1. i
Abstract
Application of Statistical Element Selection to Two-Port Aluminum Nitride
Contour-Mode Filters through 3D Integration with CMOS Circuitry
Albert Patterson
Supervisors: Gary Fedder and Gianluca Piazza
Cognitive radio is a future technology that is receiving a great deal of attention today in the radio
frequency (RF) community, as it promises to mitigate the crowding of the electromagnetic spectrum faced
by wireless device consumers. A filter that offers high performance and a reconfigurable response is a
vital building block for this technology. To achieve such a filter and increase filter yield in general,
statistical element selection (SES) was applied to an array of Aluminum Nitride (AlN) filters through 3D
integration with a switching matrix designed in CMOS technology. AlN-MEMS filters were fabricated that
operate with average center frequency, insertion loss, bandwidth and out-of-band rejection of 1.146 GHz,
2.66 dB, 3.79 MHz and 22.0 dB, respectively. Encapsulated filters with average center frequency, insertion
loss, bandwidth and out-of-band rejection of 1.146 GHz, 4.44 dB, 3.83 MHz and 24.8 dB, respectively were
also fabricated. Variation of the filter properties was studied, and it was found that for the non-
encapsulated filters, the mismatch standard deviations of the center frequency, insertion loss, bandwidth
and out-of-band rejection were 160 ppm, 4.19 %, 2.52 % and 3.52 %, respectively, while these standard
deviations were 220 ppm, 14.1 %, 1.54 % and 2.14 %, respectively for the encapsulated filters. These
variations are problematic for the yield of a single filter, but are harnessed by SES to achieve
reconfigurabiltity and high yield when applied to an array of filters, resulting in a self-healing filter. The
self-healing filter in this work chooses 4 of 12 sub-filters from an array and offers 495 possible responses
and a typical tuning range of ~500 kHz for both the bandwidth and the center frequency with insertion
loss below 8 dB and out-of-band rejection above 15 dB. An algorithm that requires measurement of only
13 of the 495 responses was developed to extract all available responses, which can be done in less than
10 seconds. This work demonstrates the feasibility and impact of applying SES to AlN-MEMS filters,
resulting in a truly self-healing filter.

2. ii
Table of Contents
Chapter 1: Introduction………………………………………………………………………………………………………….………………
Chapter 2: Contour-Mode Two-Port Resonators and Filters…………………………………………………………………..
I. Contour-Mode Resonator Operation……………………………………………………………………..………………….……
II. Resonator Parameter Extraction……………………………………………………………………………………………………
III. Third-Order Self-Coupled Filters………………………………………………………………………………..…………….……
Chapter 3: Fabrication and Measurement…………………………………………………………………………..………….……..
I. MEMS-Only Fabrication Process Flow………………………………………………………………………………..…….……..
II. MEMS-Only Device Measurements………………………………………………………………………………………………..
III. Analysis of Mode Splitting in Two-Port Resonators……………………………………………………………………….
IV. MEMS with Thin-Film Encapsulation Process Flow………………………………………………………………….…….
V. MEMS with Thin-Film Encapsulation Devices Measurements………………………………………………………..
Chapter 4: Intrinsic Filter Yield Limitation and Enhancement with Statistical Element Selection………….…
I. Filter Yield Limitation Due to Fabrication-Induced Variations……………………………………………………….…
II. Application of Statistical Element Selection for Yield Improvement and Reconfigurability………….….
III. MEMS Chip Design for Statistical Element Selection Implementation…………………………………………..
IV. CMOS Chip Design for Statistical Element Selection Implementation……………………………………….…..
V. CMOS Chip Characterization…………………………………………………………………………………………….………..….
Chapter 5: Application of Statistical Element Selection to 3D-Integrated, Self-Healing Filters…………….…..
I. 3D Integration through Solder Bump Bonding………………………………………………………………………………..
II. Measurements of Self-Healing Filters……………………………………………………………………………………..…….
III. Extraction Algorithm for Fast Characterization of Self-Healing Filters……………………………………………
IV. Assessment of Extraction Algorithm and Application of Statistical Element Selection…………….…….
Chapter 6: Conclusions and Future Work………………………………………………………………………………………….…...
Bibliography…………………………………………………………………………………………………………………………………………..
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3. 1
Introduction
Radio frequency (RF) devices have seen a sharp increase in popularity in the last decade, which
promises to continue into the future as the benefits of wireless communication are embraced in new
areas and by new customers. However, because RF bands are licensed to specific users, the proliferation
of wireless devices introduces the problem of overcrowding of the portion of the electromagnetic
spectrum licensed for such devices. Though specific bands are sometimes quite crowded, it is not the case
that the entire spectrum is occupied all of the time. If one were to survey the entire spectrum, they would
find that while some bands have heavy traffic, other bands are lightly used. Thus it would be possible to
alleviate the overcrowding of specific bands by allowing an unlicensed user to temporarily access an idle
band that is licensed to another party. Once the licensee becomes active, the unlicensed user would move
to a different band to prevent interference [1]. Cognitive radio is a technology that is envisaged to deliver
this capability by sensing the level of traffic and reconfiguring according to band availability. This project
focuses on facilitating the reconfigurability aspect of a cognitive radio’s function.
To achieve a reconfigurable radio, one can combine the two basic functions of selection and
filtering. RF switches can be reliably fabricated in CMOS technology; however it is very difficult to build
high-performance filters in CMOS. In order to achieve impressive filter functionality, AlN-MEMS, two-port,
contour-mode resonators will be implemented as the filtering elements; they offer low loss, narrow
bandwidth, high out-of-band rejection and can be matched to existing 50 Ω RF systems [2]. For this
project, the MEMS filters will be fabricated in a separate process from the CMOS chip containing the
switching elements. Solder ball bonding will be used to achieve 3D integration between the CMOS and
MEMS chips. Fabrication of the MEMS devices as well as design of the CMOS and MEMS chips according
to the combined constraints imposed by each process and the ball bonding process will be discussed. Also,
measurements from both the MEMS and CMOS devices will be presented and discussed.
Though AlN-MEMS filters display many desirable properties, their direct application is hindered
by fabrication-induced variations, which cause poor performance in some filters and inaccuracies in the
center frequency and bandwidth, resulting in low filter yield [3]. The challenges posed by variations are
addressed using statistical element selection (SES), which harnesses the variations to achieve
reconfigurability in the filter center frequency and bandwidth, while providing low loss and high rejection.
This is achieved by selecting a subset of k elements from an array of N identically laid out elements,
resulting in N
Ck=N!/(N-k)!/k! total subsets and high combinatorial redundancy [4]. Application of SES to

4. 2
the AlN-MEMS filters via switching performed on the CMOS chip and the choice of N and k to achieve high
yield and reconfigurability will be explored. Finally, preliminary results for the application of SES on the
integrated CMOS and MEMS chips will be shown.

