Atomic defects of the hydrogen-terminated Silicon(100)-2x1 surface imaged with STM and nc-AFM

The hydrogen-terminated Silicon(100)-2x1 surface (H-Si(100)-2x1) provides a promising platform for the development of atom scale devices, with recent work showing their creation through precise desorption of surface hydrogen atoms. While samples with relatively large areas of the hydrogen terminated 2x1 surface are routinely created using an in-situ methodology, surface defects are inevitably formed as well reducing the area available for patterning. Here, we present a catalog of several commonly found defects of the H-Si(100)-2x1 surface. By using a combination of scanning tunneling microscopy (STM) and non-contact atomic force microscopy (nc-AFM), we are able to extract useful information regarding the atomic and electronic structure of these defects. This allowed for the confirmation of literature assignments of several commonly found defects, as well as proposed classification of previously unreported and unassigned defects. By better understanding the structure and origin of these defects, we make the first steps toward enabling the creation of superior surfaces ultimately leading to more consistent and reliable fabrication of atom scale devices.


Introduction
Novel approaches to advance integrated circuitry beyond CMOS, including reduction in power consumption and qubit-based computing, focus on atom scale structures and their reliable fabrication 1 .
Hydrogen-terminated silicon (H-Si) surfaces are a versatile platform for the patterning and operation of atom scale devices. Such devices include qubits 2,3 and single electron transistors 4,5 made from atomically precise implanted donor atoms near the H-Si surface, and logic structures using silicon dangling bonds [6][7][8] . In many cases the structures' functional elements are comprised of few or even single atoms. At such dimensions, atomic scale defects of the surface and in the shallow subsurface region have a significant impact on device patternability and operation 9 . In order to develop suitable means to accommodate defects, whether it be by optimizing sample preparation, quantifying how defects affect device operation 9 , or by using convolutional neural networks to autonomously identify defects 10,11,12 , a comprehensive understanding of the many varieties of defects is needed.
Native silicon atoms at the unreconstructed (100) surface would extend two unsatisfied bonds into vacuum. To minimize the energy of the surface, each silicon atom bonds with a neighboring Si atom creating dimers, thus reducing the number of dangling bonds by half. Dimers extend into rows of dimers which run parallel along the surface. The study of Si(100) surface defects was one of the first applications of scanning probe microscopy 13 . The three observed species were identified as a missing silicon dimer, a pair of missing silicon dimers, and a missing pair of Si atoms on the same side of two dimers. Subsequently, the latter was re-assigned as a bonded H, OH pair from water contamination [14][15][16] .
Further insights became available by non-contact atomic force microscopy (nc-AFM), separating the electronic and structural behaviour of the Si(100) surface 17 .
The addition of hydrogen to surface silicon atoms saturates all available bonds 18 and leads to the formation of mainly three surface reconstructions. The 2x1 phase-most commonly used in hydrogen lithography due to its ease of in situ preparation of large, defect free areas 19 -has each surface Si atom in a dimer bonded to one hydrogen atom. The 1x1 phase forms when the dimer bond is broken and each surface Si atom bonds to 2 hydrogen atoms, forming a silicon dihydride (H2-Si). The 3x1 phase is a combination of the previous two, containing alternating 2x1 dimers and 1x1 dihydrides 20,21 . With continued study, it became apparent that the complexity of possible surface reconstructions and surface defects extended well beyond those initially observed. Here, we provide a comprehensive analysis of the H-terminated Si(100) surface and its structural features. Six different scanning probe imaging modes are used to confirm the atomic structure of several commonly reported defects, as well as to classify previously unknown defects. The latter includes a neutral point defect that can be found to be decorated with a single H-atom, rendering the whole structure negatively charged. Finally, we demonstrate the successful removal of the weakly bound H atom through tip manipulation. Δf(z) in bright and dark nc-AFM mode (positions indicated in (g) and (h)). The inset shows the calculated difference spectra in reference to the spectra taken between the dimer rows (blue position marker).

Results and Discussion
The variability of scanning probe imaging modes originates from the applied feedback mode, different tunneling parameters, or the functionalization of the probe tip. Figure 1 demonstrates various imaging modes for the defect-free H-Si(100)-2x1 surface. Figure 1a and 1b show a ball-and stick model of the surface reconstruction with the pairing of surface Si atoms into dimers and the termination of the residual dangling bonds with hydrogen (See Methods). For completeness, we start with the well-known STM topographies of empty and filled states (constant current imaging, sample bias as indicated, Figure   1c and 1d). Imaging both states allows for the assignment of dimer rows. Recent work has found that tip functionalization can determine the contrast sharpness and apparent atomic positions in empty state STM images of the H-Si(100) surface 22 . Three examples of this effect are displayed in Supplementary Information Figure S1, highlighting the necessity to include subtle surface features in the assignment of dimer position.
