CSEM Scientific and Technical Report 2008

Effect of Size on the Performance of BAW Resonators
C. Muller, M.-A. Dubois
The aim of this work is to establish the relation between the size of BAW resonators and their performances. Then, together with other
requirements, it is possible to optimize globally the complete electronic system, rather than by just taking into account impedance matching
considerations.
Bulk Acoustic Wave (BAW) resonators are basically
composed of a piezoelectric layer sandwiched between two
electrodes on top of an acoustic insulation. AlN is the
dominant piezoelectric material in the field and was used in
this work. BAW resonators operate in the 1 to 10 GHz range,
that is in the upper range of SAW resonators and above.
The limitations of the performances of BAW resonators can be
subdivided in two classes. In one of them there are ‘extrinsic’
limitations like the resistance of the access lines or parasitic
capacitances to the substrate. This type of performance
degradation was not considered. The work deals with ‘ideal’
resonators only, i.e. with ‘intrinsic’ limitations like material
losses inside the resonator for example.
The complete development of the model can be found in
reference [1] . The main idea is the following: BAW resonators
are subdivided in two zones. In the bulk of the resonator,
particles are relatively free to move, resulting in a high
coupling coefficient k2 eff and high series and parallel quality
factors Qs and Qp. At the edge of the resonators, the clamping
induces a reduction of the coupling, and Q-factors are lowered
by friction and energy losses to the surrounding medium. The
final performances of the resonator are somewhere between
the low performances of the edge zone and the high ones of
the bulk part. Since the edge zone is proportionally larger in
small resonators, they show largely reduced coupling and
Q-factors. More precisely, it was shown that both k2 eff and
Q-factors depend on a single parameter, A/p, which is the
ratio between the area A and the perimeter p of the resonator.
Theoretical predictions and experimental results are shown in
Figures 1, 2 and 3.
Figure 1: Ideal coupling coefficient of BAW resonators at 2.44 GHz
as a function of A/p. Circular dots from left to right represent
measured 500, 300, 100, 50, 30, 10 and 5 Ohm resonators. The
black line was calculated with the model.
Figure 1 shows that a resonator that is less than 10 µm wide
cannot vibrate because the clamping on its side is too strong.
On the other hand, an infinitely large resonator, without edge
zone, would have an asymptotic coupling of 6.77%.
Figure 2: Ideal Qp-factor for the same resonators as in Figure 1
Figure 3: Ideal Qs-factor for the same resonators as in Figure 1.
Measured real Qs are also shown (grey triangle dots).
50 Ohm resonators present a Qp factor of 800 (Figure 2). It
tends towards 0 for small resonators and is limited below 2800
for very large ones.
Figure 3 shows that Qs of small resonators is limited by an
intrinsic Qs-factor. Qs reaches then a maximum and begins to
decrease severely for larger resonators. This is due to losses
in the electrodes, which are proportionally more important in
small impedance resonators.
Figures 1 to 3 highlight the trade-offs that may appear when
designing a complete electronic system containing BAW
resonators. For example, a large coupling may be required;
then a large resonator is best suited. However, electronic
considerations may require high impedance, i.e. small
resonators. An optimum size has to be found. Similar
reasoning with respect to Q-factors can also be made.
The resonators were fabricated at the CMI center at the EPFL.
[1] C. Muller, M.-A. Dubois, “Effect of size and shape on the
performances of BAW resonators: a model and its applications”,
IEEE UFFC 2008 Beijing, in press
27