Interband and Intraband Absorption Coefficients of Silicon: Theoretical Frameworks and Formulations

Abstract

Theoretical frameworks and formulations for calculating Si interband and intraband absorption coefficients arepresented and discussed in this work. They are based on the second-order time-dependent perturbation theory of quantum mechanics which incorporates interaction matrices between electrons, photons, phonons, and charged impurities. These frameworks include the interband and intraband processes of direct and indirect transitions. The intraband indirect-transition processes include phonon-assisted and charged-impurity-assisted intravalley processes, inter-non-equivalent-valley processes, inter-opposite-equivalent-valley g-processes, and inter-non-opposite-equivalent-valley f-processes. These theoretical formulations are verified with the interband absorption coefficients from Green's data and the Rajkanan-Singh-Shewchun formula. They are also verified with the intraband free-carrier absorption coefficients from the Spitzer-Fan data in n -type Si at different doping concentrations, Green's formula, the Schroder-Thomas-Swartz formula, the Soref-Bennett formula for 1.3 and 1.55 μm wavelengths, and Ridley's equations. The agreements and discrepancies between this theoretical work and other experimental data, empirical formulas, theoretical equations are examined and investigated. This work will provide a fundamental theoretical framework and formulation for calculating Si interband and intraband absorption coefficients which could be useful for the design and modeling of Si photonic devices.