Reflections Unique paths Fraction  1 reflection  0 0.0% 2 reflections  1 68.3% 3 reflections  3 25.6% 4+ reflections  3 6.1% Total  7 100.0%		Photon current mA/cm2 Fraction Incident JInc 44.00 100.0% Reflected JR 0.93 2.1% Absorbed in films JA 0.32 0.7% Absorbed in substrate JG 42.76 97.2%

 

OPAL 2 is an optical simulator for the front surface of a photovoltaic solar cell.

The user selects the structure of a solar cell and OPAL 2 calculates the reflection from its front surface, the absorption in its thin-film coatings, and the transmission into its substrate over a range of wavelengths. OPAL 2 also calculates the photocurrent that is generated within the cell for a given incident spectrum.

When publishing work that includes the results of OPAL 2 simulations, Reference [McI12] should be cited.

The program accesses a library of refractive index data specific to photovoltaic materials.

A help file will also be developed but, until then, References [McI12, Bak10, Bak11, Bak12a, Bak12b, Bak13] provide the best explanation of the approximations and machinations of OPAL 2.

Warning 1:

The film-thickness optimisation routine can converge on local maxima rather than the global maximum. It is worth conducting manual checks before trusting the output.

Warning 2:

The refractive index of a generic material (such as sodalime glass or SiNx) can vary substantially from one sample to another. This might be due to varying levels of impurities, stoichiometry, or other chemical differences, any of which can depend on the conditions under which the material was formed and treated.

Do not consider the refractive index data provided with this calculator to be representative of all manifestations of a given material. The data simply permits an approximate analysis. It can be found in the library of refractive index data.

If you wish to add your own data to OPAL 2, please send the data and assocaited references to support@pvlighthouse.com.au.

Warning 3:

The generation profile is approximate. It is calculated under the assumptions that (i) all transmitted light travels perpendicularly to the plane of the substrate, and (ii) secondary-pass light is absorbed uniformly in the substrate. Thus, the net generation should be accurate for a given set of inputs, but the distribution of that generation within substrate is approximate.

It is instructive to quantify optical losses in terms of a 'lost generation current'. For example, reflection losses can be quantified as the current that would have been generated inside a solar cell if there had been no reflection.

In OPAL 2, the calculation of lost generation currents requires the user to select a light trapping model. More specifically, the user selects an equation for Z, a parameter that defines the light trapping and often called the 'optical pathlength enhancement factor'. It is defined as

where A is the absorption, α is the absorption coefficient of the substrate, and W is the thickness of the substrate. Thus, when Z is large, the solar cell absorbs more long-wavelength photons (i.e. more weakly absorbing light).

There are currently four options for Z. They are summarised in this table.

Option 1 invovles setting a constant value of Z. Although in practice Z varies with wavelength (primarily because it actually depends on αW), it is sometimes reasonable to approximate Z as a constant. For c-Si solar cells, a reasonable value for a constant Z can be its actual value at a long wavelength such as 1050 nm.

Options 2, 3 and 4 are equations derived from the ideal scenario in which (i) all light inside the solar cell is isotropic, (ii) there is 100% internal reflection at the rear surface (or equivalently, the cell is bifacial and illuminated with an equal intensity from front and rear), and (iii) any antireflection coatings are ideal (i.e. there is 100% transmission at surfaces for any rays that impinge at an angle within the escape cone). In addition, Option 2 assumes there is no absorption in the substrate, and Option 3 assumes that the fraction of light within the escape cones is the same as if there were no absorption in the cell. The equations for the absorption are derived in [Yab81], [Tie84] and [Gre02], and they re-expressed here in terms of Z. Note that Options 2, 3 and 4 all converge to Z = 4n² as αW approaches zero.

In solar cell analyses, each of the three latter options have been used to determine the 'ideal' light trapping within a solar cell. Option 4 is the most preferable because it has the fewest assumptions, however, although it represents an 'ideal case', it does not necessarily represent an upper limit... but that's a longer discussion.

Option 4 is the default in OPAL 2.

Neither PV Lighthouse nor any person related to the compilation of this on-line calculator make any warranty, expressed or implied, or assume any legal liability or responsibility for the accuracy, completeness or usefulness of any information disclosed or rendered by this calculator.

Version 2.6.1 (25-Aug-14) Added option to plot wavelength or photon energy on the x-axis. Photon energy also provided in the "RAT data" tab and in the Excel output.

