Scattering potential evaluation with wave expansion of a vacancy complex on a Si(1 1 1) –Ag surface

We studied a scattering of the S 1 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 d I / d V images at r o o m t e m p e r a t u r e . 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 + 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 + D wave approximation derived from the phase shifts was 1.70–1.80 eV.