A S

peci

al T

utor

ial L

ectu

re S

erie

s on

Intr

oduc

tion

to N

anos

cale

Hea

t Tra

nsfe

r

“If I

were

ask

ed fo

r an

area

of s

cien

ce a

nd

engi

neer

ing

that

will

mos

t lik

ely

prod

uce

the

brea

kthr

ough

s of

tom

orro

w, I

woul

d po

int t

o na

nosc

ale

scie

nce

and

engi

neer

ing.

”

-Nea

l Lan

eFo

rmer

Ass

ista

nt to

the

Pres

iden

t for

Sc

ienc

e an

d T

echn

olog

y

An

artis

tic v

iew

of a

ste

p-sh

aft

built

with

ato

ms

Tai-R

an H

su, P

rofe

ssor

Dep

artm

ent o

f Mec

hani

cal a

nd A

eros

pace

Eng

inee

ring

San

Jos

e S

tate

Uni

vers

ityS

an J

ose,

Cal

iforn

ia, U

SA

Par

t 1:

Ove

rvie

w o

f Nan

otec

hnol

ogy

Par

t 2:

Ato

mic

Str

uctu

re &

Qua

ntum

Phy

sics

Par

t 3:

Inte

r-M

olec

ular

Hea

t Tra

nsm

issi

on(N

anos

cale

Hea

t Tra

nsfe

r )P

art 4

:M

easu

rem

ents

of T

herm

ophy

sica

lPro

pert

ies

Par

t 1

Ove

rvie

w o

f Nan

otec

hnol

ogy

Nov

embe

r 14

, 20

06

• •••“D

ust”

size

d su

per-

inte

llige

nt c

ompu

ters

.• •••

“Nee

dle-

tip”

size

d ro

bots

for

biom

edic

alap

plic

atio

ns a

nd fo

r se

arch

and

res

cue.

•Sp

acec

raft

wei

ghin

g le

ss th

an to

day’

s fam

ily

cars

.

• •••B

iom

edic

ine,

e.g

. in-

vivo

syst

ems a

nd

surg

ery

that

can

sust

ain

hum

an li

ves t

o 15

0

year

s and

long

er.

• •••R

obot

s with

art

ifici

al h

uman

inte

llige

nce

be

com

ing

the

mai

nstr

eam

wor

kfor

ce in

our

So

ciet

y.

• •••U

nlim

ited

supp

ly o

f cle

an r

enew

able

en

ergi

es th

at r

epla

ce a

ll fo

ssil

fuel

pro

duce

d en

ergi

es o

n th

e E

arth

. •

Tel

e-tr

ansp

orta

tion

syst

ems t

hat c

an

tran

spor

t hum

an a

nyw

here

on

Ear

th in

se

cond

s.•

Spac

ecra

ft fo

r hu

man

/car

go in

ter-

plan

et

trav

elin

g.

•N

ew v

acci

nes a

nd m

edic

ines

that

cur

e m

any

in

cura

ble

dise

ases

.•

Synt

hetic

ant

ibod

y-lik

e na

nosc

ale

drug

s and

de

vice

s see

king

out

to d

estr

oy m

alig

nant

cel

ls

in h

uman

or

anim

al b

odie

s.•

In-v

ivo

med

ical

dia

gnos

tic a

nd d

rug

deliv

ery

syst

ems.

•Sm

art s

urfa

ce c

oatin

g m

ater

ials

with

self-

adju

stin

g th

erm

al c

ondu

ctan

ce fo

r bu

ildin

gs

and

refr

iger

atio

n sy

stem

s.• •••

Smar

t fab

rics

for

self-

clea

ning

clo

the.

•Su

per-

stro

ng m

ater

ials

for

light

wei

ght

airp

lane

s, ve

hicl

es a

nd st

ruct

ures

.

•C

lean

ene

rgy

conv

ersi

on sy

stem

s and

supe

r-lo

ng li

fe b

atte

ries

.

•N

ew b

reed

of c

rops

and

dom

estic

ani

mal

s tha

t ca

n fe

ed e

ntir

e w

orld

pop

ulat

ion.

“Dre

am”

Pro

duct

sN

ear-

term

Pro

duct

s

Futu

rist

ic In

dust

rial

Pro

duct

sin

the

New

Cen

tury

HS

U-2

005

The

Cor

e Te

chno

logy

for

Pro

duci

ngFu

turi

stic

Indu

stri

al P

rodu

cts

is

MIN

IATU

RIZ

ATI

ON

Two

phen

omen

al e

xam

ples

of

min

iatu

riza

tion

of in

dust

rial

pr

oduc

ts in

rec

ent y

ears

Min

iatu

riza

tion

of D

igita

l Com

pute

rs-A

rem

arka

ble

case

of m

inia

turi

zatio

n!

The

EN

IAC

Com

pute

r in

194

6A

“La

p-to

p” C

ompu

ter

in 1

996

A “

Pal

m-t

op”

Com

pute

r in

200

1

Siz

e: 1

06do

wn

Pow

er: 1

06up

Siz

e: 1

08do

wn

Pow

er: 1

08up

This

spe

ctac

ular

min

iatu

riza

tion

took

pla

ce in

50

year

s!!

Mar

ket D

eman

d fo

r S

mal

ler,

Mul

ti-Fu

nctio

nal P

rodu

cts

For e

xam

ple,

the

mar

ket d

evel

opm

ent o

f cel

lula

r pho

nes:

Less

than

10

Yea

rs A

go:

Cur

rent

Sta

te-o

f-th

e A

rt:

Tran

scei

ved

voic

e on

lyTr

ansc

eive

svo

ice+

mul

ti-m

edia

+ o

ther

s(V

ideo

-cam

era,

e-m

ails

, cal

enda

r, T

V a

nd

acce

ss to

Inte

rnet

; and

a P

C w

ith k

ey b

oard

)

Siz

e re

duct

ion

Pal

m-t

op W

irel

ess

PC

�La

test

add

ition

al fu

nctio

n to

cel

l pho

nes:

The

Glo

bal P

ositi

onin

g S

yste

ms

(GP

S)

Ena

blin

g Te

chno

logi

es fo

r M

inia

turi

zatio

n

Min

iatu

re d

evic

es(1

nm

-1

mm

)

** 1

nm

= 1

0-9m

≈ ≈≈≈sp

an o

f 10

H2

atom

s

Mic

ro S

yste

ms

Tech

nolo

gy(M

ST)

(1 µ µµµ

m -

1 m

m)*

Initi

ated

in 1

947

with

the

inve

ntio

n of

tra

nsis

tors

, but

the

term

“Mic

rom

achi

ning

”wa

s co

ined

in 1

982

* 1

µ µµµm =

10-6

m ≈ ≈≈≈

one-

tent

h of

hum

an h

air

Nano

tech

nolo

gy(N

T)(0

.1 n

m –

0. 1

µ µµµm

)**

Insp

ired

by F

eynm

an in

195

9, w

ith a

ctiv

e R&

D be

gan

in a

roun

d 19

95Th

ere

is a

long

way

to b

uild

ing

nano

dev

ices

!

A to

p-do

wn a

ppro

ach

A bo

ttom

-up

appr

oach

Nan

otec

hnol

ogy

is th

e cr

eatio

n of

USE

FUL

/FU

NC

TIO

NA

Lm

ater

ials

, dev

ices

and

syst

ems

thro

ugh

cont

rol o

f mat

ter o

n th

e na

nom

eter

leng

th (n

m) s

cale

and

expl

oita

tion

of n

ovel

phe

nom

ena

and

prop

ertie

s (p

hysi

cal,

chem

ical

, bio

logi

cal)

at t

hat l

engt

h sc

ale.

Wha

t is

Nan

otec

hnol

ogy?

A Pe

rspe

ctiv

e of

Nan

o Sc

ale:

1 nm

= 1

0-9m

= 1

0 -6

mm

= 1

0-3µm

Leng

th S

cale

in N

anot

echn

olog

y

mili

mic

rona

nopi

cofe

mto

atto

Leng

th(m

)

010

-18

10-1

510

-12

10-9

(nm

)10

-6

(µm

)10

-3

Hum

anH

air:

10-4

m

Vir

us: 1

0-7

m

DN

A <

3 n

mP

rote

in: 2

-5 n

m

Typ

ical

ato

m: 1

0-10

mor

one

Ang

stro

m

Typ

ical

ele

ctro

n R

adiu

s: 2

.8x1

0-15

m

All m

atte

rs th

at e

xist

in u

nive

rse

are

mad

e of

ato

ms

and

mol

ecul

es.

