CSE 495/595: Intro to Micro- and Nano- Embedded Systems
Prof. Darrin Hanna
Radio Basics
• Receiving signals and an oscillator
fr 
Radio Basics
• Start simple
Radio Basics
IF=455 kilohertz (AM) or
10.7 megahertz (FM/VHF)
• Super heterodyning
• It reduces the signal from very high frequency sources where ordinary
components wouldn't work (like in a radar receiver).
• It allows many components to operate at a fixed frequency (IF section) and
therefore they can be optimized or made more inexpensively.
• It can be used to improve signal isolation by arithmetic selectivity
Radio Basics
• f1 + f2 and f1 – f2
asin(2πf1t) + asin(2πf2t)
• Radio-frequency (RF) MEMS
• high volume production
• mass
• cost
• performance
• Potential markets
• cellular phones
• cordless phones for home use
• wireless computer networking
• radios
• global positioning system (GPS) receivers
• satellites
• missile guidance, military radar
• Requirements
• transmit desired signals with low loss
• do not permit external signals or noise to join the
transmitted signal
• filter out or not generate undesired signals
• higher-frequency harmonics
• At high frequencies, difficult to achieve
• Transmission lines
• wavelength on order of system size
• Conductor between ground planes
• dielectric
• system impedance (such as RF) must match transmission
line impedance
Signal Loss
• Losses
• conductor loss
• due to the resistance of materials used – heating
• modeled as resistance in series with the signal path
• low-resistive metals are used
• gold, copper, and aluminum
• contacts and between layers of different materials
also add resistance
• dielectric loss
• due to atomic-scale dipoles excited in the dielectric
• heating
• modeled as an equivalent parallel conductance
• Losses (cont’d)
• eddy currents induced in substrate
• modeled as a parallel conductance
• insulating or semi-insulating substrates minimize the
loss due to eddy currents
• high-resistivity (>5,000 Ω∙cm) silicon substrates ok
but semi-insulating gallium arsenide (GaAs) is better
• Gallium arsenide common
• microwave
• Insulators such as glass and alumina good
• process compatibility, cost, and thermal coefficient of
expansion mismatches
Capacitors and Inductors
• Capacitors and inductors have parasitics
• limits performance
• Two parameters describe their performance and enable
comparisons between devices
• quality factor Q and the self-resonance frequency fSR
• Q is measure of loss in a linear-circuit element
• maximum energy stored during a cycle divided by the
energy lost per cycle
• capacitor C with series resistance Rs, Q= 1/(2πfCRS)
Capacitors and Inductors
• Inductor quality
• inductor L with series resistance Rs, Q = 2πfL/RS
Capacitors and Inductors
• Q = 2πfL/RS and Q= 1/(2πfCRS)
• greater resistance gives a smaller Q
• as frequency goes up, current flows along an increasingly
thin layer at the surface of conductors (the skin effect),
increasing the resistance and lowering the Q
• capacitors
•dielectric loss, a function of frequency also contributes
to a lower Q
• micromachined capacitors, the dielectric is usually a
gas or vacuum, leaving series resistance as dominant
• loss can also occur in the substrate
Capacitors and Inductors
• inductors often have higher series resistance than
• far lower quality factors
• substrate loss as well
Capacitors and Inductors
• lines connecting a capacitor to a circuit and even plates have a
small parasitic inductance
• circuit model has a capacitance C in series with an
inductance Lpara
• low frequencies, the impedance of the inductor is small and
the capacitor functions as normal.
• higher frequencies, capacitor impedance falls while the
impedance of the inductor rises
Capacitors and Inductors
• lines connecting a capacitor to a circuit and even plates have a
small parasitic inductance
• circuit model has a capacitance C in series with an
inductance Lpara
• low frequencies, the impedance of the inductor is small and
the capacitor functions as normal.
• higher frequencies, capacitor impedance falls while the
impedance of the inductor rises
• limits useful frequency range
• Above fSR, inductance dominates and
capacitor looks to a circuit like an inductor!
Capacitors and Inductors
• Inductors often implemented as coils of a conductor
• have parasitic capacitance between them
• circuit model with each turn of the inductor is represented
by an incremental inductor and its parasitic capacitance
Capacitors and Inductors
• Inductor (cont’d)
• simplified model
• inductor L in parallel with a parasitic capacitor Cpara
• low frequencies, most current flows through the
• above fSR the capacitance dominates and inductor
ceases to function as one
• this often occurs at lower frequency for inductors
than for capacitors
Capacitors and Inductors
• Inductor (cont’d)
• quality factor rises with frequency
• but parallel capacitance reduces the effective
inductance at higher frequencies, Q eventually reaches a
maximum before falling.
