**4. Conclusion**

496 Acoustic Waves – From Microdevices to Helioseismology

1.88 1.92 1.96 2 2.04

1.86 1.9 1.94 1.98 2.02

1.86 1.9 1.94 1.98 2.02

Fig. 12. Measurements (filled circles are *2ω1-ω2*, empty circles are *2ω2-ω1*) and simulations (solid line is *2ω1-ω2*, dash-dot line is *2ω2-ω1*) of the 3IMD for resonators A1, A2, A3 and A4 in Fig.12.a, Fig.12.b, Fig.12.c and Fig.12.d respectively. The figures also show the dissipation in the electrodes (dashed line) and in the piezoelectric layer due to viscous losses (dotted line)

Frequency (GHz)

Frequency (GHz)

Frequency (GHz)

10 -3

10 -3

10 -3

10 -2

10 -1

(d)

Dissi

pation (

W)

10 -2

10 -1

(c)

Dissi

pation

 (

W)

10 -2

Dissipation (

W)

10 -1

(b)





3IM

D (

d

B

m)





3IMD (

d

B

m)





3IMD (d

B

m)




The role of self-heating and material nonlinearities in the generation of 3IMD in bulk acoustic wave devices has been evaluated through measurements, models and equations. Self-heating is found to have a very significant contribution to 3IMD and thus thermal considerations are critical in the device design. The presented circuit model implementation offers the possibility to predict 3IMD in BAW resonators, given their materials stack and geometry. With such information one can use the resonator model to accurately predict 3IMD in filters. Further research will be performed to investigate the relation between the electric-field contribution to 3IMD and the cancellation shown in the measurements. The development of a 3D equivalent thermal model, to take into account complex heat dissipation through the substrate, will also be investigated.
