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Noise in currents through thin insulating layers
Zijlstra,
Physica
R. J. J.
28
97 l-976
1962
NOISE
IN CURRENTS
THROUGH LAYERS
THIN
INSULATING
*)
by R. J. J. ZIJLSTRA Department
of Electrical
Engineering
University
of Minnesota,
Minneapolis,
Minnesota,
U.S.A.
synopsis Noise higher
measurements frequencies
are presented
and low
current
of currents levels
through
thin insulating
full shot noise was observed,
layers.
At
whereas
at
higher current levels the shot noise was suppressed. In addition to the shot noise lowfrequency noise was found. The mean square fluctuations of the latter in a small frequency
interval
A = contact
df could
be described
by 3 =
const IO
faAB-1
, where I = the current,
area, B N 1.7 and CCN 0.8.
Electrons can pass through thin layers of insulating 1. Introduction. materials by the quantum mechanical tunnel effect. Electron devices based on this effect can be used as cold emitters and as amplifiersr). It thus seemed worthwhile to study the noise properties of these devices. Since most of them make use of metal-metaloxide-metal sandwiches, the noise properties of these diode structures were studied. For the operation of these devices reference is made to the literaturel) 3). 2. Noise measurements. Two types of diodes were investigated. One consisted of tantalum and aluminium plates with a tantalum-oxide layer in between. The thickness of the oxide layer in this case was 128 A whereas the contact area was 6.25 x 1O-2 cm3; The other type consisted of tantalumtantalum-oxide gold. The thickness of the oxide layer in this case was 96 A and the contact area was 10-3 cm3. The noise measurements were made at low current levels and the frequency range was restricted also. There are two reasons for this: 1. Because of the relatively small thickness of the insulating layers, the two types of devices turned out to have capacitances as high as 0.1 pf and 0.0 1 pf respectively. 2. The differential resistance of the devices decreases strongly with increasing current. As a consequence, the impedance levels at high current l)
Supported
by U.S. Army
Signal Corps Contract.
-
971 -
972
R. J. J. ZIJLSTRA
levels or at high frequencies became too low for direct noise measurements with the noise analyzer availables). For a frequency interval df the noise of a two terminal network can be described
by
an appropriate
noise
current
generator
l/3
connected
in
parallel to that network. One can introduce the equivalent saturated diode current I,, of that network by putting 3 = 2eI,, df. Therefore the results of the noise measurements can be given in terms of I,, as a function of frequency
(see fig. 1 and fig 2).
Frequency (e/s) -
Fig. 1. The noise equivalent
saturated
for a Ta-Ta20s-Al
Figure
1 gives I,,
diode
current
diode at different
as a function
of frequency
I,,
as a function
of frequency
current levels.
at different
current
levels
for Ta-TasOs-Al sample. In all measurements the aluminium plate was biased positive with respect to the tantalum plate. It is observed that I,, decreases with increasing frequency at low frequencies whereas it levels off at higher frequencies. The high frequency values (at about 1 kc/s) are at the shot noise level (les = I) for small currents and somewhat lower at higher currents. Hence there is full shot noise at low current levels and suppressed shot noise at higher current levels. In addition there is extra lowfrequency noise (flicker effect) over and above the shot noise level. The frequency dependence of the flicker effect is const.lfa, where CLN 0.7. Figure 2 gives the results for the Ta-TasOs-Au device with the gold layer biased positive with respect to the tantalum layer. The results are somewhat
NOISE
IN CURRENTS
THROUGH
THIN
INSULATING
LAYERS
973
similar to those of fig. 1 but the striking difference is that the flicker noise is much higher in this case. Though a leveling off is observed at high frequencies the constant level of I,, could not be reached at any current level. Nevertheless, extrapolating the results towards higher frequencies, it is apparent that the high frequency values of I,, tend toward the shot noise level at the lower current levels, whereas at higher currents I,, tends toward a value lower than the full shot noise level. The frequency dependence of the low-frequency flicker effect is somewhat case, here a N 0.9.
