The physics of space-charge-limited current in diodes with finite electron injection velocities is investigated within the Lagrangian flow description. The space-charge-limited (SCL) current is shown to be given by where is the familiar Child–Langmuir current, 𝒰 and L are the diode voltage and length, respectively. It results from an intrinsic property of the diode rather than from electron reflexion, the current picture of SCL accepted since Langmuir’s days. For field emitted electrons, on the other hand, is proved to be universally valid, because in this case holds. A number of further diode properties are derived analytically and presented numerically.
REFERENCES
1.
A. Ya.
Ender
, H.
Kolinsky
, V. I.
Kuznetsov
, and H.
Schamel
, Phys. Rep.
328
, 1
(2000
).2.
3.
S. A.
Slutz
, J. W.
Poukey
, and T. D.
Pointon
, Phys. Plasmas
1
, 2072
(1994
).4.
P. F.
Ottinger
, P. J.
Goodrich
, D. D.
Hinshelwood
, D.
Mosher
, J. M.
Neri
, D. V.
Rose
, S. J.
Stephanakis
, and F. C.
Young
, Proc. IEEE
80
, 1010
(1992
).5.
6.
K. L.
Jensen
, M. A.
Kodis
, R. A.
Murphy
, and E.
Zaidman
, J. Appl. Phys.
82
, 845
(1997
).7.
8.
R. T.
Farouki
, M.
Dalvie
, and L. F.
Pavarino
, J. Appl. Phys.
68
, 6106
(1990
).9.
10.
11.
A. A. G.
Driskill-Smith
, D. G.
Hasko
, and H.
Ahmed
, Appl. Phys. Lett.
75
, 2845
(1999
);12.
13.
14.
15.
16.
17.
F. B. Llewellyn, Electron Inertia Effects (Cambridge University Press, London, 1941).
18.
19.
20.
V. I.
Kuznetsov
, A. V.
Solov’yev
, and A. Ya.
Ender
, Sov. Phys. Tech. Phys.
39
, 1207
(1994
).21.
22.
23.
24.
25.
In the case of a bipolar flow, for example, the Lagrangian formulation could be extended in Ref. 23 to account for the first time for counterstreaming, mobile ions.
26.
27.
28.
I. N. Bronstein, K. A. Semendjajew, G. Musiol, and H. Mühlig, Taschenbuch der Mathematik, 3rd ed. (Verlag Harri Deutsch, Frankfurt am Main, 1997).
29.
C. E.
Fay
, A. L.
Samuel
, and W.
Shockley
, Bell Syst. Tech. J.
17
, 49
(1938
).30.
31.
32.
33.
V. I. Kuznetsov and A. Ya. Ender, in Proceedings Conference on Low-Temperature Plasma (Petrozavodsk State University Publisher, Petrozavodsk, Russia, 1995), pp. 148–151 (in Russian).
34.
P. V. Akimov, H. Kolinsky, V. I. Kuznetsov, H. Schamel, and A. Ya. Ender, in Proceedings Conference on Low-Temperature Plasma (Petrozavodsk State University Publisher, Petrozavodsk, Russia, 1998), pp. 513–517 (in Russian).
35.
P. V.
Akimov
, A. Ya.
Ender
, H.
Kolinsky
, V. I.
Kuznetsov
, and H.
Schamel
, Prob. At. Sci. Technol.
1
, 155
(2000
).36.
R. C. Davidson, in Physics of Nonneutral Plasmas (Addison-Wesley, Redwood City, CA, 1990), Chap. 8, pp. 461–532.
37.
We thank the referee for pointing out some references unknown to us.
38.
39.
40.
41.
42.
C. K. Birdsall and W. B. Bridges, Electron Dynamics of Diode Regions (Academic, New York, 1966).
43.
H. Kolinsky, Ph.D. thesis, Bayreuth University, 1998 (in German).
44.
Y. Y.
Lau
, P. J.
Christenson
, and D.
Chernin
, Phys. Fluids B
5
, 4486
(1993
).45.
46.
O. M.
Bulashenko
, J. M.
Rubı́
, and V. A.
Kochelap
, Phys. Rev. B
61
, 5511
(2000
).47.
48.
P. V. Akimov, H. Schamel, H. Kolinsky, A. Ya. Ender, and V. I. Kuznetsov (unpublished).
49.
J. D.
Ivers
, L.
Schachter
, J. A.
Nation
, G. S.
Kerslick
, and R.
Advani
, J. Appl. Phys.
73
, 2667
(1993
).50.
L.
Schachter
, J. D.
Ivers
, J. A.
Nation
, and G. S.
Kerslick
, J. Appl. Phys.
73
, 8097
(1993
).51.
Y.
Modukuru
, M.
Cahay
, H.
Kolinsky
, and P.
Mumford
, J. Appl. Phys.
87
, 3386
(2000
).
This content is only available via PDF.
© 2001 American Institute of Physics.
2001
American Institute of Physics
You do not currently have access to this content.