Calculation of DC Circuits Containing the Child-Langmuir Diodes

  • Alexandr E. DUBINOV
DOI: https://doi.org/10.24160/0013-5380-2023-1-57-60
Keywords: Child–Langmuir diode, perveance, parallel and series connection

Abstract

The DC circuits containing the Child-Langmuir (CL) diodes as their components are proposed for the first time for studying and calculation. The CL-diodes have a volt-ampere characteristic in the form of the power law with an exponent of 3/2. The devices that should be related to the category of CL-diodes include vacuum thermionic diodes with direct currents limited by the electron beam own space charge, solar cells, semiconductor light-emitting diodes, high-power diodes of direct-acting electron accelerators, etc. Circuits containing several CL-diodes have not been considered before anywhere. Formulas for general perveance with parallel- and series-connected CL-diodes having different perveances are given. Two calculation examples of the general perveance of the circuit containing three and four CL-diodes are presented. The methods and results of this study can be used for calculating the volt-ampere characteristics of, e.g., complex multicomponent circuits of solar cells or light emitting diodes.

Author Biography

Alexandr E. DUBINOV

(Russian Federal Nuclear Center – All-Russia Scientific Research Institute of Experimental Physics Power Engineering Institute; Sarov Physical and Technical Institute – Branch of National Research Nuclear University “MEPhI”, Sarov, Russia) – Deputy Director of Scientific Production Center of Physics; Professor of the Experimental Physics Dept., Dr. Sci.(Phys.-Math.)

