Perovskite Photodetector (Photodiode and Photoconductor)

1. Theory

• Definition: A perovskite photodetector uses a halide perovskite $\mathrm{AB}{\mathrm{X}}_3$ (for example $\mathrm{C}{\mathrm{H}}_3\mathrm{N}{\mathrm{H}}_3\mathrm{Pb}{\mathrm{I}}_3$, or mixed cations and halides) as the absorber, deposited from solution as a film or grown as a single crystal, with a gap of about 1.5 eV to 1.6 eV (1.58 eV for $\mathrm{C}{\mathrm{H}}_3\mathrm{N}{\mathrm{H}}_3\mathrm{Pb}{\mathrm{I}}_3$, 1.52 eV for a triple-cation composition).
• Absorption: The direct gap gives a steep absorption edge with an Urbach energy of 11 meV to 16 meV in thin films, so a layer of 250 nm to 400 nm absorbs most of the visible light, with a response from 275 nm to the onset at about 780 nm to 840 nm.
• Transport: Solution-grown single crystals have a hole mobility of 105 to 164 $\mathrm{c}{\mathrm{m}}^2/Vs$, an electron mobility of about 24 $\mathrm{c}{\mathrm{m}}^2/Vs$, a trap density of $3.6\times 10^{10}\mathrm{c}{\mathrm{m}}^{-3}$ and a hole diffusion length of $175\pm 25$ μm, whereas polycrystalline films have a trap density of $2\times 10^{15}\mathrm{c}{\mathrm{m}}^{-3}$ and a diffusion length of about 1 μm.
• Device types: The photodiode (n-i-p or p-i-n), the photoconductor (two metal electrodes on the perovskite) and the phototransistor; the photodiode is fast with a low dark current, the photoconductor has gain but is slower and less sensitive, and this page treats the diode and the photoconductor.
• Photodiode stack: An absorber of 250 nm to 400 nm lies between an electron-transport layer ($\mathrm{Ti}{\mathrm{O}}_2$ or the fullerenes PCBM and ${\mathrm{C}}_{60}$) and a hole-transport layer (PEDOT:PSS, crosslinked OTPD or spiro-OMeTAD), with a thin $\mathrm{A}{\mathrm{l}}_2{\mathrm{O}}_3$ or BCP layer that passivates traps and blocks shunts.
• Dark current and noise: The dark current is set by shunt paths and trap-assisted generation, not by the theoretical saturation current of about 10 $pA/c{\mathrm{m}}^2$, and the detectivity of a photodiode scales as $J_{dark}^{-1/2}$.
• Photoconductor: A planar structure on the (100) face of a single crystal with interdigitated electrodes 20 μm apart gives a photoconductive gain, with a response that saturates with intensity as traps fill.
• Stability: $\mathrm{C}{\mathrm{H}}_3\mathrm{N}{\mathrm{H}}_3\mathrm{Pb}{\mathrm{I}}_3$ decomposes under humidity, light, oxygen and heat, ion migration moves halide ions into the metal electrodes, and encapsulated photodiodes survived $7\times 10^9$ pulses over one week.
• Figures of merit: The responsivity, the external quantum efficiency, $D^{\ast }$, the noise equivalent power, the linear dynamic range, the $-3\mathrm{dB}$ bandwidth and the stability.

2. Working Principle

• Photodiode: A photon absorbed in the perovskite creates a pair, the carriers are separated by the built-in field and the transport layers, and the photocurrent is collected at zero or small reverse bias; the responsivity stayed flat down to zero bias when the charge trapping at the junction was suppressed.
• Dark current control: A thicker fullerene layer (80 nm instead of 20 nm) lowered the dark current at -2 V from $1.6\times 10^{-7}$ to $9.1\times 10^{-9}A/c{\mathrm{m}}^2$, because it blocks the injection of holes under reverse bias.
• Noise: At -0.1 V the shot noise of the dark current and the thermal noise of the shunt gave 6.4 $fA/H{\mathrm{z}}^{1/2}$, and the measured noise between 0.3 Hz and 10 Hz was 16 $fA/H{\mathrm{z}}^{1/2}$ and frequency-independent, so that the flicker noise did not dominate in that band.
• Speed: The response time of 120 ns to 3 μs corresponds to a bandwidth of 2.9 MHz for the fastest diode, of the order of the circuit cutoff $1/(2\pi RC)$ for its capacitance of 1.5 nF.
• Photoconductor: With a bias across the 20 μm gap one carrier type crosses the gap many times during the lifetime of the other, so that the gain is $G=\tau ({\mu }_e+{\mu }_h)V/L_g^2$, and the response time is of the order of the lifetime, 74 μs for the single crystal.
• Saturation: The responsivity of the photoconductor falls from 953 A/W at 2.12 $nW/c{\mathrm{m}}^2$ to 2.55 A/W at 1 $mW/c{\mathrm{m}}^2$, as the traps fill and the lifetime shortens.

