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Lecture 2: Photodetection and PhotodetectorsECE228B, Prof. D. J. Blumenthal Lecture 2, Slide 1
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Photodetection (Continued)ECE228B, Prof. D. J. Blumenthal Lecture 2, Slide 2
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Electrical Signal-to-Noise Ratio (SNR) ➥ At the receiver, there is noise on the signal arriving at the input and and after detection added to that is noise that is injected at various stages of the receiver ➥ The current output of the receiver in(t) has current contributions from ➥ Electrical shot noise ➥ Thermal noise ➥ APD detectors have additional multiplication noise ➥ Ampliﬁer noise photodetector Popt(t) = PSig(t) + Pn(t) I(t) = Ip(t) + in(t) Receiver Detector Output Current (I) 2σ1 <I1> <I0> 2σ0 tECE228B, Prof. D. J. Blumenthal Lecture 2, Slide 3
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Modeling Detector SNR When observing the detector current output, it is difﬁcult to tell which noise was present at the optical input and which noise was generated internal to the detector. So we tend to use several different models and combine themOptical signal = DC Current = DC Current = DC Current = DCcomponent + component + component + component +variance (Poisson variance (Poisson variance (Filtered variance (FilteredProcess) Process) Poisson Process) Poisson Process + Hd(ω) = FT {hd (t)} additive noise) ! Ideal photodetector Filtering Internal Detector NoiseECE228B, Prof. D. J. Blumenthal Lecture 2, Slide 4
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Noise Current To quantify the statistical nature of noise, we can’t determine random events ahead of time, but we can use their “spectral” characteristics to quantify statistical behavior Deﬁne an Average (mean) value to quantify the amount of power (energy) in the non- time varying part of the signal Deﬁne a Variance to quantify the amount of power (energy) in the noisy part of the signal Deﬁne the “noise” current as i(t) = I DC + inoise (t)ECE228B, Prof. D. J. Blumenthal Lecture 2, Slide 5
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Shot Noise Mean and Variance For constant power illumination, the rate parameter is constant, and the signal is the mean The noise corresponds to the photocurrent variance For a ﬁlter, homogeneous Poisson process t !q Mean (Amps) is (t) = i(t) = Precvd $ hd (# )d# • Both mean and variance are h" 0 linear with Prevd t • As Prcvd is increased, both 2 !q 2 signal and noise increase Variance (Amps2) i (t) = var{i(t)} = n Precvd $ hd (# )d# h" 0 Power Spectrum 2 I DC Total Shot Noise = Area = 2qI DC B 2 in (0) = 2qI DC f B Detector BandwidthECE228B, Prof. D. J. Blumenthal Lecture 2, Slide 6
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Photodetector Shot Noise The shot noise generated in the photodetection process is physically due to the “quantum granularity” of the received (and photo converted) optical signal Shot noise sets the ultimate limit of an optical receiver Shot noise is a Poisson noise, but it is usually approximated as a Gaussian noise Hallmark of shot noise is dependence on q, the electron charge Constant Input Optical Power Detector Shot Noise Optically induced current + random electron ﬂuctuations σ2Shot = 2q(Ip + Id)Δf Popt IPin Detector <Ip> (BW = Δf) I(t) = <Ip> + ishot(t) 2σshot t tPoisson,no-modulation Thermally induced current + random electron ﬂuctuations Dark Current (Id) Detector Shot NoiseECE228B, Prof. D. J. Blumenthal Lecture 2, Slide 7
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Shot Noise with Data Modulation Consider how the picture changes when we have information modulated on the optical carrier Let m(t) be the information transmitted Then Prcvd (t) and λ(t) are functions of m(t) Assuming the photodetector ﬁlter impulse function can change in amplitude from time period to time period, let Gj be a time varying parameter N i(t) = # G j hd (t ! " j ) j =1 Power Spectrum t !is (t) = i(t) = G Prcvd (# )hd (t % # )d# $ 2 I DC Total Shot Noise = h" %& Modulation Area = 2qI DC B t2 ! 2 2 2qI DCi (t) = var{i(t)} =n G & Prcvd (# )hd (t $ # )d# h" $% f Modulation Bandwidth B Detector Bandwidth ECE228B, Prof. D. J. Blumenthal Lecture 2, Slide 8
