Atomic structure of the $Ag / Ge ( 111 ) - ( 3 × 3 )$ surface: From scanning tunneling microscopy observation to theoretical study

The study of metal growth on semiconductor surfaces is important because it provides direct information of interface structure necessary for determination of electronic properties in electronic devices.¹ In particular, Ag/Si(111) and its resembling interface, Ag/Ge(111), have received considerable attention, since both systems follow the Stranski–Krastanov growth mode with Ag growing epitaxially to form a $( 3 × 3 ) R 30 °$ first layer and thus are well-defined prototypical models for such studies.^2–4 The atomic structures of $Ag / Si ( 111 ) - ( 3 × 3 ) R 30 °$ and $Ag / Si ( 111 ) - ( 3 × 3 ) R 30 °$ [referred to as $Ag / Si ( 111 ) - 3$ and $Ag / Ge ( 111 ) - 3$ hereafter, respectively] have been extensively studied using various techniques, such as scanning tunneling microscopy (STM),^1,5–8 low-energy electron-diffraction (LEED),^9,10 atomic force microscopy,^11,12 x-ray diffraction,¹³ photoelectron diffraction (PED),¹⁴ photoemission spectroscopy,¹⁵ reflection high-energy positron diffraction (RHEPD),¹⁶ and theoretical studies by Monte Carlo simulations¹⁷ and the first-principles electronic state calculation.^18–21 Both the surfaces showed the strong similarity in the STM images at room temperature (RT). It was accepted by some research groups that both $Ag / Si ( 111 ) - 3$ and $Ag / Ge ( 111 ) - 3$ at RT can be explained by a honeycomb-chained-trimer (HCT) structure in which a missing-top-layer Si(111) or Ge(111) surface with a top Ag layer was arranged in a honeycomb network.²² Although the individual Ag atoms cannot be well resolved, the bright protrusion of the honeycomb pattern corresponding to the center of Ag trimers and the black hole in the center of honeycomb for the Si or Ge trimers were clearly observed. In this model, two equilateral triangles of Ag atoms sharing apexes with their adjacent neighbors are formed in one surface unit cell with the arrangement containing a mirror symmetry plane along the $[ 11 2 ¯ ]$ axis [Fig. 1(a)]. The most stable structure of the $Ag / Si ( 111 ) - 3$ surface were, however, found to be the inequivalent-triangle (IET) structure based on the first-principal calculation and STM studies at low temperatures (LTs).^6,18 In the IET model [Fig. 1(b)] for $Ag / Si ( 111 ) - 3$⁠, the Ag triangles (indicated by brown solid lines) and the topmost Si trimers (first-layer Si atoms indicated by green solid lines) are rotated by ±6° around the corner of the unit cell with respect to the HCT model. Consequently, the two Ag trimers in the unit cell become inequivalent, and the mirror symmetry plane along the $[ 11 2 ¯ ]$ axis disappears.²³ Since there are two opposite rotations, the IET structure can be classified into two domains $IET ( + )$ and IET(−), as shown in Fig. 1(b). As a result, two inequivalent Ag trimers of different sizes are formed in a unit cell. This new model has been confirmed by STM study in which the $Ag / Si ( 111 ) - 3$ surface showed a hexagonal pattern at a temperature as low as $∼ 60 K$⁠, instead of the honeycomb pattern observed at RT.^6,18 This asymmetric appearance of protrusions in the STM images has been interpreted as an atomic structure change resulting from two types of Ag triangles. Other works from the studies of angle-resolved photoemission spectroscopy,¹⁵ PED,²⁴ and RHEPD (Ref. 16) also supported the results for the IET structure, i.e., the symmetry breakdown in the honeycomb atomic configuration. The theoretical simulation suggested that the appearance of HCT structure at RT is a result of a time-averaged structure between $IET ( + )$ and IET(−) by thermal fluctuations.^11,21,23 Recently, high-resolution STM images of the $Ag / Si ( 111 ) - 3$ acquired at RT showed two different sizes in Ag triangles indicating the existence of the IET structure at both RT and LT.⁷ Moreover, the investigation of surface electronic structure by scanning tunneling spectroscopy concluded that no HCT-IET phase transition occurs between RT and LT. While there is still a fierce debate on the structure of $Ag / Si ( 111 ) - 3$ between IET and HCT model, the resembling $Ag / Ge ( 111 ) - 3$ surface has not been investigated as widely. Only the HCT structure has been observed and reported for $Ag / Ge ( 111 ) - 3$⁠.^1,5,8,9,19 In this work, to be the first time, a new structure with a hexagonal-lattice pattern which is consistent with the above discussed IET model for $Ag / Ge ( 111 ) - 3$ was proposed, based on density functional theory (DFT) calculations as well as bias-dependent STM experiments in the temperature range from 100 to 473 K. The Ge trimers not observed in the earlier STM measurements for $Ag / Ge ( 111 ) - 3$ were also revealed in the present study. Detailed atomic structure of $Ag / Ge ( 111 ) - 3$ is presented and discussed.