The

way

mol

ecul

es o

f var

ious

sha

pes

and

surfa

ce fe

atur

esor

gani

ze in

to p

atte

rns

on n

ano

scal

es d

eter

min

es

impo

rtant

mat

eria

l pro

perti

es(e

.g. e

lect

rical

con

duct

ivity

, op

tical

pro

perti

es, m

echa

nica

l stre

ngth

, etc

.)

Nano

tech

nolo

gy w

ill e

nabl

e us

to s

ynth

esize

nan

o st

ruct

ures

and

cont

rol h

ow s

cale

pat

tern

ing

unfo

lds.

Fro

m w

hich

we

can

desi

gn a

nd c

reat

ene

w se

ts o

f mat

ters

with

des

ired

prop

ertie

s an

d ch

arac

teris

tics.

Why

Nan

otec

hnol

ogy?

Act

ive

R&

D in

Nan

otec

hnol

ogy:

insp

ired

by

Ric

hard

Fey

nman

’s s

peec

h in

195

9

Feyn

man

, R.,

“The

re’s

Ple

nty

of R

oom

at t

he B

otto

m: A

n in

vita

tion

to

ente

r a

new

fie

ld o

f phy

sics

,”(m

inia

turiz

atio

n) fi

rst p

rese

nted

at t

he A

mer

ican

P

hysi

cal S

ocie

ty a

t Cal

iforn

ia In

stitu

te o

f Tec

hnol

ogy

on D

ecem

ber 2

9, 1

959.

S

ubse

quen

t pub

licat

ion

in ‘E

ngin

eerin

g an

d S

cien

ce’,

Cal

tech

, Feb

ruar

y 19

60.

(191

8 -1

988)

A v

isio

nary

and

a N

obel

Lau

reat

e in

Phy

sics

, 196

5

The

Ver

y Fi

rst M

an-M

ade

Nan

o S

truc

ture

-Th

e “B

ucky

ball”

Mad

e fr

om th

e B

uckm

inst

erfu

llere

ne -

a th

ird

form

of p

ure

carb

on m

olec

ule.

(a

fter t

he n

ame

of a

futu

rist,

R. B

uckm

inst

er F

ulle

r)

It co

ntai

ned

60 c

arbo

n at

oms

in th

e sh

ape

of a

so

ccer

bal

l with

a d

iam

eter

of 0

.7 n

ano

met

er.

Cre

ated

in 1

985

by a

che

mis

try p

rofe

ssor

, R

icha

rd S

mal

ley

from

Ric

e U

nive

rsity

-a

Nob

el L

aure

ate

in 1

996.

•El

ectro

nics

,Com

putin

g an

d Da

ta S

tora

ge

•M

ater

ials

and

Man

ufac

turin

g

•He

alth

and

Med

icin

e

•En

ergy

and

Env

iron

men

t

•T

rans

port

atio

n

•N

atio

nal S

ecur

ity

•Sp

ace

expl

orat

ion

• •

Nan

otec

hnol

ogy

is a

nen

ablin

g te

chno

logy

Maj

or Im

pact

s of

Nan

otec

hnol

ogy

(sou

rce:

Mey

yaM

eyya

ppan

, NA

SA

Am

es)

•Pr

oces

sors

usi

ng m

olec

ular

ele

ctro

nics

with

dec

linin

g en

ergy

use

and

cos

t per

gate

, thu

s in

crea

sing

eff

icie

ncy

of c

ompu

ter b

y 10

6 .

•Sm

all m

ass

stor

age

devi

ces:

mul

ti-te

ra(1

012) b

it le

vels

.

•In

tegr

ated

nan

osen

sors

: co

llect

ing,

pr

oces

sing

and

com

mun

icat

ing

mas

sive

am

ount

s of

dat

a w

ith m

inim

al

size

, wei

ght,

and

pow

er c

onsu

mpt

ion.

•H

ighe

r tra

nsm

issi

on fr

eque

ncie

s an

d m

ore

effi

cien

t util

izat

ion

ofop

tical

spe

ctru

m to

pro

vide

at

leas

t 10

times

the

band

wid

th n

ow.

•D

ispl

ay te

chno

logi

es.

•Q

uant

um c

ompu

ting.

Nan

otec

hnol

ogy

Ben

efits

in E

lect

roni

cs a

nd C

ompu

ting

(sou

rce:

Mey

yaM

eyya

ppan

, NA

SA

Am

es)

Hea

t = H

orre

ndou

s ch

alle

nge

to m

echa

nica

l eng

inee

rs !!

TWO

DIS

RU

PTI

VE

HE

AT

TRA

NS

FER

TE

CH

NO

LOIE

S

(1) N

anos

cale

Hea

t Tra

nsfe

r in

N

ano

Tran

sist

ors

(2) N

anos

cale

Dat

a S

tora

ge

Sys

tem

s

(1) N

anos

cale

Hea

t Tra

nsfe

r

in

Nan

oTr

ansi

stor

s

Nan

otec

hnol

ogy

Ben

efits

inE

lect

roni

cs a

nd C

ompu

ting

The

Nan

ochi

p

Nan

o tr

ansi

stor

s

Gat

es

SiO

2fil

m

Sili

con

subs

trat

e(th

in p

ure

silic

on fi

lm)

Adv

anta

ges:

(1) L

ow u

nit c

ost.

(2) N

arro

w g

ates

for

fast

er o

n-of

f �bo

ost s

peed

lim

it of

the

inte

grat

edci

rcui

ts.

Nan

otec

hnol

ogy

Ben

efits

inE

lect

roni

cs a

nd C

ompu

ting

Inte

l roa

dmap

on

nano

tran

sist

ors

usin

g m

icro

tech

nolo

gy:

90 n

m

65

45

32

22

2003

2005

2007

2009

2011

Yea

r

Transistor Size

Incr

ease

Lea

kage

-Ano

ther

maj

or c

halle

nge!

Sin

gle-

Ele

ctro

nTr

ansi

stor

?

Sili

con-

base

d�

-tech

nolo

gy

Pos

sibl

e m

ater

ials

?N

anot

echn

olog

y?(L

ikel

y te

chno

logy

)

Leng

th: 5

0 nm

L =

30

L =

20

L =

15

L =

10

Gat

e ox

ide:

1.2

nm

Gat

e ox

ide:

0.3

nm

Hea

t dis

sipa

tion

and

leak

of e

lect

rici

tyar

e tw

o cr

itica

l tec

hnic

al p

robl

ems

in fu

rthe

r m

inia

turi

zatio

n of

tran

sist

ors.

Pos

sibl

e S

olut

ions

�C

oolin

g by

nan

oflu

idic

sin

volv

ing

nano

scal

eflu

id fl

ow in

nan

osca

lech

anne

ls.

�C

oolin

g by

Nan

osca

lehe

at p

ipes

.

(2) N

anos

cale

Hea

t Tra

nsfe

r:

Nan

oD

ata

Sto

rage

Sys

tem

Nan

otec

hnol

ogy

Ben

efits

in D

ata

Sto

rage

-1

The

ever

-incr

easi

ng d

eman

d fo

r hig

h de

nsity

info

rmat

ion

stor

age:

Nan

otec

hnol

ogy

Ben

efits

in D

ata

Sto

rage

-2

Dat

a S

tora

ge R

equi

rem

ents

:

�D

ensi

ty�

Dat

a ra

te

�E

rror

rat

e�

Ove

rall

relia

bilit

y

�R

e-w

rita

bilit

y�

Dat

a re

tent

ion

�Tr

acki

ng�

Cos

t

Sou

rce:

“Sca

nnin

g P

robe

s M

icro

scop

e &

The

ir P

oten

tial f

or D

ata

Sto

rage

,”Jo

hn M

amin

, IB

M A

lmad

enR

esea

rch

Cen

ter,

San

Jos

e, C

A. (

Priv

ate

com

mun

icat

ion)

Nan

otec

hnol

ogy

Ben

efits

in D

ata

Sto

rage

-3�

The

cont

inuo

us d

eman

ds fo

r hi

gh d

ensi

ty d

ata

stor

age

has

pass

ed th

e lim

it of

trad

ition

al e

lect

rom

agne

tic m

eans

.�

A n

ew c

once

pt o

f “R

ead-

Wri

te”

is b

eing

dev

elop

ed –

the

“Mill

eped

e”pr

ojec

tby

IBM

, San

Jos

e an

d Zu

rich

, Sw

itzer

land

. �

Wor

king

pri

ncip

le in

volv

ing

inde

ntin

g th

e su

rfac

e of

pol

ymer

film

usi

ng A

FM.

