Avalanche Photodiode (APD)

1. Theory

• Definition: An avalanche photodiode (APD) is a photodiode operated at a reverse bias close to its breakdown voltage $V_{BR}$, so that the photogenerated carriers gain enough energy from the field to create further electron-hole pairs by impact ionization, and the output current is $M$ times the primary photocurrent.
• Gain: The gain $M$ is typically 50 to 500 (up to 1000) for silicon and 10 to 40 for germanium and InGaAs, at reverse voltages of 100 to 400 V for silicon and 30 to 80 V for InGaAs, and it depends strongly on the bias, $M\approx 1/[1-(V/V_{BR}{)}^n]$.
• Multiplication noise: The avalanche is random, so the multiplied current has excess noise $F(M)=kM+(1-k)(2-1/M)$ that depends on the ionization ratio $k=\beta /\alpha$; the smaller $k$ is (about 0.02 for silicon, 0.4 to 0.7 for InGaAs) the smaller the noise.
• Structures: Silicon APDs are not simple PN junctions but have a more complex profile such as a ${\mathrm{p}}^{+}$-i-p-${\mathrm{n}}^{+}$ reach-through design, and InGaAs APDs use a separate absorption layer of InGaAs and a multiplication layer of InP to reduce the tunnelling dark current and the noise.
• Materials: Silicon covers about 400 nm to 1000 nm (to 1100 nm), germanium and InGaAs up to about 1.7 μm, GaN the ultraviolet, and HgCdTe the infrared up to about 14 μm, with cooling.
• Gain-bandwidth limit: The gain is traded for bandwidth, so that the gain-bandwidth product $M{f}_{3dB}$ is the figure of merit; thin multiplication regions give products of 100 GHz and more (more than 100 GHz for InP and InAlAs designs, 424 GHz in one InGaAs design).
• Temperature: The breakdown voltage rises with temperature, at 0.65 V/°C in one silicon APD, so that the gain at a fixed bias falls as the device warms.
• Geiger mode: Biased above breakdown with the current quenched, the APD becomes a single-photon detector (separate page).

2. Working Principle

• Absorption: A photon with $h\nu \ge E_g$ creates an electron-hole pair in the absorption region, as in a PIN photodiode, with the responsivity ${\mathcal{R}}_0=\eta \lambda /1.24$ A/W at $M=1$.
• Acceleration: The carriers cross a high-field multiplication region, a few micrometres or less wide, where an electron or hole gains energy of the order of the ionization threshold before it collides.
• Impact ionization: Each ionization creates a new pair, which is accelerated in turn, and the chain gives the mean gain $M_e=(1-k)/\{\exp [-(1-k)\alpha w]-k\}$ for injection of electrons only, which diverges when $\alpha w=\ln (1/k)/(1-k)$.
• Gain control: The bias is set so that $M$ is between 10 and 100, below the breakdown voltage, and must be stable and temperature-compensated because the gain follows $V/V_{BR}$.
• Noise: The signal and the dark current of the bulk are multiplied by $M$ and carry the excess noise factor $F$, whereas the noise of the load and the amplifier is not multiplied, so the SNR improves until the multiplied shot noise equals the amplifier noise, at the optimum gain $M_{opt}$.
• Speed: The bandwidth is limited by the transit and the RC times as in the PIN photodiode, and in addition by the time that the avalanche takes to build up, which is why the product $M{f}_{3dB}$ is quoted.
• Readout: The multiplied current is converted to a voltage by a load or a transimpedance amplifier, and the high-voltage supply must be low-noise because the gain is sensitive to it.

3. Applications

• Long-haul fibre-optic receivers: InGaAs and germanium APDs, with gains of 10 to 20, raise the receiver sensitivity at 1300 nm and 1550 nm when the amplifier noise limits a PIN receiver.
• Laser rangefinders: Silicon APDs for the near infrared (400 nm to 1000 nm) detect the weak pulsed returns.
• Positron emission tomography: APDs are listed among the detectors of the scanners.
• Particle physics: APDs detect radiation, where a small excess noise factor limits the energy resolution.
• Low-light measurement: Low-light detection where the signal is below the noise of a PIN photodiode and amplifier, up to the single-photon level in the Geiger mode.

