Theoretical investigation of vibrational sum-frequency generation signatures of functionalized H-Si(111)

Developments toward a general approach for simulating and interpreting the sum-frequency generation signatures of functionalized surfaces are reported. This approach encompasses two steps: (1) The molecular properties (vibrational frequencies, IR and Raman quantities) are evaluated using first-principles approaches implemented in standard quantum chemistry programs, and (2) the macroscopic optical responses (second-order nonlinear optical susceptibility tensor) of the adsorbate on its substrate are determined within the three-layer model of the interface. A homemade code was written to carry out this second step, including (1) the evaluation of the Fresnel factor and (2) the determination of the molecular orientation in the laboratory frame. This approach and program allow for the generation of the SFG spectra for different combinations of molecular orientations and experimental setups, as well as the identification of the vibrational modes to facilitate their analysis. Then, the approach is illustrated in the case of a decyl chain covalently bonded to hydrogen-terminated Si(111) [≡Si-(CH₂)₉CH₃]. The simulated ppp spectrum agrees closely with experiment, whereas the agreement gets worse when parts of the chain are frozen, demonstrating that the SFG signature originates from a large part of the decyl chain. Calculations were also performed for the other sets of polarizations (sps, ssp, and pss), highlighting the fact that the spectral profile varies considerably from ppp to ssp, sps, and pss, which is attributed to the combined effects of the Fresnel factors and the structure of the π^(2),R tensor. The impact of the orientation of the alkyl chain (tilt and rotation angles) on the ppp SFG intensity was then monitored by reducing the system to an isolated decane molecule and determining the changes in the SFG spectral pattern related to the orientation of the IR dipole moment.