Passive Components

Contour-Mode Resonator

Q: How does a contour-mode resonator differ from an FBAR or thickness-mode BAW resonator?

In a thickness-mode bulk acoustic wave resonator such as an FBAR, the frequency is set by the piezoelectric film thickness, so a single deposition run yields essentially one frequency across the wafer. A contour-mode resonator vibrates laterally in the plane of the film, so its frequency is set by a lithographically defined in-plane pitch (for example the electrode finger spacing or plate width). Because lithography defines the dimension, dozens of different frequencies from roughly 50 MHz to 10 GHz can be patterned side by side on one aluminum nitride film in the same fabrication run. This monolithic multi-frequency capability is the main reason contour-mode resonators are attractive for reconfigurable and multi-band RF front ends, where FBAR and SAW devices would each require separate dies or separate processes.

Q: What quality factor and electromechanical coupling can an aluminum nitride contour-mode resonator achieve?

Aluminum nitride contour-mode resonators typically achieve a quality factor (Q) of 1,000 to 3,000 in air at 1 to 3 GHz, with the highest reported values around 4,000 to 5,000 under optimized anchor and electrode design. The effective electromechanical coupling coefficient k_t squared for the d31 lateral mode is modest, usually 1.2 to 2.5 percent, which is lower than the 6 to 7 percent of a thickness-mode AlN FBAR. This lower coupling limits the achievable fractional bandwidth of a filter built only from contour-mode resonators to roughly 1 to 3 percent. Scandium-doped aluminum nitride (AlScN) raises the coupling to 4 percent or more, widening usable bandwidth at the cost of slightly lower Q and higher process complexity.

Q: Why are contour-mode resonators released from the substrate, and how does the anchor affect performance?

The piezoelectric plate must be suspended over an air gap so that the lateral acoustic energy is confined within the resonator rather than radiating into the silicon substrate. The plate is released by etching a sacrificial layer, leaving it tethered by narrow anchors at acoustic nodal points. Anchor design dominates the achievable Q: tethers placed at displacement nodes and sized to quarter-wavelength acoustic dimensions minimize anchor loss, which is often the limiting loss mechanism above 1 GHz. Poor anchor placement can drop Q by a factor of two or more. Other loss contributors include thermoelastic damping, electrode ohmic loss, and air damping, the last of which is removed by vacuum or wafer-level encapsulation.

/KON-toor mohd REZ-uh-nay-tor/ (CMR)

Setting frequency by lithography rather than film thickness, this class of piezoelectric MEMS device vibrates in a lateral, in-plane contour mode so that its resonant frequency depends on a patterned in-plane dimension such as plate width or electrode pitch. Built in a thin aluminum nitride film with electrodes that exploit the piezoelectric d₃₁ effect, a contour-mode resonator places dozens of different frequencies from roughly 50 MHz to 10 GHz on one chip, then groups them into compact filter banks and stable oscillator references. The suspended plate reaches a quality factor of 1,000 to 3,000 in air, making the technology a building block for multi-band, monolithic RF front ends.

Category: Passive Components

Frequency Range: 50 MHz to 10 GHz

Quality Factor: 1,000 to 3,000

How Lithography Sets the Resonant Frequency

The defining property of a contour-mode resonator (CMR) is that its frequency is fixed by an in-plane dimension that the designer draws on the photomask, not by the thickness of the deposited piezoelectric film. A thin plate of aluminum nitride (AlN) is sandwiched between metal electrodes; applying an RF field across the film excites a lateral extensional vibration through the d₃₁ piezoelectric coefficient. The plate expands and contracts along its width, so a half-acoustic-wavelength standing wave sets up across that width. Because the acoustic velocity in AlN is fixed near 10,400 m/s, choosing the plate width W (or the electrode finger pitch in an interdigitated design) directly selects the frequency.

This is the key contrast with thickness-mode bulk acoustic wave devices such as the film bulk acoustic resonator. In those parts a single film deposition produces essentially one frequency across the entire wafer, so every band needs its own film stack or its own trimming step. A CMR process patterns many widths side by side, so a multiplexer covering several cellular and Wi-Fi bands can be a single monolithic die. That monolithic, multi-frequency capability is what makes contour-mode technology attractive for reconfigurable front ends, even though its electromechanical coupling is lower than a thickness-mode device.

