We studied mathematical models for degradation behaviors of current and voltage in electron guns especially using oxide cathodes. We found that the current and the voltage, I(t) and V(t), follow the stretched exponential decay in oxide cathodes. On this basis, we derived a general expression for the time-dependent current–voltage relation as I(t)=p(t)V(t)δ(t), where δ(t) is a time-dependent exponent and the perveance, p(t), is a function of δ(t). The exponent δ(t) indicates the deviation of the classical Child–Langmuir relation (I=pV32). This deviation is attributed to the gradual change of the electron gun geometry over time.

1.
C. D.
Child
,
Phys. Rev.
32
,
492
(
1911
).
2.
I.
Langmuir
,
Phys. Rev.
2
,
450
(
1913
);
I.
Langmuir
,
Phys. Rev.
21
,
419
(
1923
).
3.
M.
Sedlaček
,
Electron Physics of Vacuum and Gaseous Devices
(
Wiley
, New York,
1996
), pp.
67
74
.
4.
S. H.
Gold
and
G. S.
Nusinovich
,
Rev. Sci. Instrum.
68
,
3945
(
1997
).
5.
L. K.
Ang
,
T. J. T.
Kwan
, and
Y. Y.
Lau
,
Phys. Rev. Lett.
91
,
208303
(
2003
).
6.
H.
Suzuki
, in
Advances in Imaging and Electron Physics
, edited by
P. W.
Hawkes
(
Academic
, New York,
1999
), Vol.
105
, pp.
267
404
.
7.
B. M.
Weon
,
A.
van Dam
,
G. S.
Park
,
C. H.
Hwang
,
S. D.
Han
,
I. W.
Kim
,
S. K.
Seol
,
Y. B.
Kwon
,
C. S.
Cho
,
J. H.
Je
,
Y.
Hwu
,
W.-L.
Tsai
, and
P.
Ruterana
,
J. Vac. Sci. Technol. B
21
,
2184
(
2003
).
8.
B. M.
Weon
and
J. H.
Je
, in “
Proceedings of 2004 IEEE International Vacuum Electron Sources Conference
,” Invited to “
Oxide cathodes—the 100th anniversary
” (
IEEE Electron Devices Society
,
2004
), pp.
100
103
;
[
Appl. Surf. Sci.
(in press)].
9.
A.
Kadish
,
W.
Peter
, and
M. E.
Jones
,
Appl. Phys. Lett.
47
,
115
(
1985
).
10.
R. T.
Longo
,
J. Appl. Phys.
94
,
6966
(
2003
).
11.
S.
Humphries
,
S.
Russell
,
B.
Carlsten
,
L.
Earley
, and
P.
Ferguson
,
Phys. Rev. ST Accel. Beams
7
,
060401
(
2004
).
You do not currently have access to this content.