- Email: [email protected]
Micrometric investigation of external quantum efficiency in microcrystalline CuInGa(S,Se)2 solar cells
Thin Solid Films 565 (2014) 32–36
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Thin Solid Films journal homepage: www.elsevier.com/locate/tsf
Micrometric investigation of external quantum efficiency in microcrystalline CuInGa(S,Se)2 solar cells L. Lombez, D. Ory, M. Paire, A. Delamarre, G. El Hajje, J.F. Guillemoles Institute of Research and Development on Photovoltaic Energy (IRDEP), EDF R&D, UMR 7174 CNRS EDF ChimieParisTech, 78401 Chatou, France
a r t i c l e
i n f o
Article history: Received 18 January 2014 Received in revised form 17 June 2014 Accepted 23 June 2014 Available online 29 June 2014 Keywords: Copper indium gallium selenides Photovoltaics Micrometric Supercontinuum External quantum efficiency Diffusion length
a b s t r a c t We present in this paper small scale spatial fluctuations of the spectral response of CuInGa(S,Se)2 polycrystalline solar cell. The experimental method is based on light beam induced current cartographies under different excitation wavelengths. From those measurements we can map minority carrier diffusion length Ln over the cell with a spatial resolution of about 2 μm. Spatial variations of Ln are evidenced, which result in a standard deviation of around 130 nm. The experiment also evidences spatial fluctuations of the external quantum efficiency that can arise from surface recombinations. © 2014 Elsevier B.V. All rights reserved.
1. Introduction CuInGa(S,Se)2 (CIGS) solar cell shows a record conversion efficiency of more than 20%, the highest among polycrystalline thin film technologies [1,2]. Nevertheless the theoretical efficiency limit of this type of cell, the Shockley Queisser limit, is estimated to be around 30% [3–5]. A better understanding of the cell properties is thus necessary in order to diagnose the losses and then increase further the cell performances. However the complex nature of the polycrystalline materials impedes exact measurements of fundamental properties. In fact, measurements of global optoelectronic parameters are always an average of local ones. Thus they do not properly reflect the real device properties; each submicron region having its own properties. Moreover, one of the limits to the performances of those polycrystalline cells might be strong lateral inhomogeneities [6,7]. Therefore, micron scale fluctuations have been studied, for example, by mean of Photoluminescence (PL) [8] or Cathodoluminescence [9]. These studies evaluated grain boundary effects, fluctuations of the quasi Fermi level splitting (i.e. the maximum reachable open circuit voltage) or variations of the absorption properties. Nevertheless it is always a challenge to know what is actually measured. External quantum efficiency (EQE) measurement is a standard characterization method, from which one can determine optoelectronic properties such as minority carrier diffusion length, absorption properties or space charge region width [10]. However, this well-known
E-mail address: [email protected] (L. Lombez).
http://dx.doi.org/10.1016/j.tsf.2014.06.041 0040-6090/© 2014 Elsevier B.V. All rights reserved.
characterization tool always measures EQE on large areas and therefore determines global parameters of the cell. We propose in this communication to measure their spatial fluctuations of these parameters thanks to a mapping method having both high spatial and spectral resolution. The experiment is also suitable for recording spectral response of micrometric photovoltaic devices. To do so, we set up an experiment that can locally probe the EQE a micron scale. Light beam induced current (LBIC) cartographies are recorded at different excitation wavelengths allowing the evaluation of the spectral response EQE(E) at different cell positions. This experiment evidences strong lateral fluctuations of the EQE. From our cartographies, and a statistical analysis, we will also discuss the limits of different models to extract physical parameters such as diffusion lengths from EQE measurements. 2. Experimental setup and sample The excitation source is a Fianium supercontinuum laser whose wavelength is selected using a Photon Etc Laser Line Tunable Filter. The spectral resolution is 2 nm while the extinction ratio is higher than 105. The laser is coupled into an optical fiber connected to a homemade microscope (see Fig. 1). The sample is then excited using a microscope objective (either reflective or apochromatic, both giving the same results). The broadband single mode laser allows us to have a spatial resolution from of about 2 μm and to sweep the wavelength from 400 to 1100 nm. We do not aim to reach the diffraction limit spot size for two reasons: on the one hand this avoids spot size dependence with the excitation wavelength and, on the other hand, it is not necessary to go below this value as the diffusion length in CIGS absorbers is usually
L. Lombez et al. / Thin Solid Films 565 (2014) 32–36
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Fig. 1. Experimental setup and sketch of the CIGS microcell sample.
