1. Theory

Definition: A colloidal quantum-dot (CQD) photodetector uses a film of semiconductor nanocrystals, 2 nm to 10 nm in diameter, synthesized in solution, capped with ligands, and deposited by spin coating, drop casting or dip coating on a substrate or a readout circuit; the dots are PbS for 0.9 μm to 2.6 μm and HgTe for the 2 μm to 5 μm range and beyond.
Size-tuned gap: The quantum confinement raises the gap of the dot above the bulk value (about 0.4 eV for PbS) as the size falls, so that the first exciton peak of a 2.9 nm dot is at 888 nm (1.396 eV), and the absorption wavelength can be tuned up to 2.6 μm.
Absorption: The absorption coefficient is $1 0^{4} c m^{- 1}$ to $1 0^{5} c m^{- 1}$ near the onset and reaches $1 0^{6} c m^{- 1}$ far above the gap, so a film of a few hundred nanometres absorbs the light.
Transport: The carriers hop between the dots; the mobility of solution-processed films is $1 0^{- 5}$ to $1 0^{- 3} c m^{2} /Vs$ , up to about $1 0^{- 1} c m^{2} /Vs$ after ligand exchange, and the minority diffusion length is 100 nm to 200 nm, so that a fully depleted device is 100 nm to 200 nm thick.
Ligands and traps: The long oleic acid chains are replaced by short ones (ethanedithiol, tetrabutylammonium iodide, $Pb I_{2}$ , butylamine) to bring the dots together, and the trap states of the surface (oxides, sulfates) set the dark current, the noise and the speed.
Device types: The photoconductor (two electrodes on a film, with gain and a slow response), the photodiode (a junction of the dots with $ZnO$ , $Ti O_{2}$ or a second dot layer, fast and with a low dark current) and the hybrid phototransistor (dots on graphene, treated on the Phototransistor page).
Integration: The film is deposited directly on a silicon readout wafer, without the hybridization of an epitaxial detector, which is the reason for the interest in imagers: an array of 768 × 512 pixels of 5 μm was made with PbS, and a review of mercury chalcogenide dots reports arrays of 640 × 512 pixels of 15 μm in the SWIR and 320 × 256 pixels of 30 μm in the MWIR.
Figures of merit: The responsivity, the external quantum efficiency, $D^{*}$ , the noise equivalent power, the dark current density, the linear dynamic range, the bandwidth and, for arrays, the read noise, the full well and the noise equivalent temperature difference.

2. Working Principle

Photodiode: A photon creates an exciton in a dot, the pair is separated by the field of the depleted junction and by the hopping between the dots, and the photocurrent flows if the lifetime exceeds the extraction time $t_{e x t} = L^{2} / (μ V_{bi})$ , which is 100 ns for 100 nm and $1 0^{- 3} c m^{2} /Vs$ .
Dark current: The dark current of the PbS photodiode is generation through mid-gap states, with an activation energy of 0.41 eV for a gap of 0.855 eV, and it is lowered by passivating the interface ( $Pb I_{2}$ on $ZnO$ ) and by transport layers that block the injection.
Photoconductor: A bias across a gap of 2 μm to 5 μm moves the mobile carrier many times through the film during the long time that the other carrier is trapped, so that a gain $G = τ / t_{t r}$ results, with time constants of 30 ms to 2.8 s.
Infrared HgTe: Electron and hole doping of HgTe dots (a Ag $^{+}$ exchange gives the p side) makes a photovoltaic homojunction with a cutoff of 5 μm, operated at 85 K to 220 K, over which the detectivity of one diode fell by a factor 40.
Readout: In an imager the photodiode is held between reset and integration, and the dark charge of the pixel, the full well and the read noise decide the range, which was $72 dB$ for 25 electrons of read noise.

3. Applications

SWIR imaging on silicon: A PbS photodiode array on a CMOS readout has an EQE of 40% at 1450 nm and a response past the 1.12 eV edge of silicon, for vision through haze and for the night sky, with a film that avoids the hybridization step of InGaAs.
Low-cost NIR sensing: PbS photoconductors on interdigitated electrodes give 1 A/W to 46 A/W at 1.3 μm, for single-pixel detection where the slow response (0.1 Hz to some Hz) is allowed.
Mid-infrared HgTe: A photodiode with a cutoff of 5 μm reached $D^{*} \approx 3 \times 1 0^{11} cm H z^{1/2} /W$ at low temperature and a 320 × 256 array had an NETD of 102 mK at 100 K, the aim being a cheaper alternative to epitaxial HgCdTe.

