PN Photodiode

1. Theory

• Definition: A PN photodiode is a PN junction made to detect light, in which a photon of energy $h\nu \ge E_g$ creates an electron-hole pair and the electric field of the junction separates the pair, so that an external current $I_{ph}$ proportional to the optical power flows.
• Cutoff and materials: The long-wavelength limit is ${\lambda }_c\approx 1.24/E_g(\mu \mathrm{m})$ with $E_g$ in eV, so silicon (1.12 eV) detects up to about 1.1 μm, germanium (0.67 eV) up to about 1.85 μm and GaAs (1.43 eV) up to about 0.87 μm; InGaAs lattice-matched to InP covers 1.3 and 1.55 μm, and wide-gap GaN and SiC cover the ultraviolet.
• Collection regions: Carriers generated in the depletion region of width $W$ are swept out by drift; carriers generated within a diffusion length $L_p$ of the edge reach the junction by diffusion; carriers generated farther away recombine. In a simple PN diode $W$ is typically below 1 μm, so much of the light is absorbed in the field-free bulk.
• Responsivity and efficiency: The photocurrent is $I_{ph}=\mathcal{R}{P}_{in}$ with $\mathcal{R}=\eta q/h\nu =\eta \lambda /1.24$ A/W ($\lambda$ in μm), and for complete collection in a region of length $L$ the efficiency is $\eta =1-e^{-\alpha L}$ (Coldren et al., Eqs. 8.20 to 8.22), so the responsivity rises with wavelength up to the cutoff.
• Operating modes: With zero bias (photovoltaic mode) there is no dark current and the dominant noise is the Johnson noise of $R_{sh}$; with reverse bias (photoconductive mode) $W$ grows, $C_j$ falls and the response is faster and more linear, at the price of a dark current $I_d$ that adds shot noise.
• Speed limits: The bandwidth is set by the RC time constant of the junction capacitance $C_j$ and the load, by the transit time $W/v_{sat}$ across the depletion region and by the slow diffusion of carriers from the neutral regions.
• Noise limits: The noise comes from the shot noise $\sqrt{2q(I_{ph}+I_d)\Delta f}$, the Johnson noise $\sqrt{4k_{B}T\Delta f/R_{eq}}$ of the resistance seen by the diode, and the amplifier; the weakest detectable signal is given by $\mathrm{NEP}=i_n/(\mathcal{R}\sqrt{\Delta f})$.

2. Working Principle

• Absorption: A photon with $h\nu \ge E_g$ is absorbed at a depth set by $1/\alpha$ and excites an electron from the valence band to the conduction band, leaving a hole.
• Separation: In the depletion region the field of the junction, which grows with the reverse bias as $W\propto \sqrt{V_{bi}+V_R}$, pushes electrons toward the n side and holes toward the p side before they recombine.
• Collection: Minority carriers made in the neutral regions within $L_p$ or $L_n$ of the depletion edge diffuse to it and are swept across, so that the quantum efficiency is $\eta =(1-R_f)\left[1-e^{-\alpha W}/(1+\alpha L_p)\right]$ for light absorbed in an n-type substrate behind a thin p layer.
• Photocurrent: The collected carriers flow in the external circuit as $I_{ph}=\mathcal{R}{P}_{in}$ in the reverse direction of the diode, so that the characteristic is the dark curve shifted down by $I_{ph}$: $I=I_0\left[\exp (V/n{V}_T)-1\right]-I_{ph}$.
• Photovoltaic mode: With $V=0$ and a low-impedance load the current is $I_{sc}=-I_{ph}$ with no dark current, which suits low light levels and low frequencies; with a high-impedance load a voltage $V_{oc}=n{V}_T\ln (1+I_{ph}/I_0)$ appears across the junction.
• Photoconductive mode: A reverse bias $V_R$ widens $W$, lowers $C_j={\epsilon }_{s}A/W$ and makes the field strong, so that the bandwidth rises and the response is linear over many decades, while $I_d$ increases with $V_R$ and with temperature.
• Readout: The current is converted to a voltage by a load resistor, $V_{out}=I_{ph}{R}_L$, or by a transimpedance amplifier, where the largest feedback resistor that the bandwidth allows gives the lowest Johnson noise.

