Advanced Solid State Physics

Fig. 109 shows the real part of the dielectric function:

′(ω) = 1−

ω^2 p

ω^2 +τ^12

(235)

For diffusive metals the real part of the dielectric constant does not diverge.

The imaginary part depends onω! Whenτgoes to infinity the imaginary part of the dielectric constant
can be:

′′(ω) = 0 for ω > 0

′′(ω) = ∞ for ω = 0

Figure 109: Real part of the dielectric constant of an diffusive material.

13.3.1 Dielectric Function

Fig. 110 shows the dielectric functions of different metals. These dielectric function were explained by
different theories or measurements. Fig. 110 contains three types:
The first type is called reflection electron energy loss spectra (REELS). Electrons (or light) are shot
at the surface of a crystal and the measurement of the energy of the reflected electrons will give the
dielectric constant. Furthermore, the surface of the crystal must be very clean because light does not
penetrate the surface very deep.