Colloidal Quantum-Dot Material

Name	Formula	Related Formulae	Variables/Constants
Confinement and cutoff wavelength	$λ_{c} (μ m) = \frac{1.2398}{E _{g} ( eV )}$	$E_{g} (R) \approx E_{g, b u l k} + \frac{h ^{2}}{8 R ^{2}} (\frac{1}{m _{e}^{}} + \frac{1}{m _{h}^{}}) - \frac{1.8 q ^{2}}{4 π ϵ ϵ _{0} R}$ $a_{B} = \frac{4 π ϵ ϵ _{0} ℏ ^{2}}{μ ^{*} q ^{2}}$	$λ_{c} : c u t o f f w a v e l e n g t h$ $E_{g} : g a p o f t h e d o t (f i r s t e x c i t o ni c ab sor pt i o n p e ak)$ $E_{g, b u l k} : g a p o f t h e b u l k se mi co n d u c t or (ab o u t 0.4 e V f or P b S)$ $R : d o t r a d i u s$ $m_{e}^{}, m_{h}^{} : e f f ec t i v e ma sses$ $ϵ : r e l a t i v e p er mi tt i v i t y$ $μ^{*} : r e d u ce d ma ss$ $a_{B} : B o h r e x c i t o n r a d i u s (18 nm f or P b S), t h e seco n d f or m i s t h e e f f ec t i v e - ma ss es t ima t e f or a p a r ab o l i c ban d an d an in f ini t e ba r r i er$ $(an e x c i t o n p e ak a t 888 nm g i v es E_{g} = 1.396 e V f or a d o t o f 2.9 nm, 1320 nm g i v es 0.939 e V, 1450 nm g i v es 0.855 e V an d t h e q u o t e d t u nin g l imi t o f 2.6 μ m g i v es 0.477 e V, a l l co m p u t e d)$
Absorption and absorbed fraction	$η_{ab s} = (1 - R) [1 - exp (- α d)]$	$I (x) = I_{0} exp (- α x)$ $d_{90} = \frac{l n 10}{α}$	$η_{ab s} : ab sor b e d f r a c t i o n$ $R : r e f l ec t an ce$ $α : ab sor pt i o n coe f f i c i e n t$ $d : t hi c k n ess o f t h e d o t f i l m$ $I : in t e n s i t y a t d e pt h x$ $d_{90} : t hi c k n ess t ha t ab sor b s 90% o f t h e l i g h t t ha t e n t er s$ $(α = 1 0^{4} c m^{- 1} n e a r t h e o n se t an d 1 0^{5} c m^{- 1} ab o v e i t g i v e 26% an d 95% f or 300 nm w i t h R = 0, co m p u t e d, an d d_{90} = 2.3 μ m an d 230 nm)$
Mobility, diffusion length and extraction time	$L_{D} = \frac{k _{B} T μτ}{q}$	$t_{e x t} = \frac{L ^{2}}{μ V _{bi}}$ $η_{c} \approx 1 if τ > t_{e x t}$	$L_{D} : d i f f u s i o n l e n g t h o f t h e min or i t y c a r r i er$ $μ : i t s m o bi l i t y$ $τ : i t s l i f e t im e$ $t_{e x t} : e x t r a c t i o n t im e a cr oss t h e d e pl e t e d l a y er o f w i d t h L$ $V_{bi} : b u i l t - in p o t e n t ia l$ $η_{c} : co l l ec t i o n e f f i c i e n cy$ $k_{B} : B o l t z mann co n s t an t$ $(μ = 1 0^{- 3} c m^{2} /Vs an d 100 nm a t 1 V g i v e t_{e x t} = 100 n s, an d 1 0^{- 5} c m^{2} /Vs g i v es 10 μ s, co m p u t e d; L_{D} = 100 nm n ee d s τ = 3.9 μ s a t 1 0^{- 3} c m^{2} /Vs, co m p u t e d)$

