Nonthermal graphitization of diamond induced by a femtosecond x-ray laser pulse

Diamond irradiated with an ultrashort intense laser pulse in the regime of photon energies from soft up to hard x rays can undergo a phase transition to graphite. This transition is induced by an excitation of electrons from the valence band or from atomic deep shells of the material into its conduction band, which is followed by a transient rapid change of the interatomic potential. Such a nonthermal phase transition occurs on a femtosecond time scale, shortly after or even during the laser pulse. In this work we show that the duration of the graphitization depends on the incoming photon energy: the higher the photon energy is, the longer the secondary electron cascading which promotes the electrons into the conduction band will take. The transient kinetics of the electronic and atomic processes during the graphitization is analyzed in detail. The damage threshold fluence is calculated in the broad photon energy range and is found to be always $\sim$0.7 eV/atom in terms of the average dose absorbed per atom. It is confirmed that the temporal characteristics of a femtosecond laser pulse (at a fixed pulse duration and fluence) do not significantly influence the transient damage kinetics. Finally, the influence of an additional surface layer of high-$Z$ material on the damage within diamond is discussed.

Figure 1

Estimated damage threshold fluence for the graphitization of diamond as a function of photon energy.

Figure 2

Redistribution of energy among atoms, electrons, and $K$-shell holes after a 10-fs FWHM laser pulse, providing the average absorbed dose of 0.85 eV per atom. (top) The 280-eV photon energy, below the $K$ edge; (bottom) 300-eV photon energy, above the $K$ edge. The black dashed curve is the total energy of the system, the red dotted line is the sum of the energies of the atoms and electrons (the total energy excluding the energy of $K$-shell holes), the green dash-dotted line is the energy of the atoms, and the blue solid line is the potential energy of the atoms.

Figure 3

(top) Fraction of high-energy electrons (with energy above $E_{\mathrm{cut}}$, belonging to the MC domain) generated at different photon energies. (bottom) Fraction of $K$-shell holes generated at different photon energies (note the logarithmic scale). Both are normalized to the initial number of valence-band electrons. The laser-pulse profile is schematically shown as a dashed violet line.

Figure 4

(top) Fraction of conduction-band electrons normalized to the initial number of valence-band electrons for different photon energies. (bottom) Band gap of the irradiated diamond. The laser-pulse shape is schematically shown as a dashed violet line.

Figure 5

Redistribution of energy between atoms, electrons, and holes during and after the 10-fs FWHM (delivering an average absorbed dose of 0.85 eV per atom) at different photon energies: 2, 5, 8.2, and 10 keV. In all panels the black dash-dotted curve is the total energy of the system, the red dotted line is the sum of the energies of atoms and electrons (excluding the energy of $K$-shell holes), the green dashed line is the energy of the atoms, and the blue solid line is the potential energy of the atoms.

Figure 6

Energy of atoms and electrons in diamond as a function of time, recorded during and after three laser pulses with different pulse envelopes: (top) Gaussian, (middle) flat top, and (bottom) SASE.

Figure 7

Schematic picture of the multilayer tungsten-diamond structure, irradiated with a laser pulse. The violet lines represent photons ($hv$), the red arrows stand for photoelectrons and secondary electrons (marked with $e^{-}$), and the blue arrows represent Auger electrons.

Figure 8

Electron inelastic mean free path and the corresponding energy loss function in tungsten.