Name	Formula	Related Formulae	Variables/Constants
Multiplication factor (empirical, near breakdown)	$M=\frac{1}{1-{\left(V/V_{BR}\right)}^n}$	$M=\frac{I_{APD}}{I_{ph}}$ ${\mathcal{R}}_{APD}=M{\mathcal{R}}_0=M\frac{\eta \lambda }{1.24}A/W$	$\begin{array}{r}M:meanmultiplication(gain)factor,\\ divergingasthebiasVapproachesthe\\ breakdownvoltage{V}_{BR}\end{array}$ $\begin{array}{r}n:empiricalexponentfrom2to6\\ dependingonthematerial\end{array}$ $\begin{array}{r}{I}_{APD},I_{ph}:outputcurrentandprimary\\ (unmultiplied)photocurrent\end{array}$ $\begin{array}{r}{\mathcal{R}}_0:responsivityatM=1(0.50A/Wat800\\ nmforasiliconAPDwhosegainis100,so\\ that{\mathcal{R}}_{APD}=50A/W)\end{array}$ $\begin{array}{r}(typicalgainsare50to500(upto1000)\\ forsiliconand10to40forGeand\\ InGaAs;thegaindependsstronglyonthe\\ reversevoltageandsodoesthe\\ responsivity)\end{array}$
Multiplication for injection of one carrier type (McIntyre)	$M_e=\frac{1-k}{\exp \left[-\left(1-k\right)\alpha w\right]-k}$	$k=\frac{\beta }{\alpha }$ $\alpha w=\frac{\ln \left(1/k\right)}{1-k}\left(M_e\to \infty \right)$	$\begin{array}{r}\alpha ,\beta :ionizationcoefficients\\ (probabilitiesofionizationperunit\\ length)ofelectronsandholes,which\\ followtheChynowethlawoftheAvalanche\\ Diodepage\end{array}$ $w:widthofthemultiplicationregion$ $\begin{array}{r}k:ionizationratio,about0.02for\\ siliconand0.4to0.7forInGaAsinone\\ source(derivedlimits:M_e=e^{\alpha w}fork=0\\ and{M}_e=1/(1-\alpha w)fork=1)\end{array}$ $\begin{array}{r}(thelastrelationistheconditionat\\ which{M}_{e}diverges,whichisbreakdown;for\\ k=0.02itgives\alpha w\approx 4.0andfork=0.5it\\ gives\alpha w\approx 1.4(computed))\end{array}$
Excess noise factor (McIntyre)	$F\left(M\right)=kM+\left(1-k\right)\left(2-\frac{1}{M}\right)$	$k_{eff}=\frac{F-2+1/M}{M-2+1/M}$ $F\to 2-\frac{1}{M}\left(k=0\right),F=M\left(k=1\right)$	$\begin{array}{r}F:factorbywhichtheshot-noisepowerof\\ themultipliedcurrentexceedsthatofan\\ idealnoiselessgainM\end{array}$ $\begin{array}{r}k:ionizationratioofthecarrierthat\\ startstheavalanche\end{array}$ $\begin{array}{r}{k}_{eff}:valueofkthatreproducesameasured\\ FatagivenM(theinversionofthe\\ formula,derivedhere)\end{array}$ $\begin{array}{r}(FriseswithM,withk,withthereverse\\ voltageandwiththematerialanddesign;\\ onenotelistsF\approx 1foraPINdiode,3to\\ 5forsiliconAPDsand5to12forInGaAs\\ APDs)\end{array}$
