PY5020: Nanomechanics

MEMS and NEMS Toby Hallam

hallamt@tcd.ie

Nanoscience

Overview - MEMS (Micro-Electro-Mechanical Systems) - Some enabling technologies

RIE CPD

- Capacitive actuators

Pull-in instability Switches Comb Drive

Millipede - Capacitive sensors

Accelerometer

First MEMs device (1965)

Introduction • MEMS are interdisciplinary in their design, fabrication, and

operation. – Engineering

• Mechanical (structures and phenomena)

• Electrical (electrical signals: detected, generated, processed)

• Chemical and Biochemical (reactions, processes, and kinetics)

– Science • Physics and Biophysics (external world vs. materials/properties

including living organisms at macro and nano scale)

• Biology (macro and nano effects in plants, animals, and humans observed by smart transducers)

– Technology • Macro, Micro, Nano…

Intrinsic Characteristics of MEMS

• Miniaturization: dimensions of MEMS structures are much larger than in VLSI ICs (µm). Further scaling leads to NEMS (nano) that are comparable/smaller than ICs (1-100 nm).

• Scaling laws describe how properties/behavior change with dimensions

– Scaling of spring constants (ex. behavior of cantilevers

– Scaling Law of Area-to-Volume Ratio

(important in all surface effects: forces friction, surface tension, van der Waals etc)

– Microelectronics Integration - the most widely used is that with CMOS

k Ewt3

4l3

E- Young modulus of elasticity; l, w, t - dimensions

k CL4

4EL3L

lL,wL,tL,C 3

LL

L

volume

area 13

2

Decreasing length of cantilever: smaller spring constant, higher resonance frequency (GHz) and quality factor (50,000), better

sensitivity

Building Blocks • Major components in MEMS systems include

– Design • Much more difficult than IC designs due to the interdisciplinary character

of MEMS

• Design includes packaging – Packaging is one of the most challenging step both in design and realization

• Transducers must be integrated with electronics – Integration with ICs is another challenge for MEMS due to difficult issues of

process compatibility

– Fabrication • Silicon technology is widely used in MEMS with new step added

– Dimensions are usually much larger than those in ICs even for nano-transducers. To feel NANO you do not need to be in the nano-scale size!

– Other materials are included to perform required functions of transducers

• MEMS are frequently integrated with fluidics (polymers, glass…)

– Materials • Materials that can perform required functions (thermo, piezo-, magneto-

resististance…)

• Interaction with fluidics (half-cell potential, corrosion…)

Micromachining - Subtractive

Reactive Ion Etching

Wet etching Selective Undercutting Poor for high aspect ratio Reactive Ion Etching Some selectivity High aspect ratios Choice of chemistry

Material Being

Etched

Etching Chemistry

Deep Si trench HBr/NF3/O2/SF6

Shallow Si trench HBr/Cl2/O2

Poly Si HBr/Cl2/O2, HBr/O2, BCl3/Cl2, SF6

Al BCl3/Cl2, SiCl4/Cl2, HBr/Cl2

AlSiCu BCl3/Cl2/N2

W SF6 only, NF3/Cl2

TiW SF6 only

WSi2, TiSi2, CoSi2 CCl2F2/NF3, CF4/Cl2, Cl2/N2/C2F6

Si02 CF4/O2, CF4/CHF3/Ar, C2F6,

C3F8,C4F8/CO, C5F8, CH2F2

Si3N4 CF4/O2, CHF3/02, CH2F2, CH2CHF2

Deep Reactive Ion Etching

1. A standard, nearly isotropic plasma etch. Sulfur hexafluoride [SF6]

• Anisotropy is lost • Chemical etching

2. Deposition of a chemically inert passivation layer. Octafluorocyclobutane [C4F8] • Bosch process (DRIE) • Teflon-type sidewall protection • Cyclic process • Unlimited depth with high aspect ratio

Critical point drying

• Wet etching

• Surface tension scaling

• Drying from wet processing

• Exchange process liquid

• Use supercritical liquid CO2

• Continuous shift from liquid to gas

• MEMS/Biological/Aerogels

Simple cantilever fabrication

Capacitive actuator

There are two ways of changing the energy in the capacitor: a) by changing the charge, b) by changing its geometry; hence, E(Q,x), with Q and x as state variables.

