GERDA Scientific / Technical Report: GSTR-11-M001
August 16, 2011
Measuring picoamperes
Oleksandr Volynetsa,
a
Max-Planck-Institut für Physik, München, Germany
Abstract
This note was written in order to show which problems might occur while measuring small currents of the order of picoamperes or nanoamperes. It is a completely
different type of measurements than ampere-current measurements. There are some
important issues highlighted in this note that should be taken into account. Features of shielded setups are discussed and also tricks for unshielded setups are shown.
Tests of different setups were carried out to demonstrate features of the corresponding circuits.
Contents
1 Introduction
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2 Fundamental differences in low-current measurements
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3 Experimental setup
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4 Unshielded setup: problems, limitations and tricks
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5 Shielded setup: new possibilities
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6 How to check consistency with an oscilloscope?
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7 Conclusions
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8 Aknowledgement
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1
Introduction
An important difference between measurements of low currents and normal currents
is due to the circuit inside the current meter being used for the measurements. Normalcurrent measurements are carried out using a passive method while for low-current measurements an active circuit with an amplifier is used. Therefore, currents created by the
noise might affect the measurements if they are of the same order of magnitude as the
currents being measured. Usually, this happens if the measured currents are O(10nA) or
less. If the setup is not sufficiently shielded, all cables act as antennae and are sensitive
to all the radionoise around. Even the movement of a hand can affect the measurements.
However, shielding usually could be easily done as only some parts have to be shielded
(see Chap. 5). The consistency of the measurements can be checked with an oscilloscope
(see Chap. 6). In this memo, different methods are highlighted together with problems
which might occur during measurements of low currents and ways of solving them.
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Fundamental differences in low-current measurements
Figure 1: Different possible setups for normal current measurements
The two circuits shown in Fig. 1 are substantially different. However, the current
measured is usually the same. In the first case, the resistor is placed between the voltage
source and the meter. In the second case, the resistor is placed between the voltage source
and the ground. However, in the case of low currents, a meter which contains an active
circuit with an amplifier will measure different currents. Since the internal voltage source
contains a capacitor connected to the power line, this capacitor acts as a filter against the
noise coming from the power line, but only if the resistor is between the voltage source
and the “input”. Otherwise, all the noise from the power line is measured as current.
Therefore, the main point is that the load has to be placed between the voltage source
and the input of the meter, not the ground.
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This is important when a voltage source is used. If a battery is used, there should be
no difference in the circuits shown in Fig 1, because a battery is a very good low-noise
source.
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Experimental setup
Measurements and tests were carried out using a Keithley Electrometer 6517A (from
now on denoted as electrometer). It is able to measure currents down to 10 attoamperes
and resistivities up to 1017 Ω. It has different measurement ranges: 20pA, 200pA, 2nA etc.,
which correspond to different precision. For all of them, a different feedback resistivity,
RF , (see Fig. 2) is used. Low-current measurements were performed using an internal
voltage source of the electrometer and a 1 GΩ resistor. Two types of circuits - shielded
and unshielded - were used to demonstrate the problems. For additional tests, the LeCroy
Waverunner 6030A Oscilloscope with 350MHz frequency was used.
The schematic corresponding to the circuit in Fig. 2 is shown in Fig. 3.
Figure 2: Equivalent circuit for current measurements using the Oscilloscope
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Unshielded setup: problems, limitations and tricks
As was already mentioned, an active circuit is used for current measurements in the
electrometer. It contains a feedback resistor RF with a large resistivity of 1 GΩ or 1 T Ω,
depending on the range of the measurement. This means that all the noise on the cables
is also amplified. Usual levels of noise are O(nA). If the current to be measured is smaller
than this value, no reasonable measurement is possible without a special setup.
For the first measurements, an unshielded setup was used with the circuit shown in
Fig.4. The cable which connects the resistor to the input of the electrometer was a Banana
cable. It was not shielded in order to be a perfect tool to examine the influence of the
surrounding.
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Figure 3: Connections used for current measurements
Figure 4: An unshielded setup for tests on cross talk sensitivity
Range
2µA
200 nA
Value 0.0006 [µA] 0.6 [nA]
20 nA
-0.1 [nA]
2 nA
∼ ±0.01 [nA]
200 pA
∼ 5 [pA]
20 pA
??
Table 1: Current measured in the unshielded setup using different ranges of the electrometer
The measured currents are listed in Table 1.
The expected current is
I = 0.5 V /1 GΩ = 500 pA.
As can be seen, the only reasonable range in this case is 200 nA, for which RF ≈ 1 GΩ.
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For the range 20 nA, the feedback resistor is RF ≈ 1 GΩ, and thus the measurements are
much more sensitive to the noise being amplified. In addition, the electrometer does not
show “Overflow”, if the current being measured is too high for the range. This will be
explained in chapter 6.
However, there is a trick which could be applied in a case when shielding the setup is
impossible. The approach is to remove all the high frequencies which dominate the noise.
This can be done by connecting a capacitor, C, in parallel to the feedback resistor RF . In
reality, this capacitor is then placed between the “Preamp output” and the “Hi” input,
see Fig. 5.
