當對掃描穿隧顯微鏡 (STM) 探針施加高負偏壓時，會發生場發射共振 (FER)現象。雖然FER源自真空中的量子態，但其特徵如能量與線寬可反映表面與探針的物理性質。 我們於兩種情況下在高定向熱解石墨 (HOPG) 和 銀(111) 表面 觀察FER 中的波函數耗散 (WFD)：（1）相同的電流和FER 數； (2) 探針尖銳度相同但電流不同。WFD可透過量測FER能量與線寬得知。在第一情況下，我們觀察到對應於 WFD 的衰減率在 HOPG 表面上表現出比在銀(111) 表面上更大的變化。於第二種情況下，衰減率在銀(111) 表面幾乎不隨 FER 電場變化；相比之下，衰減率在 HOPG 表面會隨 FER 電場增強而線性增加。這些顯著差異可歸因於以下因素：探針透過靜電力引起的吸引變形在 HOPG 表面上比在 Ag(111) 表面上顯著得多，並且變形的 HOPG 頂層具有與單層石墨烯相似的獨特電子結構。
掃描穿隧顯微鏡的探針前端是由半徑為數十奈米的基底和具有原子級尖銳度的突出結構組成。利用FER能量可以將探針的基部半徑和尖銳度予以特徵化。我們從第一階到第六階的 FER 能量中導出了兩個量值，它們與探針的尖銳度和基底半徑有關。利用這兩個量值我們發現探針的基底半徑可以保持不變而只有尖銳度變化；探針也可以具有相同的銳度但基底半徑不同。基底半徑可以顯著影響 FER 在 銀(100) 表面上的峰強度，但在銀(111) 表面上FER的峰強度並不受基底半徑影響。這種差異是由於銀(100)表面的表面電偶極層和量子捕捉效應大於其在銀(111)表面。

Field emission resonance (FER) occurs when a high negative bias voltage is applied to the scanning tunneling microscopy (STM) tip. Although FER originates from the quantized states in the vacuum junction, its characteristics such as energies and linewidths can reflect the physical properties of the surface and the tip. The wave function dissipation (WFD) in FER has been observed by measuring FER energies and linewidth on the highly oriented pyrolytic graphite (HOPG) and Ag(111) surfaces under two conditions: (1) the same current and FER number; and (2) the same tip structure but different currents. Under the first condition, we observed that the decay rate corresponding to the WFD exhibited a larger variation on the HOPG surface than it did on the Ag(111) surface. Under the second condition, the decay rate was nearly independent of the FER electric field for the Ag(111) surface; by contrast, it was linearly proportional to the FER electric field for the HOPG surface. These remarkable differences can be attributed to the factors that the tip-induced attractive deformation caused by the electrostatic force was considerably more prominent on the HOPG surface than on the Ag(111) surface and that the deformed HOPG top layer had a unique electronic structure similar to that of single-layer graphene.
The apex structure of an STM tip consists of a base with a radius of tens of nanometers and a protrusion with atomic-scale sharpness. We characterized tip base radius and sharpness on the basis of FER energies. We derived two quantities from the first- through sixth-order FER energies, which were related to tip sharpness and base radius. The base radius can remain unchanged while the sharpness varies, and tips can have identical sharpness but different base radii. Base radius can markedly affect the peak intensities of FER on an Ag(100) surface but not those of FER on an Ag(111) surface. This difference results from the surface dipole layer and quantum trapping effect on the Ag(100) surface are greater than those on the Ag(111) surface.

1. Erwin W. Müller, Die Abhängigkeit der Feldelektronenemission von
der Austrittsarbeit, Zeitschrift für Physik 102, 734 (1936).
2. L. D. Landau and E. M. Lifshits. Quantum mechanics: non-
relativistic theory, Butterworth-Heinemann (1981).
3. K. H. Gundlach, Zur berechnung des tunnelstroms durch eine
trapezförmige potentialstufe, Solid-State Electronics 9, 949
(1966).
4. G. Lewicki and J. Maserjian, Oscillations in MOS tunneling,
Journal of Applied Physics 46, 3032 (1975).
5. G. Binnig, H. Rohrer, Ch. Gerber, and E. Weibel, Surface Studies
by Scanning Tunneling Microscopy, Physical Review Letters 49, 57
(1982).