The experiments were conducted in a dual-chamber ultrahigh vacuum system with a base pressure below $2 × 10 − 10 Torr$ for both chambers. A detailed description of the system can be found in our previous work.^22,25 Briefly, the system was equipped with a variable-temperature STM (VT STM-Omicron Vakuum Physik) chamber and a sample preparation/surface analysis chamber equipped with LEED optics (VG, RVL-900) for long-range surface structure determination, Auger electron spectroscopy (AES) for surface elemental analysis and cleanness check, a quadruple mass spectrometer for detecting gas phase species inside the chamber, and an ion sputtering gun for surface cleaning and STM tip sharpening. A STM tip mechanically cut from a 0.3 mm diameter tungsten wire (Omega) was used in this study. All the STM images were recorded in constant current mode. Unless otherwise specified, the voltage, V, corresponds to the sample bias with respect to the tip. The STM images have been slightly filtered using fast Fourier transform to remove dominant acoustic noise, to offset small inclination, and to enhance the image contrast. Image distortion was also corrected using built-in computer software to normalize the measured lattice parameters to the reported values by other works.⁹ The sample was cooled with a liquid nitrogen flow cryostat to a sample temperature at 100 K. The sample temperature was varied from 100 to 473 K by liquid nitrogen cooling and direct resistance heating.

The Ge samples $( 2 × 10 × 0.36 mm 3 )$ used in this study were cut from a single crystal, n-type $( < 0.4 Ω cm )$ Ge(111) wafer. Before Ag deposition, the Ge(111) surface was cleaned by $Ar +$ ion bombardment (1 keV, 5 min, current $∼ 35 mA$⁠) followed by annealing to 1100 K in order to remove any contamination and to smoothen the surface. The bombardment-annealing cycles were repeated until a sharp $c ( 2 × 8 )$ LEED pattern can be observed. A home-made Ag-source evaporator was built for the deposition of Ag. The $Ag / Ge ( 111 ) - 3$ substrate was prepared by Ag deposition onto Ge(111) at RT followed by annealing at 673 K for 1 min. The Ag coverages were estimated from AES measurements and structure of the Ag/Ge(111) surfaces was confirmed by LEED.

The atomic structure and electronic density distribution of $Ag / Ge ( 111 ) - 3$ were calculated by the conventional DFT using Vienna ab initio simulation package (VASP).^26–28 The plane-wave based VASP was adopted to represent wave functions of the supercell of $Ag / Ge ( 111 ) - 3$ using generalized gradient approximation (Ref. 29) with the ultrasoft pseudopotential³⁰ and cutoff energy of 300 eV. The Brillouin-zone summation was performed with a uniform mesh of $( 6 × 6 × 1 )$ k-point grid. A repeating slab including a topmost surface unit cell was adopted for simulating the Ag/Ge(111) surface. The topmost layer with coexisting Ag trimers and Ge trimers represents the regular surface structure of the Ag/Ge(111) surface. In addition, five Ge double layers with hydrogen atoms saturating the bottom surface dangling bonds and a 13 Å thick vacuum were used to produce the substrate effects and to eliminate spurious interslab interaction, respectively. While performing geometry optimizations, all the atoms (the surface layer, and upper three Ge double layers), except the two bottom Ge double layers and the hydrogen layer, were allowed to relax until the most stable structures were obtained, where all the forces on the relaxed atoms were less than 0.01 eV/Å. The surface structures were calculated with and without the mirror symmetry constraint for the HCT and the IET, respectively, until the full relaxation was achieved.

