Photodetectors and Photodiodes

A photodetector is where a beam of light stops being optics and becomes information. Everything the earlier chapters built — a mode guided down a fibre, a pulse that survived attenuation, a field prepared in the lab — arrives at a receiver that must answer one question in electrical language: how much light, and how fast is it changing? It answers through the internal photoelectric effect, the semiconductor reprise of the quantum idea Einstein introduced in 1905. A photon of energy $h\nu$ is absorbed only if it exceeds the bandgap $E_g$ ; when it does, it lifts an electron across the gap, and an applied field sweeps the resulting electron–hole pair to the terminals before it recombines. Light in, current out — the proportionality constant is the whole story. Two figures of merit fight over the design. Quantum efficiency $\eta$ wants a thick, strongly absorbing slab so no light escapes; speed wants a thin one, so carriers cross quickly and the junction capacitance stays small. The p-i-n photodiode is the negotiated truce: an intrinsic layer between the doped regions widens the high-field drift zone where carriers are collected fast, linearly, and quietly. When the signal is too faint even for that, the avalanche photodiode adds internal gain, letting one carrier ionize the next in a controlled chain reaction — buying signal at the price of excess noise. And beneath every design sits an irreducible floor: shot noise, thermal noise, dark current. Understanding those floors is what connects a piece of doped silicon to the quantum limit of measurement itself.

Key takeaways

A photodetector converts optical power to current by the internal photoelectric effect: a photon with $h\nu \ge E_g$ frees an electron–hole pair that a junction field collects.
The responsivity $\mathcal{R}=\eta e\lambda/(hc)\approx\eta\,\lambda[\mu\mathrm{m}]/1.24$ A/W gives amps per watt, rising with wavelength until the cutoff $\lambda_c=hc/E_g$ where absorption dies.
A reverse-biased p-i-n diode drifts carriers across a wide depletion layer — fast, linear over many decades, near-unity efficiency, low noise.
Bandwidth is capped two ways: carrier transit (favours a thin layer) and the RC time constant (favours a thick one), so an optimum thickness exists.
Avalanche photodiodes give internal gain $M$ but add excess noise $F(M)$ ; the fundamental floors are shot noise $2eIB$ , thermal noise $4k_BTB/R_L$ , and dark current.
Key idea: photocurrent $=\mathcal{R}P$ with $\mathcal{R}=\eta e\lambda/(hc)$ — light becomes current at a rate set by efficiency and wavelength, bounded by bandwidth and noise.

The core insight

Photocurrent $=\mathcal{R}P$ with responsivity $\mathcal{R}=\eta e\lambda/(hc)$ : light in, current out, at a rate fixed by quantum efficiency and wavelength, bounded by the transit/RC bandwidth and the shot, thermal, and dark-current noise floors.

Where this lives today

The photodiode is the quiet workhorse inside the machines that move the internet. A modern 400G or 800G coherent transceiver carries a bank of high-speed InGaAs/InP or germanium-on-silicon photodiodes running past 60 GHz, arranged as balanced pairs that mix the incoming signal with a local-oscillator laser so the receiver reads phase and amplitude, not just power. Because those detectors are pushed toward the shot-noise limit of Derivation 2, the whole link budget — how far a signal runs before regeneration — is ultimately an argument about $\eta$ , $B$ , and the noise floors on this page. Waveguide-integrated germanium on silicon photonic chips shrinks the receiver onto a few square millimetres, decoupling efficiency from speed just as the thickness derivation predicts. At the opposite extreme of light level, an avalanche photodiode driven past breakdown becomes a single-photon avalanche diode (SPAD), and arrays of SPADs are now the sensor behind automotive LiDAR, phone time-of-flight cameras, and the detectors that close a quantum-key-distribution link or tag photons in a $g^{(2)}$ correlation experiment. The same excess-noise physics that sets an APD's optimum gain in a telecom receiver decides a SPAD's dark-count rate — McIntyre's $F(M)$ , tuned to two very different jobs.

