Photodetectors and Receivers
Every optical link, and every photonic computation, ends the same way: the light must confess what it
knows to electronics. No matter how elegantly a mesh has interfered or a modulator has flickered, the
result is worthless until a photodetector turns photons back into electrons — and a
receiver decides, in the teeth of noise, what those electrons mean. The physics is
the photoelectric effect wearing
work clothes: a photon with energy above a semiconductor's band gap is absorbed, promotes an
electron across the gap, and a reverse-biased junction sweeps the resulting electron–hole pair out
as current. One absorbed photon, one elementary charge. Everything else in this lesson — responsivity,
dark current, shot noise, amplifiers, sensitivity — is bookkeeping on that one-for-one exchange, and
the bookkeeping decides the most important number in a link: how few photons a bit can be.
Germanium on silicon
Silicon itself is useless here — deliberately. Its 1.12 eV
band gap makes
it transparent at the telecom wavelengths (1.31 µm, 1.55 µm) whose photons carry only
0.8–0.95 eV — which is exactly why silicon waveguides work at all. To absorb, foundries grow a
strip of germanium (gap 0.66 eV, absorbing out to
\sim 1.6\ \mu\mathrm{m}) epitaxially on top of the silicon waveguide.
Light couples up from the waveguide into the Ge along its length, so the design escapes a classic
bind: absorption length and carrier-transit length point in different directions. The
device can be long enough to swallow every photon yet thin enough (~hundreds of nm) that carriers
reach the contacts in picoseconds — which is how a few-µm² Ge photodiode delivers both near-unity
efficiency and 50+ GHz bandwidth. Ge is no accident of physics but of economics: it is the one
strong absorber CMOS foundries already grow (SiGe transistors paved the way), so the detector comes
"for free" in the same flow as the waveguides.
Responsivity: the exchange rate
The detector's headline figure is its responsivity — amps of photocurrent per watt
of light. Each photon of energy h\nu yields at most one electron of
charge q, and a fraction \eta (the
quantum efficiency) of photons actually succeed, so
- R \;=\; \frac{I_{\text{photo}}}{P_{\text{opt}}} \;=\; \frac{\eta q}{h\nu}
\;=\; \eta\,\frac{\lambda\,[\mu\mathrm{m}]}{1.24}\ \ \mathrm{A/W};
- the exchange rate improves with wavelength: redder photons are individually cheaper
(less energy each), so a watt of them contains more, and each still buys one electron;
- it collapses to zero past the absorber's band-gap cutoff — for germanium, a little beyond
1.6 µm;
- worked example: at \lambda = 1.55\ \mu\mathrm{m} with
\eta = 0.8:
R = 0.8 \times 1.55/1.24 = 1.0\ \mathrm{A/W} — a milliwatt of light
becomes a milliamp of current.
The enemies: dark current and noise
A perfect detector would report exactly the photon arrivals. A real one lies in three ways. First,
dark current: even in total darkness, thermally generated carriers in the Ge (and
its defect-rich interface with Si) trickle across the junction — nanoamps to microamps that
masquerade as light and set a floor under weak signals. Second, shot noise: photon
arrivals (and dark-current carriers) are discrete, random events, so any current
I in bandwidth B fluctuates with variance
\sigma^2_{\text{shot}} = 2 q I B
— irreducible counting statistics; note the square root: quadrupling the current only doubles this
noise, so bright signals win. Third, thermal (Johnson) noise: the resistors and
transistors of the amplifier hiss on their own,
\sigma^2_{\text{th}} = 4kTB/R_L, independent of the light entirely.
