Ultrafast carrier dynamics in $\mathrm{Si}\left(111\right)7\times 7$ dangling bonds probed by time-resolved second-harmonic generation and two-photon photoemission

By combining time-resolved two-photon photoemission (2PPE) and optical second-harmonic generation (SHG), the dynamics of surface electronic states of $\mathrm{Si}\left(111\right)7\times 7$ has been studied. In the experiment the normally unoccupied part of the adatom dangling-bond bands are populated by $1.55\mathrm{eV}$ pump pulses. The 2PPE results show very fast relaxation within these bands with lifetimes ranging between 40 and $150\mathrm{fs}$ depending on energy relative to the Fermi level. The regime of high excitation densities was investigated by means of time-resolved SHG. With increasing pump fluence, we observed filling of the surface bands and a concomitant increase of the optical relaxation times from 0.5–$2\mathrm{ps}$. The results are interpreted in terms of electron-electron scattering within a two-dimensional metallic system that is isolated from the bulk semiconductor.

Figure 1

Schematic drawing of the electronic structure of the $\mathrm{Si}\left(111\right)7\times 7$ surface. The Brillouin zone refers to the unreconstructed $\mathrm{Si}\left(111\right)$ surface; shaded areas mark the projected bulk bands (Ref. 19). $S_1$, $S_2$, and $S_3$ denote occupied, $U_1$ and $U_2$ unoccupied surface states. Only one representative band of the adatom-induced surface states $U_1∕S_1$ is sketched. It was obtained by inverse photoemission from $\mathrm{Si}\left(111\right)\sqrt{3}\times \sqrt{3}\text{−}B$ with a similar but completely unoccupied adatom band (Ref. 20). Vertical arrows indicate the excitation (thick line) and the probe process by 2PPE (left) and SHG (right). Inset: side view of the surface geometry. The dangling bonds of the rest atoms $\left(R\right)$ are completely filled while the average occupancy of the adatom dangling bonds $\left(A\right)$ is slightly less than $1∕4$.

Figure 2

2PPE spectra at zero delay time between the ir pump and uv probe pulses. Spectrum (b) was recorded at a $2\times \mathrm{higher}$ ir fluence than spectrum (a). The energy scale refers to the excitation energy above the valence-band maximum (VBM) of bulk silicon. The Fermi level $E_{\mathrm{F}}$ and the conduction-band minimum (CBM) are indicated by dashed lines.

Figure 3

Set of 2PPE spectra recorded at various pump-probe delay times. The spectrum in the foreground was measured without ir irradiation. The partially hidden spectra taken with probe pulses arriving before the pump pulses (negative delays around $-0.4\mathrm{ps}$) are very similar to the one shown for a large positive delay of $6.3\mathrm{ps}$.

Figure 4

Lifetimes $\tau$ as a function of the energy of the excited states inside the adatom band. The values result from fitting a rate-equation model to the time-dependent transients (inset) that were obtained from constant-energy cuts through the spectra of Fig. 3. The solid line is a guide to the eye and scales like $\tau \propto (E-E_{\mathrm{F}}{)}^{-0.64}$.

Figure 5

$s$-polarized component of the second-harmonic signal from $\mathrm{Si}\left(111\right)7\times 7$ generated by $s$-polarized probe pulses $(1\mathrm{mJ}∕{\mathrm{cm}}^2,800\mathrm{nm})$ as a function of delay with respect to the $p$-polarized pump pulses $\left(800\mathrm{nm}\right)$ for various pump fluences. The top curve shows the linear reflectivity for a pump fluence of $14\mathrm{mJ}∕{\mathrm{cm}}^2$. The smooth lines are the results of numerical fits of the SHG data discussed in the text. The inset shows SHG data for a pump fluence of $5.5\mathrm{mJ}∕{\mathrm{cm}}^2$ on a longer time scale.

Figure 6

SHG transients from a clean surface, a partially oxygen-covered surface (${\mathrm{O}}_2$ exposure $1.6\mathrm{L}$) and a sample covered with native oxide. Pump fluences were $14\mathrm{mJ}∕{\mathrm{cm}}^2$ in all cases; the curves were normalized to unity. Lines represent simulations using the interference model for the nonlinear susceptibility and rate equations for the time-dependent decay discussed in the text.

Figure 7

Reduction of the SH probe signal by the pump pulse (triangles) and derived population of the adatom bands (open dots) as a function of pump fluence. Solid lines were computed by using the two-component model of SHG described in the text.

Figure 8

Variation of the relaxation time of the SH signal as a function of pump fluence as obtained by exponential fits to initial parts of time-dependent transients such as those of Fig. 5 (full symbols). The open circle denotes the result of the experiment of Ref. 32. Inset: sketch of the band filling by the pump pulse and of the relaxation of the excited electrons by intraband scattering.