3. Applications

• Light and exposure meters: Silicon photodiodes measure the intensity of visible light in photometers, light meters and exposure control.
• Optical power measurement: Calibrated silicon, germanium and InGaAs photodiodes are the sensors of optical power meters and radiometers, used in the photovoltaic mode at low levels and with bias for fast signals.
• Consumer and sensing electronics: Smoke detectors, infrared remote-control receivers, CD players, optocouplers and slotted optical switches.
• Medical instruments: Pulse oximeters, immunoassay instruments and the detectors of computed-tomography scanners, where the photodiode views a scintillator.
• Position and imaging arrays: One-dimensional arrays for position sensing and spectrometers, and two-dimensional arrays as in the sensor of an optical mouse (a 4 × 4 array in one example) and in image sensors.
• Optical communication at modest speed: PN and PIN photodiodes are the receivers of fibre links; the PIN diode is preferred where wide bandwidth is needed.

Name	Formula	Related Formulae	Variables/Constants
Cutoff wavelength	${\lambda }_c=\frac{hc}{E_g}\approx \frac{1.24}{E_g\left(\mathrm{eV}\right)}\mu \mathrm{m}$	$h\nu =\frac{hc}{\lambda }\ge E_g$	$\begin{array}{r}{\lambda }_c:longestwavelengththatcancreatean\\ electron-holepairbyband-to-band\\ absorption\end{array}$ $\begin{array}{r}{E}_g:bandgapoftheabsorbing\\ semiconductor(1.12eVforSigives1.1\\ \mu \mathrm{m},0.67eVforGegives1.85\mu \mathrm{m}and1.43\\ eVforGaAsgives0.87\mu \mathrm{m})\end{array}$ $h\nu :photonenergy,\lambda :wavelengthofthelight$
Current-voltage characteristic under illumination	$I=I_0\left[\exp \left(\frac{V}{n{V}_T}\right)-1\right]-I_{ph}$	$V_{oc}=n{V}_T\ln \left(1+\frac{I_{ph}}{I_0}\right)$ $I_{sc}=-I_{ph}$	$\begin{array}{r}I:currenttakenpositiveintheforward\\ directionofthediode,sothatthe\\ photocurrentflowsinthereverse\\ direction\end{array}$ $\begin{array}{r}{I}_0,n,V_T=k_{B}T/q:reversesaturation\\ current,idealityfactorandthermal\\ voltage(asonthePNJunctionpage)\end{array}$ $\begin{array}{r}{I}_{ph}:photocurrent,whichshiftsthewhole\\ darkcharacteristicdownward\end{array}$ $\begin{array}{r}{V}_{oc},I_{sc}:open-circuitvoltageand\\ short-circuitcurrent(derivedfromthe\\ characteristic;thezero-biasphotovoltaic\\ modeworksnear{I}_{sc})\end{array}$ $k_B:Boltzmannconstant$
Photocurrent and responsivity	$I_{ph}=\mathcal{R}{P}_{in}$	$\mathcal{R}=\frac{\eta q}{h\nu }=\frac{\eta \lambda }{1.24}A/W$ $\eta =\frac{I_{ph}/q}{P_{in}/h\nu }$	$\begin{array}{r}{I}_{ph}:photocurrent(short-circuitor\\ reverse-biased,thetwobeingequalto\\ firstorder)\end{array}$ $\begin{array}{r}\mathcal{R}:responsivityinA/W(0.5to0.6A/Wat\\ 850nmforsiliconand0.9to1.0A/Wat\\ 1550nmforInGaAsinonesource)\end{array}$ $P_{in}:opticalpowerincidentonthephotodiode$ $\begin{array}{r}\eta :externalquantumefficiency,thenumber\\ ofcollectedcarriersperincidentphoton\end{array}$ $\begin{array}{r}(thenumericalformuses\lambda inmicrometres,\\ sothat\mathcal{R}riseslinearlywithwavelength\\ uptothecutoff)\end{array}$