Colloidal Quantum-Dot Photodiode

Name	Formula	Related Formulae	Variables/Constants
Responsivity and quantum efficiency	$R = E QE \frac{q λ}{h c} = \frac{E QE \cdot λ ( μ m )}{1.2398} A/W$	$E QE = η_{ab s} η_{c}$ $E QE = \frac{I _{p h}}{q P / h ν}$	$R : r es p o n s i v i t y$ $E QE : e x t er na l q u an t u m e f f i c i e n cy$ $η_{ab s} : ab sor b e d f r a c t i o n$ $η_{c} : co l l ec t i o n e f f i c i e n cy$ $I_{p h} : p h o t oc u r r e n t$ $P : in c i d e n t p o w er$ $h ν : p h o t o n e n er g y$ $(E QE = 40% a t 1450 nm g i v es R = 0.468 A / W, co m p u t e d; a p e ak o f 0.57 A / W w a s r e p or t e d f or a P b S p h o t o d i o d e w i t h a P b I_{2} l a y er)$
Dark current and activation energy	$J_{d} (T) = J_{00} exp (- \frac{E _{a}}{k _{B} T})$	$\frac{d l n J _{d}}{d T} = \frac{E _{a}}{k _{B} T ^{2}}$ $E_{a} \approx \frac{E _{g}}{2} for generation through mid - gap states$	$J_{d} : d a r k c u r r e n t d e n s i t y$ $J_{00} : p r e f a c t or$ $E_{a} : a c t i v a t i o n e n er g y$ $T : t e m p er a t u r e$ $E_{g} : g a p, t h e seco n d f or m i s t h e in t er p r e t a t i o n o f t h e m e a s u r e d e n er g y, n o t a p r oo f$ $k_{B} : B o l t z mann co n s t an t$ $(E_{a} = 0.41 e V f or a g a p o f 0.855 e V (ha l f i s 0.428 e V); t h e c u r r e n t c han g es b y a f a c t or 205 b e tw ee n - 20 an d 80^{\circ} C an d d o u b l es e v er y 12.9 K n e a r 298 K, co m p u t e d; J_{d} = 2.0 \times 1 0^{- 6} A/c m^{2})$
Specific detectivity	$D^{*} = \frac{R}{2 q J _{d} + 4 k _{B} T / ( R _{0} A )}$	$D_{s h o t}^{} = \frac{R}{2 q J _{d}}, D_{J}^{} = R \frac{R _{0} A}{4 k _{B} T}$ $D^{*} \propto J_{d}^{- 1/2}$	$D^{} : s p ec i f i c d e t ec t i v i t y$ $J_{d} : d a r k c u r r e n t d e n s i t y$ $R_{0} A : z er o - bia s r es i s t an ce - a r e a p r o d u c t$ $R : r es p o n s i v i t y, t h e f i r s t f or m o mi t s t h e f l i c k er n o i se an d t h e n o i se o f t h e ba c k g r o u n d$ $k_{B} : B o l t z mann co n s t an t$ $(R = 0.468 A / W an d J_{d} = 2.0 \times 1 0^{- 6} A/c m^{2} g i v e D_{s h o t}^{} = 5.8 \times 1 0^{11} cm H z^{1/2} /W; R = 0.53 A / W an d J_{d} = 4.6 \times 1 0^{- 9} A/c m^{2} g i v e 1.4 \times 1 0^{13}, co m p u t e d)$