6. G. Binnig, K. H. Frank, H. Fuchs, N. Garcia, B. Reihl, H. Rohrer,
F. Salvan, and A. R. Williams, Tunneling spectroscopy and inverse
photoemission - image and field states, Physical Review Letters
55, 991 (1985).
7. R. S. Becker, J. A. Golovchenko, and B. S. Swartzentruber,
Electron interferometry at crystal-surfaces, Physical Review
Letters 55, 987 (1985).
8. K. Bobrov, A. J. Mayne, and G. Dujardin, Atomic-scale imaging of
insulating diamond through resonant electron injection, Nature
413, 616 (2001).
9. Shuyi Liu, Martin Wolf, and Takashi Kumagai, Plasmon-Assisted
Resonant Electron Tunneling in a Scanning Tunneling Microscope
Junction, Physical Review Letters 121, 226802 (2018).
10. Prabhava S. N. Barimar, Borislav Naydenov, Jing Li, and John J.
Boland, Spreading resistance at the nano-scale studied by scanning
tunneling and field emission spectroscopy, Applied Physics Letters
110, 263111 (2015).
11. J. H. Coombs, J. K. Gimzewski, B. Reihl, J. K. Sass, and R. R.
Schlittler, Photon emission experiments with the scanning
tunneling microscope, Journal of Microscopy 152, 325 (1988).
12. Jesús Martínez-Blanco and Stefan Fölsch, Light emission from
Ag(111) driven by inelastic tunneling in the field emission
regime, Journal of Physics: Condensed Matter, 27, 255008 (2015).
13. Christopher C Leon, Anna Rosławska, Abhishek Grewal, Olle
Gunnarsson, Klaus Kuhnke, and Klaus Kern, Photon superbunching
from a generic tunnel junction, Science Advances 5, eaav4986
(2019).
14. K. Schouteden and C. Van Haesendonck, Quantum confinement of hot
image potential state electrons, Physical Review Letters 103,
266805 (2009).
15. S. Stepanow, A. Mugarza, G. Ceballos, P. Gambardella, I.
Aldazabal, A. G. Borisov, and A. Arnau, Localization, splitting,
and mixing of field emission resonances induced by alkali metal
clusters on Cu(100), Physical Review B 83, 115101 (2011).
16. Fabian Craes, Sven Runte, Jürgen Klinkhammer, Marko Kralj, Thomas
Michely, and Carsten Busse, Mapping Image Potential States on
Graphene Quantum Dots, Physical Review Letters 111, 056804 (2013).
17. A. Crottini, D. Cvetko, L. Floreano, R. Gotter, A. Morgante, and
F. Tommasini, Step Height Oscillations during Layer-by-Layer
Growth of Pb on Ge(001), Physical Review Letters 79, 1527 (1997).
18. Yan-Feng Zhang, Jin-Feng Jia, Tie-Zhu Han, Zhe Tang, Quan-Tong
Shen, Yang Guo, Z. Q. Qiu, and Qi-Kun Xue, Band Structure and
Oscillatory Electron-Phonon Coupling of Pb Thin Films Determined
by Atomic-Layer-Resolved Quantum-Well States, Physical Review
Letters 95, 096802 (2005).
19. A. Mans, J. H. Dil, A. R. H. F. Ettema, and H. H. Weitering,
Quantum electronic stability and spectroscopy of ultrathin Pb
films on Si (111)7 × 7, Physical Review B 66, 195410 (2002).
20. R. K. Kawakami, E. Rotenberg, Hyuk J. Choi, Ernesto J. Escorcia-
Aparicio, M. O. Bowen, J. H. Wolfe, E. Arenholz, Z. D. Zhang, N.
V. Smith, and Z. Q. Qiu, Quantum-well states in copper thin films,
Nature 398, 132 (1999).
21. C. Pauly, M. Grob, M. Pezzotta, M. Pratzer, and M. Morgenstern,
Gundlach oscillations and Coulomb blockade of Co nanoislands on
MgO/Mo(100) investigated by scanning tunneling spectroscopy at 300
K, Physical Review B 81, 125446 (2010).
22. Silvia Schintke, Stéphane Messerli, Marina Pivetta, François
Patthey, Laurent Libioulle, Massimiliano Stengel, Alessandro De
Vita, and Wolf-Dieter Schneider, Insulator at the Ultrathin Limit:
MgO on Ag(001), Physical Review Letters 87, 276801 (2001).
