Berreman effect

The Berreman effect is a physical effect in the field of spectroscopy of molecular vibrations , e.g. B. Infrared spectroscopy and ellipsometry . It occurs in almost all (parallel polarized ) infrared spectroscopic measurements on thin layers with polar crystal lattice modes or resonances of free charge carriers . The effect was first observed and described in 1963 by Dwight W. Berreman during spectroscopic investigations of a lithium fluoride layer deposited on a metal .

description

If linearly polarized electromagnetic waves fall at an oblique angle onto a thin layer made of a material with at least one strong oscillator (including dielectric layers such as lithium fluoride or silicon dioxide ) on a highly reflective substrate, a pronounced absorption (actually a reflection minimum or a minimum ) is observed in the reflection spectrum. Reflection loss maximum) near the oscillator frequency. The wave number of this band-shaped signal is close to the wave number at which the dielectric function of the layer is zero ( ) or the refractive index is equal to the extinction coefficient ( ). ${\ displaystyle \ epsilon '= 0}$ ${\ displaystyle n = k <1}$

These signals are interpreted differently in the literature. It is often assigned to the longitudinal optical oscillation mode (LO mode) of phonons , which occurs under these conditions and can be observed with the aid of electron spectroscopy . Berreman also originally described the effect as resonant absorption of the longitudinal optical vibration mode of phonons by electromagnetic waves with an energy close to this vibration mode. To this day, this observation / explanation does not correspond to the usual textbook opinion, in which a transverse wave - as electromagnetic waves are - cannot directly excite longitudinal phonon vibrations in a material.

According to Arnulf Röseler et al. it is a pure interference- optical effect, caused by a damped waveguide. The waveguide significantly increases the effective length of the radiation-material interaction compared to the layer thickness, which can even lead to it appearing significantly stronger than the actual absorption band (the transverse optical mode, TO mode). This has been demonstrated by Röseler et al. shown by investigations of the dispersion relation of surface polaritons of a layer of a polar medium on a semi-infinite medium made of metal. Several minima and maxima of the reflection losses were found depending on the layer thickness. From this it was concluded that the absorption losses due to optical interference are connected with energy transport along the interface. Both the layer material and the substrate must have at least a low extinction coefficient so that the increase in absorption can be observed.

According to Harbecke et al. the smallest layer thickness of a reflection loss maximum is called the Berreman thickness . It is usually at layer thicknesses of approx. 50-100 nm and is calculated as follows:

{\ displaystyle d _ {\ text {B}} = {\ frac {\ lambda \ cos \ theta} {2 \ pi \ sin ^ {2} \ theta}} {\ frac {1} {\ Im {\ left ( {\ frac {1} {\ varepsilon}} \ right)}}}}

The Berreman effect can, however, usually be observed with layer thicknesses of up to 500 nm and beyond. The intensity of the band depends on the angle of incidence and the reflectivity of the layer-substrate interface. A greater reflectivity increases the lateral effective length and thus the intensity of the absorption band or the reflection minimum. A metal substrate therefore shows a stronger Berreman effect than a semiconductor, e.g. B. silicon.

The shape and position of signals caused by the Berreman effect can therefore easily be misinterpreted as absorption by a molecular oscillation and thus lead to incorrect assumptions about the composition of the sample being examined. A band close to a residual radiation band should therefore always be interpreted with the suspicion of this effect. B. can be excluded with numerical simulations.

Individual evidence

^ ^A ^b ^c Mathias Schubert: Infrared Ellipsometry on Semiconductor Layer Structures: Phonons, Plasmons, and Polaritons . Springer Science & Business Media, 2004, ISBN 3-540-23249-4 , pp. 62 ff .
↑ ^a ^b DW Berreman: Infrared Absorption at Longitudinal Optic Frequency in Cubic Crystal Films . In: Physical Review . tape 130 , no. 6 , June 15, 1963, pp. 2193-2198 , doi : 10.1103 / PhysRev.130.2193 .
^ A. Röseler: Infrared Spectroscopic Ellipsometry. Akademie-Verlag, Berlin 1990, ISBN 3-05-500623-2 , pp. 62–63.
See also A. Röseler: Spectroscopic Infrared Ellipsometry . In: Analyst Paperback . tape 14 . Springer, Berlin / Heidelberg 1996, ISBN 978-3-642-64648-5 , pp. 89-130 , doi : 10.1007 / 978-3-642-60995-4_2 .
↑ B. Harbecke, B. Heinz, P. Grosse: Optical properties of thin films and the Berreman effect . In: Applied Physics A . tape 38 , no. 4 , December 1985, pp. 263-267 , doi : 10.1007 / BF00616061 .

[Schubert2004-1] A ^b ^c Mathias Schubert: Infrared Ellipsometry on Semiconductor Layer Structures: Phonons, Plasmons, and Polaritons . Springer Science & Business Media, 2004, ISBN 3-540-23249-4 , pp. 62 ff .

[Berreman1963-2] DW Berreman: Infrared Absorption at Longitudinal Optic Frequency in Cubic Crystal Films . In: Physical Review . tape 130 , no. 6 , June 15, 1963, pp. 2193-2198 , doi : 10.1103 / PhysRev.130.2193 .

[3] A. Röseler: Infrared Spectroscopic Ellipsometry. Akademie-Verlag, Berlin 1990, ISBN 3-05-500623-2 , pp. 62–63.
See also A. Röseler: Spectroscopic Infrared Ellipsometry . In: Analyst Paperback . tape 14 . Springer, Berlin / Heidelberg 1996, ISBN 978-3-642-64648-5 , pp. 89-130 , doi : 10.1007 / 978-3-642-60995-4_2 .

[4] B. Harbecke, B. Heinz, P. Grosse: Optical properties of thin films and the Berreman effect . In: Applied Physics A . tape 38 , no. 4 , December 1985, pp. 263-267 , doi : 10.1007 / BF00616061 .