Quantum Mechanics in Functional Devices

Prof. Dr. Ekmel Ozbay Nanotechnology Research Center (NANOTAM)

Bilkent University, Ankara, TURKEY

Contents

ResearchatBilkentUniversityNanotechnologyResearchCenter•  Equa9onsthatweareworkingwith• Materialsthatweareworkingwith• Devicesthatweareworkingon•  SelectedDevices•  2DElectronGastoTransistors:HEMT•  QuantumWells,SuperlaIces,andLight:QuantumCascadeLaser

•  2DCrystaltoDiracFermions:GrapheneTransistor

Foundations: Equations that we are working with SchrödingerEqn

MaxwellEqns

Dri5-DiffusionEqns

PoissonEqn

Con<nuityEqn QuantumWell

Periodicity

PhotonicCrystal

Plasmonics

2DMaterials:Graphene

Tunneling

Semiconductor

…

…

Building Blocks: Materials that we are working with

GaAs

AlGaAs

SiGaN

InGaN

AlGaN

ZnO

InP

InGaAsP

AlAs

SiC C LiNbO3 SnO2

Building Blocks: Devices that we are working on

Photodiode

LightEmiPngDiode

LaserDiode

pn pin

SchoQky

MSM

SwitchingDiodeResonantTunnelingDiode(RTD)

QuantumWellInfraredPhotodiode(QWIP)

QuantumCascadeLaser

Mul<-QuantumWell

Transistor High-Electron-MobilityTransistor(HEMT)

Graphene

MMIC

pn-SiC

Single,Mul<-QuantumWell,SuperlaPce

Modulator LiNbO3MachZenderModulator

2D Electron Gas to Transistors: High electron mobility transistor (HEMT) Alsoknownas:•  Heterojunc9onFET(HFET)• Modula9ondopedfieldeffecttransistor(MODFET)•  Two-dimensionalelectron-gasFET(TEGFET)•  Selec9velydopedheterojunc9ontransistor(SDHT)Uniqueenergybandstructure:•  Twodimensionalelectrongas(2-DEG)•  Currentpathparalleltothechannel(Esaki,Tsu1969)•  Highmobilityinchannel(noimpurityscaXering)•  Onlyonetypeofcarriers(electrons)carriescurrent

HEMT

High Electron Mobility Transistor (HEMT)

LateralstructureofHEMT,fabricatedwithrecessetch

www.iue.tuwien.ac.at/phd/brech/ch_5_1.htm

ON-OFFEnergyBandDiagramsofaHEMT

High Electron Mobility Transistor (HEMT)

High Electron Mobility Transistor (HEMT) • GalliumNitrideHEMT•  Highpower(500W)•  Highfrequency(~THz)

Functional EHF Transponder •  Turkish Armed Forces (SSM) and

TUBITAK •  Geosynchronous satellite based

communication •  GaN MMICs in Space •  38 Million USD budget (Bilkent)

GaN based High Power MMICs for Space and Terrestrial Applications

Quantum Cascade Laser: Quantum Wells, Superlattices, and Light

Conduc<onBand

Quantum Cascade Laser: Designer lasers where you can choose the energy of the outcoming photons

QCL: Design, Active Region

E-Field=0 E-FieldApplied

FabricatedQCLStructures

QCL: Fabrication and Measurement

Graphene: 2D Crystal to Dirac Fermions Anallotropeofcarbonintheformofatwo-dimensional,atomic-scale,honey-comblaIceinwhichoneatomformseachvertex.

•  ‘Itschargecarriersmimicrela9vis9cpar9clesandaremoreeasilyandnaturallydescribedstar9ngwiththeDiracequa9onratherthantheSchrödingerequa9on.’•  ‘Althoughthereisnothingpar9cularlyrela9vis9caboutelectronsmovingaroundcarbonatoms,theirinterac9onwiththeperiodicpoten9alofgraphene’shoneycomblaIcegivesrisetonewquasipar9cles:DiracFermions’•  i.e.:electronsthathavelosttheirrestmassm0orasneutrinosthatacquiredtheelectronchargee.

•  directconsequenceofgraphene’scrystalsymmetry.

A.K.Geim,K.S.Novoselov,Nature,2007doi:10.1038/nmat1849

Dirac-likeHamiltonian

kisthequasipar-clemomentum,σthe2DPaulimatrixandthek-independentFermivelocityνFplaystheroleofthespeedoflight.

Graphene Band Structure

Graphene

A.K.Geim,Science,2009doi:10.1126/science.1158877

Graphene Band Structure

A.K.Geim,K.S.Novoselov,Nature,2007doi:10.1038/nmat1849

Effec<velydopingwithelectricfield:Ambipolarelectricfieldeffectinsinglelayergraphene.

Properties of Graphene “FineStructureConstantDefinesVisualTransparencyofGraphene”

R.R:Nairetal.,Science,2008doi:10.1126/science.1156965

“Insteadofmaterialparameters,absorp<oningrapheneisdeterminedbyfundamentalconstants.[…]Couplingbetweenlightandrela9vis9celectronsandthatistradi<onallyassociatedwithquantumelectrodynamicsratherthanmaterialsscience.”

T=(1+2πG/c)-2=(1+(1/2)πα)-2

R=(1/4)π2α2T

Opacity(1-T)≈πα≈2.3%

Properties of Graphene

EffectofelectricfieldinFew-Layer-GrapheneConduc9vitytuningwithElectricfield

K.S.Novoselov,etal,Science,2004doi:10.1126/science.1102896

“ElectricFieldEffectinAtomicallyThinCarbonFilms”

SRRsonback-gatedgraphenedevicesforcouplingenhancement

Scalebaris100nm.

S.Cakmakyapan,H.Caglayan,andE.Ozbay.Carbon80(2014).

w=70nmu=400nmg=40nmh=120nm

Reflec9vitymeasurementsandnumericalcalcula9ons

62nmshi5

95nmshi5

Acknowledgements

To all the founding fathers/mothers of quantum

mechanics who made our ongoing research possible

J