Study on the mechanism of platinum-assisted hydrofluoric acid
etching of SiC using density functional theory calculations
P. V. Bui,1 A. Isohashi,1 H. Kizaki,1 Y. Sano,1 K. Yamauchi,1,2 Y.
Morikawa,1,2 and K. Inagaki1
1Department
of Precision Science and Technology, Graduate School of Engineering, Osaka
University, Osaka 565-0871, Japan
2
Research Center for Ultra-Precision Science and Technology, Graduate School of
Engineering, Osaka University, Osaka 565-0871, Japan
1. Reaction pathways
We have investigated many possible pathways for the etching of SiC surfaces by HF without a Pt
catalyst21-23. We found that the indirect two-step process for the dissociative adsorption of HF at the step edge
of Si has a smaller activation barrier (1.2 eV) than the direct processes (2.0 eV) 22. In the indirect process, HF
is dissociatively adsorbed on a step edge of Si, forming a five-fold coordinated Si, and H is bonded to the
terminal O of a neighboring Si22 or the terminal O of the targeted Si21, forming H2O. This is followed by the
transfer of a proton, which breaks the Si–C back bond. The latter process has a lower activation barrier (1.2
eV) than the former (1.8 eV).
We did not study the direct processes with the use of a Pt catalyst because the activation barriers are very
high, as mentioned above. We investigated two possible pathways for the indirect processes. Initially, the HF
molecule dissociatively adsorbed on a step edge of Si, forming a five-fold coordinated Si in the metastable
state (MS). In the subsequent process, Si–C back bond breaking may occur through an H transfer from the
terminal O on the targeted Si or from a neighboring terminal O.
From the above results, we conclude that solvent H2O molecules do not play an important role in the
dissociative adsorption processes of HF on a Si-C surface. Solvent water molecules surrounding the etching
area may induce electric field on the SiC surface by polarization and affect the energy barrier heights of the
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reaction processes, but the effect should be minor. In particular, in the presence of the Pt layer, the effect of
the polarization induced by Pt is larger than that by water molecules. Therefore, the polarization induced by
water molecules can be neglected as a first calculation approximation.
We have investigated many possible positions of Pt relative to the SiC surfaces to achieve the indirect
pathway, with H being transferred from the terminal O on the targeted Si. Figure S1 shows the dependence of
the barrier heights for the first HF bond breaking and the second H transfer processes on the Pt positions. The
x0, y0, z0 model was named the z0 model in the manuscript, and it had the lowest barrier among all the
investigated models.
FIG. S1. Dependence of the barrier height on the Pt position (the z0 model is used as a reference). The
shaded and white columns represent the barrier heights of the H 2O dissociative adsorption and the proton
transfer processes, respectively.
The atomic geometries and energy profile of the reaction pathway of H transfer from a neighboring
terminal O are calculated and shown in Figs. S2 and S3, respectively. The activation barrier of the proton
transfer process is 2.0 eV, which is higher than that of H transfer from the terminal O of the targeted Si (0.6
eV). The large difference in the two pathways can be ascribed to the differences in the distance between the H
of the terminal O and the C of the Si–C back bond.
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FIG. S2. The atomic geometries of MS, transition state (TS), and final state (FS) for H transfer from a
neighboring terminal O to the C of the Si–C back bond
FIG. S3. The activation barrier of H transfer from a neighboring terminal O to the C of the Si–C back bond
2. Density of states
To confirm Pt–O bond formation, we calculated the density of states (DOS) of the two models in the MS.
The DOS of the targeted Si, the C back bond (denoted as Cbb), the terminal O, and Pt bonded with O for the
z0 and z1.5 models in the MS are shown in Fig. S4.
FIG. S4. DOS of Pt, O, Si, and C back bond (Cbb) in the MS for the (a) z0 and (b) z1.5 models. Black, red,
green, and blue lines represent Pt dzz, O, Si, and Cbb, respectively, and the shaded areas represent O pz.
These DOS are aligned along the vertical direction for easy comparison.
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3. Difference in charge density
To understand the Pt–O bond, the difference in charge densities ∆𝜌𝑑𝑖𝑓𝑓 between the MS and FS of the z0
and z1.5 models are calculated from differences in charge densities ρ of the corresponding system as
∆𝜌𝑑𝑖𝑓𝑓 = 𝜌[𝑆𝑖𝐶 − 𝐻𝐹 − 𝑃𝑡] − 𝜌[𝑆𝑖𝐶 − 𝐹] − 𝜌[𝑃𝑡 − 𝐻]
where 𝜌[𝑆𝑖𝐶 − 𝐻𝐹 − 𝑃𝑡], 𝜌[𝑆𝑖𝐶 − 𝐹], and 𝜌[𝑃𝑡 − 𝐻] are the charge densities of the total SiC–HF–Pt system,
SiC with terminal F, and Pt with terminal H models, respectively. The difference in charge densities of the z0
and z1.5 models at MS and FS are shown in Fig. S5.