3. Applications

• Weak-light detection in the visible: A photodiode resolved 0.64 $pW/c{\mathrm{m}}^2$ with a linear range above 1 $mW/c{\mathrm{m}}^2$, with a responsivity near 0.4 A/W at 600 nm that is comparable to that of large-area silicon photodiodes and above that of thin silicon CMOS pixels in the red.
• Solution-processed photodetection on arbitrary substrates: Films of 250 nm to 400 nm deposited from solution give detectivities of $10^{12}$ to $7\times 10^{12}\mathrm{cm}\mathrm{H}{\mathrm{z}}^{1/2}/W$ between 400 nm and 780 nm.

Perovskite Photodiode (Vertical n-i-p and p-i-n)

Name	Formula	Related Formulae	Variables/Constants
Responsivity and quantum efficiency	$\mathfrak{R}=EQE\frac{q\lambda }{hc}=\frac{EQE\cdot \lambda \left(\mu \mathrm{m}\right)}{1.2398}A/W$	$EQE=\left(1-R\right){\eta }_{abs}{\eta }_c$ ${\lambda }_c\left(\mu \mathrm{m}\right)=\frac{1.2398}{E_g\left(\mathrm{eV}\right)}$	$\mathfrak{R}:responsivity$ $EQE:externalquantumefficiency$ $R:reflectance$ ${\eta }_{abs}:absorbedfraction$ $\begin{array}{r}{\eta }_c:collectionefficiencyofthetransport\\ layers\end{array}$ $\begin{array}{r}{E}_g:gap(1.58eVforC{H}_{3}N{H}_{3}Pb{I}_3,1.52eV\\ forthetriple-cation\\ F{A}_{0.9}M{A}_{0.05}C{s}_{0.05}Pb{I}_{2.7}B{r}_{0.3})\end{array}$ $\begin{array}{r}(0.395A/Wat600nmgivesEQE=82\%,\\ computed;theonsetat780nmgives1.59\\ eV,computed;EQE=80\%foraPEDOT:PSS\\ deviceand93\%at390nmfortheothers)\end{array}$
Dark current and open-circuit voltage	$V_{oc}=\frac{n{k}_{B}T}{q}\ln \left(\frac{J_{sc}}{J_0}+1\right)$	$V_{oc}=\frac{n{k}_{B}T}{q}\ln \left(\frac{J_{sc}-V_{oc}/R_{sh}}{J_0}+1\right)$ $J_{dark}\left(V\right)=J_0\left[\exp \left(\frac{qV}{n{k}_{B}T}\right)-1\right]+\frac{V}{R_{sh}}$	$V_{oc}:open-circuitvoltage$ $n:idealityfactor$ $J_{sc}:short-circuitcurrentdensity$ $J_0:reversesaturationcurrentdensity$ $\begin{array}{r}{R}_{sh}:shuntresistance(area-normalized),\\ thesecondformincludestheshunt\end{array}$ $k_B:Boltzmannconstant$ $\begin{array}{r}(atheoretical{J}_{0}ofabout10pA/\mathrm{c}{\mathrm{m}}^{2}was\\ estimatedfrom{V}_{oc}andn;ashuntof1\\ k\Omega \mathrm{c}{\mathrm{m}}^{2}at0.1Vwouldgive0.1mA/c{\mathrm{m}}^2,\\ i.e.10^{7}timesmore)\end{array}$
