Anisotropy in Ultrafast Carrier and Phonon Dynamics in p-Type Heavily Doped Si

Abstract

We performed time-resolved reflectivity measurements in p-type heavily doped Si under non-resonant excitation. A large contribution from anisotropic state-filling is observed, indicating that the lowered Fermi energy due to the p-type heavy doping enhances the anisotropy in the hole distribution. The initial phase shift of coherent phonons induced by p-type doping is attributed to the anisotropic hole distribution.

Classical Fano oscillator

“…The Kato sample has a reported value of p between 3 × 10 19 and 1.5 × 10 20 cm −3 . 18 As several of the curves in Fig. 3 illustrate, vs photon energy log(q) varies linearly as the photon energy approaches 1.55 eV.…”

“…18 From their data, it can be deduced that the phase (as defined above) of the coherent oscillations in their degenerate sample is 32 ± 5 • larger than in undoped Si. The phase in undoped Si is (±)90 • (due to purely impulsive excitation of the optic phonon by transiently stimulated Raman scattering); 30,31 therefore, the phase of the heavily doped sample in the paper by Kato et al is −58 ± 5 • (when constrained within the bounds −π/2 < φ < π/2).…”

“…We find good agreement between the predicted and the measured phases of the coherent oscillations of the zone-center optic phonon in degenerate p-type Si. 18 …”

“…16,17 Time-domain coherent-phonon data have also been obtained from degenerate p-type Si. 18 These data exhibit a curious feature that is directly observed in the time domain: The phase of the coherent oscillations in the heavily doped material is substantially different than the phase in lightly doped Si. This observation raises the following question: Is this phase difference due to the discrete-phonon-electroniccontinuum coupling that is responsible for the Fano line shape observed in Raman spectra from degenerate p-type Si?…”

“…As we demonstrate, these results from our model are consistent with the phase difference observed in the Si experiments. 18 …”