Influence of Interface Polarization on Charge-Charge Interaction in Two-Layer Systems
DOI:
https://doi.org/10.15407/ujpe71.10.793Keywords:
two-layer structures, dielectric mismatch, charge-charge interaction, polarization forces, non-Coulombic dependenceAbstract
The influence of a plane interface between two semi-infinite dielectrically dissimilar insulators on the interaction of two point charges located near it has been analyzed. It was shown that their interaction is significantly modified by the polarization charges induced at the interface. In particular, if the charges are in the same medium, then the dependence of their interaction energy W on the distance D between the charges differs from the Coulomb law. At the same time, if the charges are in different media, the interaction law remains Coulombic, but with an effective dielectric constant value. Deviations from the Coulombic interaction were calculated quantitatively and investigated analytically. The maps W(Rs, Rp) describing the profiles of W as a function of the charges' coordinates Rs and Rp are presented. The approximations of W(D) were obtained and their validity was analyzed. It was concluded that in layered structures, polarization corrections should always be taken into account when studying various properties of charged entities, e.g., electrons and holes forming Wannier-Mott excitons.
References
1. The Electrical Researches of the Honourable Henry Cavendish, F. R. S. Written between 1771 and 1781. Edited by J.C. Maxwell (Cambridge University Press, 1879).
2. H. Cavendish. LV. An attempt to explain some of the principal phenomena of electricity, by means of an elastic fluid. Phil. Trans. R. Soc. Lond. 155, 584 (1771).
https://doi.org/10.1098/rstl.1771.0056
3. W.C.D. Whetham. The Theory of Experimental Electricity (Cambridge University Press, 1905).
4. C.A. Coulomb. Premier mémoire sur l'électricité et le magnétisme. In: Histoire de L'Academie royale des science. Avec les Mémoires de Mathématique & de Physique, pour la même Année. Tirés des Registres de cette Académie (L'Imprimerie Royale, 1785), p. 569.
5. C.A. Coulomb. Second mémoire sur l'électricité et le magnétisme. In: Histoire de L'Academie royale des science. Avec les Mémoires de Mathématique & de Physique, pour la même Année. Tirés des Registres de cette Académie (L'Imprimerie Royale, 1785), p. 578.
6. S. Weinberg. The Discovery of Subatomic Particles (W.H. Freeman and Company, 1983).
7. M. Faraday. VI. Experimental researches in electricity. - Seventh series. Phil. Trans. R. Soc. Lond. 124, 77 (1834).
https://doi.org/10.1098/rstl.1834.0008
8. M. Faraday. I. Experimental researches in electricity. - Eleventh Series. Phil. Trans. R. Soc. Lond. 128, 1 (1838).
https://doi.org/10.1098/rstl.1838.0002
9. M. Faraday. I. Experimental researches in electricity. - Twelfth Series. Phil. Trans. R. Soc. Lond. 128, 83 (1838).
https://doi.org/10.1098/rstl.1838.0008
10. M. Faraday. XIII. Experimental researches in electricity. - Fourteenth series. Phil. Trans. R. Soc. Lond. 128, 265 (1838).
https://doi.org/10.1098/rstl.1838.0014
11. M. Faraday. XXXV. On the conservation of force. Phil. Mag. 13, 225 (1857).
https://doi.org/10.1080/14786445708642290
12. I. Newton. The Principia: Mathematical Principles of Natural Philosophy (University of California Press, 1999).
13. A.H. Cook. The inverse square law of gravitation. Contemp. Phys. 28, 159 (1975).
https://doi.org/10.1080/00107518708223692
14. A.H. Cook. Experiments on gravitation. Rep. Prog. Phys. 51, 707 (1988).
https://doi.org/10.1088/0034-4885/51/5/003
15. A.B. Pippard. Forces and Particles. An Outline of the Principles of Classical Physics (Macmillan Education, 1972).
https://doi.org/10.1007/978-1-349-81595-1
16. R. Fitzpatrick. An Introduction to Celestial Mechanics (Cambridge University Press, 2012).
https://doi.org/10.1017/CBO9781139152310
17. S.D. Poisson. Mémoire sur la distribution de l'électricité à la surface des corps conducteurs. In: Mém. Classe Sci. Math. Phys. Inst. Imp. France, 1811 12, 1 (1812).
