COURSE OUTLINE. Introduction Signals and Noise Filtering Sensors: PD1 PhotoDetector Fundamentals. Sensors, Signals and Noise 1

Transcription

1 Sensors, Signls nd Noise 1 COURSE OUTLINE Introduction Signls nd Noise Filtering Sensors: PD1 PhotoDetector Fundmentls

2 Photons nd photodetector principles 2 Photons nd Spectrl rnges Reflection nd Absorption of Photons in mterils Therml Photodetector Principles Quntum Photodetector Principles Photon Sttistics nd Noise Current Signls of Quntum Photodetectors

3 3 Photons nd Spectrl rnges

4 Photons 4 Light = electromgnetic wves with frequency ν nd wvelength λ propgtion speed (in vcuum) c = 2, m/s Spectrl rnges: λ < 400nm Ultrviolet (UV) 400nm < λ < 750nm Visible (VIS) 750nm < λ < 3 μm c = ln Ner-infrred (NIR) 3 μm < λ < 30 μm Mid-infrred (MIR) 30 μm < λ Fr-infrred (FIR)

5 Photon Energy nd Momentum 5 Photon: quntum of electromgnetic energy E p = hν quntum energy ( Plnck s constnt h = 7, J s) Rther thn E p in Joules, the electron-voltge V p is employed: E p = q V p (electron chrge q = 1, C V p in Volts or electron-volts ev) from! " = $% " we get V p = hc 1 q l universl constnt hc/q = 1, m V 1,24 μm V V p 1,24 = with V l p in Volts nd λ in μm 400nm < λ < 750nm VIS rnge 3,10 ev > V p > 1,65 ev 750nm < λ < 3μm NIR rnge 1,65 ev > V p > 0,41 ev

6 6 Reflection nd Absorption of Photons

7 Reflection of Photons on the surfce 7 Incident P P I Reflected Air P R Incoming power in the mteril P T0 = P I - P R P T0 Semiconductor (or other mteril) x At the surfce strong discontinuity of the refrction index n, from n = 1 for ir to n >1 for semiconductor: e.g. for silicon it is bout n 3,4 nd depends on the wvelength. This discontinuity gives high reflection coefficient R PR R = (e.g. for silicon R > 0,4 wvelength dependent ) P I Anti-reflection coting: deposition on the reflecting surfce of sequence of thin dielectric mteril lyers with progressively decresing n vlue. It provides grdul decrese of the n vlue from semiconductor to ir nd such smoother trnsition reduces the reflection

8 Absorption of Photons in mterils 8 Incident P I P T0 1 ( ) = - R P I Reflected P R P T trnsmitted P bsorbed R = P P R I Air L Semiconductor x For moderte or low P T the bsorption in dx is proportionl to P T (liner optic effect) - = = dx dpt PTdx PT L The opticl power trnsmitted to position x is ( ) exp( ) P = P exp - x = P - x L T T0 T0 The opticl power bsorbed from 0 to x is x æ - ö - x L P = PT0 - PT = PT0( 1- e ) = PT0 1- e ç è ø α = opticl bsorption coefficient L = 1/α = opticl bsorption depth

9 Absorption of Photons For given mteril the opticl bsorption STRONGLY depends on the WAVELENGTH. Typicl exmple: Silicon bsorption coefficient 1.E+07 α Absorption Coefficient of Silicon, undoped crystl 1.E+06 1.E+05 1.E+04 1.E+03 1.E+02 1.E+01 1.E+00 1.E-01 1.E-02 1.E-03 Visible rnge 1.E-04 1.E-05 1.E-06 1.E-07 1.E

10 Absorption of Photons For given mteril the opticl bsorption STRONGLY depends on the WAVELENGTH. Typicl exmple: Silicon bsorption depth 1.E+08 L = 1/α Absorption depth in Silicon, undoped crystl 1.E+07 L [cm] log 10 scle 1.E+06 1.E+05 1.E+04 1.E+03 1.E+02 1.E+01 1.E+00 1.E-01 1.E-02 1.E-03 1.E-04 1.E-05 Visible rnge 10 9 µm = 1km 10 6 µm = 1m 10 3 µm = 1mm 1 µm 1.E-06 1.E λ [nm] liner scle 10 3 = 1nm NB: over the visible rnge L vries with λ by two orders of mgnitude!!