5. 3
Chapter 2: Contour-Mode Two-Port Resonators and Filters
Gianluca Piazza’s PMaNS group at Carnegie Mellon University has already demonstrated high-
performance filters using AlN contour-mode resonator technology which can readily be matched to 50 Ω
circuits and offer center frequency above 1GHz, insertion loss below 3 dB, bandwidth ~0.3% of center
frequency, out-of-band rejection above 20 dB [1]. In this work, filter performance will be assessed based
on center frequency, insertion loss, bandwidth and out-of-band rejection. Ripple and shape factor are also
of interest. See figure 2-1 for a graphical definition of each of the parameters of interest. In this chapter,
the basic functionality and modeling of the AlN two-port resonators and extraction of the resonator
parameters from measured data will be discussed. Also, narrowband filter synthesis via self-coupled, two-
port AlN resonators will be presented.
Figure 2-1: Graphical definition of filter properties
I. Contour-Mode Resonator Operation
Two port AlN contour-mode resonators have been studied extensively and only a cursory
overview will be given here of their operating principles and capabilities. As described in [1], the resonator
may be formed by fabricating a pair of interdigitated electrodes on a plate of AlN with a grounded bottom
electrode, as shown in figure 2-2.

6. 4
Figure 2-2: AlN resonator (a) Cross section. (b) Top view. (c) Oblique view
As AlN is a piezoelectric material, strain will be induced in the plate when a voltage is applied at
the input electrode. If the frequency of the signal matches the resonator’s natural frequency (fs), a
contour-mode vibration will occur via thickness field excitation, and strain induced charge will flow
through the output electrodes, transmitting the input signal to the output port. This behavior may be
modeled in the electrical domain using the Butterworth-Van Dyke model, as shown in figure 2-3. W, L, T,
nin, and nout are described as in figure 2-2. For resonators used in this work, nin and nout are 28 and 27, and
for simplicity, we assume nin=nout=n= 27.5. ε33 is the relative permittivity along the c-axis, d31 is the (3, 1)
element of the piezoelectric coefficient matrix, ρeq is the equivalent density of the resonator, and Eeq is
the equivalent Young’s modulus of the resonator stack. Q is the quality factor of resonance, fs is the
resonance frequency and kt
2
is the electromechanical coupling of AlN.
Figure 2-3: Equivalent circuit for AlN 2-port resonator

7. 5
Equivalent circuit components may be readily calculated from the physical properties using the following
formulas:
II. Resonator Parameter Extraction
In order to study the properties of the real two-port resonators, a robust and reliable extraction
method must be used. It is very important that this method yield repeatable results with a high degree of
accuracy. As we are interested in studying the variation of filter properties, the extraction method should
introduce as little uncertainty as possible. The physical parameters extracted will be fs, Q, kt
2
, C0 and Cf,
assuming the equivalent circuit model discussed previously. As shown in figure 2-4, the two-port
resonator equivalent circuit is a two-port pi circuit, and the Y parameters may be used to easily extract
the admittance of the shunt and series elements.
Figure 2-4: Two port resonator circuit pi model decomposition.

8. 6
Once Yshunt and Yseries are known, the physical parameters may be calculated using the following steps:
1. C0 is fit to the imaginary part of Yshunt, once pad parasitics have been subtracted
2. The series resonance (ωs) and parallel resonance (ωp) are found from Yseries
3. Rm is taken as the inverse of the real part of YSeries at ωs
4. Starting with an assumed value for Cf (typically about 15 fF) initial values for Q and kt
2
may be
calculated:
5. Once initial values of Q and kt
2
are found, Lm and Cm may be calculated and the admittance of the
motional RLC circuit may be subtracted from Yseries. Cf may be fit to the imaginary part of the
remaining admittance. This process may be repeated to obtain a more accurate extraction of Q,
kt
2
and Cf.
Additionally, because resonators will be measured using a frequency sweep that only measures at discrete
points, care should be taken in the extraction of ωs, ωp and Rm to minimize artifacts from discretization
error. This issue is addressed using parabolic interpolation at the series and parallel resonances.
III. Third-Order Self-Coupled Filters
Thanks to the capacitance at the input and output ports of the two-port resonator, a narrowband
filter response may be achieved by cascading several two-port resonators, as shown in figure 2-5.
Figure 2-5: Equivalent circuit for third-order filter

9. 7
The cascaded resonators are then intrinsically coupled by the port capacitance. As described in [2] the
filter with have three modes of resonance, which are shown in figure 2-6.
Figure 2-6: Three modes of resonance of the third-order filter
These modes are readily visible in the filter’s forward transmission when unmatched. However, with
appropriate matching and with low loss resonators, a smooth pass band and steep roll-off may be
achieved with this filter topology, as shown in figure 2-7.
Figure 2-7: Simulated frequency response of third-order filter

10. 8
Chapter 3: Fabrication and Measurement
Two port AlN CMR resonators and filters were fabricated at the A-Star Institute of
Microelectronics (IME) in Singapore. Several iterations of designs and fabrications were performed, but
the main components were the “MEMS-only” fab which consisted of standalone resonators and filters
and a “MEMS with thin-film encapsulation” (TFE) fab wherein the filters were hermetically encapsulated.
Devices were measured and fit to their respective equivalent circuits. Statistics on device performance
were also collected. Functional resonators and filters were both achieved. Extracted resonator quality
factor is lower than expected, but low loss filters were obtained. This discrepancy between the resonators
and filters is suspected to be due to mode splitting at resonance, which will only be slightly detrimental
to overall filter performance. Analysis of the split modes reveals that the single mode model is simply not
sufficient for Q extraction, and ultimately high-performance filters are expected based on the resonator
measurements. This is explained in detail in this section. Low loss filters were fabricated in the MEMS-
only process, while slightly higher loss filters were produced in the MEMS with TFE process. In the TFE
process, fewer broken devices were observed, but parasitics were higher.
I. MEMS-Only Fabrication Process Flow
In the MEMS-only process, resonators and filters were fabricated as shown in figure 3-1. Starting
from a stack of 5 µm of Si (device layer of Si) on 1 µm of SiO2, the process is initiated by defining the
isolation trench, which will confine the released areas when the device layer of Si is etched later in the
process. Next, 300 nm of SiO2 is deposited, followed by 50 nm of AlN and then 150 nm of molybdenum,
which is patterned to form the bottom electrode of the device. The surface then undergoes planarization,
which is very useful for ensuring that devices do not break upon release. Next, 1 µm of AlN is deposited,
and vias are etched through the AlN. 150 nm of molybdenum is then deposited and patterned to form the
top electrodes, connecting to the bottom electrodes through the vias. The surface is then covered with a
500 nm passivation layer of SiO2. Release holes are then etched down to the device layer of silicon. Lastly,
the devices are released from the silicon using a XeF2 etch followed by a vapor hydrofluoric acid etch to
remove residual oxide. The layout of resonators to be fabricated in the MEMS-only process at IME has
been automated with a custom script written for use with Cadence at CMU.

