Izvestiya of Saratov University.

Physics

ISSN 1817-3020 (Print)
ISSN 2542-193X (Online)


For citation:

Davidovich M. V. Maximal field emission current densities in nanostructures. Izvestiya of Saratov University. Physics , 2025, vol. 25, iss. 3, pp. 266-276. DOI: 10.18500/1817-3020-2025-25-3-266-276, EDN: AYKMGN

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
29.08.2025
Full text:
(downloads: 127)
Language: 
English
Article type: 
Review
UDC: 
535.538.935
EDN: 
AYKMGN

Maximal field emission current densities in nanostructures

Autors: 
Davidovich Mikhail Vladimirovich, Saratov State University
Abstract: 

Background and Objectives: The problems of issues of achieving high field emission current densities 2–4 orders of magnitude lower than the limit values 1015–1016 A/m2 are considered. Materials and Methods: Methods of obtaining them, field emission models, as well as possible emission structures providing large integrated currents in ribbon electron beams are analyzed. Results: It has been shown that the high current densities of the order 1010–1012 A/m2 can be achieved in vacuum quantum structures with two or more potential wells during resonant tunneling. Conclusions: Obtaining high-precision sources requires nanotechnology to create heterostructures of the metal-isolator-metal type and the use of low temperatures. Amorphous glass-like diamond (GLD) is a good material for dielectric films, and conductive glasslike carbon (GLC) is a suitable material for conductive films. In fact, the technology of creating thinfilm structures such as GLD-GLC-CLD is used.

