Several experimental studies have previously reported cross-correlation effects between optical and X-ray pulses. Kraessig et al
. made use of a change in hard X-ray absorption in krypton atoms ionized by an ultrafast infrared laser pulse6
, while Gahl et al
. measured the change in optical reflectivity from GaAs caused by 40 eV photons from an X-ray free-electron laser (XFEL)7
. We are also interested in semiconducting GaAs, and in particular how the X-ray photo-absorption process stimulates a range of many-body responses that can be probed by optical transmission at the bandgap. From these synchrotron-based X-ray pump/optical probe studies, we report three unique experimental observations: X-ray-induced optical transparency, X-ray-induced optical opacity and the evolution from non-equilibrium electronic excitations to an equilibrium temperature response over the range 1 × 10–11
to 1 × 10–4
First, it is useful to consider how X-rays create valence and conduction band excitations in a semiconductor. When X-ray absorption leads to electron ejection from an atomic core level, the photoelectron traverses dozens of unit cells while inelastically scattering hundreds or thousands of valence electrons high into the conduction band8
. These hot electrons thermalize by electron–electron and electron–plasmon scattering, and settle into the lowest states of the conduction band while interacting with lattice phonons, a process extending into picoseconds and longer9
. The deep core hole left behind is filled by a higher-level core electron, sometimes accompanied by fluorescence, but for lighter elements the emission of an Auger electron is more likely. This replaces a deep core hole with two higher ones, and the Auger electron inelastically scatters many more carriers to the conduction and valence bands. This is repeated with higher core levels, creating multiple localized holes that eventually cascade up to become mobile valence band holes10
In our experiments an ~60-μm-thick GaAs specimen absorbs an intense, 80 ps full-width at half-maximum (FWHM) synchrotron X-ray pump pulse. The transmission of a monochromatic 3 ps (FWHM) laser probe pulse near the bandgap energy was then measured as a function of the pump–probe delay time. The transmitted intensity versus time delay for λ = 860 nm, normalized to the signal without X-rays, is shown in . Also shown is the time profile of the X-ray pulse (convoluted with laser jitter) and the time-integrated fluence, which matches the initial data quite well. The specimen switched from optically opaque to transparent within the duration of the X-ray pulse. An 860 nm photon has just enough energy (1.44 eV) to excite a valence electron across the direct bandgap into the conduction band (~1.43 eV). The induced transparency decays with a time constant of 1.1 ns (, inset). Transparency was observed from ~880 to 840 nm, a bandwidth of ~70 meV. The 40-fold increase in transmitted signal suggests that this could be a useful X-ray/optical cross-correlator for high-intensity synchrotron and XFEL beams.
Transmission at 860 nm versus time after X-ray pump pulse
A simplified model for describing this result is shown in . Before X-rays arrive, the ideal semiconductor density of states at the direct bandgap is assumed to have a fully occupied valence band and an empty conduction band. The inelastic scattering of energetic photoelectrons and Auger electrons creates a high density of carriers, which fill the lowest energy levels in these bands. Originally, a photon with energy just above Egap
would be strongly absorbed by promoting an electron across the gap. Now, however, the top valence states are empty and the bottom conduction band states are occupied, blocking photon absorption at this energy. This persists until electron–hole recombination fills the valence band again (lifetime, ~1.1 ns). (A similar optically induced shift in the bandgap is sometimes referred to as the Burstein–Moss effect11,12
Model for X-ray-induced transmission and absorption
The large induced transparency response could make thin GaAs a useful cross-correlator for determining X-ray pump/optical probe arrival times. By using white pulses instead of monochromatic light, the entire spectrum could be measured in a single shot, and standard chirping techniques could provide additional sensitivity. This could be especially useful for femtosecond XFEL sources, where it is desirable to directly measure X-ray pulse jitter at the experimental station instead of relying on measurements of upstream particle bunches.
The time-dependent absorption factors (μx = –ln(T), where T is the transmitted fraction) are shown in for laser wavelengths spanning the bandgap (850–900 nm). The large X-ray-induced transparency is gradually replaced by induced absorption at 900 nm; that is, X-ray-induced opacity occurs for photon energies just below the bandgap. Absorption nearly doubles at 900 nm, where the specimen would otherwise be transparent, indicating that X-rays have somehow created a new mechanism for optical absorption below the conduction band edge. This induced optical opacity approximately follows the X-ray pulse time profile, whereas the induced optical transparency largely follows the integrated fluence (). The latter is expected, because the carrier recombination lifetime (1.1 ns) is much longer than the X-ray pulse. States responsible for opacity must have much shorter lifetimes, which excludes any absorption mechanism that directly depends on the excited carriers.