𝑑𝐸 = 𝑢𝑑𝑄 + 𝐹𝑒𝑥𝑡𝑑𝑥

u: electrostatic potential [V] Fext: external net force; x : gap

So then, the total energy of the system will be:

𝐸 𝑄, 𝑥 = −1

2𝐶𝑄2 +

1

2𝐾𝑥 2

d: separation between plates K: spring constant A: overlap area of the plates ε0: permittivity of the media between plates

𝐶 =𝜀0𝐴

𝑑 − 𝑥

x

𝐸 𝑄, 𝑥 = −𝑄2(𝑑 − 𝑥)

2𝜖𝐴+

1

2𝐾𝑥 2

𝑑𝐸 =𝜕𝐸

𝜕𝑥𝑄

𝑑𝑥 +𝜕𝐸

𝜕𝑄𝑥

𝑑𝑄

Capacitive actuator

System energy a function of x and Q

−𝜕𝐸

𝜕𝑥𝑄

= −1

2

𝑄2

𝜀𝐴− 𝐾𝑥 = 𝐹𝑒𝑥𝑡

𝐸 𝑄, 𝑥 = −𝑄2(𝑑 − 𝑥)

2𝐶+

1

2𝐾𝑥 2 Differentiate the energy equation

Force is a combination of spring and electrostatic forces

OR

−𝜕𝐸

𝜕𝑄𝑥

=𝑥𝑄

𝜀𝐴=

𝑄

𝐶= 𝑢 Potential in the system is just related to capacitance

Electrostatic part of force shows no dependence on x, (Q constant)

Also: 𝜕2𝐸

𝜕𝑥2𝑄

= K 𝜕2𝐸

𝜕𝑄2𝑥

=1

𝐶

Capacitive actuator

Instead, we should attempt to reformulate the energetic relationship for potential of the system. Recall capacitance can be written Q=Cu

𝐸 𝑢, 𝑥 = −1

2𝐶𝑢2 +

𝐾

2𝑥2 = −

𝜀𝐴𝑢2

2(𝑑 − 𝑥)+

1

2𝐾𝑥2

𝐸 𝑄, 𝑥 = −1

2𝐶𝑄2 +

1

2𝐾𝑥 2

𝐹𝑒𝑥𝑡 = −𝜕𝐸

𝜕𝑥𝑢

=𝜀𝐴𝑢2

2(𝑑 − 𝑥)2 − 𝑘𝑥 Electrostatic force component now has x dependence

We can now find some balance point where spring and electrostatic forces balance F=0

𝑘𝑥 =𝜀𝐴𝑢2

2(𝑑 − 𝑥)2

Capacitive actuator

As we did before, figure out a system stiffness. 𝜕2𝐸

𝜕𝑥2𝑢

=𝜕𝐸

𝜕𝑥𝑢

= K

𝜕2𝐸

𝜕𝑥2𝑢

= 𝑘 −𝜀𝐴𝑢2

(𝑑 − 𝑥)3

Now relate this to the balance point from the last slide.

𝜕2𝐸

𝜕𝑥2𝑢

=2𝑘𝑥

𝑑 − 𝑥− 𝑘 𝑘𝑥 =

𝜀𝐴𝑢2

2(𝑑 − 𝑥)2

Solution with F=0 𝑥 =1

3𝑑

Pull-in criteria 𝑢𝑝𝑢𝑙𝑙−𝑖𝑛 =8

27

𝑘𝑑3

𝜀𝐴

• NEM switched capacitor structure – Vertically aligned multiwalled carbon nanotubes

• mechanical movement of a nanotube relative to a carbon nanotube based capacitor defines ‘ON’ and ‘OFF’ states

• Carbon Nanotube Fabrication: – Grown with controlled dimensions at pre-defined locations on a silicon

substrate

• Compatible with existing silicon technology

• Vertical orientation allows for a significant decrease in cell area over conventional devices

JAE EUN JANG, et. al . Nature Vol 3 January 2008 doi:10.1038/nnano.2007.417

NEMS using pull-in instability

CNT-NEMS switched Capacitor

JAE EUN JANG, et. al . Nature Vol 3 January 2008 doi:10.1038/nnano.2007.417

Graphene RF NEMS switches

• Fabricate NEM capacitive switch with Con/Coff > 100.

• Optimise design for operation at 2-5 GHz.

• Low actuation voltage

• High speed

Objectives

Advantages of graphene for RF MEMS

Extracted capacitance and resistance values and their tunability with voltage

Hallam et al., Phys. Status Solidi B, 1–4 (2015)

• Graphene release by wet etching of a sacrificial layer.

• Yield limited by the releasing step.

• Successfully released membranes allowed a first assessment of graphene performance for RF NEMS applications.

Fabrication Graphene RF NEMS switches

Can use the pull-in instability to drive a microscale device Can we avoid the instability? What kind of force can we achieve?

