7η Διάλεξη. Φωτοδίοδοι
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1 7η Διάλεξη Φωτοδίοδοι Γεώργιος Έλληνας, Διάλεξη 7, σελ. 1 Περιεχόμενα Εισαγωγή Φωτοηλεκτρικό φαινόμενο Χαρακτηριστικά φωτοδιόδων Κβαντική απόδοση Αποκρισιμότητα Φωτοδίοδος p-n, p-i-n, χιονοστιβάδας Θόρυβος SNR SNR για φωτοδιόδους χιονοστιβάδας Γεώργιος Έλληνας, Διάλεξη 7, σελ. Page 1
2 Photodiode & Photodetector Basics Used to convert optical signals to electrical signals. Photodiodes and photodetectors are critical components in that they often have to deal with weak optical signals (i.e. must be highly sensitive), must be efficient in converting these optical signals to electrical (i.e. must have high quantum efficiency) and must add very little noise of their own. Γεώργιος Έλληνας, Διάλεξη 7, σελ. 3 A simple photodetector V+ bias voltage (reverse bias) input (photon stream) photodiode load resistor photocurrent AMP voltage output R L Note: photodetectors are also known as photoreceivers Γεώργιος Έλληνας, Διάλεξη 7, σελ. 4 Page
3 Photodiode Requirements High sensitivity at operating wavelengths Minimum noise High e/o conversion efficiency Fast response times High linearity Small size Low bias voltages High reliability Efficient coupling of light (anti-reflection coating) Γεώργιος Έλληνας, Διάλεξη 7, σελ. 5 Εσωτερικό φωτοηλεκτρικό φαινόμενο Ημιαγωγός Γεώργιος Έλληνας, Διάλεξη 7, σελ. 6 Page 3
4 Πλεονεκτήματα ημιαγωγικών φωτοφωρατών Υψηλή ευαισθησία Υψηλή απόδοση Μεγάλο εύρος ζώνης Χαμηλός θόρυβος Μικρό μέγεθος Αξιοπιστία Μικρό κόστος Γεώργιος Έλληνας, Διάλεξη 7, σελ. 7 Αρχή λειτουργίας Δισταθμικό άτομο Απορρόφηση e E h Συνθήκη απορρόφησης hν Eg = E E 1 Σύμβολα E g Ενεργειακό χάσμα h ν Σταθερά Planck Συχνότητα ακτινοβολίας (E field causes drift) (if they drift quickly we will have a fast photodetector) Photoconductivity in semiconductors: Absorption of photons create excited photocarriers which are quickly swept by bias Electric field Γεώργιος Έλληνας, Διάλεξη 7, σελ. 8 Page 4
5 Φωτοδίοδος p-n Αρχή λειτουργίας Γεώργιος Έλληνας, Διάλεξη 7, σελ. 9 Photodiode Semiconductor photodiodes are operated as reversed-biased p-n or p-i-n junctions. Reverse bias increases the width of the depletion region as majority carriers are swept in the minority sides by the applied E field E bias Reversed biased - + p Diffusion Drift n hv Field distribution. It is enhanced at the interface (carriers are quickly swept there). Good detector: large drift region Small diffusion region Γεώργιος Έλληνας, Διάλεξη 7, σελ. 10 Page 5
6 Photodiode Photocarriers generated by photons, incident on the depletion region quickly drift in opposite directions, under the action of the strong internal E field, towards their majority sides. In the diffusion region, away from the drift region, e-h pairs randomly diffuse, moving towards their respective majority sides are lower speeds. Γεώργιος Έλληνας, Διάλεξη 7, σελ. 11 Τwo main types of photodiode PIN photodiodes - used in state-of-the-art high bit-rate systems -no internal gain Avalanche photodiodes (APDs) - not as fast as PINs - large internal gain Γεώργιος Έλληνας, Διάλεξη 7, σελ. 1 Page 6
7 PIN Photodiodes p-intrinsic-n structure (a lightly doped (intrinsic) semiconductor layer is placed between the n and p side) operated in reverse bias intrinsic region is depleted of carriers - + bias voltage p hole i electron n + - load resistor o/p photon Γεώργιος Έλληνας, Διάλεξη 7, σελ. 13 PIN Photodiodes With the new intrinsic layer we get Broader depletion region (deeper capture region for photons -> higher quantum efficiency) Decreased diffusion region (most of the photocurrent is generated by the faster drift process) Decreased junction capacitance (faster response τ analogous to RC) Γεώργιος Έλληνας, Διάλεξη 7, σελ. 14 Page 7
8 PIN Photodiodes depleted region (περιοχή απογύμνωσης) Band gap E g photon hv > E g p + photogenerated hole - photogenerated electron i conduction band n valence band Simplified energy band diagram for a pin photodiode Γεώργιος Έλληνας, Διάλεξη 7, σελ. 15 PIN diode operation Photons with an energy greater than or equal to the band gap energy E g can generate free electronhole pairs. The e-h pairs, which act as photocurrent carriers, move towards the n and p regions. As the carriers move through the material, some e- h pairs will recombine. The diffusion lengths L n and L p moved by these carriers is the average distance travelled before recombination occurs. Γεώργιος Έλληνας, Διάλεξη 7, σελ. 16 Page 8
9 PIN diode operation Optical Radiation is absorbed in the semiconductor material according to the relationship: P(x) = P 0 [1 - exp {-α s (λ) x}] P(x) is the optical power absorbed after a distance x P 0 is the incident optical power α s (λ) is the absorption coefficient at wavelength λ Γεώργιος Έλληνας, Διάλεξη 7, σελ. 17 Καμπύλες οπτικής απορρόφησης α s (λ) as a function of λ 1973, IEEE (Miller, Marcatilli and Li) Γεώργιος Έλληνας, Διάλεξη 7, σελ. 18 Page 9
10 PIN diode operation The upper wavelength cutoff λ c is determined by the bandgap energy E g (ev): λ c (μm) = hc = 1.4 E g E g (ev) Longer wavelengths do not have high enough photon energies to excite electrons from the valence to the conduction band. h = Planck s constant = Js Γεώργιος Έλληνας, Διάλεξη 7, σελ. 19 PIN diode operation If the depletion width is w, the total power absorbed is: P(w) = P 0 [1 - exp {-α s (λ) w}] For a diode with finite reflectivity R F at the exposed facet, the primary photocurrent I P resulting from the power absorbed P(w) is: I P = q P 0 [1 - exp {-α s (λ) w}] (1 - R F ) hν Γεώργιος Έλληνας, Διάλεξη 7, σελ. 0 Page 10
11 Quantum Efficiency and Responsivity The photodetector quantum efficiency is defined as the probability that a photon is converted into an e-h pair (photocarriers) Incident photons may fail to generate current because of: Reflection at the air/semiconductor surface (typically R=30% if not anti-reflection coated). Probability of transmission is P=1-R uncomplete absorption of the photon flux (absorption coeff a) Surface recombination. E-h pairs generated near the surface quickly recombine and they do not contribute to photocurrent Γεώργιος Έλληνας, Διάλεξη 7, σελ. 1 Quantum Efficiency η (Κβαντική απόδοση) η = number of electron-hole pairs generated (ρυθμός φορέων) = I P / q P 0 / hv number of incident photons (ρυθμός φωτονίων) I P is the average photocurrent (i.e. steady-state) P 0 is the incident optical power q is the electron charge Γεώργιος Έλληνας, Διάλεξη 7, σελ. Page 11
12 Responsivity (Αποκρισιμότητα) One of the parameters describing photodiode s performance is responsivity, which can be related to η (ratio of generated photocurrent to incident optical power): Units are A/W. R = I P = η q = ηλq P 0 hf hc Useful figure of merit: specifies photocurrent that can be generated for a given optical power Γεώργιος Έλληνας, Διάλεξη 7, σελ. 3 Responsivity (Αποκρισιμότητα) Therefore R = ηλ(μm)/1.4 The detector responsivity increases linearly with wavelength, for a fixed value of η. This is because as λ increases, there are more photons to carry a given optical power P, which produces more photoelectrons. For avalanche photodiodes, the responsivity is multiplied by G (the avalanche gain) (as we will see next) Γεώργιος Έλληνας, Διάλεξη 7, σελ. 4 Page 1
13 Responsivity versus wavelength Γεώργιος Έλληνας, Διάλεξη 7, σελ. 5 Αριθμητικό παράδειγμα Χαρακτηριστικά φωτοδιόδου Μήκος κύματος η = 65% E in ph = P = 3.6 μw J hc λ = = 1.3 μm E ph Αποκρισιμότητα R = ηe = AW h ν -1 Φωτορεύμα I p = RPin =.5 μa Γεώργιος Έλληνας, Διάλεξη 7, σελ. 6 Page 13
14 Γεώργιος Έλληνας, Διάλεξη 7, σελ. 7 APD photoreceiver Avalanche photodiodes (APDs) differ from pin photodiodes in that they provide internal gain. Whereas in a pin photodiode, N incident photons can only be expected to produce η N e-h pairs, in an APD this primary photocurrent can be multiplied through the avalanche process. The advantage is that APD receivers can have higher SNR compared to pin receivers, because the photocurrent is multiplied before encountering thermal noise associated with the rest of the receiver. Γεώργιος Έλληνας, Διάλεξη 7, σελ. 8 Page 14
