PIN Photodiode

1. Theory

• Definition: A PIN photodiode is a reverse-biased diode with a lightly doped, nearly intrinsic layer of thickness $W_i$ between a heavily doped ${\mathrm{P}}^{+}$ layer and a heavily doped ${\mathrm{N}}^{+}$ layer, in which the photons are absorbed and the carriers are swept out by drift.
• Fixed depletion width: Above the reach-through voltage $V_{RT}\approx q{N}_i{W}_i^2/2{\epsilon }_s$ the i-layer is fully depleted, so the depleted thickness is set by the growth ($W_i$) and not by the bias, and the capacitance $C_j={\epsilon }_{s}A/W_i$ is almost independent of the bias.
• Collection by drift: Nearly all absorption occurs in the high-field region, so the slow diffusion tail of the simple PN photodiode is absent and the quantum efficiency is $\eta =(1-R_f)(1-e^{-\alpha W_i})$.
• Thickness trade-off: A thicker i-layer raises the efficiency but lengthens the transit time ${\tau }_{tr}=W_i/v_{sat}$, while a thinner one raises the transit-limited bandwidth $f_{tr}\approx 0.44v_{sat}/W_i$ but increases the capacitance, so an optimum thickness exists for a given area and load.
• Materials: Silicon covers the visible to about 1100 nm, germanium and InGaAs cover the 1300 nm and 1550 nm telecommunication windows (the spectral response of the InGaAs datasheets spans roughly 800 nm to 1800 nm), with quantum efficiencies above 80% to 90% at 1500 nm for Ge and InGaAs.
• Speed: Ge and InGaAs devices reach several tens of GHz, the general-purpose silicon devices BPW34 and SFH203 have bandwidths above 100 MHz, and waveguide structures are used for 10 Gb/s and beyond.
• Noise: In direct detection the thermal noise of the load, $\sqrt{4k_{B}TB/R_{eq}}$, normally dominates the shot noise; the shot noise dominates only at high optical power, as in coherent receivers.
• Role in photonic circuits: The large majority of the photodiodes used in photonic integrated circuits are reverse-biased PIN structures.

2. Working Principle

• Biasing: A reverse bias above $V_{RT}$ depletes the i-layer completely, so the field is nearly uniform, and a bias near $V_{sat}\approx E_s{W}_i$ brings the carriers to the saturated drift velocity.
• Absorption: A photon with $h\nu \ge E_g$ is absorbed in the i-layer at a depth set by $1/\alpha$ and creates an electron-hole pair; a fraction $(1-R_f)(1-e^{-\alpha W_i})$ of the incident photons is absorbed there.
• Drift and photocurrent: The field sweeps the electrons to the ${\mathrm{N}}^{+}$ side and the holes to the ${\mathrm{P}}^{+}$ side in a time ${\tau }_{tr}$, and the external current is $I_{ph}=\mathcal{R}{P}_{in}$ with $\mathcal{R}=\eta \lambda /1.24$ A/W.
• Dark current: The leakage of the reverse-biased layer grows with its area and volume, $I_d\propto A{W}_i$, and with temperature, and it sets the shot-noise floor $\mathrm{NEP}=\sqrt{2q{I}_d}/\mathcal{R}$.
• Speed: The response is limited by the transit time through $f_{tr}$ and by the RC time constant through $f_{RC}=W_i/(2\pi R{\epsilon }_{s}A)$, so that the bandwidth is $1/f_{3dB}^2\approx 1/f_{tr}^2+1/f_{RC}^2$ and a small area helps.
• Waveguide structures: The light travels along the absorber of length $L_D=\ln [1/(1-\eta )]/({\Gamma }_{xy}\alpha )$ while the carriers cross a thin i-layer, which removes the compromise between efficiency and drift time of the vertical device; evanescently coupled versions give about four times higher saturation current than edge-coupled ones.
• High power: At high optical power the photogenerated space charge reduces the field in the i-layer and increases the transit time; the uni-traveling-carrier design, with a narrow-gap p-type absorber and a wide-gap collector, avoids this.
• Readout: The photocurrent is converted to a voltage by a load resistor or a transimpedance amplifier, $V_{out}=I_{ph}{R}_L$, or is mixed with a local oscillator in coherent receivers.

