A formula is derived for the electric tunnel effect through a potential barrier of arbitrary shape existing in a thin insulating film. The formula is applied to a rectangular barrier with and without image forces. In the image force problem, the true image potential is considered and compared to the approximate parabolic solution derived by Holm and Kirschstein. The anomalies associated with Holm's expression for the intermediate voltage characteristic are resolved. The effect of the dielectric constant of the insulating film is discussed in detail, and it is shown that this constant affects the temperature dependence of the J‐V characteristic of a tunnel junction.

1.
J. C.
Fisher
 and
I.
Giaever
,
J. Appl. Phys.
32
,
172
(
1961
).
Google Scholar
Crossref
Search ADS
 
2.
A. Sommerfeld and H. Bethe, Handbüch der Physik von Geiger und Sched (Julius Springer‐Verlag, Berlin, 1933), Vol. 24/2, p. 450.
3.
R.
Holm
,
J. Appl. Phys.
22
,
569
(
1951
).
Google Scholar
Crossref
Search ADS
 
4.
R.
Holm
 and
B.
Kirschstein
,
Z. Tech. Physik
16
,
488
(
1935
).
Google Scholar
 
5.
D. Bohm, Quantum Theory (Prentice‐Hall, Inc., Englewood Cliffs, New Jersey, 1951), p. 275.
6.
By the substitution V(x) = η+φ(x), we have inherently assumed that the width Δs of the barrier in the range Ex>V(x)>η is constant and equal to the barrier width at the Fermi level. This assumption is justified for practical barriers, because Δs varies slowly below the Fermi level [Fig. 4 (a)], and the integral has effective values only when Ex≃η.
7.
Note added in proof. Simmons has shown [see
J. G.
 
Simmons
,
J. Appl. Phys.
 
34
,
238
(
1963
)]
Google Scholar
Crossref
Search ADS
 
that, at relatively low voltages, Eq. (27) reduces to
J = JL(V+βV3),
β = [(Ae)2/96φ]−[Ae2/32φ32],
which is in good quantitative agreement with the experimental results of Knauss and Breslow
[see
H. P.
Knauss
 and
R. A.
Breslow
,
Proc. IRE
50
,
1843
(
1962
)].
Google Scholar
 
8.
W. R. Smythe, Static and Dynamic Electricity (McGraw‐Hill Book Company, Inc., New York, 1950), Chap. IV.
9.
R. Holm, Electric Contacts Handbook (Springer‐Verlag, Berlin, 1958), 3rd ed., p. 433.
10.
R.
 
Holm
 and
W.
 
Meissner
,
Z. Physik
 
74
,
715
(
1932
);
Google Scholar
Crossref
Search ADS
 
R.
Holm
 and
W.
Meissner
,
86
,
787
(
1933
).,
Z. Phys.
Google Scholar
Crossref
Search ADS
 
11.
J. G.
Simmons
,
G. J.
Unterkofler
, and
W. W.
Allen
,
Appl. Phys. Letters
2
,
78
(
1963
).
Google Scholar
Crossref
Search ADS
 
12.
A. R. von Hippel, Dielectric Materials and Applications (Tech. Press, Cambridge, Massachusetts, and John Wiley & Sons, Inc., New York, 1961), Pt. V.
This content is only available via PDF.
© 1963 The American Institute of Physics.
1963
The American Institute of Physics
You do not currently have access to this content.