Nan

otec

hnol

ogy

Ben

efits

in D

ata

Sto

rage

-4

�E

ncou

ragi

ng in

itial

res

ults

of t

he M

illip

ede

deve

lopm

ent:

40 n

m b

it si

ze

Hea

t Con

duct

ion

& D

issi

patio

nin

Nan

omet

er D

ots

Bot

h th

ese

case

s re

quir

e th

e us

e of

nan

osca

lehe

at tr

ansf

er

tech

niqu

es -

A r

adic

ally

diff

eren

t fro

m m

acro

scal

ehe

at tr

ansf

er

tech

niqu

es th

at u

se:

�Fo

urie

r la

w fo

r he

at c

ondu

ctio

n in

sol

ids

�N

ewto

n’s

cool

ing

law

for

heat

con

vect

ion,

and

�K

irch

hoff

’sla

w a

nd S

tefa

n-B

oltz

man

nE

quat

ion

for

ther

mal

rad

iatio

n

Par

t 2

Ato

mic

Str

uctu

re &

Qua

ntum

Phy

sics

Nov

embe

r 16

, 200

6

�A

LL m

atte

r on

Ear

th a

re m

ade

by A

TOM

S:

Pac

ked

Ato

ms

�A

tom

s ar

e bo

nded

toge

ther

by

“C

HE

MIC

AL

BO

ND

S,”

w

hich

are

trea

ted

as e

last

ic

bond

s si

mul

ated

by

“ spr

ings

”

Sp

rin

g B

on

ds:

“Spr

ing

cons

tant

, k”

Ato

ms

or

Mo

lecu

les

The

Mak

es o

f Mat

ter

�A

“spr

ing”

can

be s

tretc

hed

orco

mpr

esse

d by

ext

erna

l ene

rgy.

�A

def

orm

ed “s

prin

g”co

ntai

nsen

ergy

, tha

t can

be

rele

ased

unde

r circ

umst

ance

s.

A s

olid

in

mac

rosc

ale:

Ato

mic

Stru

ctur

e of

Mat

ter

Bas

ic a

tom

ic s

truc

ture

NU

CL

EU

S

Prot

on Neu

tron

Ele

ctro

n

Orb

it fo

r el

ectr

ons

NO

TE:T

here

is n

o ne

utro

n in

the

nucl

eus

of H

2at

oms.

The

diam

eter

of o

uter

orb

it:2

to 3

x10-

8cm

, or

0.2

to 0

.3 n

m.

Mas

s of

pro

tons

:1.

67x1

0-24

g

Mas

s of

ele

ctro

ns:

9.11

x10-

28g

Pro

tons

carr

y +v

ech

arge

Ele

ctro

nsca

rry

–ve

char

geN

eutr

ons

carr

y no

cha

rge

No.

of p

roto

ns =

No.

of e

lect

rons

Ato

mic

Stru

ctur

e of

Mat

ter-C

ont’d

The

peri

odic

tabl

e of

ele

men

ts

�E

very

thin

g on

the

Ear

th is

mad

e by

96

stab

le a

nd 1

2 un

stab

le e

lem

ents

.

Ato

mic

Num

ber

=N

o. o

f pro

tons

in n

ucle

us

Si

Ga

Ge

As

B

P

�E

ach

elem

ent h

as d

istin

ct a

tom

ic s

truc

ture

.�

The

num

ber

of p

roto

ns (a

nd th

us e

lect

rons

) in

the

elem

ent d

eter

min

esth

e pr

oper

ties

of th

e el

emen

t.

Nuc

leus

N&

PE

lect

ron

NU

CLE

US

Pro

ton

Orb

it fo

r ele

ctro

n

A H

ydro

gen

Ato

m

One

ele

ctro

nO

ne p

roto

nN

o ne

utro

n

A S

ilico

n A

tom

-A c

omm

on s

emic

ondu

ctor

14 e

lect

rons

**14

pro

tons

14 n

eutro

ns

** T

he 4

elec

trons

on

the

outm

ost o

rbit

are

shar

ed w

ith 4

nei

ghbo

ring

atom

s in

sili

con

crys

tals

= c

oval

ent s

olid

–co

mm

on fo

r sem

icon

duct

ors

and

diel

ectri

c m

ater

ials

.

ATO

MS

:N

ucle

us +

Ele

ctro

ns

MO

LEC

ULE

S:

Com

poun

ds o

f Ato

ms

GR

AIN

S -

Cry

stal

Sys

tem

s:P

OLY

CR

YS

TAL

GR

AIN

S

Gra

ins

and

Cry

stal

s

�S

ome

mat

ter i

n na

tura

l sta

tes

with

sin

gle

atom

s.

�M

any

othe

rs a

re m

ade

with

com

bina

tions

of a

tom

s w

ith d

iffer

ent s

truct

ures

= M

OLE

CU

LES

�C

ryst

als

= ag

greg

atio

ns o

f ato

ms

or m

olec

ules

.

A s

ingl

e si

licon

cry

stal

Sili

con

atom

s ar

e sh

own

in “r

ed” a

nd

“whi

te” b

alls

bon

ded

toge

ther

by

chem

ical

bo

nds

(sho

wn

in y

ello

w

stic

ks).

�M

ost m

atte

r are

mad

e of

con

greg

atio

n of

cry

stal

s =

Gra

ins

�P

olyc

ryst

allin

e g

rain

s.

Mec

hani

cs o

f Ato

ms

NU

CL

EU

S

Prot

on Neu

tron

Ele

ctro

n

Orb

it fo

r el

ectr

ons

�Th

e po

sitio

n of

ele

ctro

ns in

ato

ms

at n

atur

al

stat

e be

com

es U

NS

TAB

LEw

hen

exte

rnal

E

NE

RG

Y(t

herm

al o

r m

echa

nica

l for

ms)

is

intr

oduc

ed �

VIB

RA

TIO

NS

from

its

initi

aleq

uilib

rium

pos

ition

.

�In

the

case

of c

oval

ent s

olid

s, th

e nu

mbe

r of e

lect

rons

at t

he o

utm

ost o

rbits

of a

bas

e m

ater

ial m

ay b

e al

tere

d (i.

e. in

crea

se o

r dec

reas

ed) b

y in

vasi

on o

f fo

reig

n at

oms

by in

put E

NE

RG

Y th

roug

h di

ffus

ion

or io

n im

plan

tatio

npr

oces

ses

–kn

own

as D

opin

gpr

oces

ses

in s

emic

ondu

ctor

indu

stry

.

�Th

e ba

se m

ater

ial,

afte

r dop

ing,

cha

nges

its

elec

troni

c pr

oper

ties.

The

radi

i of o

rbits

for e

lect

rons

in a

mat

ter

�E

xpan

dsfro

m it

s na

tura

l sta

te w

ith s

uffic

ient

adde

dE

NE

RG

Y

�S

hrin

ksw

ith lo

stE

NE

RG

Y.

Mec

hani

cs o

f Ato

ms

–co

nt’d

�A

LL m

atte

r on

Ear

th a

re m

ade

by A

TOM

S:

�A

tom

s ar

e bo

nded

toge

ther

by

“C

HE

MIC

AL

BO

ND

S,”

w

hich

are

trea

ted

as e

last

ic

bond

s si

mul

ated

by

“ spr

ings

”

Sp

rin

g B

on

ds:

“Spr

ing

cons

tant

, k”

Ato

ms

or

Mo

lecu

les

�A

tom

ic fo

rce

requ

ired

to c

hang

e th

e na

tura

l sta

te.

Inte

r-m

olec

ular

dis

tanc

e,d

Attraction force Repulsion force

d o

d o=

atom

ic d

ista

nce

in

natu

ral s

tate

�Th

e po

sitio

n of

ele

ctro

ns in

ato

ms

at n

atur

al s

tate

bec

omes

UN

STA

BLE

whe

n ex

tern

al E

NE

RG

Y(t

herm

al o

r m

echa

nica

l for

ms)

is in

trod

uced

�

VIB

RA

TIO

NS

from

its

initi

al e

quili

briu

m p

ositi

on.

Hea

t Gen

erat

ion

by M

olec

ular

Vib

ratio

ns

Sp

rin

g B

on

ds:

“Spr

ing

cons

tant

, k”

Ato

ms

or

Mo

lecu

les

The

disp

lace

men

t of a

ny a

tom

in th

e m

atte

rin

duce

d by

VIB

RA

TIO

N w

ill r

esul

t in:

(1) S

tretc

hing

or c

ompr

essi

onof

the

“spr

ings

”th

at a

re a

ttach

ed to

that

ato

m, a

nd

(2) T

he e

long

atio

n an

d co

mpr

essi

on o

fth

ese

“spr

ings

” will

cau

se th

e at

oms

atta

ched

to th

e ot

her e

nd to

dis

plac

e �

Res

ultin

g to

a “c

hain

reac

tions

”of v

ibra

tion

of o

ther

ato

ms.

(3) T

he in

itial

vib

ratio

n of

one

ato

m c

an th

us b

eTR

AN

SM

ITTE

Dou

twar

d an

d ca

use

man

yot

her a

tom

s to

vib

rate

.

Net

wor

k of

Ato

ms

by “

Spr

ing

Bon

ds”

�If

the

exte

rnal

EN

ER

GY

that

cau

se in

itial

ato

mic

vib

ratio

n =

HE

AT,

Then

, hea

t is

trans

mitt

ed fr

om o

ne a

tom

or a

set

of a

tom

s ca

nbe

TR

AN

SM

ITTE

D to

oth

er a

tom

s in

the

way

as

desc

ribed

abo

ve.

SU

MM

AR

Y

Fund

amen

tal M

echa

nism

s of

Hea

t Tra

nsm

issi

on

in M

atte

r

�La

ttic

e vi

brat

ion

of a

tom

s ge

nera

tes

heat

.

�A

tom

ic v

ibra

tion

caus

ed g

eom

etry

cha

nge

of la

ttic

e (b

ond)

an

d m

ore

atom

s to

vib

rate

, and

hen

ce tr

ansm

its th

erm

al

ener

gy a

nd th

us H

EA

T.

�Fo

r ca

ses

with

mor

e en

ergy

inpu

t, or

mat

ter

with

mor

e m

obile

ele

ctro

ns in

the

atom

s (e

.g. m

etal

s), t

here

cou

ld

be r

elea

se o

f ele

ctro

ns a

ccom

pany

ing

the

tran

smis

sion

of

ene

rgy

amon

g at

oms.

Par

t 3

Inte

r-M

olec

ular

Hea

t Tra

nsm

issi

on(N

anos

cale

Hea

t Tra

nsfe

r)

Nov

embe

r 21,

200

6

Ato

ms

Sp

rin

g B

on

ds:

“Spr

ing

cons

tant

, k”

Ato

ms

or

Mo

lecu

lesNU

CL

EU

S

Prot

on Neu

tron

Ele

ctro

n

Orb

it fo

r el

ectr

ons

THE

RM

AL

EN

ER

GY

INP

UT

Con

sequ

ence

s�

Ele

ctro

ns a

re e

nerg

ized

into

mot

ion

(met

als)

�Th

e at

om is

ene

rgiz

ed to

vib

rate

(sem

i-co

nduc

tors

or

insu

lato

rs)

�Th

e vi

brat

ing

atom

resu

lts in

EN

ER

GY

gene

ratio

n in

the

atta

ched

bon

ds

(e.g

. stre

tchi

ng a

nd c

ompr

essi

onof

the

“spr

ings

”) -

PH

ON

ON

S

�Th

e en

ergy

in b

onds

cau

ses

mor

e at

oms

to v

ibra

te �

mor

e P

HO

NO

NS

�Tr

ansf

erri

ng th

erm

al e

nerg

y (h

eat)

=P

HO

NO

N tr

avel

ing

(in s

emic

ondu

ctor

sor

insu

lato

rs).

�Tr

ansf

erri

ng th

erm

al e

nerg

y (h

eat)

=ph

onon

and

ELE

CTR

ON

S in

met

als.

The

car

rier

in r

adia

tion

is P

HO

TON

S.

PH

ON

ON

S –

The

Ther

mal

Ene

rgy

Car

rier

s

P 1

P 2

P 3

P 4

(t1)

(t2)

(t3)

(t4)

d1d 2

d3

x

y

z

Plan

e B

Plan

e A

Thi

n fi

lmth

ickn

ess,

H

Col

lisio

n of

Tra

velin

g P

hono

ns

�P

HO

NO

Nis

like

Pho

ton

phys

ical

ly e

xist

s as

ene

rgy

indu

ced

by v

ibra

ting

atom

s.�

They

are

trea

ted

as “p

artic

les”

with

virt

uals

ize

and

mas

s.�

Ther

e ar

e zi

llion

s of

ato

ms

in a

sub

stan

ce �

poss

ible

zill

ion

of p

hono

n pa

rticl

es.

Whe

n an

ene

rgy-

carr

ying

pho

non

trave

ls fr

om

one

posi

tion

(Pla

ne A

) to

anot

her p

ositi

on

(Pla

ne B

) in

a so

lid, i

t enc

ount

ers

zilli

on ti

mes

colli

sion

with

oth

er p

hono

n pa

rticl

es.

The

trave

ling

phon

on w

ould

cha

nge

itsco

urse

afte

r eac

h co

llisi

on �

No

dire

ctan

d cl

ear p

ath

from

Pla

ne A

to P

lane

B.

Free

pat

hTh

e di

stan

ce o

f fre

e tra

velin

g of

pho

nons

with

out c

ollis

ion

with

othe

r pho

non.

Free

tim

eTh

e tim

e re

quire

d fo

r a p

hono

n tra

velin

g w

ithou

t col

lisio

n w

ith a

noth

er p

hono

n.

P 1

P 2

P 3

P 4

(t1)

(t2)

(t3)

(t4)

d1d 2

d3

x

y

z

Plan

e B

Plan

e A

Thi

n fi

lmth

ickn

ess,

H

Col

lisio

n of

Tra

velin

g P

hono

ns –

Con

t’d

Ave

rage

“mea

n fre

e pa

th” (

MFP

)

33

21

dd

d+

+=

λ

Ave

rage

“mea

n fre

e tim

e” (M

FT)

()

()

()

33

14

34

23

12

tt

tt

tt

tt

−=

−+

−+

−=

τ

The

MFP

and

MFT

in N

anos

cale

Hea

t Tra

nsm

issi

on

Gra

ins

Gra

in b

ound

arie

s

Mag

nitu

des

of M

FP a

nd M

FT

depe

nd o

n:

�M

olec

ular

stru

ctur

es�

Con

greg

atio

n m

olec

ules

�G

rain

geo

met

ry�

Gra

in b

ound

arie

s�

Tem

pera

ture 10

-12

sM

FT

130

nm65

nm

>10-

8m

(=10

-7m

for d

iam

ond)

10-8

mM

FP

Liqu

ids

Gas

esP

hono

nsE

lect

rons

�Th

e ef

fect

of b

oth

MFP

and

MFT

are

neg

ligib

le in

mag

nitu

des

in m

acro

scal

ehe

at tr

ansm

issi

on e

ven

with

mill

ions

of c

ollis

ions

of p

hono

n an

d el

ectro

ns

beca

use

of th

e lo

w m

agni

tude

s of

MFP

and

MFT

, and

thei

r effe

cts

even

out

in

the

size

of t

he d

omai

n.�

In n

anos

cale

solid

s, th

e ef

fect

s of

MFP

and

MFT

bec

ome

mor

e si

gnifi

cant

an

d ne

ed to

be

acco

unte

d fo

r in

the

anal

ysis

�D

ELA

Y IN

HE

AT

FLO

W.

ATO

MS

:N

ucle

us +

Ele

ctro

ns

MO

LEC

ULE

S:

Com

poun

ds o

f Ato

ms

GR

AIN

S -

Cry

stal

Sys

tem

s:P

OLY

CR

YS

TAL

GR

AIN

S

Hea

t Tra

nsm

issi

on in

Sol

ids

of N

anos

cale

Hea

t tra

nsm

issi

on in

sol

ids

is a

chie

ved

by:

�Tr

avel

ing

of p

hono

ns in

sem

icon

duct

ors

or d

iele

ctri

c m

ater

ials

, or

�Tr

avel

ing

of p

hono

ns a

nd e

lect

rons

in m

etal

lic m

ater

ials

.�

Trav

elin

g of

pho

tons

in r

adia

tive

heat

tran

smis

sion

.

�Tr

avel

ing

of p

hono

ns a

nd e

lect

rons

in s

olid

s in

duce

d by

ther

mal

ener

gy in

volv

es c

ollis

ions

and

sca

tterin

gs a

long

thei

r way

s.

�In

sol

ids

in m

acro

scal

e, s

uch

alte

ratio

ns o

f pat

hs o

f tra

velin

g is

“AV

ER

AG

ED

”w

ith “b

ig”s

izes

. So,

the

effe

ct o

f alte

red

path

s is

not

sig

nific

ant.

In s

olid

s of

na

nosc

ale,

this

fact

or b

ecom

es s

igni

fican

t in

heat

tran

smis

sion

bec

ause

of

muc

h sh

orte

r dis

tanc

e (i.

e. s

mal

l siz

e) fo

r pho

non

to tr

avel

.

�Ti

me

asso

ciat

ed w

ith th

e tra

velin

g of

pho

nons

and

ele

ctro

ns in

diff

eren

t si

zeof

sol

ids

is s

igni

fican

t in

solid

s of

nan

osca

lefo

r the

sam

e re

ason

as in

the

alte

ratio

n of

pat

hs in

hea

t tra

nsm

issi

on.