15 APD structure and electric field distribution (provides current gain) Optical input photons absorbed here to give primary photocurrent Keiser, McGraw Hill Γεώργιος Έλληνας, Διάλεξη 7, σελ. 9 APD Device is operated under reverse bias; relatively high voltages (0 V or more) needed to achieve the high electric field in the avalanche region. Most photons are absorbed in the depletion region, where they generate electron-hole pairs in much the same way as in a pin photodiode. The resulting photocurrent is known as the primary photocurrent. Γεώργιος Έλληνας, Διάλεξη 7, σελ. 30 Page 15
16 APD In the high field region, photogenerated carriers are accelerated and gain enough energy to ionize atoms in the valance band if they collide, thus releasing more e-h pairs. This process of carrier multiplication is termed impact ionization. Newly created carriers are also accelerated by the high electric field, gaining enough energy to cause further impact ionization. This phenomenon leads to the avalanche effect. In most devices, impact ionization is confined to electrons alone. Γεώργιος Έλληνας, Διάλεξη 7, σελ. 31 APD The rate of ionization is characterized by the ionization coefficients α e and α h. The ionization ratio is given by K = α h /α e It is desirable to have the ionization process generated by only one type of carrier having for instance α e >> α h (to avoid feedback) - Random process (e, h travel with different + hv speeds and have different ionization probabilities) Γεώργιος Έλληνας, Διάλεξη 7, σελ. 3 Page 16
17 APD If the two processes occur simultaneously: Feedback adds more randomness in the process causing extra noise Avalanche multiplication is more time consuming which increases the detector response time (decreases its frequency response or BW) There is an increased risk of instability, creating damaging avalanche breakdown The best APD design consists in having separate absorption an multiplication regions so that only one type of carrier is injected in the multiplication region Γεώργιος Έλληνας, Διάλεξη 7, σελ. 33 APD Responsivity The multiplication factor M for all carriers generated in the photodiode is: M = I M is the average value of the total multiplied current and I P is the primary (i.e. unmultiplied) current Responsivity of an APD is: I I M P q = η where R M = R M 0 is the unity gain responsivity. hf R 0 Γεώργιος Έλληνας, Διάλεξη 7, σελ. 34 Page 17
18 Photodetector Noise Γεώργιος Έλληνας, Διάλεξη 7, σελ. 35 Photodetector Noise Photodiodes must detect very weak optical signals. Must maintain an adequate signal to noise ratio: SNR = signal power from photocurrent photodiode noise power + amp noise power Photodiode noise is caused by statistical nature of photonelectron conversion process, while the amplifier noise is due to thermal noise Γεώργιος Έλληνας, Διάλεξη 7, σελ. 36 Page 18
19 SNR To achieve high SNR: (1) The photodiode must have a high quantum efficiency to generate a large signal power () Photodiode and amplifier noises must be minimized. Photodiode efficiencies are normally high, hence it is the noise currents that determine the minimum optical power level that can be detected. Minimum detectable optical power = optical power needed to produce a photocurrent of same magnitude as rms of the total noise current. This is equivalent to having an SNR of unity. Γεώργιος Έλληνας, Διάλεξη 7, σελ. 37 Sources of noise in a photoreceiver bias voltage input (photon stream) quantum noise R L photodiode dark current noise output AMP thermal noise amplifier noise Γεώργιος Έλληνας, Διάλεξη 7, σελ. 38 Page 19
20 Impact on digital reception photodiode v out A R L AMP V REF B Comparator C B C A: ideal signal (no noise) B: output of photoreceiver (noise due to amplifier and photodiode) C: output of comparator; noise can generate bit errors Γεώργιος Έλληνας, Διάλεξη 7, σελ. 39 Photoreceivers and Noise Optical communications have developed through five generations Although frequency/phase modulation (coherent systems) is possible, both single wavelength and WDM systems are still based on intensity modulation of optical sources and direct detection by photoreceivers (IM/DD). IM/DD can be thought of as being analogous to amplitude modulation and envelope detection, i.e. systems-wise, it is very primitive! Γεώργιος Έλληνας, Διάλεξη 7, σελ. 40 Page 0