found between 0.5 and 3 μm. The excitation photon flux is measured using a calibrated Si photodiode. The laser pulse duration is 6 ps and the repetition rate is set to 80 MHz. The average excitation power density is 75 ± 33 nW/μm2/nm (depending on the excitation wavelength) that corresponds to about 145 ± 48 μW/μm2/nm peak power (i.e. 3.7 × 1015 incident photons/m2 per pulse at 850 nm or 2.98 × 1023 incident photons/m2/s, corresponding to about 100 Suns). In order to obtain an EQE(E) cartography, the sample is mounted on a Physik Instrumente piezoelectric stage; we can therefore map the EQE value for each excitation wavelength: spectrally resolved LBIC (SR-LBIC). Note that another method for SR-LBIC has been used on Si solar cell but without the spatial and spectral resolution required for investigating thin film polycrystalline cells [11,12]. Note also that the use of supercontinuum laser in this type of setup is a way to record spatial variations other widely used measurements such as Photoluminescence Excitation (PLE), Current Voltage curves or Time Resolved Photoluminescence signals. Nevertheless one has to keep in mind that the laser is a pulsed source and might induce artifacts or unrealistic values due to high injection regime. To minimize this problem, the sample studied in this paper is a Cu(In,Ga)Se2 based solar cell, limited in its lateral dimension [13]. These microscale cells have been previously studied under high excitation fluxes, and showed very low heating or resistive effects, as the micrometric size of the cells strongly diminishes sheet resistance losses and eases thermal evacuation. It was shown for example that the current varies linearly with the excitation power up to thousand suns in these devices, indicating a good photocurrent collection in these high injection regimes [14]. The microcells are composed of a Mo back contact, deposited on glass, and a 2.5 μm thick commercial Cu(In,Ga)Se2 coevaporated absorber layer from Würth solar. The fabrication process is explained elsewhere [14], a scheme of the device is presented in Fig. 1. Global and local measurements have been done by exciting the cell over its entire surface or, by focusing the laser spot onto the cell surface (mapping conditions). Similar behaviors are found in both cases. On the one hand it confirms that the EQE evaluation is not affected by the pulsed excitation condition (i.e. one can consider a quasi state regime).
On the other hand, the charge collection is efficient and not limited by series resistance. These good behaviors are assumed to be linked to the use of microcells. Indeed it is no longer observed at higher excitation power (above 20 μW/μm2 average power) or, when the cell diameter is too large.
3. Results and discussion We then measure LBIC cartographies on two different microcells for excitation wavelengths varying from 400 nm to 1100 nm with a 5 nm step. In Fig. 2 are displayed three examples of EQE maps: Fig. 2(b) and (d) are for cell 1 at 840 nm and 1050 nm; Fig. 2(c) is for cell 2 at 750 nm. At excitation wavelengths well above the band gap, absolute spatial variations of EQE close to 5% are observed on cell 1 or close to 10% on cell 2 (Fig. 2(b) and (c)). Larger spatial variations are observed at wavelength close to the band gap (Fig. 2(d)). Indeed, in this spectral region, the EQE value is sensitive to the diffusion lengths and the band gap as we will see later. Moreover, different spatial fluctuation ranges can be seen. Micrometric variations are attributed to intrinsic properties of the polycrystalline absorbers whereas longer range fluctuations could be linked to the fabrication process of the microcell. Thanks to the mapping, we can also determine the spectral response at each cell position. Some EQE(E) curves in a spectral range slightly above the bandgap (region of interest) are displayed in Fig. 2(a). The three higher EQE(E) curves are coming from the area A of cell 1: we can guess changes in the band gap Eg, as well as changes in the diffusion length Ln (which is, in the first order, the slope of the curve). The two lower curves are coming from the area B where low values of EQE are attributed to fabrication process artifacts leading to either optical or edge recombination effects. As we will see, even on this second area, the determined values of Ln and Eg make sense. This shows that the material quality of the absorber can still be analyzed on this region. From those EQE(E) curves, one could access the spatial variations of physical parameters, linked to transport or optical properties for example. Indeed the external quantum efficiency EQE, between the depths x1
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L. Lombez et al. / Thin Solid Films 565 (2014) 32–36
Fig. 2. Measurement of the external quantum efficiency of 25 μm diameter microcells. (a) Spectral response EQE(E) from different areas on cell 1; Lines are the experimental data, dots represent the corresponding fits; (b) EQE map of cell 1 at 870 nm (c) EQE map of cell 2 at 780 nm and (d) EQE map of cell 1 at 1050 nm.
