Minimal model for charge transfer excitons at the dielectric interface

A theoretical description of the charge transfer (CT) exciton across the donor-acceptor interface without the use of a completely localized hole (or electron) is a challenge in the field of organic solar cells. We calculate the total wave function of the CT exciton by solving an effective two-particle Schrödinger equation for the inhomogeneous dielectric interface. We formulate the magnitude of the CT and construct a minimal model of the CT exciton under the breakdown of inversion symmetry. We demonstrate that both a light hole mass and a hole localization along the normal to the dielectric interface are crucial to yield the CT exciton.

Figure 1

Schematic illustration for the electrostatic potential at $\mathit{r}$ by the presence of the source charge at ${\mathit{r}}_s$. Solid and dashed lines indicate the contribution from the bare Coulomb and induced potential, respectively. The dotted line indicates the IP contribution to the position ${\mathit{r}}_s$.

Figure 2

Self-consistent (solid) and zeroth-order (dashed) solutions to the Poisson equation given by Eq. (6). Both solutions are asymmetric with respect to $z=0$. Inset: The IP energy given by Eq. (10).

Figure 3

(a) $z_h$ dependence both of the values of $z_0-z_h$ (left) and $a_z/a_{\rho }$ (right) for the dielectric interface. The trapped hole approximation is assumed: $m_h/m_e\to \infty$ and ${\sigma }_z\to 0$. Inset: The spatial profile of $\varepsilon$ in Eq. (14). (b) $\delta V$ in Eq. (22) as a function of $z_h$. (c) The charge transfer $z_0-z_h$ as a function of ${\sigma }_z$ for $z_h=-0.2a_0$ and $m_h/m_e=2$. Inset: The charge transfer $z_0-z_h$ as a function of $m_h/m_e$ for $z_h=-0.2a_0$ and ${\sigma }_z=0.01a_0$ [see Eq. (17)]. The thin solid line indicates the CT value in the limit of $m_h/m_e\to \infty$.