In our previous work,²² an empty-state STM image of $Ag / Ge ( 111 ) - 3$ surface was taken at RT. The image shows the typical HCT structure^{1,4,5,8,9,19,31–33} in which six equally bright protrusions corresponding to the adsorbed Ag trimers are arranged in a honeycomb network. In this structure, the reconstruction of the first-layer Ge atoms forms triangles so that two of three broken bonds originally formed on the ideal Ge(111) surface bond to the neighboring Ge atoms, and the remaining one forms partial $π$ bonds, which also interacts with the surrounding Ag atoms. In the HCT model [Fig. 1(a)], two equilateral Ag triangles sharing apexes with their adjacent neighbors are formed in one surface unit cell, consistent with STM images. The surface unit cell of $Ag / Ge ( 111 ) - 3$ is shown by the parallelogram in Fig. 1(a). The Ge trimers [partially shown in the unit cell of Fig. 1(a)] are located at the four corners of $3 × 3$ unit cell appearing as black holes in STM image, and two Ag triangles in the unit cell appeared as two equally bright spots in the STM image. Nevertheless, an empty-state STM image (Fig. 2) at LT for one monolayer Ag on Ge(111), obtained in the present work, revealed a structure closer to the IET model for $Ag / Si ( 111 ) - 3$ [Fig. 1(b)]. There are obviously two types of protrusions in this image, one is bright (circled in white-yellow) and the other is slightly darker (circled in green). These two sets of bright and less bright spots form a characteristic IET hexagonal pattern, which was also observed in the above described LT STM measurements of $Ag / Si ( 111 ) - 3$⁠.^6,18 This feature is, however, the first STM observation for the $Ag / Ge ( 111 ) - 3$ surface. The corresponding IET model is illustrated in Fig. 1(b) in which the noticeable difference from the HCT model is resulted from a slight rotation of 8° (as discussed later) and dislocation of the top layered Ag atoms. The unit cell in Fig. 2 is outlined by a parallelogram. As compared to the HCT structure, the larger Ag trimer becomes slightly darker (green spots) while the smaller Ag trimer becomes brighter (white-yellow spots) in the STM image. Hence, the hexagonal STM image in Fig. 2 corresponds to the $IET ( + )$ structure shown in Fig. 1(b).

To achieve systematic comparison of STM images acquired at various conditions, two series of bias dependent high-resolution images $( 2.5 × 2.5 nm 2 )$ of the $Ag / Ge ( 111 ) - 3$ surface at RT [Figs. 3(a) and 3(b)] and LT [Figs. 3(c) and 3(d)] are displayed in Fig. 3. With positive bias $( + 0.36 V )$⁠, i.e., the empty-state images of $Ag / Ge ( 111 ) - 3$ [Figs. 3(a) and 3(c)], the previously reported discrepancy between a honeycomb pattern at RT and a hexagonal pattern at LT is clearly resolved. Under closer scrutiny, two types of protrusions arranged alternatively in the honeycomb ring are clearly seen in Fig. 3(a). At RT, although the empty state image in Fig. 3(a) shows a honeycomblike pattern, there are still slight distinction between the bright spot [pointed by the green arrow in Fig. 3(a)] and the less bright spots. Figures 3(b) and 3(d) were obtained with negative bias, i.e., the filled-state images of $Ag / Ge ( 111 ) - 3$⁠. Figures 3(b) and 3(d) (−0.47 V) show similar inequivalent honeycomb patterns [in this case, IET(−)] for $Ag / Ge ( 111 ) - 3$ at both RT and LT. The evolution of IET characteristics at RT with respect to different biases suggests that the image pattern of $Ag / Ge ( 111 ) - 3$ is not temperature but strongly bias dependent. This result is in close conformity with the observation of two different sized Ag triangles at RT for Ag/Si(111) system.⁷ More STM measurements taken at high surface temperatures (from RT to 473 K) indicated that the IET structure is still present even at such a high surface temperature. As an example, Fig. 4 shows a hexagonal STM image of $Ag / Ge ( 111 ) - 3$ taken at 423 K.