Quantum efficiency from absorption only	$\eta =\left(1-R_f\right)\left(1-e^{-\alpha W}\right)$	$\eta =1-e^{-\alpha L}$ $1-e^{-1}\approx 0.63$	$\begin{array}{r}{R}_f:powerreflectanceofthefrontsurface\\ (reducedbyanantireflectioncoating)\end{array}$ $\begin{array}{r}\alpha :absorptioncoefficientatthe\\ wavelengthused,with1/\alpha thepenetration\\ depth\end{array}$ $\begin{array}{r}W:thicknessoftheregioninwhichevery\\ generatedcarrieriscollected(the\\ depletionregion),sothatthisformholds\\ whentheneutralregionscontribute\\ nothing\end{array}$ $\begin{array}{r}L:absorberlengthinthegeneralformof\\ thebook(Eq.8.22,withtheconfinement\\ factortakenas1),and0.63isthe\\ fractionabsorbedinonepenetrationdepth\end{array}$
Quantum efficiency with diffusion from the neutral region (Gärtner type)	$\eta =\left(1-R_f\right)\left[1-\frac{e^{-\alpha W}}{1+\alpha L_p}\right]$	${\eta }_{dr}=\left(1-R_f\right)\left(1-e^{-\alpha W}\right)$ ${\eta }_{diff}=\left(1-R_f\right)\frac{\alpha L_p}{1+\alpha L_p}{e}^{-\alpha W}$ $\eta \approx \left(1-R_f\right)\alpha \left(W+L_p\right)\mathrm{for}\alpha W,\alpha L_p\ll 1$	$\begin{array}{r}{\eta }_{dr}:partcollectedbydriftfromcarriers\\ generatedinthedepletionregion\end{array}$ $\begin{array}{r}{\eta }_{diff}:partcollectedbydiffusionof\\ minoritycarriersgeneratedintheneutral\\ substratebeyondthedepletionregion\end{array}$ $\begin{array}{r}{L}_p:diffusionlengthoftheminority\\ carriers(holes)inthen-typesubstrate\end{array}$ $\begin{array}{r}(assumesafrontlayerthinenoughtolose\\ nocarriers,asubstratethickerthan{L}_p\\ andnorecombinationattheback,alimit\\ obtainedherefromthedriftanddiffusion\\ currentsofarXiv:1706.09042,Eqs.5and\\ 6)\end{array}$ $\begin{array}{r}(theeffectivecollectionlengthis\\ thereforeW+L_{p}forweaklyabsorbedlight)\end{array}$
Depletion width	$W=\sqrt{\frac{2{\epsilon }_s\left(V_{bi}+V_R\right)}{q}\left(\frac{1}{N_A}+\frac{1}{N_D}\right)}$	$W\approx \sqrt{\frac{2{\epsilon }_s\left(V_{bi}+V_R\right)}{q{N}_B}}$	$W:widthofthedepletionregion$ $V_{bi}:built-inpotential$ $\begin{array}{r}{V}_R:reversebiasapplied(V_R=-VofthePN\\ Junctionpage)\end{array}$ $N_A,N_D:acceptoranddonorconcentrations$ ${\epsilon }_s:permittivityofthesemiconductor$ $\begin{array}{r}{N}_B:dopingofthelightlydopedsidefora\\ one-sidedjunction,sothatWgrowsasthe\\ squarerootofthebiasandislargerfor\\ alighterdoping\end{array}$
Junction capacitance	$C_j=\frac{{\epsilon }_{s}A}{W}$	$C_j=A\sqrt{\frac{q{\epsilon }_s}{2\left(V_{bi}+V_R\right)}\frac{N_A{N}_D}{N_A+N_D}}$	$\begin{array}{r}{C}_j:capacitanceofthedepletionregion\\ treatedasaparallel-platecapacitor\end{array}$ $A:junctionarea$ $\begin{array}{r}(C_{j}fallsasthereversebiaswidensW,\\ andisproportionaltothearea,sothata\\ smalleractiveareagivesasmaller\\ capacitanceandasmallerdarkcurrent)\end{array}$
