PHYSICAL ELECTRONICS
I.
T. Fohl
L. E. Sprague
D. S. Dunavan
Prof. W. B. Nottingham
J. F. Campbell, Jr.
A.
ELECTRON EMISSION AND CESIUM PLASMA
1.
THERMIONIC ENERGY CONVERTERS
Thermionic diodes containing cesium vapor ionized by contact with the heated sur-
face of the diode are of increasing interest as their potentialities become established.
Many calculations demand a knowledge of the vapor pressure of the cesium or of its
mean-free path or both.
To satisfy this demand as well as is possible with our present
limited knowledge of the actual characteristics of cesium,
the following equations have
been worked out:
p = 2.45X10
p = 2.45 X 10
X
c
8
-1/2
Cs
8 -1/2
TCs
e
-89L0/TCs
-3870/TC
X
= 1.38 X 1013 T 1/2
g
X = 1.38 X 1011 T1/
c
g
mm
s mm
0
103670/TC
X 1 03670/T
m
cm
where p is the pressure in millimeters; TCs is the cesium condensation temperature
in
OK;
T
is the average temperature of cesium gas in
oK;
and X
is
the mean-free
path.
The numerical results represented by these equations have been incorporated in
a nomographic chart (Fig. I-1) prepared by J. H. Hufford, Class of '63, M.I.T. The
columns at the right give a one-to-one correspondence between pressure and cesium
temperature.
specified.
This is the pressure in equilibrium with liquid cesium at the temperature
If the temperature of the gas in some part of the diode is different from the
temperature of the cesium reservoir,
the mean-free path will be slightly greater
if the temperature in the diode is greater than the cesium temperature.
The chart also
serves to show how much change takes place in the mean-free path, and of course it can
be used to estimate the mean-free path in the immediate neighborhood of the cesium surface by setting a
straightedge,
or alignment thread, at the cesium temperature point on
scale. It is hoped that this chart will be found useful for quick estimations of
g
the pressure-temperature mean-free-path relations.
the T
W. B. Nottingham
Tg
P TCs
PTCs
Ac
3000
20
3
_
4
10
2500
102
230
370
5
3
-
380
390
2000
2
-27
10
-
3 -2
V
4 00
4 1 -410
10
1500oo
1000
2O
44
3
450
45
6
460
470
2
480
490
500
I0
8
90
p =2.45 X 10 T
8
700
-420
430
I/2 -8910
e
TCs
8
-1/2 -3870
10 T
p=2.45 X 10 T
4
mm
10
oo
Nc= 1.38 X 10 T
10
Tcs
p
mm
m
5
6
250
--
-
2
3
4
260
6
270
2
o
2
3
o
average
aTg= temperature of cesium gas K
3
4
550
-
2
6
10
6
6
--
300
Use scales a, b and c for high temperature.
600
-650
2
310
5
6
o
700
320
2
330
6
7
7504
6
10
800
c2
o
2
Fig. I-1.
360
900
4
S5
6
950
10 -
Sb
340
3
350
0.110
T
Use scales a,d and e for low temperature.
200
290
9
O
4
c = mean-free path inmeters
255
I0
-
temperature *K
245
-
6
-
pressure in mm
= cesium condensation
400
3
1
0
5
3
500oo
-240
21-
2
1
-1-4
I3
1
13 /2
-
235
5
6-
c
Temperature-pressure mean-free-path relations for cesium.
001--
d
3
4
5
6
370
e
(I.
B.
PHYSICAL ELECTRONICS IN THE SOLID STATE
1.
CHARACTERISTICS OF SEMICONDUCTOR JUNCTIONS
PHYSICAL ELECTRONICS)
In Quarterly Progress Report No. 57, measurements were reported on two type
1N670 diffused silicon diodes. The analysis of these data is essentially complete.
