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17 Fall

7. The Acoustic Equation of Motion

조영달 2017.10.23 01:12 조회 수 : 9

üIn this class, we lay the groundwork for the study of acoustic phonons in semiconductors by developing fundamental mechanical equations in one dimension, following Ch. 1 of Bulk Acoustic Wave Theory and Devices  by J.F. Rosenbaum,  and use it to formulate phononics under external bias .

üWe show that the presence of an unbalanced system of time-varying stresses results in the propagation of an acoustic phonon with its propagation velocity dependent on the material properties of the body. Attenuation, material quality factor Q, and the energy relations are more easily handled in one dimension and can be extended to three dimensions if necessary.

üThe strain and stress matrices are formulated in three dimensions, and rotational transformations, which will be increasingly important later, are developed.

üThe three-dimensional equations of motion are developed by using the stress and strain matrices. The coupling between these matrices is not developed beyond the point of stating that they are linearly related.

ü These are the pre-requisite for the electro-phononics that I have been developing recently. More specifically, the electrical modulation and switching of phonons in terms of amplitude, mode, frequency, and phase. For this purpose, we need to understand the acoustic equations.

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