and x2, can be expressed in a general manner as [15,16]: Z EQEðEÞ ¼
x2 x1
g ðx; EÞf c ðEÞdx
where g(x, E) is the generation function and can be expressed by g(x, E) = (1 − R)αe−α in a simplified case with no reflection at the back pffiffiffiffiffiffiffiffiffiffiffiffiffi side. The absorption coefficient is α∝ E−Eg . In the quasi neutral region, the collection function fc(E) depends on the minority carrier diffu sion length Ln: f c ðEÞ ¼ exp − x−w Ln . The well known Gartner model assumes that charges generated in the space charge region and at one diffusion length from the space charge region are all collected, a revision has been proposed based on a drift diffusion model [17,18]. The latter introduces a drift length influenced by CIGS/CdS interface recombinations, which results in a non perfect collection within the space charge region. The EQE becomes a function of a factor h, which depends on recombination velocity S and carrier velocity Eμ (where μ is the mobility and E is the electrical field E at the interface): −αw e ð1−RÞ EQEðEÞ ¼ h 1− 1 þ αLn where R is the macroscopic reflection coefficient with a value −1 S measured at 16% in our sample and h ¼ 1 þ Eμ . This factor is directly linked to the value of EQE well above the band gap and thus originates the spatial fluctuations we observe. Those EQE values are essentially fluctuating from 0.5. to 0.7; assuming an electric filed E of 104 V/cm and an electron mobility μ of 100 cm2/(V s), this will imply a h factor fluctuating from 0.59 to 0.83 of and thus a recombination velocity varying from 1.2 × 106 cm/s to 1.7 × 106 cm/s.
The energy dependence prefactor of α is taken spatially uniform [19]. Variations in the absorption coefficient are assumed to only originate from Eg fluctuation, due for instance, to varying gallium content. The space charge region width w, determined by capacitance spectroscopy, is considered constant at 340 nm, the doping density is assumed spatially uniform. We first determine the spatial variations of the minority carrier diffusion lengths and the band gaps, within the limits of the Gartner's model, which will be discussed later. The two cartographies and the corresponding histograms are displayed in Fig. 3. The average value of the Ln spatial distribution is found to be 1.41 μm with a Full Width Half Maximum (FWHM) of 0.31 μm (~21%). The average value of Eg is found to be 1.17 eV with a FWHM of 4 meV (b1%). The latter variations are slightly smaller to what was measured when recording optical bandgap from spectrally resolved Photoluminescence maps (~10 meV) but still very close [20,21]. We propose to evaluate the relevance of such an analysis, and possible limits of the Gartner's model for this type of experiments. In order to do so for each spatial location, we have plotted the diffusion length as a function of the band gap in Fig. 4, and, in inset, the correlation index cartography. The correlation is simply calculated by the ratio between the normalized Ln and Eg maps. Even though correlations can be found between the two parameters, the anti-correlation seems to be the dominant case: the shorter the diffusion length, the larger the band gap. This behavior has been previously observed on samples with different gallium contents [22]. A higher Ga content could induced local degradations of bulk properties [23]. Nevertheless, regarding the band gap of CuInSe2 (1 eV) and CuGaSe2 (1.7 eV) a 8 meV total gap variation is induced by about 1% Ga fluctuation. This cannot explain the variations of Ln we measure [22,23].
L. Lombez et al. / Thin Solid Films 565 (2014) 32–36
35
Fig. 3. (a, b) Cartography of the minority carrier diffusion length and its histogram from cell 1. (c, d) Cartography of the band gap fluctuations and its histogram.
