2.76 / 2.760 lecture 6: micro-nano-stm · pdf file2.76 / 2.760 lecture 6: micro-nano-stm...

2.76 Multi-scale System Design & Manufacturing

2.76 / 2.760 Lecture 6: Micro-Nano-STMMicro-scaling

Nano-scaling

STM project

X actuator

Y actuator

Z actuator

Flexurestages

10cm

SPM2.76 STM surface sensing

0

2

4

6

8

0 2 4 6 8Gap [Angstroms]

i tunnel

[nA

]


Nano

Micro

Meso

Macro

NanoNano

NanoMicro

NanoMeso

NanoMacro

MicroNano

MicroMicro

MicroMeso

MicroMacro

MesoNano

MesoMicro

MesoMeso

MesoMacro

MacroNano

MacroMicro

MacroMeso

MacroMacro

Nano

Micro

Meso

Macro

I

I

I

I

SRfSRfSRfSRf

SRfSRfSRfSRf

SRfSRfSRfSRf

SRfSRfSRfSRf

O

O

O

O

⋅

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛

=

44434241

34333231

24232221

14131211

Purpose of today

Finish micro-scale gain factors

Nano-scale phenomena (to be cont.)

STM project start


Micro-scale systems

cont.


Micro-scale physicsFor strong dependence on characteristic

length, importance of phenomena decreases with characteristic dimension

Body L3

For weaker dependence on characteristic length, phenomena become dominate at small scale

Electrostatic L2

Thermal LSurface tension L2


Micro-scale physics: Electrostatic

LFF

Body

Electric 1~

dzdUF zElectric −=−z

VLLU ozElectric ⋅

⋅⋅⋅=− 2

2ε2

22

2 zVLF o

zElectric ⋅⋅⋅

=−ε

3VFbody ⋅= ρ


Micro-scale physics: ThermalHow does thermal physics scale (small Bi #)?

inf

inf

inf TTTTe

initial

tcVAh

−−

==⎥⎦

⎤⎢⎣

⎡⋅⎟⎟⎠

⎞⎜⎜⎝

⎛⋅⋅

⋅−

θθρ

ConductionConvection

kLhBi ~⋅

=


Micro-scale physics: Dynamics

( ) ( )( )FED

CBA

n whLfwhLfE

VfE

mk

,,,,topology~

⋅⋅

→⋅

⋅=

ρρω

FEDCBA −−−++=α


Micro-scale physics: DynamicsHow does natural frequency scale?

( ) ( )( )FED

CBA

n whLfwhLfE

VfE

mk

,,,,topology~

⋅⋅

→⋅

⋅=

ρρω

1233 3

33

hwE

LFIE

LF⋅

⋅⋅=

⋅⋅=δ

m0.1 m

[ ]LCLhwE

ddFk ⋅

⋅⋅== 13

3

~12δ

[ ]32~10 LCwhLm ⋅⋅⋅⋅⋅= ρ

⎥⎦⎤

⎢⎣⎡→⋅≈=LL

LCmk

n1

33ω

L

w

h

~-3 ~3 ~1

~1 ~1 ~1

2−=α


Micro-scale physics: FluidicsHow do fluid-based physical phenomena scale?

High pressure change over narrow flow paths…

Reynolds number

D = 50 µm U = 500 µm/s L = 1000 µm

ReAir and ReH2O << 1

Heavily damped, limits response time (ms vs. µs)

LprQ

⋅⋅∆⋅⋅

=µ

π8

4

LrUp ⋅⋅⋅

−=∆ 2

8 µ LD

µρ DU ⋅⋅

=Re Ratio of inertial forces to viscous forces

2rUQ ⋅⋅= π


Micro-scale physics: FluidicsReynolds number

D = 50 µm U = 500 µm/s L = 1000 µm

ReAir and ReH2O << 1

Heavily damped

Limits response time (ms vs. µs)