Dark current	$I_d\approx qA\left(\frac{D_p{p}_{n0}}{L_p}+\frac{D_n{n}_{p0}}{L_n}\right)+\frac{qA{n}_{i}W}{2{\tau }_g}$	$I_0\propto n_i^2\propto T^3{e}^{-E_g/k_{B}T}$ $I_{gen}=\frac{qA{n}_{i}W}{2{\tau }_g}\propto n_i\sqrt{V_{bi}+V_R}$	$\begin{array}{r}{I}_d:currentwithnolight,thefirstterm\\ beingthediffusion(saturation)current\\ I_{0}oftheneutralregionsandthesecond\\ thethermalgenerationinthedepletion\\ region\end{array}$ $\begin{array}{r}{D}_p,D_n,L_p,L_n,p_{n0},n_{p0}:diffusion\\ coefficients,diffusionlengthsand\\ minority-carrierdensitiesofthetwo\\ sides(asonthePNJunctionpage)\end{array}$ $n_i:intrinsiccarrierdensity$ ${\tau }_g:generationlifetime$ $k_B:Boltzmannconstant$ $\begin{array}{r}(surfaceleakageisafurthertermthat\\ dependsonthepassivationandisnot\\ included)\end{array}$
Shunt resistance	$R_{sh}={\frac{dV}{dI}|}_{V=0}\approx \frac{n{V}_T}{I_0}$	$R_{sh}\propto \frac{1}{A}$	$\begin{array}{r}{R}_{sh}:sloperesistanceofthedark\\ characteristicattheorigin,typically\\ tenstothousandsofM\Omega (1G\Omega and50G\Omega \\ fortwosilicondiodesofonenote)\end{array}$ $\begin{array}{r}(theapproximateformfollowsfromthe\\ diodeequation,andthedependenceonarea\\ from{I}_0\propto A)\end{array}$
RC-limited bandwidth and rise time	$f_{RC}=\frac{1}{2\pi \left(R_s+R_L\right)\left(C_j+C_s\right)}$	$t_{RC}=2.2\left(R_s+R_L\right)\left(C_j+C_s\right)$	$\begin{array}{r}{R}_s,R_L:seriesresistanceofthediode(10\\ to1000\Omega )andloadorinputresistanceof\\ theamplifier\end{array}$ $\begin{array}{r}{C}_j,C_s:junctioncapacitanceandstray\\ (packageandcircuit)capacitance\end{array}$ $\begin{array}{r}{t}_{RC}:10\%to90\%risetimeofasingleRC\\ section\end{array}$
Transit-time-limited bandwidth	$f_{tr}\approx \frac{0.44}{{\tau }_{tr}}=\frac{0.44v_{sat}}{W}$	${\tau }_{tr}=\frac{W}{v_{sat}}$ ${\tau }_{drift}\sim 10\mathrm{ps}/\mu \mathrm{m},{\tau }_{diff}\sim 1\mathrm{ns}/\mu \mathrm{m}$	$\begin{array}{r}{\tau }_{tr}:timeforacarriertocrossthe\\ depletionregionatthesaturateddrift\\ velocity{v}_{sat}\end{array}$ $\begin{array}{r}{v}_{sat}:saturateddriftvelocity,about6\times 10^6\\ to10^{7}cm/sinthesemiconductorsofthe\\ sources\end{array}$ $\begin{array}{r}(thelastrelationisanorderof\\ magnitude:carriersgeneratedinthe\\ neutralregionsarrivebydiffusion,which\\ isslowerthandriftbyabouttwoorders\\ andgivesaslowtailtothepulse\\ response)\end{array}$ $\begin{array}{r}(thefactor0.44isthe3dBpointofa\\ rectangularcurrentpulse,carriersmadein\\ athinsheetatoneedgeandcrossingthe\\ wholelayer;forgenerationspread\\ uniformlythroughthelayerthecurrentis\\ triangularandthefactoris0.55,soreal\\ devicesliebetweenthetwo)\end{array}$
Overall bandwidth and rise time	$\frac{1}{f_{3dB}^2}\approx \frac{1}{f_{RC}^2}+\frac{1}{f_{tr}^2}$	$t_r=\frac{0.35}{f_{3dB}}$	$\begin{array}{r}{f}_{3dB}:frequencyatwhichtheresponsefalls\\ by3dB,thesmallerofthetwolimits\\ dominating(thediffusiontailofthe\\ neutralregionsisnotincluded)\end{array}$ $\begin{array}{r}{t}_r:10\%to90\%risetimefora\\ single-poleresponse\end{array}$
Load resistor and output voltage of a receiver	$R_L=\frac{1}{2\pi B{C}_D}$	$V_{out}=I_{ph}{R}_L$	$B:bandwidthrequired$ $\begin{array}{r}{C}_D:totalcapacitanceofthediodeandits\\ connections\end{array}$ $\begin{array}{r}{R}_L:loadresistorthatsetstheRClimit\\ equaltoB\end{array}$ $\begin{array}{r}(thebookexamplegives{R}_L=1.73k\Omega forB=1\\ GHzand{C}_D=92fF,and{V}_{out}=1.95mVfor\\ I_{ph}=1.125\mu \mathrm{A})\end{array}$