Linear dynamic range	$L D R = 20 lo g_{10} (\frac{J _{p h}}{J _{d}})$	$L D R = 20 lo g_{10} (\frac{I _{s a t}}{N E I})$ $N E I = \frac{i _{n}}{R A} B$	$J_{p h} : p h o t oc u r r e n t d e n s i t y a t t h e r e f er e n ce in t e n s i t y$ $J_{d} : d a r k c u r r e n t d e n s i t y$ $I_{s a t} : s a t u r a t i o n in t e n s i t y$ $N E I : n o i se - e q u i v a l e n t in t e n s i t y$ $i_{n} : n o i se c u r r e n t$ $A : a r e a$ $B : ban d w i d t h, t h e tw o f or m s a r e t h e d e f ini t i o n s o f tw o d i f f er e n t so u r ces$ $(101.28 d B i s a r a t i o o f 1.16 \times 1 0^{5} an d n ee d s J_{d} = 4.6 \times 1 0^{- 9} A/c m^{2} f or 0.53 mA/c m^{2}, co m p u t e d; ab o v e 112 d B w a s r e p or t e d a t 1.55 μ m f or an H g T e d i o d e)$
Speed and bandwidth	$f_{- 3 d B} = \frac{0.35}{t _{R}}$	$f_{R C} = \frac{1}{2 π R C}, C = \frac{ϵ _{0} ϵ _{r} A}{d}$ $\frac{1}{f _{- 3 d B}^{2}} \approx \frac{1}{f _{t}^{2}} + \frac{1}{f _{R C}^{2}}$	$t_{R} : 10% t o 90% r i se t im e$ $R : l o a d an d ser i es r es i s t an ce$ $C : c a p a c i t an ce$ $ϵ_{r} : r e l a t i v e p er mi tt i v i t y o f t h e d o t f i l m$ $d : t hi c k n ess$ $f_{t} : t r an s i t - l imi t e d c u t o f f$ $(t_{R} = 3.4 μ s an d a f a l l t im e o f 8.9 μ s g i v e 103 k H z an d 39 k H z; 5.3 m s g i v es 66 H z, co m p u t e d; a s t a t e d ban d w i d t h o f 5 k H z n ee d s 70 μ s)$
Dark charge and noise of an imager pixel	$N_{d} = \frac{J _{d} A _{p} t _{in t}}{q}, σ_{d} = N_{d}$	$D R = 20 lo g_{10} (\frac{N _{F W C}}{σ _{r e a d}})$ $σ_{t o t} = N_{d} + N_{p h} + σ_{r e a d}^{2}$	$N_{d} : d a r k e l ec t r o n s co l l ec t e d p er f r am e$ $A_{p} : p i x e l a r e a$ $t_{in t} : in t e g r a t i o n t im e$ $σ_{d} : s h o t n o i se o f t h e d a r k c ha r g e$ $D R : d y nami c r an g e$ $N_{F W C} : f u l l - w e l l c a p a c i t y$ $σ_{r e a d} : r e a d n o i se$ $N_{p h} : p h o t oe l ec t r o n s$ $(A_{p} = 2.5 \times 1 0^{- 7} c m^{2}, J_{d} = 2.0 \times 1 0^{- 6} A/c m^{2} an d 20 m s g i v e N_{d} = 6.2 \times 1 0^{4}, σ_{d} = 250, a g ain s t σ_{r e a d} = 25; N_{F W C} = 1.01 \times 1 0^{5} g i v es 72.1 d B, co m p u t e d)$

