# Quantum Dot Solar Cells: Small Beginnings Have Large Impacts
## 2 Timescales of Excited State Processes
### Absorption and Multiple Exciton Generation  
Propagation and absorption of light in QD materials is the critical first step in using QDs in optoelectronics. As discussed by [PERSON] et al. [42] and [PERSON] et al. [43], the absorption cross section can be written as:  
\[\sigma=\frac{\omega}{n_{s}^{\prime}c}|f(\omega)|^{2}2n_{1}k_{1}\left(\frac{4}{ 3}\pi a^{3}\right) \tag{1}\]  
where \(\omega\) is the angular frequency of light, \(c\) is the speed of light, \(n_{s}^{\prime}\) is the complex refractive index (\(n_{s}^{\prime}=n_{s}-ik_{s}\)) of the solvent or surrounding medium (\(s\) subscript), \(2n_{1}k_{1}=\alpha\) is the absorption coefficient of the bulk material (1 subscript), \(a\) is the radius of the particles, \(k\) is the extinction coefficient, and the local field factor \(f(\omega)\) is given by:  
\[f(\omega)=\frac{3{n_{s}^{\prime}}^{2}}{{n_{1}^{\prime}}^{2}+2{n_{s}^{\prime}} ^{2}} \tag{2}\]  
The overall absorption in a film of QDs can be increased by changing these properties. Increased light absorption in a solar cell typically increases the total electrical current and thus power produced. However, as we will discuss in the section on charge transport, the total film thickness for the highest  
Figure 1: Schematic outline showing the different timescales of the processes in the lifetime of a photoexcitation. efficiency devices does not fully absorb the incident light. Therefore strategies to improve this without increasing the film thickness were developed. Research groups have shown evidence of the positive impact of using plasmonic materials incorporated in QDSCs. By placing materials with a localized surface plasmon resonance (LSPR) [44] in the QDSC, the absorption, due to the higher local field factor, increased. Gold (Au) nano-shells [45], silver (Ag) nano-cubes [46], Au/Ag core/shell nano-cubes [47], and also a combination of Au bipyramids and nano-spheres [48] have been tested in QDSCs. Figure 2a shows the effect of incorporating Au nanoshells into PbS QD films. In each case, it was observed that there was an enhancement in the photocurrent due to an increase in light absorption in the near infra-red (IR) region of the solar spectrum close to the first exciton peak and also in different parts of the spectrum based on the position of the plasmonic nanocrystals (NCs). Alternatively to the PbS and PbSe QDs limited to the IR spectral region, Hg-chalcogenide QDs have spectral features and optoelectronic properties that extend into the far-IR and THz regions [49; 50]. Using plasmonic gold nanorods with HgTe QDs [51], gold nanodisk arrays with HgSe QDs [52] and HgTe QDs [53] improved the photocurrent extraction demonstrating the broad applicability of this absorption enhancement strategy. Another technique used to increase light absorption is the use of nanostructured electrodes or engineer the device layers to have constructive interference of the incident light [54; 55; 56; 57]. These electrodes reflect the incident light back into the absorber layer such that the effective path length of the light wave inside the absorber layer increases as depicted in Figure 2b. In solar cells with thin absorber layers arising from small minority carrier diffusion lengths, increasing the path length of the incident light wave through the absorber material by promoting multiple passes increases the probability of light absorption in the thin film thereby improving device performance. While this technique is difficult to implement in QDSCs due to the uneven accumulation of QD solution in the textured metal oxide electrodes during spin-coating/dip-coating [58; 59], [PERSON]'s group has optimized the steps involved in texturing to help overcome this limitation giving rise to high-performance devices [60; 61; 62].