Detectors. ex. Electron-hole pair creation in a semiconductor photodiode.

Transcription

1 Detectors Transucers that convert electromagneticwave energy into electrical current or voltage Photon etectors create electrons through absorption of photons (we refer to the resulting electrons as photoelectrons ); sometimes also calle quantum etectors. Photon etectors have an inherent cut-on frequency, above which photons have sufficient energy to cross the material energy barrier (e.g. semiconuctor bangap energy); photon at a frequency lower than this cut-on value are not etecte. The cut-on frequency correspons to the longest etectable wavelength. ex. Electron-hole pair creation in a semiconuctor photoioe.. Thermal etectors create electronic signal by a change in heat (which is itself create by absorbe photons). Thermal etectors usually respon over a very wie electromagnetic banwith. Therefore, they can be use to etect long- or short-wavelength raiation, an they usually have a rather flat spectral response. ex. esistance change in a bolometer cause by absorbe raiation. 1

2 Detector figures of merit Quantity Symbol Units Description esponsivity (etector) [A or V] Conversion of optical power to W to electrical voltage or current Noise-Equivalent Power NEP W Incient power for SN = 1 Detectivity D W -1 1 / NEP Specific Detectivity D* cm Hz 1/ W -1 bigger is better version of NEP normalize to A an f NEP i noise i ( ) A et * D f SN P NEP P D A et * f

3 Sensor system figures of merit Quantity Symbol Units Description Noise-Equivalent aiance NE W m - sr -1 Incient raiance for SN = 1 Noise-Equiv. Temp. Diff. NETD K or o C Temp. ifference for SN = 1 Signal-to-backgroun ratio SB [ ] contrast of signal & backgroun Signal-to-noise ratio SN [ ] signal mean / signal st eviation SN mean st.eviation i σ i SN P NEP P D A et * f 3

4 ecibels A commonly use logarithmic escriptor of energy an power is the ecibel, name for Alexaner Graham Bell. Originally evise to escribe auio signals in a manner that matche the logarithmic response of the human ear; now use ubiquitously. Voltage Power B = 0 log 10 (V) B = 10 log 10 (P) Especially for F etectors, it is common to refer the ecibel measure of signal or Noise to a level of one mw, which we enote as B m. mw reference B m = 10 log 10 (P mw /1 mw) Another variation is the ecibel escriptor of power relative to an isotropic raiatior, enote B i. This is most often use to escribe the strength of antenna raiation in a given irection, relative to an isotropic raiator raiating the same amount of total power. Isotropic reference B i = 10 log 10 (P / isotropic power) 4

5 Photon etector photocurrent A photon etector absorbs incient photons an generates electrons that flow as photo current. For example, electrons release from a metal surface through the photoelectric effect or electron-hole pairs create by absorption of photons in a semiconuctor p-n junction. Photocurrent = i q q h photon arrival rate = quantum efficiency (photon-electron conversion probability) [e-/ph ] q = electron charge = [C] = flux [J/s] h = Planck s constant = [J s] = optical frequency [Hz] Because of their quantum mechanical nature, both photon an electron arrival an emission rates are ranom functions governe by the Poisson istribution. This generates noise in otherwise noise-free etectors. This shot noise manifests itself as fluctuations in the photocurrent. 5

6 esponsivity The responsivity expresses how much electrical signal is generate when a given amount of optical flux (power) is incient on a etector. The electrical quantity can be current or voltage. Photocurrent = i q i h i q h Current responsivity = [A/W] = quantum efficiency (photon-electron conversion probability) [e-/ph ] q = electron charge = [C] h = Planck s constant = [J s] = optical frequency [Hz] 6

7 Signal & noise statistics Noise is any sort of ranom fluctuation of the etector output aroun its mean value. To quantify the signal an noise in a measurement, we must first unerstan a few important concepts from statistics an linear systems theory. Mean: v T 1 v( t) t T 0 Variance (mean- square eviation): v ms v( t) v t v( t) v 1 T T 0 Stanar eviation v v ( ) v v ( (rms eviation): t t t ) v rms 1 T T 0 Uncorrrelate noise sources a as rms values: rms rms rms rms... total 1 3 7

8 Noise reuction through averaging Because noise is a zero-mean ranom process an signal has a nonzero mean, temporal averaging increases the ratio of signal to noise. Consequently, noise can be reuce by averaging multiple inepenent measurements. If we average n inepenent measurements of a stochastic quantity x to prouce a quantity y, we fin that 1. The mean of y is equal to the mean of x: y x. The variance of y is equal to the variance of x ivie by n: y x n This means that by averaging n measurements, we obtain the same mean value (signal) but reuce the stanar eviation (noise) by 1 n ef: Boy pp ; Frieen 8

9 The Poisson probability istribution The Poisson istribution escribes the probability of occurrence for ranom, iscrete events. It applies to the electromagnetic etection process because iscrete photon arrival an emission events occur as ranom processes. The Poisson istribution is the limit of a binomial istribution for a large number of iscrete time perios ( trials ). As the expecte number of occurrences increases, the Poisson istribution approaches a Gaussian istribution. p(n) N, 3, 5, 10 For an average number of events N [photons / secon] in N time perios of equal length, the Poisson istribution is p( N) N N N! e N The Poisson istribution has the curious & important property that the variance is equal to the mean. Aapte from N N N N 9

10 Summary of typical noises Shot Noise i n qi( f The iscretization of electron energy levels an the ranom nature of energy transitions an photons prouces a variation in photon an electron fluxes. ) Johnson Noise (Thermal Noise) 4kT ( f ) i n f = electrical banwith = resistance Thermally excite electrons bump into atoms in an electrical evice, causing energy changes that appear as fluctuations in the electrical signal. 1/f Noise i n ~ Sometimes calle flicker noise, this is a fluctuation that increases as the electrical frequency approaches zero (DC). It occurs in many ifferent realms, but the source of the noise is still not easily explaine. The resulting slow rifts in signal level can be remove by chopping (moulating) the incient light to bring it to a higher electrical frequency. 1 f x typ. 0.8 x 10

11 Photon noise (shot noise) Photon noise arises from the ranom nature of light quite literally because the arrival rate (or emission rate) of photons is a iscrete, ranom process. Therefore, this kin of noise is not relate to any imperfection in the etector, the electronics, or any other aspect of the etection system. It is escribe by the Poisson istribution. Average number of photo-events per secon for flux : r h = quantum efficiency = probability of photon-electron conversion Average number of photo-events in time T: N rt T h The actual number of photo-events in any particular perio of time will fluctuate aroun this mean value. The probability of N events in time T is Poisson istribute. 11

12 Photon noise () Because in the Poisson istribution the variance equals the mean, the rms photon noise current is proportional to the square root of the mean photocurrent. Average photocurrent from a etector with integration time T i qn T Poisson variance = mean i qn qn q Photocurrent noise i i i i N N n T T T q N T qi T MS photon noise current using electrical banwith i n qi qif T Shot noise Here we ve use f 1 T q = electron charge = 1.6 x C 1

