Quantized acoustic phonon modes in quantum wires and quantum dots

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Abstract
Acoustic phonon modes in isotropic cubic media are derived for a number of quantum-wire and quantum-dot geometries of significant interest in nanoelectronics and optoelectronics. In each case, the mode amplitude is determined by requiring that the mode energy be given by that of the properly quantized phonon. For the case of cylindrical quantum wires and quantum dots with rectangular faces, the Hamiltonians for the deformation potential interactions are derived. These quantized acoustic modes and the associated deformation potential Hamiltonians provide a basis for modeling carrier-acoustic-phonon interactions in a variety of mesoscopic devices. Our new results supplement previous treatments of related piezoelectric effects in cylindrical quantum wires.