Spin Fine Structure Reveals Biexciton Geometry in an Organic Semiconductor

In organic semiconductors, biexcitons are key intermediates in carrier multiplication and exciton annihilation. Their local geometry governs their electronic properties and yet has been challenging to determine. Here, we access the structure of the recently discovered $S=2$ quintet biexciton state in an organic semiconductor using broadband optically detected magnetic resonance. We correlate the experimentally extracted spin structure with the molecular crystal geometry to identify the specific molecular pairings on which biexciton states reside.

Figure 1

Broadband ODMR of triplet-pair states. (a) Experimental schematic. Crystalline samples of TIPS-tetracene (oriented with $\widehat{c}$ axis as shown) were optically illuminated under amplitude-modulated microwave excitation (${\mathbf{B}}_{\mathbf{1}}$) using a broadband strip-line in liquid helium (4 K). PL was collected via optical fiber to detect the microwave-induced change in PL as a function of both microwave frequency and static magnetic field (${\mathbf{B}}_0$) with ${\mathbf{B}}_0\perp {\mathbf{B}}_1$. (b) Molecular structure of TIPS-tetracene and corresponding principal axes of the intratriplet dipolar interaction (${\widehat{x}}_t,{\widehat{y}}_t,{\widehat{z}}_t$). (c) Solid-state crystal structure of TIPS-tetracene with four rotationally inequivalent molecules per unit cell labeled 1–4 and unit cell axes ($\widehat{a},\widehat{b},\widehat{c}$).

Figure 2

Field-swept and zero-field ODMR of the triplet-pair state. (a) Energy levels of the uncoupled triplet and coupled quintet $m=0,\pm 1$ sublevels as a function of field referenced to the $m=0$ states $|T_0⟩$ and $|Q_0⟩$, respectively, with transitions at 9 GHz marked with arrows to correspond to experimentally observed transitions in (b). (b) ODMR spectrum at 9 GHz showing inner quintet transitions ($Q^{\pm }$) and outer triplet transitions ($T^{\pm }$). (c) Energy level diagram of triplet and quintet zero-field spin sublevels. Zero-field ODMR spectra with quintet transitions (d) marked with corresponding zero-field splitting parameters ($D_Q$, $E_Q$) and simulation in red and triplet transitions (e) marked with corresponding triplet parameters ($D_T$, $E_T$) and simulations in blue.

Figure 3

Fine-structure tensors from broadband ODMR. (a),(d) Energy level diagram for the quintet (a) and triplet (d) states as a function of magnetic field. Arrows indicate potential transitions, corresponding to lines in (c) and (f) respectively. (b),(e) Schematic representation of the orientation of $\mathbf{B}$ in the quintet (b) and triplet (e) fine-structure axes. (c) ODMR transitions associated with the quintet state with overlay of simulated transitions. Signal has been isolated by subtracting a scaled out-of-phase (Y)-channel signal from the in-phase signal to remove triplet contributions. Black lines show simulations given for ${\theta }_q=90°$ and ${\varphi }_q=30°$ with an uncertainty of $\pm 5°$ where solid (dashed) lines overlay (un-)observed transitions. (f) Y-channel (out-of-phase) ODMR map of the triplet state with overlay of calculated transitions in black with ${\theta }_t=90°$ and ${\varphi }_t=0$.

Figure 4

Local geometry of the quintet fine-structure tensor in the TIPS-tetracene crystal (molecules 1 and 2) with crystal and magnetic field axes shown in the top right and with an angle of ${\theta }_q=91.6°$ and ${\varphi }_q=30.6°$, where the crystal is oriented with ${\mathbf{B}}_0\parallel \widehat{c}$ with two coplanar triads of vectors, $({\widehat{x}}_q,{\widehat{y}}_q,{\mathbf{B}}_0)$ and $({\widehat{z}}_q,{\mathbf{r}}_{ab},{\mathbf{B}}_0)$.