The universal building block which is an essential part of all atomic structures on (1 1 0) silicon and germanium surfaces and their vicinals is proposed by combining first-principles calculations and scanning tunneling microscopy (STM). The atomic models for the (1 1 0)−(16×2), (1 1 0)−c(8×10), (1 1 0) − (5 × 8) and (17 15 1) − (2 × 1) surface reconstructions are developed on the basis of the building block structure. The models exhibit very low surface energies and excellent agreements with bias-dependent STM images. It is shown that the Si(47 35 7) surface shares the same building block. Our study closes the long-debated pentagon structures on (1 1 0) silicon and germanium surfaces.Over the past three decades, large efforts have been made to understand the atomic and electronic structure of (1 1 0) silicon and germanium surfaces using scanning tunneling microscopy (STM) and spectroscopy, photoelectron spectroscopy and first principles calculations [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. This indicates both the complexity of the task and its high scientific relevance. One of the reasons for the persistent interest to these surfaces is their peculiar properties, such as high hole mobility in the devices fabricated on the Si(1 1 0) surface [21] and strong surface anisotropy. The second feature became especially atrractive due to the recent success in the formation of singledomain (16 × 2) reconstruction on the Si(1 1 0) surface [22,23]. This makes (1 1 0) surfaces very convenient substrates for the growth of one-dimensional objects, such as nanowires [24][25][26][27][28][29]. It is also worth noting that, among all low-index silicon and germanium surfaces, (1 0 0), (1 1 1) and (1 1 0) [ Fig. 1(a)], only the (1 1 0) structure is still not understood, and, therefore, it is of signifcant academic interest as well.The common feature of all reconstructed (1 1 0) silicon and germanium surfaces is the presence of bright spots exhibiting pentagonal or tetragonal shapes (hereafter polygons) in high-resolution STM images depending on acquisition conditions [4,11]. When the Ge(1 1 0) surface is observed at an elevated temperature (above 430 • C), the polygons are closely packed and show no long range order [8,14,30]. However, when the temperature is lowered to about 380 • C the polygons begin to line up and their density is lowered, indicating the formation of the c(8×10) reconstruction. A very long annealing at 380 • C converts the c(8 × 10) reconstruction into the (16 × 2) surface structure. Thus, the (16 × 2) reconstruction is equilibrium, while the c(8 × 10) surface structure is only a transient (metastable) structure of the Ge (1 1 0) surface. The structural transformations on the Si(1 1 0) surface are similar to those of the Ge (1 1 0) surface, but the transient structure is (5 × 8) [16]. The formation of polygons in varied experimental conditions at various temperatures is a strong indication of their exceptional stability owing to low formation energy values. Figure 1. (a) Unit stere...