Light Harvesting and Parasitic Absorption in Perovskite Solar Cells

Ball et al. (2015): light-harvesting spectra and optical losses using the paper's refractive index data

AuthorLuke Cole

Optical properties and limiting photocurrent of thin-film perovskite solar cells

Authors: James M. Ball, Samuel D. Stranks et al.

Journal: Energy & Environmental Science 8, 602–609 (2015) · Comparison targets: Figure 4a light harvesting; Figure 4c and p. 606 optical losses

In a thin-film perovskite solar cell, the transparent electrode, absorber, hole transport layer, and metal back electrode jointly determine where incident light is absorbed. Ball et al. studied methylammonium lead iodide (MAPbI₃) devices using measured complex refractive indices and the transfer matrix method to separate active-region absorption, parasitic absorption, and reflection and transmission losses, then calculate the ideal photocurrent limit.

Figure 4a gives active-region light-harvesting efficiency (LHE); Figure 4c separates optical losses. This case reconstructs the default supplementary structure in Dreapex TMM and compares its light-harvesting spectra and loss currents with the supplementary calculation and paper text. Ideal current assumes one electron per photon absorbed in the active region.

Commercial figure reuse permission has not been confirmed, so original figures are not reproduced here. See the paper and supporting information. Paper loss values come from p. 606; reference spectra come from the authors' supplementary calculation.

Structure

Light enters the glass from air and passes through the layers below toward the Au back electrode. Both Top Medium and Bottom Medium are air with refractive index 1. Layer names and thicknesses follow the default supplementary configuration; glass is incoherent and the other layers are coherent.

Layer	Thickness	Layer state
SodaLime	2000 nm	`Inco.`
SnO2	28 nm	None
SiO2	23 nm	None
FTO	340 nm	None
FTema	29 nm	None
TPema	41 nm	None
Perov	492 nm	None
SpOxema	253 nm	None
Au	30 nm	None

Perov is the MAPbI₃ absorber, and FTO is the fluorine-doped tin oxide transparent electrode. FTema and TPema are effective-medium layers at the FTO/TiO₂ and TiO₂/MAPbI₃ interfaces; SpOxema is the doped Spiro-OMeTAD hole transport layer. Use the supplement's refractive index n and extinction coefficient k directly for the effective-medium layers.

Obtain refractive index data from n_k data.csv in the supplementary ZIP. Save each material as a three-column file: wavelength in nm, refractive index n, and extinction coefficient k. Paper data: Perov refractive index file is also available directly.

Open Structure and Add the table's nine layers. Select File, Upload each material, and set Interpolation to Linear. Enable Inco. only for SodaLime; disable Emis. and Tran. everywhere. Set the surrounding media to Constant, named Air-in and Air-out, with n of 1 and bottom k of 0.

Nine-layer structure with original dispersion inputs and incoherent glass

Material and Spectrum Inputs

Dispersion data for all nine layers cover 301–899 nm at 1 nm intervals. The Perov download comes from the Ball entry at refractiveindex.info, whose mirror uses CC0. All 599 points match the original supplement.
Current integration uses AM15 spectrum.csv from the same ZIP, with spectral power density in mW/cm²/nm. Its full-spectrum integral is approximately 100.037 mW/cm²; retain the original intensity without renormalizing.

The download perov.nk and the screenshot's Perov material use the same data.

Optical Settings

Open Optics and enable Reflectance (R), Transmittance (T), Absorptance (A), and Layer Absorption under Propagation. The first two measure light leaving the device; the other two provide total and individual-layer absorption.

UI field	Setting
`Wavelength Mode`	`Sweep`
`From (nm)`	340
`To (nm)`	795
`Step (nm)`	1
`Incident Angle`	0°
`Polarization Ratio (p-polarization)`	0.5
`Cone Angle`	Off
`Incident Spectrum`	Off

A polarization ratio of 0.5 gives equal s and p contributions. With Incident Spectrum disabled, results are optical fractions relative to incident power; solar weighting is applied separately during current integration.

340–795 nm normal incidence, four propagation detectors, and spectrum switch

Without optimization objectives and variables, the interface reports Optimizer parameters that need adjustment. These messages do not prevent Run in this case.

