Avalanche photodiode (APD)

An avalanche photodiode (APD) is a photodiode with internal current gain: its photocurrent is $M$ times what the same diode would give without gain, with $M$ typically 10 to 40 in InGaAs devices and 100 to 500 in silicon. The gain raises weak signals above the noise of the receiver's amplifier, which is why APDs are used in long-reach and passive-optical-network receivers, LiDAR and laser rangefinders; the costs are excess noise, which sets an optimum gain, and a high bias that has to track temperature. The Photodiode Noise Calculator finds the optimum gain for a given signal and front end.

The device is reverse biased close to its breakdown voltage, so that photogenerated carriers crossing a high-field region gain enough energy to create further electron–hole pairs by impact ionization, and those carriers ionize in turn. Each primary photocarrier emerges as $M$ carriers on average, and the photocurrent is

$$I_{\text{APD}}=M{\mathcal{R}}_0{P}_{\text{opt}}$$

where ${\mathcal{R}}_0$ is the unity-gain responsivity and $P_{\text{opt}}$ the incident power. Practical devices separate the two functions: light is absorbed in a low-field layer, as in a PIN photodiode, and the carriers drift into a thin multiplication layer, which in telecom InGaAs APDs is InP or InAlAs. The gain is useful because it acts before the amplifier: it raises the signal above the thermal noise of the load or transimpedance amplifier, which is the dominant noise in most fast receivers.

Excess noise

Multiplication is a random process, and the number of secondary carriers produced by each primary one fluctuates. The shot noise of the primary current is therefore multiplied by more than $M^2$:

$$i_{\text{shot}}^2=2e{M}^{2}F(M)(I_p+I_{dm})B$$

where $I_p={\mathcal{R}}_0{P}_{\text{opt}}$ is the primary photocurrent, $I_{dm}$ the part of the dark current that passes through the multiplication region, $B$ the bandwidth and $F(M)$ the excess noise factor. McIntyre's result for a uniform multiplication region, with the more strongly ionizing carrier injected, is

$$F(M)=kM+(1-k)(2-\frac{1}{M})$$

with $k$ the ratio of the ionization coefficient of the weaker ionizing carrier to that of the stronger one. When only one carrier type ionizes ($k=0$), $F$ tends to 2 at high gain; when both ionize equally ($k=1$), $F=M$ and the noise grows as $M^3$. At $M=10$ the factor is 2.06 for $k=0.02$, 3.52 for $k=0.2$, 5.95 for $k=0.5$ and 7.57 for $k=0.7$, a noise penalty of 3.1 dB to 8.8 dB on the multiplied shot noise. Injecting the wrong carrier, or letting light be absorbed inside the multiplication layer, replaces $k$ by $1\mathrm{/}k$ and makes the device far noisier, which is one reason for the separate absorption layer.

The ranges are the typical values given by Agrawal (chapter 4). Silicon, with its very small $k$, makes the quietest APDs and is used at visible and 850 nm wavelengths; germanium's $k$ near one limits it to modest gain; and InGaAs/InP is the standard at 1310 and 1550 nm. Thin InAlAs multiplication layers give lower $k$ than InP and are used in faster telecom APDs.

Optimum gain

With the primary photocurrent $I_p$ and a fixed noise density $S$ from the load resistor and amplifier, the signal-to-noise ratio in a bandwidth $B$ is

$$\text{SNR}=\frac{M^2{I}_p^2}{[2e{M}^{2}F(M)I_p+S]B}$$

neglecting dark current. At low gain the numerator grows faster than the multiplied shot noise and the SNR improves; at high gain $F(M)$ grows with $M$ and the SNR falls again. Setting the derivative to zero gives the optimum,

$$k{M}_{\text{opt}}^3+(1-k)M_{\text{opt}}=\frac{S}{e{I}_p}$$ $$M_{\text{opt}}\approx {\left(\frac{S}{ke{I}_p}\right)}^{1\mathrm{/}3}$$

with the approximation valid when $kM\gg 1$. The optimum falls as the cube root of the signal, so a strong signal wants little gain, and it rises as $k$ falls.

A worked case: an InGaAs APD with $\eta =0.8$ at 1550 nm (${\mathcal{R}}_0=1.00$ A/W) receives $-30$ dBm, a primary photocurrent of 1.00 µA, in a 10 GHz bandwidth with a 10 pA/√Hz amplifier. At $M=1$ the SNR is $-0.01$ dB, no better than a PIN. With $k=0.5$ the optimum gain is 10.7, where $F=6.3$ and the SNR is 15.4 dB; with $k=0.2$ the optimum is 14.5 and the SNR 17.2 dB. The ideal shot-noise-limited SNR at this power is 24.9 dB, and the difference is the excess noise and the amplifier noise that remains at the optimum. The cube-root approximation gives 10.8 and 14.6 for the two cases.

