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ENCASED CANTILEVERS FOR LOW-NOISE FORCE
AND MASS SENSING IN LIQUIDS

Dominik Ziegler PhD
Material Science Division, Molecular Foundry, Lawrence Berkeley National Laboratory
High Resolution
Imaging of Mica

Encased Cantilevers

Fabrication
Quantitative Mass Sensor

Gentle Imaging of
Lipid Bilayers

Interferometric
Deflection Detection

Dominik Ziegler PhD
Material Science Division, Molecular Foundry, Lawrence Berkeley National Laboratory
VISCOUS DAMPING LIMITS RESOLUTION
Fn


4k BTk
0Qi

4k BTb

Force Noise  Smallest Measurable Force
ω0≈150 kHz
Q≈200

ω0≈50 kHz
Q≈4

Fn air≈15fN/√Hz

Fn water ≈200fN/√Hz

100 m long, 30 m wide



High forces deform soft samples and limits resolution
LET`S GO SCUBA DIVING!
FABRICATION OF ENCASED CANTILEVERS

-Length of levers can be tuned
-Tip’s sharpness is maintained
FABRICATION OF ENCASED CANTILEVERS

-Length of levers can be tuned
-Tip’s sharpness is maintained
ENCASED CANTILEVER IN AIR/WATER
air
water

fair=310.280kHz
fwater=309.71kHz
Qair=210
Qwater=133

Single clean resonance peak.

High Q and high frequency, performance as in air (Fn=12 fN/sqrt(Hz))
-Only small frequency shift (1%)  No Added Mass
-Viscous damping of tip (few um) and double sided squeeze film damping
GENTLE IMAGING OF LIPID BILAYERS
height of supported DPPC
bilayers on mica
softest possible imaging
amplitude modulation
“Hydra Levers” by AppNano
Encased silicon lever (Mikromasch NSC36)
L = 200 µm, k=0.084N/m f=17 kHz
l =110 µm, k = 0.95N/m, f=85kHz

Thicker measured height
 Less deformation by tip
HIGH-RESOLUTION IMAGING OF MICA IN LIQUID

0.5 nm

MICA lattice using amplitude modulation
300mM KCl, 10mM K2HPO4, 5 lines/s
Unmodified commercial instrument
Multimode, Bruker
OSCILLATORY HYDRATION FORCE
Amplitude[mV]
Amplitude [Å]

(WATER STRUCTURE ON MICA)

20
15
10
5
0

0

1

0

1

Phase [Deg]
Phase[Deg]

60

3

2

[nm]

2

3

0.5 nm

40
20
0

-20
[nm]

~4Å

Ultra-small amplitude
displacement of the last few water layers
single curve no averaging

Kobayashi, J. CHEM. PHYS. 138, 184704 (2013)
QUANTITATIVE MASS SENSING WITH ENCASED CANTILEVERS

Indirect measurement of mass over
surface stress (DC measurement)

0

Known location of added mass  quantitative mass sensor
2
QUANTITATIVE MASS SENSING WITH ENCASED CANTILEVERS

250 nm Gold Particles

mc = 22.88ng

ne =

1
1
= 4 » 0.23
(bi L)4 Ci

Rp = -14.8mHz/fg
Known location of added mass  quantitative mass sensor
QUANTITATIVE MASS SENSING WITH ENCASED CANTILEVERS

250 nm Gold Particles

mc = 22.88ng

ne =

1
1
= 4 » 0.23
(bi L)4 Ci

Rp = -14.8mHz/fg
Cantilever Based Mass Sensing
mavg= 168 ± 12 fg

TEM Based Estimation
mavg= 175 ± 68 fg

Theory Gold Sphere
m=157 fg
SMALLEST DETECTABLE MASS
Current Cantilever Design
l = 125m m
w = 30m m
h = 2.5m m

k 10 N m
0

220kHz

A =100nm

Q 317

dm = 0.1fg / Hz » 60MDa / Hz

Optimized for Mass Sensing
l = 25m m

k = 1700 N m

w = 5m m
h = 5m m

w 0 = 11.0MHz

A =100nm

Q = 4500

dm = 20zg / Hz » 12.5kDa / Hz
Single Very Small Protein
(~100 Carbon-12 Atoms)

~60 Gold Atoms
Each 0.32 zg
SMALLEST DETECTABLE MASS
Current Cantilever Design
l = 125m m
w = 30m m
h = 2.5m m

k 10 N m
0

220kHz

A =100nm

Q 317

dm = 0.1fg / Hz » 60MDa / Hz

Optimized for Mass Sensing
l = 25m m

k = 1700 N m

w = 5m m
h = 5m m

w 0 = 11.0MHz

A =100nm

Q = 4500

dm = 20zg / Hz » 12.5kDa / Hz
Single Very Small Protein
(~100 Carbon-12 Atoms)

