Introduction to Microeletromechanical Systems (MEMS) · PDF fileIntroduction to...

11

Texas Christian University Department of Engineering Ed Kolesar

Introduction toMicroeletromechanical Systems

(MEMS)Lecture 10 Topics

• Piezoelectric Effect and PiezoelectricityPiezoelectric MaterialsApplications – Scanning Probe Microscopy

Scanning Tunneling Microscope (STM)Atomic Force Microscope (AFM)


MEMS Overview

Micromachining: lithography, deposition, etching, …

Processes & Foundries

Devices & Structures

Methodology

History & Market

Introduction &

Background

22


Piezoelectric EffectPiezoelectricity: forces applied

to a segment of material lead to the appearance of electrical charge on the surfaces of the segment.

The source of this phenomenon is the specific distribution of electric charges in the unit cell of a crystal.

Si+

Si+Si+

O- O-

O-

+-

Si+

Si+Si+

O- O-

O-

+

-F F

+ + + +

- - - -

Quartz (SiO2)


PiezoelectricityForce deforms crystals and displaces

centers of positive and negative charge

Effect is reversible: applying voltages causes the piezo crystal to deform

Typical values for d in the pC/N range

Fx

zr

xzxxzxzz A

zFdCFd

CQV

dAEdAdFdQ

εε

εσ

0

:examplefor (matrix)t coefficieny sensitivit charge

===

====

VzAz

z

33


Piezoelectricity: ExamplesApply Fx = 1N force on a 1cm × 1cm × 1mm

slab of PZT (lead zirconate titanate)

How much has the shape changed?Fz

1200 ,/370 ,/110

10

35.0

0

0

===

≈=

≈=

rzzxz

xr

zxzx

zr

zzzz

NpCdNpCd

VAxFdV

VAzFdV

εεε

εε

210 /103.8

12.0

mNE

nmEA

zFl

llEE

AF

z

zz

⋅=

≈=∆

∆=== εσ

Vz


Piezoelectricity: Examples

Change in length per unit applied voltage:

PZT:

Note: ∆l is independent of l ! It only depends on the voltage ∆V, and on material properties

⇒ piezo stacks

∆zdEldl

ldFlA

QlC

Vl rrr εε

σεεεε 000 =∆

=∆

=∆∆

=∆∆

Vz

VnmdEV

l r /23.10 ≈=∆∆ εε

44


Piezoelectric Materials

Material Type Piezoelectric Relative DepositionConstant Permittivity(pC/N) (εr)

Quartz single 2.33 4.5 growth, oxidationcrystal

PVDF polymer 20/2/-30 12 spin onBaTiO3 ceramic 78/190 1700PZT ceramic 110/370 1200 spin-onZnO metal 246 1400 sputter

oxide

[After Kovacs, 1998, p. 217]


Scanning Probe Microscopy

Limitations of optical microscopy / lithography:• Resolution (wavelength)• Complexity / cost increases with decreasing scale

Instead: use scanningprobe with extremely sharp tip (“aperture-lessmicroscopy”)

55


Scanning Probe Microscopy

Advantages:• Not limited by optics / wavelengths• Measure topography, and a wide range of phenomena

such as electrostatic, magnetic, capillary, van der Waalsforces, friction, conductivity, …

Disadvantages:• Contact with sample• Precise feedback required• Very sharp tips required (µm … nm)• Image convolution


Scanning Probe MicroscopyTip Shape

Image convolution:let A be the sample surfacelet B be the tip surfacethen A ⊕ (-B) is the image that we observe when scanning B over A

Definition: A ⊕ (-B) = a-b | a∈Aand b∈B(“Minkovski sum”)

Question: Can we reconstruct Afrom A ⊕ (-B) and B ?

Convoluted Feature

Original Feature

66


Scanning Tunneling Microscope

(G. Binnig and H. Rohrer, IBM Zürich, Switzerland, Nobel Prize in Physics, 1986)

The electron cloud associated with surface atoms extends a small distance above the surface. When a very sharp tip is brought sufficiently close to such a surface, there is a strong interaction between the electron cloud on the surface and that of the tip atom.

When a small voltage is applied, an electric tunneling current flows. At a separation of a few atomic diameters, the tunneling current rapidly increases as the distance between the tip and the surface decreases.

Tunneling current:

1nm) (typical separation face tip/sur0.5eV) (typicalheight barrier ng tunneli

)nmeV25.10 (typicalfactor conversion

geometry and materials on dependingfactor scaling 21

0

)(0

z

IeII z

φβ

φβ

−

−=


PiezoActuator

controller

Vt

STM

Tunneling current is extremely sensitive to distance z:

z = 1nm I = 7.1 10-4 I0

z = 0.1nm I = 0.48 I0

Feedback control for positioning of cantilever / tip to keep tunneling current constant.