To confine acoustic energy, the AlN plate is released from the silicon substrate over an air gap and held by narrow tethers placed at vibration nodes. Anchor loss through those tethers, along with thermoelastic damping and electrode resistance, sets the practical ceiling on quality factor above 1 GHz. Designers iterate anchor placement and electrode coverage to push Q higher while keeping the motional resistance low enough to interface with a 50-ohm system.

Governing Equations for the Lateral Mode

Resonant frequency (width-extensional mode):
f₀ ≈ (1 / 2W) × √(E_eq / ρ) ≈ v_a / (2W)

Quality factor:
Q = f₀ / BW_3dB = 2π × (energy stored / energy lost per cycle)

Effective coupling (lateral d₃₁ mode):
k_t² ≈ (π² / 8) × (C_m / C₀) (typically 1.2% to 2.5% for AlN)

Where W = plate width, E_eq = equivalent Young's modulus, ρ = mass density, v_a ≈ 10,400 m/s in AlN, BW_3dB = 3 dB bandwidth, C₀ = static capacitance, C_m = motional capacitance. Example: W = 40 μm gives f₀ ≈ 130 MHz; W = 2 μm gives f₀ ≈ 2.6 GHz.

Acoustic Resonator Technology Comparison

Technology	Frequency set by	Typical Q	k_t²	Multi-freq on one die	Best application
Contour-Mode (AlN)	Lateral dimension (lithography)	1,000 to 3,000	1.2% to 2.5%	Yes (50 MHz to 10 GHz)	Multi-band MEMS filter banks
FBAR / thickness BAW	Film thickness	1,500 to 3,000	6% to 7%	No (one band per stack)	Single-band duplexers
SAW	IDT electrode pitch	500 to 1,500	5% to 8%	Limited	Sub-2 GHz filters
Quartz crystal	Cut and thickness	10,000 to 100,000+	< 0.5%	No	Low-frequency references
AlScN Contour-Mode	Lateral dimension (lithography)	800 to 2,500	4% to 6%	Yes	Wider-band MEMS filters

Common Questions

Frequently Asked Questions

How does a contour-mode resonator differ from an FBAR or thickness-mode BAW resonator?

A thickness-mode BAW device such as an FBAR sets frequency by film thickness, so one deposition run yields essentially one frequency across the wafer. A contour-mode resonator vibrates laterally, so frequency is set by a lithographically patterned in-plane dimension (plate width or electrode pitch). Dozens of frequencies from roughly 50 MHz to 10 GHz can therefore be patterned side by side on one AlN film in the same run, enabling monolithic multi-band front ends that FBAR or SAW would need separate dies to cover.

What quality factor and electromechanical coupling can an aluminum nitride contour-mode resonator achieve?

AlN contour-mode resonators reach Q of 1,000 to 3,000 in air at 1 to 3 GHz, with optimized designs around 4,000 to 5,000. The lateral d₃₁ coupling k_t² is modest at 1.2% to 2.5%, well below the 6% to 7% of a thickness-mode AlN FBAR, which caps filter fractional bandwidth near 1% to 3%. Scandium doping (AlScN) raises coupling to 4% or more and widens usable bandwidth, at the cost of slightly lower Q and a more complex process.

Why are contour-mode resonators released from the substrate, and how does the anchor affect performance?

The plate is suspended over an air gap so lateral acoustic energy stays in the resonator instead of leaking into the silicon. It is held by narrow tethers at acoustic nodes; anchor design dominates Q, since tethers placed at displacement nodes and sized to quarter-wavelength dimensions minimize anchor loss, often the limiting mechanism above 1 GHz. Poor placement can halve Q. Thermoelastic damping, electrode ohmic loss, and air damping also contribute, with air damping removed by vacuum or wafer-level encapsulation.

Related Terms

← Continuum Theory Contour Port →