Click Run in the toolbar. After completion, open Layer Absorption and select Stack to display the individual-layer absorption fractions together.

Light-Harvesting Spectra and Optical Loss Comparison

Active-Region Absorption Spectrum (Figure 4a)

The authors define light-harvesting efficiency (LHE) as the sum of TPema and Perov absorption. These two layers form the model's active region. The following screenshot shows layer absorption from this Run.

Actual layer absorption stack for the default structure

Read reflectance R and transmittance T from their respective result pages, selecting Total in both. The following pages retain the original fractions on the same incident-power basis as layer absorption.

Actual reflectance spectrum for the default structure

Actual transmittance spectrum for the default structure

Across the 456 wavelength points from 340 to 795 nm, Dreapex TMM's R, T, and LHE overlap the authors' supplementary calculation point by point. The maximum absolute LHE difference is approximately $3\times10^{-15}$ .

Pointwise overlay of light harvesting, reflectance, and transmittance from the authors' supplementary calculation and Dreapex TMM — Light solid lines: authors' supplementary calculation. Dark dashed lines and open markers: Dreapex TMM. LHE is the sum of TPema and Perov absorption.

Dreapex TMM simulation data: layer absorption, R, T, and LHE · Authors' supplementary calculation and Dreapex TMM comparison data

Equivalent Optical Current and Losses (Figure 4c)

The currents below are obtained by integrating the simulated spectra above with the solar photon flux. Active-region absorption gives ideal photocurrent; reflection, transmission, and non-active-layer absorption give equivalent optical loss currents. All spectra retain their fractions of incident power and use the same solar weighting:

J_X=0.1q\int_{340}^{795}X(\lambda)S(\lambda)\frac{\lambda_{\mathrm m}}{hc}\,\mathrm d\lambda .

$J_X$ is current density in mA/cm², with subscript $X$ identifying the selected optical quantity. $X(\lambda)$ is a dimensionless optical fraction: LHE, R+T, or a selected layer's absorption. $\lambda$ is wavelength in nm and $\lambda_{\mathrm m}=10^{-9}\lambda$ is wavelength in m, with subscript m indicating metres.

$S(\lambda)$ is solar spectral power density in W/m²/nm, obtained by multiplying the original file values by 10. The factor 0.1 converts A/m² to mA/cm².

The elementary charge $q$ , Planck constant $h$ , and vacuum speed of light $c$ retain the supplementary values of $1.602\times10^{-19}$ C, $6.626\times10^{-34}$ J·s, and $2.998\times10^8$ m/s, respectively. Integrate over 340–795 nm using the supplement's Simpson method.

Quantity, 340–795 nm	Paper p. 606, mA/cm²	Dreapex TMM, mA/cm²
Reflection and transmission loss R+T	1.36	1.358
FTO absorption loss	1.38	1.382
Total parasitic absorption loss	1.72	1.720

Total parasitic absorption includes all finite layers except TPema and Perov, so it already includes FTO. Rounding the three calculated values to the paper's decimal places reproduces the reported values. FTO accounts for approximately 80% of the equivalent parasitic absorption current.

Comparison of three optical loss values reported in the paper and integrated from the actual calculation — Gray: rounded values on paper p. 606. Blue: integrals of the same calculated spectra shown above. FTO loss is part of total parasitic absorption.

Layer Absorption from the same run used for loss integration, including FTO and other parasitic layers

Paper text and Dreapex TMM simulation comparison data: three loss currents

TPema and Perov contribute 4.123 and 19.462 mA/cm², respectively, totaling 23.584 mA/cm², consistent with the authors' supplementary calculation. The approximately 23.8 mA/cm² in the paper additionally includes an estimated contribution below 340 nm and therefore uses a different spectral range.

Deviation Notes

The structure and all n and k data use the original default supplementary inputs without material substitution. The supplement sets SodaLime to 2000 nm; this value and its incoherent treatment are retained.
Spectra and loss integrals here cover 340–795 nm. The paper's approximately 23.8 mA/cm² includes a short-wavelength correction, whereas the present finite-band integral is 23.584 mA/cm².
The thickness in Figure 4b includes the effective-medium layer, and its internal quantum efficiency calculation requires a measurement file absent from the ZIP. That thickness sweep is therefore not reproduced here.

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