Control signal gives extremely accurate position sensing (up to 0.001 Å)

)(0

zeII φβ−=

77


Noise

• Johnson Noise: thermal noise across a resistor

White noise with flat frequency spectrumObeys Gaussian distributionReason: Brownian motion

• Shot Noise: fluctuations in current due to charge quanta

White Gaussian noise

Johnson and Shot noise set limitations on performance of STMs

bandwidth resistance

re temperatuabsolute constant sBoltzmann'J/K 101.38

4)(23-

fRTk

fkTRVrmsV nRnoise

∆

⋅=

∆==

bandwidth currentsteady

chargeelectron C1060.1

2)(19-

fIq

fqIIrmsI

dc

dcnRnoise

∆

⋅=

∆==


Noise - Sample Calculations

• Johnson Noise: probe at room temperature

• Shot Noise: calculate the ratio between noise and current response.

eV5.0nmeV25.10

A1C1060.1

Å108.72:

21

19-

-7

=Φ=

=⋅=

⋅=

Φ

∆=

−β

µ

β

dc

dc

dcdcnR

Iq

HzIfqI

dzdII

bandwidth M1

300K constant sBoltzmann'J/K 101.38

HzµV1.04)(

23-

fRTk

fkTRVrmsV nRnoise

∆Ω=

=⋅=

=∆==

88


STM Gallery

Single atoms were accurately placed with an STM tip

[“The Beginning” Xenon on Nickel (110), Eigler, IBM Zürich, 1990]“Atom” Iron on Copper (111)

[Lutz and Eigler, IBM Zürich]

[“Carbon Monoxide Man” Carbon Monoxide on Platinum (111), Lutz and Eigler, IBM Zürich]


Micro STM

• Integration of 3D (xyz) actuators and tips

• MicroinstrumentationHigh Speed Scanning (kHz - MHz)High sensitivity Microvolume (< 1 mm3) instrumentsMicroanalytic and lithographic instruments

• Massively Parallel ArchitecturesMolecular manipulationTerabit information storagenm-scale patterning and machining

[Yang Xu, Scott A. Miller and Noel C. MacDonald 1995]

99


MEMS STMTwo Micro-STM Designs Have Been Fabricated

• Single Crystal Silicon (SCS) XYZ Actuators- Lateral (xy) motion provided by comb drives- Vertical (z) motion provided by torsional drive

• Integrated SCS Tip


MEMS STM• The tunneling tip is fabricated along with the mechanical scanning stage

• The single crystal silicon tip may be silicided or metal-coated

Tip Dimensions:Height = 5 µmShank Diameter = 1 µmTip Radius ≤ 10 nm

Lateral Motion:Applied Voltage = 40 VDisplacement = 3.2 µm

Lateral Displacement of the tipClose-up of the tip on the stage

1010


MEMS STMImage Acquisition With The Micro-STM

• STM images acquired using commercial STM control electronics

• Z-Positioning of the tip provided by the torsional cantilever

SEM image of test sample Micro-STM image of test sample

200 nm

100 nm

0 nm0 nm

100 nm

200 nm0 nm

295 nm


MEMS STM

Applications:• Imaging with atomic resolution• Data storage: 1012 bits/mm2

• Sub-nanometer lithography

Problems:• Conductive material only• Tunneling current required• Brownian motion (cooling)

1111


Atomic Force Microscope

Similar to STM, but use forces (at atomic level) instead of tunneling current for feedback

Requires force feedback, usually with cantilever spring, and laser optical deflection detection or piezoresistors


AFM

Advantages:• Can be used in contact mode (atomic / ionic

repulsion forces) or non-contact mode (> 10 Å; van der Waals, electrostatic, magnetic, capillary forces)

• Non-destructive probing:Spring constants down to 1mN/m = 10-13 N/Å(compare with covalent bond 10-9 N)Motion controllable down to 1/1000 of atomic radius

• Different environments:VacuumAirLiquid

1212


Piezoresistive AFM

Tortenese et al. 1991: first AFM with integrated piezo force sensor• Scan generator moves sample in x and y direction• Controller adjusts z motion to keep atomic force constant

Piezo

scan generatorscan generator

feedback controlfeedback control

monitormonitor

x,yx,y

z


Piezoresistive AFM

N .F

PfkT

VfkTR

RR

zwLbLL

LLEtb

Fwt

LLRR

wLbLLwbEtK

-10min

min

32

32

31

211

2211

1

32

32

31

3

1045 :force Minimum

442

:signal detectable Minimum

)3)((4)(3

4)(3

:resistance in change Relative

3)(

:constant Spring

=

∆=

∆=

∆

+−−

=

−==

∆

+−=

π

πσπ

w

L1 L2

b

(Binding Force of a covalent bond: 10-9N)

1313


Scanning Probe Microscopes

The invention of the scanning tunneling microscope (STM) 15 years ago has produced new family of proximal probes:

• Atomic force microscope (AFM)• Scanning thermal microscopes• Scanning capacitance microscopes• Magnetic force microscopes• Surface probing and analytical tools for a wide variety of

phenomena and materials• Nanoassembly, nanomanipulators, and nanorobots• Nanolithography• Ultra-high density storage: towards pick-and-place of single

atoms as bits

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