Absorber thickness for a target quantum efficiency	$W=\frac{1}{\alpha }\ln \frac{1}{1-\eta }$	$L_D=\frac{1}{{\Gamma }_{xy}\alpha }\ln \frac{1}{1-\eta }$	$\begin{array}{r}W:thicknessneededforaninternal\\ efficiency\eta wheneveryabsorbedphotonis\\ collectedandthereflectionisneglected\end{array}$ $\begin{array}{r}{L}_D,{\Gamma }_{xy}:lengthandtransverseconfinement\\ factorofawaveguidephotodiode(thebook\\ examplegives92\mu \mathrm{m}for\eta =0.9,{\Gamma }_{xy}=5\%and\\ \alpha =5000c{m}^{-1})\end{array}$
Shot noise	$i_{sh}=\sqrt{2q\left(I_{ph}+I_d\right)\Delta f}$	$i_{sh,d}=\sqrt{2q{I}_d\Delta f}$	$\begin{array}{r}{i}_{sh}:rmsshot-noisecurrentfromthe\\ randomnessofthearrivalofthecarriers\\ ofthephotocurrentandthedarkcurrent\end{array}$ $\Delta f:noisebandwidthofthemeasurement$ $\begin{array}{r}{I}_d:darkcurrent(zeroatzerobias,so\\ onlythesignaltermremainsinthe\\ photovoltaicmode)\end{array}$
Thermal (Johnson) noise	$i_J=\sqrt{\frac{4k_{B}T\Delta f}{R_{eq}}}$	$i_n=\sqrt{i_{sh}^2+i_J^2+i_{amp}^2}$	$\begin{array}{r}{R}_{eq}:equivalentparallelresistance,the\\ shuntresistance{R}_{sh}inthephotovoltaic\\ modeandtheloadorfeedbackresistorin\\ serieswiththeamplifier(thelargest\\ resistorthatthebandwidthallowsreduces\\ thenoise)\end{array}$ $i_{amp}:noisecurrentoftheamplifier$ $i_n:totalrmsnoisecurrent$ $k_B:Boltzmannconstant$
Signal-to-noise ratio	$\mathrm{SNR}=\frac{I_{ph}^2}{2q\left(I_{ph}+I_d\right)\Delta f+\frac{4k_{B}T\Delta f}{R_{eq}}+i_{amp}^2}$	$\mathrm{SNR}\to \frac{I_{ph}}{2q\Delta f}(\mathrm{shot}\mathrm{noise}\mathrm{limit})$	$\begin{array}{r}\mathrm{SNR}:ratioofthemean-squaresignal\\ currenttothemean-squarenoisecurrent\\ (derivedfromthetwonoiseexpressions\\ above)\end{array}$ $k_B:Boltzmannconstant$ $\begin{array}{r}(athighpowertheshotnoiseofthe\\ signaldominatesandtheSNRgrowsonlyin\\ proportionto{I}_{ph},whileatlowpowerthe\\ thermaltermdominatesandtheSNRgrows\\ as{I}_{ph}^2)\end{array}$
Noise-equivalent power	$\mathrm{NEP}=\frac{i_n}{\mathcal{R}\sqrt{\Delta f}}$	${\mathrm{NEP}}_{shot}=\frac{\sqrt{2q{I}_d}}{\mathcal{R}}$ ${\mathrm{NEP}}_J=\frac{1}{\mathcal{R}}\sqrt{\frac{4k_{B}T}{R_{sh}}}$	$\begin{array}{r}\mathrm{NEP}:opticalpowerthatgivesa\\ signal-to-noiseratioofoneina1Hz\\ bandwidth,inW/\sqrt{Hz}\end{array}$ $\begin{array}{r}(valuesrangefromabout10^{-11}W/\sqrt{Hz}for\\ largeareastoabout10^{-15}W/\sqrt{Hz}forsmall\\ areasinonenote)\end{array}$ $k_B:Boltzmannconstant$ $\begin{array}{r}(thelimitsarethedark-current\\ shot-noiseandtheshunt-resistance\\ Johnson-noisevalues,theamplifierbeing\\ ideal)\end{array}$
Detectivity and specific detectivity	$D=\frac{1}{\mathrm{NEP}},D^{\ast }=D\sqrt{A}=\frac{\sqrt{A}}{\mathrm{NEP}}$	$D^{\ast }=\frac{\mathcal{R}\sqrt{A\Delta f}}{i_n}$	$\begin{array}{r}{D}^{\ast }:specificdetectivityincmH{z}^{1/2}/W(the\\ unitbeingtheJones),whichremovesthe\\ dependenceofthenoiseontheareaand\\ thebandwidth\end{array}$ $\begin{array}{r}A:activeareaofthephotodiode,\mathrm{NEP}:\\ noise-equivalentpowerperunitroot\\ bandwidthinW/\sqrt{Hz}(theformwiththe\\ noisecurrentfollowsfromthedefinition\\ oftheNEP,i_{n}beingthenoisecurrentin\\ thebandwidth\Delta f)\end{array}$

