lecture electron transport€¦ · • why should we care about electr ... electrochemically etched...
TRANSCRIPT
Ele
ctro
n tra
nspo
rt an
d re
sist
ance
: an
atom
istic
vie
w
1.Th
e A
bdus
Sal
am In
tern
atio
nal C
entre
for T
heor
etic
al
P
hysi
cs (I
CTP
), Tr
iest
e, It
aly
2.IN
FM D
EM
OC
RIT
OS
Nat
iona
l Sim
ulat
ion
Cen
ter,
Trie
ste,
Ital
y
Ral
ph G
ebau
er(1
,2)
Ove
rvie
w
•W
hy s
houl
d w
e ca
re a
bout
ele
ctro
n tra
nspo
rt th
roug
h ve
ry s
mal
lsy
stem
s? A
nd w
hy N
OT?
•W
hat i
s re
ally
diff
eren
t in
the
smal
l wor
ld?
Not
sim
ply
Ohm
’s la
w?
•E
xpla
in th
e m
echa
nism
s w
ith V
ER
Y e
asy
mod
els
•G
o th
ough
som
e to
y ex
ampl
es
•C
an w
e be
mor
e qu
antit
ativ
e? W
hat c
hang
es in
real
istic
cal
cula
tions
?
•A
bout
a c
ompl
etel
y di
ffere
nt a
ppro
ach
…
This
pre
sent
atio
n is
loos
ely
base
d on
:S
upriy
oD
atta
, Nan
otec
hnol
ogy 15
, S43
3 (2
004)
How
man
y se
min
ars
on m
olec
ular
ele
ctro
nics
sta
rt …
.
The
se ti
ps, i
nven
ted
at IB
M in
198
3, st
arte
d na
nofa
bric
atio
n.
Elec
troch
emic
ally
Etc
hed
Tung
sten
STM
Tip
s(E
tche
d in
the
Her
sam
Lab
at N
orth
wes
tern
Uni
vers
ity)
Firs
t Tra
nspo
rt M
easu
rem
ents
thro
ugh
Sing
le M
olec
ules
Sing
le-w
all c
arbo
n na
notu
beon
Pt
Dek
kere
t al.
Nat
ure
386
(97)
@ D
elft
Nan
opor
e
Ree
d et
al.
APL
71
(97)
@Y
ale
Bre
ak ju
nctio
n:
dith
iols
betw
een
gold
Mol
ecul
e ly
ing
on a
surf
ace
Mol
ecul
e be
twee
n
two
elec
trod
es
Dor
ogie
t al.
PRB
52
(95)
@ P
urdu
e
Au(
111)
Pt/Ir
Tip
SAM
1 nm
~1-2
nm
Self-
asse
mbl
ed m
onol
ayer
s
Ads
orbe
d m
olec
ule
addr
esse
d by
ST
M ti
p
C60
on g
old
Joac
him
et a
l. PR
L 74
(95)
@ T
oulo
use
Gim
zew
ski@
IBM
-Zür
ich
STM
tipA
u
Ree
d et
al.
Scie
nce
278
(97)
@Y
ale
Nan
otub
eon
Au
Lieb
eret
al.
Nat
ure
391
(98)
@ H
arva
rd
A B
Ral
ph, M
cEue
n, A
brun
a, C
oate
s et a
l, 2
002
expe
rimen
t:ex
perim
ent:
M.A
. Ree
d M
.A. R
eed
et. a
let
. al ,
Scie
nce
, Sci
ence
278278 ,
252
(199
7), 2
52 (1
997)
theo
ry:
theo
ry:
M.D
iM
.Di V
entra
Ven
traet
. al
et. a
l , , Ph
ys.
Phys
. Re
v.
Rev.
Let
tLe
tt ..84
, 979
(200
0).
84, 9
79 (2
000)
.
•• ref
lect
ive:
T ~
5 x
10
refle
ctiv
e: T
~ 5
x 1
0-- 44
•• sin
gle?
obs
erve
inte
ger u
nits
(1,2
,…)
sing
le?
obse
rve
inte
ger u
nits
(1,2
,…)
•• pow
er d
issi
patio
n?po
wer
dis
sipa
tion?
•• J ~
10
J ~ 1
088A
/cm
A/c
m2 2
•• P ~
1P
~ 1 µµ
W (1
mol
ecul
e ?!
)W
(1 m
olec
ule
?!)
•• T v
ery
cont
act g
eom
etry
sens
itive
T ve
ry c
onta
ct g
eom
etry
sens
itive
Mea
sure
men
t of b
enze
ne-1
,4-d
ithio
lM
easu
rem
ent o
f ben
zene
Mea
sure
men
t of b
enze
ne-- 1
,41,4 --
dith
iol
dith
iol
Kar
lsru
heK
arls
ruhe
grou
p, lo
w T
grou
p, lo
w T
Is th
ere
anyt
hing
mor
e ab
out c
ondu
ctan
ce th
an
Ohm
’s la
w ?
YE
S!
Qua
ntiz
atio
n of
co
nduc
tion,
wel
l kn
own
from
m
esos
copi
cph
ysic
s.
Hav
e a
look
at a
typi
cal d
evic
e
Wha
t mak
es th
e el
ectro
ns fl
ow ?
Ass
ume
the
cont
acts
to b
e la
rge,
met
allic
, with
a c
ontin
uous
di
strib
utio
n of
sta
tes
The
orig
in o
f qua
ntiz
ed c
ondu
ctan
ce
The
impo
rtanc
e of
the
pote
ntia
l pro
file
The
impo
rtanc
e of
the
pote
ntia
l pro
file
The
impo
rtanc
e of
the
pote
ntia
l pro
file:
A s
impl
e ca
paci
tive
mod
el
Som
e ea
sy e
xam
ples
: 1.
Cur
rent
-Vol
tage
cha
ract
eris
tics
Som
e ea
sy e
xam
ples
: 2.
The
rmoe
lect
ric e
ffect
Bec
omin
g re
alis
tic:
The
NE
GF
(Kel
dysh
) for
mal
ism
A c
ompl
etel
y di
ffere
nt a
ppro
ach:
Qua
ntum
kin
etic
mod
els
Look
at w
ell-k
now
n s
emi-c
lass
ical
mod
els
Equ
atio
ns o
f mot
ion
for a
wav
epac
ket
•D
ynam
ics
of th
e w
avep
acke
tsar
e gi
ven
by
Ham
ilton
’s e
quat
ions
:
•In
trodu
ce a
dis
tribu
tion
func
tion
f(r,k
) tha
t gi
ves
the
num
ber o
f ele
ctro
ns a
t pos
ition
ran
dw
ith m
omen
tum
k.
EF
erm
iE
Fer
mi
EF
erm
i
Bol
tzm
ann
equa
tion
in a
sim
ple
met
al EF
erm
iLe
arn
how
suc
h m
etho
ds c
an b
e us
ed in
the
quan
tum
regi
me
….
On
Thur
sday
!