Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Article
  • Published:

Distortion-free measurement of electric field strength with a MEMS sensor


Small-scale and distortion-free measurement of electric fields is crucial for applications such as surveying atmospheric electrostatic fields, lightning research and safeguarding areas close to high-voltage power lines. A variety of measurement systems exist, the most common of which are field mills, which work by picking up the differential voltage of the measurement electrodes while periodically shielding them with a grounded electrode. However, all current approaches are bulky, suffer from a strong temperature dependency or severely distort the electric field, and thus require a well-defined surrounding and complex calibration procedures. Here we show that microelectromechanical system (MEMS) devices can be used to measure electric field strength without significant field distortion. The purely passive MEMS devices exploit the effect of electrostatic induction, which is used to generate internal forces that are converted into an optically tracked mechanical displacement of a spring-suspended seismic mass. The devices exhibit resolutions on the order of 100 V m−1 Hz−1/2 with a measurement range of up to tens of kilovolts per metre in the quasi-static regime 300 Hz). We also show that it should be possible to achieve resolutions of around 1 V m−1 Hz−1/2 by fine-tuning the sensor embodiment. These MEMS devices are compact and could be mass produced easily for wide application.

This is a preview of subscription content, access via your institution

Access options

Buy this article

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Illustration of the charge separation and electrostatic forces occurring on a conducting sphere in an external electric field.
Fig. 2: MEMS embodiment of the electric field transducer.
Fig. 3: Measurement set-up for characterization of the transducer.
Fig. 4: Response of a MEMS sensor (group Ch00) to input electric fields.

Similar content being viewed by others


  1. Hill, D. A. & Kanda, M. The Measurement, Instrumentation, and Sensors Handbook XXV, Section 47, Electric Field Strength (ed. Webster, J. G.) (CRC Press, Boca Raton, FL, 1999).

    Google Scholar 

  2. Kirkham, H. On the measurement of stationary electric fields in air. Conf. Precision Electromagnetic Measurements (2002);

  3. Vasa, N., Kawata, Y., Tanaka, R. & Yokoyama, S. Development of an electric field sensor based on second harmonic generation with electro-optic materials. J. Mater. Process. Technol. 185, 173–177 (2007).

    Article  Google Scholar 

  4. Meier, T., Kostrzewa, C., Petermann, K. & Schuppert, B. Integrated optical E-field probes with segmented modulator electrodes. J. Lightwave Technol. 12, 1497–1503 (1994).

    Article  Google Scholar 

  5. Williams, K., De Bruyker, D., Limb, S., Amendt, E. & Overland, D. Vacuum steered-electron electric-field sensor. J. Microelectromech. Syst. 23, 157–167 (2014).

    Article  Google Scholar 

  6. Ando, B., Baglio, S., Marletta, V. & Bulsara, A. R. A nonlinear electric field sensor that exploits coupled oscillator dynamics: the charge collection mechanism. IEEE Trans. Instrum. Meas. 62, 1326–1333 (2013).

    Article  Google Scholar 

  7. Berthelier, J. J. et al. ICE, the electric field experiment on DEMETER. Planet. Space Sci. 54, 456–471 (2006).

    Article  Google Scholar 

  8. Peng, C., Yang, P., Zhang, H., Guo, X. & Xia, S. Design of a novel closed-loop SOI MEMS resonant electrostatic field sensor. Proc. Eng. 5, 1482–1485 (2010).

    Article  Google Scholar 

  9. Pierce, E. T. Atmospheric electricity—some themes. Bull. Am. Meteorol. Soc. 55, 1186–1194 (1974).

    Article  Google Scholar 

  10. Williams, E. & Mareev, E. Recent progress on the global electrical circuit. Atmos. Res. 135–136, 208–227 (2014).

    Article  Google Scholar 

  11. Zhang, B., Wang, W. & He, J. Impact factors in calibration and application of field mill for measurement of DC electric field with space charges. CSEE J. Power Energy Syst. 1, 31–36 (2015).

    Article  Google Scholar 

  12. Horenstein, M. N. & Stone, P. R. A micro-aperture electrostatic field mill based on MEMS technology. J. Electrostat. 51–52, 515–521 (2001).

    Article  Google Scholar 

  13. Peng, C., Chen, X., Bai, Q., Luo, L. & Xia, S. A novel high performance micromechanical resonant electrostatic field sensor used in atmospheric electric field detection. 19th IEEE Int. Conf. Micro Electro Mechanical Systems 2006, 698–701 (IEEE, 2006).

  14. Kalinowski, D., Redlich, S. & Jager, D. Novel micromachined fiber-optic E-field sensor. IEEE Lasers and Electro-Optics Society 1999 12th Annual Meeting Vol. 1, 385–386 (IEEE, 1999).