Important Questions

Ques: Why does a reverse bias speed up a PN photodiode, and what does it cost?

A reverse bias $V_R$ widens the depletion region, $W\propto \sqrt{V_{bi}+V_R}$, so the junction capacitance $C_j={\epsilon }_{s}A/W$ falls and the limit $f_{RC}=1/[2\pi (R_s+R_L)(C_j+C_s)]$ rises. The field in the depletion region also grows, so carriers cross it at the saturated velocity, and more of the light is collected by drift instead of by slow diffusion. The cost is a dark current that grows with bias, because the generation term $qA{n}_{i}W/2{\tau }_g$ grows with $W$; it adds shot noise $\sqrt{2q{I}_d\Delta f}$, and near breakdown the avalanche effects add more. One note advises at least 10 V for fast pulses and warns never to exceed the maximum reverse voltage, defined as the voltage at which the dark current reaches 10 μA in small devices. Reference: Wikipedia, Photodiode (accessed October 2026); Photodiode Parameters and Characteristics (application note hosted at wiki.physics.wisc.edu/yavuz).

Ques: Why is the photovoltaic (zero-bias) mode quieter at low light although it is slower?

At $V=0$ the junction carries no net dark current, so the shot noise $\sqrt{2q{I}_d\Delta f}$ of the dark current vanishes, and the remaining noise is the Johnson noise $\sqrt{4k_{B}T\Delta f/R_{sh}}$ of the shunt resistance $R_{sh}\approx n{V}_T/I_0$. A diode with a small $I_0$ therefore has a large $R_{sh}$ (1 GΩ and 50 GΩ for two silicon diodes of one note) and a small NEP, which makes the mode suitable for weak signals at low frequency (up to about 350 kHz in one note). The price is speed: the depletion region is at its narrowest, so $C_j$ is at its largest, and the response is limited by diffusion for areas under about $5\mathrm{m}{\mathrm{m}}^2$ and by $RC$ for larger areas. The responsivity is also slightly lower at long wavelengths. Reference: Oxford ATD group, Getting the best out of photodiode detectors (technical note, users.ox.ac.uk/~atdgroup); Photodiode Parameters and Characteristics (application note hosted at wiki.physics.wisc.edu/yavuz); Edmund Optics, Basic Principles of Silicon Detectors (application note).

Ques: Why does the responsivity of a photodiode rise with wavelength up to the cutoff and then collapse?