13 Photon noise signal-to-noise ratio (SN) Because in the Poisson istribution the variance equals the mean, the signal-to-noise ratio is proportional to the square root of the mean # of photo events. Signal-to-noise ratio = SN = i i i i n qn T q N T N This important result tells us that the photon-noise-limite (i.e., shot-noise-limite ) signalto-noise ratio is equal to the square root of the # of photo events uring the measurement. Thus, in photon counting, the SN is proportional to the mean # of photons. 13

14 Johnson noise Johnson noise arises from thermal agitation of electrons in a resistive element, which can be the etector, a feeback resistor in an electronic amplifier, or other element (most generally we nee to consier a total resistance). Essentially, the resistive element raiates blackboy raiation into the circuit. We can illustrate Johnson noise using an equivalent circuit containing an ieal (noise-free) resistor, in parallel with a noise-current source, or in series with a noise-voltage source. The equations below preict the mean current or voltage, which fluctuate with a Gaussian istribution. i n ktf v n 4kTf k = Boltzmann s constant = x 10-3 [J / K] T = physical temperature of the resistive element [K] f = electrical banwith [Hz] = resistance [] Derivation of Johnson noise equation: Kingston p

15 1/f noise At low temporal frequencies, nearly all etectors an electronic systems exhibit noise whose spectral ensity falls off with frequency accoring to approximately 1/f (this spectral ensity forms a straight line on a log-log plot, as shown below). The most effective way of reucing this noise is to moulate at a higher frequency Noise [V / Hz 1/ ] /f noise Thermal noise Frequency [Hz] Typical 1/f noise spectrum for a photoconuctor 15

16 Signal an noise currents The signal current for a signal photon flux s is i s qs h The total noise current can be foun as the square root of the sum of the squares of inepenent noise terms. For example, 4kTf i n isn ijn qif We can consier separate signal an backgroun shot noise terms with Johnson noise i n q f h 4kTf s bg 16

17 Signal-to-noise ratio (SN) Signal-to-noise ratio (SN) expresses the strength of the measure signal relative to the noise (electronic fluctuations) in the measurement. SN mean st.eviation i σ i A general signal-to-noise ratio equation can be foun from a ratio of the signal photocurrent to the rms noise current (remember that in optical etectors, photocurrent is proportional to photon flux or optical power). SN is i q qs h f s h bg 4kTf 17

18 Noise-Equivalent Power (NEP) The Noise-Equivalent Power is the optical power (or flux) that prouces SN = 1. We can relate the NEP to the responsivity, flux, an SN NEP s SN i is SN in i An equation for NEP can be foun by setting SN = 1 an solving for (= NEP). NEP is actually typically specifie in a spectral manner NEP NEPf f [W] [W Hz -1/ ][Hz 1/ ] 18

19 Specific etectivity D* The NEP cannot be use to compare two ifferent etectors because it epens on the square root of etector active area A an the square root of electronic banwith f. To compare ifferent etectors, we can efine the specific etectivity D* as the inverse NEP normalize by the square root of etector area an square root of the electronic banwith D * A f NEP A f SN A f q q h f s h bg 4kTf The NEP equations assume the following: 1. Noise is proportional to (f) 1/ (white noise). Noise is proportional to (A ) 1/ 3. Detector is at optimum bias 4. Detector is at optimum temperature 5. Detector frequency response is flat 19

20 Shot noise limit Shot noise is always present because of the quantum nature of photons an electrons. There are often other noise sources present, but if a system is esigne carefully to reuce all other noise sources to be much smaller than the shot noise, the system is shot-noise limite. SN SNL q f q f h s bg f s h NEPSNL SN1 s qs h bg 4kTf h s bg ~0 f qs h s h bg (set SN = 1 an solve for signal flux =NEP) s D * SNL A f NEP A h s bg hce hc Eq E = irraiance [W/m ] E q = photon irraiance [ph/(s m )] 0

21 Johnson noise limit (JOLI) When Johnson noise is the ominant noise source (much larger than shot noise) SN JOLI q qs h qs kt f 4kTf hc 4 f s h qs h bg ~0 4kTf NEPJOLI s SN1 hc q 4kTf D * SNL A f NEP JOLI q hc A f 4kTf q hc A kt A prouct often use for JOLI etectors. 1

22 Backgroun limit (BLIP) When the backgroun shot noise ominates, we achieve the conition sometimes referre to as BLIP = Backgroun Limite Photoetector. SN BLIP q s f q f hcfbg s h qs h bg qs h 4kTf bg h ~0 ~0 NEP BLIP s SN BLIP 1 hc fbg hc fq, bg hc f Eq, bg A D * BLIP A NEP f BLIP A hc bg hc A q, bg hc E q, bg

23 Temporal etector response Detectors, an the electronic circuits they are connecte to, cannot respon arbitrarily fast, which results in a temporal frequency banwith (this is the electrical banwith, not to be confuse with the optical banwith, which is the range of optical wave-lengths or frequencies over which the etector operates). The temporal banwith tells us how well the etector can istinguish between short optical pulses or reprouce the rising or falling eges of a signal. Furthermore, the temporal response also tells us how well the etector can recover an optical signal at a given moulation frequency. We will always use f to represent the temporal frequency (an for optical frequency). Generally, the responsivity of a etector will ecrease at higher temporal frequencies. Quite often the etector has a single time constant, typical of a C time constant of a low-pass filter type of electronic circuit. The time constant is etermine by the resistance () an capacitance (C) of the etector an its electronics. 3

24 Temporal etector response () When a elta-function raiation pulse is incient on a etector with a single time constant, the resulting output voltage signal (impulse response function) is a ecaying exponential: 0 t 0 v( t) t v 0e t 0 Because a elta function contains an infinite range of frequencies, the corresponing responsivity is proportional to the Fourier transform of the impulse response function: V ( f ) v( t) e v t 1 jf jft 0 Using 0 = v 0 /A to represent the c responsivity (A = impulse amplitue), the etector s frequency response is given by the responsivity as a function of f 0 ( f ) 1 jf Whereas the complex-value responsivity tells us there is a phase shift between input an output, ( f sometimes we only nee the magnitue ) ( f ) * ( f ) 1 0 f 4

25 Temporal cutoff frequency an rise time Cutoff frequency = temporal frequency at which ( f ) falls to one-half its maximum value. f c 1 For a step-function input, the single-time-constant etector prouces an output of the form v( t) 0 1 e t 0P0 t t 0 0 The rise time of a etector system is commonly efine as the time it takes for the output to rise from 10% to 90% of its peak value. This criterion in the equation above prouces t r f c 90% 10% t r 5

26 Electrical banwith Electrical banwith (sometimes calle the noise-equivalent banwith) is the range of temporal frequencies over which the etector collects signal an noise. It is inversely relate to the integration time For a etector whose responsivity has a maximum max an varies arbitrarily with electrical frequency, we can efine the electrical banwith as f 0 ( f max ) f, Note: the square of the normalize responsivity is use to refer to the power of the electrical signal an noise. 6

