Vibration Reed Electrometer for Accurate Measurement ... - IEEE Xplore

IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 56, NO. 2, APRIL 2007

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Vibration Reed Electrometer for Accurate Measurement of Electrical Currents Below 10 pA Gert Rietveld and Helko E. van den Brom

Abstract—We have developed a home-built vibrating reed (VR) electrometer. The heart of the meter is a VR capacitor, which excels in a stable and low input leakage current of only 8 aA with a 2 aA noise for a 1 h measurement. This paper demonstrates that this makes the instrument ideal for the characterization of subtle charge effects in, for example, connectors and cables. The exceptional sensitivity of the electrometer is proven in a measurement of the leakage resistance of an air gap capacitor which results in a value of Rleak = (8.8 ± 0.3) · 1017 Ω, obtained at a test voltage of only 10 V. Calibration of the system with both a picoampere and a picocoulomb generator shows that the instrument has an accuracy of 15 parts in 106 (k = 1) at a current of 1 pA. As far as we are aware, this is the best uncertainty for a room temperature electrometer published so far. Index Terms—Calibration, current measurement, electrometer, picoammeter, small currents.

Fig. 1. Schematic diagram of the VR electrometer. Crucial elements are the vacuum gap capacitors Cfb and Cvr . In the text, further explanations of the operation principle are given.

a frequency of 580 Hz. This vibration induces an ac current equal to Iac = Vin · dCvr /dt.

(1)

I. I NTRODUCTION

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OR A LONG TIME, picoampere currents have been measured in the area of ionizing radiation. Ionization chambers convert the radiation into a current, which is measured with a typical uncertainty of 1 % to 0.1 %. In the past decade, the interest in picoampere and even femtoampere current measurements has revived due to miniaturization in the semiconductor industry and research in the field of single electron tunneling (SET). Currently, a meter with subfemtoampere resolution and noise is even commercially available.1 Calibration and temperature dependence of the 2 TΩ input feedback resistor of this instrument limits its specifications at 1 pA to 1.7 %. In this paper, we describe a special setup for the accurate measurement of small currents, based on an input circuit taken from an old vibrating reed (VR) electrometer [1]. Here, the current is not applied to a high-ohmic input resistor but to a capacitor. This type of approach enables both high sensitivity and accuracy. The accuracy is demonstrated via calibration with recently developed picoampere and picocoulomb generators. II. VR E LECTROMETER The principle [2], [3] of the VR electrometer is schematically depicted in Fig. 1. The dc input current Iin generates a dc voltage Vin over the VR capacitor Cvr , which oscillates with Manuscript received July 11, 2006; revised November 30, 2006. The authors are with the NMi Van Swinden Laboratorium, Electricity section, 2600 AR Delft, The Netherlands (e-mail: [email protected]). Digital Object Identifier 10.1109/TIM.2007.890792 1 Keithley 6430 Sub-Femtoamp SourceMeter. See www.keithley.com for more information. The identification of commercial equipment in this paper does not imply endorsement of the NMi Van Swinden Laboratorium.

The input resistor Rin of 200 MΩ prevents this ac signal from flowing into the current source generating Iin . After passing through Cfb , the ac current is amplified and subsequently rectified by the lock-in amplifier (LIA, Stanford Research Systems model SR830). The generator (not shown in Fig. 1) that is driving the VR capacitor via an electromagnet is also used as the frequency reference for the LIA. The output of the LIA is analogically integrated to get an increasing output voltage Vfb , that is fed back via a simple first-order RC low pass filter to the feedback capacitor Cfb . The feedback loop minimizes the ac signal measured by the LIA and thus ensures that Vin is kept at 0 V, i.e., nulling the charge on the VR capacitor. In this way, a constant dc current Iin leads to a linear ramp of the feedback voltage dVfb /dt equal to dVfb /dt = Iin /Cfb .