11. 9
Figure 3-1: MEMS-only process flow: (a) Initial wafer. (b) Formation of isolation trench. (c) Deposition
and patterning of bottom molybdenum. (d) Planarization. (e) Deposition of aluminum nitride. (f)
Etching of vias. (g) Deposition and patterning of top molybdenum. (h) Deposition of silicon dioxide
passivation. (i) Etching of release holes. (j) Xenon difluoride release and vapor hydrofluoric acid etch.
II. MEMS-Only Device Measurements
Devices fabricated through the MEMS-only process are shown in figure 3-2. AlN is transparent, so
both the top and bottom metals are visible with the top Mo being slightly brighter than the bottom metal.
These resonators are laid out with pads to be probed with 150 µm pitch GSG probes, so on each side of
the resonator, there is a ground pad at the top and bottom and a signal pad in the center, with vias at the
top and bottom of the figure to ground the bottom electrode. These resonators were designed to operate
at approximately 1 GHz, thus the fingers are 2 µm wide and have a pitch of 4 µm. Release holes were
placed at both ends of the resonator and on the sides to ensure full release. Ten repetitions of these
devices were fabricated per die, and approximately 90 % of devices were measureable. No major
fabrication issues were observed for the two-port resonators and filters except that in some areas the

12. 10
isolation trench did not fully confine the etch of the device layer of silicon. Though non ideal, this extra
silicon etch was not detrimental to the project.
Figure 3-2: Resonators fabricated through MEMS-only process. (a) Optical Image. (b) SEM image
The frequency responses of two-port resonators fabricated in the MEMS-only process were
measured and the response of typical device is shown in figure 3-3. The resonators were designed to have
center frequency of 1GHz and static capacitance of 460 fF. For 50 Ω matching, a static capacitance of
approximately 3.2 pF would be required. For this fab, the thickness of AlN is fixed at 1 µm, so a very large
device would be required to match to 50 Ω. This large size would be very susceptible to breaking, and
would occupy a large chip area. Thus we chose to use smaller devices to achieve high device yield and to
increase the number of filters that can be placed on a chip, which is very important for the application of
SES, as will be presented later.
Compared to design, the resonance frequency (1.14 GHz) is higher and the static capacitance
(475 fF) is approximately correct. Center frequency may be corrected with simple layout changes. The
electromechanical coupling (2.17 %) is higher than that reported by Rinaldi et al., but the quality factor
(672) is lower [5]. The low quality factor is due to the multiple modes at resonance, which is not a feature
captured in the extraction method. However, with except for the resonance peak, the extraction method
provides a nice fit over the frequency of interest. Also, it will be demonstrated later that despite the
seemingly low Q, the split modes are, in fact, only slightly detrimental to filter performance.

13. 11
Figure 3-3: Frequency response of typical resonator fabricated through MEMS-only process
Thirty-seven total devices across four dies were measured, and the statistics of the resonator properties
are shown in table 1.
Table 3-1: Measured statistics of resonators fabricated through MEMS-only process. Standard deviation
(STD) is provided as a % of the mean value.
In addition to resonators, third-order filters were also fabricated in the MEMS-only process at
IME. Figure 3-4 shows a typical third-order filter. The third-order filter is simply three cascaded two-port
resonators, so the output signal of the left most resonator connects directly to the input signal of the
second resonator and so on. Thanks to the confinement of the release area by the isolation trench, the

14. 12
resonators may be compactly spaced without producing a large, delicate membrane. Approximately 80 %
of fabricated filters were intact and measureable, and no major fabrication issues were observed with the
third-order filters.
Figure 3-4: Filters fabricated through MEMS-only process. (a) Optical image. (b) SEM Image.
Measured frequency responses of the third-order filters are shown in figure 3-5. Despite the
multiple modes at resonance and the low Q extracted from the resonators, low loss filters were achieved.
However, the pass band and filter skirts are not as sharp as expected, and in some filters there is some
ripple. This is due to the multiple modes at resonance shown in figure 3-3. Sixteen total devices across
three dies were measured, and the compiled statistics are shown in table 2.
Figure 3-5: Frequency Response of filters fabricated through MEMS-only process, matched to 320 Ω

15. 13
Table 3-2: Measured statistics of filters fabricated through MEMS-only process, matched to 320 Ω.
III. Analysis of Mode Splitting in Two-Port Resonators
Despite the multiple modes at resonance and low Q extracted from the resonators, low loss filters
were produced. Such filters could not be produced from resonators that fit the equivalent circuit model
with a Q of 700. In order to reconcile the resonator measurements with the third-order filter
measurements, an investigation into the impact of the split resonance modes was performed. It was found
that the impact of the split modes only slightly affect the overall filter response, and that functional filters
may be achieved even with suboptimal resonators, which exhibits the robustness of the third-order filter
designs.
The two-port resonators fabricated in the MEMS-only process do not have a single sharp peak,
making Q extraction problematic. As shown in figure 3-6, there are several distinct peaks at resonance,
rather than a single sharp, distinct peak. Much of the response can be modeled by assuming three modes
with the same Q and kt
2
but different series resonance frequencies. When modeling the resonators with
split modes, the required Q is much higher (~1400), which corresponds better with the filter
measurements. While there are other spurious modes far from the resonance frequency, only the peaks
closest to resonance are modeled. A better fit of the resonator response could be obtained by varying the
Q and kt
2
of each of the modes, but this analysis is simply intended to yield a rough understanding of the
effect of the split modes on the filter performance. Thus, only the center frequency of the modes is varied
in this analysis. Also, the modes are assumed to be equally spaced, which is not exactly what occurs in the
actual filters. However, this analysis still provides a rough characterization of the observed resonator
behavior and helps to understand the impact of the split modes.