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Ideal Direct Detection (1) Ideal Ampliﬁer = unity gain, zero noise, equivalent load RL Ei(t) i’(t) Hd(ω) = FT {hd(t)} AV=1 i(t) Vout(t) Ideal Detector RL # !q Ei (t) 2 & i(t) = LPF % ( Ei (t) = 2Ps Z 0 cos(! s t + " ) % h" Z 0 ( $ Vout (t) = i(t)RL # Ei (t) 2 & # !q 2Ps Z 0 & = LPF % Cos 2 () s t + * ) ( !q % ( $ h" Z 0 = idc RL = Ps RL Pavg =% 2 ( = Ps h" % Z0 ( # !q 1 & = LPF % 2Ps [1 + cos 2() s t + * )]( % $ ( $ h" 2 !q = idc = Ps h"ECE228B, Prof. D. J. Blumenthal Lecture 2, Slide 9
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Ideal Direct Detection (2) Electrical SNR is found using the ratio between the signal power (DC) generated in the load resistor and the noise power (shot noise) generated in the load resistor 2 # !q & Psignal ( Psignal isignal RL % h" 2 $ 1 !Psignal SNRdd = = 2 = = Pnoise inoise RL 2qh" Psignal B 2 h" B This equation shows the fundamental, quantum shot noise limit, where the SNR is limited only by the shot noise itself -> Shot Noise Limited Direct (Incoherent) Detection SNR improves linearly with input signal strength We will discuss other noise contributions that exist that make it difﬁcult to reach this limitECE228B, Prof. D. J. Blumenthal Lecture 2, Slide 10
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Ideal Coherent Detection (1) Consider the following ideal Heterodyne Coherent Receiver Heterodyne implies that a non-zero intermediate frequency (ωIF) is generated prior to data recovery Elo(t) Ideal Ampliﬁer = unity gain, zero Local noise, equivalent load RL Oscillator ε Plo+ (1-ε) Psignal ε Es(t) i’(t) Hd(ω) = FT {hd(t)} AV=1 Ideal i(t) Vout(t) Input Power Detector Combiner RL !q 1 2* i(t) = LPF ) # 2Plo Z 0 cos($ lot + % ) + 1 & # 2Prcvd Z 0 cos($ s t + % ) ,Ei (t) = ! Elo (t) + 1 " ! Es (t) ( h" Z 0 + 1 1 = ! 2Plo Z 0 cos(# lot + $ ) using cos - cos . = cos(- & . ) + cos(- + . ) 2 2 + 1 " ! 2Prcvd Z 0 cos(# s t + $ ) !q * i(t) = LPF ) ( h" { ( } Plo# + Prcvd (1 & # ) + 2 Plo Prcvd # (1 & # ) cos ($ s & $ lo ) t + % * , + + % Ei (t) 2 ( * Since typically Prcvd = Plo Pavg = 2 * = Ps !q Z0 I DC ; Plo# * h" & * ) Assuming the intermmediate frequency ($ IF = $ s & $ lo ) falls within the LPF bandwidth !q i(t) = 2 Plo Prcvd # (1 & # ) cos [$ IF t + % ] h"ECE228B, Prof. D. J. Blumenthal Lecture 2, Slide 11
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Ideal Coherent Detection (2) Using the same approach as in direct detection to obtain the SNR 2 ! i peak $ SNRhet = Psignal = 2 2 isignal RL = (irms )2 = # 2 & " % Pnoise inoise RL 2qI DC BRL 2qI DC BRL 2 ! q $ 2 Plo Prcvd ) (1 * ) ) # h( & # 2 & # " & % (1 * ) )Prcvd Prcvd = = ; ! q $ h( B h( B limit Plo +,, ) +0 2q # Plo) & BRL " h( % Note that shot noise limited heterodyne coherent detection, in the limit where the local oscillator is much stronger than the received signal, Is a factor of 2 (3dB) better than the shot noise limited incoherent detectionECE228B, Prof. D. J. Blumenthal Lecture 2, Slide 12
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Ideal Coherent Detection (3) The other coherent approach is Homodyne Coherent Detection The intermediate frequency (ωIF) is driven to zero (ωIF=0) at phase is driven to φ=0 bringing the data immediately to baseband Automatic Local Ideal Ampliﬁer = unity gain, zero Frequency/Phase Oscillator noise, equivalent load RL Elo(t) Control ε Plo+ (1-ε) Psignal ε Es(t) i’(t) Hd(ω) = FT {hd(t)} AV=1 Ideal i(t) Vout(t) Input Power Detector Combiner RL !q 1 2*Ei (t) = ! Elo (t) + 1 " ! Es (t) i(t) = LPF ) # 2Plo Z 0 cos($ lot + % ) + 1 & # 2Prcvd Z 0 cos($ s t + % ) , ( h" Z 0 + = ! 2Plo Z 0 cos(# lot + $ ) + 1 " ! 2Prcvd Z 0 cos(# s t + $ ) Since we are using an AFC/APC control to drive $ IF = 0 !q * % Ei (t) 2 ( i(t) = LPF ) ( h" { } Plo# + Prcvd (1 & # ) + 2 Plo Prcvd # (1 & # ) , + * Pavg = 2 * = Ps Since typically Prcvd = Plo Z0 * !q * I DC ; Plo# & ) h" !q i(t) = 2 Plo Prcvd # (1 & # )ECE228B, Prof. D. J. Blumenthal h" Lecture 2, Slide 13
