Element-Specific Surface X-Ray Diffraction Study of $\mathrm{GaAs}(001)\mathrm{\text{−}}c(4\times 4)$

In situ structure analysis of $\mathrm{GaAs}(001)\mathrm{\text{−}}c(4\times 4)$ has been carried out by synchrotron surface x-ray diffraction, which is sensitive to the three-dimensional structure and the atomic species. On the basis of 98 independent in-plane diffractions and 11 fractional-order rod profiles, the atomic coordinates and thermal vibration parameters were determined. X-ray diffraction results show the buckling of surface dimers and a strain field extending up to the sixth layer from the surface. An anomalous diffraction technique has been employed to specify the atomic species of the surface dimers. It has provided direct evidence of the formation of Ga-As heterodimers.

Figure 1

Structure factors measured by the x-ray diffraction technique at $L=0.03$. The indices $H$ and $K$ are along $[\overline{1}10]$ and $[110]$ directions, respectively. The radius of the open and solid half circles are proportional to the observed and calculated structure factors. The abbreviation r.l.u. denotes reciprocal lattice units.

Figure 2

Structure factors along fractional-order rods. Circles represent the measured data. Solid and dashed lines are calculated curves based on the homodimer model and the heterodimer model, respectively. Note that the baseline of each curve is shifted individually.

Figure 3

Structure model of the $c(4\times 4)$ structure. The dashed lines indicate the primitive unit cell. Open and solid circles represent Ga and As atoms, respectively. In the heterodimer model, the hatched atoms are As, and the mirror symmetry with respect to the $[\overline{1}10]$ and $[110]$ axes is imposed. In the homodimer model, the hatched atoms are assumed to be Ga, and the mirror symmetry with respect to the $[\overline{1}10]$ axis is lifted. The atoms up to the sixth layer were optimized in the fitting.

Figure 4

X-ray energy dispersion of the structure factors of ($H,K$) reflections. The circles are observed structure factors. The solid and dashed lines indicate the results from calculations when the Ga-As and As-As dimers are assumed, respectively.