Another possible explanation, is that the band gap grading in the absorber, that is not taken into account in the Gartner model, or other classical models to exploit EQE measurements, should in fact be included. In the presence of constant electric field and constant diffusion length, it has been shown that the effective diffusion length can be shorten or enhanced by the presence of an electric field (due for example to the band gap grading) [15]. This relation between effective diffusion length and band gap grading could be important. Indeed, the bandgap measured in EQE is related to the minimum value of the bandgap in the depth of the absorber, a small bandgap relates to a rather steep grading, and thus a higher effective diffusion length. Therefore, taking into account the role of composition grading could explain the anticorrelation between diffusion length and optical bandgap. The spatial fluctuations as well as depth variations play clearly an important role, and it might explain the variations of Ln
found in the literature. Moreover, variations in the local absorber thickness (here a 120 nm rms roughness was measured for the 2.1 μm thick absorber) could have played a role. Nevertheless the roughness is much smaller than the total thickness suggesting no importance of such effect. 4. Conclusion The spectral variations of the external quantum efficiency were measured thanks to an original setup using a broadband visible laser. Spectrally resolved LBIC maps are therefore recorded with a spatial resolution close to the diffraction limit. The experiment evidences spatial fluctuations of the diffusion length with a standard deviation of about 130 nm (FWHM = 300 nm; 20% of Ln). Further studies will enable to propose a more complete and comprehensive model. In fact, this setup could also be used to analyze spatial variations of excitation Photoluminescence or excitation dependence of the time resolved PL. The latter experiment should be a way to correlate local carrier lifetime to the observed fluctuations of Ln. References
Fig. 4. Variation of the diffusion length with the band gap energy. Each point is a given spatial location on cell 1. Inset: Correlation map between the Eg and Ln cartography.
[1] A. Chirila, S. Buecheler, F. Pianezzi, P. Bloesch, C. Gretener, A.R. Uhl, C. Fella, L. Kranz, J. Perrenoud, S. Seyrling, R. Verma, S. Nishiwaki, Y.E. Romanyuk, G. Bilger, A.N. Tiwari, Highly efficient Cu(In,Ga)Se-2 solar cells grown on flexible polymer films, Nat. Mater. 10 (11) (2011) 857. [2] P. Jackson, D. Hariskos, E. Lotter, S. Paetel, R. Wuerz, R. Menner, W. Wischmann, M. Powalla, New world record efficiency for Cu(In, Ga)Se2 thin-film solar cells beyond 20%, Prog. Photovolt. Res. Appl. 19 (2011) 894. [3] W. Shockley, H.J. Queisser, Detailed balance limit of efficiency of p-n junction solar cells, J. Appl. Phys. 32 (3) (1961) 510. [4] S. Siebentritt, What limits the efficiency of chalcopyrite solar cells? Sol. Energy Mater. Sol. Cells 95 (6) (2011) 1471. [5] U. Rau, H.W. Schock, Electronic properties of Cu(In, Ga)Se 2 heterojunction solar cells—recent achievements, current understanding, and future challenges, Appl. Phys. Mater. Sci. Process. 69 (2) (1999) 131. [6] U. Rau, P.O. Grabitz, J.H. Werner, Resistive limitations to spatially inhomogeneous electronic losses in solar cells, Appl. Phys. Lett. 85 (24) (2004) 6010. [7] G. Brown, A. Pudov, B. Cardozo, V. Faifer, E. Bykov, M. Contreras, Quantitative imaging of electronic nonuniformities in Cu(In, Ga)Se[sub 2] solar cells, J. Appl. Phys. 108 (7) (2010) 074516.