Noise current and specific detectivity	$D^{\ast }=\frac{\mathfrak{R}\sqrt{AB}}{i_n},i_n=\sqrt{i_s^2+i_t^2}$	$i_s=\sqrt{2q{I}_{d}B},i_t=\sqrt{\frac{4k_{B}TB}{R}}$ $NEP=\frac{i_n}{\mathfrak{R}}\left(W/H{\mathrm{z}}^{1/2}\right)$	$i_s,i_t:shotandthermalnoisecurrents$ $I_d:darkcurrent$ $B:bandwidth$ $R:shuntresistance$ $A:area$ $\begin{array}{r}NEP:noiseequivalentpowerina1Hz\\ bandwidth,thewhitenoiseisthe\\ quadraturesum\end{array}$ $k_B:Boltzmannconstant$ $\begin{array}{r}(at-0.1Vand7.25\mathrm{m}{\mathrm{m}}^2:shot5.5fA/\mathrm{H}{\mathrm{z}}^{1/2},\\ thermal3.3fA/\mathrm{H}{\mathrm{z}}^{1/2},sum6.4fA/\mathrm{H}{\mathrm{z}}^{1/2}\\ (computed6.41),measured16fA/\mathrm{H}{\mathrm{z}}^{1/2}\\ between0.3Hzand10Hz;I_d=94pAandR\\ =1.5G\Omega ,computed)\end{array}$
Linear dynamic range and weak-light limit	$LDR=10{\log }_{10}\left(\frac{P_{sat}}{NEP}\right)$	$LDR=20{\log }_{10}\left(\frac{I_{max}}{I_{min}}\right)$ $P_{min}=\frac{NEP}{A}\sqrt{B}$	$\begin{array}{r}{P}_{sat}:incidentpoweratwhichthe\\ responsivitystartstofall\end{array}$ $\begin{array}{r}{I}_{max},I_{min}:largestandsmallest\\ photocurrentofthelinearrange\end{array}$ $\begin{array}{r}{P}_{min}:smallestdetectableintensity,the\\ firstformisthedefinitionofthecited\\ sourceandgiveshalfthevalueofthe\\ secondformforthesameratio\end{array}$ $\begin{array}{r}(NEP=4.3\times 10^{-14}W/H{\mathrm{z}}^{1/2}and{P}_{sat}of1.5\\ mW/c{\mathrm{m}}^2(computed)give94dB;thesame\\ ratiointhe20\log formis188dB;the\\ lowestintensitywas0.64pW/c{\mathrm{m}}^2)\end{array}$
Bandwidth and capacitance	$f_{-3dB}=\frac{0.35}{t_R},f_{RC}=\frac{1}{2\pi RC}$	$C=\frac{{ϵ}_0{ϵ}_{r}A}{d}$ $t_{tr}=\frac{d^2}{\mu V},f_t=\frac{3.5}{2\pi t_{tr}}$	$t_R:response(rise)time$ $R:loadplusseriesresistance$ $C:capacitanceofthediode$ ${ϵ}_r:relativepermittivityoftheperovskite$ $d:thickness$ $\mu :mobility$ $V:voltageacrossthelayer$ $f_t:transit-limitedcutoff$ $\begin{array}{r}(t_R=120nsgives2.9MHz;C=1.5nF,A\\ =7.25\mathrm{m}{\mathrm{m}}^{2}andd=400nmgive{ϵ}_r=9.3,\\ computed;f_{RC}=2.1MHzfor50\Omega (assumed);\\ f_t=3.5\times 10^{2}MHzfor\mu =1\mathrm{c}{\mathrm{m}}^2/Vs\\ (assumed)and1V)\end{array}$

Perovskite Photoconductor (Planar)