21 Five generations of optical communications Γεώργιος Έλληνας, Διάλεξη 7, σελ. 41 Intensity modulation/direct detection (IM/DD) The signal is conveyed by modulating the intensity (i.e. optical power) of the light beam. Envelope detection (direct detection) occurs at the photoreceiver. Modulation can be analogue, as in cable TV systems, but is mostly digital. Γεώργιος Έλληνας, Διάλεξη 7, σελ. 4 Page 1
22 Digital and Analogue Communications: Comparison Advantages of digital communications 1. Signal regeneration. Error correction is possible 3. Greater dynamic range Γεώργιος Έλληνας, Διάλεξη 7, σελ. 43 Digital and Analogue Communications: Comparison Disadvantages of digital communications: 1. Generally requires more bandwidth than analogue. Digital detection requires synchronization (i.e. clock must be recovered at the receiver from the incoming data stream). Γεώργιος Έλληνας, Διάλεξη 7, σελ. 44 Page
23 Analogue communication Transmitted signal Channel (fiber) Photoreceiver Received signal Noise Dispersion Attenuation Noise Distorted and noisy Γεώργιος Έλληνας, Διάλεξη 7, σελ. 45 t Digital communication Transmitted signal Channel (fiber) Regenerative receiver Received signal Noise Dispersion Attenuation Regenerated pulse effects of channel are mitigated Γεώργιος Έλληνας, Διάλεξη 7, σελ. 46 t Page 3
24 Digital vs. Analogue Performance Criteria Analogue systems deal with continuous waveforms. Evaluate performance by fidelity criterion, e.g. signal-to-noise ratio (SNR). i.e. SNR is a figure of merit largely used for analogue communications Γεώργιος Έλληνας, Διάλεξη 7, σελ. 47 Digital vs. Analogue Performance Criteria Digital communication systems transmit signals from a finite set ( alphabet ) that is known by the receiver. (e.g. Morse code). Hence a figure of merit for digital communications is the probability of incorrectly detecting a digit also called the probability of error often specify the bit error rate (BER) a BER of 10-9 or less is typically specified Γεώργιος Έλληνας, Διάλεξη 7, σελ. 48 Page 4
25 Signal path through an optical link Γεώργιος Έλληνας, Διάλεξη 7, σελ. 49 Photodetection in Presence of Noise Front end of photoreceiver showing various sources of noise: Optical i/p PHOTO- DIODE DETECTOR LOAD/BIAS PRE- AMPLIFIER Electrical o/p quantum dark current beat (from incoherent optical sources) thermal thermal (input resistance of amp) device (active devices) Γεώργιος Έλληνας, Διάλεξη 7, σελ. 50 Page 5
26 SNR performance of PIN photoreceiver Let detected signal (photocurrent) be I P : I P = I m + i p mean value ( DC ) signal component signal power is proportional to: i p (normalize to R) N.B. this is a mean square current, units A Γεώργιος Έλληνας, Διάλεξη 7, σελ. 51 Quantum Noise quantum noise: due to random arrival of photons hence detected current = mean value + random fluctuations Can be modelled as a current source with mean square given by B = bandwidth q = electron charge i Q = qbi m N.B. Also known as shot noise. Γεώργιος Έλληνας, Διάλεξη 7, σελ. 5 Page 6
27 Dark Current noise/thermal noise dark current noise: extra shot noise component due to dark current (i.e. current that is present in the absence of optical illumination) i D = qbi D I D = mean value of dark current thermal noise: due to bias resistor R L i T = 4kTB / R L k = Boltzmann s constant = J/K T = absolute temperature in K Γεώργιος Έλληνας, Διάλεξη 7, σελ. 53 Amplifier noise - SNR amplifier noise: introduced by amplifier circuitry. We can combine i T and i AMP as follows: i T = 4kTBF n / R L Hence: SNR = F n = amplifier noise figure average signal power average noise power = i p qb(i m + I D ) + 4kTBF n / R L Γεώργιος Έλληνας, Διάλεξη 7, σελ. 54 Page 7
28 SNR SNR is maximized by: low receiver noise figure low bandwidth large load/bias resistance, although this tends to increase receiver time constant, reducing the bandwidth Γεώργιος Έλληνας, Διάλεξη 7, σελ. 55 Typical SNR plots for APDs and PINs Γεώργιος Έλληνας, Διάλεξη 7, σελ. 56 Page 8