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[8] G.H. Bauer, L. Gütay, Lateral features of Cu(In0.7Ga0.3)Se2-heterodiodes in the μmscale by confocal luminescence and focused light beam induced currents, Thin Solid Films 515 (15) (2007) 6127. [9] M.J. Romero, K. Ramanathan, M.A. Contreras, M.M. Al-Jassim, R. Noufi, P. Sheldon, Cathodoluminescence of Cu(In, Ga)Se[sub 2] thin films used in high-efficiency solar cells, Appl. Phys. Lett. 83 (23) (2003) 4770. [10] J. Nelson, The physics of solar cells, Distributed by World Scientific Pub. Co, River Edge, NJ: Imperial College Press, London, 2003. [11] W. Warta, J. Sutter, B. Wagner, R. Schindler, Impact of diffusion length distributions on the performance of mc-silicon solar cells, Proc. Second World Conf. Photovolt. Energy Convers (1998) 1650. [12] P. Würfel, T. Trupke, T. Puzzer, E. Schäffer, W. Warta, S.W. Glunz, Diffusion lengths of silicon solar cells from luminescence images, J. Appl. Phys. 101 (12) (2007) 123110. [13] M. Paire, A. Shams, L. Lombez, N. Péré-Laperne, S. Collin, J.-L. Pelouard, J.-F. Guillemoles, D. Lincot, Resistive and thermal scale effects for Cu(In, Ga)Se2 polycrystalline thin film microcells under concentration, Energy Environ. Sci. 4 (12) (2011) 4972. [14] M. Paire, L. Lombez, N. Péré-Laperne, S. Collin, J.-L. Pelouard, D. Lincot, J.-F. Guillemoles, Microscale solar cells for high concentration on polycrystalline Cu(In, Ga)Se2 thin films, Appl. Phys. Lett. 98 (26) (2011) 264102.
[15] M. Troviano, K. Taretto, Analysis of internal quantum efficiency in double-graded bandgap solar cells including sub-bandgap absorption, Sol. Energy Mater. Sol. Cells 95 (3) (2011) 821. [16] M.A. Green, Do built-in fields improve solar cell performance? Prog. Photovolt. Res. Appl. 17 (1) (2009) 57. [17] W. Gärtner, Depletion-layer photoeffects in semiconductors, Phys. Rev. 116 (1) (1959) 84. [18] K.W. Mitchell, A.L. Fahrenbruch, R.H. Bube, Evaluation of the CdS/CdTe heterojunction solar cell, J. Appl. Phys. 48 (10) (1977) 4365. [19] J. Malmström, «On Generation and Recombination in Cu(In, Ga)Se2 Thin-Film Solar Cells», University dissertation from Uppsala: Acta Universitatis Upsaliensis, 2005. [20] L. Gütay, C. Lienau, G.H. Bauer, Subgrain size inhomogeneities in the luminescence spectra of thin film chalcopyrites, Appl. Phys. Lett. 97 (5) (2010) 052110. [21] A. Delamarre, M. Paire, J.-F. Guillemoles, et L. Lombez, To be published, 2014. [22] G.H. Bauer, R. Brüggemann, S. Tardon, S. Vignoli, R. Kniese, Quasi-Fermi level splitting and identification of recombination losses from room temperature luminescence in Cu(In1 − xGax)Se2 thin films versus optical band gap, Thin Solid Films 480 481 (2005) 410. [23] G. Hanna, A. Jasenek, U. Rau, H.W. Schock, Influence of the Ga-content on the bulk defect densities of Cu (In, Ga) Se2, Thin Solid Films 387 (1 2) (2001) 71.
Contents lists available at ScienceDirect
Thin Solid Films journal homepage: www.elsevier.com/locate/tsf
Micrometric investigation of external quantum efficiency in microcrystalline CuInGa(S,Se)2 solar cells L. Lombez, D. Ory, M. Paire, A. Delamarre, G. El Hajje, J.F. Guillemoles Institute of Research and Development on Photovoltaic Energy (IRDEP), EDF R&D, UMR 7174 CNRS EDF ChimieParisTech, 78401 Chatou, France
a r t i c l e
i n f o
Article history: Received 18 January 2014 Received in revised form 17 June 2014 Accepted 23 June 2014 Available online 29 June 2014 Keywords: Copper indium gallium selenides Photovoltaics Micrometric Supercontinuum External quantum efficiency Diffusion length
a b s t r a c t We present in this paper small scale spatial fluctuations of the spectral response of CuInGa(S,Se)2 polycrystalline solar cell. The experimental method is based on light beam induced current cartographies under different excitation wavelengths. From those measurements we can map minority carrier diffusion length Ln over the cell with a spatial resolution of about 2 μm. Spatial variations of Ln are evidenced, which result in a standard deviation of around 130 nm. The experiment also evidences spatial fluctuations of the external quantum efficiency that can arise from surface recombinations. © 2014 Elsevier B.V. All rights reserved.
