Расчет цепей постоянного тока, содержащих диоды Чайльда–Ленгмюра
Ключевые слова:
диод Чайльда–Ленгмюра, первеанс, параллельное и последовательное соединение
Аннотация
Впервые предложены к изучению и к расчетам цепи постоянного тока, содержащие в качестве своих элементов диоды Чайльда–Ленгмюра, которые имеют вольт-амперную характеристику в виде степенного закона с показателем степени 3/2. К диодам Чайльда–Ленгмюра следует относить вакуумные термоэмиссионные диоды с постоянными токами, ограниченными собственным пространственным зарядом электронного пучка, а также солнечные элементы, полупроводниковые светоизлучающие диоды, мощные диоды электронных ускорителей прямого действия и др. Цепи, содержащие несколько диодов Чайльда–Ленгмюра, нигде ранее не рассматривались. В статье приведены соотношения для общего первеанса при параллельном и последовательном соединении диодов Чайльда–Ленгмюра, имеющих разные первеансы. Приведено два примера расчетов общего первеанса цепи из трех и четырех диодов Чайльда–Ленгмюра. Методы и результаты данной работы могут быть использованы для расчета вольт-амперных характеристик, например, сложных многоэлементных цепей солнечных батарей или светоизлучающих диодов.
Литература
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.
#
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.
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.
#
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.