Acknowledgments: 
This work was supported by the Russian Science Foundation (project No. 21-19-00226) and the Ministry of Science and Higher Education of the Russian Federation within the framework of the State Assignment (no. FSR-2023-0008).
Reference: 
  1. Fowler R. H., Nordheim L. Electron Emission in Intense Electric Fields. Proc. Royal Soc. A, 1928, vol. 119, iss. 781, pp. 173–181. https://doi.org/10.1098/RSPA.1928.0091
  2. Proskurovskij D. I. Emissionnaya electronika [Emission electronics]. Tomsk, TSU Publ., 2010. 280 p. (in Russian).
  3. Fursey G. N. Field emission in vacuum micro-electronics. New York, Kluwer Academic Plenum Publishers, Springer, 2005. 205 p.
  4. Burtsev A. A., Grigor’ev Yu. A., Danilushkin A. V., Shumikhin K. V. Features of the Development of Electron-Optical Systems for Pulsed Terahertz Traveling-Wave Tubes (Review). Tech. Phys., 2018, vol. 63, no. 3, pp. 452–459. https://doi.org/10.1134/S1063784218030040
  5. Egorov N., Sheshin E. Field Emission Electronics. Springer Series in Advanced Microelectronics. New York, Springer, 2017. Vol. 60. 568 p.
  6. Eidelman E. D., Arkhipov A. V. Field emission from carbon nanostructures: Models and experiment. Phys. Usp., 2020, vol. 63, no. 7, pp. 648–667. https://doi.org/10.3367/UFNe.2019.06.038576
  7. Bushuev N. A. Tunnel current and I–V characteristics of vacuum extremely-high-frequency microelectronic structures. J. Commun. Technol. Electron., 2015, vol. 60, iss. 2, pp. 193–200. https://doi.org/10.1134/S1064226915020023
  8. Davydov A. S. Quantum Mechanics. New York, Pergamon Press, 1965. 637 p.
  9. Davidovich M. V., Nefedov I. S., Glukhova O. E., Slepchenkov M. M. Toward the theory of resonant-tunneling triode and tetrode with CNT-graphene grids. J. Appl. Phys., 2021, vol. 130, iss. 20, art. 204301. https://doi.org/10.1063/5.0067763
  10. Davidovich M. V., Nefedov I. S., Glukhova O. E., Rubi J. M. Field emission in vacuum resonant tunneling heterostructures with high current densities. Sci. Rep., 2023, vol. 13, iss. 1, art. 19365. https://doi.org/10.1038/s41598-023-44900-2
  11. Davidovich M. V. Thermal-field emission in nanostructures with resonant tunneling. Tech. Phys., 2024, vol. 69, no. 1, pp. 29–43. https://doi.org/10.61011/JTF.2024.01.56899.170-23
  12. Davidovich M. V., Yafarov R. K. Field-Emission Staggered Structure Based on Diamond–Graphite Clusters. Tech. Phys., 2018, vol. 63, no. 2, pp. 274–284. https://doi.org/10.1134/S106378421802010X
  13. Davidovich M. V., Yafarov R. K. Pulsed and Static Field Emission VAC of Carbon Nanocluster Structures: Experiment and Its Interpretation. Tech. Phys., 2019, vol. 64, no. 8, pp. 1210–1220. https://doi.org/10.1134/S106378421908005X
  14. Simmons J. G. Generalized formula for the electric tunnel effect between similar electrodes separated by a thin insulating film. J. Appl. Phys., 1963, vol. 34, iss. 6, pp. 1793–1803. https://doi.org/10.1063/1.1702682
  15. Obraztsov A. N., Pavlovsky I. Yu., Volkov A. P. Field electron emission in graphite-like films. Tech. Phys., 2001, vol. 46, no. 11, pp. 1437–1443. https://doi.org/10.1134/1.1418509
  16. Bobkov A. F., Davydov E. V., Zaitsev S. V., Karpov A. V., Kozodaev M. A., Nikolaeva I. N., Popov M. O., Skorokhodov E. N., Suvorov A. L., Cheblukov Yu. N. Some aspects of the use of carbon materials in field electronic emission cathodes. J. Vac. Sci. Technol. B, 2001, vol. 19, iss. 1, pp. 32–38. https://doi.org/10.1116/1.1340017
  17. Fursey G. N., Petrik V. I., Novikov D. V. Low-threshold field emission from carbon nanoclusters obtained by the method of cold destruction of graphite. Tech. Phys., 2009, vol. 54, no. 7, pp. 1048–1052. https://doi.org/10.1134/S1063784209070202