  15. Rogers, A. J. Optical measurement of current and voltage on power systems. IEE J. Electric Power Appl. 2, 120–124 (1979).

    Article  Google Scholar 

  16. Soref, R. A. & Bennett, B. Electrooptical effects in silicon. IEEE J. Quantum Electron. 23, 123–129 (1987).

    Article  Google Scholar 

  17. Toney, J. E. et al. in Proc. SPIE 8519, Nanophotonics and Macrophotonics for Space Environments VI (eds Taylor, E. W. et al.) 851904 (SPIE, Bellingham, Washington, 2012).

  18. Berger, J., Petermann, K., Fähling, H. & Wust, P. Calibrated electro-optic E-field sensors for hyperthermia applications. Phys. Med. Biol. 46, 399 (2001).

    Article  Google Scholar 

  19. Barthod, C., Passard, M., Fortin, M., Galez, C. & Bouillot, J. Design and optimization of an optical high electric field sensor. 2000 Conf. Precision Electromagnetic Measurements Digest 423–424 (2000).

  20. Chmielak, B. et al. Pockels effect based fully integrated, strained silicon electro-optic modulator. Opt. Express 19, 17212–17219 (2011).

    Article  Google Scholar 

  21. Zeng, R., Wang, B., Niu, B. & Yu, Z. Development and application of integrated optical sensors for intense E-field measurement. Sensors 12, 11406–11434 (2012).

    Article  Google Scholar 

  22. Bohnert, K., Gabus, P., Brändle, H. & Khan, A. Fiber-optic current and voltage sensors for high-voltage substations. Proc. 16th Int. Conf. Optical FiberSensors 13–17 (Nara, Japan, 2003).

  23. Landau, L., Lifshitz, E. & Piaevski, L. Electrodynamics of Continuous Media (Butterworth-Heinemann, Oxford, UK, 1984).

    Google Scholar 

  24. Hortschitz, W. et al. An optical in-plane MEMS vibration sensor. IEEE Sens. J. 11, 2805–2812 (2011).

    Article  Google Scholar 

  25. Hortschitz, W. et al. MOEMS vibration sensor for advanced low-frequency applications with pm resolution. Proc. Eng. 87, 835–838 (2014).

    Article  Google Scholar 

  26. Middlemiss, R. et al. Measurement of the Earth tides with a MEMS gravimeter. Nature 531, 614–617 (2016).

    Article  Google Scholar 

  27. Zhang, W.-M., Yan, H., Peng, Z.-K. & Meng, G. Electrostatic pull-in instability in MEMS/NEMS: a review. Sens. Actuat. A 214, 187–218 (2014).

    Article  Google Scholar 

  28. Boyd, E. J., Li, L., Blue, R. & Uttamchandani, D. Measurement of the temperature coefficient of Young’s modulus of single crystal silicon and 3C silicon carbide below 273 K using micro-cantilevers. Sens. Actuat. A 198, 75–80 (2013).

    Article  Google Scholar 

  29. Encke, J. et al. A miniaturized linear shaker system for MEMS sensor characterization. Proc. SPIE 8763, SmartSensors, Actuators, and MEMS VI 8763, 876315–876315 (2013);

    Google Scholar 

  30. Hortschitz, W. et al. Robust precision position detection with an optical MEMS hybrid device. IEEE Trans. Indust. Electron. 59, 4855–4862 (2012).

    Article  Google Scholar 

  31. Hortschitz, W. et al. Optimized hybrid MOEMS sensors based on noise considerations. Proc. IEEE Sensors (2012).

  32. Hortschitz, W. et al. Receiver and amplifier optimization for hybrid MOEMS. Proc. IEEE Sensors (2012).

  33. Kainz, A. et al. Accurate analytical model for air damping in lateral MEMS/MOEMS oscillators. Sens. Actuat. A 255, 154–159 (2017).

Download references


This work was supported financially by the Austrian Science Fund (FWF, research grant P 28404-NBL), the European Regional Development Fund (ERDF) and the Province of Lower Austria. The authors thank G. Diendorfer for discussions and his support on acquiring the funding for this work.

Author information

Authors and Affiliations



A.K., H.S. and W.H. carried out the design, modelling and measurements. J.S. and A.J. were responsible for manufacturing the device, while F.Ko., M.S. and F.Ke. supported the measurements and the design of the devices. R.B. supported modelling and was involved in acquiring funding for the work. All authors contributed to the manuscript.

Corresponding author

Correspondence to Andreas Kainz.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Additional information

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

Supplementary Figures 1–7

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kainz, A., Steiner, H., Schalko, J. et al. Distortion-free measurement of electric field strength with a MEMS sensor. Nat Electron 1, 68–73 (2018).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:

This article is cited by


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing