Authors
Abstract
A novel and rather simple method is presented to describe the physics of space-charge region in a planar diode. The method deals with the issue in the time domain and as a consequence transient time behavior can be achieved. Potential distributions and currents obtained using this technique, supposing zero initial velocity for electrons, reveal absolute agreement with Child's results. Moreover, applying the method for non-zero uniform initial velocity for electrons, gives results which are in good agreement with previous works
Keywords
[1] C. D. Child, “Discharge from hot cao,” Phys. Rev. (Series I)., vol. 32, pp. 492-511, May. 1911.
[2] I Langmuir, “The effect of space charge and residual gases on thermionic currents in high vacuum,” Phys. Rev., vol. 2, no. 6, pp. 450-486, Dec. 1913.
[3] I. Langmuir, K. B. Blodgett, “Currents Limited by Space Charge between Coaxial Cylinders,” Phys. Rev, vol. 22, no. 4, pp. 347-356, Oct. 1923.
[4] I. Langmuir, K. B. Blodgett, “Currents Limited by Space Charge between Concentric Spheres,” Phys. Rev, vol. 24, no. 1, pp. 49-59, Jul. 1924.
[5] J. W. Luginsland, Y. Y. Lau, R. M. Gilgenbach, “Two-Dimensional Child-Langmuir Law,” Phys. Rev. Lett., vol. 77, no. 22, pp. 4668- 4670, Nov. 1996.
[6] Y. Y. Lau, “Simple Theory for the Two-Dimensional Child-Langmuir Law,” Phys. Rev. Lett, vol. 87, no. 27, pp. 278301- 278303, Dec. 2001.
[7] R. J. Umstattd, J. W. Luginsland, “Two-Dimensional Space-Charge-Limited Emission: Beam-Edge Characteristics and Applications,” Phys. Rev. Lett, vol. 87, no. 14, pp. 145002- 145005, Sep. 2001.
[8] K. J. Kostov, J. J. Barroso, “Space-charge-limited current in cylindrical diodes with finite-length emitter,” Phys. Plasmas, vol. 9, no. 3, pp. 1039- 1042, Mar. 2002.
[9] J. W. Luginsland, Y. Y. Lau, R. J. Umstattd, J. J. Watrous, “Beyond the Child–Langmuir law: A review of recent results on multidimensional space-charge-limited flow,” Phys. Plasmas, vol. 9, no. 5, pp. 2371- 2376, May. 2002.
[10] W. S. Koh, L. K. Ang, T. J. T. Kwan, “Three-dimensional Child–Langmuir law for uniform hot electron emission,” Phys. Plasmas, vol. 12, no. 5, pp. 053107-1- 053107-6, May. 2005.
[11] Y. Y. Lau, D. Chernin, D. G. Colombant, P. T. Ho, “Quantum extension of Child-Langmuir law,” Phys. Rev. Lett., vol. 66, no. 11, pp. 1446- 1449, Mar. 1991.
[12] L. K. Ang, T. J. T. Kwan, Y. Y. Lau, “New Scaling of Child-Langmuir Law in the Quantum Regime,” Phys. Rev. Lett., vol. 91, no. 20, pp. 208303- 208306, Nov. 2003.
[13] L. K. Ang, W. S. Koh, Y. Y. Lau, T. J. T. Kwan, “Space-charge-limited flows in the quantum regime,” Phys. Plasmas, vol. 13, no. 5, pp. 056701-1-056701-6, May. 2006.
[14] S. Bhattacharjee, A. Vartak, V. Mukherjee, “Experimental study of space-charge-limited flows in a nanogap,” Appl. Phys. Lett., vol. 92, no. 19, pp. 191503-1- 191503-3, May. 2008.
[15] H. R. Jori, A. W. Trivelpiece, “Exact Relativistic Solution for the One Dimensional Diode,” J. Appl. Phys., vol. 40, no. 10, pp. 3924- 3926, 1969.
[16] A. Valfells, D. W. Feldman, M. Virgo, P. G. O'Shea, Y. Y. Lau, “Effects of pulse-length and emitter area on virtual cathode formation in electron guns,” Phys. Plasmas., vol. 9, no. 5, pp. 2377- 2382, May. 2002.
[17] L. K. Ang, P. Zhang, “Ultrashort-Pulse Child-Langmuir Law in the Quantum and Relativistic Regimes,” Phys. Rev. Lett., vol. 98, no. 16, pp. 164802- 164805, Apr. 2007.
[18] A. Pedersen, A. Manolescu, A. Valfells, “Space-Charge Modulation in Vacuum Microdiodes at THz Frequencies,” Phys. Rev. Lett., vol. 104, no. 17, pp. 175002- 175005, Apr. 2010.
[19] Y. Zhu, L. K. Ang, “Child–Langmuir law in the Coulomb blockade regime,” Appl. Phys. Lett., vol. 98, no. 5, pp. 051502-1- 051502-3, Jan. 2011.
[20] T. C. Fry, “The Thermionic Current between Parallel Plane Electrodes; Velocities of Emission Distributed According to Maxwell's Law,” Phys. Rev, vol. 17, no. 4, pp. 441- 452, Apr. 1921.
[21] I. Langmuir, “The Effect of Space Charge and Initial Velocities on the Potential Distribution and Thermionic Current between Parallel Plane Electrodes,” Phys. Rev, vol. 21, no. 4, pp. 419- 435, Apr. 1923.
[22] D. H. Parsons, “Exact Integration of the Space-Charge Equation for a Plane Diode: A Simplified Theory,” Nature, vol. 200, pp. 126- 127, Oct. 1963.
