6. Optical Detectors: Photodiodes and APDs

A photodetector turns photons back into current. Two main types in fiber-optic receivers: PIN photodiodes and avalanche photodiodes (APDs).

6.1 PIN photodiodes

A PIN diode sandwiches a wide intrinsic (lightly doped) layer between heavily-doped p and n regions. Reverse-biased to a few volts, the depletion region fills the intrinsic layer, where the field is uniform and high. Photons absorbed in the i-region create electron-hole pairs that drift quickly under the field to the contacts, generating a current.

  +V  -                     -                                              + (n+)
   ↓ 
   ▢▢▢▢ p+ layer
   ░░░░░░░░░░
   ░░░░░░░░░░  intrinsic absorption region (depletion zone)
   ░░░░░░░░░░  ─────► photon hits here, e-h pair created, swept to contacts
   ░░░░░░░░░░
   ▢▢▢▢ n+ layer
   ↑
   GND

Key parameters:

• Quantum efficiency $\eta$: fraction of incident photons that produce a useful electron. Typical 70 to 90% in the design wavelength range.
• Responsivity $R = \eta \cdot q / (h f) = \eta \lambda / 1.24$ A/W (with $\lambda$ in µm). At 1550 nm with 80% quantum efficiency, $R \approx 1$ A/W.
• Bandwidth: limited by the carrier transit time across the depletion region and the RC time constant of the device. Telecom PINs reach 10 to 50 GHz.
• Dark current: leakage in the absence of light, sets a noise floor. A few nA in InGaAs PINs.

Material choice depends on wavelength:

• Silicon PINs for 850 nm (silicon's absorption band edge is at 1100 nm).
• InGaAs PINs for 1310 and 1550 nm (silicon is transparent at these wavelengths).
• Germanium PINs also work at 1310 and 1550, but have higher dark current.

6.2 Avalanche photodiodes (APDs)

An APD adds an internal multiplication region with a strong electric field. A primary photogenerated carrier accelerates, ionizes more carriers via impact ionization, and the avalanche multiplies the original signal by a factor $M$ of 10 to 100. The result is a more sensitive receiver: the signal current is multiplied before any electronic noise gets added, so the receiver's SNR per photon goes up.

The price: avalanche multiplication adds excess noise $F(M)$, which scales roughly as $M^x$ with $x$ between 0.2 (silicon) and 1 (InGaAs). And APDs need 30 to 70 V reverse bias instead of 3 to 5 V for PINs, requiring a charge pump in pluggable optics.

APDs win in long-distance systems where sensitivity, not bandwidth, is the bottleneck. In short-reach high-speed systems (100 GbE in datacenters), simple PINs with TIA are cheaper and good enough.

6.3 Receiver noise sources

The noise that ultimately limits how few photons per bit you need to detect a 1 from a 0 has three contributions, all of which we met in Chapter 0.

• Shot noise: the photons arrive Poisson-distributed. Variance equals the mean count. For an average current $I$, shot noise has spectral density $2qI$ A$^2$/Hz.
• Thermal (Johnson) noise: the resistor in the front-end amplifier produces $4 k_B T / R$ A$^2$/Hz at temperature $T$.
• Dark current noise: shot noise on the leakage current $I_d$, contributing $2 q I_d$ A$^2$/Hz.

Total electrical noise current squared is the sum, integrated over the receiver bandwidth $B$:

$\sigma_I^2 = (2qI + 2qI_d + 4k_BT/R)\,B.$

A typical receiver at 10 Gbps with 1 nA dark current and $R = 50$ ohm at room temperature is shot-noise-limited at high signal levels and thermal-noise-limited at low signal levels.

6.4 Sensitivity and the bit error rate

For NRZ on-off keying with Gaussian noise, the bit error probability is

$P_e = \tfrac{1}{2}\text{erfc}(Q/\sqrt{2})$

with $Q$ the Q factor, the ratio of mean signal to noise in a one-vs-zero comparison. $Q = 6$ gives BER $= 10^{-9}$, the historical telecom target. $Q = 7$ gives $10^{-12}$. With forward error correction (Chapter 12), pre-FEC BER of $10^{-3}$ is acceptable because the FEC corrects to far better.

The quantum limit says that even with no electronic noise, you need about 10 photons per bit to hit BER of $10^{-9}$ — pure photon counting statistics. Real receivers need 100 to 1000 photons per bit. Coherent receivers approach within a factor of 2 of the quantum limit; PIN + TIA receivers are closer to a factor of 10.