Parameterization of the Back-Surface Reflection for PERC Solar Cells Including Variation of Back-Contact Coverage

This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. IEEE JOURNAL OF PHOTOVOLTAICS 1 Parameterization of the Back-Surface Reflection for PERC Solar Cells Including Variation of Back-Contact Coverage Aina Alapont Sabater, Andreas Fell , Andreas A. Brand, Matthias Mller , and Johannes M. Greulich AbstractSimulationisessentialforacomprehensiveanalysisof the performance of solar cells. The rear contact pitch of passivated emitter and rear cells PERC cells is a crucial device parameter that influences not only the electrical performance but also the optical performance of these cells. This article investigates the applicability of the analytical light trapping model by Basore to account for the optical influence of the rear contact pitch as a simpler alternative to ray tracing. First, we manufacture three different groups of cells with different rear contact pitches, where the metallization fraction f met varies between 0 and 54. Second, the reflectance of the cells is measured. Subsequently, we fit the model parameters R f and R b internal reflection on the front and back surface, respectively to the measured reflectance. While we confirm a nonlinear relation between f met and the measurable spectra found in previous works, our results reveal linear relations between f met and R b with the adjusted coefficients of determina- tionofR adj 0.97,aswellasbetweenf met andthechargecarrier generation rates with R adj 0.94. These relations allow a simple and rapid optical simulation of f met variation for PERC cells. The sameapproachislikelyapplicabletoanylocalcontactsalsoinother cell concepts. Index TermsLight trapping, modeling, optics, photovoltaic cells, reflectance. I. INTRODUCTION O PTICAL simulations are an essential part of solar cell research and development. A well-established approach to simulate solar cell optics is detailed 3-D ray tracing, which comes with considerable effort in gathering the simulation in- puts, setting the model up, and with significant computation time [1]–[3]. On modern computers and using cloud computing services,thecomputationtimeshavebeenreducedalotoverthe past 30 years, but still, the computation times are in the range of minutes. Additionally, the user has to select adequate models, Manuscript received February 12, 2021; revised April 13, 2021; accepted May 14, 2021. This work was supported by the German Federal Ministry for Economic Affairs and Energy within the research project “GENESIS” under Contract 0324274C. Corresponding author Johannes M. Greulich. Aina Alapont Sabater, Andreas Fell, Andreas A. Brand, and Johannes M. Greulich are with the Fraunhofer Institute for Solar Energy Systems, 79110 Freiburg, Germany e-mail ainaalapontgmail.com; andreas.fell ise.fraunhofer.de; andreas.brandise.fraunhofer.de; johannes.greulichise. fraunhofer.de. Matthias Mller is with the Technical University Bergakademie Freiberg, 09599 Freiberg, Germany e-mail matth.muellerphysik.tu-freiberg.de. Color versions of one or more figures in this article are available at https //doi.org/10.1109/JPHOTOV.2021.3082402. Digital Object Identifier 10.1109/JPHOTOV.2021.3082402 e.g.,forscatteringeffects,hastospecifythedetailedgeometries explicitly,andhastospecifyorselectappropriatespectralrefrac- tive indices. An alternative approach to 3-D ray tracing consists of using the analytical light-trapping model, as suggested by Basore [4]. It is a widely used optical model in photovoltaics to calculate reflectance, transmittance, and absorptance, as it is implemented in the 1-D device simulator PC1D [5], [6], as well as in the 3-D simulator Quokka3 [7]. This approach is much less computationally expensive and offers computation times significantly below a second, but more model parameters are lumped, i.e., are less physically detailed. If the level of detail is sufficient for the specific simulation task, the simplicity and speed can be a decisive advantage, e.g., when iteratively fitting experimental data. It has been found that the reflectance, in particular the escape reflectance, depends nonlinearly on the rear metallization frac- tion in the case of local metallized regions with a lower internal reflection, i.e., on the rear contact pitch [8]. This hindered the application of the Basore and other empirical models such as thePhongmodel[9]forpredictionoftheopticalgenerationrate of the passivated emitter and rear cells PERC cells [10] with a rear contact pitch variation. In [8], the following linear relation between the spectra of the metallized and contacted R m and passivated and uncontacted region R p of the back surface was discussed. R λf met R m λ1−f met R p λ. 1 Here, f met denotes the metallization fraction of the silicon back surface. It was shown that 1 is not valid [8] and it is, therefore, rejected. Our goal in this article is to extend and simplify the usage of the Basore model to predict the optical properties of cells with pitch variations. The rest of this article is organized as follows. In Section II, we describe the manufacturing of the samples and the approach for the optical characterization and simulation. In Section III, we present and discuss the results, finally, Section IV concludes this article. II. EXPERIMENTAL DETAILS We manufacture and investigate three groups of samples groupA1,A2,andB,seeFig.1inwhichtherearmetallization fraction f met is varied between 0 and 54. All groups have This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https//creativecommons.org/licenses/by/4.0/ This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. 2 IEEE JOURNAL OF PHOTOVOLTAICS Fig. 1. Schematic cross section of the samples of a group A with Centaurus approach and SDE rear surface, and b group B with AlO x approach with flattened pyramids at the rear surface. Fig. 2. Example of an SEM measurement of a cross section of a PERC rear contact, with semielliptical cross section and semimajor axis a corresponding to a contact width w2a. Adapted from [12]. full-area dielectric passivation with line-shaped laser contact openings LCO. The rear metal is full-area screen-printed alu- minum,whichformsalocalaluminumback-surfacefieldduring contact formation in a high-temperature step. The three groups differ in the wafer thickness, the rear side roughness, and the dielectric rear side coatings. Groups A1 and A2 are two boron-doped Czochralski Cz Si wafers2.2Ωcmresistivity,158mthicknessaftercellprocess, 156 mm edge length processed identically according to the Centaurus approach [11] with a textured phosphorous-diffused front side covered with an SiN x antireflection coating and a saw-damage-edged SDE rear side covered with a stack of SiON/SiN x .Rearsidecontactingisdonebyline-patternedlaser ablation LCO with a pitch variation on every single wafer, the usage of a commercial Al paste for only rear side Al paste screen-printing and standard peak firing in a furnace. The LCO pitchischosento100,200,400,800,1600m,andnoablation. An average contact width is estimated by evaluating scanning electron microscopy SEM cross-sectional images. The line contact has a semielliptical cross section, as exemplarily shown inFig.2.Thesemimajoraxisaoftheellipseisusedtodefinethe contact width w 2a relevant for optical considerations. With thisprocedure,acontactwidthforgroupsA1andA2of54mis determined on parallel processed samples with 1000 m pitch. Fig.3. aExemplaryline-shapedLCOofgroupB.bResultingfinalcontact geometry after aluminum etch back as seen by optical microscopy in top view. Thespectralhemisphericalreflectanceismeasuredin5nmsteps between 300 and 1200 nm using a LOANA system by PVtools GmbHonanareaof2020mmforeachmetallizationfraction 0, 3.3, 6.7, 13.5, 27, 54. A1 and A2 are basically duplicates of each other, with slight unintended differences in front reflectance. A1 and A2 are intended to show the stability of the sample preparation, measurements, and data analysis. GroupBisalsobasedonboron-dopedCz-Siwafers1.8Ωcm resistivity, 180 m final thickness, and 156 mm edge length and then processed according to the AlO x route, i.e., with KOH textured front side, POCl 3 diffused emitter and passivated with an SiN x antireflection coating, the textured rear side featuring the same textured morphology as the front, slightly planarized by the chemical emitter etch back and then coated with a stack of AlO x and SiN x . The LCO geometry is line-shaped with an ablation width of approximately 55 m 4 m depending on the optical definition of the opening, see Fig. 3a. In order to maximize the statistical robustness, each wafer contains 25 30 30 mm wide LCO fields in a 5 by 5 array with the dif- ferent line pitches distributed in a Latin hypercube design [13], preventingadirectcorrelationoflocalwaferproperties.Theline pitchesare247,386,540,690,1080,1500,and2500m.There are also fields without LCO. The rear side is then fully coated with a commercial aluminum screen printing paste designed for line-shapedLCOatathicknessofroughly20m.Nofront-side metallization is applied to the wafers. The firing furnace is set in such a way that the peak wafer temperature reaches 800 C, which is confirmed via thermocouple measurements. Then, the reflectance spectra are measured between 300 and 1200 nm in 10 nm steps, again with a LOANA system from PVtools GmbH, for each metallization fraction 0, 3.9, 6.5, 7.8, 9.8, 13, 20, 33. The wafers are then exposed to an HCl etching solution to etch away the aluminum screen printing. An additional ultrasonic cleaning step removes visible residuals, allowing an unobstructed view of the contact size for optical microscopy, as seen in Fig. 3b, from which f met is