1. Introduction CuInGa(S,Se)2 (CIGS) solar cell shows a record conversion efficiency of more than 20%, the highest among polycrystalline thin film technologies [1,2]. Nevertheless the theoretical efficiency limit of this type of cell, the Shockley Queisser limit, is estimated to be around 30% [3–5]. A better understanding of the cell properties is thus necessary in order to diagnose the losses and then increase further the cell performances. However the complex nature of the polycrystalline materials impedes exact measurements of fundamental properties. In fact, measurements of global optoelectronic parameters are always an average of local ones. Thus they do not properly reflect the real device properties; each submicron region having its own properties. Moreover, one of the limits to the performances of those polycrystalline cells might be strong lateral inhomogeneities [6,7]. Therefore, micron scale fluctuations have been studied, for example, by mean of Photoluminescence (PL) [8] or Cathodoluminescence [9]. These studies evaluated grain boundary effects, fluctuations of the quasi Fermi level splitting (i.e. the maximum reachable open circuit voltage) or variations of the absorption properties. Nevertheless it is always a challenge to know what is actually measured. External quantum efficiency (EQE) measurement is a standard characterization method, from which one can determine optoelectronic properties such as minority carrier diffusion length, absorption properties or space charge region width [10]. However, this well-known
E-mail address: [email protected] (L. Lombez).
http://dx.doi.org/10.1016/j.tsf.2014.06.041 0040-6090/© 2014 Elsevier B.V. All rights reserved.
characterization tool always measures EQE on large areas and therefore determines global parameters of the cell. We propose in this communication to measure their spatial fluctuations of these parameters thanks to a mapping method having both high spatial and spectral resolution. The experiment is also suitable for recording spectral response of micrometric photovoltaic devices. To do so, we set up an experiment that can locally probe the EQE a micron scale. Light beam induced current (LBIC) cartographies are recorded at different excitation wavelengths allowing the evaluation of the spectral response EQE(E) at different cell positions. This experiment evidences strong lateral fluctuations of the EQE. From our cartographies, and a statistical analysis, we will also discuss the limits of different models to extract physical parameters such as diffusion lengths from EQE measurements. 2. Experimental setup and sample The excitation source is a Fianium supercontinuum laser whose wavelength is selected using a Photon Etc Laser Line Tunable Filter. The spectral resolution is 2 nm while the extinction ratio is higher than 105. The laser is coupled into an optical fiber connected to a homemade microscope (see Fig. 1). The sample is then excited using a microscope objective (either reflective or apochromatic, both giving the same results). The broadband single mode laser allows us to have a spatial resolution from of about 2 μm and to sweep the wavelength from 400 to 1100 nm. We do not aim to reach the diffraction limit spot size for two reasons: on the one hand this avoids spot size dependence with the excitation wavelength and, on the other hand, it is not necessary to go below this value as the diffusion length in CIGS absorbers is usually
L. Lombez et al. / Thin Solid Films 565 (2014) 32–36
33
Fig. 1. Experimental setup and sketch of the CIGS microcell sample.
found between 0.5 and 3 μm. The excitation photon flux is measured using a calibrated Si photodiode. The laser pulse duration is 6 ps and the repetition rate is set to 80 MHz. The average excitation power density is 75 ± 33 nW/μm2/nm (depending on the excitation wavelength) that corresponds to about 145 ± 48 μW/μm2/nm peak power (i.e. 3.7 × 1015 incident photons/m2 per pulse at 850 nm or 2.98 × 1023 incident photons/m2/s, corresponding to about 100 Suns). In order to obtain an EQE(E) cartography, the sample is mounted on a Physik Instrumente piezoelectric stage; we can therefore map the EQE value for each excitation wavelength: spectrally resolved LBIC (SR-LBIC). Note that another method for SR-LBIC has been used on Si solar cell but without the spatial and spectral resolution required for investigating thin film polycrystalline cells [11,12]. Note also that the use of supercontinuum laser in this type of setup is a way to record spatial variations other widely used measurements such as Photoluminescence Excitation (PLE), Current Voltage curves or Time Resolved Photoluminescence signals. Nevertheless one has to keep in mind that the laser is a pulsed source and might induce artifacts or unrealistic values due to high injection regime. To minimize this problem, the sample studied in this paper is a Cu(In,Ga)Se2 based solar cell, limited in its lateral dimension [13]. These microscale cells have been previously studied under high excitation fluxes, and showed very low heating or resistive effects, as the micrometric size of the cells strongly diminishes sheet resistance losses and eases thermal evacuation. It was shown for example that the current varies linearly with the excitation power up to thousand suns in these devices, indicating a good photocurrent collection in these high injection regimes [14]. The microcells are composed of a Mo back contact, deposited on glass, and a 2.5 μm thick commercial Cu(In,Ga)Se2 coevaporated absorber layer from Würth solar. The fabrication process is explained elsewhere [14], a scheme of the device is presented in Fig. 1. Global and local measurements have been done by exciting the cell over its entire surface or, by focusing the laser spot onto the cell surface (mapping conditions). Similar behaviors are found in both cases. On the one hand it confirms that the EQE evaluation is not affected by the pulsed excitation condition (i.e. one can consider a quasi state regime).