27 Two examples of electrical banwith 1. Detector with a single time constant f 0 f 1 1 f 4. Detection with a temporal integration over time T: Frequency response T ) ( f ) 0 T 0 j ft e t T sin( ft ft f 0 sin( ft) ft f 1 T 7

28 Power spectral ensity & autocorrelation The power spectral ensity S(f) is the amplitue square of a function s Fourier transform. It can be thought of as the electrical power per unit frequency for a voltage across a 1- resistor. S ( f ) F v (t) V ( t) e jft t [W / Hz] Autocorrelation: 1 C( t1, t) v( t1) v( t) v( t) v( t ) v( t) v( t ) t T T T Wiener-Khinchine theorem: states that the autocorrelation an power spectral ensity are a Fourier transform pair. That is, if you take the Fourier transform of an autocorrelation, you obtain the function s power spectrum. F C ( t, ) 1 t S( f ) 8

29 Spectral response A etector s response is funamentally a function of electromagnetic frequency or wavelength. This epenence is often inicate without reference to the temporal response at all, but sometimes we combine the two with the following notation: ( ; f ) responsivity at wavelength for electrical banwith f. This is especially common in etector testing. For example, It is very common for etector manufacturers to specify a responsivity value at the wavelength of peak response an with an electrical banwith of 1 Hz, which implies a measurement with an averaging time of 1 secon. This sort of 1-secon-banwith specification is common for responsivity an other etector figures of merit. To fin the responsivity (or other specification) for an actual electrical banwith when you re given the specification at a reference banwith f ref ( ; f ) ( ; f ref ) f f ref 9

30 Detector cooling Long-wavelength etectors (e.g. for infrare an mm-wave raiation) often nee to be coole so that their own thermal energy is below that of the raiation to be etecte. It is far more common for photon etectors to require cooling, although we will encounter a few coole thermal etectors. A photon etector must be coole to a temperature where the probability of charge carriers being thermally excite above the etector bangap is low. Because these thermally excite charge carriers flow even in the absence of incient raiation, this process results in what we call ark current. As the wavelength of raiation to be etecte becomes shorter, the require etector bangap becomes smaller, thereby increasing the nee for cooling. Material co E gap kt % of E gap Si 1.1 m 1.1 ev 0.06 ev (300 K).3% InSb 5.6 m 0. ev ev (180 K) 6.8% 0.06 ev (300 K) 11.8% HgCTe ~10 m 0.1 ev ev (77 K) 5.5% 0.06 ev (300 K) % (aapte from G. Boreman, Table 5.1) 30

31 Photoemissive etectors Photomultiplier tubes are the most common etector that operates through photoinuce electron emission. In the external photoelectric effect, a surface emits electrons when struck by photons of sufficient energy. Metals Semiconuctors energy vacuum Fermi work function energy E g vacuum conuction ban Valence ban Smallest photon energy that can generate electron emission: h h E g 31

32 Photomultiplier tubes (PMTs) Photomultiplier tubes exploit the external photoelectric effect to create a etector with high gain an low noise. Incient photons pass through a vacuum-tube housing an strike a photocathoe, proucing electrons. A high voltage is use to accelerate the free electrons through the vacuum tube, from the cathoe to an anoe. The voltage is ivie in such a way that progressively higher voltage appears at each subsequent ynoe, causing the free electrons to be accelerate through the entire ynoe chain. More electrons are ejecte from each anoe, causing a large multiplicative gain, G. At the cathoe, the electron stream is capture as photocurrent. PMT Avantages: High gain Low noise (shot-noise, typ.) capable of photon counting h cathoe vacuum housing anoe ynoes L V out PMT Disavantages: Vacuum tube (fragile) High voltage (typ. 1-3 kv) -HV 3

33 PMT gain Photomultiplier tubes provie high gain through seconary electron emission from the ynoe chain, with low noise. PMTs typically are limite by shot noise in either the ark current or signal. Dark noise in PMTs arises through thermionic emission from the cathoe an can be reuce through cooling (typ. ~ 30 K). At high levels of photocurrent, the negative charge of the ense electron stream between the last ynoe an the cathoe begins repelling electrons leaving the ynoe. Such space-charge effects create an upper limit to PMT ynamic range. PMT gain: G N = Seconary emission ratio = average # of lowerenergy seconary electrons emitte by a surface when hit by a high-energy primary electron (epens on surface material an electron accelerating voltage). N = # of ynoes Typical values: N = 9, = 4 G =.6 x 10 5 Note: the epenence of gain on ynoe voltage (through means that PMTs require a very stable high-voltage supply. 33

34 PMT spectral response Photomultiplier tubes rely on the photoelectric effect, which requires reasonably high photon energies. Therefore, PMTs are only practical at visible an shorter wavelengths. Long-wavelength rolloff typically a property of the photocathoe material (energy levels). Short-wavelength rolloff typically cause by the winow Transmittance. Note that typical quantum efficiency ~

35 PMT ata sheet Burle

36 PMT ynamic range PMTs have large ynamic range (can be ~ 10 orers of magnitue) that is limite by ark current at the low en an space-charge effects at the high en. The large-current limit is where the ense electron clou between the last ynoe an the anoe begins to repel electrons streaming in from the ynoe. The low en is limite by ark current, typically arising from thermionic emission from the cathoe. Dark current can be reuce by cooling the PMT. ~ i Space-charge limit Anoe current (A) G i i ark-current limit aiant flux (W) 36

37 PMT photocurrent rms current generate by raiation of frequency an optical flux [W]: q i h rms current generate by photon flux p [photons/s]: i q p Cathoe current is the sum of signal current an ark current: i c i i q i h Anoe current is the prouct of PMT gain an cathoe current: ia Gi c 37

38 PMT noise Principal noise sources for a PMT are shot noise (in signal an ark current) an fluctuations in the number of seconary electrons prouce for each primary-electron impact, generating gain fluctuations. esistors can cause Johnson noise to be a factor as well. rms shot noise in the cathoe current: i q i i f q i f shot q h Total rms noise in the anoe current of a PMT, incluing amplifie shot noise an Johnson noise from the effective resistance of the voltage ivier: i n qg i i f 4kTf qg q i h f 4kTf Note: want high an G to achieve shot-noise limit. 38

39 Shot-noise-limite SN for a PMT PMTs are quite often shot-noise limite, in which case the gain rops out of the equation for signal-to-noise ratio (also assuming constant gain). Anoe SN: SN a i i a n Gi i n c qg Gi i i f qic i f c c i c This says that the SN of the anoe photocurrent is the same as the SN for the cathoe photocurrent. Ignoring ark current, this is the same as the SN in the incient photon stream egrae by imperfect quantum efficiency. The resulting SN is etermine from Poisson statistics for mean # of photons n : SN out SN in n E. Dereniak an D, G, Crowe, Optical aiation Detectors, Wiley

