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Title: Anisotropic small-polaron hopping in W:BiVO 4 single crystals

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Journal Article: Publisher's Accepted Manuscript
Journal Name:
Applied Physics Letters
Additional Journal Information:
Journal Volume: 106; Journal Issue: 2; Related Information: CHORUS Timestamp: 2016-12-29 08:55:31; Journal ID: ISSN 0003-6951
American Institute of Physics
Country of Publication:
United States

Citation Formats

Rettie, Alexander J. E., Chemelewski, William D., Lindemuth, Jeffrey, McCloy, John S., Marshall, Luke G., Zhou, Jianshi, Emin, David, and Mullins, C. Buddie. Anisotropic small-polaron hopping in W:BiVO 4 single crystals. United States: N. p., 2015. Web. doi:10.1063/1.4905786.
Rettie, Alexander J. E., Chemelewski, William D., Lindemuth, Jeffrey, McCloy, John S., Marshall, Luke G., Zhou, Jianshi, Emin, David, & Mullins, C. Buddie. Anisotropic small-polaron hopping in W:BiVO 4 single crystals. United States. doi:10.1063/1.4905786.
Rettie, Alexander J. E., Chemelewski, William D., Lindemuth, Jeffrey, McCloy, John S., Marshall, Luke G., Zhou, Jianshi, Emin, David, and Mullins, C. Buddie. 2015. "Anisotropic small-polaron hopping in W:BiVO 4 single crystals". United States. doi:10.1063/1.4905786.
title = {Anisotropic small-polaron hopping in W:BiVO 4 single crystals},
author = {Rettie, Alexander J. E. and Chemelewski, William D. and Lindemuth, Jeffrey and McCloy, John S. and Marshall, Luke G. and Zhou, Jianshi and Emin, David and Mullins, C. Buddie},
abstractNote = {},
doi = {10.1063/1.4905786},
journal = {Applied Physics Letters},
number = 2,
volume = 106,
place = {United States},
year = 2015,
month = 1

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record at 10.1063/1.4905786

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Cited by: 19works
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  • DC electrical conductivity, Seebeck and Hall coefficients are measured between 300 and 450 K on single crystals of monoclinic bismuth vanadate that are doped n-type with 0.3% tungsten donors (W:BiVO{sub 4}). Strongly activated small-polaron hopping is implied by the activation energies of the Arrhenius conductivities (about 300 meV) greatly exceeding the energies characterizing the falls of the Seebeck coefficients' magnitudes with increasing temperature (about 50 meV). Small-polaron hopping is further evidenced by the measured Hall mobility in the ab-plane (10{sup −1 }cm{sup 2 }V{sup −1 }s{sup −1} at 300 K) being larger and much less strongly activated than the deduced drift mobility (about 5 × 10{sup −5 }cm{sup 2 }V{sup −1 }s{supmore » −1} at 300 K). The conductivity and n-type Seebeck coefficient is found to be anisotropic with the conductivity larger and the Seebeck coefficient's magnitude smaller and less temperature dependent for motion within the ab-plane than that in the c-direction. These anisotropies are addressed by considering highly anisotropic next-nearest-neighbor (≈5 Å) transfers in addition to the somewhat shorter (≈4 Å), nearly isotropic nearest-neighbor transfers.« less
  • It was noted some time ago that many properties of amorphous semiconductors could be explained if the charge carriers self-trapped to form small polarons. Self trapping occurs when an electronic carrier lingers at a site long enough to permit surrounding atoms to displace in response to the presence of the carrier. The electronic carrier then becomes severely localized within a potential well produced by the atomic displacements. This self-trapped carrier cannot move unless the atoms alter their positions. The localized carrier together with the atomic displacement pattern that confines it is termed a small polaron. The adjective small denotes themore » severe localization of the electronic state. The energy of a small polaron in a covalent solid is lower than that of a static electron by E{sub b} {triple_bond} F{sup 2}/2k, where F is the force between the carrier and atoms adjacent to it, and k is the material`s stiffness constant. As a result of its severe localization, a small polaron generally moves by phonon-assisted hopping. Small-polarons will only form in covalent crystals whose electronic halfbandwidths are sufficiently narrow, E{sub b} > W. The absence of small polaronic carriers in most covalent crystals presumably indicates that E{sub b} < W in these instances. However, evidence of small polarons is commonly found in disordered materials despite the estimates of E{sub b} and W not being significantly different from those of crystals. It is found that only modest energetic disorder is required to induce small-polaron formation. Here the author succinctly describes essential elements of this work. Second, the author addresses the role of disorder on the adiabatic hopping motion of small polarons.« less
  • We calculate the transient motion of a well-localized charge carrier injected into a narrow-band molecular insulator. The carrier can often move with a mobility comparable to 1 cm/sup 2//VXc for a considerable time before equilibrating to form a small polaron. Thus, time-of-flight measurements on thin films may measure this mobility rather than the low, thermally activated mobility characteristic of steady-state small-polaron hopping motion.
  • The thermally activated rates for high-temperature adiabatic and nonadiabatic small-(bi)polaron hopping are calculated for a generalization of Holstein's molecular-crystal model. In the expanded model a carrier occupying a molecule is coupled to many molecular vibrational modes rather than to just the single vibrational mode envisioned in the original model. This generalization of the molecular-crystal model does not significantly affect the semiclassical small-(bi)polaron jump rates. In particular, for the generalized model the hopping activation energy becomes a sum of contributions associated with each of the vibrational modes to which the carrier is coupled. The vibrational frequency that is the preexponential factormore » for adiabatic small-(bi)polaron hopping is the square root of the sum of the squares of the vibrational frequencies weighted by their relative contributions to the net hopping activation energy.« less
  • The theory of small-polaron hopping transport in magnetic semiconductors and insulators is formulated via a many-electron generalization of the one-electron tight-binding approach utilized in standard small-polaron theory. Here the magnetic effects are taken into account from first principles by constructing the electronic wave function from linear combinations of antisymmetrized products of Wannier states involving both the itinerant electron and the valence electrons. This enables us to determine the effect of the indistinguishability of an itinerant electron from valence electrons on the transfer of an electron between two magnetic ions. To treat hopping within a magnetic lattice the magnetic environment surroundingmore » the two sites directly involved in a hop is approximated by an effective internal magnetic field. It is found that in the paramagnetic and ferromagnetic regimes the magnetic nature of the solid only reduces the small-polaron mobility by a weakly temperature-dependent factor of the order of unity. However, below the Neel temperature in an antiferromagnet it is found that electronic transitions only occur between nondegenerate states. This results in an additional activated factor in the small-polaron mobility.« less