Absorption spectroscopy, or transmission spectroscopy, measures optical absorption and absorption coefficients, and can reveal a great deal more information concerning material sample crystallinity, effective optical bandgap, and some impurities. In such measurements, a broad-band light source is passed through a monochromator, such that single wavelengths of light pass through the sample in progression. Wavelength-dependent photons transmitted through the sample are measured by a detector, as illustrated in Fig. 9.3. Light incident on the sample can be absorbed, reflected, or scattered, reducing transmission. It is possible to separate and measure the relative quantities of photons reflected or transmitted by placing the source at a small angle off the orthogonal axis and measuring small angle reflectance. However, in most cases, reflection and scattering are assumed to be a relatively small effect reducing transmission, when compared to bulk absorption. For thin or largely transparent films, care must be taken in measurement as this assumption does not always hold. In order to properly measure the absorption of highly transparent or thin films, it is recommended to measure transmission and reflection.
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Table 9.2 List of the primary spectroscopies used to evaluate the physical processes relevant to photogeneration and collection in organic BHJ solar cells
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Sample Figure 9.3 Transmission spectroscopy schematic. |
Photons normally incident on a sample, 1{, undergo a series of physical processes that reduce the number of photons transmitted,
It. Transmittance, T, is defined as the ratio between the incident and transmitted light intensity:
r = /t//,= 1-A – R-S, (9.5)
where this total fraction of incident light may be reduced by absorbance, A, reflectance, R, and scattering, S. At each interface, a fraction of the photons are reflected and transmitted, based on the difference in refractive index, n, between the two materials in intimate contact and the angle of incident light, в, according to Snell’s law. Within a material, light may be absorbed, based on the extinction coefficient, k, related to the absorption coefficient, a, and the length of the light path through the material, d. The absorption and extinction coefficients are related by the relation: a = 4nk/X, where X is the wavelength of incident light. Refractive index and extinction coefficients are simply related to the complex dielectric constant of a material:
£ = £1 + i£2; e1 = n2 – к2; e2 = 2nk (9.6)
For photon energies below their bandgap, materials are largely transparent. Light incident on a material below the bandgap is transmitted, or the material is “transparent” to photons at these wavelengths, or a(X) ~ 0. For materials with bandgap larger than the visible frequencies, such as glass, indium tin oxide, and others, the materials themselves are largely transparent to the human eye. At photon energies near the bandgap, Eg, light begins to be strongly absorbed by the material. The wavelength width of the absorption band depends on parameters of the material—specifically the width and structure (e. g., density of states) of the excited state energy band. The optical bandgap can be estimated from the wavelength – dependent absorption, but as illustrated in Fig. 9.4, amorphous organic materials often have moderately increasing absorption near the band edge and, in the case of [6,6]-phenyl-C61-butyric acid methyl ester (PCBM) illustrated here, multiple absorption edges. Furthermore, in Fig. 9.4a, a plot of absorptance versus wavelength and absorptance versus photon energy inset (absorptance data extracted from Ref. [71]), demonstrates that linear extrapolation to zero absorption does not accurately predict the optical bandgap of a material. Extrapolation in this case, Fig. 9.4a, predicts lowest unoccupied molecular orbital (LUMO) edges at 3.3 and 4.1 eV,
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underestimating the observed energy levels by over 10% in the case of the primary absorption edge.
Tauc plots are commonly utilized to extract the optical energy gap from absorption data. Classic analysis of the structure of the band edge of amorphous materials72 from 1966 from Tauc et al. has been utilized to analyze oxides, polymers, and small molecules with sufficient disorder. Tauc analysis cannot be strictly applied to conjugated semiconductors, where Bloch’s theorem does not hold—strong intramolecular bonding does not extend to a full crystal structure. Efforts have been made over the past 30 years to determine the relationship between absorptivity and the energy gap to amorphous semiconductors, under the following assumptions: selection rules, based on lattice spacing, k, are relaxed, and probability of a band-to-band transition (photon absorption) shows reduced dependence on photon energy at the band edge. Common analysis of amorphous semiconductors assumes a parabolic density of state at the band edge, such that the relationship between absorptivity and energy gap can be described: a ^ (ha> – Eg)2/ha>.73 Tauc plots may provide a better estimate of the optical energetic gap than simple absorption vs. wavelength, as illustrated in Fig. 9.4b. Here, spectrally resolved absorptance data for PCBM are used to estimate the absorption coefficient via Beer-Lambert Law: Ty = 1-Ay = e~at. Absorption coefficient may also be measured via variable angle spectroscopic ellipsometry. Assuming a highest occupied molecular orbital (HOMO) energy
level of -6.0 eV, the primary and secondary energy transition in the LUMO level can be estimated as -3.6 and -4.3 eV, respectively, significantly closer to the widely reported primary and secondary LUMO energy levels for PCBM.
