PhysicsattheNanoscaleandapplica1ons

Clemens.Winkelmann@grenoble.cnrs.frPhelma/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.