18. S.D. Poisson. Second mémoire sur la distribution de l'électricité à la surface des corps conducteurs. In: Mém. Classe Sci. Math. Phys. Inst. Imp. France, 1813 12, 163 (1814).
19. L.D. Landau, E.M. Lifshits. The Classical Theory of Fields (Pergamon Press, 1983).
20. J.D. Jackson. Classical Electrodynamics (John Wiley and Sons, 1998).
21. S.D. Poisson. Remarques sur une équation qui se présente dans la théorie des attractions des sphéroïdes. In Bull. Sci. Soc. Philomat. 3, 388 (1813).
22. S.D. Poisson. Mémoire sur la Théorie du magnétisme en mouvement. In Mémoires de L'Académie Royale des Sciences de L'Institut de France. Année 1823. Tome 6 (Chez Firmin Didot, Père et Fils, Libraires, 1827, 1827), p. 441.
23. Mathematical Papers of the Late George Green, edited by N.M. Ferrers (Macmillan, 1871).
24. C.F. Gauss. General Propositions relating to Attractive and Repulsive Forces acting in the inverse ratio of the square of the distance. In Scientific Memoirs. Selected from the Transactions of Foreign Academies of Science and Learned Societies and from Foreign Journals. Volume 3s, edited by R. Taylor (Richard and John E. Taylor, 1843), p. 153.
25. M. Faraday. I. Experimental researches in electricity. Fifteenth series. Phil. Trans. R. Soc. Lond. 129, 1 (1839).
https://doi.org/10.1098/rstl.1839.0002
26. M. Faraday. LIV. Thoughts on ray-vibrations. Phil. Mag. 28, 345 (1846).
https://doi.org/10.1080/14786444608645431
27. L.P. Williams. The Origins of Field Theory (Random House, Inc., 1966).
28. W. Berkson. Fields of Force. The Development of a World View from Faraday to Einstein (Routledge, 1974).
https://doi.org/10.1063/1.2998925
29. D. Gooding. Final steps to the field theory: Faraday's study of magnetic phenomena, 1845-1850. Hist. Stud. Phys. Sci. 11, 231 (1981).
https://doi.org/10.2307/27757480
30. Yu.A. Lyubimov. Studies on History of Electromagnetism and Dielectrics (Binom, Laboratory of Knowledge, 2008), in Russian.
31. G.E. Smith, R. Seth. Brownian Motion and Molecular Reality. A Study in Theory-Mediated Measurement (Oxford University Press, 2020).
32. A.H. Sihvola. Electromagnetic Mixing Formulas and Applications (Institution of Electrical Engineers, 1999).
https://doi.org/10.1049/PBEW047E
33. J.M. Ziman. The method of neutral pseudo-atoms in the theory of metals. Adv. Phys. 13, 89 (1964).
https://doi.org/10.1080/00018736400101011
34. G.D. Mahan. Many-Particle Physics (Kluwer Academic, 2000).
https://doi.org/10.1007/978-1-4757-5714-9
35. W. Thomson. Reprint of Papers on Electrostatics and Magnetism (Macmillan, 1884).
36. J.C. Maxwell. The Scientific Papers of James Clerk Maxwell. Volume 1 (Dover Publications, 2011).
https://doi.org/10.1017/CBO9780511710377
37. J.C. Maxwell. The Scientific Papers of James Clerk Maxwell. Volume 2 (Dover Publications, 2011).
https://doi.org/10.1017/CBO9780511710377
38. O.D. Kellogg. Foundations of Potential Theory (Springer Verlag, 1967).
https://doi.org/10.1007/978-3-642-86748-4
39. J.Z. Buchwald. William Thomson and the mathematization of Faraday's electrostatics. Hist. Stud. Phys. Sci. 8, 101 (1977).
