limits the spatial resolution. PL- and DLIT-based J 01 images agree only qualitatively. Local J 01 - maxima appeared generally weaker in PL than in DLIT [5,6], and unexpectedly also appear blurred. It was shown that the reason for this discrepancy is the influence of lateral balancing currents [7]. The Laplacian-based PL evaluation method is not disturbed by the resistive blurring effect and shows the best spatial resolution of J 01 images The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license ( doi: /j.egypro

2 Felix Frühauf and Otwin Breitenstein / Energy Procedia 92 ( 2016 ) compared to all previous published PL-based J 01 images [8]. However, previous attempts to apply this method led to systematically too low values of J 01 [1,8]. It was suspected in [8] that the reason for the quantitative discrepancy between Laplacian PL- and DLIT-J 01 might be an optical blurring effect in the light detector used for PL imaging. For the first time, Walter et al. [9] reported of light scattering in the silicon detector of CCD cameras, which smooth out local minima and maxima of the PL signal leading to blurred PL images. The mean travelling path of the detected luminescence, which shows a peak at 1000 nm wavelength at room temperature, is about 160 μm [10], but for a cooled detector it is even larger due to the increased gap energy. This is large compared to a typically 13 μm x 13 μm sized silicon detector [11]. Therefore we deconvoluted the PL images with a point spread function (PSF) determined by an alternative method [12]. As a result of the improved Laplacian-based PL evaluation method after [8] we show a PL-based J 01 image with high resolution, which is quantitatively comparable with a J 01 image obtained by DLIT. 2. Laplacian PL evaluation method The well-known and established equation of the local luminescence intensity, which depends exponentially on the local diode voltage V d,i, scales with the local calibration constant C i, which depends on the local lifetime and the optical properties of the used sample [1,2]. The equivalent electroluminescence (EL) or so-called net-pl signal used for all PL evaluation methods is obtained by subtracting the luminescence under short circuit from the measured PL-signal [2]. All net-pl images were deconvoluted by a PSF determined after [12]. A scaling measurement at V oc -condition and 0.1 sun allows to obtain the calibration constant C i assuming V d,i = V oc. This assumption holds at low intensity condition, since series resistance effects are expected to be negligible small. The local vertical current density of an illuminated diode can be described by a one-diode model, containing the dark current density J 01 and the photocurrent density J p. The Laplacian-based PL evaluation method, which was proposed by Glatthaar et al. [1], regards the distributed character of the series resistance, since here the horizontal balancing currents within the emitter are evaluated. The local vertical current density is defined as the difference of all balancing currents flowing into and out of a pixel, whereby each pixel is connected by an assumed homogeneous emitter sheet resistance (in /sq). The method after Glatthaar et al. [1] calculates the local diode current density as the differential formulation for a continuous area: J i V em, i (1) Here = 2 is the Laplacian operator, which describes the second derivative of the emitter voltage V em,i in the directions x and y. 3. Experimental results In the following we show the results for the previous Laplacian-based PL evaluation [8] without applying deconvolution and improved results after deconvoluting the PL images. Following Glatthaar [1] we assume that the local diode voltages V d,i are sufficiently close to the emitter voltages V em,i. In Fig. 1 the obtained local diode voltage V d,i is shown before (a) and after deconvolution (b). Due to light blurring in (a) local minima and maxima are smoothed out. After deconvolution the contrast and spatial resolution in (b) is increased significantly. Since the Laplacian operator strongly increases noise, the diode voltage images of Fig. 