Micro-machined capacitors
• constant capacitance fabricated side by side with transistors
• standard semiconductor integrated-circuit process
• sandwiching dielectric between two conductive layers
• on-chip capacitors
• reduces parts on a circuit board
• lowers cost
• noise reduction
• lowering both parasitic capacitance and resistance
• capacitance per unit area is relatively small
Micro-machined capacitors
• variable capacitors
• voltage-controlled oscillators (VCOs) / tuning circuits
• require variable capacitors
• varying dc voltage applied varies capacitance
• capacitance tuning ranges from 2:1 to over 10:1 with an
applied voltage of 0–5V are available commercially
• Q at most on the order of 50 in the gigahertz frequency
• example requirement is Q > 50 for a 2-pF capacitor in the
range of 1 GHz (cell phone)
Micro-machined capacitors
• surface micro-machined variable capacitors
• bottom plate residing on an insulated substrate, an air gap,
and a flat top plate suspended by a spring structure
Micro-machined capacitors
• applying dc control voltage V creates electrostatic force Fe =
• є0 is the permittivity of free space, A is the area of plate
overlap, and g is the gap
• force pulls the top plate downward, increasing capacitance
• restoring spring force
• Fs = kg, k is spring constant and g is plate displacement
• spring force increases linearly with plate motion
• electrostatic force rises faster than linearly with the plate gap
• results in both plate motion and capacitance change
• slowly at first, then rising rapidly
Micro-machined capacitors
• when displacement reaches 1/3 initial gap electrostatic force
rises more rapidly than the spring force
• top plate snaps down toward the bottom plate
• limits controllable increase in capacitance for this type of
variable capacitor to 50%
• parasitic capacitance lowers the possible tuning range.
Micro-machined capacitors
Bulk Micro-machined capacitors
• Bulk micro-machined variable capacitors
• comb-drive – most successful
Capacitance scales linearly with the number of fingers and finger
thickness and inversely to size of the gap
Bulk Micro-machined capacitors
• DRIE for high aspect ratio A:d
• typically resistance in the spring dominates Q
Bulk Micro-machined capacitors
• uses a single mask to DRIE though the top layer of Si on SOI
• stop on a 2-µm-thick buried layer of SiO2
• etch with HF to remove buried oxide
• moving parts
• supercritical drying
Bulk Micro-machined capacitors
• heavy doping (>1020 cm-3) of the silicon springs and fingers
does not yield sufficiently low resistance
• resistance is lowered by sputtering on a thin layer of Al
• coats the tops and sidewalls of the silicon
• top of the underlying silicon substrate is also coated
• gaps formed from undercut of the oxide, avoiding shorting
Bulk Micro-machined capacitors
• still substrate acts as the lossy plate of a capacitor
• low Q and a large parasitic capacitance
• changing Si substrate to highly-resistive material improves the
Q and lowers the parasitic capacitance by factor of ten
• better Q is achieved with a glass substrate
• requires major changes in process flow
Bulk Micro-machined capacitors
• These are fabricated by bonding thin-silicon side of SOI wafer
to the glass wafer with epoxy
•. Young’s moduli of epoxies are normally orders of magnitude
lower than those of silicon and glass
• provides some stress isolation between two substrates
• thick side of SOI wafer removed by grinding and polishing off
most of the silicon
• final silicon removal by etching in TMAH
• etch buried oxide to reveal thin layer of silicon
Bulk Micro-machined capacitors
• a 2-µm layer of Al is deposited for low series resistance and
patterned using plasma etching
• photoresist and Al act as a mask in a DRIE step to etch
straight down through Si to buried epoxy
• epoxy is etched in oxygen plasma
• undercuts the silicon to free the moving parts
• additional 0.25 µm Al sputtered to coat sidewalls for an even
lower series resistance.
Bulk Micro-machined capacitors
• Fabricated capacitors
• fingers 2 µm wide, 20 µm thick, a gap of 2 µm
• an initial overlap of a few micrometers
• nominal capacitance of 2 pF requires 1,200 sets of
interdigitated fingers!