~60 Gold Atoms
Each 0.32 zg
INTERFEROMETRIC READOUT

Destructive interference if path
length difference (δ) between two
beams is

Finesse F= δλ/Δλ
Detect intensity of reflected light
(Single photodiode, high BW 50MHz)
k=45N/m
f0=320kHz
F=δλ/Δλ

Finesse ~3

Position Noise ~6fm/√Hz! (@10.6mW,~770nm)
CONCLUSION
Encased cantilevers overcome the problem of
viscous damping in liquids
Compatible with commercial instruments

-Ultra-low force noise in liquids 12 fN/sqrt(Hz)

-Gentle and High-Resolution Imaging
-Water Hydration Layers
-Quantitative Mass Sensor 0.1 fg/sqrt(Hz)

-Interferometric Readout 6 fm/sqrt(Hz)
ACKNOWLEDGEMENTS
Paul D Ashby

Interferometric Readout

Adrian Nievergelt (EPFL, Switzerland)
Technical Support

Ed Wong, Virginia Altoe

Preparation of Lipid Bilayers

David Chmielewski (UC Berkeley)
Modeling of Squeeze Film Damping

Dara Badri (UC Berkeley)
Aram Klaassen (University of Twente, The Netherlands)
Frieder Muegele (University of Twente, The Netherlands)
John Sader (University of Melbourne, Australia)

National Science Foundation
Cyber-enabled Discovery and Innovation #CBET940417

www.foundry.lbl.gov

www.scubaprobe.com

US Department of Energy DOE
#DE-AC02-05CH11231

www.lbl.gov

For more information please contact Dominik Ziegler PhD, dziegler@lbl.gov, +1 510 599 4444

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Encased Cantilevers for Low-Noise Mass and Force Sensing in Liquids

