Scattering potential evaluation with S+P+DS+P+D wave expansion of a vacancy complex on a Si(1 1 1) 3×3–Ag surface

We studied a scattering of the S1S1 surface state electrons of two-dimensional electron gas (2DEG) by a vacancy complex on a Si(1 1 1) 3×3–Ag surface. The interference between the incident and scattered electrons caused a standing-wave pattern around the vacancy. The standing-wave pattern was successfully observed in scanning tunneling microscope (STM) based dI/dVdI/dV images at roomroomtemperaturetemperature. We then evaluated the scattering potential of a vacancy complex with a 1.60 nm in radius. Because the vacancy was large, S, P and D waves should be considered due to centrifugal potentials with the partial wave theory. So far, the S-wave approximation and its asymptotic form have been used without examining the validity. In the present study, we confirmed the validity of the S+P+DS+P+D wave approximation and the applicable range of their asymptotic forms to fit experimental data and obtain phase shifts. The scattering potential of the S+P+DS+P+D wave approximation derived from the phase shifts was 1.70–1.80 eV.