Further insights can be gained from constant height images. Figure 1e shows a constant height STM image of the surface at a sample bias which probes the onset of the conduction band (donor band) of our crystal 9,17,24 . Hydrogen-terminated silicon atoms within each dimer are identifiably without any significant convolution from bulk states. Figure 1f shows the final STM imaging method used, known as scanning tunneling hydrogen microscopy (STHM) 25 . The use of a flexible species at the apex of a metallic tip to provide enhanced contrast was first reported using CO-functionalized AFM tips to image the molecular structure of pentacene 26 . Other functionalizations of AFM tips have been explored including Cu-O tips 27,28 and Xe tips 29,30 . The use of H2 31,32 and D2 25 was the first successful demonstration of the enhanced imaging contrast using STHM. Rather than direct tip functionalization as done in AFM, STHM was routinely achieved by leaking in a background of molecular hydrogen (~10 -9 Torr) until an H2 molecule becomes trapped in the tip-sample junction. We are able to achieve STHM resolution by directly functionalizing the tip apex with hydrogen using voltage pulses over the H-Si surface, as discussed elsewhere 22,33,34 . Our ability to achieve STHM resolution using an H-functionalized tip aligns with recent theory that suggests the H2 molecule actually dissociates resulting in an H-functionalized tip 35 . In STHM imaging, the surface appears as a series of squares with each intersection correlating to a H-Si atom. The image's slight asymmetry is commonly attributed to the shape of the tip apex and the 5 location of the H atom. Figure S3 shows a variety of images of the H-Si(100)-2x1 surface acquired with a variety of flexible tips.
A true force feedback can be visualized with frequency-shift maps generated by non-contact AFM. Based on the apparent contrast of the hydrogen atoms with the surrounding surface we denote the two different modes as bright and dark contrast AFM. Previous studies have identified these two contrasts when imaging the hydrogen-terminated Si(100) 36 surface, where the dark contrast image corresponds to a Si-terminated tip 37 and the bright contrast image corresponds to an H-terminated tip 37 . Figure 1i shows the height-dependent frequency shift Δf(z) that is governed by the interaction between tip and sample at selected positions on the surface. To highlight the termination-dependent reactivity we calculate the difference in frequency shift 38   Combining all six imaging modes allows for an in-depth characterization of the most common surface features and their local environment as shown in Fig. 2. While not an exhaustive list, it features defects routinely seen when the surface is prepared using the procedure outlined in the Methods section. To categorize the defects, one could focus on functional aspects (charged vs. neutral features) 9 , or structural aspects including missing or additional atoms. Here, we categorize the defects solely on structural commonalities, based on the number of affected atoms.
First, we list features that involve only one side of a dimer. These include a missing H atom that leaves the dangling bond (DB) of the underlying Si atom exposed (Fig 2a), a subsurface vacancy (Fig. 2b), the substitution of an H atom with SiH3 (Fig. 2i), and an unidentified surface point defect (Fig. 2k). Second, defects affecting a whole dimer are: two missing H atoms creating a bare dimer (neutral, shown elsewhere 39,40 ), two additional H atoms on a dimer to create a dihydride pair (Fig. 2d), a single added H atom forming a dihydride on one side of the dimer (Fig 2e) that in turn requires the neighboring Si atom to be missing (Fig 2e), the removal of the whole dimer (two missing Si atoms) accommodated by Htermination or dimer formation in the second layer (dark or bright, Figs. 2f and 2g). Alternatively, the dimer bond could be replaced by either a SiH2 group (Fig. 2j) or an oxygen atom (siloxane bridge, Fig.   2h). Remaining larger features can be described as a combination of two or more of the smaller structures, like the 3x1 reconstruction which is a combination of dimer rows and dihydride atoms (Fig.   2c).
The most obvious deviation from the hydrogen-terminated surface are silicon DBs, well-understood unterminated silicon atoms [41][42][43] . In STM, the centre of a DB is imaged as a bright protrusion indicating the highly conductive orbital which extends into vacuum. Due to the degenerate doping of our substrate (see Methods) 6 Figure S2). Finally, AFM analysis in Figs. 2a-5 and 2a-6, presents the DB as a large negative frequency shift due to the strong interaction for both tip terminations (further details of all dark contrast images in column 5 are discussed with Figure 3). Figure 2b shows a suspected silicon vacancy (discussed in more detail in Figure 4) previously referred to as a type 2 (T2) defect 45 . Prior works have suggested this defect originates from many sources including a negatively charged As dopant 45 ,Si-vacancy hydrogen complexes 9 , and B dopants 46,47 . Various types of crystal vacancies have previously been identified using scanning probe microscopy including Ga vacancies in GaAs 48 , As vacancies in GaAs 49 , and P vacancies in InP(110) 50  A silicon adatom replacing an H atom (on top of one of the dimer atoms) will be fully saturated and form a raised SiH3 or silyl group (Fig. 2i) 51 . Larger clusters of these Si groups can subsequently bond and form islands 21,52 . The triangular shape of the defect as seen in the STM images demonstrates the tetrahedral bonding orientation at the Si, with the forth bond affixing it to the side of the dimer beneath. The raised nature of the silyl group dominates the current in constant height imaging which leads to extended distortions in STHM (Fig. 2i-4), partially due to the groups high flexibility, and gives rise to stronger frequency shifts in nc-AFM ( Fig. 2i-5,6).