1 (a) and (b) were used after a 2 x 2 pixel-binning to calculate the local current density after (1), assuming an emitter sheet resistance of 50 /sq. The local dark current density J 01 was calculated with a one-diode model, shown in Fig.1 before (d) and after deconvolution (e). A homogeneous photocurrent density J p used in the previous contribution [8] was improved now using a J p image obtained by light beam-induced current (LBIC) mapping at 1.5G spectrum [13], shown in Fig. 1 (c). However, we found out that this improvement does not influence the J 01 results significantly. This is due to the fact that under V oc condition in low lifetime regions the dark current exceeds the average photocurrent. The biggest improvement is due to the deconvolution procedure, which strongly increases the obtained values of J 01 in the low

3 26 Felix Frühauf and Otwin Breitenstein / Energy Procedia 92 ( 2016 ) lifetime regions [14]. After deconvolution the Laplacian-based J 01 image (e) quantitatively nearly agrees with the DLIT-J 01 image obtained at 50 Hz [4], shown in Fig. 1 (f). Since Eq. (1) only holds for the free emitter region, the Laplacian evaluation method does not work correctly in the gridline regions. (a) V d original data [600 to 635 mv] (b) V d deconvoluted [600 to 635 mv] (c) LBIC-J p [30 to 40 ma/cm 2 ] max min 2 cm (d) Laplacian PL-J 01 original data (e) Laplacian PL-J 01 deconvoluted (f) DLIT-J 01 Fig. 1. (a) Local voltage at V oc=619 mv and 1 sun, (b) local voltage at V oc=619 mv and 1 sun after deconvolution, (c) LBIC-based J p, (d) Laplacian-based J 01, (e) Laplacian-based J 01 after deconvolution and (f) DLIT-based J 01. All scaling ranges are indicated. 4. Simulation results The Laplacian evaluation method is improved by deconvoluting the PL images. Nevertheless, the Laplacian J 01 does not completely reach the value of the DLIT-based J 01 in shunt position. The remaining differences are illustrated by the shunt in the white rectangle in Fig. 1. The mean J 01 value is increased from (d) to (e) from 2 pa/cm 2 to 6 pa/cm 2 compared with 10 pa/cm 2 of the DLIT-J 01. To evaluate where the remaining differences between the improved Laplacian method and DLIT-J 01 come from, simulations of J 01 shunts have been investigated in detail. Preceding spice-based device simulations of a 2.6 x 52 mm 2 sized symmetry element of a typical 156 x 156 mm 2 sized crystalline silicon solar cell containing 3 busbars have been performed to simulate local current and voltage distributions [7]. Here geometry B of [7] containing stripes of locally increased J 01 was used. The input J 01 is shown blue in Fig. 2. V oc net-pl images for 0.1 and 1 sun were calculated, which lead to local diode voltages under these conditions. Evaluating the simulated local diode voltage at 1 sun with the Laplacian evaluation method leads to the black curve in Fig. 2. Except the clear overshoots at the sharp edges, which are due to the assumption V d,i = V em,i, the Laplacian-J 01 and the input J 01 are in good agreement, see also [8]. However, when we calculate the local diode voltage from the simulated net-pl images, we underestimate the Laplacian-J 01, which corresponds to deconvoluting the PL images (red curve). This is due to the fact that the calibration factor C i from the scaling measurement is not R s corrected. Note that, though in this V oc measurement no cell current flows, the horizontal

4 Felix Frühauf and Otwin Breitenstein / Energy Procedia 92 ( 2016 ) balancing currents may lead to local voltage drops at the horizontal series resistances. The difference between the black and the red curve is due to neglecting the voltage drop at these R s, which leads to a wrong C i. By now, a R s correction would lead to additional noise [8], which would be then additionally increased by the Laplacian operator. However, we hope to include this correction in future. The green curve in Fig. 2 corresponds to measured PL data without deconvolution and R s correction. For obtaining these data the net-pl images were artificially blurred with the PSF of our experimental setup and then evaluated with the Laplacian method. The optical blurring due to the light scattering effect leads to the difference between the red and the green curve. These simulations show that the deconvolution and the R s correction lead to similar improvements here. Fig. 2. J 01 from applying the Laplacian method to simulated local diode voltage data (black), local diode voltage data obtained from simulated PL images (red) and local diode voltage data obtained from artificially blurred PL images (green) in comparison to the input J 01 (blue) assumed in the device simulation. 