On the other hand, the charge collection is efficient and not limited by series resistance. These good behaviors are assumed to be linked to the use of microcells. Indeed it is no longer observed at higher excitation power (above 20 μW/μm2 average power) or, when the cell diameter is too large.
3. Results and discussion We then measure LBIC cartographies on two different microcells for excitation wavelengths varying from 400 nm to 1100 nm with a 5 nm step. In Fig. 2 are displayed three examples of EQE maps: Fig. 2(b) and (d) are for cell 1 at 840 nm and 1050 nm; Fig. 2(c) is for cell 2 at 750 nm. At excitation wavelengths well above the band gap, absolute spatial variations of EQE close to 5% are observed on cell 1 or close to 10% on cell 2 (Fig. 2(b) and (c)). Larger spatial variations are observed at wavelength close to the band gap (Fig. 2(d)). Indeed, in this spectral region, the EQE value is sensitive to the diffusion lengths and the band gap as we will see later. Moreover, different spatial fluctuation ranges can be seen. Micrometric variations are attributed to intrinsic properties of the polycrystalline absorbers whereas longer range fluctuations could be linked to the fabrication process of the microcell. Thanks to the mapping, we can also determine the spectral response at each cell position. Some EQE(E) curves in a spectral range slightly above the bandgap (region of interest) are displayed in Fig. 2(a). The three higher EQE(E) curves are coming from the area A of cell 1: we can guess changes in the band gap Eg, as well as changes in the diffusion length Ln (which is, in the first order, the slope of the curve). The two lower curves are coming from the area B where low values of EQE are attributed to fabrication process artifacts leading to either optical or edge recombination effects. As we will see, even on this second area, the determined values of Ln and Eg make sense. This shows that the material quality of the absorber can still be analyzed on this region. From those EQE(E) curves, one could access the spatial variations of physical parameters, linked to transport or optical properties for example. Indeed the external quantum efficiency EQE, between the depths x1
34
L. Lombez et al. / Thin Solid Films 565 (2014) 32–36
Fig. 2. Measurement of the external quantum efficiency of 25 μm diameter microcells. (a) Spectral response EQE(E) from different areas on cell 1; Lines are the experimental data, dots represent the corresponding fits; (b) EQE map of cell 1 at 870 nm (c) EQE map of cell 2 at 780 nm and (d) EQE map of cell 1 at 1050 nm.
and x2, can be expressed in a general manner as [15,16]: Z EQEðEÞ ¼
x2 x1
g ðx; EÞf c ðEÞdx
where g(x, E) is the generation function and can be expressed by g(x, E) = (1 − R)αe−α in a simplified case with no reflection at the back pffiffiffiffiffiffiffiffiffiffiffiffiffi side. The absorption coefficient is α∝ E−Eg . In the quasi neutral region, the collection function fc(E) depends on the minority carrier diffu sion length Ln: f c ðEÞ ¼ exp − x−w Ln . The well known Gartner model assumes that charges generated in the space charge region and at one diffusion length from the space charge region are all collected, a revision has been proposed based on a drift diffusion model [17,18]. The latter introduces a drift length influenced by CIGS/CdS interface recombinations, which results in a non perfect collection within the space charge region. The EQE becomes a function of a factor h, which depends on recombination velocity S and carrier velocity Eμ (where μ is the mobility and E is the electrical field E at the interface): −αw e ð1−RÞ EQEðEÞ ¼ h 1− 1 þ αLn where R is the macroscopic reflection coefficient with a value −1 S measured at 16% in our sample and h ¼ 1 þ Eμ . This factor is directly linked to the value of EQE well above the band gap and thus originates the spatial fluctuations we observe. Those EQE values are essentially fluctuating from 0.5. to 0.7; assuming an electric filed E of 104 V/cm and an electron mobility μ of 100 cm2/(V s), this will imply a h factor fluctuating from 0.59 to 0.83 of and thus a recombination velocity varying from 1.2 × 106 cm/s to 1.7 × 106 cm/s.