Bias, temperature and bandwidth

The gain rises steeply as the bias approaches the breakdown voltage $V_B$. An empirical fit due to Miller,

$$M=\frac{1}{1-(V\mathrm{/}{V}_B{)}^n},$$

with the exponent $n$ fitted to the device, shows how steep it is: for a device with $V_B=50$ V and $n=3$, the gain is 10 at 48.3 V and 20 at 49.2 V, so doubling the gain takes less than a volt. The breakdown voltage itself increases with temperature because phonon scattering takes energy from the carriers, so an APD held at fixed bias loses gain as it warms. Receivers either regulate the device temperature with a thermoelectric cooler or adjust the bias with temperature to hold $M$. The avalanche takes time to build up, and at high gain the bandwidth falls roughly as $1\mathrm{/}M$ at a fixed gain–bandwidth product, so a fast APD trades gain for speed. Biased above breakdown, the diode no longer has a finite gain: a single carrier can trigger a self-sustaining avalanche, which is the Geiger-mode operation of the single-photon avalanche diode.

When an APD helps

The APD improves sensitivity only when the fixed noise of the electronics dominates. In the worked case above, a PIN on the same amplifier needs $-22.3$ dBm to reach the 15.4 dB that the $k=0.5$ APD reaches at $-30$ dBm, an advantage of 7.7 dB of optical power (8.7 dB for $k=0.2$), and gains of this size in receiver sensitivity are why APDs are used in long-reach and passive-optical-network receivers, including burst-mode receivers. When the photocurrent is already large enough for its own shot noise to exceed the amplifier noise, the optimum gain approaches one and a PIN is simpler, more linear and needs no high-voltage bias. The Photodiode Noise Calculator applies the McIntyre factor for a chosen $M$ and $k$, plots SNR against gain, and reports the optimum gain for the chosen power and front end.

Choosing a PIN, an APD or a SPAD

Common questions

What is an avalanche photodiode?

A photodiode operated at a reverse bias close to breakdown, where each photogenerated carrier gains enough energy to free further electron-hole pairs by impact ionization. The photocurrent is multiplied by a gain $M$, typically 10 to 40 in InGaAs and 100 to 500 in silicon, which lifts weak signals above the noise of the receiver's amplifier at the cost of excess noise.

What is the difference between an APD and a PIN photodiode?

An APD has internal gain from impact ionization and a PIN does not. When the amplifier's noise dominates, the gain improves sensitivity: by about 8 dB of optical power in the worked case above. The costs are a bias of tens to hundreds of volts that must track temperature, excess noise, and a gain-bandwidth limit.

What gain should an APD run at?

At the optimum where the signal-to-noise ratio peaks, found from the formula above; it rises as the signal weakens and as $k$ falls. In the 10 GHz worked case the optimum is about 11 for an InP multiplier ($k=0.5$) and about 15 for $k=0.2$. Running above the optimum adds noise faster than signal.

What is the excess noise factor?

The factor $F(M)$ by which the random multiplication raises the shot noise above the $M^2$ that a noiseless gain would give. At $M=10$ it is 2.06 for silicon ($k=0.02$) and 5.95 for an InP multiplier ($k=0.5$).

Why are silicon APDs quieter than InGaAs APDs?

In silicon, electrons ionize far more readily than holes, so $k$ is 0.02 to 0.05 and the avalanche stays close to one-directional. The InP multiplication layer of an InGaAs APD has $k$ of 0.5 to 0.7, so both carriers feed the avalanche and the excess noise grows faster with gain.

Where APDs sit among the other detector types is summarized in Types of Photodetectors.

References: R. J. McIntyre, "Multiplication noise in uniform avalanche diodes," IEEE Transactions on Electron Devices ED-13, 164 (1966). G. P. Agrawal, Fiber-Optic Communication Systems, 4th ed. (Wiley, 2010), chapter 4. B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, 3rd ed. (Wiley, 2019). S. M. Sze and K. K. Ng, Physics of Semiconductor Devices, 3rd ed. (Wiley, 2007). S. L. Miller, "Avalanche breakdown in germanium," Physical Review 99, 1234 (1955).