https://doi.org/10.2307/27757369
40. M.N. Wise. The flow analogy to electricity and magnetism, part I: William Thomson's reformulation of action at a distance. Arch. Hist. Exact Sci. 25, 19 (1981).
https://doi.org/10.1007/BF00357201
41. R.W. Home. Poisson's memoirs on electricity: academic politics and a new style in physics. Brit. J. Hist. Sci. 16, 239 (1983).
https://doi.org/10.1017/S0007087400019798
42. W.A. Atherton. From Compass to Computer. A History of Electrical and Electronics Engineering (Macmillan Press, Ltd, 1984).
https://doi.org/10.1007/978-1-349-17365-5_7
43. A. H-D. Cheng, D.T. Cheng. Heritage and early history of the boundary element method. Eng. Anal. Bound. Elem. 29, 268 (2005).
https://doi.org/10.1016/j.enganabound.2004.12.001
44. G.C. Pantoja, W.S. Elias. Integration between Physics and Mathematics: the relation between Green's functions and method of images as a worked example. Lat. Am. J. Phys. Educ. 16, 4308 (2015).
45. G.D. Mahan, R.M. Mazo. Coulomb interactions in an atomic dielectric. Phys. Rev. 175, 1191 (1968).
https://doi.org/10.1103/PhysRev.175.1191
46. R.D. Mindlin. On the electrostatic potential of a point charge in a dielectric solid. Int. J. Solids Structures 9, 233 (1973).
https://doi.org/10.1016/0020-7683(73)90100-5
47. J.C. Inkson. Screened exchange in semiconductors. J. Phys. C 6, L181 (1973).
https://doi.org/10.1088/0022-3719/6/9/002
48. K. Schulze, K. Unger. The linear dielectric response of a semiconductor: a new analytic form for the dielectric function. Phys. Status Solidi B 66, 491 (1974).
https://doi.org/10.1002/pssb.2220660211
49. R. Resta. Macroscopic polarization in crystalline dielectrics: The geometric phase approach. Rev. Mod. Phys. 66, 899 (1994).
https://doi.org/10.1103/RevModPhys.66.899
50. R. Resta. Why are insulators insulating and metals conducting? J. Phys.: Condens. Matter. 14, R625 (2002).
https://doi.org/10.1088/0953-8984/14/20/201
51. J.G. Hedley, K.K. Bhatt, H. Berthoumieux, A.A. Kornyshev. What does an ion feel at the electrochemical interface? Revisiting electrosorption through nonlocal electrostatics. J. Chem. Phys. 162, 114703 (2025).
https://doi.org/10.1063/5.0254033
52. W.R. Smythe. Static and Dynamic Electricity (McGraw-Hill, 1950).
53. J. Heinrichs. Response of metal surfaces to static and moving point charges and to polarizable charge distributions. Phys. Rev. B 8, 1346 (1973).
https://doi.org/10.1103/PhysRevB.8.1346
54. V.V. Batygin, I.N. Toptygin. Problems in Electrodynamics (Academic Press, 1978).
55. L.D. Landau, E.M. Lifshits. Electrodynamics of Continuous Media (Pergamon Press, 1984).
https://doi.org/10.1016/B978-0-08-030275-1.50007-2
56. D.J. Griffiths. Introduction to Electrodynamics (Prentice Hall, 1999).
57. W. Thomson. III. Geometrical investigations with reference to the distribution of electricity on spherical conductors. In: The Cambridge and Dublin Mathematical Journal, Volume III. Edited by W. Thomson (Macmillan, Barclay, and Macmillan, 1848), p. 141.
