Introduction Signals and Noise Filtering Sensors: PD2 ...home.deib.polimi.it/rech/Download/20_PD_02.pdf · • Introduction • Signals and Noise ... Typical values at room ... Role

Signal Recovery, 2017/2018 – PD 2 Ivan Rech

Sensors, Signals and Noise 1

COURSEOUTLINE

• Introduction

• SignalsandNoise

• Filtering

• Sensors:PD2- PhotoTubes


Vacuum Tube Photo-Diodes or Photo-Tubes 2

• PhotoTube(PT)devicestructure

• PTcurrent-voltagecharacteristicsandstationaryequivalentcircuit

• PTdynamicresponseanddynamicequivalentcircuit

• Photo-emissionofelectrons,photocathodetechnologyandPhotocathodetypes

• DetectorDarkCurrentandNoise

• PhotocathodeNoise-Equivalent-PowerNEPandDetectivity

• Low-Noisepreamplifiersforphotodiodes


PhotoTube device structures 3

SIDE-WINDOWTUBE• Photocathode:thickopaquelayer

depositedonmetalsupportelectrode• Sidewindowoftheglasstube:

unfavourablegeometry,collection oflightonthephotocathodeisuneasyandnotveryefficient

END-WINDOWTUBE• Photocathode:thinsemitransparent layer

depositedontheinterioroftheglasstubeend

• Endwindowoftheglasstube:favourablegeometry,collection oflightonthephotocathodeiseasyandefficient

RLVAK

+-

ℎ𝜈

ℎ𝜈

A

K

-q

-q

SignaloutVA

A

RL

VAK+-

ℎ𝜈

ℎ𝜈

K

-q-q

SignaloutVA


PhotoTube stationary I-V characteristics 4

• AtlowvoltageVAK thephotocurrentcollected attheanodeislimited bytheelectronspacechargeeffect

• AsVAK isincreasedthehigherelectric fieldreducesthespacechargeandthecurrentincreases

• AsVAK exceedsasaturationvalueVAKS allphotoelectronsarecollectedandthecurrentisconstantvs.VAK

• Thesaturation valueVAKSincreaseswiththeopticalpowerPL onthedetector

• Phototubesareoperatedbiased intothecurrentsaturationregion

IA(nA)

VAK100 200 300

200

400

IL4∝ PL4

PL =opticalpower

IL3∝ PL3

IL2∝ PL2

IL1∝ PL1

Currentsaturationregion

PTstationaryequivalentcircuit:photo-controlledcurrentgenerator

A

K

L D LI S P= ⋅


Phototube Dynamic Response

5


PhotoTube Dynamic Response 6

RLVAK

+-

𝑃𝐿

CL

𝐼𝐿 VA

VA

CL RLIL

PTequivalentcircuit

1L

LL L

RZsR C

=+

Maincausesthatlimitthedynamicresponse:1. Transductionfromlightfluxtodetector

current:theSER waveformhD(t) hasfinite-widthTD

2. Loadcircuit:ithasalow-passfilteraction,δ-responsehL(t) withfinite-widthTL

( ) ( ) 11 expLL L L L

th t tR C R C

⎛ ⎞= −⎜ ⎟

⎝ ⎠

Load-circuitδ-responsewith( )L LR h t⋅

Theδ-responsefromlightpower𝑃𝐿 toVA hasoverallshapehP(t) resultingfromthecascade

thewidthTP thusresultsfromquadraticaddition

andforwellexploitingthefastintrinsicresponsehD(t) ofadetector itissufficienttohave

( ) ( ) ( )P D Lh t h t h t= ∗

2 2 2 2 2P D L D L LT T T T R C= + = +

L L L DT R C T= ≤


Fast Response AND Wide Active Area 7

Thelight-to-currenttransductionbyaphototubecanbefairlyfast,withSERpulsedurationTD around1ns.Forexploiting it,theloadfilteringmustbeadequatelylimited

• forwide-bandresponse low-valueRL isemployed;typically,RL =50Ω tomatchacoaxialcableconnection.WithTD ≈1nsandRL =50Ω, theaboverequirementimplies

• TheloadcapacitanceCL issumofCA inputcapacitanceofamplifier(orothercircuit)connected; itcanbe<1pFCS straycapacitanceofconnections; itcanbe<2pFCD electrodecapacitance;itdependsontheareaAD ofthephotocathode

