Imaging Energy-, Momentum-, and Time-Resolved Distributions of Photoinjected Hot Electrons in GaAs

Using time-and angle-resolved photoemission spectroscopy, we determine directly energy-, momentum-, and time-resolved distributions of hot electrons photoinjected into the conduction band of GaAs, a prototypical direct-gap semiconductor. The nascent distributions of photoinjected electrons are captured for different pump photon energies and polarization. The evolutions of hot electron distributions in ultrafast intervalley scattering processes are resolved in momentum space with fs-temporal resolution, revealing an intervalley transition time as short as 20 fs.

Figure 1

(a) A part of the band structure of GaAs (Ref. [22]). Energy is referenced to the conduction-band minimum. The symmetries of spatial parts of wave functions are given for the points involved in the interband transitions (Ref. [25]). Green (blue) arrows show typical allowed optical transitions for $s$-($p$-) polarized 2.21-eV photons. (b) The image of photoelectrons 20 fs after excitation with $\mathit{s}$-polarized 2.21-eV light pulses. (c) The image of photoelectrons 20 fs after excitation with $p$-polarized 2.21-eV light pulses. (d) The image of photoelectrons 10 ps after excitation with $s$-polarized 2.21-eV light pulses. In (b), (c), and (d), the color scale indicates the photoemission intensity. (e) Normal photoemission spectra in the images in (b) and (c). The intensities at $\theta =0\pm 0.5°$ are integrated. (f) Experimental geometry of photoemission measurements, and the relation between the surface Brillouin zone and bulk Brillouin zone for GaAs with (110) surface under this geometry. The plane shown by light blue is the projection plane, and the red arrow within the plane shows the direction from the $\mathrm{\Gamma }$ to $L$ points.

Figure 2

(a) Angle-integrated photoemission spectra, measured at $\mathrm{\Delta }t=20\mathrm{fs}$, excited by $s$-polarized light pulses with photon energies ranging from 1.70 to 2.38 eV. Excitation density $\rho$ is typically $\le 5\times 10^{17}{\mathrm{cm}}^{-3}$. (b) Temporal change of population at the highest-energy states of the spectra (for definition see the text) for excitation photon energies of 1.70 eV ($\rho =4.7\times {10}^{17}{\mathrm{cm}}^{-3}$), 1.80 eV ($\rho =4.5\times {10}^{17}{\mathrm{cm}}^{-3}$), and 2.21 eV ($\rho =3.2\times {10}^{17}{\mathrm{cm}}^{-3}$). The solid curves show the best-fit solutions of the optical Bloch equation, while the dashed curves display rate-equation results that incorporate cascade effects of relaxation. The black curve, labeled CC, displays the cross-correlation trace between pump and probe pulses.

Figure 3

(a) The photoemission map for hot electrons in the $\mathrm{\Gamma }$ valley injected by 2.30-eV light pulses as a function of energy and $\mathrm{\Delta }t$. The solid and broken lines labeled $E_L$ and $E_X$ show the experimental values of $L$-and $X$-valley minima. (b) Red, green, blue, light blue, and violet curves show angle integrated distribution functions measured at 20-fs intervals of $\mathrm{\Delta }t$ from 20 to 100 fs in order, and the black curve shows the function at $\mathrm{\Delta }t=200\mathrm{fs}$. (c) Temporal changes of the total photoemission intensity integrated over $ϵ$ and $\theta$, (blue line), and of the population at the highest-energy states, (red line), as a function of $\mathrm{\Delta }t$. The solid black curve shows the result of analysis by the diffusion equation, and the broken curve is the best fit of the rate equation model with the restoration of the total intensity. (d) The image of photoelectrons 70 fs after excitation with 2.30-eV $s$-polarized light. The color scale indicates the relative photoemission intensity. (e) Photoemission intensities at $ϵ=0.78\pm 0.3\mathrm{eV}$ as a function of $\theta$ for $\mathrm{\Delta }t=20\mathrm{fs}$ (red line), and 70 fs (black line).