16. 14
Figure 3-6: Modeling of resonance peak with split modes
As explained in chapter 2 and illustrated in figure 2-6, the third-order filter has three modes of
resonance. It was determined that the resonator’s split modes do not affect each of these modes to the
same degree. Using the split mode fit shown in figure 3-6, the third-order filter was simulated. Figure 3-7
shows the admittance of the three resonance modes, for which only the first mode is strongly affected by
the split modes, as it occurs at the same frequency as the resonator. Because the second and third modes
occur at higher frequencies, the split modes do not strongly affect these modes, even for a very large
separation (1 MHz) between modes.
Figure 3-7: Comparison of resonance modes of filter composed of resonators with split modes at
resonance.

17. 15
The scattering parameters were also simulated with this model, and are shown in figure 3-8,
overlaid with the measured response. As expected from the split mode simulation, the first resonance
mode is degraded, whereas the second and third are clear and distinct. The degradation of the first mode
translates to the distortion of the left skirt of the filter response, while the clear second and third modes
yield a smooth right side of the pass band and smooth right skirt. Interestingly, while the bandwidth is
strongly affected by the mode spacing, the insertion loss is not, which explains why low loss filters were
achieved with the resonators.
Figure 3-8: Comparison of measured frequency response to frequency response of simulated filters
composed of split mode resonators, matched to 320 Ω.
IV. MEMS with Thin-Film Encapsulation Fabrication Process Flow
After demonstrating low loss filters in the MEMS-only process, the MEMS with thin field
encapsulation (TFE) process was undertaken to hermetically encapsulate the filters. Encapsulation of the
filters is necessary to protect the device, provide good hermeticity and ensure high yield in the bump
bonding process. Figure 3-9 shows the MEMS with TFE process flow. The first steps of the process are
identical to those of the MEMS-only process up to step h (deposition of passivation layer SiO2), and will
not be repeated. After deposition of the passivation layer, the passivation SiO2 is etched down to the AlN
to form the anchor of the TFE, as shown in (b). This is followed by etching down to the device layer of Si

18. 16
to form the release holes for the resonator, shown in (c). Next the sacrificial layer of Si is deposited and
patterned. 1 µm of AlN is then deposited to form the capping layer. This layer completely covers the
sacrificial Si and anchors, except for small holes above the AlN etch holes, to facilitate release of the
device. With the cap layer in place, the device is then released with XeF2 etch followed by VHF etch. The
device is then hermetically sealed with 3.5 µm of SiO2. The SiO2 sealing layer is patterned to reveal the Mo
pads. Lastly gold under bump metallization (UBM) was deposited on the pads to facilitate bump bonding.
Figure 3-9: MEMS with TFE process flow: (a) Device fabricated through MEMS-only process flow up to
step h in figure 3-1 (h). (b) Etching of encapsulation anchor. (c) Etching of release holes. (d) Formation
of sacrificial silicon. (e) Deposition and patterning of AlN capping layer. (f) Xenon difluoride release and
vapor hydrofluoric acid etch. (g) Deposition and patterning of Silicon dioxide sealing layer. (h)
Deposition of under bump metallization.
V. MEMS with Thin-Film Encapsulation Device Measurements
Filters fabricated in the MEMS with TFE process are shown in figure 3-10. The sealing and capping
layers are both transparent, so the only TFE features that can be seen optically are the release holes in

19. 17
the capping layer and the edges of the TFE anchors around the resonators. In the SEM image, the topology
formed by the TFE is very clear. The features of the resonator are also present in the TFE layers due to the
topology formed on the sacrificial Si. After the focused ion beam (FIB) cut, the TFE layers are readily visible
with the released resonator in the center of the figure, the wafer layer of Si at the bottom, and the TFE at
the top. By visual inspection, it was found that all of the TFE filters were well released, and no broken
devices were found. This is an appreciable improvement in device yield over the MEMS-only fab.
Figure 3-10: Filter fabricated through MEMS + TFE process. (a) Optical Image. (b) SEM image. (c) SEM
image of FIB cut.
The frequency response of the third-order filters was measured, and example responses are
shown in figure 3-11. The TFE filters are fully functional, however the loss is higher than in the MEMS-only
process. Also, the feedthough is higher, and the spurious modes out of band are more prominent. It is

20. 18
clear that the TFE has introduced additional parasitics, but it nevertheless demonstrates a major
advancement in CMR filter technology.
Figure 3-11: Frequency Response of filters fabricated through MEMS with TFE Process, matched to
300 Ω.
Thirty six total filters across three dies were measured, and statistics are reported in table 3. The
filters with TFE are very similar to the filters without TFE, except for the ~2 dB increase in insertion loss,
which is a much greater impact than was expected. In future work, the impact of the TFE must be
minimized in order to realize low loss, high yield filters.
Table 3-3: Measured Statistics for filters fabricated through MEMS + TFE process.

21. 19
Chapter 4: Intrinsic Filter Yield Limitation and Enhancement with Statistical
Element Selection
Functional, low-loss filters were demonstrate in both the MEMS-only and MEMS with TFE
processes, which are very promising for implementation in a cognitive radio system. However fabrication-
induced variations are problematic as they will drastically reduce the filter yield. Here limitations on yield
due to fabrication-induced variations will be discussed. To compensate the yield and enable
reconfigurability we propose application of statistical element selection (SES) to the third-order filters.
Design of the system for SES implementation will be discussed.
I. Filter Yield Limitation Due to Fabrication-Induced Variations
In both the MEMS-only and MEMS with TFE Process, functional narrowband filters were
demonstrated. However, from a comercial standpoint, it is not enough to have a high percentage of the
devices functioning. They must function within certain specifications. In this regard the variation in the
filter properties can be very problematic. For example if the center frequency of the filters must be within
100 kHz of the designed frequency, for the measured intradie variation in the MEMS-only process, only
about 37% of the filters would pass the center frequency spec, as shown in figure 4-1. The filter yield
would be further reduced when specifications on the insertion loss, bandwidth and out-of-band rejection
are imposed. Thus, despite the impressive results that were dilivered by both fabs, a method of producing
filters that meet a tight set of specifications must be implemented in order to realize a commercially viable
product.
Figure 4-12: Center frequency offset distribution of filters in the MEMS-only process.

