On the optical anisotropy of conjugated polymer thin films

In this paper the problem of optical anisotropies in conjugated polymer thin films is revisited and the results in the literature are critically reappraised. Several models for upper bounds on the different types of anisotropies are developed and these are compared with experiment. We analyze both in-plane/out-of-plane and in-plane anisotropies in spin coated and oriented films, respectively. For the in-plane/out-of-plane anisotropy in spin coated films we study the reasons for the large disparity amongst the results reported in the literature, and propose the method of interference enhancement variable angle spectroscopic ellipsometry to retrieve this anisotropy more accurately. Experimental results are reported for poly(9,9-dihexyl fluorene) (spin coated), poly(9,9-dioctylfluorene) (both spin coated and uniaxially aligned), and poly(9,9-dioctylfluorene-co-benzothiadiazole) (both spin coated and uniaxially aligned). Our results concerning the measurement of optical anisotropy can be applied equally well to other molecular systems, such as self-assembled monolayers or Langmuir–Blodgett films.

Figure 1

Chemical structures of (a) PFO, (b) F6, and (c) F8BT.

Figure 2

(a) TE and TM directions for a thin film; (b) Definition of the angles for the upper limit model of the material anisotropy: All the chains are assumed to lie in planes parallel to the plane of the substrate.

Figure 3

Isotropic complex refractive index (solid line) and UV contribution to the isotropic complex refractive index (dashed line) (shown here for PFO but representative of the general situation). The values of the dielectric function (at $\lambda =850\mathrm{nm}$) deduced for PFO, F6, and F8BT are summarized in the table.

Figure 4

(a) Maximum anisotropy, $\Delta n$, deduced for PFO, F6, and F8BT; (b) Maximum $\Delta n$ derived for a distribution of PFO polymer chains consisting of $f\%$ lying parallel to the plane of the substrate and $(1-f)\%$ isotropically distributed. Both sets of data are plotted as a function of the angle $\beta$ between the HOMO-LUMO transition dipole moment direction and the polymer chain segment projection axis. $\beta \sim 22$ and $26\mathrm{deg}$ for F8BT and PFO, respectively.

Figure 5

(Color online) (a) Schematic of the reflection ellipsometry experiment, (b) schematic of Interference enhanced ellipsometry experiment. In the first case, the light collected by the detector is a combination of beams reflected from the polymer-air and polymer-substrate interfaces. In (b) the light bounces multiple times (due to the high reflectivity of Si) within the intermediate $\mathrm{Si}{\mathrm{O}}_2$ layer. The light collected by the detector has now been transmitted through the polymer layer many times, thus enhancing the sensitivity to material properties.

Figure 6

In-plane (solid line) and out-of-plane (dashed line) dispersion of the complex refractive index of PFO. The anisotropic fit was for a $48\text{−}\mathrm{nm}$-thick PFO film on top of a $1020\text{−}\mathrm{nm}$-thick $\mathrm{Si}{\mathrm{O}}_2$ layer on top of a Si substrate.

Figure 7

(a) $\mid \cos {\Delta }_{\mathit{\text{isotropic}}}-\cos {\Delta }_{\mathit{\text{experimnet}}}\mid$ (solid line) and $\mid \cos {\Delta }_{\mathit{\text{uniaxial}}}-\cos {\Delta }_{\mathit{\text{experiment}}}\mid$ (dashed line) as a function of photon energy at $\theta =54\mathrm{deg}$. (b) Mean values of $(\tan {\Psi }_{\mathit{\text{isotropic}}∕\mathit{\text{uniaxial}}}-\tan {\Psi }_{\mathit{\text{experimental}}})$ and $(\cos {\Delta }_{\mathit{\text{isotropic}}∕\mathit{\text{uniaxial}}}-\cos {\Delta }_{\mathit{\text{experimental}}})$ as a function of incidence angle, $\theta$.

Figure 8

(Color online) Comparison of $\tan \Psi$ data for PFO on Spectrosil B (left column), silicon (middle column), and $\text{silicon}+\mathrm{Si}{\mathrm{O}}_2$ (right column) substrates. The incidence angle (PFO film thickness) is fixed at $58\mathrm{deg}$ $\left(50\mathrm{nm}\right)$ in the first (second) row. See text for more details.

Figure 9

(Color online) Experimental procedure to deduce the optical constants of aligned conjugated polymers. Two VASE measurements were taken for the $\mathrm{Si}∕\mathrm{Si}{\mathrm{O}}_2∕\mathrm{P}\mathrm{I}∕\text{polymer}$ system, with the incidence plane lying parallel (or perpendicular) to the rubbing direction. The two sets of data were then analyzed together. P stands for polarizer and A for analyzer.

Figure 10

Refractive index (a) and extinction coefficient (b) data parallel to the chain direction (solid line) and in the plane perpendicular to the chain direction (dashed line) for an oriented PFO film.

Figure 11

Refractive index (a) and extinction coefficient (b) data parallel to the chain direction (solid line) and in the plane perpendicular to it (dashed line) for an oriented F8BT film.