�Th

us M

FPan

d M

FTha

ve s

igni

fican

t eff

ect i

n he

at tr

ansm

issi

on in

sol

ids

of n

anos

cale

.

Obs

erva

tions

All

nano

scal

ehe

at tr

ansm

issi

on is

tim

e-de

pend

ant

beca

use

of M

FT. S

o, th

ere

is n

o su

ch th

ing

as s

tead

y-st

ate

heat

tran

sfer

in n

anos

cale

dom

ains

.

This

impl

ies

that

sol

ids

of n

anos

cale

has

LOW

ER

ther

mal

con

duct

ivity

than

that

of t

he s

ame

mat

eria

l in

mac

rosc

ale.

Sol

ids

of n

anos

cale

is a

poo

rer

heat

con

duct

orth

an th

e sa

me

mat

eria

l in

mac

rosc

ale.

This

siz

e-de

pend

ent t

herm

ophy

sica

lpro

pert

yof

na

nosc

ale

solid

s m

ake

the

heat

con

duct

ion

anal

ysis

no

nlin

ear

in n

atur

e.

Ther

mal

Con

duct

ivity

(k) o

f Thi

n Fi

lms

A.

Mod

el b

y R

ohse

now

and

Cho

i [19

61]: λ

CV

k31

=

Para

met

ers

for T

herm

al C

ondu

ctiv

ity o

f Thi

n Fi

lms

Phon

on m

ean

free

pat

h,

λ s≅

from

10-7

m a

nd u

pE

lect

ron

mea

n fr

ee p

ath,

λe

≅10

-8m

Ave

rage

mea

n fr

ee p

ath,

λ

Vel

ocity

of p

hono

ns

(sou

nd v

eloc

ity),

Vs

≅10

3m

/sec

Ele

ctro

nFe

rmi v

eloc

ity,

Ve

≅1.

4x10

6m

/sec

Mol

ecul

ar

velo

city

, V

Spec

ific

hea

t of p

hono

ns,

Cs

Spec

ific

hea

t of e

lect

rons

, Ce

Spec

ific

hea

ts, C

Die

lect

ric

and

sem

icon

duct

ors

Mat

eria

ls

Ref

eren

ces:

Flik

et.a

l. 19

92 a

nd T

ien

and

Che

n 19

94

Ther

mal

Con

duct

ivity

(k) o

f Thi

n Fi

lms

–C

ont’d

B. M

odel

by

Flik

and

Tien

[199

0]:

Hkk ef

f

31

λ−

=

Nor

mal

to th

e th

in fi

lm:

Alo

ng th

e th

in fi

lm:

Hkk ef

f

πλ32

1−

=

whe

re k

eff=

ther

mal

con

duct

ivity

of t

hin

film

. k

= th

erm

al c

ondu

ctiv

ity o

f the

sam

e m

ater

ial i

n m

acro

scal

e.

H =

thic

knes

s of

thin

film

.

�

= M

ean

free

path

(MFP

)

Exa

mpl

e:Fo

r sili

con

thin

film

at H

= 0

.2 �

m o

r 200

nm

thic

k, w

ith

MFP

, �=

10-7

m, w

e ha

ve:

k eff/

k=

0.83

3no

rmal

to th

e th

in fi

lm a

nd k

eff/k

= 0.

894

alon

g th

e fil

m.

k eff/k

= 0.

894

k eff/k

= 0.

833

200

nm

The

Hea

t Con

duct

ion

Equ

atio

nfo

r M

acro

scal

eS

olid

s

y

z

T(x,

y,z,

t)Te

mpe

ratu

re:

The

heat

con

duct

ion

equa

tion

can

be

deriv

ed fr

om th

e Fo

urie

r law

of h

eat

cond

uctio

nan

d th

e Fi

rst l

aw o

fTh

erm

odyn

amic

s.

Tem

pera

ture

in a

sol

id in

th

erm

al e

quili

briu

m:

q in

q out

x

The

Four

ier

law

of h

eat c

ondu

ctio

n:

),

(t

rT

kq

�∇

−=

The

heat

flux

in th

e so

lid:

In th

e C

arte

sian

coo

rdin

ate

syst

em, w

e ha

ve:

xTk

qx

x∂∂

−=

yTk

qy

y∂∂

−=

zTk

qz

z∂∂

−=

in x

, y, a

nd z

-dire

ctio

n re

spec

tivel

y.

QW

U∆

+∆

=∆

In a

non

-flow

sys

tem

, suc

h as

this

, �W

= 0

that

lead

s to

: �

U=�

Q�

y

z

T(x,

y,z,

t)Te

mpe

ratu

re:q i

n

q outTh

e H

eat C

ondu

ctio

n E

quat

ion

for

Mac

rosc

ale

Sol

ids

–con

t’d

Tem

pera

ture

in a

sol

id in

th

erm

al e

quili

briu

m:

x

The

Firs

t Law

of T

herm

odyn

amic

sre

late

s en

ergy

and

wor

k as

:

in w

hich

�U

= c

hang

e of

inte

rnal

ene

rgy;

�

W =

diff

eren

ce b

etw

een

the

inpu

t and

outp

ut w

ork;

and

�

Q =

net

hea

t flo

w in

the

solid

.

Rat

e of

cha

nge

of in

tern

al

ener

gy, �

UR

ate

of n

et h

eat i

nput

to

the

solid

, �Q

=

Hea

t flu

x in

and

out

,�q

Hea

t gen

erat

ion

byth

e m

ater

ial,Q

QU

��

∆=

∆

tTvc

U∂∂

=∆

ρ�

�=

mas

s de

nsity

, c =

spe

cifi

c he

at, v

= v

olum

e

xy

z

dy

dxdz

dyyq

qy

y∂∂

+

dzzq

qz

z∂∂

+

dxxq

qx

x∂∂

+q z

q y

q x

The

Hea

t Con

duct

ion

Equ

atio

nfo

r M

acro

scal

eS

olid

s –c

ont’d

y

z

T(x,

y,z,

t)Te

mpe

ratu

re:q i

n

q out

Tem

pera

ture

in a

sol

id in

th

erm

al e

quili

briu

m:

x

x 10

6

�H

eat f

luxe

s en

terin

g th

e el

emen

t:(

)(

)(

)dx

dyq

dxdz

qdy

dzq

Qz

yx

in+

+=

�

�H

eat l

eavi

ng th

e el

emen

t is:

()

()

()

dxdy

dzzq

qdx

dzdy

yqq

dydz

dxxq

qQ

zz

yy

xx

out

� ��� ��

∂∂+

+�� ��

�� ��

∂∂+

+� ��

� ��

∂∂+

=�

�Th

e ne

t hea

t flu

xflo

w in

the

elem

ent i

s:

()

()

()

dzdx

dyzq

dydx

dzyq

dxdy

dzxq

QQ

zy

xou

tin

∂∂−

∂∂−

∂∂−

=−

��

The

Hea

t Con

duct

ion

Equ

atio

nfo

r M

acro

scal

eS

olid

s –c

ont’d

xy

z

dy

dxdz

dyyq

qy

y∂∂

+

dzzq

qz

z∂∂

+

dxxq

qx

x∂∂

+q z

q y

q xLe

t Q(x

,y,z

,t) =

hea

t gen

erat

ed b

y th

e el

emen

t in

unit

volu

me

and

time.

and

the

chan

ge o

f int

erna

l ene

rgy

in th

e el

emen

t to

be:

()

dxdy

dztT

cdv

tTc

u∂∂

=∂∂

=∆

ρρ

�

From

the

rela

tions

hip:

uQ

��

∆=

∆in

the

elem

ent,

we

have

:

()

()

()

()

()

dxdy

dztT

cdx

dydz

tz

yx

Q

dzdx

dyzq

dydx

dzyq

dxdy

dzxq

QQ

zy

xou

tin

∂∂=

+

∂∂−

∂∂−

∂∂−

=−

ρ)

,,

,(

��

()

tTc

tz

yx

Qzq

yq

xqz

yx

∂∂=

+∂∂

−∂∂

−∂∂

−ρ

,,

,

The

Hea

t Con

duct

ion

Equ

atio

nfo

r M

acro

scal

eS

olid

s –c

ont’d

But

from

Fou

rier l

aw o

f hea

t con

duct

ion:

xTk

qx

x∂∂

−=

yTk

qy

y∂∂

−=

zTk

qz

z∂∂

−=

The

heat

con

duct

ion

equa

tion

in a

mac

rosc

ale

solid

can

be

obta

ined

by

subs

titut

ing

the

abov

e re

latio

ns in

to th

e la

st e

xpre

ssio

n de

rived

from

the

Firs

t Law

of T

herm

odyn

amic

s:

tTc

zTk

zyT

ky

xTk

xz

yx

∂∂=� ��

� ��

∂∂∂∂

+ �� ���� ��

∂∂∂∂

+ � ��� ��

∂∂∂∂

ρ

For i

sotro

pic

solid

s, k

= k

x=

k y=

k z, t

he h

eat c

ondu

ctio

n eq

uatio

n be

com

es:

()

()

()

tt

rT

kt

rQ

tr

T∂

∂=

+∇

,1

,,

2�

��

α

whe

re22

22

222

zy

x∂∂

+∂∂

+∂∂

=∇

is th

e La

plac

ian

oper

ator

;

()

syst

emco

ordi

nate

Car

tesi

ana

inz

yx

vect

orpo

sitio

nr

,,

==

�

mat

eria

lof

ydi

ffusi

vit

Ther

mal

ck=

=ρ

α

The

Hea

t Con

duct

ion

Equ

atio

nfo

r N

anos

cale

Sol

ids

Hea

t tra

nsm

issi

on in

nan

osca

leso

lids

is a

chie

ved

by:

�Tr

avel

ing

of p

hono

ns in

sem

icon

duct

ors

or d

iele

ctric

mat

eria

ls,o

r�

Trav

elin

g of

pho

nons

and

ele

ctro

ns in

met

allic

mat

eria

ls.

