General theory of electronic transport in molecular crystals. I. Local linear electron–phonon coupling

An improved general theory of electronic transport in molecular crystals with local linear electron–phonon coupling is presented. It is valid for arbitrary electronic and phonon bandwidths and for arbitrary electron–phonon coupling strength, yielding small‐polaron theory for narrow electronic bands and strong coupling, and semiconductor theory for wide electronic bands and weak coupling. Detailed results are derived for electronic excitations fully clothed with phonons and having a bandwidth no larger than the phonon frequency; the electronic and phonon densities of states are taken as Gaussian for simplicity. The dependence of the diffusion coefficient on temperature and on the other parameters is analyzed thoroughly. The calculated behavior provides a rational interpretation of observed trends in the magnitude and temperature dependence of charge‐carrier drift mobilities in molecular crystals.

[1]  R. Silbey,et al.  Energy transfer and spectral line shapes of impurities in crystals , 1975 .

[2]  C. Aslangul,et al.  Density-operator description of excitons in molecular aggregates. III. Excitonic motion in one-dimensional finite chains , 1978 .

[3]  R. J. Loveland,et al.  Charge Transport in the Diatomic Molecular Solids and Liquids: N 2 , O 2 , and CO , 1972 .

[4]  D. Craig,et al.  Strong and Weak Exciton-Phonon Coupling in Molecular Crystals , 1978 .

[5]  D. Yarkony,et al.  Variational approach to exciton transport in molecular crystals , 1977 .

[6]  H. Sumi.  Theory of electrical conduction in organic molecular crystals: Temperature‐independent mobilities , 1979 .

[7]  V. Yakhot,et al.  The exciton—phonon interaction for triplet exciton bands of organic solids: An experimental and theoretical study , 1979 .

[8]  W. Siebrand,et al.  Transport of Quasilocalized Excitons in Molecular Crystals , 1970 .

[9]  R. Silbey,et al.  Theory of exciton transport with quadratic exciton-phonon coupling , 1978 .

[10]  Digby F. Williams,et al.  Temperature dependence and anisotropy of charge carrier mobilities in durene , 1977 .

[11]  A. Zahlan.  The Triplet State , 1967 .

[12]  V. M. Kenkre,et al.  Optical spectra and exciton coherence , 1976 .

[13]  L. Pietronero,et al.  Electron–vibration interactions in benzene and deuterobenzene , 1976 .

[14]  D. Yarkony,et al.  Comments on exciton phonon coupling: Temperature dependence , 1976 .

[15]  R. Silbey,et al.  Exciton line shapes and migration with stochastic exciton lattice coupling , 1978 .

[16]  P. Reineker,et al.  Exact Derivation of a Generalized Master Equation for the Motion of Excitons , 1978 .

[17]  R. Silbey,et al.  Exciton–Phonon Interactions in Molecular Crystals , 1970 .

[18]  I. Vilfan.  On the electron‐intramolecular vibration coupling in aromatic molecular crystals , 1976 .

[19]  P. K. Ghosh,et al.  Electronic transport in liquid and solid sulphur , 1968 .

[20]  L. Friedman.  Electron-Phonon Interaction in Organic Molecular Crystals , 1965 .

[21]  R. Silbey,et al.  Exciton Migration in Molecular Crystals , 1971 .

[22]  R. Munn.  Exciton transport at short times , 1974 .

[23]  P. Gosar.  Small-Polaron Propagators , 1971 .

[24]  R. Munn.  Direct calculation of exciton diffusion coefficient in molecular crystals , 1973 .

[25]  J. Ziman,et al.  In: Electrons and Phonons , 1961 .

[26]  L. Schein.  Electron drift mobilities over wide temperature ranges in anthracene, deuterated anthracene and As2S3 , 1977 .

[27]  S. Glarum,et al.  Electron mobilities in organic semiconductors , 1963 .

[28]  T. Holstein,et al.  Studies of polaron motion: Part II. The “small” polaron , 1959 .

[29]  L. Schein.  Temperature independent drift mobility along the molecular direction of As 2 S 3 , 1977 .