Frequency
Fig. 2. The
noise
equivalent Ta-TasOh-Au
saturated diode
diode
steeper than in the previous
(c/s) -
current
at different
Ies
current
versus
frequency
for
a
levels.
Figure 3 gives I,, as a function of frequency for the Ta-Au sample at three different temperatures and only slightly different current levels. Corresponding measurements at the Ta-Al sample could not be made because of breakdown of the sample at liquid nitrogen temperature. The flicker noise increases with decreasing temperature; unfortunately, no data are available at sufficiently high frequencies to observe the shot noise as a function of temperature. 3. Discussion. If the passage of electrons through the insulating layer can be considered as a series of independent events occurring at random. the electrons injected into the positive biased metal will have a Poisson
974
R. J. J. ZIJLSTRA
distribution, since the tunnelling probabillity is very small. This should give rise to full shot noise fluctuations in the current4). This explains the experimental results at high frequencies and low current levels. At higher current levels, however, the noise spectra level off towards values lower than those of full shot noise. The observed noise can in this case be interpreted as suppressed shot noise. A possible explanation for the noise suppression could be found in the presence of traps in the insulating layers that are distributed in energy as well as in space. Trapped electrons will build up a space charge in the insulating layer which in turn will influence the tunnel probability.
frequency
Fig. 3. The
noise
equivalent saturated Ta-TazOs-Au diode
kps)
-
diode current Ieq versus at different temperatures.
frequency
for
a
Evidence for the presence of trapped electrons was obtained by studying the noise behavior when no voltage was supplied. If initially a voltage was applied and thereafter the noise was measured without drawing current (i.e.. with the voltage supply switched off) the noise observed at low frequencies turned out to be at first much higher than the thermal noise of the load resistor and then gradually decreased with time towards the latter level. If, however, the noise was measured directly after the sample was short circuited, no additional noise was observed. It is believed that these traps are responsible for the low-frequency flicker effect as well, since trapping is a time dependent event. Moreover
NOISE
IN CURRENTS
THROUGH
THIN
INSULATING
LAYERS
975
there will be a distribution of relaxation times associated with traps distributed in energy and in space which might give an explanation for the frequency dependence observed. That relatively long time constants are involved is furthermore evident from the fact that it takes the current many seconds to rise to a stable value after the voltage has been applied. The current-voltage characteristic had about the same shape at liquid nitrogen temperature as at room temperature, but the whole curve was shifted towards higher voltages; a voltage shift of several volts was observed. This seems to indicate a change in shape of the potential barrier. Such a change should affect trapping in the insulating layer and this, in turn, might qualitatively explain the temperature dependence of the low-frequency noise. The current dependence of the flicker noise at 10 c/s for both samples turned out to be 10, where @ II 1.7. If one considers n samples essentially alike in parallel, one would have I’ = nI where I is the current drawn by each sample and I’ the total current. From the experimental results quoted above one has for the mean square fluctuations interval df const IS 2=
f”
As a consequence given by
2 of I in a small frequency
df.
the mean square fluctuations i’2=,7=
of the total current
I’ are
const (I’)B
fanO- df
From the dimensional reasoning given above one is tempted to give the following expression for the mean square fluctuations in the current of one sample : const IS g= p&+1
df,
where A is the contact area of the device. Comparing the results obtained for both samples with the last formula, it turns out that the difference in low-frequency noise encountered can be accounted for in order of magnitude. Considering the fact that the value of a differs in both cases and that the samples are of different makes the agreement is satisfactory. Acknowledgement. Theauthorisindebted to Professor Dr. A. vander Ziel for helpful suggestions and for reading the manuscript. He wishes to thank Mr. E. D. Savoye for making the samples available. Received 20-3-62.
976 --
NOISE
IN CURRENTS
THROUGH
THIN
INSULATING
REFERENCES 1) Mead, 2)
Fisher,
3) Nielsen,
C. A., J. appl. Phys. J. C. and Giaever,
32 (1961) 646. I., J. appl. Phys. 32 (1961) 172.
E. G. and Van der Ziel,
4) Van der Ziel,
A., Rev. sci. Instr. 25 (1954) 899.
A., Noise, Prentice Hall, New York,
1954.
