Analytical Expressions for Numerical Characterization of Semiconductors per Comparison with Luminescence

Luminescence is one of the most important characterisation tools of semiconductor materials and devices. Recently, a very efficient analytical set of equations has been applied to explain optical properties of dilute semiconductor materials, with an emphasis on the evolution of peak luminescence gain with temperature and its relation to sample quality. This paper summarizes important steps of the derivation of these expressions that have not been presented before and delivers a theoretical framework that can used to apply exactly solvable Hamiltonians for realistic studies of luminescence in various systems.