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
Maximal field emission current densities in nanostructures
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.
- 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
- Proskurovskij D. I. Emissionnaya electronika [Emission electronics]. Tomsk, TSU Publ., 2010. 280 p. (in Russian).
- Fursey G. N. Field emission in vacuum micro-electronics. New York, Kluwer Academic Plenum Publishers, Springer, 2005. 205 p.
- 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
- Egorov N., Sheshin E. Field Emission Electronics. Springer Series in Advanced Microelectronics. New York, Springer, 2017. Vol. 60. 568 p.
- 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
- 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
- Davydov A. S. Quantum Mechanics. New York, Pergamon Press, 1965. 637 p.
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- Léonard F. The Physics of Carbon Nanotube Devices. New York, William Andrew Inc., 2009. 310 p.
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- Jensen K. L. General thermal-field emission equation. Appl. Phys. Lett., 2006, vol. 88, art. 154105. https://doi.org/10.1063/1.2193776
- 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
- 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
- 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
- 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
- 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
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