Version 2.6 (22-Aug-14) Corrected a bug introduced in Version 2.5.3. The bug arose when using custom data and setting the wavelength units to anything other than Å or nm. Specifically, the wavelength was being incorrectly read from the custom data such that it was orders of magnitude smaller than it should have been. Consequently, the analysis at all wavelengths was conducted with the n & k from the custom data that had the longest wavelength. Thanks to Bart Macco (TU/e) for uncovering the problem.

Version 2.5.4 (27-Jun-14) Two new options added for light trapping (Options 3 & 4), as explained on the About tab.

Version 2.5.3 (21-Mar-14) Added options to (i) load custom spectral data, (ii) remove any film (not just the bottom film), (iii) invert the film layers. Improved integration algorithm for determining the photon flux within a wavelength interval (to become consistent with that used in the spectrum library.

Version 2.4.1 (1-Oct-13) Added option to load custom RI and IQE. Added evolutionary algorithm for fitting.

Version 2.2.0 (28-Aug-13) Converted page to new graphic design

Version 2.1.3 (13-May-13) Changed the file download to avoid warning message in Excel

Version 2.1.2 (26-Apr-13) Changed some subroutines so that they do not ignore the first point in the array.

Version 2.0.5 (21-Nov-12) Corrected a bug caused by round-off errors when calculating the generation profile (i.e. generation vs depth) for certain ranges of Z * W. The bug did not affect the calculation of the ray paths, RAT, or the current densities.

Version 2.0.4 (8-Oct-12) Added two new spectra: "Q-Flash" and "Q-Flash w/diffuser". These spectra were measured under the Q-flash that accompanies Sinton Instruments' WCT-100 photoconductance tools, the first unfiltered and the second filtered by a plastic diffuser. This data was published by Swihurn et al. [Swi11]. It has been scaled such that the number of photons with λ < 1200 nm is the same as for the AM1-5g (new) spectrum.

Version 2.0.3 Allowed user to upload experimental reflection data. It also supplies the root mean square error of the difference between the simulated and experimental reflection.

Version 2.0.2 Calculated the generation profile within the substrate and enables the output data to be downloaded in Excel files or text files for use with PC1D.

Version 2.0.1 Added the option to optimise a film's thickness to maximise the generation current in the substrate.

Version 2.0.0 (1-Jun-12) First released.

Thanks to Andreas Fell (ANU), Mattias Juhl (UNSW), Andreas Brand (Fraunhofer ISE) and Bart Macco (TU/e) for reporting bugs and giving suggestions for improvements.

[Bak10]	S.C. Baker-Finch and K.R. McIntosh, "A freeware program for precise optical analysis of the front surface of a solar cell," 35th IEEE Photovoltaic Specialists Conference, Honolulu, pp. 2184–2187, 2010.
[Bak11]	S.C. Baker-Finch and K.R. McIntosh, "Reflection of normally incident light from silicon solar cells with pyramidal texture," Progress in Photovoltaics 19 (4), pp. 406–416, 2011.
[Bak12a]	S.C. Baker-Finch, K.R. McIntosh and M.L. Terry, "Isotextured silicon solar cell analysis and modeling, 1: Optics," IEEE Journal of Photovolatics 2 (4), pp. 457–464, 2012.
[Bak12b]	S.C. Baker-Finch and K.R. McIntosh, "One-dimensional photogeneration profiles in silicon solar cells with pyramidal texture," Progress in Photovoltaics 20 (1), pp. 51–61, 2012.
[Bak13]	S.C. Baker-Finch and K.R. McIntosh, "Reflection distributions of textured monocrystalline silicon: implications for silicon solar cells," Progress in Photovoltaics 21 (5), pp. 960–971, 2013
[Gre02]	M.A. Green, "Lambertian light trapping in textured solar cells and light-emitting diodes: analytical solutions," Progress in Photovoltaics 10, pp. 235–241, 2002.
[McI12]	K.R. McIntosh and S.C. Baker-Finch, "OPAL 2: Rapid optical simulation of silicon solar cells," Proceedings of the 38th IEEE Photovoltaic Specialists Conference, Austin, in-press, 2012.
[Swi11]	J.S. Swihurn, R.A. Sinton, M.K. Forsyth and T. Mankad, "Contactless measurement of minority carrier lifetime in silicon ingots and bricks," Progress in Photovoltaics 19 (3), pp. 313–319, 2011.
[Tie84]	T. Tiedje, E. Yablonovitch, G. Cody and B. Brooks, "Limiting efficiency of silicon solar cells," IEEE Transactions on Electron Devices 31 (5), pp. 711–716, 1984.
[Yab81]	E. Yablonovitch, "Statistical ray optics," Journal of the Optical Society of America 72 (7), pp. 899–907, 1981.