(2)

If the value of Cfb is known, only the measurement of dVfb /dt is needed. dVfb /dt can be measured with a highaccuracy digital voltmeter triggered by an accurate time base for determining the unknown current Iin . Note that this method of slope integration is essentially similar to that used for decades in accurate teraohmmeters [4]. In these teraohmmeters, the current is generated by applying a voltage across a highohmic resistor. The unique element of the VR setup is the input circuit that essentially consists of the vacuum gap capacitors Cvr and Cfb without any active electronic device such as an opamp. The plates of both the feedback and VR capacitor are kept at a fixed distance by a single piece of pure sapphire. This leads to extremely low leakage currents, which is a major advantage with respect to other electrometers.

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Fig. 2. Measurement sequence used in the calibration of picoampere current sources. The null measurements are used to correct for offset currents.

Fig. 4. Current measured by the VR electrometer after the connection of an input connector (and in one case also of the cable) to the setup. Results are given for a G874 connector (circles), a BNC connector together with a Keithley low-noise BNC cable (filled triangles), and for a triax input connector with triax cable (inset).

Fig. 3. Input offset current of the bare VR electrometer (without any connection to the input) as a function of time. Each point is the average of, respectively, a 10 min (main figure) or 1 h (inset) measurement.

III. M EASUREMENT M ETHOD Measurement of a current I consists of applying several cycles of values 0, −I, 0, +I, 0 (see Fig. 2). The measurements with zero applied current give the possibility to correct for the effect of offset currents. In order to minimize the effect of leakage currents through the feedback capacitor, the voltage ramp during the current measurement is kept symmetrical around 0 V. Depending on the value of the current, the measurement time ranges from 40 s to 500 s. In order to limit leakage currents and noise we have paid extensive attention to correct shielding and guarding, especially of the input terminal. All lines containing sensitive signals are contained in a single, grounded, case (dashed line in Fig. 1). With respect to the original electrometer [1] the sensitivity was considerably increased by changing the driving frequency from 465 Hz to the 580 Hz resonance frequency of the VR capacitor, by improving the preamplifier using a low-noise opamp (OPA111), and by using a modern LIA. In practice, the resonance of the VR capacitor is so broad that it is not necessary to adjust the phase of the LIA during the experiments due to, e.g., temperature changes. The use of a sinusoidal driving signal instead of the original square wave helped to reduce the noise. An essential part of the new meter is the integrator in the feedback loop, which makes the VR capacitor a nullindicating amplifier and makes continuous measurements of current possible. Another important aspect is the automation of the instrument (including sources) so that many measurement cycles can be repeated automatically. IV. M EASUREMENT R ESULTS The first test of the instrument was the measurement of the offset current with an open input, that is with no connectors or cables connected to the input. A typical result is shown in Fig. 3.

The offset current of the “bare” VR electrometer slowly drifts to a value of only (8 ± 4) aA where the 4 aA noise (k = 1) is the standard deviation in a single 10 min measurement. When taking 1 h averages, the standard deviation of the measurement is only 1.7 aA (see the inset of Fig. 3). The distribution of the 10 min measurement values is not Gaussian—there are relatively more measurements with high current values. This is due to the occasional occurrence of small discharges—possibly due to ionizing radiation—resulting in small steps in feedback voltage and thus higher current values. The low offset current makes the setup ideal for studying subtle charge effects in different cables and connectors. In all cases, the outer conductors were connected to the case of the VR input circuit (dashed line in Fig. 1). In order to find the best type of input connector for our measurements, we have tested two types of bayonet Neill–Concelman (BNC) connectors, a triax connector, an N-connector, and a G874 connector. The N- and G874-connectors appear to give no measurable additional offset current, with a noise that only slightly exceeds that of the bare setup (typically 7 aA in a 9 min measurement). The result for the G874 connector is given in Fig. 4. There is a significant difference between the two BNC connectors we have tested, which can be related to the mechanical rigidity with which they can be put into the input head of the VR electrometer. Surprisingly, the triax connector was the worst connector giving a noise of around 20 aA, independent on how the guard was connected (either to the input terminal, or to the external case). For all connectors, the application of the connector to the VR input sometimes initiated an initial current of around 100 aA, which typically decayed in 1 h to 2 h to the final value of 10 aA. In the case of the lower quality BNC connector, the initial current could be as large as 500 aA with a decay time of 5 h to 20 h before the final value of (16 ± 13) aA was reached. The system was further used to characterize different types of cables: a regular RG58 coax cable, a triax cable, and two BNC cables that were specifically recommended by the respective manufacturers as low-noise cables. It appears that all cables significantly increase noise in the measurement, and for the majority of the cables also a higher input offset current

