Model of DED mechanism and NEB calculations

As described above, the diffusion of hydrogen substitutional sites involves the concerted motion of H and nearest Cl atoms. Si-Cl and Si-H bonds have large bond energies of 3.956 eV and 3.301 eV, respectively. If the concerted motion of the H and Cl atoms involve the simultaneous breaking of Si-Cl and Si-H bonds, then much energy will be clearly required. However, the diffusion barrier is similar to those of simple H-adatom diffusion.

Accordingly, a key question that is raised by the DED model is as follows: if two surface atoms with strong chemical bonds with a substrate are responsible for H diffusion, then how do they organize themselves into a low-energy state during the process? Notably H-Cl has a large bond energy of 4.444 eV. Hence, a natural conjecture is that two nearby intra-dimer or intra-row H and Cl atoms form an HCl-like molecular configuration as an intermediate product, and then switch positions during rebonding.

In an effort to confirm the existence of an HCl molecule as an intermediate state, the NEB method built in the VASP code was employed; the NEB technique has also been applied to determine activation energies of hopping and exchange-diffusion on surfaces. In this calculation, a “band” of intermediate states is produced by simple interpolation along an assumed reaction path that connects the initial state (with H and Cl on a single dimer or on a single side of two adjacent dimers in the same dimer row) with the final state (in which the positions of H and Cl are exchanged). Then, the atomic configurations in the different geometries are iteratively optimized using only ionic-force components that are perpendicular to the hypertangent.

Atomic configurations after NEB minimization, as presented partially in Fig. 4.4, show that H and Cl atoms move toward their final state positions approximately in the plane defined by <100> and along the line that connects initial H and Cl positions. During the transition, the relevant dimer bonds remain intact; no bridge-bonded state, such as that associated with Cl adatom diffusion, is obtained. In the image chain, the Cl atom appears to move along the outer circle, while H remains closer to the surface. The length of the bond between the H and Cl atoms is 1.32 Å, which is close to that (1.27 Å) in an HCl molecule.

The heights of the activation energy barriers obtained by comparing the initial and transition states are large (~2.860 eV) for both intra-dimer and intra-row DED, as presented

away from the surface and to form a H-Cl bond, suggesting that both Si-Cl and Si-H bonds are completely broken and HCl molecules are present. Although the experimental value may be imprecise, the heights of the energy barriers (~2.8 eV) in the LDA-DFT calculations fall outside the range of experimental uncertainty. Other modeling approaches, such as generalized gradient approximation (GGA) with spin and tight binding, have been demonstrated to yield values of energy barriers that are closer to the experimental results.

The interaction between atoms, molecules or surfaces at large separations is well known commonly to be incorrectly described in LDA or GGA, which exclude long-range interactions, such as van der Waals (vdW) forces.[58] Consider, for example, the physisorption of HCl on ice; the physisorption energy is around 0.3 ─ 0.5 eV.[59] These additional corrections and perhaps the use of more realistic image chains in NEB minimization can yield calculated values that are closer to experimental values.

Notably, sharp STM tips can yield electric fields that are sufficiently strong to break chemical bonds.[60] Additionally, as noted by Boland, at positive sample bias, the interaction of the Si-Cl dipole on Cl/Si(100) with the field effectively reduces the depth of the potential energy well at a dangling bond site, effectively reducing the barrier to Cl adatom diffusion on a clean Si(100) surface.[61] This decrease should be particularly important for sharper tips, which generate stronger fields and field gradients. Even though negative sample bias was applied during observation and small tunneling currents were used to eliminate the aforementioned complications, the possibility that a sharp STM tip may have a partial role in hydrogen diffusion cannot be excluded completely. In view of this possibility, an alternative explanation of the STM observations that is based on the assumption that the electric field (and current) is not strong enough to break the Si-H or Si-Cl bond, but is strong enough to lower the energy barriers of DED through intra- or inter-dimer channels should be considered.

Figure 4.4 Calculated barriers of three direct exchange diffusion channels as labeled.

Selective atomic geometries for intradimer diffusion show that the transition-state atomic configuration involves an HCl molecule. Silicon atoms are shown in navy blue; hydrogen atoms are shown in red; chlorine atoms are shown in green.

4.4 Conclusion

Although the concept of DED is known, DED has not experimentally observed to the best of the authors’ knowledge. Herein, a detailed atomic view of the diffusion of hydrogen substitution sites within the top chlorine layer on a Cl/Si(100)- 2×1 surface was presented.

Atomic-resolution STM images show that hydrogen diffusion occurs via direct positional exchange of an H-site and a neighboring Cl-site in the same row. Analysis of time-lapsed movies indicates a thermally activated process with a barrier of E_a = 1.29 eV and an apparent prefactor ν0 of 1.31 ×10⁹ s^-1 for intra-row diffusion and Ea = 1.17 eV; ν0 = 6.64

×10⁷ s^-1 for intra-dimer diffusion. The energy barriers are substantially lower than expected, perhaps because the DED process involves an intermediate HCl molecular state. Energy calculations based on density functional theory verify the existence of this transition state molecule, but yield higher barriers of around 2.86 eV. The discrepancy in activation energy suggests that corrections such as dispersive forces are required in the calculation.

Alternatively, a multiple-step process or the electric field under an STM tip may be involved in the exchange of positions. Our findingssuggest the need for further study of the apparent DED process and open the way to further experimental investigations and theoretical calculations of the diffusion processes.

Chapter 5 Repulsive interactions of adsorbed Cl atoms in HCl