29 SNR Performance of APDs Γεώργιος Έλληνας, Διάλεξη 7, σελ. 57 APD Internal gain mechanism increases the signal current, thereby improving the SNR of an APD photoreceiver. However, the avalanche effect is statistical in nature (i.e. random), and this introduces a new source of noise: Variable gain m: m = M + m n M = mean gain m n = random variable with zero mean Γεώργιος Έλληνας, Διάλεξη 7, σελ. 58 Page 9
30 Physical picture of noise in a pin photodiode Random arrival of photons (Poisson statistics) Photogenerated carriers (Prob. η) Corresponding current pulses Photocurrent (mean level plus noise) Both quantum noise and shot noise. t t q t Wiley Γεώργιος Έλληνας, Διάλεξη 7, σελ. 59 Physical picture of noise in an APD Random arrival of carriers These are multiplied through avalanche process, which is noisy (random nature); i.e. there is multiplication noise Photocurrent Quantum and shot noise are increased by excess noise of APD (multiplication noise) m 1 m m 3 m 4 m 5 t t t Wiley Γεώργιος Έλληνας, Διάλεξη 7, σελ. 60 Page 30
31 SNR SNR for PIN photodetector: SNR = quantum noise signal power from photocurre nt + dark current noise + thermal noise + amplifier noise i p = ishot + ita SNR for APD photodetector without multiplication noise: Both i p and i shot will be multiplied by M: SNR = M M i i shot p + i TA Γεώργιος Έλληνας, Διάλεξη 7, σελ. 61 SNR for APD photodetector with multiplication noise In this situation, the primary photocurrent will be multiplied by m = M + m n, and the multiplication noise due to m n will lead to an increase in the noise term by an excess noise factor F e : SNR = M F M i i p e shot + i TA This is because the signal current i p is multiplied by the average gain M (note that m = M), whereas the shot noise current power is multiplied by the mean square gain m. Note: m > ( m) Γεώργιος Έλληνας, Διάλεξη 7, σελ. 6 Page 31
32 Excess Noise Factor It has been found experimentally that: m where 0 < x < 1, and this value depends on the material, e.g for silicon, 0.1 < x < 0.5, for germanium, 0.85 < x < 1.0 = M + x Excess Noise Factor Definition: The ratio of the actual noise generated to the noise generated if all carrier pairs were multiplied by M. + x m M F e = = = M M M x Γεώργιος Έλληνας, Διάλεξη 7, σελ. 63 Shot Noise Power Photocurrent is increased by factor M, but the shot noise is also increased by the excess noise factor M x such that i shot APD = qb mean photocurrent Thermal and amplifier noise is unaffected by the multiplication: i = 4kTBF TA + x ( I + I ) M m D n mean dark current R L Γεώργιος Έλληνας, Διάλεξη 7, σελ. 64 Page 3
33 APD SNR Hence from the definition of SNR, SNR APD = qb M ( I + I ) m D M i p + x + 4kTBF R L n = qb i p 4kTBF R M x ( I m + I D ) M + L n Γεώργιος Έλληνας, Διάλεξη 7, σελ. 65 APD SNR Note that M = 1 gives pin-like behaviour (i.e. SNR same as that for a pin photoreceiver). Inspection of the SNR expression shows that increasing values of multiplication factor M lead to: increased shot noise influence (increases as M x ) reduced thermal noise influence (decreases as M ) the combined effect is that increasing M from the pin value of unity can lead to increasing SNR, i.e. an improvement in SNR. Γεώργιος Έλληνας, Διάλεξη 7, σελ. 66 Page 33
34 Improvement in SNR Improvement in SNR (db) (SNR) APD -(SNR) pin Avalanche multiplication factor M Γεώργιος Έλληνας, Διάλεξη 7, σελ. 67 Improvement in SNR At relatively low values of M, the operation is pin diode like, and the SNR is dominated by thermal and amplifier noise: SNR APD, small M p 4kTBF n = RL M i M i p R 4kTBF n L From which we see that increasing M will improve the SNR (see previous graph for M < 10 to 15). Γεώργιος Έλληνας, Διάλεξη 7, σελ. 68 Page 34
35 Worsening of SNR However, for high values of M, the thermal noise becomes insignificant relative to shot noise, and we have: SNR APD, big M i p qb x ( I + I ) M m D From which we see that increasing M will now lead to a worsening (i.e. decrease) of SNR. Γεώργιος Έλληνας, Διάλεξη 7, σελ. 69 Maximize the SNR There is therefore an optimum value of M which will maximize the SNR for a given value of x: M + x optimum = 4kTF xqr L n ( I + ) m I D Task: Derive this equation This is given in the homework. Γεώργιος Έλληνας, Διάλεξη 7, σελ. 70 Page 35
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