40 PMT responsivity an NEP Current responsivity of a PMT photocathoe: i q h Noise-Equivalent Power (typically limite by shot noise in the ark current ): i n h NEP qif q PMTs are one of the very fastest etectors, offering temporal response times of nanosecons. 40

41 Miscellaneous PMT effects After pulsing One of the more annoying things to eal with in PMT signals is calle after pulsing. This is a ringing effect that resembles echoes of a bright pulse. Two possible mechanisms are 1) light feeback to the cathoe from the ynoes or anoe (elay ~ 50 ns); ) ionization of gas between cathoe an first ynoe (elay ~ 00 ns 1 s). (gas ions hit the cathoe an generate an echo). Increase ark current from short-wave light exposure A PMT expose to bright blue or near-uv light will exhibit elevate ark current for many hours after exposure. Therefore, PMTs shoul be store in the ark. Sensitivity loss over time The loss of material from ynoe surfaces, an possibly other effects, cause a PMT to lose sensitivity over time. This loss is mae worse when the tube is operate with high current (an can, in fact, partially correct itself uring perios of low-current operation). Expecte lifetime of a PMT can be thousans of hours. Much more info in the Photomultiplier Hanbook, Burle, 1980 (www. Burle.com) 41

42 Photon-counting PMT moules ecently companies have begun selling photon-counting moules, which contain a PMT an all the electronics require to etect an iscriminate iniviual photon pulses. These moules are extremely convenient because you simply connect a 5V power supply, point it at your light source (not too bright!), an count TTL pulses coming out the back. Example: Hamamatsu H859 photon-counting hea Dark counts: ~ s -1 usa.hamamatsu.com 4

43 Avalanche photoioes Avalanche Photoioes (APDs) behave like soli-state PMTs in that they use an avalanche process to achieve large internal amplification of photoelectrons. High reverse bias voltage (~ 1000 V) across narrow intrinsic layer creates strong local electric-fiel graient. High photoelectron energy creates aitional free carriers Avalanche process prouces electron multiplication, resulting in photocurrent with high gain (~ 10 3 ). i i light v Avalanche current Fun Java tutorial: 43

44 APDs for photon counting An exciting evelopment in the last ecae is photon-counting APD moules, similar to the photon-counting PMT moules we iscusse earlier. There are several reasons you might choose an APD over a PMT for photon etection Avantages of APDs: + high quantum efficiency (~ ) + immune to magnetic fiels + require low currents + fairly robust Disavantages of APDs: - relatively high ark current - much smaller active area than PMT (~ 100 m) = 9% at 830 nm Max rate: 10 6 s -1 Dark count ~ 00 s -1 Diameter = 175 m 44

45 Photovoltaic etectors Photovoltaic etectors require a potential barrier to operate, which usually takes the form of a p-n junction in a semiconuctor. When a photon creates an electron-hole pair, the electric fiel across the junction prevents recombination an the carriers create a current. Photovoltaic etector energy ban iagram: E potential barrier e- E g h p region n region hole 45

46 PV (photoioe) photocurrent qv kt iark i0 e 1 Dark current through a p-n junction ioe (i 0 = reverse saturation current, strongly epenent on temperature): Current through a p-n junction ioe with light incient: i qv kt light i 0 e 1 qe p A iark ip Photocurrent i p is the short-circuit current, which is a linear function of incient flux over a ynamic range of ~ i p i light v 0 qe p A q p q hc i i ark i light Open-circuit voltage v oc kt q i ln p i i 0 0 i 0 v oc v Photovoltaic power generation (solar cell) for 0<v<v oc an 0<i<i p into a loa resistor. I p 46

47 Ieal PV responsivity Photovoltaic etectors usually are use as current sources with current responsivity: i i p q hc [A/W] i The ieal responsivity increase oes not mean the etector is funamentally better at longer wavelengths. ather, it is a consequence of using Watts instea of photons. c As E photon So for a constant # of photons, an i The ieal photon current responsivity is spectrally flat. ip i p p qe E p p A A q ip c 47

48 Actual PV responsivity The actual responsivity spectrum rolls off at both short an long wavelengths because of photon absorption at the etector surface, wavelength epenence of the absorption an other semiconuctor properties, etc. The non-unity value of quantum efficiency is a consequence of Fresnel reflection from the etector surface, surface traps or recombination centers, etc. ip c Voltage responsivity can also be foun by multiplying the current responsivity by the etector resistance,. v i [V/W] 48

49 Transimpeance amplifier for PV etector Transimpeance amplifiers often are use to amplify the PV short-circuit current. The operational amplifier has a virtual groun at the inverting input (-), so in the amplifier shown here, the etector is effectively short circuite. The result is that the current through the feeback resistor is the short-circuit current. f h - + V o = -i p f 49

50 PV temporal frequency response The temporal frequency cutoff epens on the effective resistance an capacitance of the etector an its circuit loa, as inicate in the equivalent circuit an frequency plot below. s v o C L Total effective resistance: t s 1 L 1 f c C t f Example (typical silicon photoioe into short circuit): C = F = 10 9 s = 0.01 L = 50 f c = 30 MHz Note: it is possible to reuce the capacitance by aing a reverse-bias voltage to the positive input of the op-amp, increasing the with of the p-n junction epletion region (& aing noise). Or, an intrinsic layer can be ae to wien the epletion region, resulting in a PIN ioe. 50

51 PV etector noise current Noise generate by PV etectors inclue 1/f an Johnson noise; photon noise in the signal an backgroun photon stream shows up as shot noise. Because a PV etector usually operates into a virtual short circuit (v=0), only the photon-generate current is nonzero (see eqns for photoioe current). 4kTf s b Total rms noise current: i q E E A f n Bi f f p p k = Boltamann s constant = 1.38 x 10-3 [J/K] T = temperature [K] f = electrical frequency banwith [Hz] = etector resistance [] B = constant epening on etector material i = mean (DC) current flowing through etector [A] = typ. (can be ~ 1.5 4) = typ. 1 (can be ~ ) q = electron charge [1.60 x C] = quantum efficiency E ps = signal photon irraiance [ph / (m s)] E pb = backgroun photon irraiance A = etector active area [m ] = etector resistance [] Total rms noise voltage: v n i n 51

52 Photovoltaic etector SN an NEP Fin the SN by iviing the mean photocurrent by the rms noise current. SN pv i s i i i s n q s hc bg qs hc f 4kTf Bi f f The SN an NEP equations for the shot-noise limit, JOLI, an BLIP conitions are all exactly the same as for the general cases escribe in slies

53 53 D * for PV etector an transimpeance amplifier Incluing amplifier noise voltage v amp an the Johnson noise of the feeback resistor f, the total noise voltage for a PV etector is amp 4 4 v v b p s p f f n f A E E q f f Bi f kt f kt f A q E A q f Bi A q kt A q kt hc D p f f amp * 4 4 v... * hc q f f D n n v A v A v Then the D * can be foun from

