A finite difference model for cMUT devices

IEEE Trans Ultrason Ferroelectr Freq Control. 2005 Dec;52(12):2199-210. doi: 10.1109/tuffc.2005.1563263.


A finite difference method was implemented to simulate capacitive micromachined ultrasonic transducers (cMUTs) and compared to models described in the literature such as finite element methods. Similar results were obtained. It was found that one master curve described the clamped capacitance. We introduced normalized capacitance versus normalized bias voltage and metallization rate, independent of layer thickness, gap height, and size membrane, leading to the determination of a coupling factor master curve. We present here calculations and measurements of electrical impedance for cMUTs. An electromechanical equivalent circuit was used to perform simulations. Our experimental measurements confirmed the theoretical results in terms of resonance, anti-resonance frequencies, clamped capacitance, and electromechanical coupling factor. Due to inhomogeneity of the tested element array and strong parasitic capacitance between cells, the maximum coupling coefficient value achieved was 0.27. Good agreement with theory was obtained for all findings.

Publication types

  • Evaluation Study

MeSH terms

  • Computer Simulation
  • Computer-Aided Design*
  • Electric Capacitance
  • Electronics, Medical
  • Equipment Design
  • Equipment Failure Analysis
  • Finite Element Analysis
  • Linear Models*
  • Membranes, Artificial*
  • Miniaturization
  • Transducers*
  • Ultrasonography / instrumentation*
  • Ultrasonography / methods


  • Membranes, Artificial