References

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2. Langmuir I. The Effect of Space Charge and Residual Gases on Thermionic Currents in High Vacuum. ‒ Physical Review, 1913, vol. 2(6), pp. 450‒486.
3. Bull C.S. Space-Charge in Beam Tetrodes and Other Valves. ‒ Journal of the Institution of Electrical Engineer, Part III: Radio and Communication Engineering, 1948, vol. 95(33), pp. 17‒24, DOI: 10.1049/ji-3-2.1948.0006.
4. Kompfner R. The Klystron as Amplifier at Centimetric Wavelengths. ‒ Journal of the British Institution of Radio Engineers, 1947, vol. 7(3), pp. 117‒123.
5. Liu L. et al. Efficiency Enhancement of Reflex Triode Virtual Cathode Oscillator Using the Carbon Fiber Cathode. ‒ IEEE Transactions on Plasma Science, 2007, vol. 35(2), pp. 361‒368, DOI:10.1109/TPS.2007.893266.
6. Dubinov A.E. et al. Stochastron – an SHF Generator with a Virtual Cathode Realizing the Stochastic Resonance Mode. ‒ Russian Physics Journal, 1999, vol. 42(6), pp. 574‒579.
7. Clark J.J., Linke S. Operating Modes of a Pulsed 50-GW Diode. ‒ IEEE Transactions on Electron Devices, 1971, vol. 18(5), pp. 322‒330.
8. Wittmaack K. Beam Formation in a Triode Ion Gun. ‒ Nuclear Instruments and Methods, 1974, vol. 118(1), pp. 99‒113, DOI:10.1016/0029-554X(74)90690-9.
9. Degond P., Parzani C., Vignal V.-H. A One-Dimensional Model of Plasma Expansion. ‒ Mathematical and Computer Modelling, 2003, vol. 38(10), pp. 1093‒1099, DOI:10.1016/S0895-7177(03)90109-9.
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12. Sheridan T.E., Goree J. Analytic Expression for the Electric Potential in the Plasma Sheath. ‒ IEEE Transactions on Plasma Science, 1990, vol. 17(6), pp. 884‒888, DOI:10.1109/27.41228.
13. Farouki R.T., Dalvie M., Pavarino L.F. Boundary-Condition Refinement of the Child-Langmuir Law for Collisionless DC Plasma Sheaths. ‒ Journal of Applied Physics, 1990, vol. 68(12), pp. 6106‒6116, DOI:10.1063/1.346898.
14. Sheridan T.E. Analytic Theory of Sheath Expansion into a Cylindrical Bore. ‒ Physics of Plasmas, 1996, vol. 3(9), pp. 3507‒3512, DOI: 10.1063/1.871501.
15. Benilov M.S. The Child–Langmuir Law and Analytical Theory of Collisionless to Collision Dominated Sheaths. ‒ Plasma Sources Science and Technology, 2009, vol. 18(1), DOI:10.1088/0963-0252/18/1/014005.
16. Lisovskiy V.A., Derevianko V.A., Yegorenkov V.D. The Child-Langmuir Collision Laws for the Cathode Sheath of Glow Discharge in Nitrogen. ‒ Vacuum, 2014, vol. 103, pp. 49‒56, DOI:10.1016/j.vacuum.2013.12.008.
17. Zhang P. et al. 100 Years of the Physics of Diodes. ‒ Applied Physics Reviews, 2017, vol. 4(1), DOI:10.1063/1.4978231.
18. Tong C. et al. Metal-Induced Growth of Crystal Si for Low-Cost Al:ZnO/Si Heterojunction Thin Film Photodetectors. ‒ Materials Science in Semiconductor Processing, 2018, vol. 82, pp. 92–96, DOI:10.1016/j.mssp.2018.03.038.
19. Chow K.K., Maddix H.S., Chorney P. Thermionic Emission of Alkali Ions from Impregnated Metal Matrices. ‒ Applied Physics Letters, 1967, vol. 10(9), pp. 256‒258, DOI: 10.1063/1.1754936.
20. Nath C., Kumar A. Doping Level Dependent Space Charge Limited Conduction in Polyaniline Nanoparticles. ‒ Journal of Applied Physics, 2012, vol. 112(9), DOI:10.1063/1.4763362.
21. Tan J.-H., Anderson W.A. Current Transport in Copper Indium Gallium Diselenide Solar Cells Comparing Mesa Diodes to the Full Cell. ‒ Solar Energy Materials & Solar Cells, 2003, vol. 77(3), pp. 283‒292, DOI:10.1016/S0927-0248(02)00349-5.
22. Qasrawi A.F. et al. Photovoltaic Effect and Space Charge Limited Current Analysis in TlGaTe2 Crystals. ‒ Acta Physica Polonica A, 2012, vol. 122(1), pp. 152‒155, DOI:10.12693/APhysPolA.122.152.
23. Guedes V.F., Nobrega K.Z., Ramos R.V. Analytical Solution of the Space Charge Limited Current Using Lambert–Tsallis Wq Function. ‒ IEEE Transactions on Electron Devices, 2022, vol. 69(10), pp. 5787‒5791.
24. Dubinov A.E., Kitayev I.N. Child–Langmuir Law for a Planar Diode Filled with a Two-Layer Dielectric. ‒ IEEE Transactions on Plasma Science, 2016, vol. 44(10), pp. 2376‒2381, DOI:10.1109/TPS.2016.2601492.
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1. Child C.D. Discharge from Hot CaO. ‒ Physical Review (Series I), 1911, vol. 32(5), pp. 492‒511, DOI:10.1103/PHYS REV SERIES I.32.492.
