Method for characterizing a photovoltaic material with luminescence spectrum fitting
By employing a parametric model that accounts for optical artifacts through multiple luminescence spectrum components, the method enhances the accuracy and efficiency of photovoltaic material characterization, suitable for industrial applications.
Patent Information
- Authority / Receiving Office
- FR · FR
- Patent Type
- Applications
- Current Assignee / Owner
- INSTITUT PHOTOVOLTA QUE D ILE DE FRANCE (IPVF)
- Filing Date
- 2024-10-21
- Publication Date
- 2026-04-24
AI Technical Summary
Current methods for characterizing photovoltaic materials using luminescence spectra are inaccurate due to optical artifacts, leading to erroneous characterization results.
A method involving a parametric model that sums at least two luminescence spectrum models, incorporating parameters like Urbach energy, band gap energy, and Fermi quasi-level difference, to account for optical artifacts and improve accuracy.
The method provides accurate characterization of photovoltaic materials by minimizing spectral irregularities, enabling rapid digital processing suitable for production lines.
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Abstract
Description
Title of the invention: Method for characterizing a photovoltaic material with luminescence spectrum adjustment. Technical field
[0001] The field of the invention is that of the study of photovoltaic materials by means of the acquisition and processing of a luminescence spectrum of a sample of photovoltaic material. Previous technique
[0002] The field of photovoltaic materials is constantly expanding. Despite significant advances in this area, new materials are struggling to be economically competitive with silicon-based materials. This is mainly due to a lack of understanding and control of the non-uniformity of the active layers, thus hindering the optimization of optoelectronic properties. In order to bring the next generations of solar cells to market, researchers need to be able to study the spatial variation of their materials' properties on a larger scale.
[0003] To meet this need, hyperspectral imaging provides electroluminescence (EL) and photoluminescence (PL) maps which allow for the rapid characterization of structural and physical properties of a photovoltaic material.
[0004] Some current methods for characterizing such properties by luminescence consist of carrying out an experimental survey of a luminescence spectrum of a photovoltaic material, determining a set of parameters to best fit a parametric model to the experimental spectrum, and finally deducing characteristics of the photovoltaic material from the parameter set. These characteristics typically include a band gap energy, an absorption coefficient, an Urbach energy, a voltage variation (separation of quasi-Fermi levels) between the front and back faces of the sample, and reflection coefficients on these front and back faces.
[0005] A parametric model that can be used is the so-called "Katahara" model described in the article Katahara, JK & Hillhouse, H. IV. Quasi-Fermi level splitting and sub-bandgap absorptivity from semiconductor photoluminescence. Journal of Applied Physics 116, 173504 (2014).)
[0006] While this model leads to a numerically correct result (low fitting error), the results are actually erroneous, as shown in Figure 1, which represents, as a function of the photoluminescence emission energy Eem(cn eV), the Sfk spectrum resulting from the parametric Katahara fit to an experimental Dex spectrum of PL photoluminescence (in arbitrary units). Indeed, in this [Fig. 1], an incorrect curvature of the Sfk spectrum is observed at low photoluminescence emission energies. This curvature results from optical artifacts that cause irregularities ("bumps") in the experimental Dex spectrum. The Katahara model is therefore insufficient in this respect, and the accuracy of the characterization of the examined sample is consequently affected. Description of the invention
[0007] The invention aims to improve the accuracy of the characterization of a sample of photovoltaic material by analysis of spectral luminescence data.
[0008] To this end, the invention proposes a method for characterizing a photovoltaic material, comprising: - obtaining (OBT) a luminescence spectrum of a sample of the photovoltaic material; - the determination (AJT) of a set of parameters allowing a parametric model to be fitted to the spectrum obtained; - the determination (CAR) of characteristics of the photovoltaic material from the set of parameters;
[0009] characterized in that the parametric model corresponds to the sum of at least two luminescence spectrum models.
