Cathode Field in Diodes under Partial Space-Charge Conditions

Henry F. Ivey

doi:10.1103/PhysRev.76.554

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Cathode Field in Diodes under Partial Space-Charge Conditions

Henry F. Ivey

Westinghouse Electric Corporation, Bloomfield, New Jersey

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Phys. Rev. 76, 554 – Published 15 August, 1949

DOI: https://doi.org/10.1103/PhysRev.76.554

Abstract

A method for calculating the electric field at the cathode of a diode for any condition of current flow in the diode is presented. A "universal" curve gives the cathode field as a function of diode current. The equation for this curve is $\frac{I}{I_{s}} = \frac{1}{2} [1 \pm {\{1 - \frac{27}{4} {(\frac{E}{E_{0}})}^{2} (1 - \frac{E}{E_{0}})\}}^{\frac{1}{2}}]$

where $I$ is the diode current, $I_{s}$ is the saturation current corresponding to the applied anode voltage as calculated from the Child-Langmuir equation, $E$ is the cathode field, and $E_{0}$ is the value of $E$ in the absence of current flow.

The only restrictions on the derivation are those of an equipotential, smooth cathode, and negligible initial velocities of emission. Only plane and cylindrical diodes have been considered, but the results are believed to be applicable to any geometry. Application of the results to the study of thermionic cathodes in the Schottky emission region is very straightforward.

The variation of the cathode field as a function of anode voltage is also discussed. A method for calculating the potential distribution in a plane diode for any value of diode current is given in the Appendix.

References (11)

C. D. Child, Phys. Rev. 32, 492 (1911)
I. Langmuir, Phys. Rev. 2, 450 (1913)
I. Langmuir and K. B. Blodgett, Phys. Rev. 22, 347 (1923)
Stern, Gossling, and Fowler, Proc. Roy. Soc. A124, 699 (1929)
R. Cockburn, Proc. Phys. Soc. London 47, 810 (1935) at the M.I.T. Electronics Conference (April 7, 1949)
Omitted endnote
M. E. Rose, Bartol Research Foundation, Contract OEMsr-385, First Progress Report, Supplement I (November 1942)
Crank, Hartree, Ingham, and Sloane, Proc. Phys. Soc. (London) 51, 954 (1939)
H. M. Schwartz, of the Bartol Foundation (communication from W. E. Danforth)
I. Langmuir and K. T. Compton, Rev. Mod. Phys. 3, 251 (1931)
Coomes, Buck, and Petrauskas, Third Progress Report, Contract NObsr-30028, Physics Department, University of Notre Dame (March 19, 1948)

[c1] C. D. Child, Phys. Rev. 32, 492 (1911)

[c2] I. Langmuir, Phys. Rev. 2, 450 (1913)

[c3] I. Langmuir and K. B. Blodgett, Phys. Rev. 22, 347 (1923)

[c4] Stern, Gossling, and Fowler, Proc. Roy. Soc. A124, 699 (1929)

[c5] R. Cockburn, Proc. Phys. Soc. London 47, 810 (1935) at the M.I.T. Electronics Conference (April 7, 1949)

[c6] Omitted endnote

[c7] M. E. Rose, Bartol Research Foundation, Contract OEMsr-385, First Progress Report, Supplement I (November 1942)

[c8] Crank, Hartree, Ingham, and Sloane, Proc. Phys. Soc. (London) 51, 954 (1939)

[c9] H. M. Schwartz, of the Bartol Foundation (communication from W. E. Danforth)

[c10] I. Langmuir and K. T. Compton, Rev. Mod. Phys. 3, 251 (1931)

[c11] Coomes, Buck, and Petrauskas, Third Progress Report, Contract NObsr-30028, Physics Department, University of Notre Dame (March 19, 1948)

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Cathode Field in Diodes under Partial Space-Charge Conditions

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