Name	Formula	Related Formulae	Variables/Constants
Diffusion length and trap density	$L=\sqrt{D\tau }=\sqrt{\frac{k_{B}T\mu \tau }{q}}$	$V_{TFL}=\frac{q{n}_t{L}_s^2}{2ϵ{ϵ}_0}$ $J_{MG}=\frac{9ϵ{ϵ}_0\mu V^2}{8L_s^3}$	$D:diffusivity$ $\tau :carrierlifetime$ $\mu :mobility$ $V_{TFL}:trap-filled-limitvoltage$ $n_t:trapdensity$ $\begin{array}{r}{L}_s:thicknessofthecrystalinthe\\ space-charge-limitedmeasurement\end{array}$ $J_{MG}:trap-freeMott-Gurneycurrentdensity$ $ϵ:relativepermittivity(32inthesource)$ $k_B:Boltzmannconstant$ $\begin{array}{r}({\mu }_h=164\mathrm{c}{\mathrm{m}}^2/Vsand\tau =82\mu \mathrm{s}giveL=\\ 186\mu \mathrm{m},computed,against175\pm 25\mu \mathrm{m};{\mu }_e=\\ 24.8\mathrm{c}{\mathrm{m}}^2/Vsgives72\mu \mathrm{m};n_t=3.6\times 10^{10}\mathrm{c}{\mathrm{m}}^{-3}\\ forcrystalsand2\times 10^{15}\mathrm{c}{\mathrm{m}}^{-3}forfilms)\end{array}$
Photoconductive gain and quantum efficiency	$G=\frac{\tau }{t_{tr}},t_{tr}=\frac{L_g^2}{\mu V}$	$G=\frac{\tau \left({\mu }_e+{\mu }_h\right)V}{L_g^2}$ $EQE=\eta G$	$G:photoconductivegain$ $L_g:electrodegap$ ${\mu }_e,{\mu }_h:electronandholemobilities$ $V:bias$ $\begin{array}{r}\eta :fractionofthephotonsconvertedinto\\ pairs,thegainholdsifthecarriersare\\ nottrappedandthecontactsareohmic\end{array}$ $\begin{array}{r}(anelectrodegapof20\mu \mathrm{m}and1Vgave\mathfrak{R}\\ =953A/WandEQE=2.22\times 10^5\%at532nm;\\ themobilitiesandthelifetimeofanother\\ crystalgiveG=3.9\times 10^3,computed)\end{array}$
Power-law responsivity	$\mathfrak{R}\propto P^{b-1},b=1+\frac{\ln \left({\mathfrak{R}}_2/{\mathfrak{R}}_1\right)}{\ln \left(P_2/P_1\right)}$	$I_{ph}\propto P^b$ $\mathfrak{R}\propto \frac{1}{1+P/P_0}$	$P:lightintensity$ $b:exponentofthephotocurrent$ $I_{ph}:photocurrent$ $\begin{array}{r}{P}_0:saturationintensityofthe\\ trap-limitedlifetime(Hornbeck-Haynes\\ form),theresponsivityfallswith\\ intensitywhentrapsfill\end{array}$ $\begin{array}{r}(953A/Wat2.12nW/c{\mathrm{m}}^{2}and2.55A/Wat1\\ mW/c{\mathrm{m}}^{2}giveb=0.55,computed;EQE=\\ 5.9\times 10^2\%at1mW/c{\mathrm{m}}^2,computed594\%)\end{array}$
Single crystal compared with polycrystalline film	$\frac{{\mathfrak{R}}_{sc}}{{\mathfrak{R}}_{pc}}=\frac{2.55}{0.0197}\approx 1.3\times 10^2$	$\frac{t_{pc}}{t_{sc}}\approx 10^3$ $on/off=\frac{I_{light}}{I_{dark}}$	$\begin{array}{r}sc,pc:singlecrystalandpolycrystalline\\ filmofthesamegeometry\end{array}$ $t:responsetime$ $I_{light},I_{dark}:currentsunderlightandinthedark$ $\begin{array}{r}(at1mW/c{\mathrm{m}}^{2}and532nm:2.55A/Wagainst\\ 0.0197A/W,EQE595\%against4.59\%;rise\\ anddecay74\mu \mathrm{s}and58\mu \mathrm{s};darkcurrent11\\ nAat4V;on/offratio224at3V)\end{array}$

Important Questions

Ques: Why are the diffusion lengths of a single crystal and of a film so different, and are both carriers above 175 μm?