3. Applications

• Fibre-optic receivers: InGaAs and germanium PIN photodiodes are the detectors of network cards, switches and high-speed optical telecommunication links at 1300 nm and 1550 nm.
• Receiver photonic integrated circuits: Waveguide PIN photodiodes follow an arrayed-waveguide-grating demultiplexer in multichannel receivers, such as a 40-channel receiver at 40 Gb/s, and form the balanced pairs of coherent receivers.
• General-purpose light sensing: Silicon PIN photodiodes of the BPW34 and SFH203 type, with bandwidths above 100 MHz, and fast silicon devices with cutoff frequencies of 100 MHz to 1 GHz and peak sensitivity between 760 nm and 920 nm.
• Radiation detection: The fully depleted i-layer detects ionizing radiation.
• Solar cells: Thin-film amorphous-silicon cells use the PIN structure in the photovoltaic mode.

Name	Formula	Related Formulae	Variables/Constants
Reach-through (full-depletion) voltage	$V_{RT}\approx \frac{q{N}_i{W}_i^2}{2{\epsilon }_s}$	$V_{sat}\approx E_s{W}_i$	$\begin{array}{r}{V}_{RT}:reversebiasatwhichthelightly\\ dopedi-layerisfullydepleted,above\\ whichthedepletionwidthstaysequalto\\ W_i\end{array}$ $\begin{array}{r}{N}_i,W_i:residualdopingandthicknessof\\ thei-layer(thethicknessissetbythe\\ growthandnotbythebias)\end{array}$ ${\epsilon }_s:permittivity$ $\begin{array}{r}{E}_s,V_{sat}:fieldatwhichthedriftvelocity\\ saturatesandthebiasthatputsthewhole\\ i-layeratthatfield(E_s\approx 2\times 10^{6}V/mand\\ 20Vfora10\mu \mathrm{m}siliconlayerinone\\ source)\end{array}$
Junction capacitance	$C_j=\frac{{\epsilon }_{s}A}{W_i}\left(V_R>V_{RT}\right)$	$C=C_j+C_p$	$\begin{array}{r}{C}_j:capacitanceofthefullydepleted\\ i-layer,independentofthebiasonce{V}_R>\\ V_{RT}\end{array}$ $A:junctionarea$ $\begin{array}{r}{C}_p:parasiticcapacitanceofthepad,bond\\ wireandpackage\end{array}$ $\begin{array}{r}(thecapacitancescaleswiththeareaand\\ fallswiththethicknessofthei-layer,\\ unlikethePNphotodiodewhereitfalls\\ onlyasthesquarerootofthebias)\end{array}$
Responsivity and quantum efficiency of the absorbing layer	$\eta =\left(1-R_f\right)\left(1-e^{-\alpha W_i}\right)$	$\mathcal{R}=\frac{\eta q}{h\nu }=\frac{\eta \lambda }{1.24}A/W$ $\eta =\left(1-R_f\right)\left(1-e^{-\alpha W_i}\right)\left(1+r_b{e}^{-\alpha W_i}\right)$	$\begin{array}{r}\eta :externalquantumefficiencywhenevery\\ carriergeneratedinthei-layeris\\ collected(thedopedlayersbeingthinand\\ notcounted)\end{array}$ $R_f:front-surfacereflectance$ $\begin{array}{r}\alpha :absorptioncoefficientatthe\\ wavelengthused(335c{m}^{-1}forsiliconat\\ 860nminonesource)\end{array}$ $\begin{array}{r}{r}_b:reflectanceofthebackcontactinthe\\ double-passform,inwhichthelightthat\\ wasnotabsorbedisreflectedandcrosses\\ thelayeragain(themultiplereflections\\ beingneglected)\end{array}$ $\begin{array}{r}\lambda :wavelengthinmicrometresinthe\\ numericalformoftheresponsivity\mathcal{R}\end{array}$