  18. Forbes R. G. Low-macroscopic-field electron emission from carbon films and other electrically nanostructured heterogeneous materials: Hypotheses about emission mechanism. Solid-State Electronics, 2001, vol. 45, no. 6, pp. 779–808. https://doi.org/10.1016/S0038-1101(00)00208-2
  19. Forbes R. G. Exact analysis of surface field reduction due to field-emitted vacuum space charge, in parallel-plane geometry, using simple dimensionless equations. J. Appl. Phys., 2008, vol. 104, iss. 8, art. 084303. https://doi.org/10.1063/1.2996005et
  20. Forbes R. G., Xanthakis J. P. Field penetration into amorphous-carbon films: Consequences for field-induced electron emission. Surf. Interface Anal., 2007, vol. 39, iss. 2–3, pp. 139–145. https://doi.org/10.1002/sia.2477
  21. Voznyakovsky A. P., Fursey G. N., Voznyakovsky A. A., Polyakov M. A., Neverovskaya A. Yu., Zakirov I. I. Low-threshold field electron emission from two-dimensional carbon structures. Tech. Phys. Lett., 2019, vol. 45, no. 5, pp. 467–470. https://doi.org/10.21883/PJTF.2019.09.47715.17705
  22. Fursey G. N., Polyakov M. A., Cantonistov A. A., Yafyasov A. M., Pavlov B. S., Bozhevolnov V. B. Field and explosive emissions from graphene-like structures. Tech. Phys., 2013, vol. 83, no. 6, pp. 845–851. https://doi.org/10.1134/S1063784213060121
  23. Eletskii A. V. Carbon nanotube-based electron field emitters. Phys. Usp., 2010, vol. 53, no. 3, pp. 863–892. https://doi.org/10.3367/UFNe.0180.201009a.0897
  24. De Jonge N., Bonard J.-M. Carbon nanotube electron sources and applications. Philosophical Trans. Royal Soc. A, 2004, vol. 362, iss. 1823, pp. 2239–2266. https://doi.org/10.1098/rsta.2004.1438
  25. Hojati-Talemi P., Hawkins S., Huynh C., Simon G. P. Understanding parameters affecting field emission properties of directly spinnable carbon nanotube webs. Carbon, 2013, vol. 57, pp. 388–394. https://doi.org/10.1016/j.carbon.2013.01.088
  26. Zeng B., Ren Z. Field Emission of Carbon Nanotubes. In: Shi D., ed. Nano Science in Biomedicine. Berlin, Heidelberg, Springer, 2009, pp. 586–617. https://doi.org/10.1007/978-3-540-49661-8_23
  27. Léonard F. The Physics of Carbon Nanotube Devices. New York, William Andrew Inc., 2009. 310 p.
  28. Arkhipov A., Davydov S., Gabdullin P., Gnuchev N., Kravchik A., Krel S. Field-Induced electron emission from nanoporous carbons. J. Nanomaterials, 2014, vol. 20014, art. 190232. https://doi.org/10.1155/2014/190232
  29. Arkhipov A. V., Gabdullin P. G., Mishin M. V. On possible structure of field-induced electron emission centers of nanoporous carbon. Fuller. Nanotub. Carbon Nanostruct., 2010, no. 1–2, pp. 86–91. https://doi.org/10.1080/1536383X.2010.490149
  30. Glukhova O. E., Slepchenkov M. M. Electronic properties of the functionalized porous glass-like carbon. J. Phys. Chem. C, 2016, vol. 120, iss. 31, pp. 17753–17758. https://doi.org/10.1021/acs.jpcc.6b05058
  31. Arkhipov A. V., Mishin M. V. Interpretation of dynamic and dc field-emission characteristics of nanocarbons in terms of two-stage emission model. Fuller. Nanotub. Carbon Nanostruct., 2010, no. 1–2, pp. 75–80. https://doi.org/10.1080/1536383X.2010.490146
  32. Arkhipov A. V., Eidelman E. D., Zhurkin A. M., Osipov V. S., Gabdullin P. G. Low-field electron emission from carbon cluster films: Combined thermoelectric/hot-electron model of the phenomenon. Fuller. Nanotub. Carbon Nanostruct., 2020, vol. 28, no. 4, pp. 286–294. https://doi.org/10.1080/1536383X.2019.1708727
  33. Arkhipov A. V., Gabdullin P. G., Gnuchev N. M., Emel’yanov A. Yu., Krel’ S. I. Low-voltage field emission from carbon films produced by magnetron sputtering. Tech. Phys. Lett., 2014, vol. 40, no. 12, pp. 1065–1068. https://doi.org/10.1134/S1063785014120037
  34. Dzbanovsky N. N., Minakov P. V., Pilyavsky A. A., Rakhimov A. T., Seleznev B. V., Suetin N. V., Yuryev A. Yu. High-current electron gun with a field-emission cathode and diamond grid. Tech. Phys., 2005, vol. 50, no. 10, pp. 1360–1362. https://doi.org/10.1134/1.2103286
