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The optical Hall effect is a physical phenomenon, which describes the occurrence of magnetic field induced dielectric and/or magnetic polarization at optical wavelengths, transverse and longitudinal to the incident electric field (Fig. OHE(*Not sure if it's common to reference figures in Wikipedia body text)), analogous to the static electrical Hall effect (Fig. EHE). Measurement of the optical Hall effect can be performed within the concept of generalized ellipsometry, i.e., with plane parallel waves incident at oblique angle upon a sample with plane parallel interfaces, in transmission or reflection configuration, for example.
Theory
[edit]The Optical Hall effect relates to magnetic field induced changes in the optical properties of materials, in general.
Test equation
Schematics of the electrical Hall effect in a thin conducting sheet. Free charge carriers produce a transverse voltage by charge separation under the influence of the Lorentz force due to a magnetic field $\mathbf{B}$ when driven by a DC current through the sheet. Accordingly, the longitudinal voltage required to drive the DC current differs with and without the magnetic field. Note that ideally the sheet should be infinitesimally thin~\cite{HallAJM2_1879}. The electric Hall voltage is characteristic of the sheet material, and depends on the free charge carrier types and density properties that constitute the current leading to the Hall voltage. Note that transport must occur homogeneously across the entire sheet, and which makes analyses of the electric Hall voltage measured across complex sheet structures with multiple constituents difficult. From Ref. [RefTheory]. |
Applications
[edit]Nondestructive determination of free charge carrier parameters in semiconductor materials
[edit]A specific application of the Optical Hall effect is the determination of free charge carrier parameters in doped semiconductors. The unique advantage of the Optical Hall effect over alternative methods is the ability to determine the signature of the charge (electron, hole), volume (3D) or sheet (2D) density optical mobility and effective mass including anisotropy of the latter two. The material of interest can be hidden within multiple layer stacks. Due to different signatures, multiple carrier species can be differentiated such as light and heavy hole mass carrier densities, for example, and properties of 2D densities at the top of conductive substrates can be measured. No electrical contacts are required for measurement of the Optical Hall effect.[2][3]
Terahertz Electron Paramagnetic Resonance ellipsometry
[edit]Another specific application of the Optical Hall effect is the observation of polarized spin transitions due to electron paramagnetic resonances, for example, in the Terahertz spectral region. Such resonances are due to the occurrence of magnetic polarization under the influence of an external magnetic field. This effect is called Terahertz Electron Paramagnetic Resonance and can be measured with generalized ellipsometry principles and instrumentation. [RefXXX]
Landau Level spectroscopy in quantum confined carrier systems
[edit]In semiconductor industries the microwave-detected photoconductivity method is widely used to measure excess carrier properties and characterize bulk single crystal materials.[4]
References
[edit]- ^ Schubert, Mathias; Kühne, Philipp; Darakchieva, Vanya; Hofmann, Tino (2016-08-01). "Optical Hall effect—model description: tutorial". JOSA A. 33 (8): 1553–1568. Bibcode:2016JOSAA..33.1553S. doi:10.1364/JOSAA.33.001553. ISSN 1520-8532. PMID 27505654.
- ^ Kühne, P.; Herzinger, C. M.; Schubert, M.; Woollam, J. A.; Hofmann, T. (2014-07-01). "Invited Article: An integrated mid-infrared, far-infrared, and terahertz optical Hall effect instrument". Review of Scientific Instruments. 85 (7): 071301. arXiv:1401.5372. Bibcode:2014RScI...85g1301K. doi:10.1063/1.4889920. ISSN 0034-6748. PMID 25085120.
- ^ Knight, Sean; Hofmann, Tino; Bouhafs, Chamseddine; Armakavicius, Nerijus; Kühne, Philipp; Stanishev, Vallery; Ivanov, Ivan G.; Yakimova, Rositsa; Wimer, Shawn; Schubert, Mathias; Darakchieva, Vanya (2017-07-11). "In-situ terahertz optical Hall effect measurements of ambient effects on free charge carrier properties of epitaxial graphene". Scientific Reports. 7 (1): 5151. Bibcode:2017NatSR...7.5151K. doi:10.1038/s41598-017-05333-w. ISSN 2045-2322. PMC 5506066. PMID 28698648.
- ^ Kühne, P.; Darakchieva, V.; Yakimova, R.; Tedesco, J. D.; Myers-Ward, R. L.; Eddy, C. R.; Gaskill, D. K.; Herzinger, C. M.; Woollam, J. A.; Schubert, M.; Hofmann, T. (2013-08-14). "Polarization Selection Rules for Inter-Landau-Level Transitions in Epitaxial Graphene Revealed by the Infrared Optical Hall Effect". Physical Review Letters. 111 (7): 077402. arXiv:1305.0977. Bibcode:2013PhRvL.111g7402K. doi:10.1103/PhysRevLett.111.077402. PMID 23992081.