1. Theory

Definition: A quantum-dot solar cell uses semiconductor nanocrystals of a few nm as the absorber. The gap is set by the size of the dot through quantum confinement, so a single material can cover the infrared and the visible; about half of the atoms of a dot are at its surface, so passivation by ligands decides the quality (Wikipedia; Ganesan et al.).
Materials: PbS and PbSe dots dominate the literature, with CdSe in polymer cells, AgBiS $_{2}$ (above 9 % and above 27 mA/cm $^{2}$ ), Zn-Cu-In-Se dots (above 12 %) and perovskite dots of CsPbI $_{3}$ or FAPbI $_{3}$ (Wikipedia; Ganesan et al.; pv magazine; Chintapalli et al.). PbS dots span 0.6 to 1.7 eV in one section of Chintapalli et al. and 0.75 to 1.6 eV in another.
Architectures: The early Schottky cells are limited to about half the gap in voltage; the depleted heterojunction (ZnO/PbS) and, later, a stack ITO/ZnO/PbS-TBAI/PbS-EDT/Au are used, with a long oleic-acid ligand replaced by short ligands (mercaptopropionic acid, tetrabutylammonium iodide, ethanedithiol, lead halides, methylammonium iodide) (Ganesan et al.; Chintapalli et al.).
PbS progress (Table 1 of Chintapalli et al.): 2.94 % in 2010 (0.59 V, 8.93 mA/cm $^{2}$ , 55.97 %, labelled certified), 7.4 % in 2012, 8.55 % in 2014, 10.6 % in 2016, 12.01 % in 2018, 15.45 % in 2022 (0.66 V, 31.50 mA/cm $^{2}$ , 74.6 %, with a FAPbBr $_{3 - x}$ I $_{x}$ monolayer), 13.30 to 13.40 % in 2023 to 2025, a flexible cell of 11.04 % on PET (2023) and a scaled device of 12.6 cm $^{2}$ (2025). Compound Semiconductor reported a certified 7 % in 2012 (Toronto and KAUST).
Perovskite dots: pv magazine reports 18.30 % certified (18.37 % measured, 17.85 % steady state, 17.68 % average) and 15.60 % for a cell of 1 cm $^{2}$ , made on SnO $_{2}$ with a layer-by-layer deposition, a methyl benzoate rinse and spiro-OMeTAD; Chintapalli et al. give 18.1 % certified for FAPbI $_{3}$ -MAI dots; Ganesan et al. quote 13.23 % for a CsPbI $_{3}$ dot cell (NREL) in 2018.
Voltage: The voltage is about half the gap in nearly all devices (Ganesan et al.): 0.46 to 0.70 V for PbS (Chintapalli et al.).
Multiple exciton generation: One photon above about twice the gap can make two or more excitons (Ganesan et al.); the cases reported are PbSe (Los Alamos, 2004), PbS (Wyoming, 2010, at about three times the gap), silicon nanocrystals (2.4 times the gap) and an external quantum efficiency above 100 % in PbSe devices (Wikipedia; Ma et al.; Ganesan et al.).
Limits: Wikipedia gives about 33 % (33.7 % elsewhere) at 1.34 eV for one junction, 44 % for 1.64/0.94 eV, 48 % for three junctions, 66 % for hot carriers and 86 % for an infinite stack; Ganesan et al. give about 1.3 eV as the optimum.

2. Working Principle

Absorption and confinement: A photon above the gap makes an exciton in the dot; the smaller the dot the larger the gap (Wikipedia). About half of the atoms are at the surface, and trap-assisted recombination dominates at low excitation (Ganesan et al.).
Transport: Carriers hop between dots; shorter ligands reduce the spacing and raise the mobility, and about 1 cm $^{2}$ /Vs is needed to use carrier multiplication (Ganesan et al.). The diffusion length is about 230 nm at best, so a film of 500 nm is longer than the diffusion length and depends on the depletion width (computed ratio 2.17).
Separation: The pair is separated at the junction with the ZnO (background knowledge); the dissociation energy of a pair is about 10 meV (static permittivity) or 80 meV (optical permittivity), a factor of 15.3 in the Boltzmann factor (computed).
Voltage: The deficit of the PbS cells against an assumed gap of 1.3 eV is 0.60 to 0.75 V and the non-radiative loss 0.33 to 0.48 V (computed), against 0.31 V for the perovskite dots at 1.15 V and an assumed gap of 1.76 eV.
Current and fill factor: The 15.45 % cell has 31.5 mA/cm $^{2}$ (0.879 of the limit current of a 1.3 eV absorber) and a fill factor of 0.888 of the ideal value (computed).
Carrier multiplication: An ideal staircase would add 14.1 % to the current of a 1.3 eV cell and 39.9 % for a 0.94 eV cell; with one extra exciton above 2.7 times the gap the gain is 1.2 % and 11.2 % (computed).

