We demonstrate theoretically that modification of the acoustic phonon spectrum in semiconductor heterostructures with large acoustic impedance mismatch between the core and cladding layers may lead to strong phonon depletion in the core layer. The latter is achieved if the heterostructure parameters are properly tuned, i.e., the structure thickness is in nanometer scale to ensure phonon quantization and the cladding layers are acoustically “softer” than the core layer. Using a numerical solution of the elasticity equation, we show that one can achieve conditions when almost all acoustic phonon modes are squeezed in the cladding layers with the exception of a small fraction of phonons with very small wave vectors (q0.3nm1). The predicted phonon depletion effect in the core layer of the acoustically mismatched heterostructures may lead to increased carrier mobility in certain regions of the heterostructure as well as improved thermal management of heterostructure-based devices.

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