15 Optical Properties,Lecture 4

Learning Objectives:

 

From this module students may get to know about the following:

 

  1. Dependence of conductivity on frequency.
  2. Dependence of dielectric constant on the frequency.
  3. Behavior of a free electron in presence of a oscillating field.
  4. Optical properties of metals

Optical Properties of Metals:

 

Free-carrier absorption can be viewed as intraband absorption–the electron absorbing the photon remains in the same band. Free-carrier absorption is obviously important for metals, and is often of importance for semiconductors. The electron is accelerated by the photon and gains energy, but since the wave vector of the photon is negligible, something else such as a phonon needs to be involved. For many purposes, the process can be viewed classically by Drude theory with  relaxation   time    of        = 1 .  This  relaxation  time  defines  a  frictional  force  constant 0∗/  , where the viscous like frictional force is proportional to the velocity.

 

We will use classical theory here, but it is worthwhile to make a few comments. It is common to deal with a semi classical picture of radiation. There we treat the radiation classically, but the underlying electronic systems that absorb and emit the radiation we treat quantum mechanically. Radiation can be treated classically when it is intense enough to have many photons in each mode. Free electronic systems can be treated classically when their de Broglie wavelengths are small compared to the average antiparticle separations.

 

The de Broglie wavelength can be estimated from the momentum as estimated from equipartition. In practice, this means that for temperatures that are not too low and densities that are not too high, then classical mechanics should be valid. Bound systems are more complicated, but in general, classical mechanics works at higher quantum numbers (higher bound-state energies). In any case, classical and quantum results often overlap in validity well beyond where one might naively expect.

 

The classical theory can be written, assuming a sinusoidal electric field E = 0 exp (-i t) (note these are for free-electrons (e > 0) with damping). We also generalize by using an effective mass m* rather than m:

∗ ̈+ ∗  ̇= −    exp(−    ) ………….(1)
 
    0  
     

Seeking a steady-state solution of the form     =  0 exp(−    ), we find