Persistence time of charge carriers in defect states of molecular semiconductors

Charge carriers in organic crystals are often trapped in point defects. The persistence time of the charge in these defect states is evaluated by computing the escape rate from this state using non-adiabatic rate theory. Two cases are considered (i) the hopping between separate identical defect states and (ii) the hopping between a defect state and the bulk (delocalized) states. We show that only the second process is likely to happen with realistic defect concentrations and highlight that the inclusion of an effective quantum mode of vibration is essential for accurate computation of the rate. The computed persistence time as a function of the trap energy indicates that trap states shallower than ～0.3 eV cannot be effectively investigated with some slow spectroscopic techniques such as THz spectroscopy or EPR commonly used to study the nature of excess charge in semiconductors.     

Surface states of electrified binary semiconductors

Using the recursive-Green-function (RGF) technique, we investigate the surface states of an electrified binary semiconductor, modelled by a chain of alternating s and p orbitals. The RGF provides the surface density of states (SDOS), which displays a quasi-Stark-ladder distribution of the energy levels in the two bands at the surface atom. The SDOS are discussed in terms of the applied-field and surface-perturbation parameters.     

Linear scaling calculation of band edge states and doped semiconductors

Linear scaling methods provide total energy, but no energy levels and canonical wave functions. From the density matrix computed through the density matrix purification methods, we propose an order-N [O(N)] method for calculating both the energies and wave functions of band edge states, which are important for optical properties and chemical reactions. In addition, we also develop an O(N) algorithm to deal with doped semiconductors based on the O(N) method for band edge states calculation. We illustrate the O(N) behavior of the new method by applying it to boron nitride (BN) nanotubes and BN nanotubes with an adsorbed hydrogen atom. The band gap of various BN nanotubes are investigated systematically and the acceptor levels of BN nanotubes with an isolated adsorbed H atom are computed. Our methods are simple, robust, and especially suited for the application in self-consistent field electronic structure theory.     

Photoconductivity in organopolysilanes

The photoconductivity of methylpropylpolysilane is studied. It is shown that photoconductivity is caused by delocalized σ electron excitation in the silicon skeleton. The carrier types are shown to be holes.     

Classification of molecular states

Conclusions Here we will formulate briefly a member of advantages of the chain of groups in comparison with the CNPI group. In particular, the chain of groups makes it possible to do the following: 1) to carry out an unambigous classification of molecular states (when operating with the CNPI group, several classifications that differ formall from each other can be constructed); 2) to follow easily the evolution of any physical quantity characterizing the molecule, depending on the approximation [5]; 3) to avoid writing in explicit form the wavefunctions of the zero approximation and to avoid calculating the action of the symmetry elements on these functions; and so on. But the most important advantage is that the approach based on the chain of groups does not encounter any ideological difficulties in the classification of molecules for which important symmetry elements cannot be represented in the form of elements of the CNPI group.Institute of Applied Physics, Russian Academy of Sciences. Translated from Zhurnal Strukturnoi Khimii, Vol. 33, No. 2, pp. 15–22, March–April, 1992.     

Localized states in molecular auger spectra

The influence of the degree of localization of the two final holes on the Auger spectra of a simple diatomic molecule is analysed in detail and cases where such effects may be observed experimentally are discussed. The results are compared with studies of the valence band Auger spectra of solids.     

Composite exciton-phonon states in molecular crystals

It is known that the diagonalization of the exciton-phonon Hamiltonian gives rise to the composite exciton-phonon energy states. Within the single phonon approximation, two different diagonalized Hamiltonians are obtained for 0–0 and 0–1 phonon transitions in pure molecular crystals. The resulting secular equations are solved, and analytical expressions for the energy eigenvalues corresponding to the two transitions are derived. The thermal broadening due to the composite exciton-phonon states interaction is also calculated at low temperatures, and the results agree with experiments.     

Hamiltonian for diabatic molecular states

Hyperradial-adiabatic potential curves for (dt )⁺ molecular ions calculated for states with total three-body angular momentumJ=1 and total parityp=1, i.e. for the abnormal parity ground set, are demonstrated to be exactly diabatic-hyperradial potential curves for (J=1,p=–1) symmetry adiabatic curves. This could be thought of as a formal manifestation of the -doubling effect. The projection operator method of constructing a diabatic Hamiltonian that was suggested earlier can be naturally used in our case, too.     

