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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

The Optical Hall effect relates to magnetic field induced changes in the optical properties of materials, in general.

Schematic of the optical Hall effect in a conducting sample consisting of single or multiple conducting layers and sheets, in reflection configuration. Free charge carriers produce a dielectric polarization following the electric field of an incident electromagnetic field (analogous to the longitudinal Hall voltage). Here for example parallel to the surface. The induced polarization $\mathbf{P_{FCC}}$ produces $\mathbf{P_{Hall}}$ due to the Lorentz force, oriented perpendicular to $\mathbf{B}$ and the incident electric field vector (analogous to the transverse Hall voltage). $\mathbf{P_{FCC}}+\mathbf{P_{FCC}}$ are the source of the reflected light and which contains a small circular polarization component, which informs about the type of the charge carrier, their density, mobility and effective mass properties. The physical motion of the charges remain local within the lattice of the material, describing pathways that depend on the Fermi velocity, their average scattering time, the frequency of the incident light, and the magnetic field direction. If multiple layers are thin enough against the skin depth at long wavelengths, light interacts with multiple layers and reveals, for example, free carrier properties within buried layers otherwise inaccessible to direct electrical measurements. Hence, the optical Hall effect can be measured across complex sheet and layer structures. From Ref. [RefTheory].

Test equation

$\varepsilon _{\text{OHE}}(\mathbf {B} )=\varepsilon _{_{\mathbf {B} =0}}+\varepsilon _{_{\mathbf {B} }}.$

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

Nondestructive determination of free charge carrier parameters in semiconductor materials

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.

Terahertz Electron Paramagnetic Resonance ellipsometry

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

In semiconductor industries the microwave-detected photoconductivity method is widely used to measure excess carrier properties and characterize bulk single crystal materials.

External links

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