Thickness of the i-layer for a target efficiency	$W_i=\frac{1}{\alpha }\ln \frac{1}{1-{\eta }_i}$	$L_D=\frac{1}{{\Gamma }_{xy}\alpha }\ln \frac{1}{1-\eta }$	$\begin{array}{r}{\eta }_i:internalefficiency(reflection\\ neglected)thatthei-layermustgivefor\\ anormal-incidencephotodiode\end{array}$ $\begin{array}{r}{L}_D,{\Gamma }_{xy}:lengthandconfinementfactorofa\\ waveguidephotodiode,inwhichthelight\\ travelsalongtheabsorberinsteadof\\ acrossit(Eq.8.22ofthebookwitha\\ confinementfactor)\end{array}$
Transit-time-limited bandwidth	$f_{tr}\approx \frac{0.44}{{\tau }_{tr}}=\frac{0.44v_{sat}}{W_i}$	${\tau }_{tr}=\frac{W_i}{v_{sat}}$ $B\approx \frac{0.35}{t_r}$	$\begin{array}{r}{\tau }_{tr}:timefortheslowercarriertocross\\ thei-layeratthesaturatedvelocity{v}_{sat}\\ (about6\times 10^{6}cm/sforInGaAsand10^{7}cm/s\\ forsiliconholesinthesources)\end{array}$ $\begin{array}{r}B,t_r:bandwidthand10\%to90\%rise\\ time(a10\mu \mathrm{m}siliconlayergives{\tau }_{tr}\approx 0.1\\ nsandB\approx 3.5GHzinonesource)\end{array}$ $\begin{array}{r}(validwhenthefieldishighenoughfor\\ thevelocitiestosaturate,sothatabias\\ near{V}_{sat}isneeded)\end{array}$ $\begin{array}{r}(thefactor0.44isthe3dBpointofa\\ rectangularcurrentpulse,carriersmadein\\ athinsheetatoneedgeandcrossingthe\\ wholelayer;forgenerationspread\\ uniformlythroughthelayerthecurrentis\\ triangularandthefactoris0.55,soreal\\ devicesliebetweenthetwo)\end{array}$
RC-limited bandwidth	$f_{RC}=\frac{1}{2\pi RC}=\frac{W_i}{2\pi R{\epsilon }_{s}A}$	$\frac{1}{f_{3dB}^2}\approx \frac{1}{f_{tr}^2}+\frac{1}{f_{RC}^2}$	$\begin{array}{r}R:sumoftheseriesresistanceofthe\\ diodeandtheloadresistanceseenbyit\\ (50\Omega foramatchedreceiver)\end{array}$ $\begin{array}{r}C:totalcapacitance,takenas{C}_{j}foran\\ idealdevice\end{array}$ $\begin{array}{r}(f_{RC}riseswiththethickness{W}_{i}andfalls\\ withtheareaA,theoppositebehaviourto\\ f_{tr})\end{array}$ $\begin{array}{r}{f}_{3dB}:overallbandwidth,thesmallerlimit\\ dominating(thediffusiontailisabsent\\ becausethei-layerisfullydepleted)\end{array}$
Optimum i-layer thickness and the highest bandwidth	$W_{opt}=\sqrt{2\pi \cdot 0.44v_{sat}R{\epsilon }_{s}A}$	$f_{max}=\sqrt{\frac{0.44v_{sat}}{4\pi R{\epsilon }_{s}A}}$	$\begin{array}{r}{W}_{opt}:thicknessatwhich{f}_{tr}=f_{RC},which\\ minimises1/f_{3dB}^2(derivedfromthetwo\\ limitsabove)\end{array}$ $\begin{array}{r}{f}_{max}:highestoverallbandwidthatthat\\ thickness,whichfallsonlyasthesquare\\ rootoftheareaandoftheload\\ resistance\end{array}$ $\begin{array}{r}(fora50\mu \mathrm{m}diameterInGaAsdiode,R=50\\ \Omega ,v_{sat}=6\times 10^{6}cm/sand{\epsilon }_r=13.9(assumed),\\ W_{opt}\approx 1.4\mu \mathrm{m}and{f}_{max}\approx 13GHz(computed))\end{array}$
