and applicaonsperso.neel.cnrs.fr/clemens.winkelmann/teaching/... · energy [hbar.ω] 1 2 3 ½ 3/2...
TRANSCRIPT
PhysicsattheNanoscaleandapplica1ons
[email protected]/GrenobleINPandIns1tutNéel/CNRS
PhysicsattheNanoscaleI BasicsofquantummechanicsII Sta1s1calPhysicsIII ForcesatthenanoscaleIV Electrontunnelingandapplica1onsV Quantumelectronictransport
M.F.Crommie,C.P.LutzandD.M.Eigler,Science(1993)
Scope• DensityofStates• TunnelCurrent• ScanningTunnelingMicroscopyandusesinNanoscience
• SingleElectronDevices
Totalnum
bero
fstatesa
vailableN(E)
Energy[hbar.ω]1
2
3
½ 3/2 5/20
dN/dE
Energy[hbar.ω]½ 3/2 5/20
dN/dE
Energy0
ElectronTunnelingCoun1ngavailableenergystates
HarmonicOscillator
HarmonicOscillatorHydrogenatomLeveldegeneracy=2n2
InaveragedN/dE=1/hbar.ω
E1 E2 E3
€
En =−13.6eV
n2
€
En = !ω n +1/2( )
withspin
withoutspin
Energy
Fermilevel
Electronsinasolid
T
Fermienergy
DensityofstatesandFermilevel
Temperature
Energy
FermilevelEnergyuptowhichallstatesarefilled(atT=0).
Energy
Posi9on
Quantumtunneling
Graphene Semiconductor
Superconductor
Nobelprize1973
Al-Pbtunneljunc1onat1.6K
Ge(001)Kubbyetal.,PRB(1987)
S.Mar1netal.,Phys.Rev.B2015
ElectronTunnelingDensityofStatesexamples
ElectronTunnelingTheTunneleffectagain
Conductor1 Conductor2
Thininsulator=tunnelbarrier
Conductor1 Conductor2
Conductor1 Conductor2 Conductor1 Conductor2
€
I = e× ˙ P L→R ∝ exp(−d /d0)
€
I = 0
€
I = 4e× ˙ P L→R
€
I = 3e× ˙ P L→R
Situa1
on1
Situa1
on3
Situa1
on2
Situa1
on4
ElectronTunnelingFermiGoldenRule
Numberofoccupiedstatesin1
Numberofoccupiedstatesin2
Insulator
Filledelectron
icstates
Filledelectron
icstates
Tunnelingpossible?Netcurrent?
Energy
YesI=0
ElectronTunnelingFermiGoldenRule
Numberofoccupiedstatesin1
Numberofoccupiedstatesin2
Insulator
Filledelectron
icstates
Filledelectron
icstates Tunnelingpossible?
Netcurrent?AtT=0
Energy
-V
eV
eV
Yes
I ∝ e !PL→R ρL (E − eV )ρR (E) fL (E − eV )− fR (E)[ ]∫ dE
I ∝ e !PL→R ρL (E − eV )ρR (E)dEEF
EF+eV
∫
ElectronTunnelingTunnelingSpectroscopy
Numberofoccupiedstatesin1
Numberofoccupiedstatesin2
Insulator
Filledstates
Filledelectron
icstates
Tunnelingpossible?Netcurrent(AtT=0)?IfρL≈constant
Energy
V
eV
eV
Onlyathighenoughbias
I ∝ e !PL→R ρL (E − eV )ρR (E)dEEF
EF+eV
∫
∆3.5kBT
€
dIdV
∝ρR (E + eV )
ElectronTunnelingTunnelingSpectroscopy
Superconductor
Nobelprize1973
PlanarAl-Pbtunneljunc1onat1.6K
Superconduc1ngdensityofstates(theory)
o VacuumPtIr-Aljunc1on.ScanningTunnelingSpectroscopyexperimentat80mKo LocalDOSLowTemperaturescanbecrucialforgoodspectroscopies
ElectronTunnelingTheinven1onofSTM
NobelPrize1986
Abenchmarkinsurfacescience:the7x7surfacereconstruc1onofsilicon(111)
Afewyearslater…
OmicronandSpecswebsites
InstrumentalaspectsofSTM
• Mechanicalvibra1onisola1on• Piezoelectriccomponentsforcoarseandfinedisplacement
ElectronTunnelingTheissuewithmechanicalvibra1ons
ExperimentalSTMcurrentfluctua9onsinandoutofcontact(PtIr9pongraphene).
Ques9on:es1matetheamplitudeofmechanicalvibra1onsinthesetup
Incomingvibra1ons/mechanicaldamping.Prac1callimita1on:f0>2Hz
xM=differencebetween1pandbaseposi1ons:
Drivenharmonicoscillator.
