Using the models of elastic and dielectric continuum, the system of differential equations is obtained, the exact analytical solutions of which describe the elastic displacement of the medium for nitride-based semiconductor nanostructure and the piezoelectric effect, which is caused by shear acoustic phonons. The theory of the shear acoustic phonons spectrum caused by the piezoelectric potential was developed. It is shown that shear acoustic phonons do not interact with electrons due to the deformation potential, but such interaction can occur due to the piezoelectric potential. Using the method of temperature Green’s functions and Dyson equation, expressions that describe the temperature dependences of the electronic level shifts and their decay rates are obtained. Calculations of the spectra of electrons, acoustic phonons, and characteristics that determine their interaction at different temperatures were carried out using the example of physical and geometric parameters of typical AlN/GaN nanostructure, which can function as an element of a separate cascade of a quantum cascade laser or detector.

中文翻译：

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平面对称AlN / GaN纳米结构中的剪切声子声子光谱理论以及由于压电势而与电子相互作用的理论

使用弹性和介电连续体模型，获得了微分方程组，其精确的解析解描述了基于氮化物的半导体纳米结构的介质的弹性位移和由剪切声子引起的压电效应。建立了由压电势引起的剪切声子声子谱的理论。可以看出，由于形变势能，剪切声子不与电子相互作用，但是由于压电势能发生这种相互作用。使用温度格林函数和戴森方程的方法，获得了描述电子能级位移及其衰减率的温度依赖性的表达式。电子，声子，