determined for group B. In order to separate escape reflectance R esc and front external reflectance R f,ext , whose sum is the measured reflectance R, we extrapolate R f,ext for λ 950 nm by fitting a second-degree polynomial to R in the wavelength region 800 nm 1100 nm, which confirms the nonlinearity of the reflectance and the invalidity of 1, as also found in [8]. Using the escape reflectance determined from the measured reflectance spectra as an input parameter in our simulation program, we determine the fit parameters R f and R b .Fig.5 Fig. 5. Simulated and measured escape reflectance R esc for three samples dashed line R esc sim for R b 1; dotted line R esc sim for R b − 1. TABLE I FIT AND SIMULATION RESULTS OF THE SIMPLIFIED BASORE MODEL exemplarily shows three measured escape spectra and the cor- responding fit. An excellent agreement is found. A constant value of R f for all the cells within a group is obtained, i.e., 88 for groups A1 and A2, and 93 for group B see Table I. This confirms the consistency of the measurement data and the applicability of the simplified Basore model. It must be noted that in PC1Dmod, the parameters R f and R b can be varied in steps of 1. In order to check the accuracy and to see the effect of this difference on the escape reflectance as This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. 4 IEEE JOURNAL OF PHOTOVOLTAICS Fig. 6. Back-side reflectance R b with varying metallization fraction f met of three cell groups. well as on the charge carrier generation rate, here expressed as photogeneratedcurrentdensityj ph ,weperformasmallvariation of R b in our simulations. The results, depicted in Fig. 5, show the simulated escape reflectance R esc for the three scenarios of R b best fit R b , R b 1, and R b − 1 for each of the three samples. As can be seen, the variation of R b by 1 abs induces a noticeable change in the reflectance, in particular for smaller metallization fractions f met 20, which is the relevant range for typical PERC cells. This means that a 1 error of the fit parameters can be considered as an upper bound for the R b uncertainty. For the same model parameters, we calculate j ph . When R b is varied by 1 abs , j ph is changed by up to 0.08 mA/cm 2 , i.e., 0.19 rel . These values are upper bounds of theuncertainty ofthe j ph simulation. Weconsider the values negligible for a f met optimization, and thus, judge the simulations to be sufficiently accurate for f met 20. Although the external reflectance does not depend linearly on the metallization fraction, the simulations using the Basore model yield a linear relation R b 1−f met R pass f met R met 2 betweentheinternalreflectanceR b andthemetallizationfraction f met , as can be seen in Fig. 6. The fit parameters R pass and R met correspondtotheinternalreflectionparametersinthepassivated and metallized regions, respectively. The adjusted coefficient of determination R adj varies between 0.977 and 1.000 see TableII,evidencingahighlylinearrelation.ForgroupsA1and A2, the fit parameters are the same, within the standard errors. This is expected since A1 and A2 are processed identically, further increasing the confidence in the results. The R b at f met 0, i.e., the internal reflection coefficients for the passivated areas R pass , differ between A1 and A2 ∼88.3 andgroupB91.62.Weattributethistodifferencesofthetwo rear-side properties surface morphology, passivation layers, Al TABLE II RESULTS OF THE LINEAR FITS OF 2 The standard errors are calculated from the square root of the diagonal elements of the covariance matrix multiplied with the mean residual variance. TABLE III RESULTS OF THE LINEAR FITS OF 3 paste properties and different amounts of FCA that are lumped with the internal reflectance parameters. Also, the extrapolated R b at f met 1, i.e., the reflection coef- ficientsforthemetallizedareas R met ,differbetweenA1andA2 ∼58 and group B ∼69. We speculate that this difference might be induced primarily by different rear surface roughness and different optical properties of the Al back-surface field and the eutectic layer and different amounts of void formation [18] of the two datasets and, hence, might have a physical origin in the silicon rear surface preparation, the Al pastes, and/or firing conditions, which were different for groups A and B. Comparable differences of the resulting reflection spectra are also apparent from the literature, e.g., comparing Fig. 4 in [19] andFig. 3in[20].Wejudge possibledifferences of themethods for measuring the metallization fraction to have only a small impact on R met For explaining the full difference, an error of the f met determination of 30 rel to 40 rel for groups A1 and A2wouldhaveoccurred.However, weexpect amaximumerror of 10 rel and hence can attribute only up to a third or a fourth part of the R met difference to an error in determinin