Shot-noise-limited noise-equivalent power	$\mathrm{NEP}=\frac{\sqrt{2q{I}_d}}{\mathcal{R}}$	$I_d\approx \frac{qA{n}_i{W}_i}{2{\tau }_g}\propto A{W}_i$	$\begin{array}{r}\mathrm{NEP}:noise-equivalentpowerinW/\sqrt{Hz}when\\ theshotnoiseofthedarkcurrentisthe\\ onlynoise\end{array}$ $I_d:darkcurrentattheoperatingbias$ $\begin{array}{r}(thedatasheetNEPofthreesiliconPIN\\ photodiodes,7.4,3.1and1.1\times 10^{-15}W/\sqrt{Hz},\\ isreproducedbythisexpressionfrom\\ theirtypicaldarkcurrentsand\\ sensitivities)\end{array}$ $\begin{array}{r}{n}_i,{\tau }_g:intrinsicdensityandgeneration\\ lifetimeofthei-layer,thegenerationin\\ thefullydepletedlayergrowingwithits\\ volume\end{array}$
Thermal-noise-limited minimum power of a direct-detection receiver	$P_{min}=\frac{\sqrt{\mathrm{SNR}}}{\mathcal{R}}\sqrt{\frac{4k_{B}TB}{R_{eq}}}$	$i_J=\sqrt{\frac{4k_{B}TB}{R_{eq}}}$	$\begin{array}{r}{P}_{min}:averageopticalpowerfora\\ signal-to-noiseratio\mathrm{SNR}(mean-square\\ currentratio)whentheJohnsonnoiseof\\ theloaddominatesandthedarkcurrentis\\ neglected\end{array}$ $R_{eq}:loadorfeedbackresistance$ $B:electricalbandwidth$ $i_J:rmsJohnson-noisecurrent$ $k_B:Boltzmannconstant$ $\begin{array}{r}(forthebookexample,R_{eq}=1.73k\Omega ,B=1\\ GHz,\mathcal{R}=1.125A/W,\mathrm{SNR}=1gives{i}_J\approx 98nA\\ and{P}_{min}\approx 87nW(-40.6dBm)(computed))\end{array}$
Coherent (heterodyne) detection with a PIN photodiode	$I\left(t\right)=\mathcal{R}\left[P_{LO}+P_{in}+2\sqrt{P_{LO}{P}_{in}}\cos \left(\Delta \omega t+\Delta \varphi \right)\right]$	${\mathrm{SNR}}_{shot}=\frac{\mathcal{R}{P}_{in}}{qB}=\frac{\eta P_{in}}{h\nu B}$	$\begin{array}{r}{P}_{LO},P_{in}:powersofthelocaloscillatorand\\ ofthesignal\end{array}$ $\begin{array}{r}\Delta \omega ,\Delta \varphi :differenceoftheangular\\ frequenciesandphases(Eq.8.23ofthe\\ book)\end{array}$ $\begin{array}{r}(thebeattermisproportionalto\sqrt{P_{LO}{P}_{in}}\\ andsoisamplifiedbythelocal\\ oscillator,whichmakestheshotnoiseof\\ thelocaloscillatorthedominantnoise)\end{array}$ $\begin{array}{r}{\mathrm{SNR}}_{shot}:electricalsignal-to-noiseratioof\\ thebeatsignallimitedbytheshotnoise\\ ofthelocal-oscillatorphotocurrent,\\ derivedhere,Bbeingtheelectrical\\ bandwidth\end{array}$
Waveguide photodiode length and capacitance	$L_D=\frac{1}{{\Gamma }_{xy}\alpha }\ln \frac{1}{1-\eta }$	$C_D\approx c^{\prime }{L}_D$ $R_L=\frac{1}{2\pi B{C}_D}$	$\begin{array}{r}{L}_D:lengthoftheabsorberneededforthe\\ efficiency\eta \end{array}$ $\begin{array}{r}{\Gamma }_{xy}:overlapoftheopticalmodewiththe\\ absorbinglayer(5\%inthebookexample)\end{array}$ $\begin{array}{r}{c}^{\prime }:capacitanceperunitlengthofthe\\ reverse-biasedwaveguide(about1fF/\mu \mathrm{m}in\\ thebookexample,giving92fFfor92.12\\ \mu \mathrm{m})\end{array}$ $\begin{array}{r}{R}_L:loadresistorthatmakestheRC\\ bandwidthequaltothebitrateB(1.73k\Omega \\ for1Gb/sintheexample)\end{array}$