Colloidal Quantum-Dot Photoconductor

Name	Formula	Related Formulae	Variables/Constants
Photoconductive gain	$G = \frac{τ}{t _{t r}}, t_{t r} = \frac{L ^{2}}{μ V}$	$E QE = η G, R = η G \frac{λ ( μ m )}{1.2398}$ $f_{- 3 d B} G \approx \frac{1}{2 π t _{t r}}$	$G : g ain$ $τ : l i f e t im e o f t h e l o n g er - l i v e d c a r r i er$ $t_{t r} : t r an s i t t im e o f t h e o t h er c a r r i er$ $L : e l ec t r o d e g a p$ $μ : i t s m o bi l i t y$ $V : bia s$ $η : ab sor b e d f r a c t i o n$ $f_{- 3 d B} : ban d w i d t h se t b y τ$ $(μ = 1 0^{- 3} c m^{2} /Vs (a ss u m e d), L = 5 μ m an d 1 V g i v e t_{t r} = 250 μ s; R = 30 A / W a t 1.3 μ m i s E QE = 28.6, co m p u t e d)$
Scaling of the responsivity with gap and bias	$R \propto \frac{V}{L ^{2}}$	$\frac{R _{2}}{R _{1}} = (\frac{L _{1}}{L _{2}})^{2} \frac{V _{2}}{V _{1}}$ $R \propto \frac{1}{1 + P / P _{0}}$	$R : r es p o n s i v i t y$ $V : bia s$ $L : e l ec t r o d e g a p$ $P : o pt i c a l p o w er$ $P_{0} : s a t u r a t i o n p o w er o f t h e t r a p - l imi t e d l i f e t im e, t h e f i r s t tw o f or m s h o l d f or a f i x e d l i f e t im e an d o hmi c co n t a c t s$ $(30 A / W a t L = 5 μ m w o u l d g i v e 188 A / W a t 2 μ m, co m p u t e d, w h er e a s ab o v e 40 A / W w a s m e a s u r e d a t 2 μ m an d 1 V o n an o t h er f i l m; 46 A / W w a s r e a c h e d a t 3 V)$
Noise and detectivity of the photoconductor	$i_{n}^{2} = (\frac{4 k _{B} T}{R _{d}} + 2 q I_{d}) B + i_{1/ f}^{2}$	$D^{*} = \frac{R A B}{i _{n}}$ $N E P = \frac{i _{n}}{R}$	$i_{n} : t o t a l n o i se c u r r e n t$ $R_{d} : d a r k r es i s t an ce$ $I_{d} : d a r k c u r r e n t$ $B : ban d w i d t h$ $i_{1/ f} : f l i c k er n o i se c u r r e n t$ $A : a r e a$ $N E P : n o i se e q u i v a l e n t p o w er, t h e s h o t t er m i s a l o w er b o u n d an d t h e g ain n o i se i s n o t in c l u d e d$ $k_{B} : B o l t z mann co n s t an t$ $(R_{d} = 250 k Ω an d 4 μ A a t 1 V : t h er ma l 0.26 pA/H z^{1/2}, s h o t 1.13 pA/H z^{1/2}; D^{*} = 2 \times 1 0^{10} cm H z^{1/2} /W, R = 30 A / W an d 0.015 c m^{2} im pl y 0.18 nA/H z^{1/2}, co m p u t e d)$

Mercury Telluride Quantum-Dot Photodiode (Infrared)

Name	Formula	Related Formulae	Variables/Constants
Johnson-limited detectivity of an infrared diode	$D_{J}^{*} = \frac{η q λ}{h c} \frac{R _{0} A}{4 k _{B} T}$	$R_{0} A \geq \frac{4 k _{B} T}{( i _{n} / A ) ^{2}}, \frac{i _{n}}{A} = \frac{R}{D ^{*}}$ $R = \frac{η q λ}{h c}$	$η : e x t er na l q u an t u m e f f i c i e n cy$ $R_{0} A : r es i s t an ce - a r e a p r o d u c t a t z er o bia s$ $T : t e m p er a t u r e o f t h e d e t ec t or$ $i_{n} : m e a s u r e d n o i se c u r r e n t, t h e in e q u a l i t y h o l d s b ec a u se t h e m e a s u r e d n o i se c ann o t b e b e l o w t h e J o hn so n n o i se$ $k_{B} : B o l t z mann co n s t an t$ $(R = 1.3 A / W an d D^{*} = 3.3 \times 1 0^{11} cm H z^{1/2} /W a t 85 K g i v e R_{0} A \geq 300 Ω c m^{2}, an d 1.62 A / W an d 4 \times 1 0^{11} g i v e 286 Ω c m^{2}, co m p u t e d)$
Background-limited detectivity and field of view	$D_{B L I P}^{*} = \frac{λ}{h c} \frac{η}{2 Φ _{B}}$	$Φ_{B} = sin^{2} θ \int_{0}^{λ_{c}} \frac{2 π c}{λ ^{4}} \frac{d λ}{e x p ( h c / λ k _{B} T _{B} ) - 1}$ $sin^{2} θ = \frac{1}{1 + 4 F ^{2}}$	$Φ_{B} : ba c k g r o u n d p h o t o n f l ux d e n s i t y$ $λ_{c} : c u t o f f w a v e l e n g t h$ $T_{B} : ba c k g r o u n d t e m p er a t u r e$ $θ : ha l f an g l e o f t h e f i e l d o f v i e w$ $F : f - n u mb er o f t h e co l d s hi e l d$ $η : q u an t u m e f f i c i e n cy$ $k_{B} : B o l t z mann co n s t an t$ $(300 K, λ_{c} = 5 μ m an d t h e f u l l h e mi s p h er e : Φ_{B} = 1.32 \times 1 0^{16} c m^{- 2} s^{- 1}, an d η = 0.45 g i v es 1.04 \times 1 0^{11}; F /1.3 m u l t i pl i es i t b y 2.79, g i v in g 2.9 \times 1 0^{11}, co m p u t e d)$

Important Questions

Ques: Why does the effective-mass formula fail for a PbS dot of 2.9 nm?

