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Parametric instability of mobile elastic gate in tera- and nano- high electron mobility transistor

Effective excitation of the micro- and nanometer-size resonators has number of applications at various fields of science and technology. In particular, they include wireless telecommunication technologies [1], high sensitivity measuring systems [2], quantum information processing devices [3]. At the present report we consider the mechanical cantilever oscillations parametric excitation that serves as the gate electrode of a high electron mobility transistor (HEMT). The parametric coupling between the mechanical resonator (cantilever) and the oscillations of two-dimensional electron gas (2DEG) with high electron mobility is considered. In the capacity of the mechanical resonator a clamped nanobeam or a carbon nanotube might be used. 2DEG can arise in GaAs/AlGaAs heterostructures on the basis of which high electron mobility transistors (HEMT) are produced. Previously number of authors investigated the influence of the parametric coupling between mechanical and optical resonators [4, 5]. At our recent work [6] we proposed the uniform approach to such problems that is based on the lumped parameters method and the reduction of the parametric instability occurrence conditions question to the pure mathematical problem or the numerical solution of the certain system of second-order ODEs.