Important Questions

Ques: Why does the i-layer make the capacitance of a PIN photodiode independent of the bias, and why does it remove the diffusion tail?

Above $V_{RT}\approx q{N}_i{W}_i^2/2{\epsilon }_s$ the lightly doped layer is fully depleted, so the depleted thickness is the grown thickness $W_i$ and cannot widen further with the bias; the capacitance $C_j={\epsilon }_{s}A/W_i$ is then constant, whereas a PN junction has $W\propto \sqrt{V_{bi}+V_R}$ and a capacitance that keeps changing with the bias. The same wide, field-filled layer holds nearly all the absorbed light, so carriers are made where they drift instead of where they diffuse, and the slow tail that a simple PN photodiode shows disappears. The remaining penalty is the transit time ${\tau }_{tr}=W_i/v_{sat}$, which is why the thickness has to be chosen and not simply increased. Reference: Wikipedia, PIN diode (accessed October 2026); R. S. Quimby, Photonics and Lasers, Wiley, 2006, Sec. 14.4 (as fetched at GlobalSpec).

Ques: What bias saturates the drift velocity in the i-layer?

The transit time is shortest when the field exceeds the saturation field $E_s$, which needs $V_{sat}\approx E_s{W}_i$. One source takes $E_s\approx 2\times 10^6$ V/m for silicon holes, so a 10 μm layer needs about 20 V and has ${\tau }_{tr}\approx 0.1$ ns and $B\approx 3.5$ GHz, while a 0.1 mm layer needs an inconveniently high bias of about 200 V (computed). Another source puts the saturation near $10^5$ V/cm ($10^7$ V/m), five times larger, which would give about 100 V for 10 μm. The lower value is the more likely for a silicon PIN diode, since the silicon datasheets of the sources are run at 10 V (3.3 V for the fastest one) with a 20 V maximum, and the higher value is a general figure for several semiconductors. Reference: R. S. Quimby, Photonics and Lasers, Wiley, 2006, Sec. 14.4 (as fetched at GlobalSpec); UCSB ECE162C, Lecture 16 (Blumenthal); Hamamatsu, Si PIN photodiodes S5971, S5972, S5973 series (datasheet, Nov. 2019).

Ques: Why does an optimum i-layer thickness exist, and how large is the highest bandwidth?