3. Applications

Infrared light: Chintapalli et al. state that about 101.3 W/m $^{2}$ (more than 10 %) of the AM1.5G power lies beyond the silicon gap and is within reach of PbS; the power between 0.75 and 1.1 eV is 123.1 W/m $^{2}$ (computed).
Tandem partners: Chintapalli et al. list two-terminal CQD/perovskite tandems of 16.96 % (2021), four-terminal ones of 20.2 % (2019) and 15.93 % (2021), CQD/CQD tandems of 8.9 % and 6.8 % and a CQD/organic tandem of 9.12 %; Ganesan et al. name tandems with silicon or CdTe.
Flexible and large-area cells: A PbS cell on PET reached 11.04 % (2023) and a scaled device of 12.6 cm $^{2}$ 13.40 % (2025) (Chintapalli et al.); Wikipedia’s perovskite article gives 12.3 % for a flexible dot cell.
Commercial position: Wikipedia lists four companies and a market of USD 910.49 million in 2024, with USD 3174.28 million expected for 2033 and a rate of 15.4 % (14.9 % computed); the numbers are not sourced.
Next steps: Outdoor testing, mixed halides for stability and lower-toxicity dots are the items named in the sources; heavy-metal dots (PbSe, CdSe) are called cytotoxic by Wikipedia.