LAYERS
Physica
R. J. J.
28
97 l-976
1962
NOISE
IN CURRENTS
THROUGH LAYERS
THIN
INSULATING
*)
by R. J. J. ZIJLSTRA Department
of Electrical
Engineering
University
of Minnesota,
Minneapolis,
Minnesota,
U.S.A.
synopsis Noise higher
measurements frequencies
are presented
and low
current
of currents levels
through
thin insulating
full shot noise was observed,
layers.
At
whereas
at
higher current levels the shot noise was suppressed. In addition to the shot noise lowfrequency noise was found. The mean square fluctuations of the latter in a small frequency
interval
A = contact
df could
be described
by 3 =
const IO
faAB-1
, where I = the current,
area, B N 1.7 and CCN 0.8.
Electrons can pass through thin layers of insulating 1. Introduction. materials by the quantum mechanical tunnel effect. Electron devices based on this effect can be used as cold emitters and as amplifiersr). It thus seemed worthwhile to study the noise properties of these devices. Since most of them make use of metal-metaloxide-metal sandwiches, the noise properties of these diode structures were studied. For the operation of these devices reference is made to the literaturel) 3). 2. Noise measurements. Two types of diodes were investigated. One consisted of tantalum and aluminium plates with a tantalum-oxide layer in between. The thickness of the oxide layer in this case was 128 A whereas the contact area was 6.25 x 1O-2 cm3; The other type consisted of tantalumtantalum-oxide gold. The thickness of the oxide layer in this case was 96 A and the contact area was 10-3 cm3. The noise measurements were made at low current levels and the frequency range was restricted also. There are two reasons for this: 1. Because of the relatively small thickness of the insulating layers, the two types of devices turned out to have capacitances as high as 0.1 pf and 0.0 1 pf respectively. 2. The differential resistance of the devices decreases strongly with increasing current. As a consequence, the impedance levels at high current l)
Supported
by U.S. Army
Signal Corps Contract.
-
971 -
972
R. J. J. ZIJLSTRA
levels or at high frequencies became too low for direct noise measurements with the noise analyzer availables). For a frequency interval df the noise of a two terminal network can be described
by
an appropriate
noise
current
generator
l/3
connected
in
parallel to that network. One can introduce the equivalent saturated diode current I,, of that network by putting 3 = 2eI,, df. Therefore the results of the noise measurements can be given in terms of I,, as a function of frequency
(see fig. 1 and fig 2).
Frequency (e/s) -
Fig. 1. The noise equivalent
saturated
for a Ta-Ta20s-Al
Figure
1 gives I,,
diode
current
diode at different
as a function
of frequency
I,,
as a function
of frequency
current levels.
at different
current
levels
for Ta-TasOs-Al sample. In all measurements the aluminium plate was biased positive with respect to the tantalum plate. It is observed that I,, decreases with increasing frequency at low frequencies whereas it levels off at higher frequencies. The high frequency values (at about 1 kc/s) are at the shot noise level (les = I) for small currents and somewhat lower at higher currents. Hence there is full shot noise at low current levels and suppressed shot noise at higher current levels. In addition there is extra lowfrequency noise (flicker effect) over and above the shot noise level. The frequency dependence of the flicker effect is const.lfa, where CLN 0.7. Figure 2 gives the results for the Ta-TasOs-Au device with the gold layer biased positive with respect to the tantalum layer. The results are somewhat
NOISE
IN CURRENTS
THROUGH
THIN
INSULATING
LAYERS
973
similar to those of fig. 1 but the striking difference is that the flicker noise is much higher in this case. Though a leveling off is observed at high frequencies the constant level of I,, could not be reached at any current level. Nevertheless, extrapolating the results towards higher frequencies, it is apparent that the high frequency values of I,, tend toward the shot noise level at the lower current levels, whereas at higher currents I,, tends toward a value lower than the full shot noise level. The frequency dependence of the low-frequency flicker effect is somewhat case, here a N 0.9.
Frequency
Fig. 2. The
noise
equivalent Ta-TasOh-Au
saturated diode
diode
steeper than in the previous
(c/s) -
current
at different
Ies
current
versus
frequency
for
a
levels.