RIETVELD AND van den BROM: VR ELECTROMETER FOR MEASUREMENT OF ELECTRICAL CURRENTS BELOW 10 pA

Fig. 5. VR current as a function of time for several voltages (see labels) applied to the internal feedback capacitor Cfb in order to measure the leakage resistance of Cfb .

was found. This is clearly caused by piezo- and triboelectric effects in the cables [5]. By far the best and worst results were obtained with the two BNC cables, respectively. One BNC cable, specially developed for small current measurements, showed an initial current of around 500 aA–1000 aA, but this current decayed in approximately one day to the value of the bare setup with a noise of only 11 aA (see Fig. 4). The other BNC cable produced an extremely high noise of 1300 aA, making it entirely unsuitable for our purpose. The triax and RG58 cables gave comparable results with an offset current of approximately 70 and 10 aA, respectively, and a noise in both cases of around 50 aA. The results for the triax cable with triax input connector is given in the inset of Fig. 4. As a conclusion of the testing of the input connectors and cables, we decided to use either the G874 input connector and RG58 cable (a cable that is used in our impedance laboratory) or the BNC input connector with the Keithley low-noise BNC cable. To minimize piezo- and triboelectric effects, the cables were mechanically fixed with tape to the table of the measurement setup with a minimum of mechanical stress. As a final demonstration of the exceptional sensitivity and low noise of our measurement setup, we have measured the leakage resistance of the feedback capacitor Cfb . We expect a very high value for the leakage resistance since the plates of Cfb are separated by a single crystalline piece of sapphire. The leakage resistance is determined by measuring the current of the VR setup when a constant voltage of, respectively, −9.8 V, +10.2 V, and −10.7 V is applied to Cfb (with no connections to the input). The result is given in Fig. 5. From these data, the leakage resistance Rleak,fb of the feedback capacitor is determined as (8.8 ± 0.3) · 1017 Ω. This result, obtained at a test voltage of only 10 V, can only be equaled by ultrasensitive SET electrometers operating at 50 mK [6]. V. U NCERTAINTY OF THE S YSTEM The uncertainty budget of the VR electrometer follows rather straightforwardly from (2). Timing is accurate to subpart in 106 level, and voltage measurements can readily be performed at the uncertainty of a few parts in 106 . This leaves the noise in the measurements and especially the uncertainty in the exact value of Cfb as the main uncertainty sources.

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Fig. 6. Schematic setup for calibration of the VR electrometer with a picoampere or picocoulomb generator. Calibration is achieved via application of either a known current dVcal /dt · Ccal or a known charge ∆Vcal · Ccal to the electrometer. With the optional circuitry (dashed lines, with Rcomp = 100 TΩ), a dc input offset current can be compensated for.

The feedback capacitor is specifically designed for low leakage current, and does not have a well-defined three- or fourterminal connection geometry. As a result, the values of Cfb obtained by a commercial capacitance bridge with removed outer covers of the VR input do not reproduce better than a few parts in 104 . Thus, the calibration of the VR electrometer has to be performed in a completely assembled state with an accurate picoampere or picocoulomb generator. In this way, all systematic effects can be transferred into an effective Cfb value. The basis of the picoampere generator is the reverse principle of the VR electrometer: a current Ical is generated by applying a linear voltage ramp dVcal /dt to a known capacitance Ccal . After our pioneering work with such a generator [7], significantly improved versions were made at Physikalisch-Technische Bundesanstalt (PTB) [8] and by ourselves [9]. The accuracy of the NMi Van Swinden Laboratorium (VSL) picoampere generator is 10 ppm (k = 1) at the 1-pA level. Note that this does not include the practically inevitable charge effects of cables and connectors as discussed in the previous paragraph. The total setup for calibration of Cfb is schematically depicted in Fig. 6. Apart from the main elements of the picoampere generator, Vcal and Ccal , also the possibility for compensating a dc offset current via Vcomp /Rcomp is shown. The calibration results of Cfb with the NMi VSL picoampere generator are shown in Fig. 7(a). For the measurements below 2 pA, a 10 pF calibration capacitor is used, whereas a 100 pF capacitor is used for currents in the range of 1 pA to 4 pA. The measurement sequence follows that in Fig. 2 and is typically repeated 200 times, taking one day, for a single calibration point. The values obtained for all current levels, ranging from 100 fA to 4 pA, are quite consistent. The resulting average value of Cfb is Cfb = (20.1007 ± 0.0003) pF