� T

rave

ling

of p

hoto

ns in

radi

ativ

ehe

at tr

ansm

issi

on.

�Th

us M

FP a

nd M

FT h

ave

sign

ifica

nt e

ffect

in h

eat t

rans

mis

sion

in s

olid

s of

nan

osca

le.

The

heat

con

duct

ion

equa

tion

for n

anos

cale

solid

s th

us n

eeds

to a

ccou

nt fo

r th

e he

at c

arrie

d by

trav

elin

g ph

onon

s (a

nd e

lect

rons

). C

onse

quen

tly, w

e ha

veTh

e fo

llow

ing

addi

tiona

l ter

m in

hea

t gen

erat

ion

in th

e so

lid:

Rat

e of

cha

nge

of in

tern

al

ener

gy, �

UR

ate

of n

et h

eat i

nput

to

the

solid

, �Q

=

Hea

t flu

x in

and

out

,�q

Hea

t gen

erat

ion

byth

e m

ater

ial,Q

tTvc

U∂∂

=∆

ρ�

Hea

t ass

ocia

ted

with

tr

avel

ing

phon

ons

The

Hea

t Con

duct

ion

Equ

atio

nfo

r N

anos

cale

Sol

ids-

cont

’d

The

mod

ified

Fou

rier L

aw fo

r the

rmal

wav

e pr

opag

atio

n in

sol

ids

[Cat

tane

o&

Ver

notte

]:

() t

rT

ktq

q,�

��

∇−

=∂∂

+τ

Exp

andi

ng th

e ab

ove

in (x

,y,z

) coo

rdin

ate

syst

em:

()

xt

zy

xT

ktq

qx

xx

∂∂

−=

∂∂+

,,

,τ

()

yt

zy

xT

ktq

qy

yy

∂∂

−=

∂∂+

,,

,τ

()

zt

zy

xT

ktq

qz

zz

∂∂

−=

∂∂+

,,

,τ

in th

e x-

dire

ctio

n

in th

e y-

dire

ctio

n

in th

e z-

dire

ctio

n

whe

re

τis

the

“rel

axat

ion

time”

acc

ount

ing

for t

he tr

avel

ing

of p

hono

ns

The

Hea

t Con

duct

ion

Equ

atio

nfo

r N

anos

cale

Sol

ids-

cont

’d

Follo

win

g th

e si

mila

r pro

cedu

re in

the

deriv

atio

n of

hea

t con

duct

ion

equa

tion

for m

acro

scal

eso

lids,

usi

ng th

e m

odifi

ed F

ourie

r law

of h

eat c

ondu

ctio

n,

we

will

get

the

follo

win

g eq

uatio

n fo

r hea

t con

duct

ion

in n

anos

cale

solid

s:

2

21

tTtT

zTk

zyT

ky

xTk

xz

yx

∂∂+

∂∂=� ��

� ��

∂∂∂∂

+ �� ���� ��

∂∂∂∂

+ � ��� ��

∂∂∂∂

ατα

In th

is e

quat

ion,

the

ther

mal

diff

usiv

ity, �

= �

(kx,k

y,kz,c

x,cy,c

z), i

n w

hich

c x,

c y, an

d c z

are

spec

ific

hea

ts o

f the

mat

eria

l in

x-, y

-and

z-d

irec

tion

resp

ectiv

ely.

vλτ

=

with

�=

aver

age

mea

n fre

e pa

th, a

nd V

= a

vera

ge v

eloc

ity o

f hea

t car

rier

(i.e.

pho

non

or e

lect

rons

)

The

rela

xatio

n tim

e:

We

may

find

that

to

rsse

mic

ondu

cfo

ron

dsse

c10

10−≈

τ

Suc

h a

smal

l val

ue is

insi

gnifi

cant

in h

eat c

ondu

ctio

n an

alys

is in

mac

rosc

ale

Sol

ids.

The

vari

atio

n of

ther

mop

hysi

calp

rope

rtie

s of

mat

eria

ls in

x-,

y-an

d z-

dire

ctio

ns is

indu

ced

by th

e va

riat

ion

of M

FP a

nd M

FT o

f ene

rgy

carr

ier

of p

hono

ns in

thes

e di

rect

ions

.

We

have

sho

wn

the

diff

eren

ce o

f the

rmal

con

duct

ivity

k in

the

norm

al

(z-d

irec

tion)

and

the

plan

e di

rect

ion

(x-o

r y-

dire

ctio

n) o

f a th

in s

ilico

n fil

m b

efor

e.

Var

iatio

n of

ther

mal

diff

usiv

ity �

is a

noth

er p

rope

rty

that

var

y w

ith d

irec

tions

.

The

Hea

t Con

duct

ion

Equ

atio

nfo

r N

anos

cale

Sol

ids-

cont

’d

Mea

sure

men

ts o

f the

rmop

hysi

calm

ater

ial p

rope

rtie

s of

nan

osca

leso

lids

thus

pre

sent

maj

or c

halle

nges

to r

esea

rch

com

mun

ity in

nan

otec

hnol

ogy,

and

desi

gn e

ngin

eers

.

The

solu

tion

of th

is e

quat

ion

will

ena

ble

engi

neer

s to

ass

ess

the

tem

pera

ture

var

iatio

ns w

ithin

the

thin

film

s, a

nd th

ereb

y ac

cura

tely

as

sess

the

indu

ced

ther

mal

str

esse

sdi

stri

butio

n fo

r st

reng

th, a

nd

ther

mal

str

ain

for

dim

ensi

onal

sta

bilit

y.

Con

clud

ing

Rem

arks

Alm

ost a

ll m

inia

ture

ele

ctro

mec

hani

cal d

evic

es e

ncou

nter

ser

ious

over

he

atin

g pr

oble

ms.

Ove

r he

atin

g is

a m

ajor

stu

mbl

ing

bloc

k of

nan

osca

leen

gine

erin

g su

ch a

s m

olec

ular

ele

ctro

nics

.

Exc

essi

ve h

eatin

g is

det

rim

enta

l to

relia

bilit

y of

dev

ices

in:

(1)D

rast

ic d

eter

iora

tion

of m

ater

ial s

tren

gth,

(2)D

evel

op e

xces

sive

ther

mal

str

ess,

lead

ing

to s

truc

ture

failu

re, a

nd(3

)Dev

elop

sig

nific

ant t

herm

al d

isto

rtio

n, le

adin

g to

mal

func

tioni

ng

of th

e de

vice

.

It is

thus

impe

rativ

e th

at e

ngin

eers

hav

ing

relia

ble

anal

ytic

al m

odel

s w

hen

are

invo

lved

in th

e de

sign

of m

icro

and

nan

osca

lede

vice

s.

Pro

perl

y de

rive

d he

at c

ondu

ctio

n eq

uatio

n w

ith r

elia

ble

mat

eria

lpro

pert

ies

will

pro

vide

eng

inee

rs w

ith s

uch

tool

.

The

heat

con

duct

ion

equa

tion

for

nano

scal

eso

lids

are

appl

icab

le to

th

in fi

lms

that

are

com

mon

in m

any

conc

urre

nt h

igh

tech

dev

ices

and

m

any

of th

ese

thin

film

s ar

e su

bjec

ted

to c

hang

e of

ther

mal

en

viro

nmen

ts.

The

solu

tion

of th

is e

quat

ion

requ

ires

the

avai

labi

lity

of th

erm

o-ph

ysic

al p

rope

rtie

s of

thin

film

mat

eria

ls o

f k a

nd �

, as w

ell a

s ac

coun

ting

for

the

wav

e m

otio

n of

the

ener

gy c

arri

ers o

f pho

nons

and

elec

tron

s.

