Directional sensitivity of the A1g phonon in biaxially strained bismuth heterofilms studied by transient white light reflectivity

Strain engineering in epitaxial Bi(111) films on Si(111) enables temperature-tunable phonon frequencies through thermal expansion mismatch. Using in situ low-energy electron diffraction combined with broadband femtosecond transient reflectivity on the same samples, we directly correlate anisotropic lattice parameters with the redshift of the coherent A1g phonon mode. The in-plane lattice parameter remains locked to the Si substrate and is therefore nearly temperature-independent, imposing strong biaxial compressive strain, causing an additional expansion of the Bi lattice along the c-axis. By applying an extended phonon-shift model, we disentangle the contributions of intrinsic thermal expansion, thermal-mismatch strain, and anharmonicity to the phonon softening. The enhanced redshift observed in strained films cannot be accounted for by expansion or mismatch alone; instead, it arises from a strengthened anharmonic term that additionally scales with strain along the c-axis, being insensitive to the in-plane lattice parameter and thereby enabling targeted control of phonon frequencies.