Diffusion of excessively adsorbed hydrogen atoms on hydrogen terminated Si(100)(2×1) surface Open Access

It is essentially important to understand the diffusion process of H atoms on the Si surface not only for fundamental surface science^1–9 but also for developing semiconductor device processes.^10–19 Some examples of the latter are the chemical vapor deposition (CVD) of Si thin films^10–14 and surface cleaning^15,16 or etching^17–20 of Si by H₂ plasma at low temperatures. So far, the diffusion of H atoms on the clean or almost perfectly H-terminated Si(100)(2 × 1) surfaces has been intensively studied experimentally^1–4 and theoretically^4–7,9 as summarized in the recent review by Dürr and Höfer.⁸ The activation energies for the paths along the intra-dimer, intra-row, and inter-row of Si(100) dimerized surfaces running with a vacant site of hydrogen termination have been reported as 1.46, 1.75, and 2.4 eV, respectively. These high activation barriers are attributed to the strong covalent bond character as described in Ref. 8.

In thin film fabrication processes of amorphous and micro-crystalline Si by hot-wire CVD^10,11 or plasma-enhanced CVD^12,13 at low temperatures around 200 °C, H atoms impinging on the Si surface were reported to play crucial roles in the film quality. Moreover, in hydrogen plasma processes for Si etching,^17–20 the etching rate was reported to increase significantly with decreasing substrate temperature to about 70 °C. In these low-temperature processes, excess H atoms should apparently be present on H-terminated Si surfaces under exposure to a high H atom flux. It is also expected that the Eley–Rideal (ER) abstraction of surface H atoms by impinging H atoms efficiently produces vacant sites for H-termination.²¹ H diffusion mechanisms involving vacant sites, however, should not be dominant at low temperatures because of the high activation barrier. On the contrary, the excess H atoms that are considered to take metastable and shallow energy local minimum sites may easily hop to the neighboring sites. Excess H atoms, therefore, can play important roles in CVD or etching processes in terms of high diffusivity.

In the fundamental research, the reaction behaviors of H atoms on Si(100)(2 × 1)-H surfaces exposed to H atoms have been intensively studied to elucidate the mechanism of adsorption and desorption of H atoms on Si.^22–33 One of the most important experimental findings in these studies is that the passivation of the Si surface with the H coverage of almost one monolayer is achievable. That is to say, perfectly ordered monohydride Si(100)(2 × 1)-H surfaces have been observed after the exposure to H atoms at about 600 K^33,34 despite the high probability of ER abstraction of surface H atoms.^22–32 To understand these controversial observations, detailed studies on the abstraction and desorption kinetics of hydrogen on Si(100)(2 × 1) surfaces exposed to H atoms have been reported by many researchers.^22–32 From the uptake curves of H adsorption as a function of H exposure, several kinetic models for the perfect H-termination of Si surfaces have been proposed. To summarize briefly, most of the proposed models assume the presence of excessively adsorbed H atoms on the monohydride Si(100)(2 × 1)-H surface during the H exposure, and the dangling-bond sites induced by ER abstraction are terminated by the excess H atoms. In the hot precursor model,^22–25 the excess H atom is bound in excited vibrational states over the activation barrier for surface diffusion. In the quasi-equilibrium model,^26–28 the excess existence of di-hydride species is transiently allowed during exposure. They move around on the surface via successive isomerization reactions, and collision-induced H₂ desorption takes place upon the encounter of two di-hydrides to restore the ordered monohydride Si(100)(2 × 1)-H structure after ceasing the H exposure. As for the latter model, Kubo et al. conducted a detailed investigation on the reaction between the incident atomic H beam and the D terminated Si(100) surface and explained that the peculiar D₂ desorption, which is impossible by direct ER reactions, can occur at the adjacent double di-hydrides via thermal desorption and the abstraction mechanism.³² However, further studies are still needed on the configurations of migrating H atoms on the Si(100)(2 × 1)-H surface and related phenomena including desorption during H exposure.

In addition to these investigations, recently, an extremely fast Si surface etching by high-pressure microwave hydrogen plasma with a rate of about 38 µm/min is found at a low substrate temperature condition by our group,³⁵ which may mainly be related to the high H-atom density of the order of 10¹⁷–10¹⁸ cm⁻³ in the plasma.³⁶ In such a case, it may be supposed that the density of excessively adsorbed H atoms on the Si surface should increase in high H-flux conditions, which proceed the Si etching reaction forward despite the increasing reverse reaction by ER abstraction. Thus, the role of excess H atoms on the fully H-terminated Si surface is also important in this field.^19,20,37,38 To explain all the experimental phenomena, it seems quite important to clarify the physics of excess H atoms, such as atomistic configuration or the diffusion mobility on the monohydride Si(100)(2 × 1)-H surface during H exposure.

