4.2 Acoustic Suppression Methods for Thick Film Varactors
4.2.2 Destructive Interference
The presented acoustic suppression technique is based on the work of [32, 89], where it was verified for thin-film varactors. The fundamental structure is shown in figure 4.19. A double MIM structured varactor at the acoustic resonance frequency is assumed with an infinitesimal thin electrode in between the two ferroelectric layers and infinitely thick top and bottom electrodes. The mechanic strainε(m)can be written as [27]:
ε(m) =a(Eˆ2DC+1 2Eˆ2RF)
| {z }
static
+2aEˆDCEˆRFsin(ωRFt)
| {z }
piezoelectric
− 1
2aEˆ2RFsin(2ωRFt+π 2)
| {z }
electrostrictive
,
see section 2.1.2. The suppression technique utilizes the tunable apparent piezoelectric coupling factor e = 2aEˆDC by applying an anti-polar electric DC field in the two BST layers. As a result, two antipolar apparent piezoelectric coupling factorse1 =2aEˆDCand
BST layer 1 BST layer 2
z =−h z = 0 z =h
Top electrode
Middle electrode
Bottom electrode
−E~DC E~DC
E~RF
Figure 4.19: Double MIM fundamental model. ©2018 IEEE.
e2 =−2aEˆDCin the BST layers are introduced. The mechanic strain in the layers is coupled with a 180° phase shift. Thereby, an excited acoustic wave is unable to couple to adjacent layers, resulting in significantly reduced losses. However, the technique is only applicable when both BST layers behave exactly the same properties. Otherwise, an excited acoustic wave is not confined within the dielectric but couples to adjacent layers. To further evaluate the suppression approach, an acoustic simulation of the structures is set up. The reference single MIM varactor is identical with the varactor cell presented in appendix C.3 apart from a variation in BST layer thickness to 20 µm. The electrode overlap area is 0.75 mm×1 mm, resulting in a capacitance of 76 pF estimated with the parallel plate capacitance equation and a permittivity of the printed BST thick film layer ofεr=230 [42]. Consequently, the double MIM varactor consists of two 20 µm thick BST layers and a middle electrode with a thickness of 15 µm. The electrode overlap area is the same as for the single MIM varactor, resulting in an estimated capacitance of 38 pF. The varactor designs and the DC/RF decoupling networks are shown in figure 4.20 for both, the single and double MIM varactor.
The results of the piezoelectric simulation for the double MIM structure are depicted in figure 4.21. The results of two different simulations are shown. In the homogeneous case, the material properties of both BST layers are identical. In the heterogeneous case, the elastic compliance of one BST layer is set to 6 TPa−1from 8.57 TPa−1to simulate non-ideal resonance cancellation. However, the change of other material parameters, such as piezoelectric coupling or density, lead to similar results.
Based on the presented theory, no or highly suppressed acoustic resonances should be visible in the ESR spectrum of the homogeneous case compared to the heterogeneous case and to a single MIM cell. As expected, the simulated ESR trace for the homogeneous case shows no acoustic resonance at 15 MHz in contrast to the heterogeneous case, see figure 4.21.
At 21 MHz, a highly damped spike is visible indicating a non-perfect cancellation of strain waves in the structure, caused by parasitically excited surface acoustic waves due to the
Al2O3
Ag Ag
BST 15µm
´
RFin
2 nF RFout
DCbias
100 kΩ
Al2O3
Ag Ag
Ag
BST 45µm
´
15µm 15µm
RFin RFout
DCbias
100 kΩ
RFin
MIM
100kΩ
DC Block
RFout
100kΩ 100kΩ
DC Bias
RFin
MIM1
100kΩ
MIM2
RFout
100kΩ 100kΩ
DC Bias
Figure 4.20: Cut through the single and double MIM structure with equivalent circuit model and its connection to the structures. ©2018 IEEE.
10 12.5 13.56 15 17.5 20 22.5 25
Frequency / MHz
ESR
homogeneous heterogeneous
Figure 4.21: Simulated impedance spectrum of a heterogeneously and homogeneously sintered double MIM varactor cell.
inhomogeneous model. An additional highly damped resonance at 12 MHz is visible, caused by the same reason. The trace for the heterogeneous case shows a significant acoustic resonance at 15 MHz and 21 MHz, indicating the validity of the suppression approach. A third resonance is found at 12 MHz, which occurs in the homogeneous simulation as well.
Compared to the simulation results of the single MIM cell, see figure 4.18, the homogeneous double MIM cell shows significantly reduced acoustic activity, indicating the effectiveness of the presented suppression method. To validate the approach, the matrix varactor design presented in appendix C.3 is altered by adding a middle electrode to the MIM structure creating a double MIM structure. The matrix varactor design excels for the validation of the interference based suppression approach due to its isolated miniature cell structure.
Small-signal characterization can be performed on the small varactor cells, without the parasitics introduced by the large varactor structures of the previous designs. For this, a screen is designed which enables the possibility to include an additional middle electrode layer between the two intended layers of BST. The obtained samples are characterized under small-signal conditions and the suppression approach is evaluated in regard to its effectiveness for homogeneous and heterogeneous material parameters in the BST layers.
Double MIM Structure Processing
In a first step, the bottom RF electrode is screen printed on an alumina substrate. For the electrodes the conductor paste C 1076 SD (LPA 609-022) from Heraeus is chosen. It is a solderable Ag/Pt conductor paste suitable for temperatures up to 850◦C. In a second step, two layers of BST thick film are screen printed on the bottom electrode and dried at 80◦C.
For the heterogeneous case, the structure is now sintered at 850◦C for 10 min. Subsequently, the middle electrode and two more BST layers are printed and dried at 80◦C. Eventually, the top electrode is printed and the whole structure is sintered at 850◦C for 10 min. In conclusion, for the heterogeneously processed varactors, the bottom BST layers are sintered two times and the top BST layers are sintered once. As a result, varied material properties in the top and bottom BST layers can be assumed. For the homogeneously processed case, all four BST layers are sintered at once, resulting in equal material properties in the top and bottom BST layers. A SEM cross-sectional image of the homogeneously co-sintered double MIM structure is depicted in figure 4.22.
Small-Signal Characterization
The varactors are characterized with a 1-port measurement from 5 MHz to 25 MHz with the impedance analyzer connected to a wafer prober with a 1250 µm ground-signal (GS) probe. A biasing voltage range from 0 V to 120 V is used for characterizing the varactors and a 100 kΩresistive needle is included into the measurement setup, connecting to the middle electrode of each varactor structure. The equivalent circuit diagram of the biasing
Figure 4.22: SEM cross-sectional image of the double MIM structure. ©2018 IEEE.
concept is depicted in figure 4.20. The varactors are characterized in regard to capacitance and Q-factor.
The measurement results comparing C and Q-factor for the homogeneously and hetero-geneously sintered varactors are depicted in figure 4.23. The heterohetero-geneously sintered