11 11 Therml Photodetector Principles

12 Principle of Therml Photodetectors 12 A principle for detection of light signls is to employ their energy simply for heting trget nd mesure its temperture rise ΔT. Detectors relying on this principle re clled «Therml Photodetectors» or «Power Detectors» Min dvntge: very wide spectrl rnge. Since photons just hve to be bsorbed for contributing to the detection, the rnge cn be extended fr into the infrred. Min drwbck: sensitivity is inherently poor, becuse high number of bsorbed photons is required for producing even smll vritions of temperture ΔT in tiny trget. For instnce: blue photons re required for heting by ΔT=0,1 K wter droplet of 1mm dimeter (blue photons t λ=475nm hve V p = 2,6 ev; wter hs specific het cpcity c T = 4186 [J/Kg K]= 2, [ev/kg K] nd the mss is 1mg) The dynmic response is inherently slow, becuse therml trnsients re slow. Therml detectors re minly suitble for mesurement of stedy rdition.

13 Principle of Therml Photo-Detectors 13 P p = opticl power; n p = photon rte Pp = np Ep = np qvp Electricl Signl V D Absorber vrible temp. T Temperture sensor Absorber: T = temperture, C = het cpcitnce C = c m (m = mss; c = specific het cpcitnce) R T Therml resistnce (Kelvin deg/wtt ) P d = therml power flow T - To = RT Pd nlog to Ohm lw V = R I Denoting for simplicity T = T - T o the detector energy blnce is Het sink or therml mss with constnt temp. T o T Ppdt = CdT + dt R T

14 Principle of Therml Photo-Detectors 14 From the energy blnce we get dt Pp T = - dt C R C T T Ppdt = CdT + dt R nd in Lplce trnsform The detector trnsfer function from opticl power to mesured temperture thus is T = P R p T The stedy stte response (the stedy T = P p R T obtined with stedy P p ) increses s the therml resistnce R T is incresed The dynmic response is single-pole low-pss filter with chrcteristic time constnt τ = R T C : s R T is incresed, the bndlimit f T =1/2π R T C is decresed For improving the high-frequency response without reducing the stedy response it is necessry to reduce the het cpcitnce C = c m. This implies tht ) bsorber mterils with smll specific het cpcitnce c re required b) the bsorber mss m should be minimized. Remrkble progress hs been indeed chieved in therml detectors with modern technologies of minituriztion nd integrtion (of bsorber, temperture sensor, etc.) tht mke possible to fbricte lso multipixel rrys of therml detectors T 1 1+ sr C T st P p = - C T R C T

15 Rdint Sensitivity or Spectrl Responsivity 15 Therml detectors trnsduce the opticl power P P in n electricl output signl V D of the temperture sensor (voltge signl of thermoresistnces in Bolometers nd of thermocouples in Thermopiles). The bsic quntittive chrcteriztion of the performnce of the detector is given by the Rdint Sensitivity (lso clled Spectrl Responsivity) S D, defined s electricl output voltge [in V] S D = opticl power on the detector sensitive re [in W] For given bsorbed power the detector is heted t given level, independent of the rdition wvelength λ. Therefore, uniform S D would be obtined t ll λ if the reflection nd bsorption were constnt, independent of λ. Vritions of reflection nd bsorption vs λ re kept t moderte level with modern bsorber technologies. Firly uniform S D is chieved over firly wide wvelength rnges, extended well into the infrred spectrl region.

16 16 Quntum Photodetector Principles

17 Principles of Quntum Photodetectors 17 A different principle for the detection of light signls is to exploit photo-electric effects for producing directly n electricl current in the detector. The energy of the bsorbed photons is used for generting free chrge crriers, which constitute the elements of the detector current. Detectors relying on this principle re clled «Quntum Photodetectors» or «Photon Detectors» Photon Detectors cn be vcuum-tube or semiconductor devices

18 Principles of Quntum Photodetectors 18 h" h" -q R L A K -q + - V A Vcuum-Tube detector devices: Photo-Tubes or Photo-Diodes An electrode (cthode K) in vcuum enclosure receives the photons By photo-electric effect the cthode emits electrons in vcuum. The electrons re drwn by the electric field to nother electrode bised t higher potentil (node A) Current flows through the terminls (photocthode nd node).

19 Principles of Quntum Photodetectors 19 Depletion lyer n + h" h" p -- p + R L -q -q +q + +q V A - K A Semiconductor detector devices: Photo-Diodes Photons impct on reverse-bised p-n junction diode The bsorbed photons rise electrons from vlence bnd to conduction bnd of the semiconductor, thereby generting free electron-hole pirs. The free crriers generted in the zone of high electric field (the depletion lyer) re drwn by the junction electric field (the electrons to the n-terminl nd the holes to the p-terminl) Current flows through the terminls.

20 Quntum Detection Efficiency 20 Quntum photodetectors trnsduce opticl signls in electricl current signls by collecting the free electrons generted by the photons of the opticl rdition. The bsic quntittive chrcteriztion of the performnce of the detector is given by the Quntum Detection Efficiency (or Photon Detection Efficiency) η D defined s number of photogenerted electrons (or electron-hole pirs) η D = number of photons reching the detector = N N e p However, since in mny engineering tsks the focus is on the trnsduction from opticl power to electricl current, the Rdint Sensitivity S D is often employed lso for quntum photodetectors, defined s electricl output current [in A] S D = opticl power on the detector sensitive re [in W] = I P D L [ AW]

21 Quntum Efficiency nd Rdint Sensitivity 21 Photons of wvelength λ rriving with stedy rte n p on quntum detector convey n opticl power P L the electrons (or e-h pirs) photogenerted in the detector with stedy rte n e P L = n hn p produce current The Rdint Sensitivity is nd since! " = % & % ' S D S I D = n q e I n q n l P n hn n hc q D e e = = = L p p D D D [ m] l l µ = h = h hc q 1,24 We see tht the Rdint Sensitivity of the quntum detectors intrinsiclly depends on the wvelength λ, tht is, even with constnt quntum efficiency η D. This occurs becuse given opticl power P L corresponds to different photon rtes n p t different wvelengths λ

22 22 Photon Sttistics nd Noise

23 Photon Noise 23 The opticl rdition is composed of photons rriving rndomly in time; the photon number! " in given time intervl T is sttisticl vrible with men! " nd vrince # " $ =! " $! " $ The rndom fluctutions of the photons re the noise lredy present t opticl level. This opticl noise cn be due to bckground photon flux nd to the ctul desired opticl signl. In most cses the photon sttistics is well pproximted by the Poisson sttistics, so tht it is s = 2 p N p The opticl power rriving to the detector is composed of qunt with energy hν rriving rndomly t rte n p. It is the nlog t opticl level of shot electricl current: the men opticl power is P p = n p hν (nlog to I e = n e q ) ; the shot opticl noise hs unilterl spectrl density S p (nlog to ' ( = 2*+, ) hc S = 2hn P = 2 P l p p p Note tht for given opticl power P p the shot noise density decreses s the wvelength λ is incresed

24 24 Current Signls of Quntum Photodetectors

25 Detector Current Pulse Signl 25 In the trnsduction of opticl signls to current signls by Quntum Photodetectors the dynmic response hs cut-off t high frequency. Ultrfst opticl pulses re trnsduced to current pulses tht re still fst, but hve longer durtion. The response to multi-photon opticl signl is the liner superposition of the elementry responses to individul photons. The response to single photon is lso clled Single-Electron-Response SER becuse photon genertes just one free electron (or one electron-hole pir). It is simply wrong to consider the SER δ-like current pulse occurring t the time where the photogenerted chrge crrier impcts on the collector electrode. The crrier induces chrge in the collector electrode before reching it; the induced chrge vries with the crrier position, so tht current flows during ll the crrier trvel in the electric field. The wveform of the current signl is obtined by tking the derivtive of the chrge induced on the collector electrode s function of time. To compute this chrge is n electrosttic problem not esy to solve in generl. However, the mthemticl tretment cn be remrkbly simplified by preliminrly computing the motion of the chrge crriers nd exploiting then the Shockley-Rmo theorem.