The transit limit $f_{tr}\approx 0.44v_{sat}/W_i$ falls with the thickness, and the RC limit $f_{RC}=W_i/(2\pi R{\epsilon }_{s}A)$ rises with it because $C_j={\epsilon }_{s}A/W_i$ falls. Minimising $1/f_{3dB}^2=1/f_{tr}^2+1/f_{RC}^2$ gives equal limits at $W_{opt}=\sqrt{2\pi \cdot 0.44v_{sat}R{\epsilon }_{s}A}$, and $f_{max}=\sqrt{0.44v_{sat}/(4\pi R{\epsilon }_{s}A)}$. For a 50 μm diameter InGaAs diode with $R=50$ Ω, $v_{sat}=6\times 10^6$ cm/s and an assumed ${\epsilon }_r=13.9$ this is $W_{opt}\approx 1.4$ μm and $f_{max}\approx 13$ GHz (computed), above the 8 GHz typical of the FD50 datasheet, which also includes parasitic capacitance. Halving the area raises $f_{max}$ by $\sqrt{2}$. Reference: RF Essentials, Bandwidth of a Photodiode; UCSB ECE162C, Lecture 16 (Blumenthal); LASER COMPONENTS, FD50 and FD500 InGaAs PIN photodiode datasheets.

Ques: Why does a silicon PIN photodiode need a much thicker i-layer than an InGaAs one?

The absorption of silicon is weak near its band edge: $\alpha =335\mathrm{c}{\mathrm{m}}^{-1}$ at 860 nm in one source, so the penetration depth $1/\alpha$ is about 30 μm (computed). With $\eta =(1-R_f)(1-e^{-\alpha W_i})$ and $R_f=0.32$, a 0.1 mm layer gives $\eta =0.66$ and a 10 μm layer only 0.19 (computed), so the layer must be tens of micrometres thick and the transit time is long: 10 μm already limits the bandwidth to about 3.5 GHz. InGaAs absorbs more strongly at 1550 nm ($\alpha$ of 5000 to $10000\mathrm{c}{\mathrm{m}}^{-1}$, see the next question), so one to three micrometres are enough and tens of GHz are possible. The link to the indirect gap of silicon is textbook knowledge and is not stated in the sources. Reference: R. S. Quimby, Photonics and Lasers, Wiley, 2006, Sec. 14.4 (as fetched at GlobalSpec); RF Essentials, Bandwidth of a Photodiode; L. A. Coldren, S. W. Corzine and M. L. Mašanović, Diode Lasers and Photonic Integrated Circuits, 2nd ed., Wiley, 2012, Sec. 8.3.1 and 8.4.2.

Ques: What is the absorption coefficient of InGaAs at 1550 nm: $5000\mathrm{c}{\mathrm{m}}^{-1}$ or $10000\mathrm{c}{\mathrm{m}}^{-1}$?

The book example takes $\alpha =5000\mathrm{c}{\mathrm{m}}^{-1}$ for the active region at 1550 nm, whereas a bandwidth page states that a 1 μm InGaAs layer absorbs about 63%, which means $\alpha =1/(1\mu \mathrm{m})=10^4\mathrm{c}{\mathrm{m}}^{-1}$ (computed from $1-e^{-1}=0.63$). The book value is stated explicitly, while the second is implied by a rounded efficiency, so the $5000\mathrm{c}{\mathrm{m}}^{-1}$ is the more reliable figure; the true value lies between the two and depends on the wavelength, because the lattice-matched layer has $E_g\approx 0.74$ eV, a cutoff of about 1.68 μm (computed from the composition formula of the material page), and the absorption rises steeply from the edge. A 1 μm layer would absorb 39% at $5000\mathrm{c}{\mathrm{m}}^{-1}$ instead of 63% at $10000\mathrm{c}{\mathrm{m}}^{-1}$ (computed), which shows how much the choice matters. Reference: L. A. Coldren, S. W. Corzine and M. L. Mašanović, Diode Lasers and Photonic Integrated Circuits, 2nd ed., Wiley, 2012, Sec. 8.3.1 and 8.4.2, Example 8.8; RF Essentials, Bandwidth of a Photodiode.

Ques: Why is the capacitance of a PIN photodiode proportional to its area, and what thickness do the datasheets imply?