The physical picture

Picture the semiconductor bandgap as a toll gate of height $E_g$ . A photon may pass an electron across only if it pays the toll — if $h\nu \ge E_g$ . A red-enough photon has too little energy, sails through untouched, and produces nothing. This one inequality is why silicon sees the visible brilliantly but goes stone blind past about 1.1 μm, while germanium and InGaAs, with smaller gaps, still see the 1.3 and 1.55 μm telecom bands — a hard wall at the cutoff wavelength $\lambda_c=hc/E_g$ fixed by the material. Once a pair is born, the reverse-biased junction acts like a conveyor belt. The intrinsic layer of a p-i-n diode is nearly free of carriers, so almost the whole applied voltage drops across it as a strong, roughly uniform field. The instant a photon makes an electron–hole pair there, the field yanks the two apart and drifts them to opposite contacts in tens of picoseconds, long before they recombine. Widen and strengthen that field region and you collect nearly every pair: exactly the job the intrinsic layer was invented for.

Figure

A reverse-biased p-i-n photodiode: a photon with hν greater than E_g is absorbed in the intrinsic layer of width w ≈ 3 μm, and the field E drifts the electron to the n side and the hole to the p side, producing the photocurrent i_ph

Responsivity climbs with wavelength for a reason that has nothing to do with the device and everything to do with counting. A fixed power $P$ is fixed joules per second, but each photon carries $hc/\lambda$ joules, so longer wavelength means more photons per watt — and since each collected photon yields at most one electron, that means more amps per watt. Responsivity rises linearly with $\lambda$ even at constant efficiency, right up to the cutoff where efficiency collapses and the curve falls off a cliff. The second figure shows this for the two workhorse materials, against the ideal $\eta=1$ line.

Figure

Responsivity 𝓡 versus wavelength against the ideal η = 1 ceiling 𝓡 = λ/1.24 A/W: silicon peaks near 0.52 A/W at 850 nm and cuts off at λ_c ≈ 1.1 μm, while InGaAs reaches about 0.88 A/W at 1.55 μm before its cutoff at λ_c ≈ 1.65 μm

Avalanche gain is the last idea, and the most double-edged. Push the reverse field high enough and a drifting carrier gains enough energy between collisions to knock a second electron across the gap — impact ionization — and that pair ionizes again, a chain reaction multiplying one photo-carrier into $M$ inside the semiconductor, before any amplifier sees the signal — a head start that lets an APD beat its amplifier's thermal noise. But where and how many ionizations happen is random, and that randomness injects excess noise growing with gain, so there is always an optimum $M$ beyond which more gain makes the receiver worse.

The core equations

The defining relation is the responsivity, the linear conversion from optical watts to electrical amps, which every other result here modifies. It follows from a two-step chain: power $P$ delivers photons at rate $P/h\nu$ , a fraction $\eta$ are collected, and each contributes charge $e$ , so $i_{ph}=\eta eP/h\nu$ .

i_{ph}=\mathcal{R}\,P,\qquad \mathcal{R}=\frac{\eta e}{h\nu}=\frac{\eta e\lambda}{hc}\approx\frac{\eta\,\lambda[\mu\mathrm{m}]}{1.24}\ \mathrm{A/W} \qquad (1)

where: $i_{ph}$ — photocurrent (A); $P$ — optical power (W); $\mathcal{R}$ — responsivity (A/W); $\eta$ — quantum efficiency (0 to 1); $e=1.602\times10^{-19}$ C; $h\nu=hc/\lambda$ — photon energy. Physically: amps out per watt in, rising linearly with $\lambda$ because a watt holds more lower-energy photons. The efficiency $\eta$ is not a free parameter but the product of three fractions — what gets in past the surface, what gets absorbed in a finite thickness, and what gets collected before recombining.

\eta=(1-R_f)\,\zeta\,\big(1-e^{-\alpha w}\big) \qquad (2)

where: $R_f$ — surface (Fresnel) reflectance, cut by anti-reflection coatings; $\zeta\approx1$ — fraction of pairs collected before recombination; $\alpha(\lambda)$ — absorption coefficient (m⁻¹); $w$ — absorber thickness. Physically: $1-e^{-\alpha w}$ is Beer–Lambert absorption in a slab — thicken $w$ and you approach full absorption. Absorption switches off once photons drop below the bandgap, and the wavelength where that happens is the single most important spec of a detector material — a restatement of $h\nu=E_g$ .

