The theory of the absorption edge in semiconductors - Loudon, R (1959)
The thesis is concerned with optical absorption by a semiconductor due to the excitation of electrons from the valence band to the conduction band giving rise to the phenomenon of the absorption edge. In treating the final state of the semiconductor in such an absorption process it is shewn that the system Bay be considered as a two particle one in which the excited electron in the conduction band is bound to the hole left behind in the valence band, which behaves in many ways like a positively charged particle. A bound system of this type is called an exciton. The theory of the exciton is developed in some detail in the effective mass approximation for the case of a semiconductor with spherical energy bands. The effect of an externally applied uniform magnetic field is calculated. Using the exciton wave-function derived in this way, a general expression for the absorption coefficient due to exciton creation in a magnetic field is obtained. The evaluation of this formula requires a knowledge of the wave-functions of the hydrogen atom in a magnetic field. For special cases, e.g. zero magnetic field it is shewn how the general absorption coefficient formula leads to expressions previously derived by other authors. The ware-equation for the hydrogen atom in a magnetic field in solved by a perturbation theory approach for the case where the magnetic field energy is larger than the Coulomb energy, a case of some importance in semiconductors since the Coulomb interaction is reduced by the dielectric constant and the electron or hole effective masses are usually small. Both bound and free states of the exciton are considered, and formal expressions for f-values and absorption coefficients are presented. These formal expressions are evaluated numerically for some important cases. The positions and intensities of the lowest observable absorption lines are calculated when the electronic transition from the valence band to the conduction band is either allowed or forbidden, and the values of the absorption coefficients close to the absorption edge are determined. Finally the accuracy of the perturbation theory method used is assessed and recent experimental work on the absorption edge is discussed.