  • 1. ENCASED CANTILEVERS FOR LOW-NOISE FORCE AND MASS SENSING IN LIQUIDS Dominik Ziegler PhD Material Science Division, Molecular Foundry, Lawrence Berkeley National Laboratory
  • 2. High Resolution Imaging of Mica Encased Cantilevers Fabrication Quantitative Mass Sensor Gentle Imaging of Lipid Bilayers Interferometric Deflection Detection Dominik Ziegler PhD Material Science Division, Molecular Foundry, Lawrence Berkeley National Laboratory
  • 3. VISCOUS DAMPING LIMITS RESOLUTION Fn  4k BTk 0Qi 4k BTb Force Noise  Smallest Measurable Force ω0≈150 kHz Q≈200 ω0≈50 kHz Q≈4 Fn air≈15fN/√Hz Fn water ≈200fN/√Hz 100 m long, 30 m wide  High forces deform soft samples and limits resolution
  • 4. LET`S GO SCUBA DIVING!
  • 5. FABRICATION OF ENCASED CANTILEVERS -Length of levers can be tuned -Tip’s sharpness is maintained
  • 6. FABRICATION OF ENCASED CANTILEVERS -Length of levers can be tuned -Tip’s sharpness is maintained
  • 7. ENCASED CANTILEVER IN AIR/WATER air water fair=310.280kHz fwater=309.71kHz Qair=210 Qwater=133 Single clean resonance peak. High Q and high frequency, performance as in air (Fn=12 fN/sqrt(Hz)) -Only small frequency shift (1%)  No Added Mass -Viscous damping of tip (few um) and double sided squeeze film damping
  • 8. GENTLE IMAGING OF LIPID BILAYERS height of supported DPPC bilayers on mica softest possible imaging amplitude modulation “Hydra Levers” by AppNano Encased silicon lever (Mikromasch NSC36) L = 200 µm, k=0.084N/m f=17 kHz l =110 µm, k = 0.95N/m, f=85kHz Thicker measured height  Less deformation by tip
  • 9. HIGH-RESOLUTION IMAGING OF MICA IN LIQUID 0.5 nm MICA lattice using amplitude modulation 300mM KCl, 10mM K2HPO4, 5 lines/s Unmodified commercial instrument Multimode, Bruker
  • 10. OSCILLATORY HYDRATION FORCE Amplitude[mV] Amplitude [Å] (WATER STRUCTURE ON MICA) 20 15 10 5 0 0 1 0 1 Phase [Deg] Phase[Deg] 60 3 2 [nm] 2 3 0.5 nm 40 20 0 -20 [nm] ~4Å Ultra-small amplitude displacement of the last few water layers single curve no averaging Kobayashi, J. CHEM. PHYS. 138, 184704 (2013)
  • 11. QUANTITATIVE MASS SENSING WITH ENCASED CANTILEVERS Indirect measurement of mass over surface stress (DC measurement) 0 Known location of added mass  quantitative mass sensor 2
  • 12. QUANTITATIVE MASS SENSING WITH ENCASED CANTILEVERS 250 nm Gold Particles mc = 22.88ng ne = 1 1 = 4 » 0.23 (bi L)4 Ci Rp = -14.8mHz/fg Known location of added mass  quantitative mass sensor
  • 13. QUANTITATIVE MASS SENSING WITH ENCASED CANTILEVERS 250 nm Gold Particles mc = 22.88ng ne = 1 1 = 4 » 0.23 (bi L)4 Ci Rp = -14.8mHz/fg Cantilever Based Mass Sensing mavg= 168 ± 12 fg TEM Based Estimation mavg= 175 ± 68 fg Theory Gold Sphere m=157 fg
  • 14. SMALLEST DETECTABLE MASS Current Cantilever Design l = 125m m w = 30m m h = 2.5m m k 10 N m 0 220kHz A =100nm Q 317 dm = 0.1fg / Hz » 60MDa / Hz Optimized for Mass Sensing l = 25m m k = 1700 N m w = 5m m h = 5m m w 0 = 11.0MHz A =100nm Q = 4500 dm = 20zg / Hz » 12.5kDa / Hz Single Very Small Protein (~100 Carbon-12 Atoms) ~60 Gold Atoms Each 0.32 zg
  • 15. SMALLEST DETECTABLE MASS Current Cantilever Design l = 125m m w = 30m m h = 2.5m m k 10 N m 0 220kHz A =100nm Q 317 dm = 0.1fg / Hz » 60MDa / Hz Optimized for Mass Sensing l = 25m m k = 1700 N m w = 5m m h = 5m m w 0 = 11.0MHz A =100nm Q = 4500 dm = 20zg / Hz » 12.5kDa / Hz Single Very Small Protein (~100 Carbon-12 Atoms) ~60 Gold Atoms Each 0.32 zg
  • 16. INTERFEROMETRIC READOUT Destructive interference if path length difference (δ) between two beams is Finesse F= δλ/Δλ Detect intensity of reflected light (Single photodiode, high BW 50MHz) k=45N/m f0=320kHz F=δλ/Δλ Finesse ~3 Position Noise ~6fm/√Hz! (@10.6mW,~770nm)
  • 17. CONCLUSION Encased cantilevers overcome the problem of viscous damping in liquids Compatible with commercial instruments -Ultra-low force noise in liquids 12 fN/sqrt(Hz) -Gentle and High-Resolution Imaging -Water Hydration Layers -Quantitative Mass Sensor 0.1 fg/sqrt(Hz) -Interferometric Readout 6 fm/sqrt(Hz)
  • 18. ACKNOWLEDGEMENTS Paul D Ashby Interferometric Readout Adrian Nievergelt (EPFL, Switzerland) Technical Support Ed Wong, Virginia Altoe Preparation of Lipid Bilayers David Chmielewski (UC Berkeley) Modeling of Squeeze Film Damping Dara Badri (UC Berkeley) Aram Klaassen (University of Twente, The Netherlands) Frieder Muegele (University of Twente, The Netherlands) John Sader (University of Melbourne, Australia) National Science Foundation Cyber-enabled Discovery and Innovation #CBET940417 www.foundry.lbl.gov www.scubaprobe.com US Department of Energy DOE #DE-AC02-05CH11231 www.lbl.gov For more information please contact Dominik Ziegler PhD, dziegler@lbl.gov, +1 510 599 4444

Editor's Notes

  1. Tip sticks out by only several 3-5 um, Maskless Post-processing of Regular Silicon CantileversAdjust Final length by Sacrificial Layer Release
  2. Tip sticks out by only several 3-5 um, Maskless Post-processing of Regular Silicon CantileversMight look simple, but important that depositons are uniform and free of stress.
  3. Sometimes positive frequency shift, repulsive, I,e. cantilever hydrophobic.
  4. High-Angle Annular Dark-Field (HAADF) Microscopy
  5. High-Angle Annular Dark-Field (HAADF) Microscopy
  6. STEM HAADF, Icosahedral dodecahedron.
  7. If delta is Odd multiple of lambda/2----- Meeting Notes (10/3/12 04:02) -----Add OBD