\lambda_c=\frac{hc}{E_g}\approx\frac{1.24\ \mu\mathrm{m}\cdot\mathrm{eV}}{E_g[\mathrm{eV}]} \qquad (3)

where: $\lambda_c$ — longest detectable wavelength; $E_g$ — bandgap energy. Physically: for $\lambda>\lambda_c$ the crystal is transparent, $\mathcal{R}\to0$ . Si (1.12 eV) cuts off at 1.11 μm, InGaAs (0.75 eV) at 1.65 μm, Ge (0.66 eV) at 1.88 μm. Speed is limited by two independent clocks, both set by the same width $w$ : the transit time carriers need to cross the depletion layer, and the RC time in which the junction capacitance charges through the load. The two respond oppositely to $w$ .

\tau_{tr}=\frac{w}{v_s},\quad f_{tr}\approx\frac{0.44\,v_s}{w};\qquad C_j=\frac{\varepsilon A}{w},\quad f_{RC}=\frac{1}{2\pi R_L C_j} \qquad (4)

where: $\tau_{tr}$ — transit time; $v_s\sim10^5$ m/s — saturation drift velocity; $C_j$ — depletion capacitance; $\varepsilon$ — permittivity; $A$ — junction area; $R_L$ — load plus series resistance. Physically: a thicker $w$ slows transit (lower $f_{tr}$ ) but shrinks $C_j$ (higher $f_{RC}$ ) — the tension that fixes the optimum thickness. Every measurement sits on a noise floor from two independent sources that add in quadrature: shot noise from the granularity of charge, and thermal (Johnson–Nyquist) noise from the load. Dark current $i_d$ flows and shot-fluctuates even in darkness.

\langle i_{sh}^2\rangle=2e\,(i_{ph}+i_d)\,B,\qquad \langle i_{th}^2\rangle=\frac{4k_BT}{R_L}\,B \qquad (5)

where: $\langle i_{sh}^2\rangle,\langle i_{th}^2\rangle$ — mean-square noise currents (A²); $i_d$ — dark current; $B$ — bandwidth (Hz); $k_B=1.381\times10^{-23}$ J/K; $T$ — temperature. Physically: shot noise grows with the signal it rides on, thermal noise is fixed by the circuit — which one dominates decides the design. An avalanche diode multiplies the signal by the mean gain $M$ , but its shot noise multiplies by $M^2F(M)$ with an excess-noise factor $F(M)\ge1$ — the term that makes more gain eventually counterproductive.

i_{APD}=M\,\mathcal{R}\,P,\quad \langle i_{sh}^2\rangle=2e\,\mathcal{R}P\,M^2F(M)\,B,\quad F(M)=kM+(1-k)\Big(2-\frac{1}{M}\Big) \qquad (6)

where: $M$ — mean gain; $F(M)$ — excess-noise factor (McIntyre); $k=\alpha_h/\alpha_e$ — hole-to-electron ionization ratio. Physically: when one carrier dominates ionization ( $k\to0$ ), $F\to2-1/M$ stays near 2; when both ionize equally ( $k=1$ ), $F=M$ and noise races the signal. Finally, all of this rolls into one figure of merit: the optical power giving unity signal-to-noise — the faintest the detector can honestly see.

\mathrm{NEP}=\frac{\sqrt{\langle i_N^2\rangle}}{\mathcal{R}}=\frac{h\nu}{\eta e}\sqrt{\langle i_N^2\rangle}\quad\big[\mathrm{W}\ \text{or}\ \mathrm{W}/\sqrt{\mathrm{Hz}}\big] \qquad (7)

where: $\mathrm{NEP}$ — noise-equivalent power; $\langle i_N^2\rangle$ — total mean-square noise current. Physically: NEP refers all noise to an equivalent optical input, so detectors of different responsivity compare as light sensors, not ammeters.

Derivation ASignal-to-noise ratio and the quantum limit

The goal is to combine the signal photocurrent with the shot and thermal noise floors into a working receiver SNR, then show that when the signal's own shot noise dominates the elementary charge cancels and the SNR collapses to a pure photon-counting expression. That quantum limit is the deepest statement here: the best an ideal photodetector can do is set by Poisson statistics of photon arrivals, not by any cleverness in the electronics.

Step 1. Take the mean-square signal current as $\langle i_{ph}^2\rangle=(\mathcal{R}P)^2$ . Why: under constant illumination the signal is the DC photocurrent, and SNR compares its power (current squared) against the noise variance.

