phonon mode analysis

**Phonon Mode Analysis** is the **systematic characterization of lattice vibrational modes (phonons) using Raman and infrared spectroscopy** — determining mode frequencies, symmetry, and behavior to understand crystal structure, composition, stress, and thermal properties. **Key Phonon Parameters** - **Frequency**: Peak position (cm$^{-1}$) — fingerprint for phase identification, shifts with stress/composition. - **Linewidth (FWHM)**: Broadens with crystal disorder, temperature, and phonon confinement. - **Intensity**: Proportional to mode oscillator strength and scattering geometry. - **Number of Modes**: Group theory predicts the number and symmetry of allowed modes. **Why It Matters** - **Stress**: Si Raman peak shifts ~1.8 cm$^{-1}$ per GPa of biaxial stress — the standard stress measurement. - **Composition**: SiGe alloy composition from the Si-Si, Si-Ge, and Ge-Ge mode frequencies. - **Crystal Quality**: Amorphous, nanocrystalline, and single-crystal phases have distinct phonon signatures. **Phonon Mode Analysis** is **reading the crystal's vibrational fingerprint** — extracting stress, composition, and structure from the frequencies of atomic vibrations.