^{1,a)}, Mengtao Sun

^{2}, Pär Kjellberg

^{2}, Tönu Pullerits

^{2}and Olle Inganäs

^{3}

### Abstract

In a joint experimental and theoretical work the optical response and excited-state character of two novel conjugated polymers for photovoltaic applications are studied. The polymers, alternating polyfluorene (APFO) Green 1 and APFO Green 2, are both copolymers of fluorene, thiophene, and electron accepting groups. The band gaps are extended into the red and near infrared with onsets of 780 and 1000 nm, respectively, due to alternating donor and acceptor moieties along the polymer chain. Spectroscopic ellipsometry and subsequent modeling made it possible to extract the dielectric function in the range of 260–1200 nm. Semiempirical quantum chemical calculations (ZINDO) revealed the character of the main electronic transitions in the studied spectral region. The spectral band just above 400 nm was assigned to a delocalized transition for both polymers. The red band lying at 622 and 767 nm in the two polymers corresponds to an electronic state mainly occupying the acceptor units and having a strong charge-transfer character. We show that the ZINDO transition energies are valuable input to the application of Lorentzoscillators in modeling of the dielectric function of the polymer material.

This work was supported by the Swedish Research Council, and the Center of Organic Electronics at Linköping University, financed by the Swedish Strategic Research Foundation. We thank Professor Mats Andersson at Chalmers University of Technology for materials.

INTRODUCTION

EXPERIMENT

RESULTS AND DISCUSSION

Ellipsometry

Modeling procedures

Quantum chemical calculations

From quantum chemistry to dielectric functions: Lorentz modeling

SUMMARY

### Key Topics

- Polymers
- 35.0
- Oscillators
- 15.0
- Excited states
- 12.0
- Dielectric function
- 11.0
- Anisotropy
- 10.0

## Figures

Chemical formulas and oligomeric units used for ZINDO calculations of APFO Green 1 and APFO Green 2. (1) is (a part of) APFO-Green 1, and (2) is (a part of) APFO-Green 2. Sidechains are not included in the ZINDO calculations. Numbering of units is used in Fig. 5 (where numbering of units has been continued in an obvious manner) for correlated electron-hole density maps.

Chemical formulas and oligomeric units used for ZINDO calculations of APFO Green 1 and APFO Green 2. (1) is (a part of) APFO-Green 1, and (2) is (a part of) APFO-Green 2. Sidechains are not included in the ZINDO calculations. Numbering of units is used in Fig. 5 (where numbering of units has been continued in an obvious manner) for correlated electron-hole density maps.

The structure of a sample, with coordinate system, incoming and reflected light, plane of incidence, angle of incidence, and the decomposition of light into and light. The direction is parallel to . The thicknesses (polymer, silicon oxide, and silicon wafer) are not drawn to scale. An ideal model is a model with flat and parallel interfaces.

The structure of a sample, with coordinate system, incoming and reflected light, plane of incidence, angle of incidence, and the decomposition of light into and light. The direction is parallel to . The thicknesses (polymer, silicon oxide, and silicon wafer) are not drawn to scale. An ideal model is a model with flat and parallel interfaces.

APFO Green 1: (a) The overlap between experimental and model data based on multisample analyze and four angles of incidence (58, 67, 76, and 85) in the wavelength interval UV-Vis-NIR. (b) and for APFO Green 1 as from ellipsometric investigation. is parallel to the surface plane (ordinary direction) is normal to the sample plane (extraordinary). (c) The absorption coefficient as a function of wavelength. Bars refer to transitions in Table III, arrows that what axis to read off.

APFO Green 1: (a) The overlap between experimental and model data based on multisample analyze and four angles of incidence (58, 67, 76, and 85) in the wavelength interval UV-Vis-NIR. (b) and for APFO Green 1 as from ellipsometric investigation. is parallel to the surface plane (ordinary direction) is normal to the sample plane (extraordinary). (c) The absorption coefficient as a function of wavelength. Bars refer to transitions in Table III, arrows that what axis to read off.

APFO Green 2: (a) The overlap between experimental and model data based on multisample analyze and four angles of incidence (58, 67, 76, and 85) in the wavelength interval UV-Vis-NIR. (b) and for APFO Green 2 as from ellipsometric investigation. is parallel to the surface plane (ordinary direction) is normal to the sample plane (extraordinary). (c) The absorption coefficient as a function of wavelength. Bars refer to transitions in Table IV, arrows that what axis to read off.

APFO Green 2: (a) The overlap between experimental and model data based on multisample analyze and four angles of incidence (58, 67, 76, and 85) in the wavelength interval UV-Vis-NIR. (b) and for APFO Green 2 as from ellipsometric investigation. is parallel to the surface plane (ordinary direction) is normal to the sample plane (extraordinary). (c) The absorption coefficient as a function of wavelength. Bars refer to transitions in Table IV, arrows that what axis to read off.

(Color online) Isodensity plots of TDs and CDDs of the two strongest transitions of APFO Green 2. The green and red colors correspond to negative and positive densities, respectively. In case of TDs the absolute sign does not have any significance since the transition dipole moment can be turned by 180°. However, in CDDs the negative density (green) corresponds to the hole and positive density (red) to the electron density. Yellow is the sulfur atoms.

(Color online) Isodensity plots of TDs and CDDs of the two strongest transitions of APFO Green 2. The green and red colors correspond to negative and positive densities, respectively. In case of TDs the absolute sign does not have any significance since the transition dipole moment can be turned by 180°. However, in CDDs the negative density (green) corresponds to the hole and positive density (red) to the electron density. Yellow is the sulfur atoms.

(Color online) Correlated electron-hole pair distribution grids for transitions 1 and 5 of APFO Green 2. For numbering see Fig. 1.

(Color online) Correlated electron-hole pair distribution grids for transitions 1 and 5 of APFO Green 2. For numbering see Fig. 1.

## Tables

Thickness in nanometers for the samples examined.

Thickness in nanometers for the samples examined.

Interesting values for the curves. Onset is not well defined and we have done no more elaborate analysis of this. 1 and 2 simply refer to the two absorption bands seen. 1 is the higher and 2 is the lower in wavelength.

Interesting values for the curves. Onset is not well defined and we have done no more elaborate analysis of this. 1 and 2 simply refer to the two absorption bands seen. 1 is the higher and 2 is the lower in wavelength.

Properties of the ten lowest singlet excited states for the oligomer corresponding to APFO Green 1 polymer as obtained from ZINDO calculations. For the assignment 1 253 481 see Fig. 1. The character is only investigated for the S1, S7, and S9.

Properties of the ten lowest singlet excited states for the oligomer corresponding to APFO Green 1 polymer as obtained from ZINDO calculations. For the assignment 1 253 481 see Fig. 1. The character is only investigated for the S1, S7, and S9.

Properties of the ten lowest singlet excited states for the oligomer corresponding to APFO Green 2 polymer as obtained from ZINDO calculations. For the assignment 1 23 478 see Fig. 1. The character is only investigated for the S1, S5, and S7.

Properties of the ten lowest singlet excited states for the oligomer corresponding to APFO Green 2 polymer as obtained from ZINDO calculations. For the assignment 1 23 478 see Fig. 1. The character is only investigated for the S1, S5, and S7.

Lorentz oscillators for APFO Green 2.

Lorentz oscillators for APFO Green 2.

Ordinary Lorentz energies, amplitudes, and broadenings for APFO Green 1.

Ordinary Lorentz energies, amplitudes, and broadenings for APFO Green 1.

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