58. W. Thomson. XLV. On the mutual attraction or repulsion between two electrified spherical conductors. Phil. Mag. 5, 287 (1853).
https://doi.org/10.1080/14786445308647247
59. M. Abraham, R. Becker. The Classical Theory of Electricity and Magnetism (Blackie and Son, 1932).
60. G.D. Mahan. Surface polaritons and the theory of image charge. Phys. Rev. B 5, 739 (1972).
https://doi.org/10.1103/PhysRevB.5.739
61. A.A. Kornyshev. Non-local enhancement of the dipole-dipole interaction at the interface of two dielectrics. J. Electroanal. Chem. 255, 297 (1988).
https://doi.org/10.1016/0022-0728(88)80022-6
62. A.M. Gabovich, A.I. Voitenko. Electrostatic interaction near the interface between dielectric media taking into account the nonlocality of the Coulomb field screening. J. Mol. Liq. 267, 166 (2018).
https://doi.org/10.1016/j.molliq.2017.09.044
63. A.M. Gabovich, A.I. Voitenko. The "non-Coulombic" character of classical electrostatic interaction between charges near interfaces. Eur. J. Phys. 39, 045203 (2018).
https://doi.org/10.1088/1361-6404/aabbf9
64. A.M. Gabovich, A.I. Voitenko. Electrostatic interaction of point charges in three-layer structures: The classical model. Condens. Matter. 4, 44 (2019).
https://doi.org/10.3390/condmat4020044
65. A.M. Gabovich, M.S. Li, H. Szymczak, A.I. Voitenko. Non-Coulombic behavior of electrostatic charge-charge interaction in three-layer heterostructures. J. Electrostat. 102, 103377 (2019).
https://doi.org/10.1016/j.elstat.2019.103377
66. A.M. Gabovich, M.S. Li, H. Szymczak, A.I. Voitenko. Electric dipole image forces in three-layer systems: The classical electrostatic model. J. Chem. Phys. 152, 094705 (2020).
https://doi.org/10.1063/1.5142280
67. A.M. Gabovich, A.I. Voitenko. Orientation of adsorbed polar molecules (dipoles) in external electrostatic field. J. Phys.: Condens. Matter. 33, 035004 (2021).
https://doi.org/10.1088/1361-648X/abb997
68. A.M. Gabovich, A.I. Voitenko. Electrostatic image force energy for charges in three-layer structures: Exact formulas and their approximations. J. Phys.: Condens. Matter. 33, 205002 (2021).
https://doi.org/10.1088/1361-648X/abeca5
69. A.M. Gabovich, M.S. Li, H. Szymczak, A.I. Voitenko. Charge-charge interaction in three-layer systems: Classical approach. Phys. Rev. B 105, 115415 (2022).
https://doi.org/10.1103/PhysRevB.105.115415
70. A.M. Gabovich, V.N. Gorshkov, V.F. Semeniuk, A.I. Voitenko. Influence of image forces on charge-dipole interaction in two-layered systems. J. Chem. Phys. 160, 184710 (2024).
https://doi.org/10.1063/5.0208114
71. S. Earnshaw. On the nature of the molecular forces which regulate the constitution of the luminiferous ether. Transact. Cambridge Philosoph. Soc. 7, 97 (1842).
72. R. Weinstock. On a fallacious proof of Earnshaw's theorem. Amer. J. Phys. 44, 392 (1970).
https://doi.org/10.1119/1.10449
73. W. Jones. Earnshaw's theorem and the stability of matter. Eur. J. Phys. 1, 85 (1980).
https://doi.org/10.1088/0143-0807/1/2/004
74. M.D. Simon, A.K. Geim. Diamagnetic levitation: Flying frogs and floating magnets (invited). J. Appl. Phys. 87, 6200 (2000).
https://doi.org/10.1063/1.372654
75. Y. Levin. Strange electrostatics in physics, chemistry, and biology. Physica A 352, 49 (2005).
https://doi.org/10.1016/j.physa.2004.12.033
76. V. Ivchenko. Minimum energy principles in electrostatics. Eur. J. Phys. 46, 015201 (2025).
https://doi.org/10.1088/1361-6404/ad9186
77. N. Bruch, M. Eikerling, T. Binninger. Classical theory of electron-ion correlations at electrochemical interfaces: Closing the circuit from double-layer charging to ion adsorption. PRX Energy 5, 013009 (2026).
https://doi.org/10.1103/65xq-svmf
78. E.H. Lieb. The stability of matter. Rev. Mod. Phys. 48, 553 (1976).
https://doi.org/10.1103/RevModPhys.48.553
79. E.H. Lieb, R. Seiringer. The Stability of Matter in Quantum Mechanics (Cambridge University Press, 2009).
https://doi.org/10.1017/CBO9780511819681
80. A.V. Sidyakin. Calculation of the polarization contribution to the energy of interaction of a charge with the surface of a metal. Zh. Eksp. Teor. Fiz. 58, 573 (1970).
