QUANTIZED ACOUSTIC-PHONON MODES IN QUANTUM WIRES AND QUANTUM DOTS

Acoustic phonon modes in isotropic cubic media are derived for a numbe r of quantum-wire and quantum-dot geometries of significant interest i n nanoelectronics and optoelectronics. In each case, the mode amplitud e is determined by requiring that the mode energy be given by that of the properly quantized phonon. For the case of cylindrical quantum wir es and quantum dots with rectangular faces, the Hamiltonians for the d eformation potential interactions are derived. These quantized acousti c 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.