astronomical observing techniques lecture 9: silicon eyes 1

AstronomicalObservingTechniques

Lecture9:SiliconEyes1

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Overview

1.  SolidStatePhysics2.  IntrinsicPhotoconductors3.  ExtrinsicPhotoconductors4.  Readout&OperaEons5.  DetectorNoise

4 April 2016 Astronomical Observing Techniques: Detectors 1 2

ModernDetectors

1.   PhotondetectorsResponddirectlytoindividualphotons->releasesboundchargecarriers.

UsedfromX-raytoinfrared.Examples:photoconductors,photodiodes,photoemissivedetectors

2.   ThermaldetectorsAbsorbphotonsandthermalizetheirenergy->changesresistance->

modulateselectricalcurrent.UsedmainlyinIRandsub-mmdetectors.Examples:bolometers

3.   CoherentreceiversResponddirectlytoelectricalfieldandpreservephaseinformaEon(but

needareferencephase“localoscillator”).Mainlyusedinthesub-mmandradioregime.

Examples:heterodynereceivers4 April 2016 Astronomical Observing Techniques: Detectors 1 3

4 April 2016 4

DiamondLaFce•  Elementswith4e–invalenceshellformcrystalswithdiamond

laYcestructure(eachatombondstofourneighbors).•  Thesedouble-bondsbetweenneighboursaredueto“shared”

electrons


DiamondLaFceDiamondlaYcenotonlyformedbygroupIVelements(C,Si,Ge)butalsobyIII-Vsemiconductors(InSb,GaAs,AlP)


ElectronicStatesandBandsSingleatomicsystemExample:Hatom

AtomiccrystalWavefuncEonsΨoverlapàEnergylevelsofindividual

atomssplitduetoPauliprinciple(avoidingthesamequantumstates)

àMulEplespliYngè“bands”

4 April 2016 7

Fermi Energy •  FermienergyEFdeterminesconcentraEonofthermallyexcited

electronsinconducEonband•  Energyvalenceband:EV;EnergyconducEonband:EC•  FermifuncEonf(E):probabilitythatstateofenergyEisoccupied

attemperatureT.

n0 = Nc f Ec( ), Nc = 22πmeff kT

h2

⎛

⎝⎜⎞

⎠⎟

3/2

, f Ec( ) = 11+ e Ec−EF( )/kT ≈

Ec−EF>>kTe− Ec−EF( )/kT

Fermienergy=energyofthehighestoccupiedquantumstateinasystemoffermionsatT=0K

QM:fermionsobeythePauliexclusionprincipleàtwofermionscannotoccupythesamequantumstate.FermionsconsecuEvelyfilluptheunoccupiedquantumstatesstarEngwiththelowestenergy;whenalltheparEcleshavebeenputin,theFermienergyistheenergyofthehighestoccupiedstate.

Fermilevel=chemicalpotenEal

TheFermilevelistheenergyatwhichthereisa50%chanceoffindinganoccupiedenergystate.TheFermilevelcanbecalculatedfromthedensityofstatesintheconducEonandvalencebands.TheFermilevelmayincrease,remainthesameordecreasewithincreasingtemperature,dependingonthenumberofstatesintheconducEonandvalencebands.

FermienergyandFermilevelareonlythesameatabsolutezero.AtabsolutezerotemperaturetheFermilevelcanbethoughtofastheenergyuptowhichavailableelectronstatesareoccupied.Athighertemperatures,theFermilevelistheenergyatwhichtheprobabilityofastatebeingoccupiedhasfallento0.5.

TheFermifuncJonf(E)givestheprobabilitythatagivenavailableelectronenergystatewillbeoccupiedatagiventemperature.Typically,mostofthelevelsuptotheFermilevelE-Farefilled,andrelaEvelyfewelectronshaveenergiesabovetheFermilevel.

ThepopulaEonofstatesdependsupontheproductoftheFermifuncEonandtheelectrondensityofstates:

•  Inthegaptherearenoelectronsbecausethedensityofstatesiszero.•  IntheconducEonbandat0K,therearenoelectronseventhoughthereareplentyofavailablestates,buttheFermi

funcEoniszero.•  Athightemperatures,boththedensityofstatesandtheFermifuncEonhavefinitevaluesintheconducEonband,so

thereisafiniteconducEngpopulaEon.

ElectricConducJvityConducEvityrequireschargecarriersintheconducEonband

OvercomebandgapEgtoliie–intoconducEonband:1.  externalexcitaEon,e.g.viaaphotonßphotondetector2.  thermalexcitaEon3.impuriEes

Eg


IntrinisicPhoto-Conductors:BasicPrinciple-  semi-conductor:fewchargecarriersàhighresistance-  chargecarriers=electron-holepairs-  photonliise-intoconducEonband-  appliedelectricfielddriveschargestoelectrodes


Photo-Current•  ConducEvity:j=σE •  Current:I=jwd •  V=RI, E=V/l where:Rd=resistancew,d,l=geometricdimensionsq=elementaryelectricchargen0=numberdensityofchargecarriersφ=photonfluxη=quantumefficiencyτ=meanlifeEmebeforerecombinaEonμn=electronmobility~meanEmebetweencollisions.

driivelocityv=μnE,currentdensityj=n0qv

nd

qnwdl

Rµσ 0

1 ==

n0 =ϕητwdl


ImportantQuanJJesandDefiniJons

electrical output signal Responsivity S = input photon power

Photoconductive gain G:

TheproductηGdescribestheprobabilitythatanincomingphotonwillproduceanelectricchargethatwillreachanelectrode.

# absorbed photons Quantum efficiency η = # incoming photons

metransit tilifetimecarrier ===

t

ph

qI

Gττ

ϕη

Wavelength cutoff: [ ]eVE

mEhc

ggc

µλ 24.1==

Photo-current: GqI ph ϕη=


•  long-wavelengthcutoffs

•  non-uniformityofmaterial•  problemstomakegoodelectricalcontactstopureSi•  difficulttoavoidimpuriEesandminimizethermal(Johnson)noise

gc Ehc=λ

à  Germanium: 1.85µm à  Silicon: 1.12µm

à GaAs: 0.87µm

LimitaJonsofIntrinsicSemiconductors


ExtrinsicSemiconductors

Example:addi?onofborontosiliconinthera?o1:100,000increasesitsconduc?vitybyafactorof1000!

•  extrinsicsemiconductors:chargecarriers=electrons(n-type)orholes(p-type)

•  achievedbyaddiEonofimpuriEesatlowconcentraEontoprovideexcesselectronsorholes

à muchreducedbandgap->longerwavelengthcutoff


ExtrinsicSemiconductorBandGapsGeSi

Problem:absorpEoncoefficientsmuchlessthanforintrinsicphotoconductorsàlowQEàacEvevolumes(pixels)mustbelarge


BlockedImpurityBand(BIB)Detectors

•  IR-acEvelayer:heavilydoped

•  Blockinglayer:thinlayerof highpurity(intrinsicphotoconductor)

•  TypicalspeciesareSi:AsorSi:SbBIBs

Solution: use separate layers to optimize the optical and electrical properties independently:


Photodiodes•  junction between two oppositely doped zones •  Two adjacent zones create a depletion region with high

impedance

1.  Photongetsabsorbede.g.inthep-typepart2.  AbsorpEoncreatesane–-holepair3.  Thee–diffusesthroughthematerial4.  Voltagedrivesthee–acrossthedepleEonregionàphoto-current4 April 2016 Astronomical Observing Techniques: Detectors 1 18

ChargeCoupledDevices(CCDs)CCDs=arrayofintegraEngcapacitors.Pixelstructure:metal“gate”evaporatedontoSiO2(isolator)onsilicon=MOS

bias voltage

Vg

1.  photonscreatefreee-inthephotoconductor2.  e–driitowardtheelectrodebutcannotpenetratetheSiO2layer3.  e–accumulateattheSi—SiO2interface4.  totalchargecollectedatinterfacemeasuresnumberofphotons

duringtheexposure5. àreadoutthenumberofe–4 April 2016 Astronomical Observing Techniques: Detectors 1 19

ChargeCoupledReadoutsTi

me

sequ

ence

here: 3 sets of electrodes à 3-phase CCD

Collected charges are passed along the columns to the edge of the array to the output amplifier.

Be aware of charge transfer (in-)efficiencies (CTEs) due to electrostatic repulsion, thermal diffusion and fringing fields. 4 April 2016 Astronomical Observing Techniques: Detectors 1 20

http://solar.physics.montana.edu/nuggets/2000/001201/ccd.png 4 April 2016 Astronomical Observing Techniques: Detectors 1 21

ChargeTransferEfficiency(CTE)Time-dependentmechanismsthatinfluencetheCTE:1.  ElectrostaEcrepulsioncauseselectronstodriitotheneighbouringelectrode

withEmeconstantforchargetransferτSI.

2.  Thermaldiffusiondriveselectronsacrossthestoragewellatτth.

3.  “Fringingfields”duetodependencyofthewellonthevoltagesofneighbouringelectrodes(τff).

( )mteCTE τ/1 −−=ApproximaEonfortheCTEofaCCDwithmphases:

Noisefromchargetransferinefficiency:ε=(1-CTE)


CCDColorSensors1.  Takethreeexposuresthroughthreefilterssubsequently–only

worksforfixedtargets(standardforastronomy).2.  Splittheinputbeaminthreechannels,eachwithaseparateand

opEmizedCCD(professionalvideocameras).3.  BayermaskoverCCD–eachsubsetof4pixelshasonefiltered

red,oneblue,andtwogreen.


G-R noise

Johnson or kTC noise

1/f noise

fundamental statistical noise due to the Poisson statistics of the photon arrival à transferred into the statistics of the generated and recombined holes and electrons.

ffII f Δ∝2

2/1

fRkTIJ Δ= 42

fGqI RG Δ=−222 4 ϕη

MainDetectorNoiseComponents

fundamental thermodynamic noise due to the thermal motion of the charge carriers. Consider a photo-conductor as an RC circuit. Since <Q2> = kTC, the charge noise is also called kTC noise or reset noise.

increased noise at low frequencies, due to bad electrical contacts, temperature fluctuations, surface effects (damage), crystal defects, and JFETs, …

The total noise in the system is: 2/1

222fJRGN IIII ++= −

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Operationally, background-limited performance (BLIP)

is always preferred:

The noise equivalent power (NEP) is the signal power that

yields an RMS S/N of unity in a system of Δf = 1 Hz:

In BLIP the NEP can only be improved by increasing the

quantum efficiency η.

BLIPandNEP

2/1

22fJRG III +>>−

2/12

⎟⎟⎠

⎞⎜⎜⎝

⎛=− ηϕ

λhcNEP RG

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astronomical observing techniques lecture 9: silicon eyes 1

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