Direct Measurement of Lattice Dynamics and Optical Phonon Excitation in Semiconductor Nanocrystals Using Femtosecond Stimulated Raman Spectroscopy

We report femtosecond stimulated Raman spectroscopy measurements of lattice dynamics in semiconductor nanocrystals and characterize longitudinal optical (LO) phonon production during confinement-enhanced, ultrafast intraband relaxation. Stimulated Raman signals from unexcited CdSe nanocrystals produce a spectral shape similar to spontaneous Raman signals. Upon photoexcitation, stimulated Raman amplitude decreases owing to experimentally resolved ultrafast phonon generation rates within the lattice. We find a $\sim 600\mathrm{fs}$, particle-size-independent depletion time attributed to hole cooling, evidence of LO-to-acoustic down-conversion, and LO phonon mode softening.

Figure 1

An actinic pump photon, having energy greater than the NC energy gap, excites a hot electron-hole pair, denoted by “$X$”. The ladder levels represent exciton (i.e., $\mathrm{\text{electron}}+\mathrm{\text{hole}}$) states. As the system evolves in time, hot carriers cool via various pathways including phonon emission and Auger-like electron-to-hole energy transfer. The Raman pump, which is resonant with electronic transitions in the NC, and probe pulses stimulate Raman transitions at various time delays, generating FSRS signal. Inset: Absorption spectrum of 3.1-nm radius CdSe nanocrystals capped with octadecylamine and suspended in hexane. The actinic pump and Raman pump wavelengths are indicated relative to the $1S_{3/2}\mathrm{\text{−}}1S_e$ exciton transition.

Figure 2

(a) Raw ground-state FSRS spectrum for 3.1 nm radius CdSe NCs suspended in hexanes at negative time delay (prior to photoexcitation by the actinic pump). 1LO and 2LO phonon features are indicated. The inset displays a fit of the background-subtracted anti-Stokes peak to the sum of two Gaussian functions. The blue line indicates the overall fit, with the two individual Gaussian functions shown (red and green) and labeled according to their physical origin. In accordance with previous reports, the main peak is assigned to the LO phonon mode, while the low-energy shoulder is assigned to the SO phonon mode. (b) Background-subtracted anti-Stokes phonon peak for 3.1-nm radius CdSe NCs at indicated pump probe time delays. (c) Normalized anti-Stokes phonon band for a 2.4-nm radius CdSe NC at the indicated time delays. The vertical lines serve as a guide to the eye and represent the location of the LO phonon peak center as determined by fits of the phonon band to two Gaussian functions. (d) Dynamics of the LO phonon peak center for a 2.4-nm radius CdSe NC derived from the two-Gaussian fit. The location of the phonon peak center prior to photoexcitation is indicated by the dotted black line.

Figure 3

(a) Anti-Stokes gain amplitude dynamics at the 1LO phonon frequency for CdSe NCs having radii of 1.2 nm (blue circles), 2.4 nm (green circles), and 3.1 nm (red circles). Data are presented for time delays corresponding to the first few picoseconds before and after the actinic pump arrival ($\Delta t=0$). The dotted gray line shows the IRF. The vertical red lines indicate the signal depletion time, defined here as the time taken for the signal to drop from 80% to 20% of its initial ($\Delta t<0$) intensity. The inset displays transient absorption dynamics of the $1S_{3/2}\mathrm{\text{−}}1S_e$ bleach feature for the same set of NCs. (b) Anti-stokes gain amplitude dynamics for 1.5 nm (navy circles), 2.4 nm (green triangles), and 3.1 nm (red diamonds) radius CdSe NCs at time delays up to 1 ns. The inset shows the same dynamics for time delays from 0 to 12 ps. (c) Comparison of measured depletion times for the FSRS 1LO phonon anti-Stokes gain feature (crosses) and the $1S_{3/2}\mathrm{\text{−}}1S_e$ exciton bleach formation time constants (triangles) as a function of NC radius. Error bars represent the standard deviation from multiple measurements, when available.

Figure 4

Following photoexcitation, Auger energy transfer provides the primary relaxation pathway for the electron. Auger energy transfer rates are dependent on NC size. Conversely, hole cooling is primarily facilitated by LO phonon generation, a process with little or no dependence on NC size for CdSe.