54 BLIP PV etectors In high-performance PV etectors, 1/f noise often is eliminate by ajusting a variable bias voltage on the positive op-amp input to where the net c current is zero. Also, the amplifier noise can be reuce to where it is negligible. Uner these conitions, the D* is D * (, f ) hc 4kT q A 4kT f q A f E p Photon noise ominates if the following uncertainty is satisfie: Conitions that lea to this being true inclue: low resistor temperatures, high quantum efficiency, an high A prouct. k E p q A T T f f The etector can then be backgroun limite: D * BLIP(, f ) hc E p 54

55 BLIP an actual D* for PV etectors PV PC Dereniak & Boreman, Infrare Detectors & Systems, Wiley

56 JOLI PV etectors Uner conitions of extremely low backgroun irraiance, PV etectors usually are limite by Johnson noise. For example, space sensors often have Johnson-noise limite PV. Previous D* eqn w/only Johnson. D (, f ) hc q * JOLI kt A kt f f If the sensor uses a coole feeback resistor that isn t too large, then D A kt * q i JOLI (, f ) hc A kt Note that a large A prouct helps achieve either BLIP or JOLI operation. 56

57 Photoconuctive etectors Electron-hole pairs are create When light impinges on a photoconuctive semiconuctor (homogeneous, with no junction). The increase charge-carrier ensity is manifeste as a larger electrical conuctivity. A bias voltage is require to measure the conuctivity change. Although a photoconuctive (PC) etector is mae of homogeneous material, it can be either intrinsic (pure) or extrinsic (ope). The aition of an impurity into an intrinsic semiconuctor (oping) results in energy levels that can lie between those of the intrinsic material, allowing etection of raiation at longer wavelengths. However, extrinsic PCs have lower quantum efficiency because of the relatively low opant concentration. Electron energy Conuction ban h Valence ban electron hole impurity level Intrinsic E g ope E g 57

58 PC etector examples Photoconuctor cut (m) Camium Sulfie (CS) ~ 0.7 (low cost, room temp.) Silver Chlorie (AgCl) 0.4 (ultraviolet - violet) Germanium (Ge) 1.8 Lea sulfie (PbS) 3 Lea selenie (PbSe) 4.5 (TE coole ~ 53 K) Mercury Camium Tellurie (HgCTe) 5 (LN coole ~ 77 K) Inium-ope Silicon (Si:In) 7 Mercury-ope Germanium (Ge:Hg) 14 Gallium-ope Germanium (Ge:Ga) 00 (He coole ~ 4 K) CS photocell HgCTe Typical NEP: to 10-1 W (except CS, which is a very low-cost sensor use in camera light meters, automatic light turn-on/off switch, etc. Photos: usa.hamamatsu.com HgCTe coolers 58

59 Photoconuctor = light-sensitive resistor Photoconuctive etectors are light-sensitive conuctors whose resistance varies inversely with the amount of incient light. A PC etector usually is use in a circuit that allows measurement of the etector resistance compare to that of a known loa resistor. L V o V b h CS resistance-light curves: usa.hamamatsu.com 59

60 PC theory Photoconuctors exhibit a relative conuctivity change owing to increase charge-carrier concentration create by absorbe photons. This relative conuctivity change is given by: s q( e h p L ) A W = electrical conuctivity per unit length [1/( cm)], q = electron charge [1.60 x C], e, h = mobility of electrons an holes, respectively [cm /(s V)], = quantum efficiency p s = signal photon flux [photons/s], L = carrier lifetime [s], A = etector active area [cm ], W = etector thickness [cm]. In practice, we usually think of a change in resistance rather than conuctivity (where the minus sign inicates the inverse relationship between conuctivity an resistance): s q( e h) p L A W E. Dereniak an D, G, Crowe, Optical aiation Detectors, Wiley

61 PC theory () The photon-flux expressions can be expresse in terms of signal power in Watts through the use of. s h s p hc s p s q ( e h) L hc A W V b L V o h The output voltage from the Vb L voltage-ivier circuit is. V o L The change in output voltage for a change in etector resistance is foun by ifferentiating V o (This, then, represents the AC signal voltage that fluctuates aroun the mean DC voltage): V o V b L L Substituting from the equation above: v 0 V b L L q L ( e h) s hca W E. Dereniak an D, G, Crowe, Optical aiation Detectors, Wiley

62 PC theory (3) The voltage responsivity is foun by iviing the AC voltage by the signal power an replacing V b /( L + ) with the DC current i: v V o s iq L e h hca W L L [V/W] The current responsivity is foun by iviing the output voltage by the loa resistance, which gives the current through the loa resistor: i i s Vo s L iq L e h hca W L [A/W] E. Dereniak an D, G, Crowe, Optical aiation Detectors, Wiley

63 PC spectral response The ieal photoconuctor responsivity (previous page) is linearly epenent on wavelength, suggesting that a PC etector s response becomes steaily larger at longer wavelengths. however, several practical issues cause the actual PC responsivity to eviate from ieal at both short an long wavelengths. Short-wave response is limite by Fresnel reflection losses at the etector surface Long-wave response is limite funamentally by photoconuctor material bangap, but also rolls off towar this cutoff because of increasing transmission through the etector at longer wavelengths (corresponing to ecreasing reflection, consistent with the increasing reflectivity at shorter wavelengths, which limits short-wave ). v ieal actual Wavelength c 63

64 Photoconuctive gain If we rearrange the equation for current responsivity, we can express it as i q hc G pc With the photoconuctive gain for extrinsic semiconuctors efine as G pc i L ( e h) A W L E l L = carrier lifetime time constant = ominant carrier mobility E = electric fiel [V/m] l = spacing between etector electroes [m] For uniform electric fiel E, we typically have 0.5 < G pc < 1 (= 0.5 for low backgroun light). However, for some etectors (such as PbS), natural or inuce iscontinuities in the semiconuctor cause localize regions of high electric fiel where carriers experience increase velocity. The result is an amplifie photocurrent that can be represente with a large value of G pc, much greater than 1. 64

65 Generation-recombination (G-) noise G- noise is unique to PC etectors. It shows up as fluctuations in free carrier concentration, cause by fluctuations in electron-hole generation rate an recombination rate. G- noise has a thermally inuce component, which is negligible for most coole PC etectors, an a photon-inuce component that appears as photon noise in coole PC etectors. rms G- noise current in a coole photoconuctor: i G qgpc ( E p A ) f q = electron charge G pc = PC gain = quantum efficiency E p = photon irraiance [photons / (m s) f = electrical banwith [Hz] Note that G- noise is a form of photon noise, with a magnitue that is larger than shot noise. This can be consiere to be a consequence of either: 1) two inepenent ranom processes (generation rate an recombination rate), ) two inepenent irections of electrical conuction in a PC. E. Dereniak an D, G, Crowe, Optical aiation Detectors, Wiley