Very recently, the atomistic configurations of an H atom inserted into the Si(100)(2 × 1)-H surface have been investigated³⁹ in relation to the development of atomic scale devices in Si using hydrogen-based scanning probe lithography.^40,41 Several metastable configurations of adsorbed H atoms on the fully H-terminated Si(001)(2×1) surface have been determined by first-principles calculations³⁹ and compared with the observations by scanning probe microscopy.^42,43 On the other hand, the studies on the diffusion properties of excess H atoms on the H-terminated Si surface are very limited. The only report concerning the behavior of an H atom trapped in a metastable state atop of the dimer bond on the Si(100)(2 × 1) surface is that by Tok et al.⁴⁴ Therefore, in the present study, the detailed first-principles calculations have been conducted to clarify the configuration and the mobility of excessively adsorbed H atoms on the fully H-terminated Si(100)(2 × 1)-H surface.

First-principles calculations were performed by means of the “STATE” (Simulation Tool for Atom TEechnology) code.^45,46 The calculations are based on the spin polarized density functional theory (DFT) within the spin-dependent generalized gradient approximation (GGA) proposed by Perdew et al.⁴⁷ Electron–ion interactions were described by ultrasoft pseudopotentials.⁴⁸ The reaction paths and transition states were calculated by using the nudged elastic band (NEB) method and the climbing image (CI) NEB method.^49,50 Wave functions and the augmented charge density were expanded by a plane-wave basis set with the cutoff energies of 25 and 225 Ry, respectively. We employed a repeated slab model, which consists of 2 × 4 units of the H-terminated Si (100)(2 × 1) dimer with a square surface supercell, the side length of which was 15.35 Å, as depicted in Fig. 1. The surface Brillouin zone was sampled using a 2 × 2 Monkhorst–Pack mesh, and the occupation numbers are calculated using the Fermi level smearing technique. The number of slab layers has been changed from 5 to 12 with a constant vacuum height to check the thickness dependence of the calculated energies for five structures shown in Fig. 2. For each structure, the energy difference was within 0.05 eV between 5 and 8 slabs and within 0.07 eV between 5 and 12 slabs. The thickness of the vacuum region between neighboring slabs was about 7.6 Å. In this report, the number of slab layers was fixed at 5 for structural optimizations and NEB calculations. All dangling bonds of the bottom Si atoms were terminated by H atoms with the unbuckled di-hydride structure. For surface Brillouin zone sampling, the gamma k-point was used. During the optimization of structures and diffusion paths, Si atoms at the bottom layer and the terminating H atoms were fixed.

First, we have explored the metastable structures of the H-terminated Si(100)(2 × 1) dimer surface with a single excess H atom. They were obtained by optimizing the atomic structures, which were prepared by placing an excess H atom on various positions in the vicinity of a H-terminated Si dimer so as to cover all the topologically feasible structures. In the construction, Si surface atoms were fixed at their original positions on the Si(100)(2 × 1)-H surface in most cases, but for a case where the adsorbing H atom was inserted in between a Si–Si bond, the Si–Si bond was elongated by keeping the other Si–Si bond lengths the same. The obtained metastable structures and the adsorption energies are summarized in Fig. 2 and Table I. The adsorption energies recently calculated by Pavlova³⁹ for the corresponding configurations for M1 and M4 are 1.17 and 0.97 eV, respectively. These values are close to our results of 1.20 and 0.99 eV (Table I). Although the adsorption energy for M5 is 0.01 eV in our result, Pavlova showed that this configuration is not stable in a neutral supercell.³⁹ The small differences in the adsorption energies between these results may be attributed to the smaller supercell size (5 layer slab with 7.6 Å vacuum space) in our calculation than that (8 layer slab with 21 Å vacuum space) by Pavlova with the same in-plane cell size.³⁹ 

From Table I, the most stable structure is M1, which consists of SiH₂ and SiH with a weakened dimer bond [Fig. 2(a)]. The adsorption energy of H in the M1 structure is ∼1.2 eV (Table I). The M2 structure also consists of SiH₂ and SiH, but the dimer bond is not weakened and the back bond is elongated to form a five-coordinated (FC) structure [Fig. 2(b)]. It has been reported that the trigonal bipyramid structure of pentacoordinated Si anions in the SiH₄X⁻ molecule is a transition (local minimum) state for the Berry pseudorotational process.⁵¹ The metastable structure M2 in Fig. 2(b), which consists of an in-plane threefold triangle structure (formed by one central and two corner Si atoms with one corner H atom) and a twofold axial bond (Si–Si–H) perpendicular to the triangle plane, resembles the above trigonal bipyramid structure. The length of one Si–Si back bond forming the twofold axial structure becomes longer (3.24 Å) compared to the original length (2.36 Å). It is reasonable that such elongation takes place due to the formation of over saturated binding states by excess H atom adsorption.