(k = 1).

This 15-ppm uncertainty of Cfb includes the noise in the measurement and thus is equal to the total uncertainty of the VR electrometer. Note that this hardly exceeds the 10 ppm (k = 1) uncertainty of the picoampere generator. In this initial calibration, the facility for compensating a dc offset current via Vcomp and Rcomp was not used. The main reason is that there is a risk of systematic deviations in the calibration due to the extra circuitry connected to the input. The downside of not compensating a dc offset current is that

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+Qcal and −Qcal , and takes about 2.5 h measurement time. A complete calibration run takes one day and covers all ten charge levels given in Fig. 7(b), ranging from 2 to 20 pC. The values obtained for all applied charge levels and for different calibration runs, some with and some without offset current compensation, are quite consistent. The resulting average value of Cfb obtained with the picocoulomb generator is Cfb = (20.1048 ± 0.0003) pF

(k = 1).

In order to verify the results of the picocoulomb generator, the calibration was again performed with the picoampere generator as well giving a value of Cfb = (20.1051 ± 0.0005) pF

(k = 1).

The agreement between the two methods is excellent; the difference in values is only (15 ± 27) parts in 106 (k = 1). The value of Cfb is about 200 parts in 106 different from that obtained in the earlier calibration, indicating a significant drift over the period of nine months between the calibrations. An additional subject of further study is the influence of the environment (pressure, temperature, humidity) on the value of Cfb . Fig. 7. (a) Results of the calibration of the VR electrometer with the picoampere generator or (b) the picocoulomb generator. The solid lines in both graphs indicate the average value of all measurements (uncertainty 15 ppm, k = 1). The dotted line in (b) is the average value of the picoampere generator results performed in the same period showing excellent agreement between the two methods. The difference in the value of Cfb for (a) and (b) is probably caused by drift in the 9 month time period between the two calibrations.

typically several days had to be waited for after connection of the calibration capacitor Ccal to the VR electrometer until the offset current was below 1 fA. Such a low offset current is essential for not having the VR electrometer drift into overload output voltage during the one day calibration time with the picoampere generator. Nine months after the initial calibration the idea arose to additionally calibrate the system with a picocoulomb generator, since the VR electrometer essentially is a charge and not a current measuring device. The setup is exactly the same as given in Fig. 6, but now a step ∆Vcal instead of a stable dVcal /dt is applied to Ccal , resulting in the application of a calibration charge of Qcal = ∆Vcal · Ccal . The value of Cfb now directly follows from the measured ratio of step size in Vcal and Vfb and the known value of Ccal . When the offset current compensation is used, the value of Rcomp should be at least 100 TΩ for having an error less than ten parts in 106 . With a 1 TΩ compensation resistor an error is found of 800 ppm, caused by charge leakage immediately after the applied voltage step due to the nonzero time constant of the VR electrometer feedback loop. Note that the picocoulomb generator is much more straightforward to apply than the picoampere generator, since no additional software or hardware is required to obtain a stable input value (see [8] and [9]). Fig. 7(b) shows the results of several calibration runs with the picocoulomb generator, all obtained using a 10 pF calibration capacitor. A single point is the result of 140 steps for both

