Photophysics of excitons in quasi-one-dimensional organic semiconductors: Single-walled carbon nanotubes and $\pi$-conjugated polymers

The nature of the primary photoexcitations in semiconducting single-walled carbon nanotubes (S-SWCNTs) is of strong current interest. We have studied the emission spectra of S-SWCNTs and two different $\pi$-conjugated polymers in solutions and films, and have also performed ultrafast pump-probe spectroscopy on these systems with unprecedented spectral range from $0.1\text{to}2.6\mathrm{eV}$. The emission spectra relative to the absorption bands are very similar in S-SWCNTs and polymers, with redshifted photoluminescence in films showing exciton migration. We also found that the transient excited state spectra of both polymers and SWCNTs contain two prominent photoinduced absorption (PA) bands (${\mathrm{PA}}_1$ and ${\mathrm{PA}}_2$) that are due to photogenerated excitons; in the polymers these PA bands are correlated with a stimulated emission band, which is absent in the S-SWCNTs. In order to understand the similarities in the PA spectra we have performed theoretical calculations of excited state absorptions in $\pi$-conjugated polymers as well as S-SWCNTs within the same correlated electron Hamiltonian. We find strong similarities in the excitonic energy spectra of these two classes of quasi-one-dimensional materials, although there exist also subtle differences such as the occurrence of dark excitons below the optical excitons in the S-SWCNTs. In the polymers ${\mathrm{PA}}_1$ is an excited state absorption from the optical exciton to a two-photon exciton that occurs below the continuum band threshold. In the S-SWCNTs ${\mathrm{PA}}_1$ occurs from both the optical exciton and the dark exciton, to final states which are close in energy and again below the continuum band threshold. ${\mathrm{PA}}_1$ therefore gives the lower limit of the binding energy of the lowest optical exciton in both $\pi$-conjugated polymers and S-SWCNTs. The binding energy of lowest exciton that belongs to the widest S-SWCNTs with diameters $⩾1\mathrm{nm}$ in films is $0.3–0.4\mathrm{eV}$, as determined by both experimental and theoretical methods.

Figure 1

(Color online) Photoluminescence (PL) emission and absorption $\alpha \left(\omega \right)$ spectra of (a) PFO solution and film, and (b) isolated SWCNTs in ${\mathrm{D}}_2\mathrm{O}$ solution and PVA matrix film. The optical transitions 1-1 and 2-2 for SWCNT are assigned.

Figure 2

(Color online) Transient PM spectra at $t=0$ of films of DOO-PPV (a), PFO (b), and isolated SWCNT in PVA matrix (c). Various PA, PB, and SE bands are assigned. The vertical dashed lines at $E_c$ between ${\mathrm{PA}}_1$ and ${\mathrm{PA}}_2$ denote the estimated continuum band onset (see text).

Figure 3

(Color online) Transient PM dynamics at various probe energies in (a) DOO-PPV, (b) PFO, (c) SWCNT in PVA matrix, and (d) SWCNTs in ${\mathrm{D}}_2\mathrm{O}$ solution.

Figure 4

Schematics of the excitonic electronic structures of (a) a light-emissive $\pi$-conjugated polymer and (b) a S-SWCNT. In (a) the lowest triplet exciton $1{}^{3}B_u$ occurs below the lowest singlet exciton $1{}^{1}B_u$. The lowest two-photon state $2{}^{1}A_g$ is composed of two triplets and plays a weak role in nonlinear absorption. Transient PA is from the $1{}^{1}B_u$ to the $m{}^{1}A_g$ two-photon exciton which occurs below the continuum band threshold state $n{}^{1}B_u$, and to a high energy $k{}^{1}A_g$ state that occurs deep inside the continuum band. In (b), $n=1$ and $n=2$ energy manifolds for S-SWCNT are shown. $\mathit{Ex}n$ and $Dn$ are dipole-allowed and forbidden excitons, respectively. Shaded area indicate continuum band for each manifold. (Note that exciton levels of the $n=2$ manifold should be buried in the $n=1$ continuum band, but for clarity, the $n=1$ continuum band ends below $D2$.)

Figure 5

Normalized transition dipole moments between S-SWCNT exciton states $\mathit{Ex}1$ and $D1$ and all other excited states $e_j$, where $j$ is the quantum number of the state in the total space of single excitations from the H-F ground state. The numbers along the upper horizontal axes are energies in eV. Results shown are for (a) the (10,0), and (b) the (6,2) S-SWCNTs, respectively. Solid (dotted) lines correspond to $e_i=\mathit{Ex}1$ $\left(D1\right)$. The solid and dashed arrows denote the quantum numbers of $\mathit{Ex}1$ and $D1$, respectively.

Figure 6

SCI energies of optically relevant states in (from left to right) PPV, (10,0) SWCNT and (6,2) SWCNT, respectively. In all cases the $m{}^{1}A_g$ $(m“{}^{1}A_g”)$ is an exciton and ${\mathrm{PA}}_1$ gives the lower limit of the exciton binding energy.