22. 20
II. Application of Statistical Element Selection for Yield Improvement and Reconfigurability
In order to address the challenges presented by filter variations, we propose the use of statistical
element selection (SES), which can both improve yield and provide reconfigurability. As described in [1],
SES will be applied by using an array of N identical elements and selecting a subset k, providing a total of
N
Ck combinations. N will be referred to as the array size, and k will be referred to as the selection size.
Thanks to the exponential increase in combinations, even a modest size array can produce a large number
of combinations. Although the probability that a single element of the array will satisfy a given set of specs
is low, the large set of configurations may be searched until a configuration that meets the required
specifications is found. For the filters, SES was implemented using the circuit shown in figure 4-2, in which
filters will be combined by connecting them in parallel. Each branch of the circuit, which consists of two
switches and one filter connected in series will be referred to as a sub-filter. Thus the array will consist of
N sub-filters, and a subset of k sub-filters will be selected.
Figure 4-13: Circuit topology for application of SES to AlN Filters
In order to gauge the feasibility of applying SES to the AlN filters, Monte Carlo analysis was
performed in Matlab. A custom program was produced to perform scattering parameter calculations and
switching between combinations within the Monte Carlo analysis. This was performed by randomly
generating resonators using the equivalent circuit model and measured resonator statistics, calculating
third-order filter responses from the generated resonators, and exhaustively searching all possible

23. 21
combinations of sub-filters connected in parallel until one that satisfies the given specs was found. Figure
4-3 shows the impact of this approach on the center frequency offset. In this simulation, four sub-filters
were chosen from an array of 12, yielding a total of 495 combinations. Compared to figure 4-1, it is clear
that SES has provided a much tighter spread and higher yield, with all of the 1000 samples tuned to within
the 100 kHz of the target frequency.
Figure 4-14: Simulated center frequency offset distribution of filters after SES
III. MEMS Chip Design for Statistical Element Selection Implementation
Although there will be N
Ck possible sub-filter combinations to choose from, different selection
sizes (number of sub-filters in parallel) will require different termination impedances. As the termination
impedance will not be variable in practice, it is necessary to demonstrate SES with a single selection size.
Thus, it is important to choose the optimum selection size. To this end, the Monte Carlo analysis was
applied to a variety of array and selection sizes. Figure 4-4 shows the filter yield vs. selection size for a
variety of array sizes, where the termination impedance was adjusted to match the selection size. The full
set of specifications applied in this analysis were Δf0 < 100 MHz, insertion loss below 3 dB, bandwidth
between 3 and 4 MHz, and out-of-band rejection above 25 dB. In this analysis a mean Q of 2000 was
assumed, which will yield filters with insertion loss of approximately 2.1 dB. For the TFE filters, which
have an average insertion loss of 4.5 dB, the insertion loss spec will ultimately have to be relaxed.

24. 22
However, this analysis is still useful for guiding the application of SES. As expected, yield increased with
array size, while the optimum selection size for almost all array sizes is four. Interestingly, this is the same
optimum value found in [1] for a very different application of SES. Furthermore, we see that the yield falls
off much more slowly after four for larger array sizes. In some applications, it may be necessary to have a
larger selection size for matching purposes, and if this is the case, a large array size will be useful.
Figure 4-15: Parametric Monte Carlo simulation of SES applied to AlN filters
IV. CMOS Chip Design for Statistical Element Selection Implementation
According to the Monte Carlo analysis, we would like to maximize the array size; however, for this
project, the MEMS chip, containing the filter array must be smaller than the CMOS chip to leave space for
probing. The CMOS chip, fabricated in the IMB 65 nm process was 2 mm by 2 mm, which constrains the
maximum size of the MEMS chip to approximately 1.8 mm by 2 mm. Furthermore, the anchor layer on
the MEMS was required to be 70 µm in width between resonators, which significantly increases the size
of the filters. Lastly, the minimum spacing of the solder balls was 120 µm. Considering all design
constraints, the largest array size that could be laid out was N=12. The filter signal pads were staggered
and the ground pads were shared between filters to save space. Input bump pads were separated as much
as possible from output bump pads to minimize feed through. The MEMS chip with the array of 12 AlN
TFE filters is shown in figure 4-5.

25. 23
Figure 4-16: MEMS chip with array of 12 AlN TFE filters
In order to implement SES, it will be necessary to build a switching array that will allow the sub-
filters to be easily switched on and off. This is easily accomplished in CMOS technology. Thus, the switches
and routing for the circuit were designed in a 65 nm CMOS technology. The chip concept is shown in figure
4-6. Bump pads are placed on the CMOS chip to facilitate bonding to the MEMS chip. Physically, the bump
pads correspond to openings in the passivation layers, which allow solder balls to later be deposited
directly onto the top metal layer. RF switches connect the bump pads to the RF in and RF Out routing. In
the design of the RF switches, there is a tradeoff between the on impedance of the switches and the
parasitic shunt capacitance. The same tradeoff exists between the resistance of the routing and the
parasitic capacitance to ground. Both the routing and the switches were sized to minimize the insertion
loss of the filter according to (PEX) simulation. Also, the input and output routing was designed to ensure
that the resistance and shunt capacitance due to the switch and the routing was the same for each sub-
filter. This required longer routing, but it is undesirable to introduce mismatch between the sub-filters
due to routing. To limit feedthrough, a grounded plate was placed between input and output routing in
any location of overlap. This slightly increased the shunt capacitance, but shunt capacitance is preferable
to feedthrough capacitance, as the shunt capacitance can be partially canceled with shunt inductors at
the input and output of the filter. As probing will be performed on the CMOS chip, it is necessary to use
as little space as possible for probe pads to maximize the size of the MEMS chip and thus the array size.
This is accomplished by implementing a shift register to activate and deactivate each branch.

26. 24
Figure 4-17: Conceptual Layout of CMOS chip.
The CMOS chip was produced by MOSIS in the IBM 65 nm process. 50 µm diameter solder balls
were patterned on the chip by Tag and Label Manufacturers Institute (TLMI, Gloucester, MA). The CMOS
chip without solder balls is shown in figure 4-7(a). In figure 4-7(b) the CMOS chip is shown with the solder
balls in place over the bump pads. The probe pads are visible at the top portion of the chip, and the smaller
bump pads are visible below the probe pads. The bump pads were laid out to be the reverse mirror image
of the UBMs on the MEMS chip to facilitate bump bonding. In order to save space, the probe pads are laid
out such that the logic and RF pads are all in the group in the center, with the port 1 signal being the left
most pad in the center group and the port 2 signal pad being the right most pad. The larger rectangular
pads at the top corners are intended for wire bonding to a matching network.
Figure 4-18: CMOS chip. (a) Prior to solder ball deposition. (b) After solder ball deposition