VI. C ONCLUSION We have further improved and characterized our VR setup for measurements of currents at the (sub)picoampere level. Due to the input circuitry of only vacuum gap capacitors, the input offset current of the setup is lower than 10 aA with a noise of only 1.7 aA (1 h average). The setup has been used to characterize subtle charge effects in different types of (input) connectors and cables. Connectors with rigid constructions, like N-connectors, G874 connectors, and good quality BNC connectors, hardly add any additional offset and noise to the measurement. Cables generally add at least several tens of attoamperes noise. Best results are obtained with short cables designed for low leakage current. The exceptional sensitivity and low noise of the electrometer is proven in a measurement of the leakage resistance of the air gap feedback capacitor in the electrometer, which results in a value of Rleak,fb = (8.8 ± 0.3) · 1017 Ω, obtained at a test voltage of only 10 V. The VR electrometer was calibrated using two methods, a picoampere generator and a picocoulomb generator, each having a total uncertainty of 15 ppm (k = 1). The results of the two methods agree within the k = 1 combined uncertainty of the calibration. As far as we are aware, the 15 ppm uncertainty of the VR electrometer makes the instrument the most accurate room temperature instrument for the measurement of currents of 10 pA and below. R EFERENCES [1] Model 401 Vibrating Reed Electrometer, Cary Instruments, Monrovia, CA, 1969. instrument manual. [2] H. Paleosky, R. K. Swank, and R. Grenchik, “Design of dynamic condenser electrometers,” Rev. Sci. Instrum., vol. 18, no. 5, pp. 298–314, May 1947. [3] W. R. Williams and R. C. Hawes, “Vibrating reed electrometers,” Instrum. Control Syst., vol. 36, no. 11, pp. 112–118, 1963.

RIETVELD AND van den BROM: VR ELECTROMETER FOR MEASUREMENT OF ELECTRICAL CURRENTS BELOW 10 pA

[4] G. C. C. Chen, W. Y. C. Lin, J. C. M. Hsu, and S. H. Tsao, “Accurate selfchecking digital teraohmmeter,” IEEE Trans. Instrum. Meas., vol. 44, no. 2, pp. 192–195, Apr. 1995. [5] Low Level Measurements Handbook, 6th ed., Keithley, Cleveland, OH, 2004. [6] A. F. Clark et al., “Application of single electron tunneling: Precision capacitance ratio measurements,” Appl. Phys. Lett., vol. 66, no. 19, pp. 2588–2590, May 1995. [7] G. Rietveld and H. Heimeriks, “Highly sensitive picoampere meter,” in CPEM Conf. Dig., 1996, pp. 332–333. [8] G.-D. Willenberg, H. N. Tauscher, and P. Warnecke, “A traceable precision current source for currents between 100 aA and 10 pA,” IEEE Trans. Instrum. Meas., vol. 52, no. 2, pp. 436–439, Apr. 2003. [9] H. E. van den Brom, P. de la Court, and G. Rietveld, “Accurate subpicoampere current source based on a differentiating capacitor with software-controlled nonlinearity compensation,” IEEE Trans. Instrum. Meas., vol. 54, no. 2, pp. 554–558, Apr. 2005.

Gert Rietveld was born in HardinxveldGiessendam, The Netherlands, in 1965. He received the M.Sc. and Ph.D. degrees in experimental lowtemperature and solid-state physics, both from Delft University of Technology, Delft, The Netherlands, in 1988 and 1993, respectively. In 1993, he joined the NMi Van Swinden Laboratorium (VSL), Delft, where he is heading the DC/LF group of the electrical metrology section. He is involved in the development of electrical quantum standards, especially the quantum Hall resistance standard. Other work concerns the measurement of very small electrical currents and evaluation of “self-calibrating” instruments. He is currently also a staff scientist, coordinating the scientific work in the NMi VSL laboratory.

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Helko E. van den Brom was born in Utrecht, The Netherlands, in 1971. He received the M.Sc. degree in theoretical solid-state physics from Utrecht University in 1995 and the Ph.D. degree in experimental solid-state physics from Leiden University, Leiden, The Netherlands, in 2000. In 2000, he joined the NMi VSL, Delft, The Netherlands, where he started working on the development of Josephson and single-electron-tunnelingbased electrical quantum standards. His current research interests are in dc and ac Josephson, dc low current and LF impedance measurements.