The formula $E_{g} \approx E_{g, b u l k} + \frac{h ^{2}}{8 R ^{2}} (1/ m_{e}^{*} + 1/ m_{h}^{*}) - 1.8 q^{2} / (4 π ϵ ϵ_{0} R)$ with the reduced mass $μ^{*} = 0.05 m_{0}$ of the source and $ϵ = 17$ gives 3.58 eV of confinement energy and a Coulomb term of 0.105 eV, i.e. a gap of 3.9 eV (computed), whereas the exciton peak at 888 nm is at 1.396 eV, about 1.0 eV above the bulk gap. The Bohr radius of 18 nm is 12 times the dot radius of 1.45 nm, the regime of strong confinement, in which the parabolic band and the infinite barrier of the model overestimate the shift. The reduced mass of the source belongs to the hot exciton near 5 eV, not to the band edge, so the result is only an order-of-magnitude check, and the gap is read from the absorption peak. Reference: Patil and Datta, Do we need to revisit the Bohr exciton radius of hot excitons?, arXiv:1105.2205; Qiao et al., Efficient interface and bulk passivation of PbS quantum dot infrared photodetectors by PbI2 incorporation, RSC Adv. 7, 52947 (2017).

Ques: Why is the photodiode so much more detective than the photoconductor, although its responsivity is lower?

The PbS photoconductor had a dark current density of 0.3 $mA/c m^{2}$ at 1 V and a responsivity of 1 A/W to 30 A/W, with $D^{*} = 2 \times 1 0^{10}$ at 1.3 μm, while a photodiode with $R = 0.53$ A/W had $D^{*} = 1.3 \times 1 0^{13}$ at 0 V. The dark current implied by the second value in the shot-noise form is $5 \times 1 0^{- 9} A/c m^{2}$ (computed), about $6 \times 1 0^{4}$ times lower than that of the photoconductor, so that the shot noise current falls by about 240, more than the factor 57 by which the responsivity falls (computed). In the photoconductor the noise of 0.18 $nA/H z^{1/2}$ (computed from the printed $D^{*}$ ) is 160 times the shot noise of its dark current, which points to flicker noise, reported to dominate up to 100 kHz. Reference: De Iacovo et al., PbS Colloidal Quantum Dot Photodetectors operating in the near infrared, Sci. Rep. 6, 37913 (2016); Qiao et al., Efficient interface and bulk passivation of PbS quantum dot infrared photodetectors by PbI2 incorporation, RSC Adv. 7, 52947 (2017); Noise performance of PbS colloidal quantum dot photodetectors (repository abstract).

Ques: Are the dark current, the linear dynamic range and the detectivity of the PbI2 photodiode consistent?

They are consistent only if the dark current is that at 0 V. The printed dark current of $2.85 \times 1 0^{- 5}$ A over 0.09 $c m^{2}$ is $3.2 \times 1 0^{- 4} A/c m^{2}$ , which with 0.53 $mA/c m^{2}$ of photocurrent at 1 $mW/c m^{2}$ gives only $4.5 dB$ , not $101.28 dB$ , and $D_{s h o t}^{*} = 5 \times 1 0^{10}$ (computed). The LDR requires $J_{d} = 4.6 \times 1 0^{- 9} A/c m^{2}$ , and the shot-noise form with this value gives $1.4 \times 1 0^{13}$ , close to the reported $1.3 \times 1 0^{13}$ at 0 V (computed). The first dark current is therefore at a forward or a larger reverse bias, which the source does not state, and the detectivity is derived from the dark current without a noise measurement. Reference: Qiao et al., Efficient interface and bulk passivation of PbS quantum dot infrared photodetectors by PbI2 incorporation, RSC Adv. 7, 52947 (2017).

