By analyzing the equilibrium shape of vacancy islands on the Ge(001) surface we have determined the surface stress anisotropy, i.e., the difference between the compressive stress component along the substrate dimer rows and the tensile stress component perpendicular to the substrate dimer rows. In order to extract the surface stress anisotropy we have used a model recently put forward by Li et al. [Phys. Rev. Lett. 85, 1922]. The surface stress anisotropy of the clean Ge(001) surface is found to be 80 6 30 meV͞Å 2 . This value is comparable to the surface stress anisotropy of the closely related Si(001) surface. DOI: 10.1103/PhysRevLett.88.196105 PACS numbers: 68.35.Md, 68.37.Ef Among the most intriguing and frequently studied surfaces belong to the semiconductor group-IV (001) surfaces [1,2]. Because of its technological importance, the majority of studies have been devoted to the Si(001) surface rather than to the closely related Ge(001) surface. In many aspects the Ge(001) surface is very similar to the Si(001) surface. Both surfaces reconstruct to form rows of dimerized atoms, yielding a ͑2 3 1͒ surface unit mesh. The surface dimers can buckle with respect to the surface plane leading to higher-order reconstructions, such as c͑4 3 2͒ and p͑2 3 2͒. The dimerization of these surfaces in the ͑2 3 1͒, p͑2 3 2͒, or c͑4 3 2͒ reconstruction induces an anisotropic surface stress tensor: the surface is under a compressive stress along the substrate dimer row direction and under a tensile stress in a direction perpendicular to the substrate dimer rows. If the surface exhibits a slight miscut with respect to the [001] direction, single layer steps are found. The monatomic steps separate terraces with alternating ͑2 3 1͒ and ͑1 3 2͒ reconstruction. After cleaning, Ge(001) exhibits a well-ordered domain pattern consisting of ͑2 3 1͒ and c͑4 3 2͒ stripes and almost no missing dimer defects [3].The missing dimer concentration on Si(001) can be increased by ion bombardment with noble gases [4][5][6][7][8], etching [9 -13] (O 2 , H 2 , Br 2 , I 2 , etc.), or metal contamination [14-18] (Ni, Cu, Co, Ag, etc.). For sufficiently high temperatures those missing dimers order into vacancy islands. The equilibrium shape at low vacancy concentrations (,0.2 0.3 monolayers) [19] of these vacancy islands is elongated in a direction perpendicular to the substrate dimer rows. At vacancy concentrations above 0.2 0.3 monolayers the vacancy islands rotate shape and are aligned parallel to the substrate dimer rows [8]. The absence of dimerization at the bottom of the narrow vacancy islands in combination with the specific rebonding at the island edges is believed to be responsible for this shape transformation [19][20][21][22][23][24]. Ab initio calculations [20] and tight-binding total-energy calculations [21] are in perfect agreement with the experimental observations of the shape transformation. Such a shape transformation has not been observed for the Ge(001) surface. Experiments performed on Ge(001) so far have revealed that the bo...