81. N.D. Lang. The density-functional formalism and the electronic structure of metal surfaces. Solid State Phys. 28, 225 (1973).
https://doi.org/10.1016/S0081-1947(08)60204-0
82. P.J. Jennings, S.M. Thurgate. The inner potential in LEED. Surf. Sci. 104, L210 (1981).
https://doi.org/10.1016/0039-6028(81)90056-X
83. A.M. Gabovich, A.I. Voitenko. Surface tension at the interface between electrolyte solution and metal (semiconductor) electrode. Spatial dispersion effects. Electrochim. Acta 28, 1771 (1983).
https://doi.org/10.1016/0013-4686(83)87012-1
84. P.J. Jennings, R.O. Jones. Beyond the method of images - the interaction of charged particles with real surfaces. Adv. Phys. 37, 341 (1988).
https://doi.org/10.1080/00018738800101389
85. D.K. Saldin, J.C.H. Spence. On the mean inner potential in high- and low-energy electron diffraction. Ultramicroscopy 55, 397 (1994).
https://doi.org/10.1016/0304-3991(94)90175-9
86. J.A. Sobota, Y. He, Z-X. Shen. Angle-resolved photoemission studies of quantum materials. Rev. Mod. Phys. 93, 025006 (2021).
https://doi.org/10.1103/RevModPhys.93.025006
87. L. Onsager, N.N.T. Samaras. The surface tension of Debye-Hückel electrolytes. J. Chem. Phys. 2, 528 (1934).
https://doi.org/10.1063/1.1749522
88. V.E. Bravina. Some problems in the theory of the surface tension of strong electrolyte solutions. Herald Moscow University, N2, 85 (1958).
89. V. Sahni. Quantum mechanics of asymptotic effective potential and "image" charge at metal surfaces. Progr. Surf. Sci. 54, 115 (1997).
https://doi.org/10.1016/S0079-6816(97)00003-8
90. H.A. Bethe, E.E. Salpeter. Quantum Mechanics of One- and Two-Electron Atoms (Springer Verlag, 1957).
https://doi.org/10.1007/978-3-662-12869-5
91. W.E. Lamb, Jr, R.C. Retherford. Fine structure of the hydrogen atom by a microwave method. Phys. Rev. 72, 241 (1947).
https://doi.org/10.1103/PhysRev.72.241
92. I.J.R. Aitchison. Nothing's plenty. The vacuum in modern quantum field theory. Contemp. Phys. 26, 333 (1985).
https://doi.org/10.1080/00107518508219107
93. V.B. Berestetskii, E.M. Lifshitz, L.P. Pitaevskii. Relativistic Quantum Theory (Pergamon Press, 1982).
94. The Cambridge and Dublin Mathematical Journal, Volume III. Edited by W. Thomson (Macmillan, Barclay, and Macmillan, 1848).
95. J.W. Gadzuk. The effects of screened exchange and correlation on the surface potential of an electron gas. Surf. Sci. 11, 465 (1968).
https://doi.org/10.1016/0039-6028(68)90057-5
96. J.C. Inkson. The electron-electron interaction near an interface. Surf. Sci. 28, 69 (1971).
https://doi.org/10.1016/0039-6028(71)90085-9
97. R.H. Ritchie. Surface plasmons and the image force in metals. Phys. Lett. A 38, 189 (1972).
https://doi.org/10.1016/0375-9601(72)90471-9
98. R. Ray, G.D. Mahan. Dynamical image charge theory. Phys. Lett. A 42, 301 (1972).
https://doi.org/10.1016/0375-9601(72)90431-8
99. M. Jonson. The dynamical image potential for tunneling electrons. Solid State Commun. 33, 743 (1980).
https://doi.org/10.1016/0038-1098(80)90821-2
100. A.M. Gabovich, V.M. Rosenbaum, A.I. Voitenko. Dynamical image forces in three-layer systems and field emission. Surf. Sci. 186, 523 (1987).
