Optical Characterization of the Hole Polaron in a Series of Diketopyrrolopyrrole Polymers Used for Organic Photovoltaics

Abstract: A strategy that is often used for designing low band gap polymers involves the incorporation of electron-rich (donor) and electron-deficient (acceptor) conjugated segments within the polymer backbone. In this paper we investigate such a series of Diketopyrrolopyrrole (DPP)-based co-polymers. The co-polymers consisted of a DPP unit attached to a phenylene, naphthalene, or anthracene unit. Additionally, polymers utilizing either the thiophene-flanked DPP or the furan-flanked DPP units paired with the naphthalene comonomer were compared. As these polymers have been used as donor materials and subsequent hole transporting materials in organic solar cells, we are specifically interested in characterizing the optical absorption of the hole polaron of these DPP based copolymers. We employ chemical doping, electrochemical doping, and photoinduced absorption (PIA) studies to probe the hole polaron absorption spectra. While some donor-acceptor polymers have shown an appreciable capacity to generate free charge carriers upon photoexcitation, no polaron signal was observed in the PIA spectrum of the polymers in this study. The relations between molecular structure and optical properties are discussed. Keywords: organic solar cell; organic photovoltaic; diketopyrrolopyrrole; chemical doping; spectroelectrochemistry; photoinduced absorption; hole polaron

Small Polaron Hopping And High-Temperature Dc Conductivity Of Chalcogenide Glasses

D.C. conductivity behaviour of a variety of chalcogenide glasses have been analysed using ln σ vs Image plots as suggested in the multiphonon assisted polaron hopping model of Triberis and Friedman. The agreement with the model is very satisfactory and further analysis of the model using c.

Angle-resolved photoemission spectroscopy of the insulating NaxWO3: Anderson localization, polaron formation, and remnant Fermi surface

The electronic structure of the insulating sodium tungsten bronze, Na0.025WO3, is investigated by high-resolution angle-resolved photoemission spectroscopy. We find that near-E-F states are localized due to the strong disorder arising from random distribution of Na+ ions in the WO3 lattice, which makes the system insulating. The temperature dependence of photoemission spectra provides direct evidence for polaron formation. The remnant Fermi surface of the insulator is found to be the replica of the real Fermi surface in the metallic system

Polaron effects on the optical absorptions in asymmetrical semi-parabolic quantum wells

The linear and nonlinear optical absorptions considering the weak-coupling electron-LO-phonon interaction in asymmetrical semiparabolic quantum wells are theoretically investigated. The numerical results for the typical GaAs/AlxGa1-xAs material show that the factors of Al content x, the relaxation time and the photon energy have great influence on the optical absorption coefficients. Moreover, the theoretical values of the optical absorptions are more than a factor of 2-3 higher than the one in the structure without considering the electron-LO-phonon interaction by calculating. (C) 2007 Elsevier B.V. All rights reserved.

Polaron hopping in olivine phosphates studied by nuclear resonant scattering

Valence fluctuations of Fe²⁺ and Fe³⁺ were studied in a solid solution of Li_xFePO₄ by nuclear resonant forward scattering of synchrotron x rays while the sample was heated in a diamond-anvil pressure cell. The spectra acquired at different temperatures and pressures were analyzed for the frequencies of valence changes using the Blume-Tjon model of a system with a fluctuating Hamil- tonian. These frequencies were analyzed to obtain activation energies and an activation volume for polaron hopping. There was a large suppression of hopping frequency with pressure, giving an anomalously large activation volume. This large, positive value is typical of ion diffusion, which indicates correlated motions of polarons, and Li⁺ ions that alter the dynamics of both.

In a parallel study of Na_xFePO₄, the interplay between sodium ordering and electron mobility was investigated using a combination of synchrotron x-ray diffraction and nuclear resonant scattering. Conventional Mossbauer spectra were collected while the sample was heated in a resistive furnace. An analysis of the temperature evolution of the spectral shapes was used to identify the onset of fast electron hopping and determine the polaron hopping rate. Synchrotron x-ray diffraction measurements were carried out in the same temperature range. Reitveld analysis of the diffraction patterns was used to determine the temperature of sodium redistribution on the lattice. The diffraction analysis also provides new information about the phase stability of the system. The temperature evolution of the iron site occupancies from the Mossbauer measurements, combined with the synchrotron diffraction results give strong evidence for a relationship between the onset of fast electron dynamics and the redistribution of sodium in the lattice.

Measurements of activation barriers for polaron hopping gave fundamental insights about the correlation between electronic carriers and mobile ions. This work established that polaron-ion interactions can alter the local dynamics of electron and ion transport. These types of coupled processes may be common in many materials used for battery electrodes, and new details concerning the influence of polaron-ion interactions on the charge dynamics are relevant to optimizing their electrochemical performance.

I. Electronic processes in α-sulfur. II. Polaron motion in a D.C. electric field

Part I: The mobilities of photo-generated electrons and holes in orthorhombic sulfur are determined by drift mobility techniques. At room temperature electron mobilities between 0.4 cm²/V-sec and 4.8 cm²/V-sec and hole mobilities of about 5.0 cm²/V-sec are reported. The temperature dependence of the electron mobility is attributed to a level of traps whose effective depth is about 0.12 eV. This value is further supported by both the voltage dependence of the space-charge-limited, D.C. photocurrents and the photocurrent versus photon energy measurements.