Nan

osca

lem

etro

logy

is th

us a

n em

ergi

ng c

halle

ngin

g te

chno

logy

fo

r en

gine

ers.

Con

clud

ing

Rem

arks

-Con

t’d

Par

t 4

Mea

sure

men

ts o

f The

rmal

Con

duct

ivity

of

Thi

n Fi

lms

Nov

embe

r 28,

200

6

Ther

mal

con

duct

ivity

k o

f a m

ater

ial i

s a

mea

sure

of h

ow w

ell

it ca

n co

nduc

t hea

t.

Ther

mal

con

duct

ivity

is c

onsi

dere

d to

be

a m

ater

ial p

rope

rty

of s

olid

s in

mac

rosc

ale

in m

oder

ate

tem

pera

ture

ran

ges.

For

solid

s of

nan

osca

le, k

is s

ize-

depe

nden

t.

Met

als

are

bett

er h

eat c

ondu

ctor

s th

an s

emic

ondu

ctor

s an

d in

sula

tors

.

Ove

rvie

w

Dat

abas

e of

k o

f nan

osca

lem

ater

ials

, e.g

. thi

n fil

ms

is th

usof

cri

tical

impo

rtan

ce fo

r pe

rfor

man

ce a

nd s

truc

tura

l des

ign

anal

yses

.

Cre

dibl

e m

easu

rem

ent t

echn

ique

s fo

r k

of s

emic

ondu

ctor

s an

din

sula

tors

has

bec

ome

a m

ajor

R&

D a

ctiv

ity o

f nan

otec

hnol

ogy.

Ther

mal

con

duct

ivity

of s

olid

s k

is u

sual

ly d

eter

min

ed

by m

easu

ring

the

tem

pera

ture

gra

dien

tpro

duce

d by

a

stea

dy fl

ow o

f hea

tin

a on

e-di

men

sion

al g

eom

etry

.

Rel

iabl

e an

d ac

cura

te m

easu

rem

ents

of k

rel

y on

the

one-

dim

ensi

onal

hea

t flo

w.

Pri

ncip

le o

f k-M

easu

rem

ents

Theo

retic

al B

ackg

roun

d

Hea

t con

duct

ion

in s

olid

s is

gov

erne

d by

Fo

urie

r la

w o

f hea

t con

duct

ion:

xz

yx

TkA

q x∂

∂−

=)

,,

(

whe

req x

= he

at c

ondu

ctio

n ra

te, B

TU/h

, or W

att

A =

are

a th

roug

h w

hich

the

heat

is tr

ansf

erre

d, ft

2or

m2

k =

ther

mal

con

duct

ivity

of t

he m

ater

ial,

BTU

/h-ft

-oF

or W

/m-o

C

xT ∂∂=

Tem

pera

ture

gra

dien

t in

the

dire

ctio

n of

hea

t flo

w, o

F/ft

or o

C/m

Mea

sure

men

t of k

may

be

cond

ucte

d on

a fl

at s

lab:

A

�x

T 1T 2

q(

)2

1T

TA

xq

k−∆

=

whe

re T

1an

d T 2

are

tem

pera

ture

of t

he

rear

and

fron

t sur

face

s re

spec

tivel

y

Mea

sure

men

t of k

of C

ondu

ctor

s, e

.g. M

etal

s

Two

met

al r

od s

ampl

es:

Sam

ple

Aw

ith k

now

n k A

Sam

ple

B w

ith K

Bto

be

dete

rmin

ed.

B

Hea

t Sou

rce

Hea

t Sin

k

� � � �

A q�

T A

�T B

Ther

moc

oupl

es

Insulator

L A L B

From

Fou

rier

law

of h

eat c

ondu

ctio

n:B

BB

B

A

AA

A

LT

Ak

LT

Ak

q∆

=∆

=

whe

re

AA

= A

B=

cros

s-se

ctio

n of

the

Sam

ple

A a

nd B

.L A

= L B

= th

e di

stan

ces

betw

een

ther

moc

oupl

es in

S

ampl

e A

and

B�

T A, �

T B=

mea

sure

d te

mpe

ratu

re d

iffer

ence

s in

S

ampl

e A

and

B re

spec

tivel

y.H

ence

the

ther

mal

con

duct

ivity

of S

ampl

e B

is d

eter

min

ed b

y:

ABA

Bk

TTk

∆∆=

Mea

sure

men

t of k

of S

emic

ondu

ctor

s an

d In

sula

tors

Thes

e m

ater

ials

typi

cally

hav

e lo

w k

-val

ue.

Mai

ntai

ning

one

-dim

ensi

onal

flow

of h

eat i

n th

e sa

mpl

es is

a m

ajor

issu

e.

Gua

rd H

eate

r

Coo

led

Pla

te

Coo

led

Pla

te

Sam

ple

Sam

ple

Hea

t Sin

k, T

c

Hea

t Sin

k, T

c

Hea

t Sou

rce,

Th

d d

q q

Mea

sure

men

t set

-up

requ

ires

stric

t con

trol o

f tem

pera

ture

s in

bot

h he

at s

ourc

e (g

uard

hot

pla

te) T

han

d he

at s

ink

T c.

One

-dim

ensi

onal

hea

t flo

w is

ens

ured

by

the

diffe

renc

e of

Th

and

T c.

The

ther

mal

con

duct

ivity

of t

he s

ampl

es(

)qT

TA

dk

ch

−=

whe

re A

= c

ross

-sec

tiona

l are

a fo

r hea

t flo

w; q

= h

eat o

utpu

t of t

he h

eate

r

Mea

sure

men

t of k

of S

emic

ondu

ctor

s or

Insu

lato

rsin

Sub

-mic

rom

eter

and

Nan

omet

er S

cale

Maj

or is

sues

�Th

ese

mat

eria

ls h

ave

low

k-v

alue

s. C

onse

quen

tly, r

equi

re

high

pre

cisi

on m

easu

rem

ent t

echn

ique

s w

ith h

igh

reso

lutio

ns.

�S

ampl

es a

re n

orm

ally

thin

and

sm

all i

n si

ze. P

rope

r po

sitio

ning

an

d st

atio

ning

in th

e fix

ture

are

diff

icul

t.

�B

eing

thin

in s

ampl

e si

ze (e

.g. s

ilico

n w

afer

s), i

t is

not p

ossi

ble

to e

nsur

ing

one-

dim

ensi

onal

hea

t flo

w.

�Th

e te

mpe

ratu

re g

radi

ent a

long

the

sam

ple

thic

knes

s is

too

smal

l to

be m

easu

rabl

e.

�Th

ere

is n

o pl

ace

for

ther

moc

oupl

es in

the

sam

ples

.

Two

Pri

ncip

al T

echn

ique

s fo

r M

easu

rem

ents

of

k in

Thi

n Fi

lms

of S

emic

ondu

ctor

s an

d In

sula

tors

�Th

e 3

–O

meg

a M

etho

d

�S

cann

ing

Ther

mal

Mic

rosc

ope

The

3-O

meg

aM

etho

d fo

r S

emic

ondu

ctor

s an

d D

iele

ctri

c M

ater

ials

Theo

retic

al b

asis

of 3

-Om

ega

met

hod

[Cah

ill 1

990]

:Te

mpe

ratu

re d

istri

butio

n of

a s

emi-i

nfin

ite s

olid

indu

ced

by a

fini

te li

nehe

at s

ourc

e[C

arsl

awan

d Ja

eger

195

9]

y

x

p(x,

y)

The

tem

pera

ture

rise

at p

oint

P in

side

th

e ha

lf-vo

lum

e is

:

Per

iodi

call

ine

heat

so

urce

@ �

freq

.(e

.g. a

c po

wer

sup

ply)

()(

)qr

KLP

kr

To

� ��� ��

=∆

π1

whe

re P

= th

e am

plitu

de o

f the

pow

erge

nera

ted

at a

ang

ular

freq

uenc

y �

in th

e lin

e so

urce

.L

= le

ngth

of t

he li

ne h

eat s

ourc

ek

= th

erm

al c

ondu

ctiv

ity o

f the

sol

idK

o(r)

= M

odifi

ed B

esse

l fun

ctio

n of

seco

nd k

ind

at z

erot

hor

der

ωα 21

iq

==

wav

elen

gth

of th

e di

ffusi

ve th

erm

al w

ave

with

to

be

the

diffu

sivi

ty o

f the

sol

id

The

ther

mal

con

duct

ivity

k m

ay b

e ca

lcul

ated

from

the

mea

sure

d te

mpe

ratu

re r

ise

as s

how

n ab

ove

22

yx

r+

=

The

3-O

meg

aM

etho

d –

Exp

erim

enta

l Set

-up

Thin

film

sam

ple

Sub

stra

te

I+ I-V+ V-

ac c

urre

ntI (t

)=P

Sin

(�t)

V

L~5 mm

2b~

50 �

m

Met

al li

ne b

y ph

otol

ithog

raph

y:

I+ I-

V+ V

-

L2b

Met

al li

ne b

y ev

apor

atio

n:

�S

uppl

y cu

rren

tI ~

1�

�Te

mpe

ratu

re r

ise

T~

I2~

2��

Res

ista

nce

in m

etal

line

R ~

T ~

2�

�M

easu

red

volta

ge o

utpu

t V~

IR ~

3�

Met

al li

ne m

ater

ials

:A

u, A

g, P

t, et

c.

