Advancingthe performance ofquartz crystal resonatorsGREGORY A. BURNETT, PH.D.SENIOR ENGINEER, R&D

STATEK CORPORATION

EFCC 2015

Topics• Statek Corporation’s role in quartz crystal resonator development

• Miniaturization

• Rugged resonators for high-shock applications

• Minimizing acceleration sensitivity

• Crystals for high-temperature applications

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Statek Corporation

• Founded in 1970, in Orange, CA• Principal founder: Juergen Staudte• Invented & patented the photolithographic & chemical-

milling processes for micromachining resonators within quartz wafers

• Market focus• 1970s: Focused on supplying crystals for watches• 1980s: Pagers, computers, military, industrial, etc.• 1980s – 1990s: Worked with medical companies to

develop crystals for the burgeoning field of medical implantable electronics

• 1990s – 2010s: Major supplier for implantable medical electronics; military, industrial

• Product focus• Highly reliability, rugged, high temperature• Quartz crystal resonators (AT, tuning-fork, extensional)• Quartz crystal oscillators (mainly XOs)• Quartz crystal sensors (temperature, force/acceleration)

Nearing 50 years in frequency control

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MiniaturizationTOWARDS MAKING SUBMILLIMETER RESONATORS

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1950s (est.)

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Prior to 1970• Typical AT was a large round blank, supported by metal wires/clips,

housed in a leaded metal packages (tens of mm)

• Made using mechanical processes

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Still in use

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1970 to 2000• Micro-miniature tuning-fork / rectangular blank, epoxied mounted

with a surface-mount ceramic package that is hermetically sealed.

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CX1: 8 mm x 3.5 mmCX4: 5 mm x 1.8 mm

2000 to 2010• Market demands smaller resonators!

• CX9: 4.1 mm x 1.5 mm

• CX11: 3.2 mm x 1.5 mm

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2010s• Market demands even smaller resonators!

• CX16: 2.0 mm x 1.2 mm

• CX18: 1.55 mm x 0.95 mm

• Problem: Traditional designs don’t work at these small sizes

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Scale down existing design?• How about taking a given design

and scale it down uniformly?

• Capability• Resolution down to about 1 μm

• Could make devices down to about 100-200 μm

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𝑙

𝑤ℎ

𝑙 → 𝜆𝑙𝑤 → 𝜆𝑤ℎ → 𝜆ℎ

One path to miniaturization is to move to higher frequencies:More difficult to make (thin)Higher currentSweet spot is about 20 MHz to 50 MHz

𝑓~1

𝜆

Smaller version of existing design?• Frequency thickness (h)

• Optimize width (w) and length to minimize coupling to flexure modes

• Much of miniaturization involves finding a shorter version of any existing design.

• How do we:• Make the resonator the right frequency?

• Make it narrow & short?

• Keep 𝑅1 low (high 𝑄)?

Frequency[MHz]

Narrowestwidth (w)

[mm]

“Shortest”length (l)

[mm]

10.0 1.00 2.00

20.0 0.50 1.00

40.0 0.25 0.50

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Oscillator circuits don’t care whether the crystal is large or small, but they do care about its resistance

Challenge: Make resonator small & low 𝑅1• Smaller blank

Smaller electrode

Higher resistance

• Smaller blank

Higher mounting losses

Lower Q

Higher resistance

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𝑅1~1

𝐴

Mode trapping• AT resonators oscillate in a

thickness-shear mode:• Main motion is a shearing of the

thickness direction

• Oscillations trapped under the electrode

• To maintain high 𝑄 (low 𝑅1), oscillations must decay away sufficiently fast near mounting end and far end

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thickness

width direction

Methods of trapping• Electrode• Works well when there’s enough room for the falloff

(e.g. larger crystals and/or higher frequency).

• Method used by Statek for CX1 through CX9 (mostly)

• Geometrical• Mechanical beveling• The method used in the mechanical processing. Used for years and works very well.

• Photolithographic steps• Step-mesa approximation to mechanical beveling.