27. 25
V. CMOS Chip Characterization
To roughly characterize the CMOS chip, DC measurement of the resistance between the RF signal
pads and the bump pads were performed. The measurement setup for these measurements is shown in
figure 4-8(a); figure 4-8(b) shows a zoomed view of the custom mixed signal probe from Cascade
Microtech beside a DC probe. In figure 4-8(a) the mixed signal probe is mounted on the probe station in
the bottom right corner of the picture. On the monitor on the left is the custom Labview software written
at CMU to control the switch matrix. Switches were controlled via a shift register on the chip, which is
controlled by logic signals using NI-DAQmx software. An example of the logic signal provided to access a
combination of switches is shown on the oscilloscope in the bottom right of the figure. On the screen on
the right is the microscope view which shows the mixed signal probe and DC probe over the CMOS chip,
ready for measurement.
Figure 4-19: Measurement setup for CMOS switching matrix using custome mixed signal probe. (a) Full
Setup. (b) Mixed signal probe (left) and DC probe (right).
Resistance measurements were made between the RF signal pads and the probe pads, and all switches
were found to be fully functional with an average value of ~30 Ω (including CMOS trace resistance) for the
on resistance and ~1 MΩ for the off resistance, no difference was observed between bumped and
unbumped chips. Unfortunately, the value for the on resistance is ~15 Ω higher than simulated, which will
increase the insertion loss of the filter. Also the frequency response of the chip was measured with all
switches on and all switches off and for bumped and unbumped chips. The measured response and the
simulated response are shown in figure 4-9. The frequency response did not change appreciable
depending on the switch configuration, or whether the chip was bumped or unbumped. Unfortunately,
the measurement is quite different from the simulation performed using PEX in Cadence. From the simple

28. 26
measurement, it is clear from the higher than expected S21 that the feed through on the chip is much more
problematic than expected, which will degrade the OBR of the filter. It is suspected that rules files may
have been incorrectly configured for PEX, resulting in an underestimate of parasitics.
Figure 4-20: Frequency response of CMOS chip.

29. 27
Chapter 5: Application of Statistical Element Selection to 3D-Integrated, Self-
Healing Filters
Functionality of the two key components of the self-healing filter, namely the encapsulated filters
and the CMOS switching matrix have been demonstrated. In this chapter, integration of the two chips is
discussed. Several 3D-integrated self-healing filter samples were measured and found to be fully
functional, though insertion loss is ~7 dB and rejection is ~16 dB. Statistical element selection was applied
to these samples, using an extraction method that will be discussed in detail. The accuracy of this
extraction method was also assessed.
I. 3D Integration through Solder Bump Bonding
With fully functional MEMS chips and CMOS chips with solder balls completed, the process of flip
chip bonding was undertaken at IME. Figure 5-1 shows a cross sectional view of the flip chip bonding
process. Figure 5-1(a) shows the CMOS chip, and Figure 5-1(b) shows the MEMS chip. Both have been
discussed in detail in previous chapters. The two chips are bonded together by aligning the solder balls on
the CMOS chip with the UBM pads on the MEMS chip. The resulting stack is shown in figure 5-1(c), in
which the RF signal and ground pads are now bump bonded to the CMOS chip. As the bonding of the chips
requires careful handling and application of force to join the two chips together, the TFE is essential in
this case for protecting the resonators from physical damage and ensuring that no devices are broken
during the bonding process.
Figure 5-21: Flip chip bump bonding (a) CMOS chip with solder balls. (b) MEMS Chip. (c) MEMS chip
flip chip bonded to CMOS chip

30. 28
At the time of this writing, 8 flip chip stacks have been delivered with additional samples expected
in the future. A 3D stack is shown in figure 5-2(a) with the CMOS chip on the bottom facing upward and
the MEMS chip on top facing downward. The probe pads on the CMOS chip are facing the camera and are
clearly visible. The reflection of the CMOS probe pads can be seen on the silicon of the MEMS chip. The
gap between the pads on the CMOS chip and the reflection on the MEMS chip is the physical separation
between the two chips. The group of pads in the center of the chip is designed to be probed with a custom
mixed signal probe in order to measure the frequency response of the sample. An optical image of the
diameter solder ball is shown in figure 5-2(b), and an SEM image of the solder ball is shown in figure 5-
2(c). In the SEM, the UBM deposited by TLMI onto the CMOS chip is clearly visible; whereas the UBM on
the MEMS chip has been enveloped in the solder during reflow. Also, there has been some widening of
the solder ball during the bonding process to ~80 µm diameter.
Figure 5-22: Flip chip stack (a) Full Stack. (b) Optical image of solder ball. (c) SEM image of solder ball.
II. Measurement of Self-Healing Filters
Of the eight 3D stacks delivered, six have been measured. Due to variation in the dicing of the
MEMS chips, there is variation in the clearance between the probe pads and the MEMS chip. It would be
very expensive and time consuming to replace the custom probe, so no risk was taken to measure the flip
chip stacks with low probe pad clearance. Measurements were made with the custom mixed signal probe

31. 29
from Cascade Microtech using the setup described in the previous chapter. All measured flip chip stacks
were found to be fully functional, with all switches controllable and all filters showing a clear pass band.
In order to cancel some of the shunt capacitance from the switches and CMOS traces, a matching network
with a shunt inductor with a Q of 40, as shown in figure 5-3 was included via simulation.
Figure 5-23: matching network used with 3D stack filter
Measurements of three of the 495 available responses are shown in figure 5-4. Notice the small
variation in center frequency and bandwidth. This small shift from one filter to another allows very fine
tuning through SES. Notice also that there is some variation in the feedthrough out of band. This is
unexpected from the model and requires further investigation.
Figure 5-24: Three of the 495 available filter responses available from self-healing filter, matched to 40
Ω
As expected, from measurements of the TFE filters and the CMOS chip, the Insertion loss of the
self-healing filter is higher than designed; similarly, the out-of-band rejection is much lower. It is suspected

32. 30
that higher than expected parasitics on both the CMOS and MEMS chips contribute to the decreased
performance. Shown in figure 5-5 is a comparison of typical responses from each stage of the project. In
the response for the self-healing filter, four sub-filters are activated, so to make a fair comparison, each
of the other responses shown is that of four identical elements of the specified filter in parallel (i.e., a
single filter was measured, Y parameters were multiplied by 4, resulting S parameters are shown in plot).
Filters fabricated in the MEMS-only process had very low loss and overall good performance,
demonstrating the merit of the AlN-MEMS filters. Encapsulated filters showed very promising results, but
insertion loss increased by ~2 dB. This is certainly undesirable, and future work should focus on reducing
the loss and parasitics of encapsulated filters now that their functionality has been confirmed. Accounting
for the simulated parasitics of the CMOS chip, ~1 dB further insertion loss increase and some feedthrough
was expected. This was considered acceptable when ideal filters were assumed, as the insertion loss was
still below 3 dB and the out-of-band rejection remained above 25 dB, while achieving reconfigurability.
Regrettably, as expected from the initial measurements of the CMOS chip, the impact of the parasitics is
much higher than simulated, resulting in insertion loss ~2 dB higher than that of the encapsulated filters
and out-of-band rejection below 20 dB. It is suspected that PEX was not correctly configured in Cadence,
resulting in the discrepancy. However, despite suboptimal performance, the self-healing filter shows clear
responses which are easily selectable. This demonstrates the concept of application of SES to the AlN-
MEMS filters using a CMOS switch matrix through 3D integration. Moving forward, it is crucial to minimize
parasitics and loss in both the MEMS and CMOS to improve both the insertion loss and the out-of-band
rejection.
Figure 5-25: Evolution of filter performance