• CD issmallevenforwidesensitiveareaAD ,becausethedielectric isvacuumandtheelectrodespacingiswide.Inplanegeometrywithcathode-to-anodespacingwa

e.g.withwa ≈1cm itis 𝐶( 𝑝𝐹 ≈ 0,09𝐴( 𝑐𝑚2 .It’sonly9pF forAD=100cm2

• Inconclusion: adefiniteadvantageofVacuumPhototubesisthattheyofferverywidesensitiveareatogetherwithfastresponse.Wewillseethatwithsemiconductorphotodiodesthisisnotachievable

L L DR C T≤

20LC pF≤

DD o

a

ACw

ε= ( 8,86 )o pF mε =


Electron Photoemission and Photocathode Technology

8


Photo-emission of electrons 9

Itisathree-stepprocess:• freeelectrongenerationbyphotonabsorption• electrondiffusioninthephotocathode layer• escapeofelectronintothevacuumSuitablematerialsaresemiconductors.Metalsareunsuitable becauseofthehighreflectivity,smalldiffusionlengthandlowescapeprobability(highpotentialstepfrominsideuptothevacuumlevel).

VacuumpotentiallevelEa ElectronAffinity

Valenceband

Conductionband

EnergyGap

VACUUM

E0

SEMICONDUCTOR

ThermalizedElectronDiffusionLengthLet ≈1– 10μm(DirectGap)

High-EnergyElectronDiffusionLengthLeh≈0,01μm(DirectGap)

Electroncollisionswithphonons≈50meVenergyloss


Ordinary photocathodes with positive Ea 10

1.Freeelectronsaregeneratedwithenergyhigherthanthevacuumlevelandaresloweddownbyphononcollisionswhilediffusingafew10nm

4.Atthebottomofconductionbandanelectroncandiffusefurtherafewμmandabout100psbeforerecombining(i.e.gettingdowntovalenceband)butitcannotescapeanymoreintovacuum

2.Aslongasanelectron hasenergylevelhigherthantheexternalpotentialitcanescape intovacuum

3.Ifitdoesnotescape,inafewpsitthermalizesdowntothebottomoftheconductionband


Ordinary photocathodes with positive Ea 11

Inordertooffergoodquantumdetectionefficiency,thephotocathodematerialmustfulfillsomebasicrequirements.• Theinside-to-vacuumenergybarrierEg +Ea mustbe smallerthanthephoton

energyEp .Inthevisiblerange1,6eV<Ep<3,1eV andEg ≈1eV forsemiconductors;therefore,theelectronaffinitymustbelimited

• Electronsgeneratedindeep layersarenotemitted;escapeprobabilityishighonlyforelectronsgeneratedinasurfacelayerthatisverythin,aboutadiffusionlengthLeh ofhigh-energyelectrons.Forasignificantabsorptioninthis layertheopticalpenetration lengthLa mustanywaybeNOTmuchhigherthanLeh ;forahighabsorptionitshouldbecomparable

Inconclusion,thethicknessofthephotocathodelayercontributingtotheelectronemission isintrinsically limitedtoaboutLeh inanycase.Thatis,theactivelayerisverythin, independent fromthetotalthicknessofthephotocathode.

1aE eV≤

a ehL L≈


Semitransparent PhotoCathodes 12

Theactivelayerofthephotocathodeisalwaysverythin,alsoforthickcathodesdepositedonametalelectrode.Thisremarkledtodevelopthinphotocathodes(withthicknessabout≈Leh )depositedontheinterioroftheglasstubeintheend-windowofthedetector.Theyarecalledsemitransparentcathodes.Theyareilluminated ontheoutersidethroughtheglasswindowendemitphotoelectronsfromtheinnerside.Theymakepossibleandeasyamuchbetteropticalcollection thantheside-windowgeometry

hν

hν


Semi-transparent photocathode 13


PhotoCathode Types 14

• S1 wasintroducedinthe’30sandisstill inuse.TheQEislow(peakηD≈0,4%at=800nm)butcoversawidespectrumintheIR.ItisamatrixofCesiumoxidethatincludessilvermicroparticlesandit’scurrentlydenotedAg-O-Cs.