[23] P. V. Akimov, H. Schamel, H. Kolinsky, A. Ya. Ender, V. I. Kuznetsov, “The true nature of space-charge-limited currents in electron vacuum diodes: A Lagrangian revision with corrections, ” Phys. Plasmas., vol. 8, no. 8, pp. 3788- 3791, May. 2001.
[2] I Langmuir, “The effect of space charge and residual gases on thermionic currents in high vacuum,” Phys. Rev., vol. 2, no. 6, pp. 450-486, Dec. 1913.
[3] I. Langmuir, K. B. Blodgett, “Currents Limited by Space Charge between Coaxial Cylinders,” Phys. Rev, vol. 22, no. 4, pp. 347-356, Oct. 1923.
[4] I. Langmuir, K. B. Blodgett, “Currents Limited by Space Charge between Concentric Spheres,” Phys. Rev, vol. 24, no. 1, pp. 49-59, Jul. 1924.
[5] J. W. Luginsland, Y. Y. Lau, R. M. Gilgenbach, “Two-Dimensional Child-Langmuir Law,” Phys. Rev. Lett., vol. 77, no. 22, pp. 4668- 4670, Nov. 1996.
[6] Y. Y. Lau, “Simple Theory for the Two-Dimensional Child-Langmuir Law,” Phys. Rev. Lett, vol. 87, no. 27, pp. 278301- 278303, Dec. 2001.
[7] R. J. Umstattd, J. W. Luginsland, “Two-Dimensional Space-Charge-Limited Emission: Beam-Edge Characteristics and Applications,” Phys. Rev. Lett, vol. 87, no. 14, pp. 145002- 145005, Sep. 2001.
[8] K. J. Kostov, J. J. Barroso, “Space-charge-limited current in cylindrical diodes with finite-length emitter,” Phys. Plasmas, vol. 9, no. 3, pp. 1039- 1042, Mar. 2002.
[9] J. W. Luginsland, Y. Y. Lau, R. J. Umstattd, J. J. Watrous, “Beyond the Child–Langmuir law: A review of recent results on multidimensional space-charge-limited flow,” Phys. Plasmas, vol. 9, no. 5, pp. 2371- 2376, May. 2002.
[10] W. S. Koh, L. K. Ang, T. J. T. Kwan, “Three-dimensional Child–Langmuir law for uniform hot electron emission,” Phys. Plasmas, vol. 12, no. 5, pp. 053107-1- 053107-6, May. 2005.
[11] Y. Y. Lau, D. Chernin, D. G. Colombant, P. T. Ho, “Quantum extension of Child-Langmuir law,” Phys. Rev. Lett., vol. 66, no. 11, pp. 1446- 1449, Mar. 1991.
[12] L. K. Ang, T. J. T. Kwan, Y. Y. Lau, “New Scaling of Child-Langmuir Law in the Quantum Regime,” Phys. Rev. Lett., vol. 91, no. 20, pp. 208303- 208306, Nov. 2003.
[13] L. K. Ang, W. S. Koh, Y. Y. Lau, T. J. T. Kwan, “Space-charge-limited flows in the quantum regime,” Phys. Plasmas, vol. 13, no. 5, pp. 056701-1-056701-6, May. 2006.
[14] S. Bhattacharjee, A. Vartak, V. Mukherjee, “Experimental study of space-charge-limited flows in a nanogap,” Appl. Phys. Lett., vol. 92, no. 19, pp. 191503-1- 191503-3, May. 2008.
[15] H. R. Jori, A. W. Trivelpiece, “Exact Relativistic Solution for the One Dimensional Diode,” J. Appl. Phys., vol. 40, no. 10, pp. 3924- 3926, 1969.
[16] A. Valfells, D. W. Feldman, M. Virgo, P. G. O'Shea, Y. Y. Lau, “Effects of pulse-length and emitter area on virtual cathode formation in electron guns,” Phys. Plasmas., vol. 9, no. 5, pp. 2377- 2382, May. 2002.
[17] L. K. Ang, P. Zhang, “Ultrashort-Pulse Child-Langmuir Law in the Quantum and Relativistic Regimes,” Phys. Rev. Lett., vol. 98, no. 16, pp. 164802- 164805, Apr. 2007.
[18] A. Pedersen, A. Manolescu, A. Valfells, “Space-Charge Modulation in Vacuum Microdiodes at THz Frequencies,” Phys. Rev. Lett., vol. 104, no. 17, pp. 175002- 175005, Apr. 2010.
[19] Y. Zhu, L. K. Ang, “Child–Langmuir law in the Coulomb blockade regime,” Appl. Phys. Lett., vol. 98, no. 5, pp. 051502-1- 051502-3, Jan. 2011.
[20] T. C. Fry, “The Thermionic Current between Parallel Plane Electrodes; Velocities of Emission Distributed According to Maxwell's Law,” Phys. Rev, vol. 17, no. 4, pp. 441- 452, Apr. 1921.
[21] I. Langmuir, “The Effect of Space Charge and Initial Velocities on the Potential Distribution and Thermionic Current between Parallel Plane Electrodes,” Phys. Rev, vol. 21, no. 4, pp. 419- 435, Apr. 1923.
[22] D. H. Parsons, “Exact Integration of the Space-Charge Equation for a Plane Diode: A Simplified Theory,” Nature, vol. 200, pp. 126- 127, Oct. 1963.
[23] P. V. Akimov, H. Schamel, H. Kolinsky, A. Ya. Ender, V. I. Kuznetsov, “The true nature of space-charge-limited currents in electron vacuum diodes: A Lagrangian revision with corrections, ” Phys. Plasmas., vol. 8, no. 8, pp. 3788- 3791, May. 2001.
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