The capacitance $C_j={\epsilon }_{s}A/W_i$ is that of a parallel-plate capacitor, so it scales with the area and falls with the thickness. Two InGaAs datasheets at $V_R=5$ V give 0.25 pF for a 50 μm diameter and 15 pF for 500 μm, a ratio of 60 for an area ratio of 100 (computed). Fitting $C=C_p+kA$ to them with an assumed ${\epsilon }_r=13.9$ gives a thickness $W_i\approx 1.6$ μm and a parasitic capacitance $C_p\approx 0.1$ pF (computed), values that fall in the 1 to 3 μm range of other sources. The datasheets do not state the thickness, so this is an inference from two devices that may belong to different designs. The dark current also rises from 0.1 nA to 8 nA, a factor of 80, close to the area ratio. Reference: LASER COMPONENTS, FD50 and FD500 InGaAs PIN photodiode datasheets; RF Essentials, Bandwidth of a Photodiode.

Ques: Why is the cutoff frequency of a silicon PIN photodiode lower for a larger area, and is the RC formula enough?

The RC limit $f_{RC}=1/(2\pi RC)$ falls as the area grows because $C\propto A$. The Hamamatsu series follows this trend: 100 MHz at a $1.1\mathrm{m}{\mathrm{m}}^2$ area and 3 pF, 500 MHz at $0.5\mathrm{m}{\mathrm{m}}^2$, and 1 GHz at 1.6 pF for the S5973, so the bandwidth rises tenfold as the active area shrinks. The formula alone is not sufficient, however: a 3 pF capacitance with 50 Ω would give 1.06 GHz (computed), ten times the quoted 100 MHz of the S5971, and, if the whole capacitance is that of the junction, the layer would be 39 μm thick with ${\epsilon }_r=11.9$, whose transit limit at $10^7$ cm/s is about 1.1 GHz (computed). The extracted datasheet does not give the test load, so the formulas are upper bounds, the rest being unexplained. Reference: Hamamatsu, Si PIN photodiodes S5971, S5972, S5973 series (datasheet, Nov. 2019).

Ques: Why can the noise-equivalent power of a PIN photodiode be computed from its dark current?

When no light falls on the diode the only noise at low frequency and a high load resistance is the shot noise of the dark current, $\sqrt{2q{I}_d}$ per $\sqrt{\mathrm{Hz}}$, and dividing by the responsivity gives the power that equals it: $\mathrm{NEP}=\sqrt{2q{I}_d}/\mathcal{R}$. For the three silicon PIN photodiodes of one datasheet, the typical dark currents 0.07, 0.01 and 0.001 nA with sensitivities 0.64, 0.57 and 0.52 A/W give 7.40, 3.14 and 1.09 $\times 10^{-15}$ W/$\sqrt{\mathrm{Hz}}$ (computed), against the listed 7.4, 3.1 and 1.1 $\times 10^{-15}$ W/$\sqrt{\mathrm{Hz}}$. This also shows that a smaller area, with a smaller $I_d\propto A{W}_i$, lowers the NEP, and that the listed NEP is consistent with the detector alone, without the amplifier. Reference: Hamamatsu, Si PIN photodiodes S5971, S5972, S5973 series (datasheet, Nov. 2019); the PN Photodiode page.

Ques: Why does thermal noise limit direct detection while shot noise limits coherent detection?

In direct detection the photocurrent is only $\mathcal{R}{P}_{in}$, small compared with the Johnson current $\sqrt{4k_{B}TB/R_{eq}}$ of the load. For the book example (1.73 kΩ, 1 GHz, 1.125 A/W) this noise is 98 nA, so $P_{min}\approx 87$ nW or $-40.6\mathrm{dBm}$ for an SNR of one (computed). In coherent detection the beat current $2\mathcal{R}\sqrt{P_{LO}{P}_{in}}$ is raised by the local oscillator until its shot noise exceeds the thermal noise, giving $\mathrm{SNR}=\eta P_{in}/(h\nu B)$, which is an SNR of one at 0.13 nW or $-69\mathrm{dBm}$ for $\eta =1$ at 1550 nm and 1 GHz (computed). The book states only that about ten times less power is needed in practice for the same error rate, so the ideal gain is much larger than the practical one, and the sources do not reconcile them. Reference: L. A. Coldren, S. W. Corzine and M. L. Mašanović, Diode Lasers and Photonic Integrated Circuits, 2nd ed., Wiley, 2012, Sec. 8.3.1 and 8.4.2, Sec. 8.3.1 and Eq. 8.23.