2. Langmuir I. The Effect of Space Charge and Residual Gases on Thermionic Currents in High Vacuum. ‒ Physical Review, 1913, vol. 2(6), pp. 450‒486.
3. Bull C.S. Space-Charge in Beam Tetrodes and Other Valves. ‒ Journal of the Institution of Electrical Engineer, Part III: Radio and Communication Engineering, 1948, vol. 95(33), pp. 17‒24. DOI: 10.1049/ji-3-2.1948.0006.
4. Kompfner R. The Klystron as Amplifier at Centimetric Wavelengths. ‒ Journal of the British Institution of Radio Engineers, 1947, vol. 7(3), pp. 117‒123.
5. Liu L. et al. Efficiency Enhancement of Reflex Triode Virtual Cathode Oscillator Using the Carbon Fiber Cathode. ‒ IEEE Transactions on Plasma Science, 2007, vol. 35(2), pp. 361‒368, DOI:10.1109/TPS.2007.893266.
6. Dubinov A.E. et al. Stochastron – an SHF Generator with a Virtual Cathode Realizing the Stochastic Resonance Mode. ‒ Russian Physics Journal, 1999, vol. 42(6), pp. 574‒579.
7. Clark J.J., Linke S. Operating Modes of a Pulsed 50-GW Diode. ‒ IEEE Transactions on Electron Devices, 1971, vol. 18(5), pp. 322‒330.
8. Wittmaack K. Beam Formation in a Triode Ion Gun. ‒ Nuclear Instruments and Methods, 1974, vol. 118(1), pp. 99‒113, DOI:10.1016/0029-554X(74)90690-9.
9. Degond P., Parzani C., Vignal V.-H. A One-Dimensional Model of Plasma Expansion. ‒ Mathematical and Computer Modelling, 2003, vol. 38(10), pp. 1093‒1099, DOI:10.1016/S0895-7177(03)90109-9.
10. Weber B.V. et al. Plasma Erosion Opening Switch Research for ICF. ‒ Laser and Particle Beams, 1987, vol. 5(3), pp. 537‒548.
11. Abdallah N.B., Degond P., Mehats F. Mathematical Models of Magnetic Insulation. ‒ Physics of Plasmas, 1998, vol. 5(5), pp. 1522‒1534, DOI:10.1063/1.872810.
12. Sheridan T.E., Goree J. Analytic Expression for the Electric Potential in the Plasma Sheath. ‒ IEEE Transactions on Plasma Science, 1990, vol. 17(6), pp. 884‒888, DOI:10.1109/27.41228.
13. Farouki R.T., Dalvie M., Pavarino L.F. Boundary-Condition Refinement of the Child-Langmuir Law for Collisionless DC Plasma Sheaths. ‒ Journal of Applied Physics, 1990, vol. 68(12), pp. 6106‒6116, DOI:10.1063/1.346898.
14. Sheridan T.E. Analytic Theory of Sheath Expansion into a Cylindrical Bore. ‒ Physics of Plasmas, 1996, vol. 3(9), pp. 3507‒3512, DOI: 10.1063/1.871501.
15. Benilov M.S. The Child–Langmuir Law and Analytical Theory of Collisionless to Collision Dominated Sheaths. ‒ Plasma Sources Science and Technology, 2009, vol. 18(1), DOI:10.1088/0963-0252/18/1/014005.
16. Lisovskiy V.A., Derevianko V.A., Yegorenkov V.D. The Child-Langmuir Collision Laws for the Cathode Sheath of Glow Discharge in Nitrogen. ‒ Vacuum, 2014, vol. 103, pp. 49‒56, DOI:10.1016/j.vacuum.2013.12.008.
17. Zhang P. et al. 100 Years of the Physics of Diodes. ‒ Applied Physics Reviews, 2017, vol. 4(1), DOI:10.1063/1.4978231.
18. Tong C. et al. Metal-Induced Growth of Crystal Si for Low-Cost Al:ZnO/Si Heterojunction Thin Film Photodetectors. ‒ Materials Science in Semiconductor Processing, 2018, vol. 82, pp. 92–96, DOI:10.1016/j.mssp.2018.03.038.
19. Chow K.K., Maddix H.S., Chorney P. Thermionic Emission of Alkali Ions from Impregnated Metal Matrices. ‒ Applied Physics Letters, 1967, vol. 10(9), pp. 256‒258, DOI: 10.1063/1.1754936.
20. Nath C., Kumar A. Doping Level Dependent Space Charge Limited Conduction in Polyaniline Nanoparticles. ‒ Journal of Applied Physics, 2012, vol. 112(9), DOI:10.1063/1.4763362.
21. Tan J.-H., Anderson W.A. Current Transport in Copper Indium Gallium Diselenide Solar Cells Comparing Mesa Diodes to the Full Cell. ‒ Solar Energy Materials & Solar Cells, 2003, vol. 77(3), pp. 283‒292, DOI:10.1016/S0927-0248(02)00349-5.
22. Qasrawi A.F. et al. Photovoltaic Effect and Space Charge Limited Current Analysis in TlGaTe2 Crystals. ‒ Acta Physica Polonica A, 2012, vol. 122(1), pp. 152‒155, DOI:10.12693/APhysPolA.122.152.
23. Guedes V.F., Nobrega K.Z., Ramos R.V. Analytical Solution of the Space Charge Limited Current Using Lambert–Tsallis Wq Function. ‒ IEEE Transactions on Electron Devices, 2022, vol. 69(10), pp. 5787‒5791.
24. Dubinov A.E., Kitayev I.N. Child–Langmuir Law for a Planar Diode Filled with a Two-Layer Dielectric. ‒ IEEE Transactions on Plasma Science, 2016, vol. 44(10), pp. 2376‒2381, DOI:10.1109/TPS.2016.2601492.
Published
2022-11-17
Issue
No 1 (2023): Issue № 1
Section
Article