33. 31
III. Extraction Algorithm for Fast Characterization of Reconfigurable Filters
In the self-healing filter, there are far more available responses than the three shown in figure 5-
4, and it would be trivial to switch on any desired combination. However, it would be very time consuming
to exhaustively measure all of the possible combinations. Thus to expedite the process of applying SES,
an algorithm for extracting the individual sub-filter responses and calculating the frequency responses of
the combinations, rather than measuring them all was employed. Figure 5-6 shows the simple model of
the self-healing filter, which was used in this extraction. The CMOS chip contributes feedthrough
admittance, shunt admittance and series impedance to the self-healing filter. The model in figure 5-6(a)
may be rearranged as shown in figure 5-6(b), where the CMOS parasitics are lumped into the sub-filter
blocks. In light of figure 5-6(b), it is apparent that the overall response of the filter may be computed by
summing the Y parameters of the sub-filters lumped with the CMOS parasitics. This model is intended to
be very rough and thus will not capture all features of the self-healing filter; however, thanks to its
simplicity, each of the components that make up the circuit can be easily extracted from measurements.
Figure 5-26: Model of 3D stack (a) Full model. (b) Decomposition into open CMOS and sub-filters.

34. 32
Using this model, extraction of all filter combinations is performed as follows:
 Extraction of sub-filter on and off Y parameters
o Measure self-healing filter with all sub-filters off
o Calculate Y parameters and divide by 12 to obtain approximate Y parameters of a single
off sub-filter, Yoff
o Measure all combinations with a single sub-filter on
o Calculate Y parameters and subtract 11Yoff to obtain the Y parameters of the individual
sub-filter, YN
 Extraction of response of with sub-filters A,B,C and D on
o YA+YB+YC+YD+8Yoff
This requires a total of only 13 measurements, and the calculation is easily performed in Matlab. Less
than 10 seconds are required to compute the full set of 495 responses, which is less time than is required
to measure a single configuration. As expressed previously, the circuit model of the self-healing filter is
very simple, and within a chip, the frequency response of all sub-filters in the off state is assumed to be
the same, which will likely cause some error. Thus the extraction method offers a tradeoff between speed
and accuracy.
IV. Assessment of Extraction Algorithm and Application of Statistical Element Selection
Several self-healing filter samples were measured, and the extraction method was used to apply
SES. In addition to the 13 required measurements, measurements of configurations of the self-healing
filter with four sub-filters on were made in order to assess the accuracy of the method. For all
measurements, 40 Ω termination and a 6.2 nH shunt inductor are assumed. Figure 5-7 shows two
examples of extracted responses vs. their actual response. Figure 5-7(a) shows the best response, which
overlaps quite closely, though it is apparent that there is a small frequency shift, and the magnitude is
slightly off out of the pass band. For the more typical response shown in figure 5-7(b), the extraction still
reflects the shape of the actual response, but the magnitude is slightly incorrect, which will result in error
in the insertion loss and out-of-band rejections. Also, this extraction exhibits a similar frequency shift as

35. 33
in the best overlap. This confirms the expectation of some error due to the simplicity of the model, but is
promising in that the shape of the actual response is reflected in the extracted response.
c
Figure 5-27: Comparison of measurement and extraction of frequency response of self-healing filter
using 40 Ω termination and 6.2 nH shunt Inductor. (a) Best Overlap. (b) Typical Overlap.
In order to assess the accuracy of the extraction method, sixteen configurations of the self-healing
filter with four sub-filters activated were measured, and the extraction method was used to predict their
response. Figure 5-8 shows the comparison between the measured filter properties and the extracted
filter properties, while table 5-1 lists the correlation and error. In figure 5-8, red points indicate the data,
while the horizontal axis represents the true filter property value and the vertical axis represents the
extracted property value. For the point, (x,y), if x and y are equal, the predicted value of the filter property
is perfect, thus if all of the predictions are correct, all red points will fall on the black line, which has slope
of 1 and intercept of 0. Unfortunately this is not the case. As was seen in figure 5-7, the center frequency
and thus the center frequency offset is shifted, but the shift is very consistent and correlation is very high.
However, the magnitude of the error is concerning, as it is similar to the mismatch of the filters, and thus
not trivial. The comparison with regards to insertion loss is similar, though the correlation is lower.

36. 34
Furthermore, the extraction of bandwidth appears quite reliable, but the out-of-band rejection extraction
is not reliable. As explained before, the impact of parasitics is much higher than expected. This impact is
not captured well in the primitive model of used for extraction. This further stresses the need to reduce
parasitics.
Despite the significant error in the extraction results, the high correlation is promising. If
measurements of several configurations of the self-healing filter with four sub-filters activated are
recorded and the mean error is calculated for each of the properties, this value can be subtracted from
the value predicted by the extraction to yield an adjusted prediction. If the adjusted prediction is correct,
then all data points will fall on the line with slope 1 and y intercept equal to the mean error, which is the
blue line in figure 5-8. It is clear that such an adjustment significantly improves the prediction, but this
would require additional measurements and additional characterization time. Again it is apparent that
there is a tradeoff between speed and accuracy.
Figure 5-28: Comparison of Measured and Extracted filter properties

37. 35
Table 5-4: Correlation and error between extracted and measured filter properties
The extraction methods detailed previously were applied in Matlab to several self-healing filter
samples. Figure 5-9 shows the bandwidth vs center frequency offset spread of a typical self-healing filter
using the extraction algorithm, while figure 5-10 shows the same plot computed using the extraction
algorithm, and adjusting the predicted values by the estimated error. For this filter, the specifications
applied were f0 Є 1.14 GHz ± 100 kHz, IL ≤ 8 dB, BW Є 3 MHz ±250 kHz, OBR ≥ 15 dB. The region of the
plot for which the center frequency and bandwidth specs are satisfied is shaded purple. Data points that
corresponds to filter configurations whose extracted properties pass all of the specs are shown as green
dots, while the points that pass the insertion loss and out-of-band rejection specs but not the bandwidth
or center frequency specs are shown as orange dots, and points that fail either the insertion loss or out-
of-band rejection specs are shown as red dots. Notice that while most points do not pass the full set of
specs, there is a very wide spread of points among the green and orange points, meaning the self-healing
filter has a center frequency tuning range of ~500 kHz and a bandwidth tuning range of ~500 kHz. Although
too few samples of self-healing filters are available at this time to perform an analysis of yield, the large
tuning range is promising for correcting variations in center frequency and bandwidth.
For select configurations, the measured data point is also shown in figure 5-9 as a square marker,
using the same color convention as described previously to indicate which specs are passed. As discussed
previously, the extraction method alone results in substantial error in the prediction of the filter
properties with some points that are predicted to pass specs actually failing specs and vice versa. When
the estimate of the mean error is subtracted, a great improvement is obtained. While there is still some
error, predictions of the filter properties are much more reliable. This demonstrates that such an
extraction method can be useful for application of SES, but future work should focus on reducing the
impact of the CMOS chip to improve the accuracy of the extraction as well as improve performance.

