Electronic structure of the surface unoccupied band of Ge(001)-$c(4\times 2)$: Direct imaging of surface electron relaxation pathways

We have studied the electronic structure of the surface unoccupied band (SUB) of clean Ge(001)-$c(4\times 2)$, with high energy and momentum resolution, by means of time- and angle-resolved two-photon photoelectron spectroscopy. The time evolution of photoelectron intensity images, measured as functions of energy and emission angle after photoexcitation with laser pulses (1.5 eV, 200 fs), provides a momentum space view of the relaxation pathways of surface excited electrons toward the bottom of the SUB. Surface excited electrons relax in several picoseconds along the strongly dispersive directions ($\overline{\mathrm{\Gamma }}\overline{J^{\prime }}$ and $\overline{\mathrm{\Gamma }}\overline{{J_2}^{\prime }}$) and then accumulate near the band bottom. Taking into account the ultrafast change of surface potential, possibly due to the spatial redistribution of nonthermal carriers generated by photoexcitation, an energy width of 0.22 eV was determined as the surface band gap, as well as the surface dispersion properties along three high-symmetry directions.

Figure 1

Logarithmic images $I\left(\varepsilon ,\theta \right)$ for clean Ge(001)-$c(4\times 2)$ probed at (a) −5, (b) 0, (c) 1, (d) 2, (e) 3, and (f) 4 ps after the pump laser pulses. The experimental geometry is shown in (g). The measurements were carried out with the azimuthal angle of the specimen kept at $\phi =0^{\circ }$, corresponding to the $\overline{\mathrm{\Gamma }}\overline{J}$ and $\overline{\mathrm{\Gamma }}\overline{J^{\prime }}$ directions. Surface atomic arrangements and the SBZs of two domains separated by a single atomic step are shown in (h) and (i).

Figure 2

Logarithmic images $I\left(\varepsilon ,\theta \right)$ for clean Ge(001)-$c(4\times 2)$ probed at (a) $-5$, (b) 0, (c) 1, (d) 2, (e) 3, and (f) 4 ps after the pump laser pulses. The experimental geometry is shown in (g). The measurements were carried out with the azimuthal angle of the specimen kept at $\phi ={45}^{\circ }$, corresponding to the $\overline{\mathrm{\Gamma }}\overline{{J^{\prime }}_2}$ directions. Surface atomic arrangements and the SBZs are shown in (h) and (i).

Figure 3

(a) Angle-integrated spectra acquired at several delay times between the pump and probe laser pulses; the spectrum without pump laser pulse is shown for comparison. (b) The photoinduced energy shift $\mathrm{\Delta }E$ of the spectra is plotted as a function of delay time. The magnitude of $\mathrm{\Delta }E$ is given by the energy shift of the bulk-originating structure, B. (c) Angle-integrated spectra with and without pump laser pulses. The spectrum acquired at $-1\mathrm{ps}$ is shifted by $\mathrm{\Delta }E$ to account for the photoinduced change of the surface potential.

Figure 4

Relaxation pathways of the surface electrons on Ge(001)-$c(4\times 2)$ surface imaged in (${\varepsilon }^{\prime }$, $\overrightarrow{k_s}$) space, derived from the time evolution of photoelectron images measured at (a) $\phi =0^{\circ }$ and (b) ${45}^{\circ }$. Each image is obtained by integrating $I\left(\varepsilon ,\theta \right)$ acquired every 200 fs from $t_{\mathrm{d}}=0$ to 1.5 ps, taking the dynamical change of surface potential into account. (c) Energy dispersion relations of the SUB along the three high-symmetry directions are depicted by red solid lines. Circles, triangles, and diamonds indicate the previous experimental data from Refs. [4], [9], and [12], respectively; orange, black, and blue dotted lines show the calculated bands from Refs. [2], [4], and [10], respectively.