23. P. Wahl, M. A. Schneider, L. Diekhöner, R. Vogelgesang, and K.
Kern, Quantum Coherence of Image-Potential States, Physical Review
Letters 91, 106802 (2003).
24. J. I. Pascual, C. Corriol, G. Ceballos, I. Aldazabal, H.-P. Rust,
K. Horn, J. M. Pitarke, P. M. Echenique, and A. Arnau, Role of the
electric field in surface electron dynamics above the vacuum
level, Physical Review B 75, 165326 (2007).
25. C. L. Lin, S. M. Lu, W. B. Su, H. T. Shih, B. F. Wu, Y. D. Yao, C.
S. Chang, and T. T. Tsong, Manifestation of Work Function
Difference in High Order Gundlach Oscillation, Physical Review
Letters 99, 216103 (2007).
26. Hsu-Sheng Huang, Wen-Yuan Chan, Wei-Bin Su, Germar Hoffmann, and
Chia-Seng Chang, Measurement of work function difference between
Pb/Si(111) and Pb/Ge/Si(111) by high-order Gundlach oscillation,
Journal of Applied Physics 114, 214308 (2013).
27. Fabian Schulz, Robert Drost, Sampsa K. Hämäläinen, Thomas
Demonchaux, Ari P. Seitsonen, and Peter Liljeroth, Epitaxial
hexagonal boron nitride on Ir(111): A work function template,
Physical Review B 89, 235429 (2014).
28. Zhe Li, Hsin-Yi Tiffany Chen, Koen Schouteden, Ewald Janssens,
Chris Van Haesendonck, Peter Lievens, and Gianfranco Pacchioni,
Spontaneous doping of two-dimensional NaCl films with Cr atoms:
aggregation and electronic structure, Nanoscale 7, 2366 (2015).
29. Koen Schouteden, Behnam Amin-Ahmadi, Zhe Li, Dmitry Muzychenko,
Dominique Schryvers, and Chris Van Haesendonck, Electronically
decoupled stacking fault tetrahedra embedded in Au(111) films,
Nature Communications 7, 14001 (2016).
30. Christopher Gutiérrez, Lola Brown, Cheol-Joo Kim, Jiwoong Park,
and Abhay N. Pasupathy, Klein tunnelling and electron trapping in
nanometre-scale graphene quantum dots, Nature Physics 12, 1069
(2016).
31. Qiang Zhang, Jin Yu, Philipp Ebert, Chendong Zhang, Chi-Ruei Pan,
Mei-Yin Chou, Chih-Kang Shih, Changgan Zeng, and Shengjun Yuan,
Tuning Band Gap and Work Function Modulations in Monolayer
hBN/Cu(111) Heterostructures with Moiré Patterns, ACS Nano 12, 9,
9355 (2018).
32. Zhichao Huang, Zhen Xu, Junyi Zhou, Haoran Chen, Wenhui Rong,
Yuxuan Lin, Xiaojie Wen, Hao Zhu, and Kai Wu, Local work function
measurements of thin oxide films on metal substrates, Journal of
Physical Chemistry C 123, 17823 (2019).
33. Joshua Neilson, Harutiun Chinkezian, Himanshu Phirke, Alexander
Osei-Twumasi, Yanbang Li, Carlos Chichiri, Jongweon Cho, Krisztián
Palotás, Liangbing Gan, Simon J. Garrett, Simon J. Garrett, Kah
Chun Lau, and Li Gao, Nitrogen-Doped Graphene on Copper: Edge-
Guided Doping Process and Doping-Induced Variation of Local Work
Function, The Journal of Physical Chemistry C 123, 8802 (2019).
34. Bogdana Borca, Carolien Castenmiller, Martina Tsvetanova, Kai
Sotthewes, Alexander N Rudenko, and Harold J W Zandvliet, Image
potential states of germanene, 2D Materials 7, 035021 (2020).
35. K. Bobrov, L. Soukiassian, A. J. Mayne, G. Dujardin, and A.
Hoffman, Resonant electron injection as an atomic-scale tool for
surface studies, Physical Review B 66, 195403 (2002).
36. Emile D. L. Rienks, Niklas Nilius, Hans-Peter Rust, and Hans-
Joachim Freund, Surface potential of a polar oxide film: FeO on
Pt(111), Physical Review B 71, 241404 (R) (2005).
