The physics of space-charge-limited current (JSCL) in diodes with finite electron injection velocities v0 is investigated within the Lagrangian flow description. The space-charge-limited (SCL) current is shown to be given by JSCL=(X+1+X2)3JCL, where JCLU3/2/L2 is the familiar Child–Langmuir current, X=(mv02/2eU)1/2, 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, JCL is proved to be universally valid, because in this case v0=0 holds. A number of further diode properties are derived analytically and presented numerically.

1.
A. Ya.
Ender
,
H.
Kolinsky
,
V. I.
Kuznetsov
, and
H.
Schamel
,
Phys. Rep.
328
,
1
(
2000
).
2.
S. A.
Slutz
and
M. P.
Desjarlais
,
J. Appl. Phys.
67
,
6705
(
1990
).
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.
P. D.
Mumford
and
M.
Cahay
,
J. Appl. Phys.
84
,
2754
(
1998
).
6.
K. L.
Jensen
,
M. A.
Kodis
,
R. A.
Murphy
, and
E.
Zaidman
,
J. Appl. Phys.
82
,
845
(
1997
).
7.
Yu. N.
Gartstein
and
P. S.
Ramesh
,
J. Appl. Phys.
83
,
2958
(
1998
).
8.
R. T.
Farouki
,
M.
Dalvie
, and
L. F.
Pavarino
,
J. Appl. Phys.
68
,
6106
(
1990
).
9.
E.
Hernández
,
Cryst. Res. Technol.
33
,
285
(
1998
).
10.
C.
Litwin
and
R.
Rosner
,
Phys. Rev. E
58
,
1163
(
1998
).
11.
A. A. G.
Driskill-Smith
,
D. G.
Hasko
, and
H.
Ahmed
,
Appl. Phys. Lett.
75
,
2845
(
1999
);
W. A.
de Heer
and
R.
Martel
,
Phys. World
13
,
49
(
2000
).
12.
V. T.
Binh
and
Ch.
Adessi
,
Phys. Rev. Lett.
85
,
864
(
2000
);
K.
Jensen
,
Phys. World
13
,
25
(
2000
).
13.
C. D.
Child
,
Phys. Rev.
32
,
492
(
1911
).
14.
I.
Langmuir
,
Phys. Rev.
2
,
450
(
1913
);
I.
Langmuir
,
Gen. Electr. Rev.
38
,
180
(
1935
).
15.
W.
Schottky
,
Z. Phys.
14
,
63
(
1923
) (in German).
16.
V. R.
Bursian
and
V. I.
Pavlov
,
Zh. Russ. Fiz.-Khim. O-va
55
,
71
(
1923
) (in Russian).
17.
F. B. Llewellyn, Electron Inertia Effects (Cambridge University Press, London, 1941).
18.
B. B.
Godfrey
,
Phys. Fluids
30
1553
(
1987
).
19.
Y. Y.
Lau
,
Y.
Liu
, and
R. K.
Parker
,
Phys. Plasmas
1
,
2082
(
1994
).
20.
V. I.
Kuznetsov
,
A. V.
Solov’yev
, and
A. Ya.
Ender
,
Sov. Phys. Tech. Phys.
39
,
1207
(
1994
).
21.
H.
Schamel
and
S.
Bujarbarua
,
Phys. Fluids B
5
,
2278
(
1993
).
22.
H.
Schamel
and
V.
Maslov
,
Phys. Rev. Lett.
70
,
1105
(
1993
).
23.
H.
Kolinsky
and
H.
Schamel
,
Phys. Plasmas
1
,
2359
(
1994
).
24.
H.
Kolinsky
and
H.
Schamel
,
J. Plasma Phys.
57
,
403
(
1997
).
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.
I.
Langmuir
,
Phys. Rev.
21
,
419
(
1923
).
27.
S.
Liu
and
R. A.
Dougal
,
J. Appl. Phys.
78
,
5919
(
1995
).
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.
E. A.
Coutsias
and
D. J.
Sullivan
,
Phys. Rev. A
27
,
1535
(
1983
).
31.
R. J.
Lomax
,
Proc. IEE C
108
,
119
(
1961
).
32.
A. V.
Paschenko
and
B. N.
Rutkevich
,
Sov. J. Plasma Phys.
3
,
437
(
1977
).
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.
E. W. B.
Gill
,
Philos. Mag.
49
,
993
(
1925
).
39.
W.
Kleen
and
H.
Rothe
,
Z. Phys.
104
,
711
(
1937
) (in German).
40.
B.
Salzberg
and
A. V.
Haeff
,
RCA Rev.
2
,
336
(
1938
).
41.
G.
Jaffé
,
Phys. Rev.
65
,
91
(
1944
).
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.
A similar in this respect wrong identification between JSCL and JL was made recently in Ref. 46.
46.
O. M.
Bulashenko
,
J. M.
Rubı́
, and
V. A.
Kochelap
,
Phys. Rev. B
61
,
5511
(
2000
).
47.
R. H.
Fowler
and
L.
Nordheim
,
Proc. R. Soc. London, Ser. A
119
,
173
(
1928
).
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.
You do not currently have access to this content.