[0010] Some preferred but not limiting aspects of this process are as follows:
[0011] - the luminescence spectrum models are represented by the same function parametric,
[0012] - the parameter set includes at least one parameter common to the models of luminescence spectrum,
[0013] - at least one common parameter includes an Urbach energy and a temperature,
[0014] - the parametric model is expressed according to the following sum of 1 spectrum models of luminescence represented by the same parametric function FP, with ' an integer greater than or equal to 2: T, A fi to luminescence spectrum models, T the temperature common to luminescence spectrum models, Eg. a band gap energy associated with the luminescence spectrum model of index z, A fi. a gap in the quasi-Fermi levels associated with the luminescence spectrum model of index 1 and E a luminescence excitation energy, \, where Eu is the common Urbach energy i) PL(E) = PE, Egh E
[0015] - the parametric function FP is expressed according to FP(^E, Egb Eu, T, A pj = A(E, Egb Eu) E2^n where k denotes the Boltzmann constant and where A( E, Egb Eu} denotes an absorbance defined according A(E,Egi. E„) =
[0016] - the luminescence spectrum models include a first model represented by a first parametric function and a second model represented by a second parametric function resulting from a low-pass filtering of the first parametric function,
[0017] - the first parametric function has as parameters an Urbach energy Eu, a temperature F, a band gap energy Eg, and a Fermi quasi-level gap A / / ,
[0018] - the first parametric function is expressed according to FP ( E, Eg, Eu, T, Ap)=A(E, Eg, Eu ) E2e~ tê désiëne la constant de Boltzmann et où A(E, Eg, Eu) denotes an absorbance defined according A(E,Eg,Eu) =““W” 1+^
[0019] - low-pass filtering is characterized by a cutoff energy a factor amplification factor (amP) and attenuation factor (Oit),
[0020] - low-pass filtering is implemented by a filter which is expressed according to F (E, Eg, amp,ait) = y"77" •'
[0021] - low-pass filtering is implemented by a filter which is expressed according to F(E, Ec amp, att) - amp^ threshold (Ec) ^F^ati)} Oa (Ec) designates a threshold function equal to 1 for E<Ec et 0 pour E> Ec, 0 denotes the convolution operator and p^att) denotes a normalized widening function with parameter att such that its area is equal to one.
[0022] The invention further relates to a data processing unit, comprising a processor configured to implement the process as defined above.
[0023] The invention also relates to a computer program product comprising instructions which, when the program is executed by a computer, lead the computer to implement the process as defined above. Brief description of the drawings
[0024] Other aspects, objects, advantages and features of the invention will become more apparent upon reading the following detailed description of preferred embodiments thereof, given by way of non-limiting example, and made with reference to the accompanying drawings in which:
[0025] - Fig. 1, already discussed previously, illustrates the fitting of a model of Katahara to experimental data of a photoluminescence spectrum;
[0026] - the [Fig.2] is a flowchart of a process according to the invention;
[0027] - Figure 3 illustrates the adjustment, according to a first possible embodiment of the invention, of a parametric model to experimental data of a photoluminescence spectrum;
[0028] - Figure 4 illustrates the adjustment, according to a second possible embodiment of the invention, of a parametric model to experimental data of a photoluminescence spectrum;
[0029] - [Fig. 5] represents the variation, as a function of the product aO.w of the amplitude absorption of the material and its thickness w, on the one hand the difference in energy AE between the first spectrum and the second spectrum of the second embodiment of the invention and, on the other hand, the ratio Rp of the maximum of these spectra;
[0030] - [Fig. 6] represents the variation, as a function of the voltage difference AAp between the two faces of the material, on the one hand the difference in energy AE between the first spectrum and the second spectrum of the second embodiment of the invention and, on the other hand, the ratio Rp of the maximum of these spectra.
[0031] DETAILED DESCRIPTION OF SPECIFIC EMBODIMENTS
[0032] The invention relates to a method for characterizing a photovoltaic material by processing a luminescence spectrum of a sample of the photovoltaic material. This method is implemented by a processor of a data processing unit.
[0033] By way of non-limiting agreement, the photovoltaic material may be a Perovskite, cadmium telluride CdTe or copper, indium and gallium selenide CIGS.
[0034] The sample comprises a thin layer of the photovoltaic material carried by a substrate, for example glass.