The M3 structure includes an H atom inserted in between the dimer Si and the second-layer Si atoms [Fig. 2(c)]. The Si–Si distance is elongated from 2.36 to 3.24 Å. These elongation properties are consistent with the previous result obtained by Windus et al.⁵¹ 

In M4, the excess H binds at the second-layer Si atom, forming the FC structure similar to M2 [Fig. 2(d)]. The M5 structure includes an H atom inserted in between the dimer Si atoms [Fig. 2(e)]. The distance between the dimer Si atoms is elongated from 2.42 to 3.48 Å. Several authors have reported the values for the distance between the Si atoms in the hydrogen-bridge bonding structure (M5 in our study) in their first-principles studies.^39,44,53 Pavlova has reported 3.27 Å,³⁹ Tok et al., 3.48 Å,⁴⁴ and Ripalda et al. the value between 3.46–3.51 Å,⁵² which showed good agreement with our result. The adsorption energies of H atoms in the metastable structures shown in Table I are small compared to the ordinal Si–H bond (3.9 eV estimated from SiH₄) of the H-terminated Si(100)(2 × 1) surface. The above results seem reasonable because these adsorption structures hold unpaired electrons.

These adsorbed metastable atomic structures are categorized into three types of structures: a dimer-bond broken structure (M1), the FC structures (M2 and M4), and the H-inserted structures (M3 and M5). Although M1 and M5 (and also M2 and M3) structures are in different categories, they have configurations somewhat similar to each other. This comes from a bistability that takes place as a consequence of a competitive stabilization/destabilization between a nonlinear energy dependence of the attractive interaction between H in Si–H and the nearest Si and a linear dependence of the elastic distortion of the Si lattice.

Their experimental observation, however, might be difficult because they should disappear by diffusion and recombination with a surface dangling bond formed during H exposure. In the theoretical results obtained by Hansen and Vogl⁶ based on the empirical potential investigations, the existence of the following H adsorption sites has been suggested. One is at around a dimer bond, and the other is outside of a dimer Si atom, which corresponds to our M5 and M1 structures, respectively. In first-principles calculations by Tok et al.⁴⁴ and Ripalda et al.,⁵² a Si–H–Si structure at a dimer bond (M5) have been shown. In the recent first-principles calculations by Pavlova,³⁹ M1, M4, and M5 structures have been reported as mentioned before.

Among all the analyzed configurations, the lowest energy metastable M1 is chosen as the initial and the final structure for intra-dimer, intra-row, and inter-row diffusion paths.

Each diffusion path is expressed by a sequence of hops from one adsorption site to the other. For the intra-row diffusion, the considered path is M1 → M2 → M3 → M4 → M3′ → M2′ → M1′ as shown in Fig. 3(a). The structures M1′, M2,′ and M3′ are the mirror symmetric configurations of M1, M2, and M3, respectively, with respect to the mirror plane between the dimer bonds of M1 and M1′ [a white broken line in Fig. 3(a)]. In the inter-row migration, the considered path is M1 → M2 → M3 → M4 → M4′ → M3″ → M2″ → M1″ [Fig. 3(b)]. M1″, M2″, M3″, and M4′ structures are the mirror symmetric configurations of M1′, M2′, M3′, and M4, respectively, with respect to the mirror plane at the center of the dimer rows [a black dotted line in Fig. 3(b)]. In the intra-dimer diffusion, the path is M1 → M5 → M1‴ [Fig. 3(c)]; similarly, M1‴ is a mirror symmetric configuration of M1. To evaluate the barrier heights along the reaction paths, CI-NEB calculations were performed for all the paths mentioned above. The initial configurations from one adsorption structure to another for NEB calculations are prepared by interpolating the initial and final atomic configurations of the hops. The obtained atomic configurations of the metastable and transition states along diffusion paths and their diffusion barriers are shown in Figs. 4 and 5, respectively. It can be clearly seen in Fig. 4(a) that smooth motions of the excess H atom toward the adjacent equivalent sites are obtained for the intra-row diffusion from the M1 to M4 sites [Fig. 3(a)]. In Fig. 4(a), TS12 (TS34) is the transition state between the metastable states M1 (M3) and M2 (M4). It should be noted that if a direct transition from M2 to M4 was explored (namely, even if the M3 structure was omitted from the assumed intra-row path), we found that the M3 structure was spontaneously generated in the NEB optimization. This fact apparently shows the validity of the M3 structure as the intermediate state of the intra-row diffusion path [Figs. 4(a) and 5(a)].

