Finite Element Modeling of CMUTs

Finite element models (3D and 2D) have been developed for the CMUTs to calculate collapse voltage, output pressure, bandwidth and crosstalk [1]. Fig. 1.a. shows the FEM model of a section of an element. A typical 1D transducer array is composed of long rectangular elements. The length of the array element is usually much longer than its width. The width of the element is set to half-wavelength at the maximum operation frequency. Therefore, a typical element is composed of hundreds of CMUT cells in the elevation, but it is usually only 4 to 6 cells in width. The high aspect ratio of the element allowed us to model only one row of the CMUT cells, greatly reducing the model size and computation time. Symmetry boundary conditions were applied on the bottom and the top edges of the CMUT row. This replicated the model infinitely many times in the elevation direction and generated an infinitely long element where all the rows were driven by the same phase. Because the row was also symmetric with respect to the centerline along the elevation, the model size was further reduced. Therefore, modeling of the one half of the row is sufficient.

FIGURE 1. Finite element model of a CMUT.

We also investigated dynamic analysis of CMUTs. We developed a finite element model to analyze and optimize the collapsed mode [Bayram05B]. The model uses a commercially available FEM tool, LS-DYNA. LS-DYNA has been developed especially for the time domain analysis of contacting surfaces. It employs an explicit non-linear solver. The required electrostatic actuation part was developed and integrated with the model. Fig. 2.a shows the time domain response of a CMUT cell both in normal and collapsed modes. Appropriate boundary conditions were added such that the model reflects the properties of a cell operating in an infinitely large 2-D membrane array. In the given example, the square membrane is made of silicon and is 30-µm wide and 1.2- µm thick. The collapse voltage of the cell was 96 V. In normal mode, the membrane was biased at 83 V and a 5-V positive unipolar pulse was applied. This excitation generated 100 kPa output pressure in the far field of the membrane. Then, the membrane was first biased past collapse and then the voltage reduced to 83 V, larger than the snapback voltage (70 V). Therefore, the membrane stayed in contact with the substrate. The output pressure corresponding to the 5-V positive pulse is shown in the same figure. The pressure increased approximately 6 times and the center frequency shifted to a higher frequency as shown in the frequency spectrum in of Fig. 2.b.

FIGURE 2. Time-domain and frequency domain FE simulations in conventional and collapse modes.

References

[1] G. G. Yaralioglu, A. S. Ergun and B. T. Khuri-Yakub, “Finite-element analysis of capacitive micromachined ultrasonic transducers,” IEEE Trans. Ultrason., Ferroelect., Freq. Contr., vol. 52, no. 12, pp. 2185-2198, Dec. 2005.

[2] Bayram B, Yaralioglu GG, Kupnik M, Ergun AS, Oralkan Ö, Nikoozadeh A, and Khuri-Yakub BT, “Dynamic Analysis of Capacitive Micromachined Ultrasonic Transducers,” IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, vol. 52, no.12, pp. 2242-2258, Dec. 2005.