Ques: Is the bandwidth of 5 kHz of the PbI2 photodiode consistent with its response time?

No. The text gives a rise time of 5.3 ms and a decay time of 4.9 ms, while the abstract speaks of microseconds and the $3 dB$ bandwidth is 5 kHz. The relation $f = 0.35/ t_{R}$ gives 66 Hz and 71 Hz for the times in milliseconds (computed), and 5 kHz needs 70 μs. A PbS imager had a 10% to 90% rise of 3.4 μs and a fall of 8.9 μs (103 kHz and 39 kHz, computed), so that microseconds are physically possible, and the extraction time of 100 ns for 100 nm and $1 0^{- 3} c m^{2} /Vs$ does not forbid them. The slow transient may be the trap emptying seen at long times, the slow tail of 396.7 μs that the imager showed when the signal was followed down to 0.04% of its value. Reference: Qiao et al., Efficient interface and bulk passivation of PbS quantum dot infrared photodetectors by PbI2 incorporation, RSC Adv. 7, 52947 (2017); Kim et al., Detailed Characterization of SWIR-sensitive Colloidal Quantum Dot Image Sensors, International Image Sensor Workshop (2021).

Ques: What does the activation energy of the dark current of the SWIR imager tell about the origin of the current?

The Arrhenius fit over the whole chip gave 0.41 eV, and the pixels spread from 0.23 eV to 0.43 eV, against 0.428 eV for half of the gap of 0.855 eV (1450 nm). A value near $E_{g} /2$ is the signature of generation through levels near mid-gap, not of diffusion from the neutral region, which would show $E_{g}$ , so the source attributes the current to traps. With $d ln J_{d} / d T = E_{a} / (k_{B} T^{2})$ the current changes by 205 between -20 °C and 80 °C and doubles every 12.9 K near 298 K (computed). Cooling by 26 K would lower the dark charge about four times, an extrapolation and not an experiment of the source, and the bias and temperature of $2.0 \times 1 0^{- 6} A/c m^{2}$ are not stated. Reference: Kim et al., Detailed Characterization of SWIR-sensitive Colloidal Quantum Dot Image Sensors, International Image Sensor Workshop (2021).

Ques: Is the SWIR imager limited by read noise or by the shot noise of the dark charge?

For a pixel of 5 μm ( $2.5 \times 1 0^{- 7} c m^{2}$ ) and $J_{d} = 2.0 \times 1 0^{- 6} A/c m^{2}$ the dark current is 0.5 pA, or $3.1 \times 1 0^{6}$ electrons per second (computed). At 50 frames per second, 20 ms, the pixel collects $6.2 \times 1 0^{4}$ electrons, 62% of the full well of $1.01 \times 1 0^{5}$ , with a shot noise of 250 electrons, ten times the read noise of 25 electrons. At 1 ms the dark charge is 3100 electrons and the shot noise 56. The imager is therefore dark-current-limited at video rates unless the dark current is lower or the pixel cooled. Two checks fail: $72.1 dB$ agrees with 25 and $1.01 \times 1 0^{5}$ , but $1.01 \times 1 0^{5}$ electrons at a conversion gain of 9.526 μV per electron is 0.96 V, above the swing of 0.7 V. Reference: Kim et al., Detailed Characterization of SWIR-sensitive Colloidal Quantum Dot Image Sensors, International Image Sensor Workshop (2021).

Ques: How thick must the dot film be, and what limits the EQE of 40%?

A film with $α = 1 0^{4} c m^{- 1}$ absorbs 26% in 300 nm and 39% in 500 nm, and with $1 0^{5} c m^{- 1}$ 95% and 99% (computed), so a few hundred nanometres suffice above the onset but not at the exciton peak. The collection needs a depleted width and a diffusion length of 100 nm to 200 nm, which is the reason why a fully depleted device is only 100 nm to 200 nm thick and why a thicker film loses carriers; a resonant cavity (see the Resonant-Cavity-Enhanced Photodetector page) can raise the absorption without adding thickness. The thickness of the imager of the 40% is not reported, so that its EQE cannot be split into $η_{ab s}$ and $η_{c}$ . Reference: Konstantatos and Sargent, Colloidal quantum dot photodetectors (2011); Kim et al., Detailed Characterization of SWIR-sensitive Colloidal Quantum Dot Image Sensors, International Image Sensor Workshop (2021).