Step 2. Sum the independent noise variances in quadrature: $\langle i_N^2\rangle=2e(\mathcal{R}P+i_d)B+4k_BTB/R_L$ . Why: shot noise (signal plus dark) and thermal noise come from unrelated processes, so their variances add, not their amplitudes.

Step 3. Form the general SNR a designer maximizes, $S/N=(\mathcal{R}P)^2/[\,2e(\mathcal{R}P+i_d)B+4k_BTB/R_L\,]$ . Why: this exposes two regimes — thermal-limited, where SNR grows as $P^2$ , and shot-limited, where the denominator tracks the signal.

Step 4. Drive the signal strong enough that its own shot noise dominates ( $\mathcal{R}P\gg i_d$ and $\mathcal{R}P\gg 2k_BT/eR_L$ ); the denominator becomes $2e\mathcal{R}PB$ and $S/N\to\mathcal{R}P/(2eB)$ . Why: once shot noise wins, load resistance and cooling no longer help — the noise is intrinsic to the detected light.

Step 5. Substitute $\mathcal{R}=\eta e/(h\nu)$ so the charge cancels: $S/N=\eta P/(2h\nu B)$ , one-half the detected photon rate per bandwidth. Why: the vanishing of $e$ is the signature of a quantum limit — the SNR now counts photons, and $\eta P/(h\nu B)$ is (photons/s)/(Hz), a pure number.

Go deeper · Derivation B · 1 minOptimal absorber thickness: efficiency versus bandwidth

Derivation BOptimal absorber thickness: efficiency versus bandwidth

The goal is to make quantitative the central design tension of a photodiode: the same depletion width $w$ that high efficiency wants thick, speed wants thin. Writing efficiency and both bandwidth limits as functions of $w$ shows why an intermediate thickness of a few micrometres is optimal, and why waveguide-coupled detectors escape the trade-off entirely.

Step 1. Efficiency rises toward unity with thickness, $\eta\propto1-e^{-\alpha w}$ , so absorption always favours larger $w$ . Why: a thicker slab gives each photon more length to be absorbed (Beer–Lambert) — the light-capture side wants thick.

Step 2. Transit bandwidth falls with thickness, $f_{tr}\approx0.44\,v_s/w$ , because carriers drift at a fixed saturation velocity and a wider layer takes longer to cross. Why: once the field saturates the drift velocity, the only way to speed transit is to shorten the distance — the speed side wants thin.

Step 3. RC-limited bandwidth rises with thickness, $f_{RC}=1/(2\pi R_L C_j)=w/(2\pi R_L\varepsilon A)$ , because $C_j=\varepsilon A/w$ shrinks as the plates separate. Why: a thicker layer is a smaller capacitor that charges faster through the load — so the RC clock wants thick, opposing the transit clock.

Step 4. Combine the two clocks as cascaded first-order responses, $1/f_{3\mathrm{dB}}^2=1/f_{tr}^2+1/f_{RC}^2$ , so the slower dominates. Why: transit and RC act as two low-pass filters in series; because $f_{tr}$ falls and $f_{RC}$ rises with $w$ , bandwidth peaks at an intermediate $w\sim1$ – $3\ \mu$ m for high-speed diodes.

Step 5. Escape the trade-off by decoupling the directions: in a waveguide- or cavity-coupled detector, light travels along the absorber while carriers drift across a thin transverse dimension. Why: the trade-off exists only because photons and carriers share the axis $w$ ; rotate the light path 90° and a thin, fast layer can still be optically long.

Limiting cases

Case	Result	Meaning
Long-wavelength cutoff	$\lambda>\lambda_c=\dfrac{hc}{E_g}\Rightarrow\mathcal{R}\to0$	Sub-bandgap photons are not absorbed; the crystal is transparent. Si blinds past 1.11 μm, InGaAs past 1.65 μm.
Transit-time limit	$f_{3\mathrm{dB}}\approx\dfrac{0.44\,v_s}{w}$	For a thick layer, speed is set by carrier drift; larger $w$ raises efficiency but lowers bandwidth.
RC limit	$f_{3\mathrm{dB}}=\dfrac{1}{2\pi R_L C_j},\ C_j=\dfrac{\varepsilon A}{w}$	For a thin or large-area diode, capacitance dominates; a wider $w$ (smaller $C_j$ ) helps — the limits pull oppositely.
Thermal-noise limit	$\dfrac{S}{N}=\dfrac{(\mathcal{R}P)^2 R_L}{4k_BTB}$	Weak signal into a load: SNR grows as $P^2$ ; APD gain or a transimpedance front end beats the load noise.
Shot-noise (quantum) limit	$\dfrac{S}{N}=\dfrac{\eta P}{2h\nu\,B}$	Signal shot noise dominates: SNR counts detected photons per bandwidth, the charge cancels — the irreducible floor.

