Effect of Confined Phonons on Temperature Renormalization of Spectral Characteristics of Quantum Cascade Detector Operating in Far Infrared Range

The theory of electron-phonon interaction in a separate cascade of the broadband quantum cascade detector operating in far-infrared range is developed within the models of rectangular potentials and position-dependent effective mass, taking into account a nonparabolic shape of the conduction band, for an electron and isotropic dielectric continuum model for optical confined phonons. In the one-phonon approximation, the mass operator of the electron-phonon interaction is analytically calculated. Calculations of the total shifts and decays of cascade electron states are performed within the framework of the temperature Green's function method. Both at cryogenic and at room temperature, an analysis of the electron spectral parameters renormalization due to different mechanisms of the electron-phonon interaction is carried out, depending on the geometric design of the cascade two-well active region. It is shown that, irrespective of the temperature, the shifts caused by the intralevel electron interaction with phonons prevail over the shifts at interlevel interactions. At cryogenic temperature, the decay of the electron ground state is impossible. At a finite temperature, the intralevel interaction of the ground state with phonons causes a greater decay than the interlevel one. The excited states decays caused by the total interlevel interaction prevail over decays due to the intalevel interaction. It is established that with increasing temperature, the confined phonons cause broadening and weak high-energy shift of the detector absorption band, and temperature changes of the physical parameter lead to a significant low-energy shift. This hierarchy of partial contributions explains the experimentally known redshift of the absorption band of quantum cascade detectors with increasing temperature.