• measured value for Q is 61 at 1 GHz
• self-resonance frequency is 5 GHz
• tuning range 4.55:1 at 5.2V from finger motion of 23 µm
Bulk Micro-machined capacitors
• Other concerns
• unintentional movements when device is subject to an
external acceleration, such as vibration
• noise
• unintentional displacement depends on the
acceleration, the mass, and the spring constant in the
direction of motion
• finger capacitors
• motion of the movable fingers sideways, perpendicular
to the intended direction of travel
• gap on one side is reduced, electrostatic force
increases and eventually pulls the fingers together
• electrical short
Micro-machined inductors
• low-cost discrete inductors
• many have inductances in the range of a few to tens of
• when used with an IC, suffer from parasitic capacitance in
traces and bond pads on the chip, in the bond wires
connecting the chip to the circuit board, and in the inductor
• limits the self-resonance frequency and therefore
maximum operating frequency
• consume board space in portable electronics
• on-chip inductors are desirable
Micro-machined inductors
• Example inductor parameters for on-chip VCOs in cellular
phones in the 1–2 GHz range
• L = 5 nH and Q >30
• Inductors are readily fabricated on ICs using CMOS
• spiral in one layer of metal and a connection to the center
of the spiral in another layer of metal
• Losses from the resistance of the metal and eddy currents in
the substrate limit the Q to less than 10 at 2 GHz
Micro-machined inductors
• improving both quality factor and self-resonance frequency
• reduce parasitic capacitance and substrate conductive loss
by changing to an insulating substrate
• not possible if circuitry is integrated on same chip
• raise the inductor above the substrate using an air gap or
form cavity underneath to reduce parasitic cap. to substrate
• As an example, 24-nH inductors were made using a 12.5-turn
spiral with an outer diameter of 137 µm
• on the substrate have a self-resonance frequency of 1.8
• raised 250 µm above the substrate have an fSR of 6.6 GHz
Micro-machined inductors
• small solenoids on top of the substrate
• closely spaced ribbons of copper-plated metal make coils
• bottoms of the coils attached to substrate
• thick copper shield placed under the coils prevents eddy
• low loss
• an example
• inductor with three turns, each 200 µm wide and 535
µm in diameter, has an inductance of 4 nH, a high Q of
65 at 1 GHz, and a self-resonance frequency of 4.2 GHz
• using thin aluminum shield from CMOS process instead
of thick copper (MEMS) lowers the Q by about 25%
Micro-machined inductors
MEMS Resonators
• mechanical system of a spring with spring constant k and a
mass m has a resonant frequency
 1  k
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 2  m
• In electronics, this is analogous to a series or parallel
combination of capacitor and inductor, with a small series
resistance (damper).
MEMS Resonators
• Illustration of Q (review from before)
MEMS Resonators
• quartz crystals
• IC oscillators have not been able to achieve large Q
• typical quartz crystal has a Q that reaches 10,000 or more
• quality factors above 1,000 are considered high for many
electronic and RF applications
• frequencies of interest cover the range between 800 MHz and
2.5 GHz for front-end wireless reception and intermediate
frequencies at 455 kHz and above
Comb Drive Resonator
• folded springs supporting a shuttle
• plate oscillates back and forth in
the plane of the wafer surface
• applied voltage, either positive or
negative, generates an electrostatic
force between the left anchor comb
and shuttle comb that pulls the shuttle
plate to the left
Comb Drive Resonator
Comb Drive Resonator
• A comb-drive resonator made of polycrystalline silicon
• standard surface-micromachining
• beams with a thickness 2 µm, widths of 2 µm, and lengths
of 185 µm
• system spring constant of 0.65 N/m
• moveable mass equal to 5.7 × 10-11 kg
• resonates at 17 kHz
• same beam thickness and width but reducing the length to
33 µm
• resonates at 300 kHz
• Q can be over 50,000 in vacuum but rapidly decreases to
below 50 at atmospheric pressure
• damping in air
Comb Drive Resonator
• higher resonant frequency
• total spring constant increased or the motional mass
• increase the beam width and decreasing its length –
increase spring k
• reducing motional mass is hard
• electron-beam lithography to write submicron linewidths,
single-crystal silicon beams with lengths of 10 µm and
widths of 0.2 µm reached a resonant frequency of 14 MHz
• same resonator dimensions
• use material with a larger ratio of Young’s modulus, E,
to density than silicon
• silicon carbide and polycrystalline diamond
Beam Resonator
• MEMS with higher resonant frequency
• beam resonators
• University of Michigan, Ann Arbor
• reference frequency oscillators to replace quartz crystals in
cell phones
• much smaller size
• ability to build several different frequency references
on a single chip
• higher resonant frequencies
• ability to integrate circuitry, either on the same chip or
on a circuit chip bonded to the MEMS
• all at a lower cost than the traditional technology
Beam Resonator
• simplest beam resonator
• clamped on both ends and driven by an electrode
Beam Resonator
• dc voltage applied between the beam and drive electrode
• center of the beam deflects downward
• removal allows it to travel back upward
• ac drive signal causes the beam to flex up and down
• large dc bias VD
• similar to comb-drive resonator