Common trapMore responsivity, or more gain, always means a better detector

Neither is true, and both mistakes cost real designs. Responsivity is not a fixed merit but a function of wavelength that falls to zero beyond $\lambda_c=hc/E_g$ , so an InGaAs diode with higher $\mathcal{R}$ than silicon at 1.55 μm is not "better" — it is the only one that works there, and would be noisier and slower for a visible job silicon does cleanly. And avalanche gain does not monotonically help: signal grows as $M$ but multiplication noise as $M^2F(M)$ , so past an optimum $M_{opt}$ the excess noise overtakes the very thermal noise the gain was meant to beat, and SNR turns over. The figure of merit is never responsivity or gain alone — it is the signal-to-noise ratio, or the noise-equivalent power.

Worked examples

1 · A telecom receiver photocurrent (confidence builder)

An InGaAs p-i-n photodiode with quantum efficiency $\eta=0.75$ receives $P=10\ \mu$ W (that is, −20 dBm) of 1.55 μm light at the end of a fibre link. Find its responsivity and the photocurrent it produces.

Step 1. Apply the numerical rule at $\lambda=1.55\ \mu$ m: $\mathcal{R}\approx\eta\,\lambda[\mu\mathrm{m}]/1.24=0.75\times1.25=\mathbf{0.94\ A/W}$ — below the $\eta=1$ ceiling of $1.25$ A/W by exactly the factor $\eta$ .

Step 2. Apply $i_{ph}=\mathcal{R}P=0.9375\times10\times10^{-6}\ \mathrm{A}\approx\mathbf{9.4\ \mu A}$ — a ten-microwatt signal has become a nine-microamp current, small but linear and clean.

Step 3. Sanity-check by counting photons: the arrival rate $P/(h\nu)\approx7.8\times10^{13}$ /s, of which $\eta=75\%$ are collected; times $e$ that is $5.9\times10^{13}\times1.602\times10^{-19}=9.4\ \mu$ A, matching Step 2. 𝓡 = 0.94 A/W and i_ph = 9.4 μA.

2 · The bandwidth trade-off in the same diode

The diode above has $w=2\ \mu$ m, a $30\ \mu$ m-diameter area ( $A=7.1\times10^{-10}$ m²), $\varepsilon=13.9\,\varepsilon_0$ , $v_s=10^5$ m/s, and $R_L=50\ \Omega$ . Find the transit, RC, and overall 3-dB bandwidths.

Step 1. Transit: $\tau_{tr}=w/v_s=2\times10^{-6}/10^5=20$ ps, so $f_{tr}=0.44\,v_s/w=0.44\times10^5/(2\times10^{-6})=\mathbf{22\ GHz}$ .

Step 2. Capacitance: $C_j=\varepsilon A/w=13.9\times8.854\times10^{-12}\times7.1\times10^{-10}/(2\times10^{-6})=43.5$ fF, so $f_{RC}=1/(2\pi R_L C_j)=1/(2\pi\times50\times4.35\times10^{-14})=\mathbf{73\ GHz}$ .

Step 3. Combine: $1/f_{3\mathrm{dB}}^2=1/22^2+1/73^2\Rightarrow f_{3\mathrm{dB}}=\mathbf{21\ GHz}$ — transit-limited, since 22 GHz is the slower clock. Doubling $w$ to 4 μm for more efficiency would halve $f_{tr}$ to 11 GHz while doubling $f_{RC}$ to 146 GHz, slowing the diode to $\approx11$ GHz — the trade-off, made numerical. f_3dB ≈ 21 GHz, set by carrier transit.

3 · The quantum limit of the link

The same $\eta=0.75$ receiver detects $P=1\ \mu$ W at 1.55 μm over an electrical bandwidth $B=1$ GHz, in the shot-noise-limited regime. Find the best possible SNR and the corresponding sensitivity.

