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Optical Hall effect

Optical Hall effect (OHE) is a physical phenomenon that describes the magnetic-field induced birefringence by free-charge carrier excitations upon interaction with electromagnetic waves. The behavior of free charge carriers in a wide variety of materials can be described by the Drude model. The dielectric tensor of the Drude model has two independent parameters - the plasma frequency and broadening:

The plasma frequency and broadening depend on the carriers concentration, mobility and effective mass,  and therefore cannot be independently determined by standard measurements. However, this degeracy can be broken if the measurements are performed in an external magnetic field. In external magnetic field the optical response of free charge carriers has to be expressed by a dielectric tensor:

 

where the external magnetic field vector B is given by B=(bx,by,bz) and ω c=e|B|/m* is the cyclotron frequency. Thus, measurements in a magnetic field allows to determine the carrier concentration, mobility and effective mass separately.

The measurement of the optical Hall effect can be conveniently performed in reflection and transmission by generalized ellipsometry at an oblique angle of incidence, and is typically quantified in terms of the Mueller matrix. Ellipsometry is a contactless measurement and thus allows to extract information on the free-charge carrier properties in a contactless and non-invasive manner. Furthermore, OHE measurements can reveal the anisotropy of the effective mass and/or mobility parameters, and allow to determine the carrier type.

The THz OHE technique is very sensitive and has been shown to yield complete information on the transport properties of free charge carriers in very-low doped materials, thin films, nanostructures and spatially confined electron systems, e.g. 2D materials and 2DEG in HEMT structures. The THz OHE also allows for differentiation of multiple conductive channels in multilayered or nanoscopically inhomogeneous samples.

More resources on Optical Hall effect

A comprehensive tutorial on OHE

Cavity-enhanced OHE

Ellipsometry

J.A. Woollam company has exellent ellipsometry resources

Wikipedia: Polarization, Fresnel equations, Ellipsometry

Refractive Index Database

Refractive Index Database

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