• beam oscillates at same frequency as the drive signal
• at resonance deflection amplitude is at its greatest
Beam Resonator
• An example polysilicon beam
• 41 µm long, 8 µm wide, 1.9 µm thick
• gap of 130 nm
• Applying voltages VD = 10V and ía = 3 mV
• measured resonant frequency is 8.5 MHz
• Q is 8,000 at a pressure of 9 Pa
• deflection amplitude is only 4.9 nm at center of beam
• at atmospheric pressure Q drops to 1,000
• to maintain high Q, vacuum sealed cap in packaging
Beam Resonator
• dc bias adds downward electrostatic force
• force varies with distance
• opposes mechanical restoring force of the beam
• makes effective mechanical spring constant smaller
• resonant frequency falls by a factor proportional to
• C is the initial capacitance, k is the mechanical spring
constant, and g is the gap without a dc bias
• resonant frequency can be electrically tuned
Beam Resonator
• Variance with temperature is a problem
• rate at which the resonant frequency falls
• polysilicon clamped-clamped beams
• –17 ×10–6/K (ppm/K)
• quartz crystals
• –1 ×10–6/K range (much better)
• compensation
Beam Resonators (dual)
• place an electrode with a dc bias VC over a beam
• an effective second electrical spring is added to system
• reduces overall system spring constant
Beam Resonators (dual)
• mounting ends of this top electrode on top of metal supports
with faster thermal expansion rate
• gap increases with temperature
• reduces the electrical spring constant opposing mechanical
• mechanical spring constant falls
• results in combination varying much less with
temperature than single beam
• +0.6 × 10–6/K
• polysilicon clamped-clamped be
–17 ×10–6/K (ppm/K)
• quartz crystals
–1 ×10–6/K range (much
Beam Resonators (dual)
• entire top electrode is made of metal
• process compatibility
• expands faster laterally than the underlying Si substrate
• it is clamped at the ends
• undesirably bows upward
• suspending the ends of beam off the substrate and
putting slits near its ends, bowing is greatly reduced
Beam Resonators (dual)
• with bias reduces the frequency shift with temperature
• –0.24 × 10–6/K
• comparable to the best quartz crystals
• specifications for this prototype beam
• length of 40 µm, width of 8 µm, thickness of 2 µm
• gap below resonant beam during operation of 50 nm
• gap above beam of ~ 250 nm
• with dc bias VD of 8V (lower) and VC also of 8V (upper)
• resonant frequency is 9.9 MHz
• Q of 4,100
Beam Resonators (dual)
• bottom electrode and resonant beam
• fabricated from polysilicon
• sacrificial silicon dioxide layer in between
• sacrificial oxide layer also on top of the resonant beam
• sacrificial nickel spacer on sides of beam
• gold electroplated through a photoresist mask for top metal
• nickel and silicon dioxide etched away to leave freestanding
Coupled Resonators as Bandpass Filters
• MEMS resonators have very
narrow bandpass characteristic
• suitable for setting the
frequency in an oscillator circuit
but not for a more general
bandpass filter
• bandpass filters pass a range of
frequencies, with steep roll-off on
both sides
• two or more micro-resonators can
be linked together by weak springs or
flexures to create bandpass filters
Q = fR / BW
So for Q = 4,100 and
fR=9.9 MHz
BW = 2.4 kHz
Highly selective
Coupled Resonators as Bandpass Filters
• in phase
• no relative
displacement between
two masses
• oscillation
frequency equal to
natural frequency of a
single resonator
• out of phase
• displacements in
opposite directions
• higher oscillation
Coupled Resonators as Bandpass Filters
• physical coupling of the two
masses effectively split the two
overlapping resonant
frequencies into two distinct
• how far apart these
frequencies are depends on the
stiffness of the coupling flexure
• for compliant coupling spring,
the two split frequencies are
sufficiently close to each other
that they effectively form a
narrow passband.
Coupled Resonators as Bandpass Filters
• increasing number of
oscillators in a linear chain
widens the passband
• also increases the number of
• in general, the total number of
oscillation modes is equal to the
number of coupled oscillators in
the chain
MEMS Switches
• key desirable parameters in RF switches are
• low insertion loss and return loss (reflection) in closed state
• high isolation in the open state
• high linearity
• high power-handling capability during switching
• low operating voltage (for portables)
• high reliability (particularly a large number of cycles before
• small size
• and low cost
• MEMS switches to be designed into new products, must surpass
the performance of, or offer some other advantage over existing
MEMS Switches
• membrane shunt switch
• University of Michigan
• 2-µm-thick layer of gold suspended 2 µm above a 0.8-µmthick gold signal line
• coated with ~0.15 µm of insulating SiN
• membranes span 300 µm and lengths of 20 to 140 µm
• 15-V dc voltage to signal line (in addition to the ac signal)
pulls gold membrane down to the nitride
MEMS Switches
• membrane shunt switch (cont’d)
• use of insulator prevents switch from working at dc and low
frequency but is expected to be more reliable than metal-tometal contacts
• sides of gold membrane are supported by wide strips of
same gold film
• in closed state, the connection is made by capacitive
coupling, which is only useful at high frequency
• insertion loss in the closed state is less than 0.6 dB over the
range of 10–40 GHz,
MEMS Switches
• cantilever series switch
• when closed, measured insertion loss of the switch is less
than 0.2 dB from dc to 2 GHz