€
TS =xM0
x0=
ω# ω 0
$
% &
'
( )
2
1− ω# ω 0
$
% &
'
( )
2$
% & &
'
( ) )
2
+ω# Q # ω 0
$
% &
'
( )
2
€
T =x0
xS0=
1+ω
Qω0
#
$ %
&
' (
2
1− ωω0
#
$ %
&
' (
2#
$ % %
&
' ( (
2
+ω
Qω0
#
$ %
&
' (
2
€
xS t( ) = xS0 sin ωt( )
€
x t( ) = x0 sin ωt +ϕ( )
€
xM t( ) = xM0 sin ωt + # ϕ ( )
base
ElectronTunnelingVibra1onisola1on
Need for a double stage mechanical isolation
Exercice:a1µmrmsvibra1onsourceat500HzperturbstheSTMfromtheoutside.Es1matethetransferamplitudeforoneortwoisola1onstages,andtheresul1ngrela1ve1p-sampledistancevibra1onamplitude.(Answer:300pmand1pmrespec1vely)
TCurie=200-300°C,tobeusedwellbelow.polariza1onprocess(6kV/mm,1h)alignsdipolesalongz.Depolariza1onpossibleifE>1kV/mm.-d31=1-3Å/Vd33=2-6Å/V
T<TCurie
T>TCurie
3
OPbTi,Zr
Beforepoling
Duringpoling
Aver
LeadZirconateTitanates(PZT)
€
∂L = Ld31Ez = d31LtV
€
∂X = 0.9d31L2
D× tV
Piezo-electricscannertubes
Highvoltageamplifiersnoise?:about1mVover0to5kHz.Mechanicalresonances?:Elonga1on:
Flexion:Temperaturedependenceofd13:afactor5to10smalleratlowtemperatures
€
felongation=c4L
€
fflexion = 0.56 D2 + d2
8c
4L2
Experimentalistsconsidera9ons
Exercice:proposeatubedesignthatallowsahorizontalscanrangeof2µmusinga±100Vsourceatlowtemperatureandhasamaximum(felonga1on,fflexion).Es1matethenoiseinposi1onatroomtemperatureduetotheamplifiers.(c=5000m/satlowtemperature,depolariza1onfield1kV/mm,d31=1.5Å/Vatroomtemperature)
Contribu1onsofSTMtosolidstatephysics
• Carbonnanotubes:LDOSvs.structure• Manipula1ngsingleatomsandmolecules
Carbonnanotubes
(n,m)definesthetubegeometry.n=m:armchairm=0:zig-zagn≠m:chiral
Theore1calpredic1onforachiralnanotube:
n-m=3k:metallicn–m≠3k:semiconductor
CNT imaging
Wildoeretal,Nature(1998)
CNTsonaAusurface.
zig-zag
armchair
chiral
CNT spectroscopy
metallic
semi-conduc1ng
Metallicandsemiconduc1ngtubesiden1fied.Sta1s1csagreeswith1/3ofchiralonesbeingmetallic.EnergygapinSCtubes:
€
Egap = 2γa 3d
Cu{ngananotube
Voltagepulse(5V)intheSTMmode.L.C.Venemaetal.,Appl.Phys.Le|.(1997).
Atommanipula1on
D.M.EiglerandE.K.Schweizer,Nature344,524(1990)
Atommanipula1on
CleanNisurfacewithXeatoms:UHVnecessary
Lowtemperature(4K)tofreezeatomdiffusion.
Tunnelimageat10mV/1nA,Atommanipula1onbyincreasingcurrentupto16nA.
Themakingof
Thequantummirage
H.C.Manoharan,C.P.LutzandD.M.Eigler,Nature403,512(2000)
ElectronTunnelingSingleElectronDevices:ChargingEnergy
Addinganelectrontoabulkconductor:E>EF
NeglectedhererepulsiveCoulombianinterac1onbetweenelectrons.
Anyclosedconductorhasa chargingenergy
Promo9ng1e-≠adding1e-€
Ec =e2
C
ElectronTunnelingSingleElectrondevices:CoulombBlockade
Coulombdiamondsinaver1calislandstructure(Delv’98)
CoulombBlockadeonlyeffec9veifkBT<Ec
ElectronTunnelingSingleElectrondevices:experimentalrealiza1ons
Horizontal2DEGSET(Stanford)
Electromigra1onsinglegoldnanopar1cleSET(Cornell)
Ver1cal2DEGSET(Delv&Tokyo)
Shadowevapora1onmetallicSET(Helsinki)
WhatistheexperimentaltemperaturerequiredforobservingCoulombBlockadeineachoftheabovesystems?
ElectronTunnelingSingleElectrondevices:be|ertransistors?
Drawbacks:o Stateoftheartnanofabrequired.Massproduc1onimpossibleatpresent.o (Very)Lowtemperaturesnecessaryo Resis1ve(R>h/2e2=12.9kΩ).Advantages:o conductancechangesoveraverynarrowgatevoltagerange hugeswing.o Canbefast(>GHz).o Func1onali1esbeyondclassicalelectronics
Conclusionso SingleElectronTunneling:atoolforspectroscopyo STMsensi1vetobothtopographyanddensityofstates.• Extremelyfineandconstrainingmeasurements:∂z≈1pm,usuallyhighvacuum,some1meslowtemperatures,mechanicalmobility,…• Adoortothenanoworld:localDOS,localmanipula1on
o SingleElectronDevices:frombasicphysicstonewpromisinglogicdevices.