Real-space investigation of fast diffusion of hydrogen on Si(001) by a combination of nanosecond laser heating and STM

The rearrangement of silicon dangling bonds induced by pulsed laser heating of monohydride-covered Si(001) surfaces has been studied by means of scanning tunneling microscopy (STM). The initial configurations, which were created by laser-induced thermal desorption, consist of isolated pairs of dangling bonds at two adjacent dimers and represent an excited state of the surface. Hydrogen diffusion causes this arrangement to change during only a few nanosecond laser pulses into the equilibrium configuration with most of the dangling bonds being paired up at a single dimer. STM images taken after different numbers of heating pulses show snapshots of the surface configuration frozen at various stages of the fast equilibration process. In this way, hydrogen diffusion associated with rates as high as ${10}^8{\mathrm{s}}^{-1}$ could be monitored with atomic resolution. Comparison with Monte Carlo simulations of the diffusion processes allows for the precise determination of both the diffusion rates and the pairing energies between dangling bonds at high surface temperature.

Figure 1

(Color online) Illustration of the time dependent surface temperature (lower box) and surface diffusion rate (upper box) for a $9\mathrm{ns}$ and $240\mathrm{mJ}∕{\mathrm{cm}}^2$ heating pulse as calculated by solving the Fourier heat conduction equation using extrapolated rate parameters. The Gaussian profile of the laser intensity is shown by the dashed line (lower box). The experimental setup is shown in the upper right part. The silicon surface is heated by focusing the nanosecond laser pulse on the sample. A reference beam from the beam splitter (BS) is used to characterize the pulses with a power meter (PM). A shutter gives the possibility to vary the number of laser pulses that are shot onto the sample.

Figure 2

STM image of a monohydride Si(001) surface taken at a negative sample voltage $U=-2.0\mathrm{V}$ and sample bias $I=0.4\mathrm{nA}$. The dimer rows are visible with each dimer (small oval) consisting of two silicon atoms saturated with two hydrogen atoms. Only a few defects (dark), dihydrides (symmetrically split dimer), and unoccupied dangling bonds (bright) are visible. In the upper right part, a close-up of a single unreacted dangling bond (taken from a different area) sitting asymmetrically on one dimer is shown.

Figure 3

$50\times 50{\mathrm{nm}}^2$ STM images of the monohydride Si(001) surface after (a) one, (b) two, and (c) three consecutive heating pulses. Nearly the same amount of hydrogen was desorbed per heating pulse. Tunneling conditions were the same as in Fig. 2. (d) The dependence of desorbed hydrogen on number of laser pulses.

Figure 4

$50\times 50{\mathrm{nm}}^2$ STM image of the saturated Si(001) surface after two heating pulses taken at a negative sample voltage $U=-2.0\mathrm{V}$ and sample bias $I=0.4\mathrm{nA}$. The bright spots represent empty dangling bonds that are created due to the desorption of the hydrogen atoms. The detailed images in the lower part show the different configurations of paired dangling bonds that can be identified and the corresponding sketches: two dangling bonds on the same Si dimer (intra), two dangling bonds on neighboring dimers adverse (cis) and transverse (trans) from each other, and two dangling bonds separated by two (sep-2) and by three (sep-3) dimers.

Figure 5

(Color online) Distributions of dangling-bond configuration for the different numbers of heating pulses as shown in Fig. 3. The dark bars correspond to the experimental results and the light bars to the results of the Monte Carlo simulation.

Figure 6

(Color online) $50\times 50{\mathrm{nm}}^2$ STM images of the monohydride Si(001) surface after ten consecutive heating pulses ($U=-2.0\mathrm{V}$, $I=0.4\mathrm{nA}$). The darker bars in the bar plot correspond to the experimental dangling-bond configuration after the ten heating pulses. The lighter bars represent the results for the simulation of the dangling-bond configuration for the thermal equilibrium.

Figure 7

Schematic sketch of the Monte Carlo simulation for a single dimer row. The black circles represent hydrogen atoms adsorbed on the surface, whereas the white circles represent unsaturated dangling bonds. (a) Possible diffusion pathways for a single hydrogen atom. (b) Illustration of a diffusion process influenced by the intradimer pairing energy $\epsilon$. (c) Illustration of a diffusion process influenced by the interdimer pairing energy $\omega$.

Figure 8

(Color online) (a) Calculated deviation between experiment and simulation for different values of interdimer jumps per dangling bond per heating pulse for one heating pulse. The solid line is the best fit for the data points. (b) Bar plots of the simulated dangling-bond configuration for different values of interdimer jumps. The darker bars correspond to the experimental results and the lighter bars to the results of the Monte Carlo simulation. In the middle is the configuration that leads to the best agreement between experiment and simulation. The upper and lower bar plots show the results of the simulation for lower and higher values of interdimer jumps.

Figure 9

(a) Calculated deviation between experiment and simulation for different values of intradimer pairing energies. The solid line is the best fit for the data points. (b) Calculated deviation between experiment and simulation for different values of interdimer pairing energies. The solid line is the best fit for the data points.

Figure 10

(Color online) Arrhenius plot of the interdimer hopping rate. The results from our experiment (diamonds) are compared with earlier experiments by Owen et al. (Ref. 6) (solid line) and Hill et al. (Ref. 7) (dashed line) that were carried out at lower temperatures between 400 and $700\mathrm{K}$ and are extrapolated for higher temperatures. Also shown is the range of reaction rates which is accessible to observation by means of video STM.