Noise current of an APD receiver	$i_n^2=2q\left[I_{ds}+\left(I_{ph}+I_{db}\right)M^{2}F\right]B+\frac{4k_{B}TB}{R_{eq}}+i_{amp}^2$	$i_{sh,d}=\sqrt{2q{I}_{db}{M}^{2}FB}$ $i_{sh,s}=\sqrt{2q\left(I_{ph}+I_{db}\right)M^{2}FB}$	$\begin{array}{r}{I}_{db},I_{ds}:bulkdarkcurrent,whichis\\ multiplied,andsurfaceleakagecurrent,\\ whichisnot\end{array}$ $I_{ph}:primaryphotocurrent$ $\begin{array}{r}{M}^{2}F:gainandexcessnoiseofthe\\ shot-noisepowerofthemultiplied\\ currents(thefirsttwoformsarethoseof\\ theOxfordnote,thesplitofthedark\\ currentinthetotalbeingastandard\\ assumption)\end{array}$ $\begin{array}{r}{R}_{eq},i_{amp}:equivalentresistanceoftheload\\ andnoisecurrentoftheamplifier,which\\ arenotmultiplied\end{array}$ $B:bandwidth$ $k_B:Boltzmannconstant$
Signal-to-noise ratio with gain	$\mathrm{SNR}=\frac{{\left(M{I}_{ph}\right)}^2}{2q\left(I_{ph}+I_{db}\right)M^{2}FB+2q{I}_{ds}B+4k_{B}TB/R_{eq}+i_{amp}^2}$	$\mathrm{SNR}\to \frac{I_{ph}}{2qFB}\left(\mathrm{shot}\mathrm{noise}\mathrm{limit}\right)$	$\begin{array}{r}\mathrm{SNR}:mean-squaresignalcurrentdividedby\\ themean-squarenoisecurrent(derived\\ fromthenoiseexpressionabove)\end{array}$ $k_B:Boltzmannconstant$ $\begin{array}{r}(thegainraisesthesignalabovethe\\ noiseoftheamplifierandtheload,which\\ arenotmultiplied,butintheshot-noise\\ limittheSNRissmallerthanthatofa\\ PINdiode,whichis{I}_{ph}/2qB,bythefactor\\ F)\end{array}$
Optimum gain	$M_{opt}\approx {\left(\frac{i_{eq}^2}{q{I}_{ph}Bk}\right)}^{1/3}$	$i_{eq}^2=\frac{4k_{B}TB}{R_{eq}}+i_{amp}^2$	$\begin{array}{r}{M}_{opt}:gainthatmaximisestheSNRwhenthe\\ darkcurrentisneglectedandkM\gg 1so\\ thatF\approx kM(derivedbysettingthe\\ derivativeoftheSNRtozero)\end{array}$ $\begin{array}{r}{i}_{eq}:rmsnoisecurrentoftheloadandthe\\ amplifier(thebookexample,R_{eq}=1.73k\Omega \\ andB=1GHz,gives98nA)\end{array}$ $k_B:Boltzmannconstant$ $\begin{array}{r}(M_{opt}ishigherforasmallerkandfalls\\ asthesignalgrows,andagainmuchabove\\ M_{opt}lowerstheSNR)\end{array}$
Gain-bandwidth product	$\mathrm{GBP}=M{f}_{3dB}$	$f_{3dB}\approx \frac{0.35}{t_r}$	$\begin{array}{r}{f}_{3dB}:3dBbandwidthatthegainM,which\\ fallsasthegainisraisedbecauseofthe\\ avalanchebuild-uptime,inadditionto\\ thetransit-timeandRClimitsofthePIN\\ photodiode\end{array}$ $\begin{array}{r}(asiliconAPDhas{f}_{3dB}=900MHzatM=100\\ andarisetimeof0.39ns,givingGBP=\\ 90GHzand0.35/t_r=0.90GHz(computed);\\ upperlimitsof180to220GHzforInPand\\ InAlAs,290GHzand424GHzforInGaAs\\ designswiththinmultiplicationlayers)\end{array}$ $\begin{array}{r}(forashortmultiplicationregionthe\\ productisindependentofthegain,and\\ thebandwidthrisesastheregionismade\\ thinner)\end{array}$
Temperature shift of the breakdown voltage	$V_{BR}\left(T\right)=V_{BR}\left(T_0\right)+C_{bd}\left(T-T_0\right)$	$\Delta V=C_{bd}\Delta T$	$\begin{array}{r}{C}_{bd}:temperaturecoefficientofthe\\ breakdownvoltage(0.65V/{}^{\circ }Cforasilicon\\ APDof150Vtypicalbreakdown)\end{array}$ $\begin{array}{r}\Delta V:changeofbiasthatkeepsV/V_{BR},and\\ thereforethegain,constantwhenthe\\ temperaturechangesby\Delta T(32Vfor50\\ {}^{\circ }C,or22\%of150V(computed))\end{array}$