The relation $L=\sqrt{k_{B}T\mu \tau /q}$ with the hole mobility of 164 $\mathrm{c}{\mathrm{m}}^2/Vs$ and a lifetime of 82 μs gives 186 μm (computed), in line with the $175\pm 25$ μm of the source. The film has a trap density of $2\times 10^{15}\mathrm{c}{\mathrm{m}}^{-3}$ against $3.6\times 10^{10}\mathrm{c}{\mathrm{m}}^{-3}$ for the crystal, almost five orders more, and its diffusion length is about 1 μm. The statement that the electrons and the holes both exceed 175 μm is not reproduced by the printed electron mobility of 24.8 $\mathrm{c}{\mathrm{m}}^2/Vs$, which gives 72 μm to 78 μm for lifetimes of 82 μs to 95 μs (computed). The hole value is therefore the more likely meaning of the 175 μm, and the electron diffusion length is smaller by about $\sqrt{164/24.8}=2.6$. A microwave-conductivity study of films bounded the deep defects by $8\times 10^{13}\mathrm{c}{\mathrm{m}}^{-3}$, below the space-charge-limited value, so the film trap density depends on the method. Reference: Dong et al., Electron-hole diffusion lengths > 175 μm in solution-grown CH3NH3PbI3 single crystals, Science 347, 967 (2015); Wang et al., A Review of Perovskite-Based Photodetectors and Their Applications, Nanomaterials 12, 4390 (2022); Caselli et al., ACS Energy Lett. 5, 3821 (2020).

Ques: Why is the external quantum efficiency of the vertical photodiode below 100% while that of the planar crystal detector is $2.2\times 10^5\%$?

In the photodiode every absorbed photon yields at most one collected pair, so that 0.395 A/W at 600 nm corresponds to 82% (computed) and the best devices reach 93% at 390 nm. In the planar photoconductor one carrier crosses the 20 μm gap many times during the lifetime, $G=\tau ({\mu }_e+{\mu }_h)V/L_g^2$, and 953 A/W at 532 nm equals $2.22\times 10^5\%$ (computed 2221 in units of EQE = 1). The mobilities and the lifetime of another crystal (164 and 24.8 $\mathrm{c}{\mathrm{m}}^2/Vs$, 82 μs) give $G=3.9\times 10^3$ for 1 V (computed), which exceeds the measured $2.2\times 10^3$, as it must for $\eta <1$, although the crystals are not the same. The gain is the price of the slower response of 74 μs, close to the lifetime. Reference: Sutherland et al., Sensitive, Fast, and Stable Perovskite Photodetectors Exploiting Interface Engineering, ACS Photonics (2015); Lian et al., High-Performance Planar-Type Photodetector on (100) Facet of MAPbI3 Single Crystal, Sci. Rep. 5, 16563 (2015); Dong et al., Electron-hole diffusion lengths > 175 μm in solution-grown CH3NH3PbI3 single crystals, Science 347, 967 (2015); Fang and Huang, Resolving Weak Light of Sub-picowatt per Square Centimeter by Hybrid Perovskite Photodetectors Enabled by Noise Reduction, Adv. Mater. 27, 2804 (2015).

Ques: Why does the responsivity of the planar single-crystal detector fall with intensity?

The responsivity fell from 953 A/W at 2.12 $nW/c{\mathrm{m}}^2$ to 2.55 A/W at 1 $mW/c{\mathrm{m}}^2$, and the EQE from $2.22\times 10^5\%$ to 595%. For a power law $I_{ph}\propto P^b$ the two points give $b=0.55$ (computed), the sublinear behaviour that appears when traps fill and the lifetime of the free carriers falls, as in the Hornbeck-Haynes form $\mathfrak{R}\propto 1/(1+P/P_0)$. The source attributes the high gain to a low trap density and a long diffusion length of the single crystal, and does not give the mechanism of the saturation; the single crystal was about 130 times more responsive than a film of the same geometry (2.55 against 0.0197 A/W) and three orders faster. Reference: Lian et al., High-Performance Planar-Type Photodetector on (100) Facet of MAPbI3 Single Crystal, Sci. Rep. 5, 16563 (2015).

Ques: Is the noise of the perovskite photodiode at the shot-noise and thermal limit?

