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The Quantum photo-stimulated Peltier effect has been theoretically studied under the influence of confined acoustic phonon in a cylindrical quantum wires with an infinite potential by using the quantum kinetic equation method. In this work, we assume that the confined electrons-confined acoustic phonons scattering is essential. Moreover, the presence of a strong electromagnetic wave (EMW) is also taken into account to determine the influence of confined phonons on the aforementioned effects. We have defined the analytical expressions for the kinetic tensors and the Peltier coefficients (PC). In detailed consideration, the quantum number m1, m2 were changed in order to characterize the influence of confined acoustic phonon (confined AP). As the radius of the wire increases to infinity, we obtained the results that corresponded to the case of bulk phonons (unconfined AP). The theoretical results have been numerically evaluated and discussed for the GaAs/AlGaAs cylindrical quantum wires (CQW). The change of PC in two cases unconfined AP and confined AP have been found according to augment of EMW frequency. The value of resonant peaks has altered under the effect of confined AP. The difference of PC also has been discovered when investigating its dependence on the cyclotron frequency. Furthermore, the PC reduced suddenly when considering the dependence of PC on the radius of wire and PC on the low temperature. All numerical showed that the magnitude of PC diverse significantly in comparison with unconfined AP case and doped two - dimensional semiconductor superlattice. This means that the confinement of the phonon affects the Peltier effect quantitatively and qualitatively. These results are new and provide to completing the theory of the Peltier effect in low-dimensional semiconductor systems.

Based on the kinetic equation method, the quantum Peltier effect has been theoretically studied under the influence of confined optical phonons in a rectangular quantum wire (RQW) of infinite high potential when placed in perpendicular electric and magnetic fields. There were complicated dependences of the analytical expression of the Peltier coefficient (PC) on quantities such as the size of the wires amplitude of the laser radiation, the cyclotron frequency of electrons and temperature of the system. Moreover, the presence of a strong electromagnetic wave (EMW) is also taken into account to determine the influence of confined phonons on the aforementioned effects. We have defined the analytical expressions for the kinetic tensors and PC. In detailed consideration, the quantum numbers m1, m2 were changed in order to characterize the influence of confined optical phonons. The results of setting the m1, m2 to zero showed that this case can be seen asthe unconfined optical phonon. This means that the confinement of the phonon affects the Peltier effect quantitatively and qualitatively. The theoretical results have been numerically evaluated and discussed for the GaAs/GaAsAl quantum wires. The change of the confinement and non-confinement phonons upon the change of the magnetic field shows that the height of the resonance peaks in the confinement case is about 4 times larger than the non-confinement case. The position of the resonance peak in the two cases are also shifted. The size of the wire in the case of the confinement phonon is more pronounced and stable than in the non-confinement case. The new results obtained can provide for completing the theory of the Peltier effect in low - dimensional semiconductor systems.

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We applied the quantum kinetic equation method to investigate the influence of confined optical phonons (confined OP) on the photo-stimulated Ettingshausen effect in rectangular quantum wires (RQW) subjected to a perpendicular magnetic field. We considered the case where the confined electrons-confined OP scattering is the dominant mechanism. Analytical expressions for the kinetic tensors, the EC are obtained. The EC is a function of external fields, the temperature of the system, especially the quantum numbers m1 and m2 characterizing confined OP. When the width of the wire increases to infinity, the results of the bulk semiconductors can be gained. The numerical results are numerically evaluated and discussed for the GaAs/AlGaAs RQW. The magnitude of the resonance peaks has been increased for each value of m1, m2, found when examining the dependence of the EC on the photon energy. Furthermore, the EC is decreased considerably when the amplitude of EMW increases, which is obtained when investigating the dependence of the EC on the amplitude of EMW (laser). These results are important for further researches and could be helped to complete the theory of the thermo - magnetoelectric effects in the low dimensional system.