Free carrier absorption

Free carrier absorption occurs when a material absorbs a photon, and a carrier (electron or hole) is excited from an already-excited state to another, unoccupied state in the same band (but possibly a different subband). This intraband absorption is different from interband absorption because the excited carrier is already in an excited band, such as an electron in the conduction band or a hole in the valence band, where it is free to move. In interband absorption, the carrier starts in a fixed, nonconducting band and is excited to a conducting one. Free carrier absorption occurs when a material absorbs a photon, and a carrier (electron or hole) is excited from an already-excited state to another, unoccupied state in the same band (but possibly a different subband). This intraband absorption is different from interband absorption because the excited carrier is already in an excited band, such as an electron in the conduction band or a hole in the valence band, where it is free to move. In interband absorption, the carrier starts in a fixed, nonconducting band and is excited to a conducting one. It is well known that the optical transition of electrons and holes in the solid state is a useful clue to understand the physical properties of the material. However, the dynamics of the carriers are affected by other carriers and not only by the periodic lattice potential. Moreover, the thermal fluctuation of each electron should be taken into account. Therefore a statistical approach is needed. To predict the optical transition with appropriate precision, one chooses an approximation, called the assumption of quasi-thermal distributions, of the electrons in the conduction band and of the holes in the valence band. In this case, the diagonal components of the density matrix become negligible after introducing the thermal distribution function, ρ λ λ 0 = 1 e ( ε λ , k − μ ) β + 1 = f λ , k {displaystyle ho _{lambda lambda }^{0}={frac {1}{e^{(varepsilon _{lambda ,k}-mu )eta }+1}}=f_{lambda ,k}} This is the famous Fermi-Dirac distribution for the distribution of electrons energies ε {displaystyle varepsilon } . Thus, summing over all possible states (l and k) yields the total number of carriers N. N λ = ∑ λ f λ , k {displaystyle N_{lambda }=sum limits _{lambda }{f_{lambda ,k}}}