66 PC noise & temporal frequency response Principal noise sources in a photoconuctor are: 1. 1/f noise, which usually is avoie by signal moulation. G- noise (photon noise) 3. Johnson noise (thermal noise) Each ominates in its own range of temporal frequencies, as shown here. i n 1/f G- carrier-lifetime roll-off (6 B/octave) Johnson 1 f (Hz) L Note: typical response times for PC etectors are on the orer of s. 66

67 PC Johnson noise For operation of a PC in the circuit shown below, both the loa an etector resistances must be inclue, along with their respective temperatures, in calculating Johnson noise. V b L V o i 4kf J T T L L h 67

68 Photon-noise limite PC Photon noise is always present, since it arises as a funamental consequence of a quantize, stochastic photon flux. Therefore, the ieal situation is to have all other noises be much smaller than the photon noise. For this to occur, at moulation frequencies above the 1/f range, the mean-square G- noise must ominate the mean-square Johnson noise: i G i J or T 4q G pc E p A f 4k f L T L Often the loa resistor is mounte on the same heat sink as the etector, a situation which also helps reuce Johnson noise if the etector is coole. Uner this conition, the two temperatures are equal an we can solve for the temperature/resistance ratio (when this inequality hols, the PC etector is photon-noise limite): T eff q G pc E k p A Where eff is the parallel Combination of L an 68

69 Backgroun-limite PC If the irraiance on a photon-noise-limite etector is primarily from backgroun light, the etector is sai to be backgroun-noise limite. Because this most often occurs at thermal infrare wavelengths, the situation usually is calle Backgroun Limite Infrare Photoetector (BLIP). NEP BLIP (, f ) i G i qg pc E B p q G hc pc A f hc E B p A f D * BLIP, f A NEP f BLIP hc B E p E p B = backgroun photon irraiance [photons / (m s)] 69

70 BLIP an actual D* for PC etectors BLIP PV PC Dereniak & Boreman, Infrare Detectors & Systems, Wiley

71 BLIP an actual D* for extrinsic PCs Dereniak & Boreman, Infrare Detectors & Systems, Wiley

72 JOLI PC As we reuce the photon irraiance on a etector, the BLIP D* gets larger (i.e. better). However, at some low value of irraiance, Johnson noise becomes ominant. We then leave the BLIP omain an enter the Johnson-Noise-Limite (JOLI) moe. NEP JOLI (, f ) i J i TL 4kf L q Gpc hc T If T = T L = T, an if L <<, then NEP JOLI (, f ) hc qg pc 4kfT eff D * JOLI, f A NEP f JOLI q hc G pc kt eff A Note: A prouct is use as a figure of merit for JOLI etectors (bigger is better). 7

73 Low-noise PC amplifier Especially for high-performance photoconuctors, carefully esigne low-noise amplifiers must be use. The circuit below is an appropriate voltage amplifier. Dereniak & Boreman, Infrare Detectors & Systems, Wiley 1996, 73

74 Thermal etectors The etection mechanism for this class of etectors is to measure a temperature change that results from absorbe raiation. Often the temperature change is measure through a temperature-epenent resistance or other parameter. This is funamentally ifferent from a photoconuctor, however, because no electron-hole pairs are create irectly by the absorbe raiation. In fact, some thermal etectors absorb raiation in a black surface coating, which transfers heat to the unerlying temperature-epenent resistor material. In this manner, the absorption an resistance changes are ecouple. Avantages Nearly flat spectral response over extremely wie wavelength range (Typ. limite by winow or material absorption) Capable of uncoole operation at long wavelengths. Disavantages Low sensitivity (NEP ~ W) Slow temporal response (~ ms) relate to thermal mass Easy to use; low cost 74

75 Bolometers Bolometers are one of the olest optical etectors still in wie use. Develope by Langley in 1881, a bolometer etects raiation through a resistance that changes when the etector material is change by absorbe raiation. Bolometers are the thermal equivalent of a photoconuctor, but they have no bangap an o not operate through a photon mechanism. Temperature Coefficient Fractional resistance change per egree of temperature change 1 T material %/ o C semiconuctors ~ -0.5 metals ~ 0.5 superconuctors ~ 10 3 Typical ~

76 Bolometer responsivity Bolometers, an most thermal etectors, are analyze with heat-balance equations (see Dereniak an Boreman, Infrare Detectors an Systems, Wiley 1996, p. 413 for the etails). Voltage esponsivity: v v b 4Ke 1 th = temperature coefficient of resistance [%/K] = etector emissivity (equal to the absorptivity) V b = bias voltage [V] K e = effective thermal conuctance from element to heat sink [W/K] = raian frequency = f [s -1 ] th = thermal time constant [s] v Thermal etectors can be esigne to trae lower responsivity for faster response. f Typ. cutoff frequency ~ Hz 76

77 Bolometer circuit Bolometers can be use in a voltage-ivier circuit (like a PC), but a more accurate metho is to use a brige circuit with two ientical etectors, with one element shiele from light to remove any ambient-temperature epenence. 1 v b v o v b 4 (V o across ) 3 77

78 Backgroun-limite bolometer Bolometers usually exhibit Johnson noise an Temperature noise (which is a fluctuation in the etector temperature cause by photon noise in the incoming raiation). Photon-noise-limite operation is possible if we reuce the Johnson noise sufficiently. Since thermal etectors o not really respon to photons irectly, it is not really proper to call this photon-noise-limite operation, but it is common to o so. In reality, we are referring to the noise in the incoming raiation flux. NEP 8A kf T 5 T 5 b A = etector active area [m ] k = Boltzmann s constant = 1.38x10-3 [J/K] f = electrical banwith [Hz] = Stefan-Boltzmann constant [5.67x10-8 W/(m K 4 )] T = etector temperature [K] T b = backgroun temperature [K] = etector emissivity Example A = 1 mm, = 1, T = T e = 300 K, f = 1 Hz NEP = 5.6 x 10-1 W Hz -1/ (T = 0 only gives us!) 78

79 Low-temperature bolometers Although simple bolometers often fin use in low-cost room-temperature systems, much more sophisticate bolometers quite often are coole for high-sensitivity etection of weak raiation in a wie spectral range. A common application of this sort of high-en bolometer is astronomical imaging in the mm-wave an far-infrare wavelength ranges. Germanium bolometers are coole with liqui helium to ~ 3-4 K. To achieve cooling to such low temperatures, usually the helium ewar is insie of a liqui-nitrogen ewar (77 K). Low-temperature bolometers provie high sensitivity but slow response. NEP ~ W f c ~ 100 Hz Dewar rawing: 79

80 Sub-mm-wave imaging with bolometers The Submm-wave Common User Bolometer Array (SCUBA) is a sub-mm-wave camera use on the James Maxwell Telescope on Mauna Kea in Hawaii. It can image in several bans within m on a bolometer array that is coole with liqui helium. 80