  35. Aban’shin N. P., Avetisyan Yu. A., Akchurin G. G., Loginov A. P., Morev S. P., Mosiyash D. S., Yakunin A. N. A planar diamond-like carbon nanostructure for a low-voltage field emission cathode with a developed surface. Tech. Phys. Lett., 2016, vol. 42, no. 5, pp. 509–512. https://doi.org/10.1134/S1063785016050175
  36. Aban’shin N. P., Gorfinkel’ B. I., Morev S. P., Mosiyash D. S., Yakunin A. N. Field emission structures of nanosized carbon with ionic protection structures. Tech. Phys. Lett., 2014, vol. 40, no. 5, pp. 404–407. https://doi.org/10.1134/S1063785014050022
  37. Konakova R. V., Okhrimenko O. B., Svetlichnyi A. M., Ageev O. A., Volkov E. Yu., Kolomiytsev A. S., Jityaev I. L., Spiridonov O. B. Characterization of Field Emission Cathodes Based on Graphene Films on SiC. Semiconductors, 2015, vol. 49, no. 9, pp. 1242–1245. https://doi.org/10.1134/S1063782615090146
  38. Shesterkin V. I. Emission and operational characteristics of various type of field emission cathodes. J. Comm. Tech. Electron., 2020, vol. 65, no. 1, pp. 1–26. https://doi.org/10.31857/S0033849420010040
  39. Stratton R. Theory of Field Emission from Semiconductors. Phys. Rev., 1962, vol. 125, iss. 1, pp. 67–82. https://doi.org/10.1103/PhysRev.125.67
  40. Murzin V. N., Mityagin Yu. A. Resonance tunneling, electric and optical phenomena in long-period semiconductor superlattices. Phys. Usp., 1999, vol. 42, no. 4, pp. 396–399. https://doi.org/10.1070/PU1999v042n04ABEH000459
  41. Arseev P. I., Mantsevich V. N., Maslova N. S., Panov V. I. Tunneling features in semiconductor nanostructures. Phys. Usp., 2017, vol. 60, no. 11, pp. 1067–1086. https://doi.org/10.3367/UFNe.2017.01.038055
  42. He J., Cutler P. H. Generalization of Fowler–Nordheim field emission theory for nonplanar metal emitters. Appl. Phys. Lett., 1991, vol. 59, iss. 13, pp. 1644–1648. https://doi.org/10.1063/1.106257
  43. Fursey G. N., Glazanov D. V. Deviations from the Fowler–Nordheim theory and peculiarities of field electron emission from small-scale objects. J. Vac. Sci. Technol. B, 1998, vol. 16, iss. 2, pp. 910–915. https://doi.org/10.1116/1.589929
  44. Forbes R. G., Deane J. H. B. Reformulation of the standard theory of Fowler–Nordheim tunnelling and cold field electron emission. Proc. Royal Soc. A, 2007, vol. 463, iss. 2087, pp. 2907–2927. https://doi.org/10.1098/rspa.2007.0030
  45. Forbes R. G. Physics of generalized Fowler–Nordheim-type equations. J. Vac. Sci. Technol. B, 2008, vol. 26, iss. 2, pp. 788–793. https://doi.org/10.1116/1.2827505.S2CID 20219379
  46. Kyritsakis A., Xanthakis J. P. Derivation of a generalized Fowler–Nordheim equation for nanoscopic field-emitters. Proc. Royal Soc. A, 2015, vol. 471, iss. 2174, art. 20140811. https://doi.org/10.1098/rspa.2014.0811
  47. Robertson J. Diamond-like amorphous carbon. Materials Science and Engineering R: Reports, 2002, vol. 37, iss. 4–6, pp. 129–281. https://doi.org/10.1016/S0927-796X(02)00005-0
  48. Sunil D., Vankar V. D., Chopra K. L. Infrared and ellipsometric studies of amorphous hydrogenated carbon films. J. Appl. Phys., 1991, vol. 69, iss. 6, pp. 3719–3722. https://doi.org/10.1063/1.348464
  49. Dmitriev V. K., Il’ichev E. A., Kirpilenko G. G., Petrukhin G. N., Rychkov G. S., Frolov V. D. Characteristics of amorphous silicon-carbon and metal-silicon-carbon films, areas of possible applications. Review. Proc. Universities. Electronics, 2023, vol. 28, no.1, pp. 24–48 (in Russian). https://doi.org/10.24151/1561-5405-2023-28-1-24-48
  50. Giubileo F., Di Bartolomeo A., Lemmo L., Luongo G., Urban F. Field Emission from Carbon Nanostructures. Appl. Sci., 2018, vol. 8, iss. 4, art. 526. https://doi.org/10.3390/app8040526
