Dynamics of bulk-to-surface electron transitions on $\text{Si}(001)\text{\ensuremath{-}}(2\ifmmode\times\else\texttimes\fi{}1)$ studied by time-resolved two-photon photoemission spectroscopy

Dynamics of bulk-to-surface electron transitions on $Si (001) − (2 \times 1)$ studied by time-resolved two-photon photoemission spectroscopy

S. Tanaka, T. Ichibayashi, and K. Tanimura

Phys. Rev. B 79, 155313 – Published 20 April 2009

Abstract

The carrier dynamics on $Si (001) − (2 \times 1)$ have been studied by means of time- and angle-resolved two-photon photoemission spectroscopies at 291 K. Temporal changes in electron populations at the normally unoccupied surface band $(D_{down})$ and at the bulk conduction-band minimum (CBM) have been probed simultaneously to characterize the pathways of bulk-to-surface electron transfer. The decay kinetics of the electron population at the bottom of $D_{down}$ and at the CBM, obtained at two different excitation wavelengths, where the bulk absorption coefficient differs significantly, show a strong dependence on wavelength. Analysis shows that the dependence of the population at the CBM is characterized by carrier diffusion away from the surface and by rapid surface recombination, with a surface-recombination velocity of $1.2 \times 10^{6} cm / s$ . The surface-recombination pathway from the CBM to the high-lying state along the $\bar{Γ} - {\bar{J}}^{'}$ dispersive branch of the $D_{down}$ band has been directly probed by an angle-resolved technique. Quantitative comparisons of electron flows into the $D_{down}$ band and the decay kinetics of the population of the bottom of $D_{down}$ reveal an efficient quadratic decay channel of the surface electron-hole recombination.

Received 27 October 2008

DOI:https://doi.org/10.1103/PhysRevB.79.155313

Authors & Affiliations

S. Tanaka, T. Ichibayashi, and K. Tanimura

The Institute of Scientific and Industrial Research, Osaka University, 8-1 Mihogaoka, Ibaraki, Osaka 567-0047, Japan

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Vol. 79, Iss. 15 — 15 April 2009

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Figure 1
(Color online) Schematic drawing of the electronic structure of $Si (001) − (2 \times 1)$ . Shaded area marks the projected bulk conduction band and the solid curve is the dispersion of the normally unoccupied dangling-bond band $(D_{down})$ (Ref. 24). Point T represents a high-lying level on the dispersive branch of the $D_{down}$ band. Arrows show possible processes in the bulk-to-surface electron transition. Arrows (1), (2), and (3) represent the energy relaxation process of hot electrons near the CBM, the bulk-to-surface state transition, and intraband relaxation of the $D_{down}$ band. Inset: A schematic model of an asymmetric Si dimer on the surface. The $D_{down}$ band is composed of the unoccupied dangling bond labeled $D_{down}$ . Surface Brillouin zone for the $(2 \times 1)$ structure, solid line, and for the $c (4 \times 2)$ structure, dotted line, are shown as well.Reuse & Permissions
Figure 2
(a) Time-resolved 2PPE spectra for the $s$ -polarized $ω$ excitation and [(b) and (c)] for the $s$ -polarized $2 ω$ excitation. The energy scale of photoemission spectra is referred to the VBM. In (a) and (b), the spectra, measured for electrons emitted along the surface normal, at the $Δ t$ ’s indicated, are displayed after subtracting the spectrum at $Δ t = - 1 ps$ for $ω$ - or $2 ω$ -pump pulse. In (c), the spectra measured at $Δ t = - 1 ps$ and at 5 ps are shown for $2 ω$ excitation. Inset shows the spectrum at $Δ t = 1 ps$ in an expanded scale $(\times 30)$ in (a), that at $Δ t = 5 ps (\times 100)$ in (b) and that at $- 1 ps (\times 30)$ in (c).Reuse & Permissions
Figure 3
(Color online) Temporal changes in the photoemission intensities under $p$ -polarized $ω$ excitation (a) from the bottom of the $D_{down}$ , (b) from the CBM, and (c) from the high-lying level of the dispersive branch of the $D_{down}$ . The changes under $s$ -polarized $2 ω$ excitation for the corresponding peaks for $ω$ excitation shown in (a), (b), and (c) are displayed in (d), (e), and (f). Red curves pertaining data points in (a) and (d) are the calculated decay curves of the photoemission from the $D_{down}$ at $\bar{Γ}$ (see text).Reuse & Permissions
Figure 4
(a) The time-resolved 2PPE spectra under $ω$ excitation measured in normal emission $(θ = 0 °)$ at $Δ t = 0 ps$ , gray, and $Δ t = 1 ps$ , black. (b) The time-resolved 2PPE spectra under $ω$ excitation measured with the off-angle $θ = 20 °$ at $Δ t = 0 ps$ , gray, and $Δ t = 1 ps$ , black. (c) The peak energies of the photoemission peaks from a high-lying level of the dispersive branch $D_{down}$ $(T)$ and the bottom of the $D_{down}$ band as a function of parallel momentum $k_{∥}$ , detected for $p$ -polarized $ω$ excitation (○), $s$ -polarized $ω$ excitation (●), and $s$ -polarized $2 ω$ excitation (◼).Reuse & Permissions
Figure 5
(a) Temporal changes in photoemission intensity from the high-lying level at the dispersive branch of $D_{down}$ measured at the off-angle of $20 °$ . The gray and broken gray curves are the fit of the rate-equation model (see text). (b) Temporal changes in photoemission intensity from the bottom of $D_{down}$ measured in normal emission. The gray curve shows the cross-correlation trace between pump and probe pulses determined by the temporal evolution of the coherent two-photon photoemission of the 1.0 eV peak in Fig. 4a.Reuse & Permissions
Figure 6
(Color online) Logarithmic plot of temporal changes in photoemission intensity from the CBM under $ω$ excitation at a fluence of $18.8 μ J / {cm}^{2}$ and $2 ω$ excitation at a fluence of $0.83 μ J / {cm}^{2}$ . The calculated results, based on the diffusion-equation model, for $S = 0$ (broken curves) and for $S = 1.2 \times 10^{6} cm / s$ (red curves) are compared to the experimental results.Reuse & Permissions

Physical Review B

covering condensed matter and materials physics

Dynamics of bulk-to-surface electron transitions on $Si (001) − (2 \times 1)$ studied by time-resolved two-photon photoemission spectroscopy

S. Tanaka, T. Ichibayashi, and K. Tanimura

Phys. Rev. B 79, 155313 – Published 20 April 2009

Abstract

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Physical Review B

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Dynamics of bulk-to-surface electron transitions on Si(001)−(2×1) studied by time-resolved two-photon photoemission spectroscopy

S. Tanaka, T. Ichibayashi, and K. Tanimura

Phys. Rev. B 79, 155313 – Published 20 April 2009

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Dynamics of bulk-to-surface electron transitions on $Si (001) − (2 \times 1)$ studied by time-resolved two-photon photoemission spectroscopy