5. Conclusions We introduce a Laplacian-based PL evaluation method implying image deconvolution, which leads to PL-based J 01 data that nearly agree for the first time quantitatively with DLIT-based data. Besides the R s correction, remaining differences may be due to lateral light scattering and/or lateral carrier diffusion in the cell. The Laplacian-based PL evaluation measures the total current flow in the emitter, which also contains J 02 and ohmic contributions. Therefore this PL-based evaluation method has the potential to image these different dark current contributions separately, as DLIT can do it with the Local-I-V 2 code already now [4]. Furthermore, the deconvolution procedure described in [9,12] improves all quantitative luminescence-based evaluation methods, but may degrade the signal-to-noise ratio of the luminescence images. Nevertheless, Fig. 1 (e) shows no significantly increased noise compared to (d), which points to the excellent quality of our PL imaging system. References [1] M. Glatthaar, J. Haunschild, R. Zeidler, M. Demant, J. Greulich, B. Michl, W. Warta, S. Rein, R. Preu, Evaluating luminescence based voltage images of silicon solar cells, J. Appl. Phys. Lett. 108 (2010) [2] T. Trupke, E. Pink, R.A. Bardos, and M.D. Abbott, Spatially resolved series resistance of silicon solar cells obtained from luminescence imaging, J. Appl. Phys. Lett. 90 (2007) [3] C. Shen, H. Kampwerth, and M. Green, Spatially resolved photoluminescence imaging of essential silicon solar cell parameters, Proc. 38th IEEE Photovoltaic Specialists Conference, Austin, USA 2012, pp [4] O. Breitenstein, Nondestructive local analysis of current-voltage characteristics of solar cells by lock-in thermography, Sol. Energy Mater. Sol. Cells 95 (2011) [5] O. Breitenstein, J. Bauer, K. Bothe, D. Hinken, J. Müller, W. Kwapil, M.C. Schubert, W. Warta, Can luminescence imaging replace lock-in thermography on solar cells? IEEE Journal of Photovoltaics, vol. 1, no. 2 (2011) [6] O. Breitenstein, C. Shen, H. Kampwerth, M.A. Green, Comparison of DLIT- and PL-based local solar cell efficiency analysis, Energy Procedia 38 (2013) 2-12.

5 28 Felix Frühauf and Otwin Breitenstein / Energy Procedia 92 ( 2016 ) [7] O. Breitenstein, J. Bauer, D. Hinken, and K. Bothe, The reliability of thermography- and luminescence-based series resistance and saturation current density imaging, Solar Energy Mat. Solar Cells 137 (215) [8] O. Breitenstein, J. Bauer, D. Hinken, and K. Bothe, Towards an improved Laplacian-based photoluminescence image evaluation method, Sol. Energy Mater. Sol. Cells 142 (2015) [9] D. Walter, A. Liu, E. Franklin, D. Macdonald, B. Mitchell, and Th. Trupke, Contrast enhancement of luminescence images via point-spread deconvolution, Proc. 38th IEEE PVSC, Austin, TX 2012, pp [10] M.A. Green, M.J. Keevers, Optical properties of intrinsic silicon at 300 K, Prog. Photovolt. Res. Appl. 3 (1995) [11] Data sheet of ANDOR ikon-m PV Inspector camera, scientific-cameras/ikon-ccd-camera-series/pv-inspector. [12] O. Breitenstein, F. Frühauf, and A. Teal, An improved method to measure the point spread function of cameras used for electro- and photoluminescence imaging of silicon solar cells, IEEE Journal of Photovoltaics, vol. 6, no. 2 (2016) [13] M. Padilla, B. Michl, B. Thaidigsmann, W. Warta, M.C. Schubert, Short-circuit current density mapping for solar cells, Sol. Energy Mater. Sol. Cells 120 (2014) [14] F. Frühauf, O. Breitenstein, Laplacian photoluminescence image evaluation employing image deconvolution, Sol. Energy Mater. Sol. Cells 146 (2016)