Ques: Does the HgTe diode reach the background limit, and at which field of view?

The 300 K hemisphere at a cutoff of 5 μm gives a photon flux of $1.32 \times 1 0^{16} c m^{- 2} s^{- 1}$ and $D_{B L I P}^{*} = 1.04 \times 1 0^{11}$ for $η = 0.45$ at 5 μm (computed). A cold shield of F/1.3 multiplies it by 2.79, i.e. $2.9 \times 1 0^{11}$ , close to the reported $3 \times 1 0^{11}$ and to the F/1.3 used for the NETD of 14 mK, but the source does not state the f-number of the $D^{*}$ measurement. The second device, $4 \times 1 0^{11}$ at 4.5 μm, corresponds to F/2.1 (computed) and the 1.62 A/W gives $η = 0.446$ , matching the 45%. The statement of the background limit is therefore true for a field of view of about F/1.4 to F/2, not for the full hemisphere. Reference: Guyot-Sionnest et al., final technical report on HgTe colloidal quantum-dot photodiodes, DTIC AD1071078 (2018); Tian et al., Mercury chalcogenide colloidal quantum dots for infrared photodetection: from synthesis to device applications, Nanoscale (2023).

Ques: Why must the HgTe diode be cooled, and what does the temperature dependence say?

The 2018 diode with a plasmonic structure had $D^{*} = 4 \times 1 0^{11}$ at 85 K and $1 0^{10}$ at 220 K, a factor 40 (computed), and the background limit was reported only up to 140 K for mid-infrared photodiodes. The Johnson bound gives $R_{0} A \geq 286 Ω c m^{2}$ at 85 K, a lower bound because the measured noise also contains the background and the flicker noise, and the sources do not report the $R_{0} A$ of these diodes. The room-temperature operation is achieved only in the SWIR, where the review claims a better sensitivity-range balance than InGaAs without giving numbers, and a 2022 HgTe diode measured at 1.55 μm had $2.3 \times 1 0^{- 6} A/c m^{2}$ at -0.4 V with a rectification ratio of 2000. Reference: Tian et al., Mercury chalcogenide colloidal quantum dots for infrared photodetection: from synthesis to device applications, Nanoscale (2023); Guyot-Sionnest et al., final technical report on HgTe colloidal quantum-dot photodiodes, DTIC AD1071078 (2018).

Ques: Why is the gain of the PbS photoconductor so slow, and what do its time constants mean?

The photoconductor had a rise time of 160 ms and a fall time of 3 s at 1 μW and 1 V, fitted by time constants of 30 ms, 300 ms and 2800 ms, and the stated bandwidth of about 0.1 Hz agrees with $0.35/3 s = 0.117$ Hz (computed). Since $G f_{- 3 d B} \approx 1/ (2 π t_{t r})$ , a long trap lifetime buys gain at the cost of speed. With an assumed $1 0^{- 3} c m^{2} /Vs$ , 5 μm and 1 V, $t_{t r} = 250$ μs and the product would be 640 Hz (computed), whereas 30 A/W (EQE 28.6) at 0.1 Hz gives about 3 Hz. The mobility is therefore lower than assumed: for $η = 1$ , $μ = 2.4 \times 1 0^{- 4} c m^{2} /Vs$ for $τ = 30$ ms and $2.4 \times 1 0^{- 6}$ for 3 s (computed), and the two measurements were made under different conditions. Reference: De Iacovo et al., PbS Colloidal Quantum Dot Photodetectors operating in the near infrared, Sci. Rep. 6, 37913 (2016); Konstantatos and Sargent, Colloidal quantum dot photodetectors (2011); Colace et al., Fabrication and Characterization of Lead Sulphide Colloidal Quantum Dot Photodetectors for the Near Infrared, PHOTOPTICS 2019, 79.

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Colloidal Quantum-Dot Photodetector (CQD)