37. Keisuke Sagisaka and Daisuke Fujita, Unusual mosaic image of the
Si(111)−(7×7) surface coinciding with field emission resonance in
scanning tunneling microscopy, Physical Review B 77, 205301
(2008).
38. W. B. Su, S. M. Lu, C. L. Lin, H. T. Shih, C. L. Jiang, C. S.
Chang, and T. T. Tsong, Interplay between transmission background
and Gundlach oscillation in scanning tunneling spectroscopy,
Physical Review B 75, 195406 (2007).
39. H. Yang, G. Baffou, A. J. Mayne, G. Comtet, G. Dujardin, and Y.
Kuk, Topology and electron scattering properties of the electronic
interfaces in epitaxial graphene probed by resonant tunneling
spectroscopy, Physical Review B 78, 041408(R) (2008).
40. Wei-Bin Su, Chun-Liang Lin, Wen-Yuan Chan, Shin-Ming Lu, and Chia-
Seng Chang, Field enhancement factors and self-focus functions
manifesting in field emission resonances in scanning tunneling
microscopy, Nanotechnology 27, 175705 (2016).
41. Shin-Ming Lu, Wen-Yuan Chan, Wei-Bin Su, Woei Wu Pai, Hsiang-Lin
Liu, and Chia-Seng Chang, Characterization of external potential
for field emission resonances and its applications on nanometer-
scale measurements, New Journal of Physics 20, 043014 (2018).
42. A. Kubetzka, M. Bode, and R. Wiesendanger, Spin-polarized scanning
tunneling microscopy in field emission mode, Applied Physics
Letters 91, 012508 (2007).
43. W. B. Su, S. M. Lu, H. T. Shih, C. L. Jiang, C. S. Chang, and Tien
T. Tsong, Manifestation of the quantum size effect in transmission
resonance, Journal of Physics: Condensed Matter 18, 6299 (2006).
44. P. R. Wallace, The band theory of graphite, Physical Review 71,
622 (1947).
45. David Tománek and Steven G. Louie, First-principles calculation of
highly asymmetric structure in scanning-tunneling-microscopy
images of graphite, Physical Review B 37, 8327 (1988).
46. Yongfeng Wang, Yingchun Ye, and Kai Wu, Simultaneous observation
of the triangular and honeycomb structures on highly oriented
pyrolytic graphite at room temperature: An STM study, Surface
Science 600, 729-734 (2006).
47. E. Cisternas, F. Stavale, M. Flores, C. Achete, and P. Vargas,
First-principles calculation and scanning tunneling microscopy
study of highly oriented pyrolytic graphite (0001), Physical
Review B 79, 205431 (2009).
48. J. Tersoff and N. D. Lang, Tip-dependent corrugation of graphite
in scanning tunneling microscopy, Physical Review Letters 65, 1132
(1990).
49. O. Marti, Gerd Binnig, Heinrich Rohrer, and H. Salemink, Low-
temperature scanning tunneling microscope, Surface Science 181,
230-234 (1987).
50. H. W. M. Salemink, Inder P. Batra, Heinrich Rohrer, E. stole, and
E. Weibel, Topography of defects at atomic resolution using
scanning tunneling microscopy, Surface Science 181, 139 (1987).
51. J. M. Soler, A. M. Baro, N. Garcia, and Heinrich Rohrer,
Interatomic Forces in Scanning Tunneling Microscopy: Giant
Corrugations of the Graphite Surface, Physical Review Letters 57,
444 (1986).
52. Inder P. Batra, N. García, Heinrich Rohrer, H. Salemink, E. Stoll,
and S. Ciraci, A study of graphite surface with stm and electronic
structure calculations, Surface Science 181, 126 (1987).
53. S. R. Snyder, W. W. Gerberich, and H. S. White, Scanning-
tunneling-microscopy study of tip-induced transitions of
dislocation-network structures on the surface of highly oriented
pyrolytic graphite, Physical Review B 47, 10823 (1993).
54. Hong Seng Wong, Colm Durkan, and Natarajan Chandrasekhar,
Tailoring the Local Interaction between Graphene Layers in
Graphite at the Atomic Scale and Above Using Scanning Tunneling
Microscopy, ACS Nano 3, 3455 (2009).
