Smoluchowski Effect at a Sub-Å Step on Pb/Cu (111) Revealed by Field Emission Resonance Spectroscopy

The Smoluchowski effect [1], in which electrons flow from upper to lower terraces to form an electric dipole at the step, is a fundamental surface phenomenon. While confirmed for atomic steps (2–3 Å) on metals, it remains uncertain whether such charge redistribution can survive at smaller height discontinuities. Pb/Cu (111) system provides an ideal platform to explore this limit. Because the Cu (111) step height (2.1 Å) differs from Pb (111) interlayer spacing (2.86 Å), sub-Å steps (< 0.8 Å) can form on Pb films exhibiting quantum size effects (QSE) [2]. QSE induces oscillatory variations in the work function with the number of atomic Pb layers [3]. In this work, we observe the Smoluchowski effect at a 0.5-Å step between the nine-layer and eight-layer terraces using field emission resonance (FER) spectroscopy. Analysis of the FER energies using the triangular potential model reveals a distinct peak-and-dip feature in the charge density across the step from the upper (nine-layer) to the lower (eight-layer) terrace, corresponding to the positive and negative components of the electric dipole. This dipole arises from the Smoluchowski effect rather than a work-function difference, since the nine-layer terrace exhibits a higher work function than the eight-layer one.

Keywords: Smoluchowski effect, field emission resonance spectroscopy, sub Å-high step.

References

[1] R. Smoluchowski, “Anisotropy of the Electronic Work Function of Metals,” Phys. Rev. 60, 661 (1941).

[2] M. C. Yang et al., “Phase Contribution of Image Potential Empty Quantum Well States in Pb Islands on the Cu (111) Surface,” Phys. Rev. Lett. 102, 196102 (2009).

[3] C. L. Lin et al., “Work Function Oscillation of Pb Quantum Islands on Cu (111) Surface: Observation by Gundlach Oscillation,” Chin. J. Phys. 48, 855 (2010).