As the field is increased from 10 kV/cm to 30 kV/cm a second mechanism for electron transport becomes appreciable and eventually dominates. Evidence that this is due to impurity band conduction at an appreciably lower mobility (4.10^-4 cm²/V-sec) is presented. No low mobility hole current could be detected. When fields exceeding 30 kV/cm for electron transport and 35 kV/cm for hole transport are applied, avalanche phenomena are observed. The results obtained are consistent with recent energy gap studies in sulfur.

The theory of the transport of photo-generated carriers is modified to include the case of appreciable thermos-regeneration from the traps in one transit time.

Part II: An explicit formula for the electric field E necessary to accelerate an electron to a steady-state velocity v in a polarizable crystal at arbitrary temperature is determined via two methods utilizing Feynman Path Integrals. No approximation is made regarding the magnitude of the velocity or the strength of the field. However, the actual electron-lattice Coulombic interaction is approximated by a distribution of harmonic oscillator potentials. One may be able to find the “best possible” distribution of oscillators using a variational principle, but we have not been able to find the expected criterion. However, our result is relatively insensitive to the actual distribution of oscillators used, and our E-v relationship exhibits the physical behavior expected for the polaron. Threshold fields for ejecting the electron for the polaron state are calculated for several substances using numerical results for a simple oscillator distribution.

Direct observation of excitonic polaron in InAs/GaAs quantum dots

We report a direct observation of excitonic polaron in InAs/GaAs quantum dots using the photoluminescence (PL) spectroscopy. We observe that a new peak s' emerges below the s-shell which has anomalous temperature dependence emission energy. The peak s' anticrosses with s at a certain temperature, with a large anticrossing gap up to 31 meV. The behavior of the new peak, which cannot be interpreted using Huang-Rhys model, provides a direct evidence for strong coupling between exciton and LO phonons, and the formation of the excitonic polaron. The strong coupling between exciton and phonons opens a way to coherently control the polaron states.

Effects of lattice vibration on the effective mass of quasi-two-dimensional strong-coupling polaron

The effects of lattice vibration on the system in which the electron is weakly coupled with bulk longitudinal optical phonons and strongly coupled with interface optical phonons in an infinite quantum well were studied by using Tokuda' linear-combination operator and a modified LLP variational method. The expressions for the effective mass of the polaron in a quantum well QW as functions of the well's width and temperature were derived. In particular, the law of the change of the vibration frequency of the polaron changing with well' s width and temperature are obtained. Numerical results of the effective mass and the vibration frequency of the polaron for KI/AgCl/Kl QW show that the vibration frequency and the effective mass of the polaron decrease with increasing well's width and temperature, but the contribution of the interaction between the electron and the different branches of phonons to the effective mass and the vibration frequency and the change of their variation with the well's width and temperature are greatly different.

Energy of a polaron in a wurtzite nitride finite parabolic quantum well

The effects of electron-phonon interaction oil energy levels of a. polaron in a wurtzite nitride finite parabolic quantum well (PQW) are studied by using a modified Lee-Low-Pines variational method. The ground state, first excited state, and transition energy of the polaron in the GaN/Al0.3Ga0.7N wurtzite PQW are calculated by taking account of the influence of confined LO(TO)-like phonon modes and the half-space LO(TO)-like phonon modes and considering the anisotropy of all kinds of phonon modes. The numerical results are given and discussed. The results show that the electron phonon interaction strongly affects the energy levels of the polaron, and the contributions from phonons to the energy of a polaron hi a wurtzite nitride PQW are greater than that in all AlGaAs PQW. This indicates that the electron-phonon interaction in a wurtzite nitride PQW is not negligible.

Electron effective mass and resonant polaron effect in CdTe/CdMgTe quantum wells

Cyclotron resonance in CdTe/CdMgTe quantum wells (QWs) was studied. Due to the polaron effect the zero-field effective mass is strongly influenced by the QW width. The experimental data have been described theoretically by taking into account electron-phonon coupling and the nonparabolicity of the conduction band. The subband structure was calculated self-consistently. The best fit was obtained for an electron-phonon coupling constant alpha = 0.3 and bare electron mass of m(b) = 0.092m(0).

Temperature dependence of polaron cyclotron resonance mass in GaAs/AlGaAs heterostructures

The temperature dependence of polaron cyclotron resonance mass in GaAs/AlGaAs heterostructures is reinvestigated theoretically. By taking into account the electron-longitudinal-optic phonon interaction with temperature-dependent many-body effects, the conduction band non-parabolicity, and the influence of nonzero magnetic field, a good agreement with experiment is obtained.

Blocking of the polaron effect and spin-split cyclotron resonance in a two-dimensional electron gas

Cyclotron resonance (CR) of high density GaAs quantum wells exhibits well-resolved spin splitting above the LO-phonon frequency. The spin-up and spin-down CR frequencies are reversed relative to the order expected from simple band nonparabolicity. We demonstrate that this is a consequence of the blocking of the polaron interaction which is a sensitive function of the filling of the Landau levels.

Electron effective mass and resonant polaron effect in CdTe/CdMgTe quantum wells

Cyclotron resonance in CdTe/CdMgTe quantum wells (QWs) was studied. Due to the polaron effect the zero-field effective mass is strongly influenced by the QW width. The experimental data have been described theoretically by taking into account electron-phonon coupling and the nonparabolicity of the conduction band. The subband structure was calculated self-consistently. The best fit was obtained for an electron-phonon coupling constant alpha = 0.3 and bare electron mass of m(b) = 0.092m(0).