[0035] With reference to [Fig. 2], the method according to the invention comprises a first OBT step for obtaining, by the data processing unit's processor, the luminescence spectrum of the photovoltaic material sample. The spectrum is an experimental spectrum that may have been previously acquired by a luminescence spectroscopy system capable of exciting the photovoltaic material at different excitation energies and measuring the luminescence emitted by the photovoltaic material as a function of the emission wavelength. The excitation may be optical or electrical, the measured luminescence being, respectively, photoluminescence or electroluminescence.
[0036] The method according to the invention then comprises an AJT step in which the data processing unit's processor determines a set of parameters for fitting a parametric model to the experimental spectrum. This parametric fitting includes, in a manner known per se, the resolution of a problem The optimization problem allows us to determine an optimal set of parameters in the sense that the difference between the experimental spectrum and the parameterized model using this set of parameters is minimal. The optimization problem can be solved iteratively, for example by following the least squares method, and the difference between the experimental spectrum and the parameterized model can be considered minimal when a stopping criterion is met (for example, when the difference is less than a threshold, or when a predetermined number of iterations has been performed, or when the decrease in the difference between two successive iterations is less than a threshold).
[0037] In the context of the invention, the parametric model corresponds to the sum of at least two luminescence spectrum models. By fitting the spectrum as the sum of two components, the invention makes it possible to account for optical artifacts that cause irregularities ("bumps") in the spectrum. The invention thus differs from current methods of processing luminescence spectra, which do not take into account the existence of multiple spectral components that can result in such irregularities.
[0038] Thus, in the invention, the parametric model of the luminescence spectrum PL(E) sums at least two contributions according to PL( E) = ^PLj(E) °where denotes the energy of the luminescence excitation and PL^E} denotes the luminescence associated with the luminescence spectrum model of index i. This luminescence associated with each of the luminescence spectrum models is represented by a parametric function.
[0039] In a preferred embodiment, the parametric functions exploit the same set of parameters {p^ ..., pn]. These parameters include, for example (and preferably consist of), an Urbach energy, a bandgap energy Eu, a temperature E, and a Fermi quasi-level difference Ap. The Urbach energy Eu typically determines the slope at low emission energies of a luminescence spectrum model, for a fixed temperature, while the temperature T determines the slope at high emission energies. The bandgap energy Eg determines the energy position of the luminescence peak, while the Fermi quasi-level difference Ap determines the amplitude of this peak.
[0040] The parametric adjustment then leads to the determination of a set of parameters consisting of several subsets, the subset [p.? p.} being associated with the luminescence spectrum model with index i. For example, after the fitting, PL(E) ^.FP^E, E^, E^T^ where FPj denotes the parametric function associated with the luminescence spectrum model of index i, denotes the Urbach energy associated with the luminescence spectrum model of index i, Eg. the band gap energy associated with the luminescence spectrum model of index ', the temperature associated with the luminescence spectrum model of index * and A p the gap quasi-Fermi levels associated with the spectral index model '.
[0041] In a first embodiment, the luminescence spectrum models are represented by the same parametric function. Referring back to the previous example, we thus obtain, after the adjustment PL(E) =^1^' E^ E^T, where FP denotes the parametric function common to the different luminescence spectrum models.
[0042] This parametric function common to the different models can in particular be expressed according to FP(E, Egj, E^T* Ap.} ^A(E,Egh E^) E2frw, where * denotes the Boltzmann constant and where A ( E, Egi, Euj ) denotes an absorbance. This absorbance can in turn be expressed as A(E,Egh E^) = -W
[0043] In a variant of this first embodiment, the parameter set resulting from the fitting includes at least one parameter common to the luminescence spectrum models. This at least one common parameter may, in particular, include the Urbach energy Eu and the temperature T. Using the previous example, the fitting thus yields PL( E^T, at,,)
[0044] In such a case, the spectra resulting from the fitting of the different models exhibit the same slope at low emission energies (fixed by the Urbach energy Eu common to the different models) and the same slope at high emission energies (fixed by the temperature T common to the different models). They differ, however, in the position and amplitude of their peak. This is shown in [Fig. 3], which represents the experimental data Dex of PL photoluminescence from [Fig. 1], a spectrum Sft resulting from the fitting, according to this variant of the first mode of the invention, of a parametric model to the experimental data, this spectrum Sft corresponding to the sum of a first spectrum Sfl and a second spectrum Sf2 which are based on the same model but whose values of certain parameters differ (in this case the band gap energy and the gap between the quasi-Fermi levels).
