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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
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