The energy dependence prefactor of α is taken spatially uniform [19]. Variations in the absorption coefficient are assumed to only originate from Eg fluctuation, due for instance, to varying gallium content. The space charge region width w, determined by capacitance spectroscopy, is considered constant at 340 nm, the doping density is assumed spatially uniform. We first determine the spatial variations of the minority carrier diffusion lengths and the band gaps, within the limits of the Gartner's model, which will be discussed later. The two cartographies and the corresponding histograms are displayed in Fig. 3. The average value of the Ln spatial distribution is found to be 1.41 μm with a Full Width Half Maximum (FWHM) of 0.31 μm (~21%). The average value of Eg is found to be 1.17 eV with a FWHM of 4 meV (b1%). The latter variations are slightly smaller to what was measured when recording optical bandgap from spectrally resolved Photoluminescence maps (~10 meV) but still very close [20,21]. We propose to evaluate the relevance of such an analysis, and possible limits of the Gartner's model for this type of experiments. In order to do so for each spatial location, we have plotted the diffusion length as a function of the band gap in Fig. 4, and, in inset, the correlation index cartography. The correlation is simply calculated by the ratio between the normalized Ln and Eg maps. Even though correlations can be found between the two parameters, the anti-correlation seems to be the dominant case: the shorter the diffusion length, the larger the band gap. This behavior has been previously observed on samples with different gallium contents [22]. A higher Ga content could induced local degradations of bulk properties [23]. Nevertheless, regarding the band gap of CuInSe2 (1 eV) and CuGaSe2 (1.7 eV) a 8 meV total gap variation is induced by about 1% Ga fluctuation. This cannot explain the variations of Ln we measure [22,23].
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Fig. 3. (a, b) Cartography of the minority carrier diffusion length and its histogram from cell 1. (c, d) Cartography of the band gap fluctuations and its histogram.
Another possible explanation, is that the band gap grading in the absorber, that is not taken into account in the Gartner model, or other classical models to exploit EQE measurements, should in fact be included. In the presence of constant electric field and constant diffusion length, it has been shown that the effective diffusion length can be shorten or enhanced by the presence of an electric field (due for example to the band gap grading) [15]. This relation between effective diffusion length and band gap grading could be important. Indeed, the bandgap measured in EQE is related to the minimum value of the bandgap in the depth of the absorber, a small bandgap relates to a rather steep grading, and thus a higher effective diffusion length. Therefore, taking into account the role of composition grading could explain the anticorrelation between diffusion length and optical bandgap. The spatial fluctuations as well as depth variations play clearly an important role, and it might explain the variations of Ln
found in the literature. Moreover, variations in the local absorber thickness (here a 120 nm rms roughness was measured for the 2.1 μm thick absorber) could have played a role. Nevertheless the roughness is much smaller than the total thickness suggesting no importance of such effect. 4. Conclusion The spectral variations of the external quantum efficiency were measured thanks to an original setup using a broadband visible laser. Spectrally resolved LBIC maps are therefore recorded with a spatial resolution close to the diffraction limit. The experiment evidences spatial fluctuations of the diffusion length with a standard deviation of about 130 nm (FWHM = 300 nm; 20% of Ln). Further studies will enable to propose a more complete and comprehensive model. In fact, this setup could also be used to analyze spatial variations of excitation Photoluminescence or excitation dependence of the time resolved PL. The latter experiment should be a way to correlate local carrier lifetime to the observed fluctuations of Ln. References
Fig. 4. Variation of the diffusion length with the band gap energy. Each point is a given spatial location on cell 1. Inset: Correlation map between the Eg and Ln cartography.
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