To facilitate a comparison between RT and LT images of $Ag / Ge ( 111 ) - 3$⁠, cross-sectional corrugation profiles taken along the green arrow through the Ag trimers in Figs. 5(a) and 5(b) are shown in Figs. 5(c) and 5(d), respectively, which were separately recorded at RT and LT at the same bias of −0.37 V. The result shows that the main difference between RT and LT line profiles is the contrast height between bright spots and dark spots for Ag trimers of $Ag / Ge ( 111 ) - 3$⁠. At LT, these two types of Ag trimers are well split with a large height difference of $∼ 24 pm$⁠, while smaller height difference of $∼ 11 pm$ is observed at RT. The distances between two adjacent Ag trimers [marked with “a” in Figs. 5(c) and 5(d)] and two alternative Ag trimers [marked with “b” in Figs. 5(c) and 5(d)] are $∼ 0.50$ and $∼ 1.31 nm$ for both RT and LT images. This result indicates that except the contrast difference, the atomic structures of $Ag / Ge ( 111 ) - 3$ surface at RT and LT are substantially identical. The best images were usually obtained within tunneling bias of ±0.5 V. Under such low bias condition, we could not see the symmetric HCT pattern from 100 to 473 K throughout this study. Therefore, we would like to conclude that the IET is a reasonable model for the surface structure of $Ag / Ge ( 111 ) - 3$⁠. The conclusion to this part is based on the similarity in STM images between $Ag / Ge ( 111 ) - 3$ and $Ag / Si ( 111 ) - 3$⁠.

The surface structure of $Ag / Ge ( 111 ) - 3$ has been studied by STM for a long time and the remarkable bright spots in the $3 × 3$ unit cell are consistently assigned to be the center of Ag trimers. One important feature that has never been detected by STM for $Ag / Ge ( 111 ) - 3$⁠, however, is the “missing” Ge trimers which contain halves of the surface units and always appear as black holes in the honeycomb pattern. This is due to the very fast decay of surface electronic density that is localized between Ag top layer and first Ge layer. Since STM only sense the tails of wave functions at the distance of a few angstrom outside the surface, it is much easier to see the Ag trimers than the Ge trimers, especially under the condition of low bias and low tunneling current. In this study, we demonstrate the successful observation of Ge trimers with the IET structure by STM on $Ag / Ge ( 111 ) - 3$⁠. Figure 6 is the STM image taken just after the image in Fig. 5(a) was finished using a similar condition (−0.47 V and 0.46 nA) but with a larger scan size $( 10 × 10 nm 2 )$⁠. It is a typical IET pattern except the noticeable spot shown in the middle of six inequivalent bright trimers as pointed out by a white arrow in the bottom-left magnified image. According to the atomic model of IET structure shown in Fig. 1(b), this center smudge must be the mysterious “missing” Ge trimers, in previous works.²² This can be confirmed by the theoretical calculation discussed in the following section [Fig. 7(b)]. Normally the observation of a special feature like Ge trimer would need a special tip. That is why this Ge trimer was not always found in most scans. During this particular scan, the tip may undergo temporary reconstruction so that a special tip state allowed us to observe the Ge trimer. Zhang and co-workers⁷ also used a special tip to visualize the Si trimers on $Ag / Si ( 111 ) - 3$⁠, and they discussed in details why the Si trimers were seen in their STM images. Their explanations can probably be applied to the present study.