Highlyefficientphotocathodesforthevisiblerangewereintroducedinthe’50sandprogressivelydevelopedemployingcompoundsofalkalimetals (Na,K,Cs,whichhavelowworkfunctions)andAntimony(Sb).Maintypes:• S11 rangesfrom300nmto600nm,peakηD≈15%at450nm;alkalihalideCs3Sb• S20 rangesfrom300nmto800nm,peakηD≈20%at350nm;multi-alkalihalideNa-

K-Sb-Cs• S25 extendstherangeupto800nm,peakηD≈5%at600nm;multi-alkaliNa-K-Sb-Cs

likeS20,butwithathicker layerthatgiveshighersensitivity inthered,atthecostoflowersensitivity intheblue-green

Classifications ofPhotocathodetypesaremadebyindustrialstandardcommittees.MostwidelyusedisthatbyJEDEC(JointElectronDevicesEngineeringCouncilUS),which denotescathodetypesS1,S2,...andclassifies thembyspectralresponsivitytype(ratherthanbychemicalcompositionorfabricationrecipe).


Radiant Sensitivity or Spectral Responsivity 15

(Logscale)

(Logscale)

PHOTOCATHODETYPES

• S1(Ag-O-Csoldesttypeinfrared-sensitive)

• S11(Cs3Sbalkalihalide)

• S20Na-K-Sb-CsMulti-alkalihalide

• S25Multialkalihalideextendedredsensitivity

NB:theauxiliarylinesmarkedwithQuantumDetectionEfficiency(QE)in%makepossibletoreaddirectlyfromthediagramalsotheQE


PhotoCathodes with negative Ea 16

Progressinsemiconductorphysicsandtechnologyledinthe’70stodeviseanewclassofphotocathodes,calledphotocathodeswithNegativeElectronAffinity(NEA)• OnaGaAscrystalsubstrate,afewatomic

layersofCesiumOxide(Cs-O)aredepositedandactivated,thusformingaverythinpositivechargelayerofCs+ ions.

• Theelectric fieldgeneratedatthesurfacecurvesdownwardtheenergybands:thevacuumpotential levelisnowlowerthanthebottomofconductionband,i.e.theelectronaffinityEa isnegative

• Electronscannowescape intovacuumalsowhenthermalizedatthebottomofconductionband;QEisthusenhanced

• Photoelectronemission isobtainedalsowithphotonswithlowerenergyEp ,downtotheGaAsenergygapEg

Inconclusion:NEAcathodesofferhigherQEvalueandbroaderspectralrange,extendinguptotheabsorptionedgeofGaAs(i.e.λ≈900nm correspondingtothegapEg ≈1,4eV)


Detector Dark Current and Noise

17


Detector Dark Current 18

• Afinitecurrentisemittedbyanyphotocathodeevenwhenkeptinthedark,withoutanylightfallingonit.

• Itisaspontaneousemissionduetothermaleffects(phonon-electroninteractions inthecathode)andiscalledDarkCurrent.

• ThedarkcurrentdensityjB (perunitareaofcathode)dependsonthecathodetypeandonthecathodetemperature.TypicalvaluesatroomtemperaturearereportedintheTable

PhotoCathodetype

DarkCurrent densityjB inA/cm2

DarkElectronRatedensitynB inelectrons/s·cm2

S1 ≈10-13 ≈106

S11 10-16 - 10-15 103 - 104

S20andS25 10-19 - 10-16 1 - 103

GaAsNEA 10-18 - 10-16 10 - 103


Detector Internal Noise 19

ThetotalDarkCurrentis𝐼3 = 𝑗3𝐴( whereAD istheareaofthephotocathode.TheshotnoiseofIB isthephotodetectorunavoidableinternalnoise,witheffectivepowerdensity(unilateral)

Typicalvaluesof 𝑆3 arereportedintheTable

PhotoCathodetype

DarkCurrent densityjBA/cm2

ShotNoiseEffectivedensity 𝑆3𝑝𝐴 𝐻𝑧 𝑐𝑚2⁄

S1 ≈10-13 ≈10- 4

S11 10-16 - 10-15 ≈ 10 -5

S20andS25 10-19 - 10-16 ≈10 - 7 – 10 - 6

GaAsNEA 10-18 - 10-16 ≈ 10 – 6

2 2B B B DS qI q j A= =


Role of the Detector Internal Noise 20

CLSi

Sv

SB

• Weknowthatforoperatingwithlow-noiseahighimpedancesensormustbeconnectedtoapreamplifierwithhighinput impedanceandlowinputnoise.Thebestavailablepreamplifiershavecurrentnoiseatroomtemperature

• Thecircuitnoise 𝑆: isalwaysdominantandthedetectorinternalnoise 𝑆3 playsinpracticenorole withanyphototube,evenfordetectorswithS1photocathodes(thathavethehighestnoise)andevenwithverywidesensitivearea(uptomanysquarecentimeters). Infact,forproducingshotnoisewithpowerdensityhigherthanthatofthecircuitnoise,thephototubedarkcurrentshouldbeIB>300pA,correspondingtoanemissionratenB >109 electrons/s.