LD

µρ DU ⋅⋅

=Re Ratio of inertial forces to viscous forces


Cross-scale couplingMacroMeso

Micro

Nano

FunctionFormFlowsPhysicsFabrication

GeometryMotion

InterfacesConstraints

Form

Etc…

MassMomentum

EnergyInformation

Flow

Etc…

ApplicationModelingLimiting

Dominant

Physics

Etc…

CompatibilityQualityRateCost

Fabrication

Etc…

WhatWhoWhy

Where

Function

Etc…


Strategies for jumping scales 1. Functional requirements

System

Subsystem

FR-DP relationships

GeometryMotion


Form

Etc…

MassMomentum

EnergyInformation

Flow

Etc…


Dominant

Physics

Etc…


Fabrication

Etc…

WhatWhoWhy

Where

Function

Etc…


Strategies for jumping scales 2. Form & concept layout

DP/module layout

GeometryMotion


Form

Etc…

MassMomentum

EnergyInformation

Flow

Etc…


Dominant

Physics

Etc…


Fabrication

Etc…

WhatWhoWhy

Where

Function

Etc…


Strategies for jumping scales 3. ALL Flow/physics lines

Intra and Inter

GeometryMotion


Form

Etc…

MassMomentum

EnergyInformation

Flow

Etc…


Dominant

Physics

Etc…


Fabrication

Etc…

WhatWhoWhy

Where

Function

Etc…


Strategies for jumping scales 4. Flow physics

List macro assmpts.

Use ratios & OOM

Select those to model

GeometryMotion


Form

Etc…

MassMomentum

EnergyInformation

Flow

Etc…


Dominant

Physics

Etc…


Fabrication

Etc…

WhatWhoWhy

Where

Function

Etc…


Strategies for jumping scales 5. System model

Sensitivity/gain check

Flow & fab compatibility

Un/de coupling

GeometryMotion


Form

Etc…

MassMomentum

EnergyInformation

Flow

Etc…


Dominant

Physics

Etc…


Fabrication

Etc…

WhatWhoWhy

Where

Function

Etc…


Strategies for jumping scales 6. Parametric optimization

Excel works great

GeometryMotion


Form

Etc…

MassMomentum

EnergyInformation

Flow

Etc…


Dominant

Physics

Etc…


Fabrication

Etc…

WhatWhoWhy

Where

Function

Etc…


Strategies for jumping scales 7. Concept selection

GeometryMotion


Form

Etc…

MassMomentum

EnergyInformation

Flow

Etc…


Dominant

Physics

Etc…


Fabrication

Etc…

WhatWhoWhy

Where

Function

Etc…


Nano-scale system

components


Nano-scale for todayDriving tunneling current relationship

How this drives design

Gain and noise factors

Discussion

Group work


Gain factors to consider

Nano

Micro

Meso

Macro

NanoNano

NanoMicro

NanoMeso

NanoMacro

MicroNano

MicroMicro

MicroMeso

MicroMacro

MesoNano

MesoMicro

MesoMeso

MesoMacro

MacroNano

MacroMicro

MacroMeso

MacroMacro

Nano

Micro

Meso

Macro

I

I

I

I

SRfSRfSRfSRf

SRfSRfSRfSRf

SRfSRfSRfSRf

SRfSRfSRfSRf

O

O

O

O

⋅

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛

=

44434241

34333231

24232221

14131211


Nano-scaleMacro/meso/micro can be looked at with

common Newtonian physical descriptions

For Nm-scale Quantum Mechanics dominates

Approach to teaching Nano-scale (example)Tunneling (Qualitative/Quantitative)Nano-scale structures

TodayGoverning tunneling equationHow to apply to designMajor design issues

Reading


TunnelingElectrons have wave-like characteristics

Enables them to tunnel through space when ordinarily don’t have enough kinetic energy to get through




Ek

φ

0 a

Classical theory = particle to beExcluded from x > a

Particle thought




φ

0 a

Quantum theory = finite probabilitythat particle can exist at x > a

If so, is said to have tunneled

Wave thought




What should “?” depend upon?

[ ]gapeI ⋅−∝ ?Solution to Schrodinger’s equation




[ ]gapkeI ⋅⋅−∝ 2 m = Electron mass= 9.11 x 10-31 kg

Local potential barrier heightanalogous to work (~ 5 ev)1 eV = 1.6 x10-19 J

h = Planks constant / 2 π= 1.05 x10-34 J-s

hm

kφ⋅⋅

=2


Fundamental issue for semesterSensitivity

Assuming a barrier width of 5 Angstroms

Barrier height of 4 eV

Exponential is on the order of 10-5

Current is on the order of nAmps

[ ]gapkeI ⋅⋅−∝ 2hm

kφ⋅⋅

=2


AssignmentForm your STM groups

List of CS and FRs for the STM

List of 5 F’s you have to model

FR-DP mapping and de/un coupling plans

Schedule meeting with Culpepper next FridayDiscuss theoryDesign approachFR-DP MatchingGain matrices


Fundamental issue for semesterWhat is the sensitivity of current to gap over

the range of gap you will have to design for?

Gap of few angstroms to 10 angstroms

[ ]gapkeI ⋅⋅−∝ 2hm

kφ⋅⋅

=2

2.76 / 2.760 lecture 6: micro-nano-stm · pdf file2.76 / 2.760 lecture 6: micro-nano-stm...

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