[0045] In a second embodiment, the luminescence spectrum models comprise a first model represented by a first parametric function and a second model represented by a second parametric function resulting from a low-pass filtering of the first parametric function.
[0046] As in the first embodiment, the parameters of the first parametric function include for example (and preferably consist of) an Urbach energy E^ a band gap energy Eu, a temperature E and a Fermi quasi-level gap A p.
[0047] The second parametric function can be expressed according to FP(e)*F(E, Ec amp, ait) where FP(E) denotes the first parametric function and F(E, Ec amp, ait) denotes a low-pass filter characterized by a cutoff energy Ec, an amplification factor amP, and an attenuation factor Mt. For example, the low-pass filter is expressed as E(Ef) * F(Ec amp, ait) * Ec amp, μt
[0048] Another formulation of the low-pass filter can be, 0 denoting the convolution operator, F(E,EC, amp,ait) ^amp^ threshold (EA^F^ati)], threshold (Ec) designates a threshold function equal to 1 for E<E c et 0 pour E> E cet où Fjiait) denotes a broadening function with parameter att, normalized so that its area is equal to one. Such a broadening function may be a hyperbolic secant or of Gaussian type.
[0049] The first parametric function can be expressed according to FP(E, Eg,Eu,T, Ap)=A(E,Eg,Eu) E2e& which can be expressed according to 4 ( EE^ ) — —L_.
[0050] Figure 4 shows the experimental Dex data of PL photoluminescence from Figure 1, an SFT spectrum resulting from the fitting, according to this second embodiment of the invention, of a parametric model to the experimental data. This SFT spectrum corresponds to the sum of a first spectrum SF1 and a second spectrum SF2 obtained from a low-pass filtering of the first spectrum SF1. Figure 4 also shows the magnitude FO of this low-pass filtering, a quantification of which is indicated on the right-hand scale in arbitrary units.
[0051] Still with reference to [Fig.2], following the determination AJT of the set of parameters allowing the adjustment of the model to the experimental data, the process according to the invention includes a step of determining CAR of characteristics of the photovoltaic material from the set of parameters.
[0052] In the first embodiment, the actual Eg max band gap value of the material is that of the highest energy fitted spectrum
[0053]
[0054]
[0055]
[0056]
[0057]
[0058]
[0059] A fi kTln r true \pLexvdE f-^dE characteristic. In the variant mentioned above, the Urbach energy of the material and the measurement temperature are common to the models. The Fermi quasi-level gap is a function of the characteristics of the experimental spectrum and the obtained parametric functions. In the most general case, it is possible to write the following equation: , where PLexp denotes the experimental spectrum, h the Planck's constant, etc., the speed of light. This equation means that the A sought is that of the fictitious spectrum without optical artifacts ("bump") which would have the desired E gmax (i.e., that of the highest energy contribution) and an area equal to that of the experimental spectrum PLexp. This also means the equality of the number of emitted photons. In the second embodiment, the determination of the characteristics of the photovoltaic material is based on the physical principle that a semiconductor subjected to illumination can, according to its absorption, recombination, and reflection properties at the interfaces, exhibit a voltage difference (quasi-Fermi level splitting, or QFLS, or Ap according to the notations) between its two faces. This difference, denoted AAp, is an indicator of charge mobility, absorption, and electronic losses in the material. The energy difference between the first and second spectra of the second embodiment of the invention is denoted AE, while the ratio of the maximum of these spectra is denoted Rp. Furthermore, the product aO.w of the absorption amplitude aO of the material (in cm⁻¹) and its thickness w (in cm) is considered. Figures 5 and 6 respectively show the variation of the energy difference AE and the luminescence maximum ratio Rp as a function of the product aO.w and the difference AAp, respectively. These figures illustrate that it is possible to establish a one-to-one correspondence between the physical parameters AAp and aO.w characteristic of the material under experimental conditions and the maximum properties Rp and AE of the spectral models fitted by processing according to the second embodiment of the invention. A similar type of curve can be obtained by matching the properties {Ec, amp, att] of the low-pass filter applied to the first spectral model. The invention thus makes it possible to establish a one-to-one relationship between the pair {Eg-Ec, Rp] obtained by digital processing of the experimental spectrum and the pair {AAp, aO.w] characteristic of the material and the experimental conditions. This leads to the possibility of establishing a physical diagnosis of said material, more comprehensively than without the invention. Conclusions can notably be deduced concerning a variation in thickness or recombination on the front or back face.