55. Wen-Yuan Chan, Shin-Ming Lu, Wei-Bin Su, Chun-Chieh Liao, Germar
Hoffmann, Tsong-Ru Tsai, and Chia-Seng Chang, Sharpness-induced
energy shifts of quantum well states in Pb islands on Cu(111),
Nanotechnology 28, 095706 (2017).
56. Wei-Bin Su, Shin-Ming Lu, Horng-Tay Jeng, Wen-Yuan Chan, Ho-Hsiang
Chang, Woei Wu Pai, Hsiang-Lin Liu, and Chia-Seng Chang, Observing
quantum trapping on MoS2 through the lifetimes of resonant
electrons: revealing the Pauli exclusion principle, Nanoscale
Advances 2, 5848 (2020).
57. Wei-Bin Su, Shin-Ming Lu, Ho-Hsiang Chang, Horng-Tay Jeng, Wen-
Yuan Chan, Pei-Cheng Jiang, Kung-Hsuan Lin, and Chia-Seng Chang,
Impact of band structure on wave function dissipation in field
emission resonance, Physical Review B 105, 195411 (2022).
58. G. Binnig, H. Rohrer, C. Gerber, and E. Weibel, Tunneling Through
a Controllable Vacuum Gap, Applied Physics Letters 40, 178 (1982).
59. G. Binnig, H. Rohrer, Scanning tunneling microscopy, Surface
Science 126, 236 (1983).
60. G. Binnig, H. Rohrer, Scanning tunneling microscopy, IBM Journal
of Research and Development 30, 355 (1986).
61. Michael Schmid, TU Wien; adapted from the IAP/TU Wien STM Gallery.
62. J. Bardeen, Tunneling from a Many-Particle Point of View, Physical
Review Letters 6, 57 (1961).
63. J. J. Sakurai, Modern Quantum Mechanics: First Edition. Benjamin-
Cummings New York (1985).
64. R. Shankar. Principles of Quantum Mechanics: Second Edition.
Springer (1994).
65. C. Julian Chen, Introduction to Scanning Tunneling Microscopy,
Oxford University Press (1993).
66. Chunli Bai, Scanning tunneling microscopy and its application,
Second, Revised Edition. Springer (2000).
67. J. Tersoff and D. R. Hamann, Theory of the scanning tunneling
microscope, Physical Review B 31, 805 (1985).
68. M. Ziegler, N. Néel, A. Sperl, J. Kröger, and R. Berndt, Local
density of states from constant-current tunneling spectra,
Physical Review B 91, 039902 (2015).
69. M. C. Yang, C. L. Lin, W. B. Su, S. P. Lin, S. M. Lu, H. Y. Lin,
C. S. Chang, W. K. Hsu, and Tien T. Tsong, Phase Contribution of
Image Potential on Empty Quantum Well States in Pb Islands on the
Cu(111) Surface, Physical Review Letters 102, 196102 (2009).
70. S. M. Lu, W. B. Su, C. L. Lin, W. Y. Chan, H. L. Hsiao, C. S.
Chang and Tien T. Tsong, Electron relaxation in empty quantum-well
states of a Pb island on Cu(111) studied by Z-V(distance-voltage)
spectroscopy in scanning tunneling microscopy, Journal of Applied
Physics 108, 083707 (2010).
71. L. Limot, T. Maroutian, P. Johansson, and R. Berndt, Surface-State
Stark Shift in a Scanning Tunneling Microscope, Physical Review
Letters 91, 196801 (2003).
72. W. B. Su, S. M. Lu, C. L. Jiang, H. T. Shih, C. S. Chang, and Tien
T. Tsong, Stark shift of transmission resonance in scanning
tunneling spectroscopy, Physical Review B 74, 155330 (2006).
73. S. Ogawa, S. Heike, H. Takahashi, and T. Hashizume, Tip-induced
energy shift in Au/Fe(100) quantum wells, Physical Review B 75,
115319 (2007).
74. W. Y. Chan, H. S. Huang, W. B. Su, W. H. Lin, H.-T. Jeng, M. K.
Wu, and C. S. Chang, Field-induced expansion deformation in Pb
islands on Cu(111): Evidence from energy shift of empty quantum-
well states, Physical Review Letters 108, 146102 (2012).