A different capacitive actuator

Capacitive drive Capacitive switch

Electrostatic comb drive

Movable fingers Fixed fingers

Axis of motion • Multiple capacitive elements • Staggered fingers • Capacitive gradient

We can characterise one pair of fingers such that:

Electrostatic comb drive

And the work equation (from before) can be written with a modified capacitive term

𝐸(𝑄, 𝑥) =𝑄2𝑑

2𝜀𝑎 𝑏 − 𝑥+

𝐾

2𝑥 − 𝑥0

2

d=finger separation a=finger depth

Electrostatic comb drive

The capacitive area for the fingers A=ab is modified to a(b-x) when the structure moves in x

𝐹𝑒𝑥𝑡 = −𝜕𝐸

𝜕𝑥𝑄

=𝑄2𝑑

2𝜀𝑎 𝑏 − 𝑥 2 + 𝐾 𝑥 − 𝑥0

Here the force is dependent on position as the area of the capacitive element changes (even at constant charge)

E(𝑢, 𝑥) =𝑢2𝜀𝑎 𝑏 − 𝑥

2𝑑+

𝐾

2𝑥 − 𝑥0

𝐹𝑒𝑥𝑡 = −𝜕𝐸𝑢

𝜕𝑥𝑢

=𝑢2𝜀𝑎

2𝑑+

𝐾

2𝑥 − 𝑥0 𝐾𝑢 =

𝜕2𝐸

𝜕𝑥2𝑢

= K > 0

So, the instability is in d rather than the actuation direction (x) The electrostatic force is also proportion to the voltage!!

Electrostatic comb drive – Much force, wow!

𝐹𝑎𝑟𝑟𝑎𝑦 = 𝜀𝑎

𝑑𝑢2𝑁 N: number of finger pairs

Micromachining: a ≅ 2µm, b ≅ 2µm and u=15V 1000 fingers for 1 µN

DRIE: a ≅ 200µm, b ≅ 2µm and u=15V 10000 fingers for 1 mN

Electrostatic comb drive - design

Folded beams (movable support)

Ground plate Anchor points

Moving comb

Fixed comb

Journal of Micromechanics and Microengineering, Volume 23, Number 10 (2013)

What are comb drives used for?

• Large stroke (225um)

• Small footprint

• Fully integrated

Magnetic HDD head

What are comb drives used for?

IBM – Millipede Project 2000-2010

• Multiple AFM heads

• Direct write on polymer storage media

• 1TB/inch2

• Graham Cross

What are comb drives used for?

Thermal indentation PMMA write media SU-8 silicon based underlayer Decreased pitch for erasure

Capacitive sensing

𝐶 =𝜀𝑟𝜀0𝐴

𝑑=

𝜀𝐴

𝑑=

𝜀𝑤𝑙

𝑑

Gap closing capacitor

𝜕𝐶

𝜕𝑑= −

𝜀𝑤𝑙

𝑑2 = 𝑓(𝑑)

∆𝐶 =𝜕𝐶

𝜕𝑑∆𝑑 = −

𝜀𝑤𝑙

𝑑2 ∆𝑑

Big nonlinear response

Try to determine conditions for linear response

𝐶 𝑑 + ∆𝑑 =𝜀𝐴

𝑑 + ∆𝑑 Taylor expansion

𝐶 𝑑 + ∆𝑑 = 𝐶 𝑑0 +𝜕𝐶

𝜕𝑑𝑑0

∆𝑑 +1

2

𝜕2𝐶

𝜕𝑑2𝑑0

∆𝑑2 + 𝑜 ∆𝑑 3 =𝜀𝐴

𝑑01 −

∆𝑑

𝑑0+

∆𝑑

𝑑0

2

− 𝑜 ∆𝑑 3

For large 𝑑0 and small ∆𝑑 we can ignore higher order terms and use linear relation

Typical 𝜕𝐶

𝜕𝑑 = 1pF/m

Capacitive Sensing: Lateral Comb Drive

𝐶 =𝜀𝑤𝑥

𝑑

𝜕𝐶

𝜕𝑥=

𝜀𝑤

𝑑 ∆𝐶 =

𝜕𝐶

𝜕𝑥∆𝑥

Constant term linearity !!

Significant reduction in footprint Increase in sensitivity!!

Accelerometer from Comb sensor

Test mass

∆𝐶 =𝜕𝐶

𝜕𝑥∆𝑥

𝑉𝑠𝑒𝑛𝑠𝑒 = −∆𝐶

𝐶0𝑉 =

𝜀𝑤∆𝑥

𝑑∙

𝑑

𝜀𝑤𝑥𝑉

𝐶 =𝜀𝑤𝑥

𝑑

𝑉𝑠𝑒𝑛𝑠𝑒 = 𝑉∆𝑥

𝑥

Basic laws of motion can be applied Damped Hook’s law

And I want to offer a … prize – if I can figure out how to

phrase it so that I don't get into a mess of arguments about

definitions – of … $1,000 to the first guy who makes an

operating electric motor – a rotating electric motor which

can be controlled from the outside and, not counting the

lead-in wires, is only 1/64 inch cube.

- Feynman, Plenty of room at the bottom (1959)

Next Lecture:

Ink-Jet printing

12pm Mon 23rd November