Lifetimes of charge-transfer states in molecular crystals

A simple microscopic model is proposed to described the transition rates to, from and within the manifold of charge-transfer states. The results suggest possible reasons for the existense of long-lived CT states in molecular crystals.     

Atomic valence states in molecular orbital theory

Atomic valence states in simple valence bond and molecular orbital theories of electronic structure have been compared. A basic difference emerges which can be characterised by the presence of one-centre Coulomb terms in the molecular orbital valence state energy. The recognition of this difference is important when performing generalised Hückel calculations: the Coulomb integrals are now given by charge dependent orbital electronegativities, and not the negative of the appropriate ionisation potentials of the kind available in the existing tabulations by Hinze and Jaffé and other authors. The analysis is given in detail for the special case of tetrahedrally coordinated boron and nitrogen, as found in cubic boron nitride.

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Zusammenfassung Es werden atomare Valenzzustände in einfachen Valenzbindungen und MO Theorien der Elektronenstruktur verglichen. Ein wesentlicher Unterschied ergibt sich durch die Anwesenheit von Einzentren-Coulomb-Termen in den MO-Valenzzustandsenergien. Das Erkennen dieser Unterschiede spielt eine entscheidende Rolle bei der Durchführung von Berechnungen nach der allgemeinen Hückel-Theorie: die Coulomb-Integrale sind nun durch Z-abhängige Orbitalelektronennegativitäten und nicht durch geeignete Ionisationspotentiale, wie sie in den Tabellen von Hinze und Jaffé und anderen Autoren verfügbar sind, gegeben. An Hand des tetraedisch gebundenen Bors und Stickstoffs, wie sie in kubischen Bornitriden vorkommen, wird eine genaue Analyse der Methode an einem speziellen Beispiel durchgeführt.

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Résumé Comparaison des états de valence atomiques dans les méthodes de la mésomérie et des orbitales moléculaires. Il apparait une différence fondamentale, que l'on peut caractériser par la présence de termes coulombiens monocentriques dans l'énergie de l'état de valence en orbitales moléculaires. Il importe d'être conscient de cette différence lorsqu'on effectue des calculs Hückel-étendu: les intégrales coulombiennes sont alors données par des électronégativités orbitales dépendant de la charge et non par l'opposé des potentiels d'ionisation du type de ceux que l'on obtient dans les tables de Hinze et Jaffé ou d'autres auteurs. On donne une analyse détaillée pour le cas particulier de l'azote et du bore à coordination tétraédrique, tel qu'il apparait dans le nitrure de bore cubique.

     

Atomic and molecular intracules for excited states

Intracules in position space, momentum space and phase space have been calculated for low-lying excited states of the He atom, Be atom, formaldehyde and butadiene. The phase-space intracules (Wigner intracules) provide significantly more information than the position- and momentum-space intracules, particularly for the Be atom. Exchange effects are investigated through the differences between corresponding singlet and triplet states.     

Photoconductivity in Mesostructured Thin Films

Mesostructured silica films are widely studied due to their different structures, properties and variety of possible applications. Sodium dodecyl sulfate (SDS)-templated sol-gel silica films possess highly ordered lamellar phase structure. It is expected that molecules and polymer chains line up with these layered structures when incorporated into the films. Mesostructured thin films were doped with Dispersed Red 1 (DR1) and carbazole ((C₆H₄)₂NH)). The films were poled by corona discharge at 120 C. Absorption spectra were recorded as function of the polarization time. Dependence of the absorption coefficient with polarization time was fitted with a Langevin-Debye equation. It shows a saturation level after 60 minutes of polarization. We compare the efficiency of mesostructured thin films with that of amorphous films. The photoconductivity technique was used to determine the charge transport mechanism of these films. From current density versus electrostatic applied field, the parameters for the photovoltaic effect and photoconductivity were determined. Results of the mesostructured thin films are also compared to those of KNbO₃ crystals.     