https://doi.org/10.1016/S0039-6028(87)80392-8
101. P. Guéret, E. Marclay, H. Meier. Experimental observation of the dynamical image potential in extremely low GaAs/AlxGa1−xAs/GaAs tunnel barriers. Appl. Phys. Lett. 53, 1617 (1988).
https://doi.org/10.1063/1.99929
102. A.M. Gabovich, V.M. Rozenbaum, A.I. Voitenko. Importance of the plasmon damping for the dynamical image forces. Phys. Status Solidi B 214, 29 (1999).
https://doi.org/10.1002/(SICI)1521-3951(199907)214:1<29::AID-PSSB29>3.0.CO;2-G
103. A.M. Gabovich, A.I. Voitenko. Dynamic image forces near a metal surface and the point-charge motion. Eur. J. Phys. 33, 1289 (2012).
https://doi.org/10.1088/0143-0807/33/5/1289
104. M.A. Vorotyntsev. Model nonlocal electrostatics: II. Spherical interface. J. Phys. C 11, 3323 (1978).
https://doi.org/10.1088/0022-3719/11/15/030
105. A.A. Kornyshev, M.A. Vorotyntsev. Model nonlocal electrostatics: III. Cylindrical interface. J. Phys. C 12, 4939 (1979).
https://doi.org/10.1088/0022-3719/12/22/033
106. R. Messina. Image charges in spherical geometry: Application to colloidal systems. J. Chem. Phys. 117, 11062 (2002).
https://doi.org/10.1063/1.1521935
107. A.A. Kornyshev, D.J. Lee, S. Leikin, A. Wynveen. Structure and interactions of biological helices. Rev. Mod. Phys. 79, 943 (2007).
https://doi.org/10.1103/RevModPhys.79.943
108. F. Loran, S. Moghimi-Araghi. Does a curved mirror honestly reflect your identity? A study of multipole images in front of a grounded sphere. Eur. J. Phys. 47, 015104 (2026).
https://doi.org/10.1088/1361-6404/ae21a3
109. G. Wang, A. Chernikov, M.M. Glazov, T.F. Heinz, X. Marie, T. Amand, B. Urbaszek. Colloquium: Excitons in atomically thin transition metal dichalcogenides. Rev. Mod. Phys. 90, 021001 (2018).
https://doi.org/10.1103/RevModPhys.90.021001
110. H.T. Nguyen-Truong. Exciton binding energy and screening length in two-dimensional semiconductors. Phys. Rev. B 105, L201407 (2022).
https://doi.org/10.1103/PhysRevB.105.L201407
111. A.M. Gabovich, A.I. Voitenko. Electrostatic charge-charge and dipole-dipole interactions near the surface of a medium with screening non-locality (Review Article). Fiz. Nizk. Temp. 42, 841 (2016).
https://doi.org/10.1063/1.4960496
112. F.S. Cipcigan, J. Crain, V.P. Sokhan, G.J. Martyna. Electronic coarse graining: Predictive atomistic modeling of condensed matter. Rev. Mod. Phys. 91, 025003 (2019).
https://doi.org/10.1103/RevModPhys.91.025003
113. C. Kittel. Introduction to Solid State Physics (John Wiley and Sons, 2005).
114. J. Tersoff. Theory of semiconductor heterojunctions: The role of quantum dipoles. Phys. Rev. B 30, 4874 (1984).
https://doi.org/10.1103/PhysRevB.30.4874
115. M. Peressi, N. Binggeli, A. Baldereschi. Band engineering at interfaces: Theory and numerical experiments. J. Phys. D 31, 1273 (1998).