Instead of bonding with the neighbouring Si atom creating a dimer bond, the Si atom could bond with 2 H atoms, whereby a dihydride is created (Fig. 2e). Although not formally reported, it has been observed in the past (such as the top right of Figure 2 in Ref. [ 53 ]). The remaining Si atom of the dimer is either absent (Fig. 2e) or also bonds with 2 H atoms creating a pair of dihydrides (Fig 2d) 20,[53][54][55] . Based on their appearance, the latter defect is commonly referred to as the "bow-tie" defect 56 or simply a dihydride.
The concentration of dihydrides can be controlled by the annealing temperature during sample preparation 18,57 .  The bridging oxygen in Figure 2h forms a siloxane dimer (see structure in Fig 2h-7), sometimes described as a split dimer 64,65 or incorrectly identified as a dihydride 2,66 . STM imaging reveals a very localized defect with only subtle impact on neighboring dimers (Figs. 2h-1,2,3).  Fig. 2h-6). A defect of similar appearance was found on chlorine-terminated silicon 67 , and was associated with water contamination in the vacuum chamber (observed as H and OH bonded to the unterminated surface 15,68,69 ) where a mild annealing followed by halogen termination allowed the oxygen to enter into the dimer bond. The authors comment that they expect this feature to also be present on hydrogen-terminated silicon.  The two raised Si species in Figures 3m,n,o,p present an extra challenge to analyze because they must be imaged with a larger tip-sample separation to prevent tip-defect contact. As a result, the frequency shift of the surface is of smaller magnitude compared to the defect signal (compare blue and grey line traces in Figure 3n,p). Despite Figure 3n,p showing the defect as a mostly featureless peak in both cases, the position of the defect with respect to the lattice can still be extracted; comparing the two panels it can be confirmed that the SiH3 originates above one side of a dimer while the SiH2 is centered between the two atoms of a dimer. Additionally, the singly bonded SiH3 is a narrower peak (blue cross section of Figure 3n) than the doubly bonded SiH2 one (blue line Figure 3p), perhaps due to the extra degrees of freedom allowing the defect to bend more upon AFM examination.
The neutral point defect in Figure 3q,r displays as a slight decrease in the minima above the defect, suggesting a similarly coordinated substitutional species of enhanced electronegativity compared to a H-Si atom.
Lastly, a lone DB is shown in Figure 3s,t. As expected, the DB shows up as a localized feature of enhanced reactivity when compared to the surface. This reactivity extends spatially away from the DB location, generating a broad minimum that eclipses the signal from neighboring lattice sites.
A more in-depth analysis of the silicon vacancy defect from Figure 2b is now given. While all of the other examined defects are observed with the same consistent appearance, the Si vacancy has been found to vary. Figure 4 Figure 4c, it appears that no atom is present at the defect lattice site. This is supported through examination of the AFM line cuts of this defect in Figure 4q,r (and Figure S4). A more negative frequency shift minimum is seen in the remaining atom of the dimer, with a shift of the minimum toward the site of the vacancy as shown in 4r. The vacancy itself shows a smaller minimum above its location (blue curve in 4r), with the magnitude of this minimum comparable to measurements over equivalent second layer Si atoms as would be measured in a cross section taken between dimers (burgundy line in 4q). This observation suggests there is no atom present, leading to a classification of this species as a Si vacancy 70,71 . These are predicted to exist as negative charge centers due to the degenerate doping of the crystal (See Methods). Figure 4e,h shows another silicon vacancy (labelled II), but now positioned at a different lattice site one atomic layer below the surface (as referenced to the Si atoms of the dimers). While the broad features of the STM probing in Figure 4e-g are similar, it can be seen that the defect no longer appears to affect a single atomic site, but rather reduces the apparent height of two adjacent dimers as shown in 4g. While the subsurface defect cannot be directly probed, the similarities it shares with Figure 4a strongly supports its assignment as a Si vacancy below the surface (See the ball and stick model in Figure 4t). This is further corroborated by line-cut analysis in    Our assignment of the neutral point defect as a hydrogen trap is motivated by two observations, the first indication being the change in contrast in the AFM panel of Figure 5h. As discussed earlier, dark contrast AFM is from a silicon-terminated apex and bright contrast from a hydrogen-terminated one.