The simulation results of atomic configurations and diffusion barriers along the inter-row pathway are shown in Figs. 4(b) and 5(b), respectively. Similarly, those for the intra-dimer pathway are shown in Figs. 4(c) and 5(c), respectively. The reaction barriers for intra-row, inter-row, and intra-dimer pathways turn out to be 0.54 eV at TS34, 0.74 eV at TS44′, and 0.11 eV at M5, respectively. These barrier heights are summarized and compared with the diffusion barriers on a clean Si (100)(2 × 1) surface or an H-terminated one with an H vacancy in Table II.⁷ It can be seen that the activation barriers obtained in this study are far smaller than those reported for the surface diffusion models with vacant sites without excess H atoms. Such a difference should be attributed particularly to the fact that the metastable states of the excess H atom adsorption are energetically shallow.

The above obtained results of the diffusion of excessively adsorbed H atoms may explain some aspects of the experimental findings reported so far. One of the examples is the Si etching mechanism, which involves the saturation of surface dangling bonds by excessively adsorbed H atoms as proposed by Abrefah and Olander.³⁷ These H atoms are assumed to be weakly bound and mobile and saturate Si dangling bonds as soon as they are created. The present surface diffusion model of excessively adsorbed H atoms on the H-terminated Si(100)(2 × 1) surface may be a candidate for the weakly bound H atoms assumed by Abrefah and Olander.

The other applicable example is the H adsorption induced desorption (AID) of D₂ from the deuterium-terminated Si(100)(2 × 1)-D surface.^32,53–55 This phenomenon was found during the investigation of H atom exposure to the Si(100)(2 × 1)-D surface. Impinging H atoms on the surface simply induce HD desorption via the ER reaction at temperatures lower than ∼400 K. D₂ molecules also desorb in the higher temperature range^32,53–55 by AID. Our diffusion model may be capable of explaining the D₂ desorption as described below. The desorption rate of D₂ depends on the fourth-order of D coverage on the Si(100)(2 × 1) surface, and its temperature dependence shows a similar behavior to the D₂ desorption from di-deuteride Si(100) surfaces.^32,,54 Therefore, the D₂ desorption is attributed to the thermal desorption from an adjacent double di-deuteride (SiD₂ + SiD₂) structure.^32,54 However, the SiD₂ structure cannot be formed by the spontaneous adsorption of impinging H atoms. Figure 6 schematically shows a diffusion model to form the double di-deuteride structure from two SiHD-SiD structures. Apparently, a SiHD-SiD structure is first formed in the SiD–SiD dimer site. In Fig. 6(a), two SiHD-SiD structures are located in the top and bottom of the dimer row. Then, the D atom in each SiHD structure moves to the other SiD–SiD dimer site [Fig. 6(b)]. Once the D atom moves, the formed structure and the diffusion species become SiD₂-SiD. Finally, the D atom in one of the two SiD₂-SiD structures moves to the other SiD₂-SiD to structure form the double di-deuteride (SiD₂ + SiD₂) structure [Fig. 6(c)]. So far, the diffusion model of the local Si(100)(3 × 1) structure has been proposed as a physical mechanism of the motion of double di-deuteride.^32,55 It is expected that the diffusion of the local (3 × 1) structure should have high diffusion barriers (probably more than 2 eV) because the breaking and reformation of the Si–Si dimer bond are required in the process. Compared to this process, the diffusion of excessively adsorbed H(D) atoms is simple and has low activation barriers (smaller than 1 eV). It can be said that the physical substance of the “hot atom mechanism” proposed in the early stage of AID investigation⁵² is attributed to the diffusion of excessively adsorbed hydrogen atoms, and the rate limiting step is the thermal D₂ desorption from the adjacent double di-deuteride (SiD₂ + SiD₂) structure.

We conducted the detailed first-principles calculations to clarify the diffusion properties of excess H atoms on the fully H-terminated Si surface. In order to cover all the topologically feasible surfaces, the metastable structures of the H-terminated Si(100)(2 × 1) dimer surface with a single excess H atom (M1–M5), which might hardly be experimentally observed, were first explored. In the calculation, the most stable M1 structure was chosen as the initial and the final structure for intra-dimer, intra-row, and inter-row diffusion paths. The CI-NEB method was used to evaluate the barrier heights along the considered diffusion paths. The results showed that the activation energies for the diffusion along intra-dimer, intra-row, and inter-row paths were 0.11, 0.54, and 0.74 eV, respectively, which are quite small in comparison with the common H diffusion running with a vacant site of hydrogen termination. The diffusion model of excessively adsorbed H atoms on the H-terminated Si(100)(2 × 1) surface proposed in this study can be a candidate for explaining the experimental findings concerning the hydrogen-related surface reactions.

The authors thank Dr. Takahiro Yamada of Osaka University for his valuable discussions. This work was supported by JST, CREST.

The data that support the findings of this study are available from the corresponding author upon reasonable request.