Figure 3 gives I,, as a function of frequency for the Ta-Au sample at three different temperatures and only slightly different current levels. Corresponding measurements at the Ta-Al sample could not be made because of breakdown of the sample at liquid nitrogen temperature. The flicker noise increases with decreasing temperature; unfortunately, no data are available at sufficiently high frequencies to observe the shot noise as a function of temperature. 3. Discussion. If the passage of electrons through the insulating layer can be considered as a series of independent events occurring at random. the electrons injected into the positive biased metal will have a Poisson
974
R. J. J. ZIJLSTRA
distribution, since the tunnelling probabillity is very small. This should give rise to full shot noise fluctuations in the current4). This explains the experimental results at high frequencies and low current levels. At higher current levels, however, the noise spectra level off towards values lower than those of full shot noise. The observed noise can in this case be interpreted as suppressed shot noise. A possible explanation for the noise suppression could be found in the presence of traps in the insulating layers that are distributed in energy as well as in space. Trapped electrons will build up a space charge in the insulating layer which in turn will influence the tunnel probability.
frequency
Fig. 3. The
noise
equivalent saturated Ta-TazOs-Au diode
kps)
-
diode current Ieq versus at different temperatures.
frequency
for
a
Evidence for the presence of trapped electrons was obtained by studying the noise behavior when no voltage was supplied. If initially a voltage was applied and thereafter the noise was measured without drawing current (i.e.. with the voltage supply switched off) the noise observed at low frequencies turned out to be at first much higher than the thermal noise of the load resistor and then gradually decreased with time towards the latter level. If, however, the noise was measured directly after the sample was short circuited, no additional noise was observed. It is believed that these traps are responsible for the low-frequency flicker effect as well, since trapping is a time dependent event. Moreover
NOISE
IN CURRENTS
THROUGH
THIN
INSULATING
LAYERS
975
there will be a distribution of relaxation times associated with traps distributed in energy and in space which might give an explanation for the frequency dependence observed. That relatively long time constants are involved is furthermore evident from the fact that it takes the current many seconds to rise to a stable value after the voltage has been applied. The current-voltage characteristic had about the same shape at liquid nitrogen temperature as at room temperature, but the whole curve was shifted towards higher voltages; a voltage shift of several volts was observed. This seems to indicate a change in shape of the potential barrier. Such a change should affect trapping in the insulating layer and this, in turn, might qualitatively explain the temperature dependence of the low-frequency noise. The current dependence of the flicker noise at 10 c/s for both samples turned out to be 10, where @ II 1.7. If one considers n samples essentially alike in parallel, one would have I’ = nI where I is the current drawn by each sample and I’ the total current. From the experimental results quoted above one has for the mean square fluctuations interval df const IS 2=
f”
As a consequence given by
2 of I in a small frequency
df.
the mean square fluctuations i’2=,7=
of the total current
I’ are
const (I’)B
fanO- df
From the dimensional reasoning given above one is tempted to give the following expression for the mean square fluctuations in the current of one sample : const IS g= p&+1
df,
where A is the contact area of the device. Comparing the results obtained for both samples with the last formula, it turns out that the difference in low-frequency noise encountered can be accounted for in order of magnitude. Considering the fact that the value of a differs in both cases and that the samples are of different makes the agreement is satisfactory. Acknowledgement. Theauthorisindebted to Professor Dr. A. vander Ziel for helpful suggestions and for reading the manuscript. He wishes to thank Mr. E. D. Savoye for making the samples available. Received 20-3-62.
976 --
NOISE
IN CURRENTS
THROUGH
THIN
INSULATING
REFERENCES 1) Mead, 2)
Fisher,
3) Nielsen,
C. A., J. appl. Phys. J. C. and Giaever,
32 (1961) 646. I., J. appl. Phys. 32 (1961) 172.
E. G. and Van der Ziel,
4) Van der Ziel,
A., Rev. sci. Instr. 25 (1954) 899.
A., Noise, Prentice Hall, New York,
1954.
LAYERS