Important Questions

Ques: Why is the gain of an avalanche photodiode so sensitive to the bias voltage?

The gain $M=1/[1-(V/V_{BR}{)}^n]$ diverges as the bias approaches the breakdown voltage, and the device is used at gains of tens to hundreds, so it works close to that divergence. For $n=3$ a gain of 100 needs $V/V_{BR}=0.99^{1/3}\approx 0.9967$ (computed), within 0.3% of the breakdown voltage, and a small change of the bias or of $V_{BR}$ moves the gain by a large fraction. The sources therefore state that the responsivity depends strongly on the reverse voltage, that manufacturers specify a voltage range for a given gain, and that the bias supply must be low-noise. The empirical formula with $n$ of 2 to 6 is an approximation near breakdown and the sources give no value of $n$ for a given device. Reference: RF Essentials, Avalanche Photodiode (glossary page); RP Photonics Encyclopedia, Avalanche Photodiodes; Wikipedia, Avalanche photodiode (accessed October 2026).

Ques: Why does a small ionization ratio $k$ reduce the excess noise of an avalanche photodiode?

If only one carrier type ionizes ($k=0$) each primary carrier creates a chain that grows in one direction, the number of generations is less random, and $F=2-1/M$ stays below 2. If both types ionize equally ($k=1$), the secondary carriers start chains in both directions, the gain fluctuates strongly, and $F=M$. For $M=100$ and $k=0.02$ the formula $F=kM+(1-k)(2-1/M)$ gives 3.95, while for $M=10$ and $k=0.5$ it gives 5.95 (computed); the sources quote 3.9 and 5.9 for these cases. This is why silicon, with $k\approx 0.02$, has the lowest excess noise, and why injecting the carrier with the higher ionization coefficient (electrons in the alloy of one source) gave the lowest measured excess noise there. Reference: RF Essentials, Avalanche Photodiode (glossary page); RP Photonics Encyclopedia, Avalanche Photodiodes; J. P. R. David et al., IEEE Trans. Electron Devices (2002), as summarised from eprints.whiterose.ac.uk/id/eprint/900.

Ques: What is the ionization ratio of silicon: 0.02 or 0.03?

One source gives $k\approx 0.02$ for silicon, which with $M=60$ gives $F=3.14$ (computed). Another source lists a silicon APD with $M=60$ and $F=3.7$ at 960 nm, and inverting the formula, $k_{eff}=(F-2+1/M)/(M-2+1/M)$, gives $k_{eff}=0.030$ (computed). The second value is an effective one for the illumination used, because the same note states that the excess noise factor depends on the wavelength and on the gain, probably through the mixture of electron and hole injection, though the note gives no reason. The value 0.02 is therefore the more likely intrinsic ratio, and 0.02 to 0.03 is the practical range for silicon. Reference: RF Essentials, Avalanche Photodiode (glossary page); Oxford ATD group, Getting the best out of photodiode detectors (technical note).

Ques: Why is there an optimum gain, and how much does an APD improve a receiver?

The gain raises the signal $M{I}_{ph}$ above the noise $i_{eq}$ of the amplifier and the load, which is not multiplied, but the multiplied shot noise grows as $M^{2}F\approx k{M}^3$ in power. Setting the derivative of the SNR to zero gives $M_{opt}\approx (i_{eq}^2/q{I}_{ph}Bk{)}^{1/3}$. For the book receiver (98 nA of noise at 1 GHz, 1.125 μA primary current), $k=0.5$ gives $M_{opt}\approx 4.7$ and an SNR 7.9 dB above that of the PIN diode, and $k=0.02$ gives $M_{opt}\approx 12.7$ and 10.8 dB (all computed with the full expression for $F$). These agree with the +5 to +8 dB for InGaAs and +10 to +15 dB for silicon of one source. When the shot noise of the signal dominates, an APD is worse than a PIN diode by the factor $F$. Reference: RF Essentials, Avalanche Photodiode (glossary page); RP Photonics Encyclopedia, Avalanche Photodiodes; L. A. Coldren, S. W. Corzine and M. L. Mašanović, Diode Lasers and Photonic Integrated Circuits, 2nd ed., Wiley, 2012, Sec. 8.3.1.