https://doi.org/10.1088/0022-3727/31/11/002
116. X. Crispin. Interface dipole at organic/metal interfaces and organic solar cells. Solar Energy Materials and Solar Cells 83, 147 (2004).
https://doi.org/10.1016/j.solmat.2004.02.022
117. N.C. Bristowe, P.B. Littlewood, E. Artacho. The net charge at interfaces between insulators. J. Phys.: Condens. Matter. 23, 081001 (2011).
https://doi.org/10.1088/0953-8984/23/8/081001
118. R. Kipling. In the neolitic age. In: The Seven Seas (Methuen and Co., 1986), p. 125.
119. R.T. Senger, K.K. Bajaj. Binding energies of excitons in polar quantum well heterostructures. Phys. Rev. B 68, 205314 (2003).
https://doi.org/10.1103/PhysRevB.68.205314
120. L.S.R. Cavalcante, A. Chaves, B. VanDuppen, F.M. Peeters, D.R. Reichman. Electrostatics of electron-hole interactions in van der Waals heterostructures. Phys. Rev. B 97, 125427 (2018).
https://doi.org/10.1103/PhysRevB.97.125427
121. E.C. Regan, D. Wang, E.Y. Paik, Y. Zeng, L. Zhang, J. Zhu, A.H. MacDonald, H. Deng, F. Wang. Emerging exciton physics in transition metal dichalcogenide heterobilayers. Nat. Rev. Mater. 7, 778 (2022).
https://doi.org/10.1038/s41578-022-00440-1
122. C.F. Gallo, W.L. Lama. Electrostatic model for the correlation between the work function and the ionization energy of the metallic elements. IEEE Trans. Ind. Appl. IA-10, 496 (1974).
https://doi.org/10.1109/TIA.1974.349185
123. C.F. Gallo, W.L. Lama. Classical electrostatic description of the work function and ionization energy of insulators. IEEE Trans. Ind. Appl. IA-12, 7 (1976).
https://doi.org/10.1109/TIA.1976.349379
124. C.F. Gallo, W.L. Lama. Some charge exchange phenomena explained by a classical model of the work function. J. Electrostatics 2, 145 (1976).
https://doi.org/10.1016/0304-3886(76)90005-X
125. A.G. Bailey. Electrostatic phenomena during powder handling. Powder Technol. 37, 71 (1984).
https://doi.org/10.1016/0032-5910(84)80007-8
126. K. Wong, S. Vongehr, V.V. Kresin. Work functions, ionization potentials, and in between: Scaling relations based on the image-charge model. Phys. Rev. B 67, 035406 (2003).
https://doi.org/10.1103/PhysRevB.67.035406
127. M. Kumagai, T. Takagahara. Excitonic and nonlinear-optical properties of dielectric quantum-well structures. Phys. Rev. B 40, 12359 (1989).
https://doi.org/10.1103/PhysRevB.40.12359
128. K.S. Thygesen. Calculating excitons, plasmons, and quasiparticles in 2D materials and van der Waals heterostructures. 2D Mater 4, 022004 (2017).
https://doi.org/10.1088/2053-1583/aa6432
129. H. Zahra, A. Hichri, S. Jaziri. Comparative study of the exciton binding energies of thin and ultrathin organic-inorganic perovskites due to dielectric mismatch effects. J. Appl. Phys. 122, 015701 (2017).
https://doi.org/10.1063/1.4989838
130. J.R. Barker, A. Martinez. Image charge models for accurate construction of the electrostatic self-energy of 3D layered nanostructure devices. J. Phys.: Condens. Matter. 30, 134002 (2018).
https://doi.org/10.1088/1361-648X/aaaf98
131. C. Katan, N. Mercier, J. Even. Quantum and dielectric confinement effects in lower-dimensional hybrid perovskite semiconductors. Chem. Rev. 119, 3140 (2019).
https://doi.org/10.1021/acs.chemrev.8b00417
132. C. Jiao, S. Pei, S. Wu, Z. Wang, J. Xia. Tuning and exploiting interlayer coupling in two-dimensional van der Waals heterostructures. Rep. Prog. Phys. 86, 114503 (2023).