81 Microbolometers Microbolometers are not cool. That, in fact, is their primary attraction they allow infrare imaging without a troublesome liqui-nitrogen ewar. The technology for microbolometers, evelope by Honeywell in the 1980s uner classifie military contracts, was eclassifie in 199. In the last ecae, the commercial market for uncoole infrare imagers has experience extraorinary growth. Microbolometers are mae with silicon micromachining. Each pixel is a miniature bolometer that changes resistance in response to a temperature change. Silicon nitrie (Si 3 N 4 ) coate with a thin film of bolometric vanaium oxie (VO x ). h Silicon nitrie legs Silicon substrate (monolithic transistors).5 m eflective layer 81

82 Microbolometer noise Microbolometers experience Johnson noise an temperature noise in a manner similar to that of iscrete bolometers. The analysis an equations are basically the same. A common figure of merit for infrare imagers is the Noise Equivalent Temperature Difference (NETD). o = optics transmittance; (E/T) = blackboy irraiance change with temperature, measure within spectral ban. NETD A o 4F v v n ΔE ΔT F = 1/(sin), where is the half angle of the light cone focuse by the optics to the etector. With the optics focuse at infinity, F F # f / D. 8

83 Pyroelectric etectors Pyroelectric materials are ielectrics that possess a natural polarization in the absence of an electric fiel. When incient raiation heats the etector, the crystal lattice expans an prouces a temperature-inuce change of polarization (material polarization, not EM-wave polarization). The change in surface-charge ensity constitutes a current. The etector respons only to changes in incient raiation. A pyroelectric etector has zero response to raiation that is not changing in time, regarless of brightness. The temporal response is limite by thermal mass (not pyroelectric effect). Common pyroelectric materials triglycerine sulphate (TGS) lithium tantalate (LiTaO 3 ) strontium barium niobate (SBN) Common absorbing coatings (enhances sensitivity) gol black carbon black organic black Applications of pyroelectrics range from low-cost motion etectors to high-en imagers

84 Pyroelectric current ecall that in soli state physics, the term polarization means a surface-charge ensity (this is totally ifferent from the concept of wave polarization, which escribes the irection of preferre wave oscillation). Charge ensity on the electroes flow because of an external bias voltage, which creates a photocurrent. Pyroelectric current is proportional to the time erivative of temperature: T i p( T ) A t p(t) = pyroelectric coefficient [C/(m K) (typ ) A = etector active area [m ] T = temperature [K] t = time [s] For the equivalent circuit shown below for a pyroelectric etector, the current is a function of raian frequency : i p A T C v o 84

85 v o i Z Pyroelectric temporal responsivity The output voltage is given by the prouct of current an impeance: 1 jc i 1 1 C jc i i 1 e e = electrical time constant The temperature change can be expresse as (Dereniak & Crowe p. 48): T P t 1 t = etector emissivity P = incient optical power [W] t = thermal resistance to heat sink t = thermal time constant [s] Following etails in Dereniak & Crow, p. 48, an using r = pyroelectric coefficient of the etector material, the resulting voltage responsivity is: v t 1 e 1 t A 85

86 Pyroelectric temporal responsivity () The output voltage given on the previous page prouces two frequency break points, one electrical an one thermal. The responsivity can be foun by iviing the output voltage by the optical power, as shown below. v pa 1 e 1 t t v f t f e f Note: in practice, the etector resistance is replace by the parallel combination of etector an loa resistance. Because the loa usually is much smaller, the parallel combination usually is effectively equal to the loa resistance. 86

87 esponsivity variation with loa resistance There is a traeoff between responsivity an temporal banwith. A higher loa resistance generates a higher peak responsivity, but with a lower-frequency electrical cutoff. Dereniak & Crowe, Wiley

88 Noise in pyroelectrics Primary noises in pyroelectrics are temperature noise (thermal manifestation of photon noise), Johnson noise of the etector, Johnson noise of the loa, an preamplifier noise. Temperature noise usually is irrelevant because pyroelectric etectors are not often backgroun limite. Preamplifier noise is mae to be less than etector noise in a goo esign. Johnson noise usually is the ominant noise source in pyroelectrics. rms Johnson noise voltage: v J 4kT f NEP JOLI v J v 4kTf 1 1 p t e A t D * JOLI A f NEP JOLI p A t 4kT 1 e 1 t A 88

89 aio etectors Some common etectors of raio energy inclue Schottky-barrier, PIN, an tunnel ioes. These are essentially very long-wavelength photoioes (often JOLI moe). Common specifications: Electromagnetic Frequency ange [Hz] Sensitivity [mv/mw] Tangential sensitivity = signal power for SN = 8 B at the amplifier output [Bm]. VSW (voltage staning wave ratio) = relative amplitue of the staning wave forme by the superposition of incient an reflecte waves (ieal value is 1)

90 UV etectors Ultraviolet sensor systems often nee to view uv raiation without seeing visible an longerwavelengths. Ultraviolet photons have high energy, but the Earth s atmosphere oes not transmit this raiation well at most wavelengths, so vacuum operation is necessary. One uv etector type of current interest is wie-bangap semiconuctors, such as Gallium Nitrie (GaN). The bangap is large enough that visible photons are not etecte, allowing solar-blin operation. Another type of uv etector is a vacuum tube containing gas that emits electrons when hit by energetic ultraviolet photons. This kin of etector is use in flame etectors. usa.hamamatsu.com Microchannel plates (MCPs) are the most common uv etectors. These are photon-counting etectors that are Similar to photomultiplier tubes. They contain numerous conuctive glass capillaries fuse together an cut into a thin plate. Each capillary acts as an inepenent seconaryelectron multiplier. MCPs respon from the uv to x-rays an can be use as imaging etectors when combine with a phosphor screen. 90

91 X-ay etectors X-ray etectors often use a combination of an x-ray capturing scintillation plate an a visiblelight etector. The scintillation plate emits visible photons when hit by x-rays; the optical etector then sees the visible photons. Photon etectors use in these arrangements inclue photomultiplier tubes, microchannel plates, CCDs, an photoioes. The type an thickness of scintillator etermines the energy range of x-rays that are capture. Common scintillator materials are crystals of camium tungstate an cesium ioie, or phosphor layers eposite on screens. If coole (typically with Peltier coolers), these etectors an their electronics are often x-ray quantum-noise limite (i.e., photon-noise limite by fluctuations in the x-ray stream), which is the theoretical ieal. 91