Step 1. The photon energy is $h\nu=hc/\lambda=1.28\times10^{-19}$ J (0.80 eV), so the detected photon rate is $\eta P/(h\nu)=0.75\times10^{-6}/(1.28\times10^{-19})=5.9\times10^{12}$ /s.

Step 2. Apply the quantum-limit SNR: $S/N=\eta P/(2h\nu B)=0.75\times10^{-6}/(2\times1.28\times10^{-19}\times10^{9})\approx\mathbf{2900}$ , or $10\log_{10}(2900)=\mathbf{34.7\ dB}$ .

Step 3. Invert for the sensitivity, the power giving $S/N=1$ : $P_{min}=2h\nu B/\eta=2\times1.28\times10^{-19}\times10^{9}/0.75=\mathbf{0.34\ nW}$ . No electronics can push an ideal receiver of this efficiency and bandwidth below about a third of a nanowatt. S/N ≈ 2900 (34.7 dB); sensitivity ≈ 0.34 nW.

Physics of the portrait

Every noise floor in this article traces to one experimentalist who spent his career listening to the crackle of moving charge.

Origins · 1 minWalter Schottky and how this was discovered

Walter Schottky

1886–1976 · shot noise and the semiconductor photodiode

Walter Hermann Schottky, born in Zürich and trained in Berlin under Max Planck, gave photodetection two permanent pillars. In 1918, studying current fluctuations in vacuum tubes, he showed that because charge comes in indivisible lumps of $e$ , any steady current carries an irreducible fluctuation of mean-square value $2eIB$ — the Schroteffekt, or shot noise, the very floor that Derivation 2 turns into the quantum limit. The fluctuation, he realized, was not a defect of the apparatus but a fingerprint of the electron's discreteness. His second pillar came from solids: the Schottky barrier, the rectifying metal–semiconductor junction, underlies metal–semiconductor–metal photodetectors and the contact physics of every photodiode. Along the way he invented the screen-grid (tetrode) tube and worked out the thermionic-emission relations (the Schottky effect) that still bear his name. Both his noise theory and his barrier outlived the vacuum tube intact — which is why a physicist who never built a modern photodiode presides over how well one can possibly work.

History

1873

— Willoughby Smith observes light-dependent conductivity in selenium, the first photoconductor

1905

— Einstein explains the photoelectric effect with light quanta of energy hν

1918

— Schottky derives the shot-noise formula ⟨i²⟩ = 2eIB for fluctuating current

1940

— Russell Ohl at Bell Labs discovers the silicon p-n junction photovoltaic response

1966

— McIntyre publishes the excess-noise theory F(M) of avalanche photodiodes

Going further

Texts. Saleh & Teich, Fundamentals of Photonics, 2nd ed., Ch. 18 · Sze & Ng, Physics of Semiconductor Devices, 3rd ed., Ch. 13 · Loudon, The Quantum Theory of Light, 3rd ed., Ch. 6 · Hecht, Optics, 5th ed., §3.4 · Demtröder, Laser Spectroscopy, Vol. 1, §4.5.

Provenance. The responsivity $\mathcal{R}=\eta e\lambda/(hc)\approx\eta\lambda[\mu\mathrm{m}]/1.24$ A/W follows from Saleh & Teich Ch. 18 (0.8 μm silicon gives 0.58 A/W, 1.55 μm InGaAs 0.94 A/W, both recomputed here). The constant $hc/e=1.240\ \mu\mathrm{m}\cdot$ eV gives $\lambda_c$ : Si (1.12 eV) 1.11 μm, InGaAs (0.75 eV) 1.65 μm, Ge (0.66 eV) 1.88 μm (Sze & Ng). Shot noise $2eIB$ , thermal noise $4k_BTB/R_L$ , and the shot-limited SNR $\eta P/(2h\nu B)$ are from Saleh & Teich and Loudon Ch. 6; McIntyre's $F(M)=kM+(1-k)(2-1/M)$ and the 0.44 transit factor with the reciprocal-square transit/RC combination follow Sze & Ng. Constants: $e=1.602\times10^{-19}$ C, $h=6.626\times10^{-34}$ J·s, $k_B=1.381\times10^{-23}$ J/K, $c=2.998\times10^8$ m/s.

Prerequisites. Fiber Attenuation and Loss Mechanisms · Single-Mode and Multimode Operation. Leads to. Integrated Photonic Waveguides and Circuits · Microring Resonators and Optical Cavities on Chip.

