Theoretical Studies of Plasmonic Effects in Organic Solar Cells

Abstract

The book chapter provides a systematic study on plasmonic effects in organic solar cells (OSCs). We first introduce the concepts, significance, and recent progress of OSCs incorporating plasmonic nanostructures. On the basis of unique features of OSCs, we exploit versatile resonance mechanisms acting on the absorption enhancement of OSCs; for example, Fabry-Pérot mode, quasi-guided mode, and plasmonic mode. Next, we present rigorous theoretical models to characterize optical properties of OSCs. The key physical quantities, as well as the pros and cons of different models, are described in detail. After that, we show some theoretical results to unveil the fundamental and device physics of plasmonic effects in typical OSC structures. Finally, we conclude the chapter and identify future opportunities in this field.

Appendix—Biconjugate Gradient Stabilized Algorithm

The resulting VIE matrix equation can be expressed as

$$\begin{aligned} Ax=b \end{aligned}$$

The procedure of the biconjugate gradient stabilized (BI-CGSTAB) algorithm is given as follows:

Give an initial guess $x_0$, we have

$$\begin{aligned}&r_0=b-Ax_0,\,\hat{r}_0=r_0\\&\rho _0=\alpha =\omega _0=1 \\&v_0=p_0=0 \end{aligned}$$

Iterate for $i=1,2,\ldots ,n$

$$\begin{aligned} \rho _i&=\langle \hat{r}_0,r_{i-1}\rangle \\ \beta&=\left(\rho _i/\rho _{i-1}\right)\left(\alpha /\omega _{i-1}\right)\\ p_i&=r_{i-1}+\beta (p_{i-1}-\omega _{i-1}v_{i-1})\\ v_i&=Ap_i\\ \alpha&=\rho _i/\langle \hat{r}_0,v_{i}\rangle \\ s&=r_{i-1}-\alpha v_i\\ t&=As\\ \omega _i&=\langle t,s\rangle /\langle t,t\rangle \\ x_i&=x_{i-1}+\alpha p_i+\omega _i s\\ r_i&=s-\omega _i t \end{aligned}$$

Terminate when

$$\begin{aligned} \frac{||r_{i}||_2}{||b||_2}<\eta \end{aligned}$$

where $\eta$ is the tolerance that specifies the desired accuracy of solution.