At -0.1 V the shot noise of the dark current (5.5 $fA/H{\mathrm{z}}^{1/2}$) and the thermal noise of the shunt (3.3 $fA/H{\mathrm{z}}^{1/2}$) add to 6.4 $fA/H{\mathrm{z}}^{1/2}$ (computed 6.41), whereas the average measured noise between 0.3 Hz and 10 Hz was 16 $fA/H{\mathrm{z}}^{1/2}$, 2.5 times higher. The reported $D^{\ast }$ of $7.4\times 10^{12}\mathrm{cm}\mathrm{H}{\mathrm{z}}^{1/2}/W$ at 680 nm uses a noise current from the measurement; with the calculated white noise it would be $1.8\times 10^{13}$ (computed, from the implied $\mathfrak{R}=0.44$ A/W). A second device was described as within a factor of 10 of the shot-noise limit under reverse bias. The measured noise is the more likely one for the detectivity, since the instrument limited the band to 0.3 Hz to 10 Hz. Reference: Fang and Huang, Resolving Weak Light of Sub-picowatt per Square Centimeter by Hybrid Perovskite Photodetectors Enabled by Noise Reduction, Adv. Mater. 27, 2804 (2015); Sutherland et al., Sensitive, Fast, and Stable Perovskite Photodetectors Exploiting Interface Engineering, ACS Photonics (2015).

Ques: Is the speed of the photodiode limited by the transit time or by the RC time?

The 400 nm diode had a response time of 120 ns, i.e. $f_{-3dB}=0.35/t_R=2.9$ MHz, and a capacitance of 1.5 nF. The transit time for a mobility of 1 $\mathrm{c}{\mathrm{m}}^2/Vs$ (assumed) and 1 V is 1.6 ns, which gives $f_t=3.5/(2\pi t_{tr})$ of about 350 MHz (computed), two orders above the measured value, whereas $1/(2\pi RC)$ with 50 Ω (assumed) is 2.1 MHz, the same order as the measurement. The speed is therefore limited by the circuit, and a smaller area would raise it. The capacitance of 1.5 nF over 7.25 $\mathrm{m}{\mathrm{m}}^2$ corresponds to ${ϵ}_r=9.3$ (computed), far below the 32 used in the crystal study, which suggests that the high-frequency permittivity applies. Reference: Fang and Huang, Resolving Weak Light of Sub-picowatt per Square Centimeter by Hybrid Perovskite Photodetectors Enabled by Noise Reduction, Adv. Mater. 27, 2804 (2015); Dong et al., Electron-hole diffusion lengths > 175 μm in solution-grown CH3NH3PbI3 single crystals, Science 347, 967 (2015); Sutherland et al., Sensitive, Fast, and Stable Perovskite Photodetectors Exploiting Interface Engineering, ACS Photonics (2015).

Ques: Why do the thick fullerene layer and the passivation layers lower the dark current, and is it diffusion-limited?

The device with a fullerene layer of 80 nm had $9.1\times 10^{-9}A/c{\mathrm{m}}^2$ at -2 V against $1.6\times 10^{-7}A/c{\mathrm{m}}^2$ for the first device (a factor 18, computed), because the thick layer blocks the injection of holes under reverse bias; the $\mathrm{A}{\mathrm{l}}_2{\mathrm{O}}_3$ and PCBM layers lowered the current of another device by an order of magnitude by passivating the traps of $\mathrm{Ti}{\mathrm{O}}_2$ and by blocking the shunts. The theoretical saturation current estimated from $V_{oc}$ is about 10 $pA/c{\mathrm{m}}^2$, while a shunt of 1 $\mathrm{k\Omega }\mathrm{c}{\mathrm{m}}^2$ at 0.1 V would give $0.1mA/c{\mathrm{m}}^2$, so the measured current lies between the two and is set by shunts and traps, not by diffusion. Reference: Fang and Huang, Resolving Weak Light of Sub-picowatt per Square Centimeter by Hybrid Perovskite Photodetectors Enabled by Noise Reduction, Adv. Mater. 27, 2804 (2015); Sutherland et al., Sensitive, Fast, and Stable Perovskite Photodetectors Exploiting Interface Engineering, ACS Photonics (2015); Wang et al., A Review of Perovskite-Based Photodetectors and Their Applications, Nanomaterials 12, 4390 (2022).

Ques: Why do two reports of the linear dynamic range, $94\mathrm{dB}$ and above $80\mathrm{dB}$ over four decades, not contradict each other?