In Fig. I-2 is shown a semilogarithmic plot of the forward part of the characteristic
0
of one of the diodes at several temperatures from 20 C to 140'C. The slight bend in
the characteristic was previously mentioned in connection with other diodes that were
studied (1). In order to understand the reason for this bend, measurements were made
of the ac forward conductance of the diodes as a function of applied voltage. The results
(Fig. 1-3) show that the conductance at higher forward voltages is about what would be
expected from the measured dc conductance, calculated as dI/dV. This is represented
• .• • .
0-2 --
102
1N670-I
1400
120
600
10000
-5-
10
20'
_
o -
u
10
.
.
10_
8
-
10
10 10
0
1.10 0.20 0.30 0.40
I
I
050 060
I
070
V (VOLTS)
Fig. I-2.
Forward characteristic of diode 1N670-1.
by the solid line in the upper end of the curve.
At smaller applied voltages the conduc-
tance is always larger than would be expected from the dc characteristic. This is the
behavior expected from a surface channel viewed as a lossy transmission line.
On the basis of this evidence that a surface channel existed and was responsible for
(I.
PHYSICAL ELECTRONICS)
10r
IN670-1
IOOoC
AC CONDUCTANCE
10-22
0-3
10
0
100 KC
12
A
IKC
A
1
Fig. 1-3.
I
0
0.10
I
I
0.20
j
I
0.30
040
V(VOLTS)
I
0.50
0.60
Forward ac conductance (diode 1N670-1).
part of the forward current, we made an analysis of the forward characteristic,
the theory of Cutler and Bath (2).
using
This analysis shows that the part of the current from
the channel should be
c
c 0p(
where VT = q/kT.
T)T- VT
By assuming another current component,
I , given by
I = Iu [exp(V/nVT)-1 ]
a three-point fit was made to the forward characteristic.
forward characteristic after the determination of Ic
fit to the entire forward characteristic below
10
o
S-30
,
Reconstruction of the entire
I
, and n produced an excellent
o
ampere.
Furthermore,
comparison
of the constants determined here with the measured low-voltage dc conductance,
through the relation Ic
= 2VTg
c
shows excellent agreement.
consideration of the channel as a transmission line.
go
This relation follows from
Here gc is the conductance of the
channel alone.
This is calculated from the observed conductance by subtracting from go
a reasonable (but small) estimate of the conductance of I u .
In Fig. I-4 is shown a plot of Iu , I
Ou
cO
, I'
and the reverse current at three different
O
(I.
PHYSICAL ELECTRONICS)
We see the general trend of agreement between I c o and I'
voltages.
o
.
In addition, the
temperature variation of the reverse current is similar - a fact that shows that it, too,
arises from a surface channel. The other current component, I u , displays a completely
different temperature behavior.
This component is thought to be a combination of
diffusion and space-charge recombination currents.
28
30
32
Fig. I-4.
36
34
VT
38
40
-
(VOLTSI ) ')
(VOLTS
Temperature dependence of current components.
The diode on which data have been presented here shows behavior that is completely
consistent with conventional channel behavior.
Another diode,
tion, shows incomplete agreement with the channel picture.
quite similar in construcIn
contrast with diode
which showed a reverse current that always increased with time after appli-
1N670-1,
cation of a reverse bias, this diode (1N670-2) shows a reverse current that decreases
with time.
This observation indicates that the density of slow surface states must be
changing, probably as the result of migration of ions along the surface of the diode.
A
rough calculation shows that the mobilities required for this behavior are in the range
of 10 -
3
to 10 -
4
cm 2/volt-sec, which suggests the presence of a surface film of water.
This is unlikely, however, because diodes that have been freshly evacuated also show the
(I.
PHYSICAL ELECTRONICS)
downward creep of current with time.
More complete results of this study are presented in a Ph.D. thesis, Department
of Physics, M.I.T. (1960).
J. F. Campbell, Jr.
References
1. J. F. Campbell, Jr., Characteristics of semiconductor junctions, Quarterly
Progress Report No. 55, Research Laboratory of Electronics, M.I.T., Oct. 15, 1959,
pp. 1-3.
2. M. Cutler and H. M. Bath, Surface leakage current in silicon fused junction
diodes, Proc. IRE 45, 39-43 (1957).