Interpretation of electron diffusion coefficient in organic and inorganic semiconductors with broad distributions of states

The carrier transport properties in nanocrystalline semiconductors and organic materials play a key role for modern organic/inorganic devices such as dye-sensitized (DSC) and organic solar cells, organic and hybrid light-emitting diodes (OLEDs), organic field-effect transistors, and electrochemical sensors and displays. Carrier transport in these materials usually occurs by transitions in a broad distribution of localized states. As a result the transport is dominated by thermal activation to a band of extended states (multiple trapping), or if these do not exist, by hopping via localized states. We provide a general view of the physical interpretation of the variations of carrier transport coefficients (diffusion coefficient and mobility) with respect to the carrier concentration, or Fermi level, examining in detail models for carrier transport in nanocrystalline semiconductors and organic materials with the following distributions: single and two-level systems, exponential and Gaussian density of states. We treat both the multiple trapping models and the hopping model in the transport energy approximation. The analysis is simplified by thermodynamic properties: the chemical capacitance, C(mu), and the thermodynamic factor, chi(n), that allow us to derive many properties of the chemical diffusion coefficient, D(n), used in Fick's law. The formulation of the generalized Einstein relation for the mobility to diffusion ratio shows that the carrier mobility is proportional to the jump diffusion coefficient, D(J), that is derived from single particle random walk. Characteristic experimental data for nanocrystalline TiO(2) in DSC and electrochemically doped conducting polymers are discussed in the light of these models.     

Effect of electronic polarization on charge-transport parameters in molecular organic semiconductors

Theoretical investigations of charge transport in organic materials are generally based on the "energy splitting in dimer" method and routinely assume that the transport parameters (site energies and transfer integrals) determined from monomer and dimer calculations can be reliably used to describe extended systems. Here, we demonstrate that this transferability can fail even in molecular crystals with weak van der Waals intermolecular interactions, due to the substantial (but often ignored) impact of polarization effects, particularly on the site energies. We show that the neglect of electronic polarization leads to qualitatively incorrect values and trends for the transfer integrals computed with the energy splitting method, even in simple prototypes such as ethylene or pentacene dimers. The polarization effect in these systems is largely electrostatic in nature and can change dramatically upon transition from a dimer to an extended system. For example, the difference in site energy for a prototypical "face-to-edge" one-dimensional stack of pentacene molecules is calculated to be 30% greater than that in the "face-to-edge" dimer, whereas the site energy difference in the pentacene crystal is vanishingly small. Importantly, when computed directly in the framework of localized monomer orbitals, the transfer integral values for dimer and extended systems are very similar.     

Charge transport in high mobility molecular semiconductors: classical models and new theories

The theories developed since the fifties to describe charge transport in molecular crystals proved to be inadequate for the most promising classes of high mobility molecular semiconductors identified in the recent years, including for example pentacene and rubrene. After reviewing at an elementary level the classical theories, which still provide the language for the understanding of charge transport in these systems, this tutorial review outlines the recent experimental and computational evidence that prompted the development of new theories of charge transport in molecular crystals. A critical discussion will illustrate how very rarely it is possible to assume a charge hopping mechanism for high mobility organic crystals at any temperature. Recent models based on the effect of non-local electron-phonon coupling, dynamic disorder, coexistence of localized and delocalized states are reviewed. Additionally, a few more recent avenues of theoretical investigation, including the study of defect states, are discussed.     

Time-reversal symmetry in molecular rovibronic states and in second-order processes

A unified treatment of time-reversal symmetry is given for molecular systems. The treatment allows for interconversion of electronic, rotational, and vibrational angular momenta on equal footing because of a coherent phase choice. It also allows for correlation from a continuous group (of spherical or cylindrical symmetry) to lower point groups (such as C₃, C₄, C₆, S₄, S_g, T, etc.). General, many-electron molecular states that form time-reversal degenerate components are constructed. Attention is called to the Kramers' doublets as the special odd-electron case of such double degeneracy. Specific examples of a spiropentane and a 5-azoniaspiro(4.4) nonane with S₄ symmetry and possible time-reversal degeneracy are given. The optical rotation due to a time-odd polarizability tensor in one of the two time-degenerate components is shown to be of an opposite sign to that in the other component. The above result is from a second-order matrix element (over the polarizability tensor) and is proved to be independent of even- or odd-number of electron spins. It is shown to hold also for Kramers' doubly degenerate components. This result is contrasted with that of a first-order Jahn-Teller effect which depends on the number of electron spins.     

Manifestation of electrode surface states in molecular conduction

We present a conduction mechanism across molecular junctions which derives from conductance resonances that are not associated with particular molecular orbitals. Instead, the resonances are induced by states localized at the surface of the electrodes. To this end, we studied the conductance of a C₆₀ molecule bridging two carbon nanotubes. A simple tight-binding model is employed to investigate analytically the basic features of the effect.