The responsivity $\mathcal{R}=\eta q/h\nu =\eta \lambda /1.24$ A/W ($\lambda$ in μm) is the charge collected per unit of optical energy, and a longer wavelength carries less energy per photon, so the same fraction $\eta$ of photons gives more carriers per watt. At the ideal $\eta =1$ this is 0.69 A/W at 0.85 μm and 1.25 A/W at 1.55 μm (computed); the 0.5 to 0.6 A/W quoted for silicon at 850 nm corresponds to $\eta \approx 0.7$ to 0.9 (computed). Beyond ${\lambda }_c\approx 1.24/E_g$ the photons cannot cross the gap and $\eta$ falls to zero, which ends the curve (about 1.1 μm for Si). At short wavelengths the light is absorbed so close to the surface that surface recombination destroys the carriers, so the curve also falls there. 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, Eqs. 8.20 to 8.22; halbleiter.org, Photodiodes and Photodetectors; Edmund Optics, Basic Principles of Silicon Detectors (application note).

Ques: Why is a PN photodiode slower and less efficient than a PIN photodiode?

The depletion width $W$ of a PN junction is fixed by the doping and is typically below 1 μm, which is shorter than the penetration depth $1/\alpha$ of light near the band edge, so a large share of the carriers is generated in the neutral regions. They reach the junction only by diffusion within $L_p$, as the term $\alpha L_p{e}^{-\alpha W}/(1+\alpha L_p)$ of the efficiency shows, and those generated farther away recombine, so $\eta$ is reduced. Diffusion is also much slower than drift (about 1 ns/μm against 10 ps/μm in one source), so the pulse response has a slow tail. The intrinsic layer of a PIN diode, 10 to 50 μm thick, makes the whole absorbing region a strong-field region, so the carriers drift and the bandwidth reaches the GHz range. Reference: halbleiter.org, Photodiodes and Photodetectors; UCSB ECE162C, Lecture 16 (Blumenthal); arXiv:1706.09042 (Eqs. 1, 5 and 6).

Ques: Why does the thickness of the depletion region set a compromise between sensitivity and speed?

A thicker absorber increases the absorbed fraction, $\eta =1-e^{-\alpha W}$, but lengthens the transit time ${\tau }_{tr}=W/v_{sat}$ and so lowers $f_{tr}\approx 0.44v_{sat}/W$, while the RC limit $f_{RC}\propto W/A$ improves with $W$ because $C_j={\epsilon }_{s}A/W$ falls. The two limits combine as $1/f_{3dB}^2=1/f_{RC}^2+1/f_{tr}^2$, so an optimum exists, and a smaller area $A$ moves it to a higher speed. For InGaAs with $v_{sat}\approx 6\times 10^6$ cm/s, a 1 μm layer absorbs about 63% and gives a transit limit of 26 GHz, whereas 3 μm absorbs about 95% and gives about 9 GHz (computed from the formula; the source also lists 0.5 and 0.8 A/W). Reference: RF Essentials, Bandwidth of a Photodiode; UCSB ECE162C, Lecture 16 (Blumenthal).

Ques: Why do the dark current and the shunt resistance change with temperature at different rates?

The diffusion part of the dark current is proportional to $n_i^2\propto T^3{e}^{-E_g/k_{B}T}$, which doubles about every 4.5 K for silicon at 300 K (computed with $E_g=1.12$ eV), whereas the generation part is proportional to $n_i$ and doubles about every 9 K (computed). One note states that the dark current in photoconductive mode roughly doubles for every 10 °C, close to the generation-dominated rate, and that $R_{sh}$ roughly doubles for every 6 °C of cooling, between the two rates. A plausible reading is that the generation current dominates under reverse bias and the diffusion current weighs more near zero bias, where $R_{sh}$ is defined. The sources do not give this split, so the explanation is an interpretation of the rates, not a measured fact. Reference: Photodiode Parameters and Characteristics (application note hosted at wiki.physics.wisc.edu/yavuz).

Ques: Why are NEP and $D^{\ast }$ normalised by the square root of the bandwidth and of the area?