The $94\mathrm{dB}$ of the photodiode was calculated as $10{\log }_{10}(P_{sat}/NEP)$, and for $NEP=4.3\times 10^{-14}W/H{\mathrm{z}}^{1/2}$ and a saturation at about 1.5 $mW/c{\mathrm{m}}^2$ over 7.25 $\mathrm{m}{\mathrm{m}}^2$ the ratio is $2.5\times 10^9$ (computed). The other report quotes more than $80\mathrm{dB}$ over four decades of intensity, i.e. $20{\log }_{10}(10^4)$, the form used for the amplitude of the current. In the second form the first device would have $188\mathrm{dB}$ (computed), and in the first the second about $40\mathrm{dB}$. The numbers are comparable only after the same definition is chosen, and the limit of the photodiode is the noise at the low end and the fall of the responsivity above 3 $mW/c{\mathrm{m}}^2$ at the high end. Reference: Fang and Huang, Resolving Weak Light of Sub-picowatt per Square Centimeter by Hybrid Perovskite Photodetectors Enabled by Noise Reduction, Adv. Mater. 27, 2804 (2015); Sutherland et al., Sensitive, Fast, and Stable Perovskite Photodetectors Exploiting Interface Engineering, ACS Photonics (2015).

Ques: Does the perovskite photodiode match silicon in detectivity?

A silicon detector typically peaks near $4\times 10^{12}\mathrm{cm}\mathrm{H}{\mathrm{z}}^{1/2}/W$, and the stack with $\mathrm{A}{\mathrm{l}}_2{\mathrm{O}}_3$ and PCBM had $10^{12}$ at -0.2 V and 600 nm, with a responsivity comparable to that of large-area silicon, while the device with the thick fullerene layer reached $7.4\times 10^{12}$ at 680 nm. The two numbers are not equivalent: the second was obtained from the noise between 0.3 Hz and 10 Hz at -0.1 V, the first at a different bias and light level, and the bandwidth used in $D^{\ast }$ was not stated in the second paper. The advantage claimed is in the red, where the absorption of silicon is weaker, and the detectivity of the perovskite diode is better described as comparable to silicon than as higher. Reference: Sutherland et al., Sensitive, Fast, and Stable Perovskite Photodetectors Exploiting Interface Engineering, ACS Photonics (2015); Fang and Huang, Resolving Weak Light of Sub-picowatt per Square Centimeter by Hybrid Perovskite Photodetectors Enabled by Noise Reduction, Adv. Mater. 27, 2804 (2015).

Ques: What limits the stability of a perovskite photodetector?

The methylammonium compound decomposes in humid, illuminated, oxygen-containing or hot ambient: $\mathrm{C}{\mathrm{H}}_3\mathrm{N}{\mathrm{H}}_3\mathrm{Pb}{\mathrm{I}}_3\rightleftharpoons \mathrm{C}{\mathrm{H}}_3\mathrm{N}{\mathrm{H}}_3\mathrm{I}+\mathrm{Pb}{\mathrm{I}}_2$, $\mathrm{C}{\mathrm{H}}_3\mathrm{N}{\mathrm{H}}_3\mathrm{I}\rightleftharpoons \mathrm{C}{\mathrm{H}}_3\mathrm{N}{\mathrm{H}}_2+\mathrm{HI}$, $4HI+{\mathrm{O}}_2\rightleftharpoons 2{\mathrm{I}}_2+2{\mathrm{H}}_2\mathrm{O}$ and $2HI\to {\mathrm{H}}_2+{\mathrm{I}}_2$, and the formamidinium compound converts from the α to the δ phase. Halide ions migrate into metal electrodes and form silver halides, which low-dimensional compositions with isolated octahedra reduce. A photodiode stayed stable for 24 h in air after $10^9$ pulses and an encapsulated one for one week after $7\times 10^9$ pulses, and a single crystal lost 6% of its photocurrent in 40 days in a desiccator. Reference: Wang et al., A Review of Perovskite-Based Photodetectors and Their Applications, Nanomaterials 12, 4390 (2022); Sutherland et al., Sensitive, Fast, and Stable Perovskite Photodetectors Exploiting Interface Engineering, ACS Photonics (2015); Lian et al., High-Performance Planar-Type Photodetector on (100) Facet of MAPbI3 Single Crystal, Sci. Rep. 5, 16563 (2015).

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