Ask the tutor: Want to work through why an avalanche photodiode has an optimum gain, or size a real 1.55 μm coherent receiver from its noise floors? Ask me to walk through it step by step.

Why is responsivity capped at λ/1.24 A/W — where does that ceiling come from?

The ceiling is the $\eta=1$ case: if every incident photon produced exactly one collected electron, then $\mathcal{R}=e\lambda/(hc)=\lambda[\mu\mathrm{m}]/1.24$ A/W. Real detectors sit below it by the factor $\eta<1$ , folding in surface reflection, incomplete absorption, and recombination losses. You cannot beat it with an ordinary photodiode — it is one photon in, at most one electron out. The only way past is genuine internal gain, as in an avalanche photodiode where one photon triggers a cascade of $M$ carriers, but that gain buys extra noise, so the effective responsivity $M\mathcal{R}$ is not free.

What is the difference between quantum efficiency and responsivity?

They measure the same conversion in different currencies. Quantum efficiency $\eta$ is dimensionless — the probability, per incident photon, of collecting a carrier pair — bounded between 0 and 1 for a non-multiplying detector. Responsivity $\mathcal{R}$ is that same efficiency as amps per watt, and because it carries the factor $e\lambda/(hc)$ it depends on wavelength even when $\eta$ is flat — a detector can hold 80% efficiency across a band while its responsivity climbs, simply because a watt of longer-wavelength light is more photons. Use $\eta$ to compare the physics of absorption and collection; use $\mathcal{R}$ to size a real photocurrent.

Why does a thicker absorber make a photodiode both better and worse?

Because thickness $w$ pulls three ways at once. It raises efficiency ( $\eta\propto1-e^{-\alpha w}$ , more light absorbed in a longer path). It lowers the transit bandwidth, since carriers drift at fixed saturation velocity and a wider layer takes longer to cross ( $f_{tr}\approx0.44v_s/w$ ). And it raises the RC bandwidth, since a thicker depletion layer is a smaller capacitor ( $C_j=\varepsilon A/w$ ) that charges faster. Transit and RC oppose, so bandwidth peaks at an intermediate $w\approx$ 1–3 μm while efficiency keeps wanting more. The clean escape is a waveguide-coupled detector, where light runs along the absorber and carriers cross a thin dimension, so the two stop competing.

What actually is dark current, and why does it matter?

Dark current is what a reverse-biased photodiode passes with no light — thermally generated electron–hole pairs in the depletion region, plus surface leakage. It matters twice over. First, it is an offset that must be subtracted and drifts with temperature. Second, it shot-fluctuates just like the real photocurrent, contributing $2ei_dB$ to the noise variance, so it sets the noise-equivalent power in the dark. This is why low-light detectors are cooled: lowering the temperature suppresses the thermal generation exponentially, shrinking both the offset and its shot noise. A strong telecom signal dwarfs it; a photon-counting experiment can be dominated by it.

When should I choose an avalanche photodiode over a p-i-n?

Choose an APD only when your receiver is thermal-noise-limited — the signal so weak that load and amplifier noise, not its own shot noise, dominate. There the internal gain $M$ multiplies the signal before the noisy amplifier, lifting it above a thermal floor a p-i-n could never clear and improving sensitivity by several decibels. But the gain multiplies noise as $M^2F(M)$ , so past an optimum gain the excess multiplication noise overtakes the thermal noise you were fighting and sensitivity worsens. If the signal is already shot-noise-limited, an APD only adds noise and complexity, and it needs high, temperature-stabilized bias a p-i-n does not.

Why does the quantum-limit SNR not depend on the elementary charge?

It is the tell that you have hit a limit set by light, not electronics. In the general SNR the charge $e$ appears in both the signal (via $\mathcal{R}=\eta e/h\nu$ , squared) and the shot-noise denominator ( $2e\mathcal{R}PB$ ); when shot noise dominates, one power of $\mathcal{R}$ and the $e$ cancel, leaving $S/N=\eta P/(2h\nu B)$ — just the detected photon rate per bandwidth. Physically the discreteness of charge and of photons are the same granularity: each photon makes one carrier, so counting electrons is counting photons, and Poisson arrival statistics set the noise. No better electronics can help — the fluctuation is in the light itself.