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Journal of Physical Studies 25(3), Article 3706 [10 pages] (2021)
DOI: https://doi.org/10.30970/jps.25.3706 PECULIARITIES OF ELECTRON SPECTRUM RENORMALIZED BY OPTICAL PHONONS IN THE CASCADE OF QUANTUM CASCADE DETECTOR
Ju. Seti Yuriy Fedkovych Chernivtsi National University, 2, Kotsyubynsky St., UA–58012, Chernivtsi, Ukraine
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In the model of position-dependent effective mass of an electron and isotropic dielectric continuum for confined and interface phonons, the Hamiltonian of the electron-phonon system is obtained in the representation of the second quantization over all variables. Using it, the spectral characteristics of the electron renormalized due to the interaction with all phonon modes in the cascade of a broadband quantum cascade detector operating in the far infrared range are calculated in one-phonon approximation using the method of Green's functions. The influence of confined and interface phonons both on the electron operating states and the states of the ‟phonon ladder” in the nanodevice cascade is studied depending on the width of the potential barrier in the double-well active region at cryogenic and room temperature. It is established that regardless of the geometric configuration of the active region, the interaction with phonons leads to a low-energy shift and the decay of the electron states, whose magnitudes increase at higher temperatures. It is revealed that interface phonons produce an order of magnitude stronger effect on all electronic states of the cascade than that of confined phonons. Since, the features caused by interface phonons are mainly manifested in the complete shifts and decays. With an increase in temperature, according to the experiment, the shifts and decays of the states, renormalized due to the interaction with phonons, only increase. It is shown that by varying the width of the potential barrier in the double-well active region a sharp increase in both characteristics – the shift and the decay of high-energy electron states – can be achieved. This is provided by the condition that the difference between the energies of two-electron states is equal to the energy of longitudinal phonons of the materials of nanostructure wells or barriers. Since the detected effect is caused by the inter-level electron-phonon configurational interaction, the values of the extremes of the shifts and decays increase if the wave functions of both states overlap more and reach larger magnitudes for high-energy states. This effect will play an important role in the functioning of quantum cascade detectors with a multi-well active region, renormalizing both the operating states of the device, when their energy differences are close to the energies of longitudinal phonons, and the state of the ‟phonon ladder” of extractors.
Key words: nanosystem, electron, phonon, quantum cascade detector, Green's function
