Coherent excitation of the optic phonon in Si: Transiently stimulated Raman scattering with a finite-lifetime electronic excitation

Using 28-fs, 800-nm laser pulses we have coherently excited and subsequently probed, with time-dependent reflectivity, the Si zone-center optic phonon. The phonon-induced reflectivity change ΔR∕R is well described by the response of an underdamped oscillator: ${{Δ}}R∕R{∝}{{0.2em}{0ex}}exp({-}t∕{{τ}}ₚₕ){{0.2em}{0ex}}cos(2{π}t∕{T}ₚₕ+{φ})$. The measured phase ${φ}$ indicates that transiently stimulated Raman scattering (TSRS) is responsible for the coherent-phonon generation: our results are in good agreement with a recent theory of TSRS for opaque materials [T. E. Stevens et al., Phys. Rev. B 65, 144304 (2002)] when we extend the theory to include the finite lifetime of the excited charge density that couples to the oscillation. We also discuss previous experimental results on Te, Bi, Sb, Si, and Ge in light of this extended theory. Additionally, our measured period Tₚₕ and decay time τₚₕ of the Si coherent oscillation are consistent with carrier-density-dependent Raman-scattering measurements.