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Ideal Coherent Detection (4) Using the same approach as in direct detection to obtain the SNR SNRhet = Psignal = 2 isignal RL = (irms )2 2 Pnoise inoise RL 2qI DC B 2 % !q ( 2 Plo Prcvd # (1 $ # ) * & h" ) ! 2(1 $ # )Prcvd !P = = ; 2 rcvd % !q ( h" B h" B limit Plo +,, # +0 2q Plo# * B & h" ) Note that shot noise limited homodyne coherent detection, in the limit where the local oscillator is much stronger than the received signal, Is a factor of 2 (3dB) better than the shot noise limited heterodyne receiver and factor of 4 (6dB) better than the shot noise limited incoherent detectionECE228B, Prof. D. J. Blumenthal Lecture 2, Slide 14
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PhotodetectorsECE228B, Prof. D. J. Blumenthal Lecture 2, Slide 15
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Photoconductors (1) ➱ Photon absorption in semiconductor materials. ➱ Three main absorption mechanisms: Intrinsic (band-to-band), Free-Carrier Absorption and Band-and-Impurity Absorption ➱ Intrinsic (band-to-band) is the dominant effect in most SC photoconductors Intrinsic (band-to-band) Free-Carrier Absorption Band-and-Impurity Absorption e- e- Ephoton = hν Ec h+ Ec e- Ec Ephoton = hνEphoton = hν + Donor Level - Acceptor Level Ephoton = hν h+ Ev Ev Ev h+ •Incident photon Ephoton= hν= Ec - Ev ECE228B, Prof. D. J. Blumenthal Lecture 2, Slide 16
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Photoconductors (2) ➱ For intrinsic absorption, photons can be absorbed if hc 1.24 ! ( µ m) > = Ec " EV Eg (eV ) 1240 ! (nm) > Eg (eV ) Material Bandgap (eV) Maximum λ (nm) Typical Operating Range (nm) Si 1.12 1110 500-900 Ge 0.67 1850 900-1300 GaAs 1.43 870 750-850 InxGa1-xAsyP1-y 0.38-2.25 550-3260 1000-1600ECE228B, Prof. D. J. Blumenthal Lecture 2, Slide 17
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Photoconductors (3) Ephoton = hν Semiconductor ➱ Deﬁne: ➱ Pi = incident optical power ➱ R(λ) power reﬂectivity from input Pi medium to semiconductor Pi(1-R) Pi(1-R)e-αx ➱ α(λ) = 1/e absorption length ➱ 1/ α(λ) = penetration depth x 1/α ➱ Power absorbed by the semiconductor is Pabs (x) = Pi (1 ! R)(1 ! e!" ( # )x ) = $(#, x)Pi ➱ deﬁning the efﬁciency number of photocarriers produced !(", x) = number of incident photons = (1 # R)(1 # e#$ ( " )x ) 0 % !(", x) % 1ECE228B, Prof. D. J. Blumenthal Lecture 2, Slide 18
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Photoconductive Photodetectors (1) Photogenerated current will have time and wavelength dependence !q i photo (t) = GPrcvd (t) + idark h" Pi # carrier = mean free carrier lifetime # transit = transit time between eletrical contacts $# G = & carrier ) = photoconductive gain % # transit ( idark = dark current Metal Metal Semiconductor The transit time for electrons and holes can be different and in many SCs the eletron mobility is greater than that of the hole ! e = µe E > µh E = ! h + iphoto The SC must remain charge neutral, for every electron generated, multiple holes will get pulled in until the photogenerated electron reaches the other contact. The carrier and transit times are limited by the slower carrier and the photoconductive Vbias gain is given by the ratio of the transit times L ! carrier = a "h L ! transit = a "e ECE228B, Prof. D. J. Blumenthal Lecture 2, Slide 19
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Photoconductive Photodetectors (2) The carrier velocity is a linear function of electric ﬁeld strength up to a saturation velocity (which is the same for both electrons and holes) Field strength of about 105 V/cm result in velocities in range of 6x106 to 107 cm/s Some materials have an electron drift velocity that peaks at 2x107 cm/s at 104 V/cm When photoconductive gain is desirable, detector is operated at low voltages Carrier lifetime also impacts the frequency response of the photoconductive photodetector Prcvd (! ) i photo (! ) = "G 2 #!& 1+ % ( $ !c 1 !c = = cutoff frequency ) carrierECE228B, Prof. D. J. Blumenthal Lecture 2, Slide 20
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