Effective-Mass Theory and its Use

Abstract

A historical perspective of the early developments on the theory of impurity levels in semiconductors can be found in the review by Pantelides [47]. The measurement of the IR absorption of p-type silicon at low temperature in the mid-1950s revealed broad features, which could be attributed to the electronic absorption of dopants, and a correlation between the chemical nature of the dopant and the spectra was established [15]. They provided spectroscopic estimations of the ionization energies of the dopant atoms, which were earlier derived from electrical measurements. The results thus derived stimulated theoretical developments aimed at calculating the ionization energies of shallow dopants in silicon and germanium [28], and later of the discrete spectrum [32-34], which demonstrated the significance of the free-carrier effective masses and of the static dielectric constant to explain the experimental results. The generalization of these ideas led to the concept of effective-mass (EM) centres and to the development of effective-mass theory (EMT), which was proved to be successful in predicting the energy of the excited levels of some donors and acceptors in many materials, and the relative intensities of the lines of the spectra of many acceptor or donor centres.