• Vacuumtubephotodiodescanthusbeemployedforoperatingatlownoisewithoutstringentlimits tothesensitive area.Aswewillsee,thisisadefiniteadvantageoversemiconductorphotodiodes.

0,01iS pA Hz≈


Low-noise preamplifiers for photodiodes

21


Voltage Buffer Preamplifier 22

• Photodiodesarehigh-impedancesensors(boththevacuumphototubesandthesemiconductorphotodiodes),henceforlow-noiseoperationtheymustbeconnectedtopreamplifierswithhighinputresistance* RiA à∞ (seeslidesinOPF2)

• Simpleconfiguration:voltagebufferbasedonahigh-input-impedance andlow-noiseamplifier

*RiA =truephysicalresistancebetweentheinputterminals,notthedynamicinputresistanceincludingfeedbackeffects

Sv

iAR →∞

+

CLSiT

LR →∞ Outputvb signalSb noise

IS ≈Qδ(t)

• CL totalloadcapacitance=CD (detectorcap.) +CiA (amplifiercap.)+CS (connectioncap.)• RL totalloadresistanceà∞• Sv amplifiervoltagenoise• SiT totalcurrentnoise=SiD detectornoise+SiA amplifiernoise(+SiR loadresistornoise)

L

QC


Voltage Buffer Preamplifier 23

Buffervoltageoutput:

Stepsignal

NoiseSpectrum

Thebufferconfigurationhassomenoteworthydrawbacks.• ThesignalamplitudeQ/CLisruledbythetotalcapacitanceCL =CD +CiA +Cs ,whose

valueisnotverysmallandnotwellcontrollable,particularlyincaseswherelongsensor-preamplifier connectionscontributearemarkableCs .CLmaybedifferentfromsampletosampleoftheamplifier,evenofthesameamplifiermodel.

• Withsignals inhigh-ratesequence,thesuperposition ofvoltagestepsmaybuild-upandproduceasignificantdecreaseofthephotodiodebiasvoltage.Thismaychangetheoperatingconditionsandconsequentlytheparametersandperformanceofthedetector,particularlyifthephotodiode isbiasednotmuchabovethesaturationvoltage.

( ) ( )1bL

Qv t tC

= ⋅

2 2

1b v iT

L

S S SCω

= +


Alternativeconfiguration:operationalintegratorbasedonalow-noiseamplifierwithhighinput impedance

Charge Preamplifier or Transimpedance Preamplifier 24

Sv

iAR →∞+CL SiT

LR →∞

Outputvc signalSc noise

IS ≈Qδ(t) F D

Q QC C

?

FR →∞

CF

• CL totalloadcapacitance=CD (detectorcap.) +CiA (amplifiercap.)+CS (connectioncap.)• RL totalloadresistanceà∞• Sv amplifiervoltagenoise• SiT totalcurrentnoise=SiD detectornoise+SiA amplifiernoise(+SiR loadresistornoise)

• CF capacitorinfeedback.TheCF valuecanbeverysmallandisaccuratelysetbythecapacitorcomponent,becausetheinherentstraycapacitancebetweenoutputandinputpinsoftheamplifierisnegligible.Therefore,onecanworkwithCF <<CL

• RF feedbackresistorà∞

ZL

ZF



OutputSignal:

infrequencydomainintime

Withrespecttothebuffer,theamplitude isgreaterbythegainfactorGc =CL/CF>>1

Advantages:• Thehighersignalmakeslessrelevantthenoiseofthefollowingcircuits• Thesignalamplitude isruledbythewellcontrolledandstableCF ,nomorebythe

othercapacitancesCD ,CiA andCs• Thedetectorterminal isconnectedtotheamplifiervirtualground,hence itstays

atconstantbiasvoltageevenwithsignals inhigh-ratesequenceThenoiseanalysis(seenextslide)confirmsthattheseadvantagesareobtainedwithoutdegradingtheS/N.Thechargeamplifierconfigurationthus isthesolutionofchoiceinmostcasesmetinpractice.