  51. Sun J. P., Haddad G. I., Mazumder P., Schulman J. N. Resonant tunneling diodes: Models and properties. Proc. IEEE, 1998, vol. 86, no. 4, pp. 641–660. https://doi.org/10.1109/5.663541
  52. Elesin V. F. Theory of coherent generation in resonant-tunneling diodes. JETP, 1999, vol. 89, no. 8, pp. 377–383. https://doi.org/10.1134/1.558994
  53. Kluksdahl N. C., Kriman A. M., Ferry D. K. Self-consistent study of the resonant-tunneling diode. Phys. Rev. B, 1989, vol. 39, iss. 11, art. 7720. https://doi.org/10.1103/PhysRevB.39.7720
  54. Pinaud O. Transient simulations of a resonant tunneling diode. J. Appl. Phys., 2002, vol. 92, iss. 4, pp. 1987–1994. https://doi.org/10.1063/1.1494127
  55. Mennemann J. F., Jungel A., Kosina H. Transient Schrodinger-Poisson Simulations of a High-Frequency Resonant Tunneling Diode Oscillator. J. Comput. Phys., 2013, vol. 239, pp. 187–205. https://doi.org/10.1016/j.jcp.2012.12.009
  56. Grishakov K. S., Elesin V. F. Transition times between the extremum points of the current–voltage characteristic of a resonant tunneling diode with hysteresis. Semiconductors, 2016, vol. 50, no. 8, pp. 1092–1096. https://doi.org/10.1134/S1063782616080121
  57. Davidovich M. V. Time-dependent resonant tunneling in a double-barrier diode structure. JETP Lett., 2019, vol. 110, no. 7, pp. 472–480. https://doi.org/10.1134/S0370274X19190068
  58. Spindt C. A. Physical properties of thin-film field emission cathodes with molybdenum cones. J. Appl. Phys., 1976, vol. 47, iss. 12, pp. 5248–5263. https://doi.org/10.1063/1.322600
  59. Dyke W. P., Trolan J. K. Field emission: Large current densities, space charge, and the vacuum arc. Phys. Rev., 1953, vol. 89, iss. 4, pp. 799–808. https://doi.org/10.1103/PhysRev.89.799
  60. Everhart T. E. Simplified analysis of point-cathode electron sources. J. Appl. Phys., 1967, vol. 38, iss. 13, pp. 4944–4957. https://doi.org/10.1063/1.1709260
  61. Smith R. C., Forrest R. D., Carey J. D., Hsu W. K., Silva S. R. P. Interpretation of enhancement factor in nonplanar field emitters. Appl. Phys. Lett., 2005, vol. 87, iss. 1, art. 013111. https://doi.org/10.1063/1.1989443
  62. Forbes R. G. Description of field emission current/voltage characteristics in terms of scaled barrier field values (f-values). J. Vacuum Sci. Technol. B, 2008, vol. 26, iss. 1, pp. 209–2013. https://doi.org/10.1116/1.2834563
  63. Cabrera H., Zanin D. A., De Pietro L. G., Michaels Th., Thalmann P., Ramsperger U., Vindigni A., Pescia D. Scale invariance of a diodelike tunnel junction. Phys. Rev. B, 2013, vol. 87, iss. 11, art. 115436. https://doi.org/10.1103/PhysRevB.87.115436
  64. Davidovich M. V. Peculiarities of Vacuum Resonant Tunneling at One- and Two-Well Barrier Potentials. Tech. Phys., 2022, vol. 67, no. 9, pp. 361–375. https://doi.org/10.1134/S1063784222060019
  65. Jensen K. L. General thermal-field emission equation. Appl. Phys. Lett., 2006, vol. 88, art. 154105. https://doi.org/10.1063/1.2193776
  66. Liang S.-D. Theory of field emission. Europ. Phys. J. B, 2018, vol. 91, art. 182. https://doi.org/10.1140/epjb/e2018-90181-x
  67. Herring C., Nichols M. Thermionic Emission. Rev. Mod. Phys., 1949, vol. 21, no. 2, pp. 185–270. https://doi.org/10.1103/RevModPhys.21.185
  68. Murphy E. L., Good R. H. Thermionic Emission, Field Emission, and the Transition Region. Phys. Rev., 1956, vol. 102, iss. 6, pp. 1464–1473. https://doi.org/10.1103/PhysRev.102.1464
  69. Davidovich M. V. High-current field emission nanostructure with a ribbon beam. Tech. Phys. Lett., 2024, vol. 50, no. 8, pp. 22–25. https://doi.org/10.61011/PJTF.2024.16.58533.19626
  70. Fitting H.-J., Hingst Th., Schreiber E. Breakdown and high-energy electron vacuum emission of MIS-structures. J. Phys. D: Appl. Phys., 1999, vol. 32, pp. 1963–1970. https://doi.org/10.1088/0022-3727/32/16/303
Received: 
05.05.2024
Accepted: 
15.05.2025
Published: 
29.08.2025