38. 36
Figure 5-29: Full set of data points using SES applied with extraction algorithm.
Specs: f0 Є 1.14 GHz ± 100 kHz, IL ≤ 8 dB, BW Є 3 MHz ±250 kHz, OBR ≥ 15 dB
Figure 5-30: Full set of data points using SES applied with extraction algorithm and adjusting for
estimated error
Specs: f0 Є 1.14 GHz ± 100 kHz, IL ≤ 8 dB, BW Є 3 MHz ±250 kHz, OBR ≥ 15 dB

39. 37
Chapter 6: Conclusions and Future work
In this work, self-healing filters were demonstrated by applying statistical element selection
through 3D integration of a switching matrix designed in IBM’s 65 nm CMOS with an array of bandpass
filters designed in IME’s AlN-MEMS with TFE process. This work demonstrates the feasibility of applying
statistical element selection by combining CMOS circuitry with AlN-MEMS filters and the impact of doing
so, which is to enable a wide (500 kHz) tuning range for both the bandwidth and center frequency of the
filter.
In the development of the MEMS filters, there were two main iterations, a MEMS-only process
in which only the AlN resonators and filters were fabricated and a MEMS with TFE process in which the
AlN filters were encapsulated in a hermetically sealed package. In the MEMS-only process, resonators had
an average center frequency, quality factor, electromechanical coupling and static capacitance of 1.144
GHz, 741, 2.18 % and 474 fF, respectively, while filters had an average center frequency, insertion loss,
bandwidth and out-of-band rejection of 1.146 GHz, 2.66 dB, 3.79 MHz and 22.0 dB respectively. For such
low loss filters, a much higher resonator quality factor would be required. Upon investigating the Q
extraction, it was found that the resonator peaks were not sharp but showed several closely spaced peaks
(split modes). These split modes were modeled as extra motional branches in the resonator. Using the
split mode model of the resonator, it was found that, while the split modes make the Q of the resonator
appear low, their effect of the split modes on insertion loss is very low, explaining the low loss of the filters
in spite of the low Q extracted from the resonators. Filters fabricated in the MEMS with TFE process have
an average center frequency, insertion loss, bandwidth and out-of-band rejection of 1.146 GHz, 4.44 dB,
3.83 MHz and 24.8 dB, respectively.
Despite the low loss of the filters, fabrication-induced variations present a significant limitation
to the application of these devices as commercial products. In the MEMS-only process, the mismatch
standard deviations of the center frequency, insertion loss, bandwidth and out-of-band rejection were
160 ppm, 4.19 %, 2.52 % and 3.52 %, respectively. These standard deviations were 220 ppm, 14.1 %, 1.54
% and 2.14 %, respectively in the MEMS with TFE process. Variations of this magnitude make it unlikely
that a single filter will meet a tight set of specs, which would be required in a commercial product. In order
to address this yield limitation, statistical element selection was applied to an array AlN-MEMS filters.
Statistical element selection was implemented by solder bump bonding a switching matrix designed in
IBMS 65 nm CMOS technology to the array of AlN-MEMS filters, each filter and the switches required to

40. 38
modulate transmission is referred to as a sub-filter. The required termination impedance will depend on
the number of activated sub-filters, thus only a single selection size can be used. Monte Carlo analysis was
applied to determine the optimum array size and selection size, and it was found that the optimum
selection size is four and that yield increases with array size. Due to design constraints, the maximum
array size achievable for this work was 12. Thus, four out of 12 sub-filters were chosen, providing 495 total
combinations. This high number of combinations both increases yield and enables reconfigurability, as
the combination of sub-filters can be changed as needed. 16 combinations were measured and found to
have an average insertion loss of 7.6 dB and average out-of-band rejection of 15.7 dB. The high loss and
low rejection of the self-healing filter is believed to be due to non-idealities in both the CMOS and the
TFE.
As measuring every combination to find a response with desired characteristics would be very
time consuming, an algorithm for expediting the application of SES was devised. This algorithm requires
only N+1 measurements to roughly extract the properties of each response. For the array size used in this
work, all responses can be computed in less than 10 seconds. Using this algorithm, it was found that the
self-healing filters have a typical frequency tuning range of 500 kHz and bandwidth tuning range of 500
kHz. The algorithm was checked against measurement, and it was found that some error exists. However,
this error can be reduced if additional measurements are taken to estimate the error and correction is
made.
Moving forward, the most pressing issues for the self-healing filter are to reduce the loss and
increase the rejection. As parasitics on the CMOS chip are believed to be the main contributor to sub-
optimal performance, focus should be placed on improving the routing, either with better design in CMOS
or by routing on a low loss redistribution layer on the MEMS. This latter approach will be pursued by
another student at CMU.
Additionally, the TFE design should be improved to both reduce loss and save space. The non TFE
filters demonstrate that low loss filters are possible in IME’s AlN process, but the TFE filters showed an
increase of ~2 dB in insertion loss. In the future the loss due to the TFE should be minimized to realize the
true potential of the AlN-MEMS filters. Additionally, the required spacing of the TFE layers (specifically the
anchor) was a major limitation to the number of MEMS filters that could be placed on a chip. As discussed
previously, a larger array size should increase yield; therefore, it would be worthwhile to reduce the size
of the TFE anchor.

41. 39
Lastly, application of SES should be explored using different circuit topologies and designs from
that presented here. Some promising designs include that presented by Wang [8] as well as self-healing
filters that use ladder filters build from one-port contour-mode resonators and self-healing filters that use
low noise amplifiers, rather than switches to modulate the transmission of the sub-filters. Research into
the latter two approaches is currently underway at CMU, promising to take self-healing filtering through
SES to even greater heights.

42. 40
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