[0060] The method according to the invention also has the advantage of being able to be rapidly implemented by digital processing. It can therefore be used on a photovoltaic module production line.
[0061] The invention is not limited to the process as previously described but also extends to a data processing unit, comprising a processor configured to implement this process and to a computer program product comprising instructions which, when the program is executed by a computer, cause the computer to implement this process.
Claims
Demands
1. A method for characterizing a photovoltaic material, comprising: - obtaining (OBT) a luminescence spectrum of a sample of the photovoltaic material; - determining (AJT) a set of parameters allowing fitting a parametric model to the spectrum obtained; - determining (CAR) characteristics of the photovoltaic material from the set of parameters; characterized in that the parametric model corresponds to the sum of at least two luminescence spectrum models.
2. A method according to claim 1, wherein the luminescence spectrum models are represented by the same parametric function.
3. A method according to claim 2, wherein the parameter set includes at least one parameter common to the luminescence spectrum models.
4. A method according to claim 3, wherein at least one common parameter comprises an Urbach energy and a temperature.
5. A method according to claim 4, wherein the parametric model is expressed as the following sum of i luminescence spectrum models represented by the same parametric function FP, with 1 an integer greater than or equal to 2: PL(E) = ^EP^E, Egi, Eu, T, A yw.)' where E“ is the Urbach energy common to the luminescence spectrum models, T the temperature common to the luminescence spectrum models, Eg. a band gap energy associated with the luminescence spectrum model of index 1, A p a gap in the quasi-Fermi levels associated with the luminescence spectrum model of index 1 and E a luminescence excitation energy.
6. A method according to claim 5, wherein the parametric function FP is expressed according to FP ( E, Egi, Eu, T, A p.)=A(E, Egb Eu ) EV at ^where k denotes the Boltzmann constant and where A ( E, Egb Eu ) denotes an absorbance defined according to A(E, Eab Eu) = —•
7. A method according to claim 1, wherein the luminescence spectrum models comprise a first model represented by a first parametric function and a second model represented by a second parametric function obtained from a low-pass filtering of the first parametric function.
8. Method according to claim 7, wherein the first parametric function has as parameters an Urbach energy Eu, a temperature T, a band gap energy Eg and a Fermi quasi-level gap A / / .
9. A method according to claim 8, wherein the first parametric function is expressed as FP(E, Eg, Eu, T, A) = A(E, Eg, E^2^^ where k denotes the Boltzmann constant and where A(E, Eg, Eu) denotes an absorbance defined according
10. A method according to any one of claims 7 to 9, wherein the low-pass filtering is characterized by a cutoff energy Ec, an amplification factor amP and an attenuation factor said.
11. A method according to claim 10, wherein the low-pass filtering is implemented by a filter expressed as F(E, Ec amp, ait) = ■;—• i+t* ntt
12. The method according to claim 10, wherein the low-pass filtering is implemented by a filter expressed as F(E, Ec, amp, att) = amp^threshold(Ec)®F^att)], where threshold(Ec) denotes a threshold function equal to 1 for E<E c et 0 pour E> E c, 0 denotes the convolution operator and denotes a normalized parameter broadening function att such that its area is equal to one.
13. Data processing unit, comprising a processor configured to implement the method according to any one of claims 1 to 12.
14. Product computer program comprising instructions which, when the program is executed by a computer, lead this one to implement the process according to one of claims 1 to 12.