Plasma resonance

The plasmon resonance is a phenomenon in solids that a sufficient amount of free electrons in the conduction band have. Then there is a point in the spectrum where the real part of the dielectric constant has a zero. ${\displaystyle \varepsilon _{1}}$

The name plasma comes from the fact that the electrons in the conduction band are no longer localized to their respective atomic cores, but can move freely through the crystal lattice. They act like a gas, which is why we also speak of electron gas or electron plasma.

With metals (example: silver ) the effect can be explained well according to the Drude theory :

${\displaystyle \varepsilon _{1}=1-\omega _{\mathrm {p} }^{2}\cdot {\frac {\tau ^{2}}{1+\omega ^{2}\cdot \tau ^{2}}}}$

It is

${\displaystyle \omega _{\mathrm {p} }^{2}={\frac {Ne^{2}}{\varepsilon _{o}m^{*}}}}$

the plasma frequency according to Drude.

In it are:

• τ = peak time
• ω = light frequency
• N = carrier density
• e = elementary charge
• m ^* = effective mass

If you set ε _{1 to} zero in the above formula , you get the solution for the plasma resonance frequency according to Drude:

${\displaystyle \omega _{s}^{2}={\frac {\tau ^{2}\cdot \omega _{\mathrm {p} }^{2}-1}{\tau ^{2}}}=\omega _{\mathrm {p} }^{2}-{\frac {1}{\tau ^{2}}}}$

The plasma resonance frequency is therefore not identical to the plasma frequency . The above formula for ε ₁ also only includes the contribution of the free electrons according to Drude's theory. In practice, however, various contributions from interband excitations must also be taken into account in the case of metals , which are added together. They lead to a further shift in the plasma resonance frequency compared to the simple plasma frequency (see sample spectrum ).

Such a zero in the spectrum of the dielectric constant has of course serious effects when converted to the optical constants refractive index n and absorption coefficient k and the reflection and absorption spectra that depend on them. In the optical properties of the material, the plasma resonance is noticeable through the characteristic plasma edge in the reflection spectrum.