https://doi.org/10.1088/1361-6633/acfe89
133. G.D. Scholes. Insights into excitons confined to nanoscale systems: Electron-hole interaction, binding energy, and photodissociations. ACS Nano 2, 523 (2008).
https://doi.org/10.1021/nn700179k
134. D. Neilson, A. Perali, A.R. Hamilton. Excitonic superfluidity and screening in electron-hole bilayer systems. Phys. Rev. B 89, 060502 (2014).
https://doi.org/10.1103/PhysRevB.89.060502
135. T.A.S. Pereira, J.S. deSousa, J.A.K. Freire, G.A. Farias. On the interplay between quantum confinement and dielectric mismatch in high-κ based quantum wells. J. Appl. Phys. 108, 054311 (2010).
https://doi.org/10.1063/1.3460631
136. J.M. Garcia-Lastra, K.S. Thygesen. Renormalization of optical excitations in molecules near a metal surface. Phys. Rev. Lett. 106, 187402 (2011).
https://doi.org/10.1103/PhysRevLett.106.187402
137. A. Garg. An instructive paradox in the method of images. Amer. J. Phys. 94, 197 (2026).
https://doi.org/10.1119/5.0283441
138. A.G. Bailey. Charging of solids and powders. J. Electrostatics 30, 167 (1993).
Downloads
Published
Issue
Section
License
Copyright Agreement
License to Publish the Paper
Kyiv, Ukraine
The corresponding author and the co-authors (hereon referred to as the Author(s)) of the paper being submitted to the Ukrainian Journal of Physics (hereon referred to as the Paper) from one side and the Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, represented by its Director (hereon referred to as the Publisher) from the other side have come to the following Agreement:
1. Subject of the Agreement.
The Author(s) grant(s) the Publisher the free non-exclusive right to use the Paper (of scientific, technical, or any other content) according to the terms and conditions defined by this Agreement.
2. The ways of using the Paper.
2.1. The Author(s) grant(s) the Publisher the right to use the Paper as follows.
2.1.1. To publish the Paper in the Ukrainian Journal of Physics (hereon referred to as the Journal) in original language and translated into English (the copy of the Paper approved by the Author(s) and the Publisher and accepted for publication is a constitutive part of this License Agreement).
2.1.2. To edit, adapt, and correct the Paper by approval of the Author(s).
2.1.3. To translate the Paper in the case when the Paper is written in a language different from that adopted in the Journal.
2.2. If the Author(s) has(ve) an intent to use the Paper in any other way, e.g., to publish the translated version of the Paper (except for the case defined by Section 2.1.3 of this Agreement), to post the full Paper or any its part on the web, to publish the Paper in any other editions, to include the Paper or any its part in other collections, anthologies, encyclopaedias, etc., the Author(s) should get a written permission from the Publisher.
3. License territory.
The Author(s) grant(s) the Publisher the right to use the Paper as regulated by sections 2.1.1–2.1.3 of this Agreement on the territory of Ukraine and to distribute the Paper as indispensable part of the Journal on the territory of Ukraine and other countries by means of subscription, sales, and free transfer to a third party.
4. Duration.
4.1. This Agreement is valid starting from the date of signature and acts for the entire period of the existence of the Journal.
5. Loyalty.
5.1. The Author(s) warrant(s) the Publisher that:
– he/she is the true author (co-author) of the Paper;
– copyright on the Paper was not transferred to any other party;
– the Paper has never been published before and will not be published in any other media before it is published by the Publisher (see also section 2.2);
– the Author(s) do(es) not violate any intellectual property right of other parties. If the Paper includes some materials of other parties, except for citations whose length is regulated by the scientific, informational, or critical character of the Paper, the use of such materials is in compliance with the regulations of the international law and the law of Ukraine.
6. Requisites and signatures of the Parties.
Publisher: Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine.
Address: Ukraine, Kyiv, Metrolohichna Str. 14-b.
Author: Electronic signature on behalf and with endorsement of all co-authors.
.png){kind=small}