The noise currents $\sqrt{2q{I}_d\Delta f}$ and $\sqrt{4k_{B}T\Delta f/R_{sh}}$ are white, so their power grows in proportion to $\Delta f$ and the current as $\sqrt{\Delta f}$; the NEP is therefore quoted for 1 Hz in W/$\sqrt{\mathrm{Hz}}$. Since $I_d\propto A$ and $R_{sh}\propto 1/A$, both noise currents grow as $\sqrt{A}$ while the responsivity does not depend on area, so $\mathrm{NEP}\propto \sqrt{A}$ and $D^{\ast }=\sqrt{A}/\mathrm{NEP}$ is independent of the area. One note gives the NEP range $10^{-11}W/\sqrt{\mathrm{Hz}}$ for large areas to $10^{-15}W/\sqrt{\mathrm{Hz}}$ for small areas, which is this scaling. The NEP ignores the capacitance, so detectors of different speeds should be compared with care. Reference: Oxford ATD group, Getting the best out of photodiode detectors (technical note, users.ox.ac.uk/~atdgroup); Photodiode Parameters and Characteristics (application note hosted at wiki.physics.wisc.edu/yavuz); Wikipedia, Photodiode (accessed October 2026).

Ques: Why does thermal noise dominate the receiver of a photodiode at a power of 1 μW?

For the book example, $I_{ph}=1.125$ μA at 1 μW and 1550 nm, with $R_L=1.73$ kΩ and $B=1$ GHz, the Johnson current is $\sqrt{4k_{B}TB/R_L}\approx 98$ nA at 300 K, whereas the shot noise of the signal is $\sqrt{2q{I}_{ph}B}\approx 19$ nA (both computed, dark current neglected). The thermal term is therefore about 96% of the noise power and the electrical SNR is $\approx 127$, or 21 dB (computed). The load is small because $R_L=1/(2\pi B{C}_D)$ is chosen for the bandwidth, and the thermal current falls only as $1/\sqrt{R_L}$; shot noise takes over only when $I_{ph}$ is much larger. This agrees with the statement of the book that thermal noise dominates direct detection by PIN photodiodes. 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, Example 8.8; Oxford ATD group, Getting the best out of photodiode detectors (technical note, users.ox.ac.uk/~atdgroup).

Ques: Is the typical quantum efficiency of a photodiode 60% to 80% or close to 1?

The two values come from different cases. One source lists a typical quantum efficiency of 60% to 80%, and another says that well-designed devices have $\eta$ near 1. The responsivity of 0.6 A/W of a silicon diode at 960 nm in a third source corresponds to $\eta =0.6\times 1.24/0.96\approx 0.78$ (computed), in the first range. Values near 1 need $\alpha W\gg 1$, which means a thick PIN absorber, and a small $R_f$ from an antireflection coating, so they hold for optimised PIN structures, not for a simple PN diode with $W<1$ μm. The 60% to 80% range is more likely for a PN photodiode. Reference: Wikipedia, Photodiode (accessed October 2026); halbleiter.org, Photodiodes and Photodetectors; Oxford ATD group, Getting the best out of photodiode detectors (technical note, users.ox.ac.uk/~atdgroup).

Ques: Why is the rise time written both as $0.35/f_{3dB}$ and as $2.2RC$?

For a single-pole response, the output to a step is $1-e^{-t/RC}$, which takes $RC\ln 9\approx 2.2RC$ to go from 10% to 90% of the final value, and the 3 dB frequency is $f_{3dB}=1/(2\pi RC)$. Eliminating $RC$ gives $t_r=2.2/(2\pi f_{3dB})\approx 0.35/f_{3dB}$ (computed, 0.350), so the two statements in the sources are the same relation. It is exact only for a single pole; when the transit time and the diffusion tail add to the RC response, the combined bandwidth $1/f_{3dB}^2=1/f_{RC}^2+1/f_{tr}^2$ is used and the rise time is no longer an exact $0.35/f_{3dB}$. Reference: Photodiode Parameters and Characteristics (application note hosted at wiki.physics.wisc.edu/yavuz).

Related pages in this vault: PIN Photodiode, Schottky-Barrier Photodiode, Metal-Semiconductor-Metal Photodetector (MSM), Avalanche Photodiode (APD), Pinned Photodiode (CMOS Image Sensor Pixel), Photodetectors (PIN and Avalanche Photodiodes), Diodes (PN, PIN, Schottky, Zener), Solar Cell Fundamentals, PN Junction.