Ques: Why does the bandwidth of an APD fall as the gain rises, and why do thin multiplication regions help?

The avalanche takes a time to build up, because each generation of carriers must cross the multiplication region and the holes and electrons feed each other, and this time grows with the gain; hence the gain-bandwidth product $M{f}_{3dB}$. A silicon APD with $f_{3dB}=900$ MHz at $M=100$ has a product of 90 GHz, and its rise time of 0.39 ns agrees with $0.35/t_r=0.90$ GHz (computed). For short regions the product no longer depends on the gain and the bandwidth rises as the region is made thinner; the dead space needed to gain the ionization energy delays the avalanche, but the higher carrier velocity outweighs it, and products of 290 and 424 GHz are reported for InGaAs designs. The sources give no closed formula for the bandwidth. Reference: Edmund Optics / Hamamatsu, S12023-05 0.5 mm NIR Si APD (specification table); J. P. R. David et al., IEEE Trans. Electron Devices (2002), as summarised from eprints.whiterose.ac.uk/id/eprint/900; RP Photonics Encyclopedia, Avalanche Photodiodes.

Ques: Why must the bias of an avalanche photodiode follow the temperature?

The breakdown voltage rises with temperature because the carriers lose more energy in collisions with the lattice, so at a fixed bias the ratio $V/V_{BR}$ and the gain fall as the device warms. A silicon APD with a coefficient $C_{bd}=0.65$ V/°C needs $\Delta V=C_{bd}\Delta T=32$ V for a 50 °C change, 22% of its 150 V breakdown voltage (computed), to keep the same gain. The remedies are thermoelectric cooling or a bias-compensation circuit. The sources give no numerical coefficient for the gain itself, and the explanation of the sign by lattice collisions is textbook knowledge, not stated in them. Reference: Edmund Optics / Hamamatsu, S12023-05 0.5 mm NIR Si APD (specification table); RP Photonics Encyclopedia, Avalanche Photodiodes; Wikipedia, Avalanche photodiode (accessed October 2026).

Ques: Why do InGaAs APDs separate the absorption and the multiplication regions?

InGaAs is the right absorber for 1.0 to 1.6 μm, and a few micrometres absorb nearly all the light, but its small band gap (0.74 eV, from the composition formula of the material page of the vault, computed) makes band-to-band tunnelling a likely source of dark current at the field required for multiplication (the mechanism is textbook knowledge). In the separate-absorption-and-multiplication structure the avalanche takes place in InP, and the source states that this reduces the tunnelling dark current and the noise. The gains of 10 to 40 and the ratios $k$ of 0.4 to 0.7 given in the sources show that the structure improves the dark current but leaves the excess noise higher than that of silicon. Reference: RP Photonics Encyclopedia, Avalanche Photodiodes; Wikipedia, Avalanche photodiode (accessed October 2026); RF Essentials, Avalanche Photodiode (glossary page).

Ques: What gain and bias are typical for a silicon APD?

The sources do not agree on one range. One states about 100 to 200 V and a gain of about 100 for standard silicon APDs, another a gain of 50 to 1000, a third 50 to 500 at 150 to 400 V, and a datasheet lists a breakdown voltage of 150 V typical (200 V maximum) at $M=100$. A difference of structure is a plausible reason, but the sources do not state it. The datasheet value together with the Wikipedia range makes a gain of about 100 at 100 to 200 V the most likely for a general-purpose device, with the larger gains for specialised devices. Reference: Wikipedia, Avalanche photodiode (accessed October 2026); RP Photonics Encyclopedia, Avalanche Photodiodes; RF Essentials, Avalanche Photodiode (glossary page); Edmund Optics / Hamamatsu, S12023-05 0.5 mm NIR Si APD (specification table).

Related pages in this vault: PN Photodiode, PIN Photodiode, Photodetectors (PIN and Avalanche Photodiodes), Phototransistor (HPT and Photo-FET), Single-Photon Avalanche Diode and Silicon Photomultiplier (SPAD, SiPM), HgCdTe Photodiode, Avalanche Diode, Diodes (PN, PIN, Schottky, Zener).