FIG. S5: The difference in charge densities (isovalue of 0.009) of Pt with SiC at the (a) MS and (b)
FS of the z0 model and at the (c) MS and (d) FS of the z1.5 model. The red and blue clouds represent
the accumulation and depletion of the electron densities, respectively. Only interacting molecules
between the Pt and SiC surfaces are shown for easy interpretation.
If there is no interaction between the O and Pt (111) surfaces, the difference in charge density vanishes.
However, for the interacting O, the difference in charge density is nonzero, indicating a mutual polarization.
The difference in charge density of the Pt and O is described by accumulation (red clouds) of electron density
at the O and depletion (blue clouds) of electron density at the Pt. This difference in charge density reflects the
electron transfer from the Pt to the O. Because of the bond formation between Pt and O, the H of the terminal
OH easily transfers to the C of Si–C back bond. The difference in charge density of the Pt and the O at the
MS in the z1.5 is weaker than that in the z0 because of the longer distance separating Pt and O in the z1.5
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model compared with that in the z0 model. This difference causes the increase in the energy barrier for the
transfer of H from OH to the C of the Si-C back bond. The difference in charge density of the Pt and the O at
the FS in the z1.5 is quite similar to that in the z0 because Pt and O are separated by similar distances in the
two models.
4. Difference in charge distribution along the z-direction
Charge distribution differences along the z-direction are calculated as
∆𝜌 𝑧 = 𝜌 𝑧 [𝑆𝑖𝐶 − 𝐻𝐹 − 𝑃𝑡] − 𝜌 𝑧 [𝑆𝑖𝐶 − 𝐹] − 𝜌 𝑧 [𝑃𝑡 − 𝐻]
where 𝜌 𝑧 [𝑆𝑖𝐶 − 𝐻𝐹 − 𝑃𝑡], 𝜌 𝑧 [𝑆𝑖𝐶 − 𝐹], and 𝜌 𝑧 [𝑃𝑡 − 𝐻] are the charge densities of the total SiC–HF–Pt
system, separated SiC with terminal F, and separated Pt with terminal H models, respectively. The charge
distribution differences along the z-direction at the MS of the z0 and z1.5 models are plotted in Fig. S6.
The z-positions of the Pt bonded with the terminal O of the z0 and z1.5 models are 15.0 and 16.5 a0,
respectively. The dipole that forms between the two surfaces points from the SiC to the Pt, meaning that
electrons are transferred from the Pt to the SiC through the terminal O. In the z1.5 model, high charge
densities are located between the SiC and Pt surfaces. Moreover, in the z0 model, the charge densities
decrease because of the neutralization caused by the Pt moving nearer to the SiC surface.
FIG. S6: Charge distribution along the z-direction at the MS of the z0 and z1.5 models. The position of
Pt along the z-direction in the z1.5 model is 1.5 a0 higher than that in the z0 model.
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5. Proton transfer
In our study of the first Si–C back-bond breaking process, the HF is dissociated to H and F. The H is
adsorbed on the Pt surface, while the F is adsorbed on the targeted Si, as shown in Fig. 2. In the next step, the
H belonging to OH, which is the terminal group on the targeted Si, is transferred to the C of the Si–C backbond, leaving the Si–O–Pt bond at the FS.
After the Si–C back-bond breaking process, the H adsorbed on the Pt surface is expected to be transferred
to the terminal O, forming both F and OH terminations at the step-edge Si. This means that the OH terminal
group is reconstructed on the targeted Si. Accordingly, in the subsequent step involving the breaking of Si–C
bonds, the OH terminal group might play a similar role as that in the first Si–C back-bond breaking process.
Fig. S7. Atomic geometries of the IS, MS, and FS of the reaction of H, which is adsorbed on the Pt surface,
being transferred to the terminal O.
To evaluate the possibility of the reaction of the H, which is adsorbed on the Pt surface, being transferred
to the terminal O, we have determined the geometries of IS, MS, and FS of the reaction pathway and the
energy profile, as shown in Figs. S7 and S8, respectively. As seen in Fig. S8, the activation barrier is about
0.85 eV. Our calculations clearly indicate that the reaction can occur at room temperature.
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Fig. S8. Energy profile of the reaction of H, which is adsorbed on the Pt surface, being transferred to the
terminal O.
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