26 Shockley-Rmo theorem 26 The output current due to n electron trveling towrds the collector electrode cn be obtined by pplying the Shockley-Rmo theorem in three steps 1. The motion of the electron must be computed; i.e. the trjectory nd the velocity! " t every point of it must be known 2. A reference electric field E v must be computed, which is the field tht would exist in the device (in prticulr long the electron trjectory) under the following circumstnces: electron removed output electrode rised t unit potentil ll other conductors t ground potentil 3. The Shockley-Rmo theorem sttes tht the current i c tht flows t the output electrode due to the electron motion cn be simply computed s where denotes sclr product nd # $" is the component of the field # $ in the direction of the velocity! "

27 Crrier motion in phototube (PT) 27 K -q h" A VACUUM PHOTOTUBE WITH PLANAR GEOMETRY w = cthode to node distnce V A = bis voltge # $ = & ' ( ) true electric field (in the - x direction) * $ = * +, ( ) potentil distribution w E D Electric Field Potentil V D 0 I D - V A + w x V w A V A R L x x ELECTRON MOTION IN VACUUM (-q chrge; m mss) qed qva ccelertion c = = m mw qv Velocity A vc = ct = t mw 0 v c Trnsit time t 2qVA m t 2m t = w qv A

28 SER current in phototube (PT) 28 K E v 0 - A w 1 V A = 1 + w x 1 w x Reference electric E v field computed with electron removed; V A = 1 ; V K = 0 E True electron velocity v c v = 0 v c w qv mw SR theorem: the output current due to single electron is = A t t prllel to the x-xis prllel to the x-xis 2qVA m t 2 qva 2 mw i = qe v = t c v c i c q w 2qVA m 0 t t

29 SER current in phototube (PT) 29 In phototube with plnr geometry the single electron response (SER) is pulse with tringulr wveform c v c 2 qva 2 mw = = ( t t ) i qe v t 0 i c q w 2qVA m 0 t t The frequency response is the Fourier trnsform of the SER pulse, which hs high frequency cutoff inversely proportionl to the pulse width. The pulse width is set by the trnsit time t of the electron from cthode to node t m w - 6 w = 2 = 3,37 10 q V V A A Typicl vlues for phototubes re round w = 1cm = 0,01m nd V A = 100V, which correspond to trnsit time round t 3,3 ns

30 Screened-Anode PT: crrier motion 30 G K w w g A A shorter SER pulse cn be obtined by inserting metl wire grid in front of the node V D E D V G + V A + w g x V A w V w V A x G x w = w g V A The bsic ide is tht the grid cts s electrosttic screen tht does not llow n electron trveling from x=0 (cthode) to x=w g (grid) to induce chrge on the node. The grid bis voltge is selected to minimize the perturbtion to the electron motion; i.e. it is set to the potentil V G corresponding to x=w g in bsence of the grid (or slightly below it). In these conditions, the electric field is prcticlly the sme s in the phototube structure without grid nd the motion of n electron in vcuum is lso the sme.

31 Screened-Anode PT: SR theorem 31 K w w g G A Sme electron motion s in the phototube without grid Different evolution in time of the induced chrge on the node. V G = 0 V A = 1 x In fct, the reference field E v is now very different nd netly shows tht chrge is induced on the node only during the lst prt of the electron trjectory, i.e. from x=w g (grid) to x=w (node) E v w g w w 1 - w x g ìev = 0 for 0< x < wg ï í 1 ï E = for w < x < w î w - wg v g The SR theorem sttes tht the SER current is i = qe v c v c

32 Screened-Anode PT for fster response 32 K E v 0 w w g V G = 0 V A = t - t = t g G w g w w A x - w w g w 1 - w x g v c True electron velocity qva = mw t 0 v c 0 i c i t Reference field of SR theorem SR theorem = qe v c v c t 2qVA m ìev = 0 for 0< x < wg ï í 1 ï E = for w < x < w î w - wg i c without grid v g t g t i c with grid t