The

3-O

meg

aM

etho

d k-

Mea

sure

men

ts

Sub

stra

te

Sup

ply

ac c

urre

ntI ~

1�

Mea

sure

d V

olta

ge c

hang

e V

~ 3�

2�~

Tem

pera

ture

ris

e �

T w

ith c

alib

ratio

n2�

~ R

esis

tanc

e ch

ange

�R

with

cal

ibra

tion

The

ther

mal

con

duct

ivity

of t

he th

in fi

lm is

:

()

()

()

ωωπ

ωω

224

2,31,3

212

3

↔∆

↔∆

−

�� ���� ��

=TR

VV

LR

nV

k�

�1,

�2

= M

easu

rem

ents

with

two

angu

lar f

requ

enci

es o

f sup

ply

curr

ent

R =

resi

stan

ce in

the

line

heat

sou

rce

V =

vol

tage

acr

oss

met

al li

ne a

t �V

3,1

and

V3,

2=

mea

sure

d vo

ltage

s ac

ross

the

heat

er @

3�

with

�1

and �

2 po

wer

sup

plie

s re

spec

tivel

y.

L

Thin

Film

Ther

mal

Mic

rosc

opy

of M

icro

-Nan

o D

evic

es

< 10

0 nm

(= 0

.1 �

m)

Sca

nnin

g Th

erm

al M

icro

scop

y

< 1 �

mN

ear-

Fiel

d O

ptic

al T

herm

omet

ry

1 �

mLi

quid

Cry

stal

s

1 �

mR

aman

Spe

ctro

scop

y

1 �

mLa

ser

Sur

face

Ref

lect

ance

1-10

�m

Infr

ared

ther

mom

etry

Spa

tial R

esol

utio

nTe

chni

ques

Sca

nnin

g Th

erm

al M

icro

scop

e

�Fo

r m

easu

ring

k fo

r th

in fi

lms

in th

e th

ickn

ess

rang

e of

10

nmto

10 �

m.

�Th

e m

etho

d is

bas

ed o

n he

ated

tip

that

sca

n ac

ross

the

surf

ace

of

the

sam

ple.

�Th

e he

at fl

owin

g in

to s

ampl

e is

cor

rela

ted

to lo

cal t

herm

al

cond

uctiv

ity o

f the

sam

ple.

�M

odifi

ed v

ersi

on o

f sca

nnin

g th

erm

al m

icro

scop

e –

calle

d th

erm

oref

lect

ance

ther

mom

etry

can

mea

sure

k o

f thi

n fil

ms

in b

oth

norm

al a

nd la

tera

l dir

ectio

ns.

�A

tom

ic fo

rce

mic

rosc

ope

(AFM

), la

ser

beam

, pho

to-a

ndth

erm

al s

enso

rs a

re m

ajor

com

pone

nts

in th

is ty

pe o

f mea

sure

men

t sy

stem

s.

�Th

e A

FMco

nsis

ts o

f a m

icro

scal

eca

ntile

verw

ith a

sha

rp ti

p (p

robe

)

�Its

end

is u

sed

to s

can

the

spec

imen

su

rface

.

�Th

e ca

ntile

ver i

s ty

pica

lly s

ilico

nor

sili

con

nitri

dew

ith a

tip

radi

us o

f cur

vatu

reon

the

orde

r of

nano

met

ers.

�W

hen

the

tip is

bro

ught

into

pro

xim

ity o

f a s

ampl

e su

rface

, for

ces

betw

een

the

tip

and

the

sam

ple

lead

to a

def

lect

ion

of th

e ca

ntile

ver b

y H

ooke

’sla

w.

�D

epen

ding

on

the

situ

atio

n, fo

rces

that

are

m

easu

red

in A

FM in

clud

e:�

mec

hani

cal c

onta

ct fo

rce,

�

Van

der

Waa

lsfo

rces

, cap

illar

y fo

rces

, �

chem

ical

bon

ding

, ele

ctro

stat

ic fo

rces

, �

mag

netic

forc

es,e

tc.

�Ty

pica

lly, t

he d

efle

ctio

n is

mea

sure

d us

ing

a la

sers

pot r

efle

cted

from

the

top

of th

e ca

ntile

ver

into

an

arra

y of

pho

todi

odes

.

Ato

mic

For

ce M

icro

scop

e (A

FM)

Mirr

or For l

inea

r tra

nsla

tion

of s

ampl

e in

x-,

y-an

dZ-

dire

ctio

n

Maj

or C

ompo

nent

s of

Sca

nnin

g Th

erm

al M

icro

scop

e

X-Y

-ZA

ctua

tor

Sam

ple

Def

lect

ion

Sen

sing

Laser

Can

tilev

er

T(x)

x

Z

x

AFM

+Th

erm

al P

robe

Sam

ple

surfa

ce to

pogr

aphy

(exa

gger

ated

)

T(y)

y

Hea

ted

Tip

Tem

pera

ture

Sen

sor

�-r

esis

tive

tip

In th

eory

, kz

may

be

mea

sure

d by

hea

t flo

w in

z-d

irec

tion

whe

reas

kx

and

k ym

ay b

e m

easu

red

by m

appi

ngth

eTe

mpe

ratu

re T

(x) a

nd T

(y).

Mea

sure

men

t of k

of T

hin

Film

Usi

ng 3

-Om

ega

Met

hod

and

Sca

nnin

g Th

erm

al M

icro

scop

eFi

ege,

G.B

.M, A

ltes,

A.,

Hei

derh

offa

nd B

alk,

L.J

. “Q

uant

ativ

eth

erm

al C

ondu

ctiv

ity

Mea

sure

men

ts w

ith N

ano

Res

olut

ion,

”J. P

hysi

cs D

: App

lied

Phy

sics

, vol

. 32,

No.

5, 1

999.

AFM

mad

e of

wir

es(H

eate

r and

ther

mom

eter

)

(wire

dia

: 5 �

m)

(75 �

m d

ia)

200 �m

long

Per

iodi

c he

atin

g:I(t

) = I o

Sin�

tfo

r 3-�

k-m

easu

rem

ents

.Th

e sc

anni

ng th

erm

al m

icro

scop

efo

r in-

plan

e k-

mea

sure

men

ts.

SU

MM

AR

Y�

Ther

mal

con

duct

ivity

is a

n im

porta

nt m

ater

ial c

hara

cter

istic

inm

icro

and

nan

osca

lede

vice

des

ign.

�H

eat t

rans

mis

sion

in m

atte

r rel

y on

the

trave

ling

of e

nerg

y ca

rrie

rs, s

uch

as

phon

ons,

ele

ctro

ns a

nd p

hoto

ns.

�Th

e ab

ility

of c

ondu

ctin

g he

at b

y m

atte

r, i.e

. the

rmal

con

duct

ivity

, dep

ends

on

how

free

thes

e en

ergy

car

riers

can

trav

el in

the

mat

ter.

�Th

erm

al c

ondu

ctiv

ity o

f mat

ter k

, dep

ends

on

the

size

of t

he m

atte

r:

k eff

7�

(�=

MFP

)Th

in fi

lm T

hick

ness

,t

k

�M

easu

rem

ents

of k

for t

hin

film

s pr

esen

ts a

maj

or c

halle

nge

to e

ngin

eers

.

�Tw

o pr

inci

pal m

etho

ds fo

r mea

surin

g k

of th

in fi

lms

are:

�Th

e 3-

Om

ega

met

hod

usin

g pe

riodi

c lin

e he

at s

ourc

e, a

nd�

Sca

nnin

g th

erm

al m

icro

scop

eus

ing

scan

ning

AFM

with

hea

ted

cont

act t

ips.

�C

ombi

ned

3-O

meg

a m

etho

d an

d sc

anni

ng th

erm

al m

icro

scop

y w

as u

sed

to m

easu

reth

e k-

valu

es o

f thi

n fil

ms

of 3

0 nm

thic

kin

bot

h no

rmal

and

late

ral d

irect

ions

.