Modeling ultrafast out-of-equilibrium carrier dynamics and relaxation processes upon irradiation of hexagonal silicon carbide with femtosecond laser pulses

We present a theoretical investigation of the yet unexplored dynamics of the produced excited carriers upon irradiation of hexagonal silicon carbide (6H-SiC) with femtosecond laser pulses. To describe the ultrafast behavior of laser-induced out-of-equilibrium carriers, a real-time simulation based on density-functional theory methodology is used to compute both the hot-carrier dynamics and transient change of the optical properties. A two-temperature model (TTM) is also employed to derive the relaxation processes (i.e., thermal equilibration between carrier and lattice through carrier-phonon coupling) for laser pulses of wavelength 401 nm, duration 50 fs at normal incidence irradiation which indicate that surface damage on the material occurs for fluence $\sim 1.88\mathrm{J}\mathrm{c}{\mathrm{m}}^{-2}$. This approach of linking real-time calculations, transient optical properties, and TTM modeling, has strong implications for understanding both the ultrafast dynamics and processes of energy relaxation between carrier and phonon subsystems and providing a precise investigation of the impact of hot-carrier population in surface damage mechanisms in solids.

Figure 1

Structure of 6H-SiC: Silicon atoms are represented by large spheres (in red) correspond while carbon atoms are represented by small spheres (in blue) The cell parameters are $a=b=3.095\AA ,c=15.18\AA$ [35].

Figure 2

Simulated results for the real and imaginary part of dielectric function (a), (b) and (c) reflectivity at various photon energies assuming longitudinal and transverse dielectric constant components.

Figure 3

Processes following irradiation with ultrashort pulses: Regime 1: energy absorption, production of hot (out-of-equilibrium) carriers, carrier thermalization, regime 2: Carrier cooling through lattice-carrier interaction and equilibration process.

Figure 4

Evolution of (a) real part, (b) imaginary part of dielectric constant, (c) reflectivity $\left({\lambda }_L=401\mathrm{nm},{\tau }_p=50\mathrm{fs}\right)$. Black solid line shows the laser intensity profile.

Figure 5

Evolution of carrier density (a) through DFT calculations, (b) results for $E_p=1.88\mathrm{J}/\mathrm{c}{\mathrm{m}}^2\left({\lambda }_L=401\mathrm{nm},{\tau }_p=50\mathrm{fs}\right)$. Inset illustrates the carrier evolution at larger timepoints through Eq. (5). Black solid line shows the laser intensity profile.

Figure 6

Evolution of electron and lattice temperature $\left({\lambda }_L=401\mathrm{nm},{\tau }_p=50\mathrm{fs},E_p=1.88\mathrm{J}/\mathrm{c}{\mathrm{m}}^2\right)$.

Figure 7

Threshold fluences in various conditions: experimental measurements and prediction of RT+TTM model (NA corresponds to the numerical aperture of the lens used in the experiment [82]).

Figure 8

Spatial distribution of carrier density at $t=300\mathrm{fs}\left({\lambda }_L=401\mathrm{nm},{\tau }_p=50\mathrm{fs},E_p=1.88\mathrm{J}/\mathrm{c}{\mathrm{m}}^2\right)$.