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FEA Modeling (COMSOL)

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Step-mesa approximation to beveling

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A A

SECTION: A - A

Varying width only (12 MHz)

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CX1-12 MHz, Symemtrical Electrode (50.7milx120 mil)

11,940,000

11,960,000

11,980,000

12,000,000

12,020,000

12,040,000

12,060,000

12,080,000

62.5 63 63.5 64 64.5 65 65.5 66 66.5 67 67.5

Crystal Width, mil

Fre

q, H

z

Main Mode

Other Mode

FEA provides• Crystal parameters 𝐹𝑠, 𝑅1, 𝐶1, 𝐶0 , 𝑄

• Mode pattern• Gives good insight into the design

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Varying length and width (24 MHz)

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Further Optimization• FEA provides a helpful initial

design• Does not take into everything about

the full geometry of the resonator

• Test by making real parts

• Optimized from there

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Tuning-fork resonators

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TOP VIEW

A

B

C

A

B

C

A-A

(-)

(+)

(+)

(-)

B-B

(+)

(-)

(-)

(+)

(+)

(-) (-)(+)

(-) (+)

C-C

32.768 kHz tuning-fork resonator

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Assembly (wafer package)

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Where we are today• Smallest AT quartz resonator (unpackaged)• Length = 1.1 mm

• Width = 0.5 mm

• Smallest tuning-fork (unpackaged)• Length = 1.5 mm

• Width = 0.7 mm

• Greatest challenging is making these with sufficiently low 𝑅1.

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Rugged resonators for high-shock applications

100,000 G AND MORE

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History• Pre 1970 – High shock was a few 100 g’s

• 1970s – Statek resonators could survive shock levels of a few 1,000 g’s.

• 1980s – 10,000 g (HG products)

• 2000s – 100,000 g CX4HG and HGXO

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Two basic failure mechanisms• Dismount• Is the epoxy mount strong enough to hold the resonator in place?

• Breakage• Is the resonator design robust enough to survive the stresses induced by high

shock events?

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Keys to ruggedness• Small size• Smaller devices typically experience

lower stresses under acceleration

• Stress length2/thickness

• Maintain scale, then stress size

• Fixed frequency, stress length 2

• Smaller size• Lower stress

• Can withstand higher accelerations (shocks)

• Mechanical support• Single end mount is good

• Dual end mount is better• Lower stress

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max stress ∝ 𝜌𝑎𝑙2

ℎ

max stressdual−end

=1

6max stress

single−end

Avoiding dismount• Shorten resonator• Shear dismount: Fixed frequency and bonding area 𝐴, mass ∝ length , so

𝐹 𝐴 ∝ length , so shorter resonator is less likely to dismount.

• Peel dismount: Torque τ ∝ length × mass ∝ length 2,so shorter resonator is less likely to dismount.

• The right adhesive• Strong

• Low outgassing

• Doesn’t de-Q the resonator

• Plenty of it

• Dual-end mount, for AT (introduces other issues)• Force distributed

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Avoiding breakage• Simple geometry (avoiding weak structures)• Fairly easy for ATs

• More challenging for tuning-forks

• Small resonator (Stress length2/thickness)

• Dual-end mount (reduces stress)

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Where we are today• AT crystals• Most products offer 10,000 g or more

• Some offer up to 100,000 g

• Could achieve 200,000 g or more• Would pursue if there were a market demand for this

• Tuning-fork crystals• Many offer up to 5,000 g

• Up to 30,000 g in preferred directions in some cases

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Minimizingacceleration sensitivity

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Why we care• C = Quiescent phase noise

• A = Phase noise under vibration• Random 0.05 g2/Hz 20 Hz to 2 kHz

• Vibration induced phase noise dominates quiescent phase noise by a factor of about 10,000(+40 dB)

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Acceleration Sensitivity• Crystal changes frequency changes under acceleration

• Direction of Γ depends on the resonator design• Statek AT resonators: Γ points normal to the face of the blank

• Many others: Γ points along the length of the blank

• Typical AT crystal sensitivities are about 2-4 ppb/g.