To explain the experimentally found IET structure for $Ag / Ge ( 111 ) - 3$⁠, theoretical calculations were also carried out using the DFT as described in the experimental section. The optimized structure of the HCT model under a constrained mirror axis in the $[ 11 2 ¯ ]$ direction is calculated and shown schematically with the top and side views in Fig. 7(a). It has been characterized by Ag triangles in a honeycomb arrangement. The basic structural parameters of this lowest-energy HCT model are summarized in Table I, which includes the nearest-neighbor Ag–Ag distance (⁠$d Ag 1$⁠, blue triangles), the side length $( d Ag 2 )$ of the Ag triangle (the big triangle by brown lines) enclosing the Ge trimer, the nearest-neighbor Ge–Ge distance (⁠$d Ge$⁠, the triangle by green line), the value of $θ Ag$ as defined in the top view structure, the top interlayer distance between Ag and the second Ge layer $( Z Ag )$ and the distance between the first Ge layer and the second Ge layer $( Z Ge )$⁠. These data provide a complete description of the lateral positions of the atoms in the Ag top layer and in the first Ge layer.

The same optimization procedure for $Ag / Ge ( 111 ) - 3$ was carried out without the symmetry imposition and a different surface structure was obtained, As shown in Fig. 7(b), the most stable configuration, as a typical IET(−) structure, contains two inequivalent Ag triangles (marked with the red and the purple triangles in the parallelogram unit cell) with different sizes formed in a unit cell and the mirror symmetry plane along $[ 11 2 ¯ ]$ axis [Fig. 7(a)] disappears. The basic structural parameters of this IET model are also listed in Table I for comparison. Two values of $d Ag 1$ corresponding to two nearest-neighbor Ag–Ag distances in two different-sized Ag triangles were obtained. A rotational angle $( θ Ag ∼ 52 ° )$ is −8° off from the HCT $( θ Ag = 60 ° )$ structure and is almost consistent with the IET(−) model of the $Ag / Si ( 111 ) - 3$ surface [Fig. 1(b)]. Obviously, all the Ag atoms originally in the HCT unit cell execute 8° rotation around the fixed centers of the Ag triangles [Fig. 7(a)] toward the same direction. Note that one of the $d Ag 1$⁠, 2.93 Å, in the asymmetric IET structure is about the nearest-neighbor Ag–Ag distance (2.89 Å) in the face-centered cubic silver crystal. This finding indicates that the smaller Ag triangle is more stable than the Ag triangle with side length of 3.66 Å in the HCT model, and this explains why the Ag atoms will assume an IET instead of HCT structure on Ge(111) or Si(111). Compared to the STM images (Figs. 3 and 5), the smaller red triangles and the larger purple triangles in Fig. 7(b) most likely show up as the bright spots and less bright spots, respectively, in the STM images (Figs. 3 and 5). Furthermore, the solid green triangle in Fig. 7(b) corresponds to the first layer Ge triangles, which appear as black holes in the STM image (Fig. 6). Figure 8 shows the simulated filled state STM images for (a) HCT and (b) IET(−) model. The alternating bright and dark features in the IET model, corresponding to small and large Ag triangles, respectively, indeed mimic the characteristics of the measured STM images in the present work.

Earlier for the $Ag / Si ( 111 ) - 3$⁠, based on the DFT total-energy calculation, the IET model was reported to be energetically more stable than the HCT model by 0.1 eV per $3 × 3$ unit cell. We have carried out the same calculation on the HCT and IET structures for $Ag / Ge ( 111 ) - 3$⁠. The IET structure [Fig. 7(b)] was calculated to be 0.20 eV more stable than the HCT structure [Fig. 7(a)]. The calculated energetics and simulated images are consistent with the STM results that the more frequently observed image for $Ag / Ge ( 111 ) - 3$ is an IET pattern.

In conclusion, the STM results and DFT total-energy calculation for $Ag / Ge ( 111 ) - 3$ are consistent with each other, suggesting that a STM image with a hexagonal pattern in the temperature range from 100 to 473 K is the result of an IET structure. In this IET model, the two inequivalent Ag trimers in each unit cell are displaced by a rotation of 8° (6° in Si case) in the same direction from those of the HCT structure. Furthermore, we demonstrate that the Ge triangle, surrounded by six inequivalent Ag triangle spots, is precisely located at center of the hexagonal pattern by STM observation.

We gratefully acknowledge the financial support from Academia Sinica and the National Science Council of Taiwan (Contract No. NSC 97-2113-M-001-017 and NSC 96-2113-M-027-005-MY2) for this research.