Ques: Why does a PIN photodiode slow down at high optical power, and how does the uni-traveling-carrier design avoid it?

At high power the photogenerated electrons and holes are present in the i-layer in large numbers, and their space charge opposes the applied field, which reduces the drift velocity below $v_{sat}$ and increases ${\tau }_{tr}=W_i/v_{sat}$. In the uni-traveling-carrier photodiode the absorber is a narrow-gap p-type layer, separated from a wide-gap collector by a diffusion-blocking layer, so only the fast electrons cross the collector in a strong drift current while the holes are captured quickly by the p-contact. This allows higher saturation power, and the book mentions high-speed applications up to several hundred GHz; the sources give no formula for the field screening, so it is described only qualitatively. Reference: L. A. Coldren, S. W. Corzine and M. L. Mašanović, Diode Lasers and Photonic Integrated Circuits, 2nd ed., Wiley, 2012, Sec. 8.3.1 and 8.4.2, Sec. 8.3.1.

Ques: Why are waveguide PIN photodiodes needed at 10 Gb/s and beyond?

In a normal-incidence device the same thickness sets both the absorbed fraction and the transit time, so a high efficiency forces a thick layer. For $\eta =0.9$ and $\alpha =5000\mathrm{c}{\mathrm{m}}^{-1}$ the thickness is $\ln (10)/\alpha \approx 4.6$ μm and $f_{tr}=0.44v_{sat}/W_i\approx 5.7$ GHz with $v_{sat}=6\times 10^6$ cm/s (computed). In a waveguide device the light runs along the absorber, whose length is $L_D=92$ μm in the book example for a 5% confinement, while the carriers cross a thin layer; a thickness of 0.5 μm (assumed) would give 53 GHz (computed). The capacitance grows with the length, about 1 fF/μm, so the length is a compromise with the load $R_L=1/(2\pi B{C}_D)$, which was 1.73 kΩ at 1 Gb/s. Reference: L. A. Coldren, S. W. Corzine and M. L. Mašanović, Diode Lasers and Photonic Integrated Circuits, 2nd ed., Wiley, 2012, Sec. 8.3.1 and 8.4.2, Sec. 8.3.1 and Example 8.8; RF Essentials, Bandwidth of a Photodiode.

Ques: Why do the rise time and the bandwidth in a datasheet not satisfy $t_r=0.35/f_{3dB}$?

The FD50 datasheet lists a typical rise time of 100 ps and a typical analog bandwidth of 8 GHz at 5 V, but a single-pole response with $t_r=0.35/f_{3dB}$ would give 3.5 GHz for 100 ps or 44 ps for 8 GHz (computed). The datasheet does not explain the difference. The measured rise time includes the response of the pulse source and the oscilloscope, which can only make it longer than that of the diode, so the 8 GHz value is the more likely to be near the intrinsic limit; it is below the 13 GHz upper bound estimated above for such a diode, while 3.5 GHz would be far below it. The response of a real PIN diode is also not exactly single-pole. Reference: LASER COMPONENTS, FD50 and FD500 InGaAs PIN photodiode datasheets; UCSB ECE162C, Lecture 16 (Blumenthal).

Related pages in this vault: PN Photodiode, Waveguide Photodiode, Uni-Traveling-Carrier Photodiode (UTC-PD), Avalanche Photodiode (APD), Metal-Semiconductor-Metal Photodetector (MSM), PIN Diode, Photodetectors (PIN and Avalanche Photodiodes), Diodes (PN, PIN, Schottky, Zener), Germanium and Silicon-Germanium Electroabsorption Modulator.