75. Romain Breitwieser, Yu-Cheng Hu, Yen Cheng Chao, Ren-Jie Li, Yi
Ren Tzeng, Lain-Jong Li, Sz-Chian Liou, Keng Ching Lin, Chih Wei
Chen, and Woei Wu Pai, Flipping nanoscale ripples of free-standing
graphene using a scanning tunneling microscope tip, Carbon 77, 236
(2014).
76. Shao-Wei Weng, Wei-Hsiang Lin, Wei-Bin Su, En-Te Hwu, Peilin Chen,
Tsong-Ru Tsai, and Chia-Seng Chang, Estimating Young’s modulus of
graphene with Raman scattering enhanced by micrometer tip,
Nanotechnology 25, 255703 (2014).
77. Xingzhong Zeng, Yitian Peng, Lei Liu, Haojie Lang, and Xing'an
Cao, Dependence of the friction strengthening of graphene on
velocity, Nanoscale 10, 1855 (2018).
78. Yitian Peng, Xingzhong Zeng, Kang Yu, Haojie Lang, Deformation
induced atomic-scale frictional characteristics of atomically thin
two-dimensional materials, Carbon 163, 186 (2020).
79. Emile D. L. Rienks, Niklas Nilius, Hans-Peter Rust, and Hans-
Joachim Freund, Surface potential of a polar oxide film: FeO on
Pt(111), Physical Review B 71, 241404 (2005).
80. Newton Ooi, Asit Rairkar, and James Adams, Density functional
study of graphite bulk and surface properties, Carbon 44, 231
(2006).
81. E.V. Rut'kov, E.Y. Afanas'eva, and N.R. Gall, Graphene and
graphite work function depending on layer number on Re, Diamond
and Related Materials 101, 107576 (2019).
82. S. Belaidi, P. Girard, and G. Leveque, Electrostatic forces acting
on the tip in atomic force microscopy: Modelization and comparison
with analytic expressions, Journal of Applied Physics 81, 1023
(1997).
83. D. B. Dougherty, P. Maksymovych, J. Lee, M. Feng, H. Petek, and J.
T. Yates, Jr., Tunneling spectroscopy of Stark-shifted image
potential states on Cu and Au surfaces, Physical Review B 76,
125428 (2007).
84. Shengxue Yang, Yujia Chen, Chengbao Jiang, Strain engineering of
two-dimensional materials: Methods, properties, and applications,
InfoMat 3, 397 (2021).
85. Chendong Zhang, Ming-Yang Li, Jerry Tersoff, Yimo Han, Yushan Su,
Lain-Jong Li, David A. Muller, and Chih-Kang Shih, Strain
distributions and their influence on electronic structures of
WSe2–MoS2 laterally strained heterojunctions, Nature
Nanotechnology 13, 152 (2018).
86. Shin-Ming Lu, Hsu-Sheng Huang, Wei-Bin Su, Pei-Hong Chu, Chia-Seng
Chang, Hsi-Lien Hsiao, and Tien Tzou Tsong, Disappearance of
Lowest-Order Transmission Resonance in Ag Film of Critical
Thickness, Japanese Journal of Applied Physics 50, 08LB01 (2011).
87. Kishu Sugawara, Insung Seo, Shiro Yamazaki, Kan Nakatsuji,
Yoshihiro Gohda, Hiroyuki Hirayama, Effective quantum-well width
of confined electrons in ultrathin Ag(111) films on Si(111)7 × 7
substrates, Surface Science 704, 121745 (2021).
88. Munir Hasan Nayfeh and Morton K Brussel, Electricity and
Magnetism, John Wiley & Sons, Ltd. pp 49 (1985).
89. N. D. Lang and W. Kohn, Theory of Metal Surfaces: Work Function,
Physical Review B 3, 1215 (1971).
90. S. Schuppler, N. Fischer, Th. Fauster, and W. Steinmann, Lifetime
of image-potential states on metal surfaces, Physical Review B 46,
13539 (1993).
91. L. Jurczyszyn, N. Mingo, and F. Flores, The influence of the geometry of the tip on the STM images, Czechoslovak Journal of Physics 47, 407 (1997).
92. T. Hashizume, I. Kamiya, Y. Hasegawa, N. Sano, T. Sakurai, and H. W. Pickering, A role of a tip geometry on STM images, Journal of Microscopy 152, 347 (1988).