Carrier-Density-Dependent Lattice Stability in InSb

The ultrafast decay of the x-ray diffraction intensity following laser excitation of an InSb crystal has been utilized to observe carrier dependent changes in the potential energy surface. For the first time, an abrupt carrier dependent onset for potential energy surface softening and the appearance of accelerated atomic disordering for a very high average carrier density have been observed. Inertial dynamics dominate the early stages of crystal disordering for a wide range of carrier densities between the onset of crystal softening and the appearance of accelerated atomic disordering.

Figure 1

Normalized time-dependent diffracted intensity for the (111) Bragg peak with corresponding fits. (a) Observation of the carrier density threshold for the onset of inertial atomic motion with $37\mathrm{mJ}{\mathrm{cm}}^{-2}$ (▿) and $44\mathrm{mJ}{\mathrm{cm}}^{-2}$ (○) at 0.4° x-ray angle of incidence. (b) Observation of predominantly inertial dynamics for 0.4° x-ray angle of incidence and $180\mathrm{mJ}{\mathrm{cm}}^{-2}$ laser fluence (▿) and accelerated atomic disordering with 0.3° x-ray angle of incidence and $160\mathrm{mJ}{\mathrm{cm}}^{-2}$ laser fluence (○). The 0.4° data are shown with a fits to the normalized sum of a Gaussian and exponential, while the 0.3° data is shown with a fit to the accelerated dynamics model, both of which are described in the text. Inset displays the msd for the data and fits as extracted from Eq. (1) as $\Delta u(t)=\sqrt{-\frac{3\ln [I(t)]}{Q^2}}$.

Figure 2

Plot of the predicted time-dependent diffraction intensity as given by the model described in the text for $\alpha {\omega }_D=0.3\mathrm{THz}$, $\alpha {\omega }_D=0\mathrm{THz}$, and $\alpha {\omega }_D=0.6i\mathrm{THz}$. Predicted diffraction intensity has oscillatory character for positive softening on longer time scales. Inset displays ${\tau }_{1/e}$ as a function of $\alpha {\omega }_D$.

Figure 3

Log plot of ${\tau }_{1/e}$ as a function of carrier density. Inset displays the high carrier density regime. See text for the definition of ${\tau }_{1/e}$ and method of estimation for the carrier density.