The amplifier matters because the raw photocurrent is tiny — microamps that must become clean
volt-scale logic decisions within tens of picoseconds. The standard first stage is the
transimpedance amplifier (TIA): an op-amp with feedback resistor
R_F that pins the photodiode to a virtual ground (preserving bandwidth by
never letting the diode's capacitance charge up) and outputs
V = R_F I. In practice the receiver's noise is usually
thermal/amplifier-dominated at the low powers where links actually operate — the shot-noise
limit is the aspiration, the TIA's input-referred noise the reality — and "receiver sensitivity",
the minimum power for a target error rate, is mostly a statement about the TIA.
const q = 1.602e-19; // C
const h = 6.626e-34; // J·s
const c = 3e8; // m/s
// Responsivity at 1550 nm, eta = 0.8
const lambda = 1.55e-6;
const hnu = h * c / lambda; // photon energy, J
const R = 0.8 * q / hnu;
console.log("photon energy: " + (hnu / q).toFixed(2) + " eV");
console.log("responsivity : " + R.toFixed(2) + " A/W");
// A -28 dBm signal at 10 Gb/s: how many photons is a bit?
const P = 1e-3 * 10 ** (-28 / 10); // -28 dBm in watts
const bitRate = 10e9;
const photonsPerBit = P / (hnu * bitRate);
console.log("received power: " + (P * 1e6).toFixed(2) + " uW");
console.log("photons per bit: " + photonsPerBit.toFixed(0));
// Shot noise on the resulting photocurrent, in 10 GHz bandwidth
const I = R * P;
const sigma = Math.sqrt(2 * q * I * 10e9);
console.log("photocurrent: " + (I * 1e6).toFixed(3) + " uA, shot sigma: " +
(sigma * 1e9).toFixed(1) + " nA");
Read that middle number again: a respectable received signal is only about a thousand photons
per bit, and the practical floor for direct detection sits around a few hundred (coherent
receivers and avalanche gain push lower; the unbeatable quantum limit for ideal direct detection of
OOK is a famous ~10 photons/bit at 10^{-9} error rate). Photons are not a
continuous fluid at the receiving end — they are countable, and counted.
At 1.55 µm a perfect detector reaches R = 1.25\ \mathrm{A/W} — more
current out than watts in, which looks scandalously like gain. It isn't. Amps and watts are
different currencies, and the exchange rate hides the photon bookkeeping: a 1.55 µm photon
carries only 0.8 eV, so one watt delivers 1/(0.8 \times 1.602\times10^{-19})
\approx 7.8\times10^{18} photons each second, and even at one electron apiece that is
1.25 A of charge flow. Quantum efficiency is still capped at one electron per photon;
R exceeds 1 only because infrared photons are individually cheap. The
clean test: convert to \eta = R \times 1.24/\lambda[\mu\mathrm{m}] and
check \eta \le 1. Devices that genuinely break the one-per-photon rule
exist — avalanche photodiodes multiply each photoelectron in a controlled carrier avalanche, buying
sensitivity at the price of extra multiplication noise — but a bare Ge photodiode quoting
1.1 A/W is not one of them; it is just an honest detector working in a currency where photons
cost less than an electron-volt.
Next lesson will make much of the fact that silicon and germanium have indirect band gaps —
fatal for building lasers. So why do indirect-gap materials detect light perfectly well? Because
absorption and emission are not symmetric burdens. An emitter must channel every
recombination through the slow, phonon-assisted radiative path before faster non-radiative
processes steal the energy — a race indirect materials always lose. An absorber has no race to win:
a photon-plus-phonon absorption event is merely somewhat less probable per micron, and the fix is
simply more microns — make the absorber long enough (or resonant) and quantum efficiency
approaches one anyway. Detection is forgiving; emission is not. That asymmetry — germanium
detectors are easy, group-IV lasers are a forty-year research grail — is the whole reason the next
lesson exists.
Where this goes next
The photonic link is now complete except for its first component: light enters the story modulated,
guided, filtered and detected — but so far it is always brought from an external laser
through a coupler. The next lesson
confronts the awkward question the platform has been dodging: why the one component silicon
photonics cannot make out of silicon is the light itself, and what the industry does about it. The
receiver, meanwhile, returns in Module 5 with a starring role: in a photonic accelerator the
detector is not just a data endpoint, it is the summation node — photocurrents add — and
its noise, via this lesson's formulas, is what ultimately sets the precision of optical
analog
computation.