Low power device for measuring electric fields at low temperatures

Low power device for measuring electric fields at low temperatures X.L. Hu, Y. Carmi and A.J. Dahm Physics Department, Case Western University, Cleveland, OH 44106, USA

Reserve

Received 15 January 1992 An electrode driven by a low power piezoelectric transducer was used to measure weak d.c. electric fields at low temperatures. This device had a vibration amplitude at resonance of - 7 / ~ m per volt of excitation voltage with a power dissipation of - O . 5/xW at 1 V of excitation voltage. The minimum detectable electric field of interest in our cell was limited by stray fields and was - 2 V cm -1, Changes in a d.c. electric field of 0.2 V cm-1 could be detected.

Keywords: electric field measurement; vibrating electrodes; low power devices

A Kelvin probe consisting of a transducer-driven electrode was used to measure the electric field above a twodimensional array of electrons. The electron density is deduced from a measurement of this field which is the sum of an applied field and the field due to the electron array. High resolution in the electron density measurement at low temperatures requires a low power, stable transducer with a large vibration amplitude. A vibrating electrode was first used for this purpose by Crandall and Williams j. The design described here is much more sensitive. A schematic of the device is shown in Figure I. The transducer used was a 25 m m × 6.4 mm, series-poled, lead-zirconate-titanate bimorph*. The dimensions of the

transducer, and thus the amplitude of vibration, were limited by the size of our experimental cell. The transducer was clamped at one end. The vibrating electrode of diameter 12.7 mm was made from a 0.8 mm thick, double-sided, copper-clad epoxy board. It was centred in the experimental cell and was attached to the transducer via an aluminium post which was epoxied to the transducer 13 mm from the clamp. The transducer was located inside a metal box with a small hole for the post. The box, aluminium post and the back side of the epoxy board were grounded to shield against pick-up from the excitation voltage applied to the transducer. The voltage induced on the vibrating electrode was fed to a phase sensitive detector. The electrode and all surfaces which are capacitively coupled to it were plated with gold by chemical deposition to reduce contact potentials. The dominant factor limiting the sensitivity in measuring the applied field was the dipole field of adsorbed contaminants. It was essential to work with a clean pumping capillary and to take precautions in evacuating and filling the cell with helium. An extension of the fill capillary to the bottom of the cell seemed to reduce problems with adsorbents. To test the device a voltage was applied to a gold plated disc located 4 mm below the vibrating electrode. Traces of signals taken at 4 K in an applied field of 5 V cm-I and zero applied field are shown as a function of driving frequency in Figure 2. The mechanical resonance of the structure occurs at 477 Hz at low temperatures. For a bimorph transducer clamped at one end, the motion of the electrode is not solely vertical. The temperature-independent vertical component of the amplitude of vibration at resonance was 7/~m per volt of excitation voltage, and the transducer response was nearly linear in excitation voltage to about 5 V rms. The power dissipated in the device at low temperatures was 0.5 V 2 ~W, where V is the excitation voltage. The two traces of the background (zero applied field) response shown in Figure 2 were taken with an interval of 10 min. The signal stabilized after about 30 min. The background varied from run to run. It could be eliminated at 300 K by heating the cell while pumping

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Frequency (Hz) Figure 2 A m p l i t u d e of the signal induced on the vibrating elect r o d e versus f r e q u e n c y . H e a v y line: applied d.c. field o f 5 V cm -~. Fine lines: t w o traces in zero applied field taken 10 rain apart. The excitation v o l t a g e w a s 7.4 V rms

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Research and technical note

on it. This background was temperature dependent, and for a mica substrate located above the gold-plated disc it varied with temperature as exp(W/kBT), with W = 1200 K. We attribute it to a polarized layer of an absorbent. The traces shown in Figure 2 are typical for a gold coated disc where the effect of adsorbent on the gold plated disc and vibrating electrode cancel. Limits on measuring the absolute value of an electric field of interest were set by the background. With care these were limited to less than 2 V cm -~. The background signal had a component which was orthogonal to the applied field response, and smaller fields could be detected at a particular detector phase setting. Changes in d.c. electric fields of - 0 . 2 V cm -1 could be detected. An electric field of 0.2 V cm -l is

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caused by a change in electron density of - 2 x 105 cm -2 on a bulk surface with typical experimental cell dimensions and a change of - 1 0 ~° cm -2 for electrons located on a 100 A helium film above a metallic substrate.

Acknowledgement This work was supported in part by NSF grants Nos. DMR-9014865 and DMR-9100242.

Reference 1 Crandall, R.S. and Williams, R. Properties of electron surface states on liquid helium Phys Rev A (1972) 5 2183-2190