The change between these two contrasts at the middle of the frame suggests the tip has potentially picked up a hydrogen atom from the defect, changing the AFM imaging character. The second observation supporting a hydrogen trap is the similarity of the negative state of the defect to physisorbed hydrogen atoms on the surface. Prior work reported that hydrogen atoms on the surface are negative under degenerate n-type doping 9 , while another showed they could be picked up from the surface with filled-states STM imaging 33 . Their similarity in appearance can also be observed in Figure S7.
This evidence, together with the fact our sample preparation methodology produces many hydrogen radicals that can penetrate the surface, supports the idea that the neutral point defect behaves as a hydrogen trap. It has been reported in the literature that boron, when added to silicon, can behave as a hydrogen trap [72][73][74][75] . However, the areal concentration these neutral point defects are observed at (0.8-7.6 defects/10 nm 2 ) is higher than would be expected for our arsenic doping level, or for contaminant boron from the commercial wafer processing 45 . Further investigation into the origin of this defect will be required for a conclusive determination. The arrows in the lower left indicate the scan direction, with contrast changes in the scan indicating a removal event has occurred. (c,f,i) Empty states STM images of the same frames as (a,d,g), but after the H removal. The point defects no longer display charge-induced band-bending around their location. The white box in (i) indicates the size of the scan frame in (h). Scale bars are 1 nm.

Conclusion
In this work we have created a comprehensive list of commonly found defects on the H-Si(100)-2x1 surface analyzed using a combination of several STM and nc-AFM imaging modes. Through this analysis we are able to extract information about the electronic states of the defects, as well as probe their atomic structure using differently reactive AFM tips. As a result, we were able to confirm the classification of several surface defects, as well as more confidently identify the previously reported T2 45 defect as having character more consistent with a silicon vacancy. Finally, we examined the previously unreported neutral point defect, observing their transition from a negatively charged species through the proposed liberation of an atomic hydrogen from the defect site. While the origin of the defect remains unknown at this time, these results provide a foundation for future potential classification.
It is expected that other sample termination methods, Si wafers, and vacuum systems could potentially lead to additional defects not reported here. While this may mean this is not an exhaustive list, our analysis provides critical insight into the nature of many commonly observed defects. As many groups are now exploring fabrication of larger and more sophisticated atom-scale devices on this substrate, defects interrupting the needed large patterning areas are quickly becoming a limiting factor. Through this now enhanced understanding of the nature of the most common defects, we enable informed refinement of standard H-Si wafer preparation methods, leading to a more reliable platform for the creation of these devices.

Methods
Experiments were performed using an Omicron LT STM and an Omicron qPlus LT AFM 76,77 system operating at 4.5 K and ultrahigh vacuum (3 x 10 -11 Torr). STM tips were electrochemically etched from polycrystalline tungsten wire, resistively heated, and field evaporated to clean and sharpen the apex using a field ion microscope (FIM) 78 . AFM tips used the third-generation Giessibl tuning forks with a FIB mounted tungsten wire (f0 ~ 28 kHz, Q-factor ~ 16k-22k) 79 . The tip was cleaned and sharpened in vacuum using a FIM 78 . In situ tip conditioning was done by executing controlled contact on a hydrogendesorbed patch of Silicon 80,81 . Bright contrast AFM tips were formed with controlled contact on both desorbed and H-terminated portions of the surface, while dark contrast AFM tips were formed using only desorbed patches. STHM tips were achieved by creating DBs via tip pulsing until the tip contrast changed to that shown in Fig S1c. Samples used were highly arsenic-doped (~1.5 x 10 19 atoms/cm 3 ) Si(100). Samples were degassed at 600 °C overnight followed by flash annealing at 1250°C. The samples were then terminated with hydrogen by exposing them to molecular hydrogen (10 -6 Torr) while the Si sample was held at 330 °C for 2 minutes. The molecular hydrogen was cracked using a tungsten filament held at 1600 °C 82 .
Image and data acquisition were done using a Nanonis SPM controller and software, imaging parameters for each of the 6 modes are described in the text. The height setpoint was taken as the tipsample separation over a H-Si atom with an imaging bias of -1.8V and a current setpoint of 50 pA. The exact magnitude of the Δf(Z) spectroscopy changed between tip shaping events but the general shape and behavior for bright and dark contrast remained consistent throughout multiple tips and tip terminations.
The defect free H-Si Ball and Stick model was the same as in 80 . Defects were manually inserted using Avogadro 83,84 . The geometry of the defect atoms within the lattice were positioned using a Merck Molecular force field (MMFF94) 85 using steepest descent and a convergence of 10e-7. Images of the lattice were colorized and rendered using Mercury 86 .