Form factor increase and its physical origins in electron-modulated acoustic phonon interaction in a free-standing semiconductor plate

Impacts of acoustic phonon modulation on the electron–acoustic phonon interaction in a free-standing semiconductor plate are theoretically investigated. In formulating the electron–phonon interaction, the differences between bulk and modulated acoustic phonons are encapsulated into the form factor. The form factors calculated using modulated acoustic phonons are larger than those obtained using bulk phonons, regardless of electronic states, plate thickness, or plate material. The form factor explains the behavior of the momentum relaxation rate and electron mobility qualitatively, but consistently. When properly normalized, the form factors show an universality. The form factor increase can be attributed to an increase in the number of phonon modes having longitudinal vibration due to surface mode generation and mode conversion.