92 Charge-couple evices (CCDs) CCDs cause the igital imaging revolution. The Charge-Couple Device (CCD) concept was propose by Boyle an Smith in an the first evice was built by Amelio, Tompsett, an Smith in The CCD is a microelectronic system for moving charge aroun after it has been collecte by an optical etector. This mae it possible to collect an transfer charge from etector arrays base on silicon microelectronic technology, thereby proviing low-cost prouction of high-en igital imaging systems. CCDs serve three functions: charge collection charge transfer charge-to-voltage conversion A CCD can be couple to a variety of etector arrays. For example, visible-wavelength Imagers usually use monolithic CCDs built together with silicon photoioes or photo gates (Metal Oxie Semiconuctor, or MOS, capacitor). MOS capacitors in the CCD control the transfer of electronic charge prouce by the etectors. Infrare arrays can use a hybri CCD with long-wave photo-conuctor arrays (e.g. HgCTe). 1 W. S. Boyle an G. E. Smith, Charge Couple Semiconuctor Devices, Bell Systems Technical Journal 49, (1970). G. F. Amelio, M. F. Tompsett, an G. E. Smith, Experimental Verification of the Charge Couple Dioe Concept, Bell Systems Technical Journal (1975). 9

93 CCD charge collection The basic element of a CCD is a Metal-Oxie-Semiconuctor (MOS) capacitor. Voltage applie to the gate repels holes, creating a epletion region. Photon absorbe in the silicon layer creates an electron-hole pair. The epletion region acts as a potential well that collects electrons. Well capacity is proportional to the applie voltage, silicon layer thickness, an gate electroe area (well capacity = # of electrons that can be store). polysilicon gate epletion region v gate h silicon oxie insulator layer p-type silicon 93

94 CCD charge transfer Once electrons are collecte in a MOS capacitor, the charge is transferre from one gate to the next, until it reaches the reaout. 1 1 well 1 well potential charge in well 1 voltage applie to well equal charge reuce gate 1 voltage full charge transferre Aapte from G. C. Holst, CCD Arrays, Cameras, an Displays, SPIE

95 CCD charge reaout Each row of pixels is shifte own into the next row. The last row is rea out in a horizontal Serial shift before the next ownwar parallel shift occurs. channel stop parallel shift own serial shift across 95

96 CCD terminology Charge Transfer Efficiency = efficiency of charge transfer from one gate to the next ( means that 99.99% of the charge is transferre). ea noise = uncertainty in charge measurement at reaout amplifier output [electrons]; this etermines the smallest packet of charge that can be measure. Focal Plane Filling Efficiency = ratio of photo-active area to total area in a etector array. 96

97 CCD architectures Full Frame (FF) Frame Transfer (FT) Imaging array equires shuttering to avoi smearing. Imaging array Image transferre in parallel at high spee. serial reaout Useful for astronomy Storage array serial reaout Storage array rea out at normal spee. Interline Transfer (IT) Frame Interline Transfer (IT) FT & IT combine. Fast frame rate. Low smear. x H resolution loss. Storage array Faster frame rate. serial reaout Aliasing problem in H. serial reaout Can elec. shutter. 97

98 Color CCDs Other than the inherent bangap- an material-inuce wavelength sensitivity, CCDs o not have any metho of selecting a specific wavelength for etection. Therefore, to prouce a color CCD camera requires the aition of some sort of color filter. 3-chip color camera Bayer pattern of colore filters Two green pixels for each re an blue Because the human eye is much more Sensitive to green (also, green carries more image information to the human eye-brain system than other colors. 98

99 Noise in CCD imaging In CCD imaging, noise is expresse in units of electrons. CCD imaging is affecte by noise in each of the three CCD operations: noise in the etector (charge collection) noise in the CCD MOS array (charge transfer) noise in the preamplifier output (charge-voltage conversion) etectors CCD preamplifier output signal + backgroun optics photon noise Johnson noise input noise transfer loss noise trapping noise ark current clock feethrough floating iffusion reset noise MOSFET noise After Dereniak & Crowe,

100 Noise in the etector rms shot noise for a photovoltaic etector: i qif q SN E p A f rms G- noise for a photoconuctor: ig 4Gpc qif 4G pc q E p A f rms Johnson noise current: i J ktf 4 For CCDs we usually convert the noise from current to # of electrons: rms PV photon noise in units of electrons: n SN E p A f rms Johnson noise in units of electrons: 4kTf q ij Dereniak & Crowe,

101 Noise in the CCD n i ktc q Input noise (fluctuation in charge transfer onto a capacitor): [# e - ] C = capacitance [F], T = temperature [K], k = Boltzmann s constant, q = electron charge [C]. n (1 CTE) Transfer loss noise (fluctuation in transfer efficiency): [# e - ] tl N s CTE = charge-transfer efficiency [%], N s = # electrons in signal (Poisson statistics) Trapping noise (fluctuation in electron trapping uring transit) n t MkTA N ss ln() (M = # of gate transfers, N ss = ensity of surface states) Dark current noise (fluctuation in ark current) J = ark current ensity [A/(m s)], i = integration time [s]. n c J i A q Clock feethrough noise (fluctuation in clock pulses through CCD) Dereniak & Crowe,

102 Noise in the reaout preamplifier Floating Diffusion eset noise (fluctuation in # electrons rea from a MOS capacitor): C o = output capacitance n fr ktc q o Preamplifier MOSFET noise (fluctuation in MOSFET signal): g m = MOSFET transconuctance n pa C q o 8kTf 3g m Dereniak & Crowe,

103 Uniformity noise Uniformity noise (fluctuation in the pixel-to-pixel output for a constant input) A. Fixe pattern noise (pixel-to-pixel fluctuation in image brightness that is inepenent of scene irraiance). Can arise from spatial variations of etector temperature, lattice efects, etc; input-coupling variations In hybri arrays, fabrication errors, etc. B. esponsivity variations (pixel-to-pixel fluctuation in image brightness that is epenent on scene irraiance). Arises from pixel-to-pixel variation of oping, etc, Dereniak & Crowe,

104 CMOS imagers Complementary Metal-Oxie Semiconuctor (CMOS) technology is base on silicon processing, just like CCDs. However, CMOS provies the option of integrating analog an igital circuitry onto the imaging chip, making possible a camera on a chip. CCDs are, generally speaking, superior to CMOS imagers for high-en imaging, but CMOS technology is improving an expaning rapily. CMOS imagers enable low-cost, mass-market commercial cameras. $30 PC webcam es. = 70p HD $63 webcam with wifi es. = 640 x 480 $00 iphone; es. = 8 Mpixels 104

105 CMOS vs. CCD CMOS + integrate imaging & processing (sensor, reaout, processing; even ADC & power supply on one chip) + ranom access to each pixel + low power & voltage + active pixels possible (etector + amplifier) + fewer charge transfers + easier high frame-rate operation - low fill factor - higher ark current - lower well capacities (because of low voltages) - lower ynamic range - lower charge-transfer efficiency (because of low voltage) - high reset noise - higher electrical groun-bounce (from on-boar igital circuitry) CCD + lower noise (~ a few electrons total) (because of quieter sensor substrates, common output amplifier, larger amplifier that can be optimize for low noise). + low ark current + high quantum efficiency + high fill factor + high well capacity & ynamic range + high charge-transfer efficiency + low reset noise (correlate ouble sampling) - serial reaout - multiple chips for sensor, river, & signal conitioning - many charge transfers require - ifficult to achieve high frame rates 105