Absorption factor (μ(λ)L = –ln(T)) versus time delay
In considering how X-ray-induced optical absorption arises, it is important to remember a crucial difference between these measurements and ultrafast laser studies of GaAs: intense X-ray pulses produce a large number of localized core holes that are absent when pumping with optical lasers. The density of X-ray absorption sites created by each X-ray pump pulse is ~0.5 × 1017
. A localized core hole has a Coulomb potential like that of an ionized donor atom. In transport studies, doping levels of ~1 × 1017
and above have caused observable bandgap narrowing due to induced band tail states13,14
. The 1 × 1017
absorption site density, however, must be corrected for the core hole lifetime relative to the 100 ps pulse duration to obtain the instantaneous density. A K-shell hole with a 1 × 10–15
s lifetime would yield an effective dopant density of only 1 × 1012
; the multiple shallower holes from subsequent Auger processes may increase this by another order of magnitude. These effective dopant densities seem small, but the lower detectable limit in optical measurements (as opposed to transport studies) is not clear15
. On the other hand, these localized core holes ultimately convert into delocalized valence band holes, but their long lifetimes (1 × 10–9
s) preclude them from causing the induced absorption. Given the high density of X-ray absorption sites and the range of lifetimes experienced by the subsequent core holes, we suggest that theoretical treatments of bandgap changes in highly excited GaAs be expanded to include the localized core holes, to better understand the origins of X-ray induced optical absorption.
Because excited electrons can be a source of phonons as they thermalize, the possibility of absorption assisted by longitudinal optical (LO) phonons must be considered. Several ultrafast laser pump–probe transmission studies of GaAs have been carried out near the bandgap16–19
, but none reports evidence for phonon-assisted absorption, even for pair densities in the 1 × 1018
to 1 × 1019
range (the pair density in our measurements is estimated to be ~0.5 × 1020
; see Methods). Recent theoretical studies of optical refrigeration in GaAs have considered the possibility of phonon-assisted absorption. However, there is only limited comparison with experiment20–22
. Furthermore, experiment and theory15,21,23
agree that increasing electron–hole pair densities cause a decrease in any LO-phonon assisted absorption, because the plasma effectively screens the transient dipole moments from the LO phonons. With densities near 1 × 1020
, this suggests that phonon-assisted absorption should be greatly suppressed in the X-ray-pumped results.
Finally, we show () sub-bandgap transmission (at 890 nm) for time delays from 1 × 1011
s to 1 × 10–4
s. The induced opacity that tracks the X-ray pulse is seen as the dip below 100 ps. The drift upwards after ~1 × 10–7
s is consistent with an elevated temperature gradually cooling to room temperature, because the bandgap in GaAs narrows with increased temperature24,25
By assigning the drop in transmission to a shift in the bandgap, we can use the published temperature dependence of the GaAs bandgap to equate this to a temperature increase of ~4 K at 1 × 10–7
Transmission at 890 nm from 1 × 10–11 to 1 × 10–4 s
For times less than 1 × 10–8
s, however, it appears that non-equilibrium processes dominate the optical transmission. A second dip in transmission (that is, increased opacity) is seen at ~1 × 10–9
s. There is clearly a competition among mechanisms responsible for this complex behaviour, for example, induced band tail states, electron–hole recombination, free-carrier scattering, non-equilibrium phonon excitations, and so on. Recent work on InP and InSb have also shown non-equilibrium phonon distributions for nanoseconds after laser excitation26
. We see here that X-ray pumping causes the system to remain out of equilibrium for even longer times. Comparing these data with future X-ray pump/optical probe transmission measurements on an indirect-gap semiconductor (such as germanium) could help separate phonon and electron contributions.
In conclusion, we have demonstrated that intense X-ray illumination of GaAs generates ultrafast many-body responses at the semiconductor bandgap that are readily probed with optical pulses. The X-ray excitations can induce optical transparency above the gap and optical absorption just below the gap, using intense 80 ps pulses from an X-ray synchrotron. Additional non-equilibrium phenomena are evident at gap energies for many nanoseconds after excitation. The extension of these measurements with femtosecond XFEL pulses would provide greater insight into the ultrafast many-body response of semiconductors to X-ray excitation.