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𝐹 𝑎 = 𝐹0 1 + Γ ⋅ 𝑎 Γ

Δ𝐹

𝐹= Γ ⋅ 𝑎

Effect of acceleration sensitivity• Sinusoidal vibration• Creates sidebands

• Random vibration• Creates phase noise

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ℒ1 = Γ ∙ 𝐴 𝑓0

2𝑓v

2 𝐴 = Acceleration direction and amplitude𝑓0 = Oscillator frequency𝑓v = Vibration frequency

ℒ 𝑓 =1

2

Γ ∙ 𝑛 𝑓0

𝑓

2

𝐺 𝑓𝐺 𝑓 = Acceleration spectral density𝑛 = Acceleration direction𝑓0 = Oscillator frequency𝑓 = Offset frequency

R. L. Filler, “The acceleration sensitivity of quartz crystal oscillators: A Review,” IEEE Transactions on Ultrasonics, Ferroelctrics, and Frequency Control, Vol. 35, No. 3, pp. 297-305, May 1988.

Minimizing acceleration sensitivity“Theorem”: If the mode of vibration and the stress are symmetric, the acceleration sensitivity is zero.

1. How do we make mode symmetric?a. Symmetric electrode, symmetric plating, avoid sloppiness.

2. How do make the stress symmetric?a. Single-end mount

i. Stress gradient across blank (maximum near mount, minimal near end)

ii. Can minimize by placing electrode near unmounted end

b. Dual-end mounti. Put electrode between both mounts, symmetric!

ii. Also lower stress!

Dual-end mount ~ 10% to 20% the acceleration sensitivity of single-end mount

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Smaller crystal?• Recall: Stress length2/thickness

• Shorter crystal can have lower acceleration sensitivity than it’s longer brethren.

• But beware of bringing electrode closer to the base (higher gradient)

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Where we are today (AT resonators)• Standard crystals• Γ is about 2.0 to 4.0 ppb/g

• Low acceleration sensitivity designs• Γ is about 0.1 to 0.5 ppb/g

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Measuring acceleration sensitivity

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Sideband at vibration frequency (90 Hz)

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Two-crystal method• Greenray makes oscillators with acceleration sensitivities better than

0.05 ppb/g by pairing crystals

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Γ = 12

Γ1 + Γ2

Crystals forhigh-temperatureapplicationsACHIEVING RELIABLE OPERATION ABOVE 200 °C

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Background• Many applications -40 °C to 85 °C is sufficient

• Military often requires up to 125 °C

• Down-hole applications• Some up to 175 °C

• More recently 200 °C, 225 °C, 250 °C, and hotter…

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Difficulty• Well-behaved design• Wider temperature range, more opportunity for interfering modes to be a

problem

• Bonding• Adhesive must maintain strength at high temperatures

• Outgassing of the adhesive (aging)

• Packaging• Solder sealed packages limit upper temperature

• Package with Kovar seal-rim sealed with Kovar lid avoids this

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Oscillators• Oscillator IC• High temperature operation and reliability are a huge concern

• Some available and made for high-temperature work (very expensive)

• Wire-Bonding• Cleanliness – Good, clean, strong

• Intermetallics: Al pad on IC, Au pad in package• Au wire Au+Al intermetallic on IC pad

• Al wire Au+Al intermetallic on package pad

• Reliability• Can it survive 1,000+ hours at the desired temperature?

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Where we are today• Crystals• Surface-mount crystals up to 200 °C

• Thru-hole up to 260 °C

• Oscillators• Up to 250 °C.

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Further topics for advancement• Aging• What good is tight tolerance if you can’t hold it?

• Hysteresis• Need < 0.1 ppm for high-performance TCXOs

• Microjumps• GPS requires no discontinuous changes in frequency > 10 ppb

• Drive-Level dependency• Reliable startup

• Repeatable behavior in tight-tolerance TCXOs

• Drive-level dependent modes (parametric resonance)• At high drive, modes at 2𝑓 can strongly perturb frequency-temperature curve

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