Figure 5: A capacitor, C, connected in parallel to the feedback resistor RF acts as a
high-pass filter
In this case, the capacitor is being charged for some time t ≈ RF C. Therefore low
values of C are preferable. However, the lower C, the higher is the cut-off frequency.
So there should be a balance between these two factors. The tests presented here are in
the 2 nA and above with RF ≈ 1 GΩ and C = 0.33 nF. The charge-up time is therefore
t ≈0.33 s. After 10 seconds the measured currents were reasonable. For the range 200 pA
the charge-up time would have been 330 s due to RF ≈ 1 T Ω. This was not tried out.
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Shielded setup: new possibilities
For the second set of measurements, a shielded setup was used with the circuit shown
in Fig. 6. The cable which connected the resistor to the input of the electrometer was a
BNC cable. Also the resistor itself was placed in a metal box, so both the resistor and
the cable were shielded.
Values of the current measured are shown in Table 1. The expected current is still
I = 0.5V /1GΩ = 500 pA.
In this case, all the values are reasonable as the shielding protects the circuit from
noise. Thus, only the signal is amplified and measured. However, if the box was opened,
the setup became sensitive to the surrounding again.
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Figure 6: Shielded setup
Range 200 nA
Value 0.5 [nA]
20 nA
0.5 [nA]
2 nA
0.5 [nA]
200 pA
Overflow
Table 2: Value of the current measured in the shielded setup using different ranges of the
electrometer
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How to check consistency with an oscilloscope?
Sometimes the setup is not properly shielded and the current is not measured correctly.
However, it is often difficult to discover this. An oscilloscope can help checking the
consistency of a measurement. The 2V analog output of the electrometer was connected
to the “signal” of the oscilloscope and the “Low” cable was connected to the “ground”
of the oscilloscope input. The oscilloscope shows the behaviour of the analog output
voltage during the measurements, see Fig. 2. An expected behaviour for the full range
of measurements, say, 20 nA constant current measured at 20 nA measurement range,
is a constant voltage at 2 V. If the setup is not shielded properly, there should be a
dominant noise with 50Hz frequency from the power line. During a current-measurement
the electrometer averages the current over some time and if there is some AC noise above
the constant DC current to be measured the readings would be correct (see Fig. 2-A in
[1]).Fig. 7 shows the voltage monitored by the oscilloscope the shielded setup for different
V /1 GΩ
2V . Every plot
ranges selected on the electrometer. The expected voltage is V = 0.5range
shows the same behaviour but with different average. In all cases, the voltage measured
by the electrometer falls into the voltage range 0..2 V.
The same plots are shown in Fig. 8 for the unshielded setup. In this case the AC
noise above the DC current being measured is much larger than the range. Therefore, the
signal is clipped. This is described in details in chapter 2.3.2 of [1]. In short, the signal
is a superposition of a DC component (say, 300 pA) and an AC component (say, 20pA).
The current is larger than the measurement range (say, 200 pA) and the clipping occurs
at 220 pA. As the average after the clipping is still larger than the range, the electrometer
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Figure 7: Voltage seen on the “2V output” versus time for different ranges of the electrometer and the shielded setup.
should show “Overflow”. However, as noise provides an additional AC component (say,
2000 pA) it is added to the signal. This is also clipped at 220 pA and the average of the
sum Signal + Noise is below 200 pA and a wrong current is measured. The same happens
to the voltage monitored on the oscilloscope. This is shown in Fig. 8.
A capacitor connected to the “Preamp output” and the “Hi” input reduces the highfrequency noise and therefore only the signal is measured. Also there remain a 50-Hz
component from the power line which is not filtered bu the capacitor. If the signal value
is too high, the electrometer shows “Overflow” as the average of the signal is more than
the range. The plots for an unshielded setup with the capacitor are shown in Fig. 9.
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Conclusions
An important thing to be kept in mind during low-current measurements is that
the setup should be shielded as much as possible. There are two crucial conditions for
a meaningful measurement. One is that the current should be measured between the
voltage source and the “Hi” input of the Oscilloscope. The second one is that the cable
leading to the “Hi” input of the electrometer is the most sensitive component in the circuit
and must be shielded against noise. If it is not, this cable acts as an antenna for all the
radionoise around which is then amplified.
To check whether measurements make sense, one can connect the oscilloscope to the
“2V output” and see the structure of the signal. It gives a hint about the consistency of
any measurement.
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Figure 8: Voltage seen on the “2V output” versus time for different ranges of the electrometer and the unshielded setup.
Figure 9: Voltage seen on the “2V output” versus time for different ranges of the electrometer and the unshielded setup with a capacitor in parallel to the feedback resistor.
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Aknowledgement
The idea to write this note was developed after a very nice conversation with the
Keithley employee Norbert Willnecker who explained a lot about electronics and especially
about low-current measurements. I want to thank him for the very nice discussions about
all the tricks and features explained in this note, and for his kindness to help me to
understand electronics.
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References
[1] Model 6517A Electrometer User’s Manual
[2] http://www.lecroy.com/ – LeCroy webpage
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