L Lc b c b

F F L F

C CQ Qv v G vC C C C

= = ⋅ = ⋅ = ⋅

( ) ( )1cF

Qv t tC

= − ⋅c FF

QV QZj Cω

= − = −



OutputNoiseSpectrum:• thecurrentnoiseSiT isprocessedbythesametransferfunctionasthecurrentsignal• thevoltagenoiseSv isprocessedwiththetransferfunctionfromnon-invertinginput

toamplifieroutput.DenotingbyZL theloadimpedanceandbyZF thefeedbackimpedance

inourcaseZL ≈1/jωCL andZF ≈1/jωCF sothat

ifCF/CL <<1 ,withgoodapproximationitis

Withrespecttothebuffer,thesignalandnoisethusbenefitofthesamegainGc :therefore,theattainableS/Nisthesamewiththechargepreamplifieraswiththevoltagebufferpreamplifier

2 2 2

2 2 2 2

1 11 1L L Fc v iT v iT

F F F L L

C C CS S S S SC C C C Cω ω

⎡ ⎤⎛ ⎞ ⎛ ⎞⎢ ⎥= + + = + +⎜ ⎟ ⎜ ⎟⎢ ⎥⎝ ⎠ ⎝ ⎠⎣ ⎦

2 22

2 2

1L Lc v iT b c b

F L F

C CS S S S G SC C Cω⎛ ⎞ ⎡ ⎤ ⎛ ⎞

≈ + = =⎜ ⎟ ⎜ ⎟⎢ ⎥⎝ ⎠ ⎣ ⎦ ⎝ ⎠

221 F

c v iT FL

ZS S S ZZ

= + +


NEP and Detectivity

27


NEP and Detectivity 28

• EvaluationsandcomparisonsofPhotocathodesarecurrentlybasedontheNoiseEquivalentPowerNEP,afigureofmeritthattakesintoaccountthephotondetectionefficiencyandthedetectordark-currentnoise,butnotthepreamplifiernoise.

• NEPisdefinedwithreferencetoasituationwherethelimittotheminimummeasurablesignalissetbytheinternalnoiseofthedetector andnotbytheelectroniccircuitnoise.Wehaveseenthatthisis NOTthecasewithPhotoTubes butwewillseethatitisthecasewithPhotoMultiplierTubes.NEPwasdevisedasanfigureofmeritforcomparingobjectivelytheintrinsicqualityofdifferentdetectors.LetaphotocathodehaveareaAD ,signalcurrentIp andDarkCurrentIBwithareadensity jB .Employingafilterwithbandwidth(unilateral)Δfwehavenoise

and

Theminimummeasurablecurrentsignal Ip,min (correspondingtoS/N=1)is

ForilluminationwithopticalpowerPp atagivenλ theDetectorResponsivity is

2 2 2n B B Di qI f qj A f= Δ = Δ2

p

n

ISN i=

2,min 2p n B DI i qj A f= = Δ

[ ]1,24

pD D D

p

I mS

P hc qλ µλ

η η= = ⋅ = ⋅


NEP and Detectivity 29

• NEPisdefinedastheinputopticalpowerPp,min correspondingtotheminimummeasurablesignal

Inessence: NEP=detectornoisereferredtothe input(inthiscasetheopticalinput).• However,theNEPisnotafullyobjectivefigureofmeritforassessingandcomparing

thequalityofphotocathodes:infact,cathodesofequalqualityhavedifferentNEPiftheyhavedifferentarea.Furthermore,theNEPisaninversescale,thatis,thebestphotocathodeshavethelowestNEPfigures.

• AdifferentfigurenamedDetectivityD*wasthereforederivedfromtheNEPbya)consideringtheNEPvaluenormalizedtounitsensitivearea(AD =1cm2)andtounitfilteringbandwidth(Δf =1Hz)b)definingtheDetectivityD*asthereciprocalofthenormalizedNEP

thatis

2,min

,min

2p n B Dp

D D D

I i qj A fNEP P

S S SΔ

= = = =

* DA fD

NEPΔ

=[ ]* 11,242 2

DD

B B

mSDqj qj

λ µη= = ⋅

Introduction Signals and Noise Filtering Sensors: PD2 ...home.deib.polimi.it/rech/Download/20_PD_02.pdf · • Introduction • Signals and Noise ... Typical values at room ... Role

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