Carrier Multiplication, Transport and Dissociation

Name	Formula	Related Formulae	Variables/Constants
Threshold of multiple exciton generation	$E_{t h} = m E_{g}, m \geq 2$	$f_{P} (E_{t h}) = \frac{1}{P _{in}} \int_{E_{t h}}^{\infty} E Φ d E$	$E_{g} : g a p o f t h e d o t$ $m : t h r es h o l d r a t i o, G an es an e t a l . g i v e an o n se t ab o v e 2 E_{g}, M a e t a l . a t h r es h o l d o f 2.4 \pm 0.1 E_{g} f or s i l i co n nan ocr y s t a l s (2.6 e x c i t o n s p er p h o t o n a t 3.4 E_{g}) an d m or e t han 100 % ab sor b e d - p h o t o n e f f i c i e n cy ab o v e ab o u t 2.7 E_{g} f or P b S (E_{g} = 0.94 e V), W ik i p e d ia g i v es ab o u t 3 E_{g} f or P b S (W y o min g, 2010)$ $f_{P} : f r a c t i o n o f t h e A M 1.5 G p o w er ab o v e t h e t h r es h o l d, P_{in} = 1000.37 W / m^{2}; W ik i p e d ia an d G an es an e t a l . s a y t ha t im p a c t i o ni s a t i o n in b u l k se mi co n d u c t or s s t a r t s o n l y ab o v e ab o u t 3 e V, u n d er 1 % o f t h e so l a r s p ec t r u m$ $(co m p u t e d : f_{P} = 42.1 % ab o v e 1.88 e V (2 \times 0.94), 36.4 % ab o v e 2.0 e V, 14.8 % ab o v e 2.6 e V (2 \times 1.3), 9.2 % ab o v e 2.82 e V (3 \times 0.94), 6.1 % ab o v e 3.0 e V an d 0.10 % ab o v e 3.9 e V; t h e p h o t o n c u r r e n t ab o v e 3.0 e V i s 1.86 m A / c m^{2}, 2.7 % o f t h e 68.98 m A / c m^{2} ab o v e 0.3 e V)$
Current gain from multiple exciton generation	$J_{M E G} = q \sum_{n = 1}^{\infty} \int_{n E_{g}}^{\infty} Φ d E$	$J_{1} = q \int_{E_{g}}^{\infty} Φ d E + q \int_{m E_{g}}^{\infty} Φ d E$	$J_{M E G} : c u r r e n t o f an i d e a l s t ai r c a se in w hi c h e v er y p h o t o n ab o v e n E_{g} mak es n e x c i t o n s an d a l l a r e co l l ec t e d (an u pp er b o u n d, ba c k g r o u n d k n o w l e d g e)$ $J_{1} : c u r r e n t w h e n o n e e x t r a e x c i t o n i s ma d e ab o v e t h e t h r es h o l d m E_{g}$ $Φ : p h o t o n f l ux o f t h e A M 1.5 G s p ec t r u m, m e a s u r e d v a l u es a r e f a r b e l o w t h e s t ai r c a se : 2.6 e x c i t o n s p er p h o t o n a t 3.4 E_{g} (s i l i co n nan ocr y s t a l s, M a e t a l .), e x t er na l q u an t u m e f f i c i e n cy ab o v e 100 % in P b S e d e v i ces an d ab o v e 120 % in P b T e d e v i ces (G an es an e t a l .)$ $(co m p u t e d : E_{g} = 0.94 e V 51.46 m A / c m^{2} w i t h o u t an d 71.98 m A / c m^{2} w i t h t h e s t ai r c a se (+ 20.52, + 39.9 %), a s in g l e e x t r a e x c i t o n ab o v e 2.0, 2.4, 2.7 an d 3.0 E_{g} a dd s 17.46, 9.66, 5.74 an d 2.95 m A / c m^{2}; E_{g} = 1.3 e V 35.82 m A / c m^{2} an d + 5.07 (+ 14.1 %) f or t h e s t ai r c a se, + 5.04, + 1.27, + 0.42 an d + 0.03 m A / c m^{2}; E_{g} = 1.76 e V + 0.41 m A / c m^{2} (+ 2.0 %))$
Diffusion length and film thickness	$L_{D} = D τ, D = μ \frac{k _{B} T}{q}$	$d ≲ w_{d e p} + L_{D}$	$L_{D} : min or i t y - c a r r i er d i f f u s i o n l e n g t h, ab o u t 230 nm a t b es t (T M S - C l t r e a t m e n t w i t h p a r t ia l f u s i o n o f t h e d o t s)$ $D : d i f f u s i o n coe f f i c i e n t$ $μ : m o bi l i t y (ab o u t 1 c m^{2} / V s i s n ee d e d t o u se c a r r i er m u l t i pl i c a t i o n, G an es an e t a l .)$ $τ : l i f e t im e$ $d : f i l m t hi c k n ess (ab o v e 500 nm in t h e ce l l o f C r i s p e t a l .)$ $w_{d e p} : d e pl e t i o n w i d t h, t h e t hi c k n ess i s l imi t e d b y t h e d e pl e t i o n w i d t h pl u s t h e d i f f u s i o n l e n g t h (G an es an e t a l .)$ $k_{B} : B o l t z mann co n s t an t$ $(co m p u t e d : μ = 1 c m^{2} / V s g i v es D = 0.02569 c m^{2} / s an d L_{D} = 230 nm n ee d s τ = 20.6 n s; 500/230 = 2.17; f or τ = 20 n s, μ = 0.01, 0.1 an d 1 c m^{2} / V s g i v e L_{D} = 22.7, 71.7 an d 226.7 nm)$
Exciton dissociation probability	$P_{d i s} \propto e^{- E_{d i s} / k_{B} T}$	$E_{d i s} = \frac{q ^{2}}{4 π ε ε _{0} r}$	$E_{d i s} : e n er g y n ee d e d t o se p a r a t e an e l ec t r o n - h o l e p ai r in t h e d o t f i l m, G an es an e t a l . q u o t e ab o u t 10 m e V w i t h t h e s t a t i c p er mi tt i v i t y an d ab o u t 80 m e V w i t h t h e o pt i c a l p er mi tt i v i t y f or P b S e w i t h 1, 2 - e t han e d iamin e (t h e o pt i c a l v a l u e w a s co n f i r m e d e x p er im e n t a l l y; t h e e x t r a c t e d e x p o n e n t l a c k s t h e min u s s i g n)$ $r : p ai r d i s t an ce (t h e seco n d e x p r ess i o n i s ba c k g r o u n d k n o w l e d g e)$ $k_{B} : B o l t z mann co n s t an t$ $(co m p u t e d a t 298.15 K : e^{- 10/25.693} = 0.678 an d e^{- 80/25.693} = 0.0444, a r a t i o o f 15.3)$

Radiative Limit, Voltage and Efficiency Checks

Name	Formula	Related Formulae	Variables/Constants
Radiative limit at the gap of the dots	$η_{r a d} = \frac{V _{oc, r a d} J _{sc, r a d} F F _{0}}{P _{in}}$	$J_{sc, r a d} = q \int_{E_{g}}^{\infty} Φ d E$	$E_{g} : g a p o f t h e d o t s, G an es an e t a l . g i v e an o pt im u m o f ab o u t 1.3 e V an d m os t P b S ce l l s u se d o t s n e a r i t (t h e g a p s o f t h e ce l l s in T ab l e 1 o f C hin t a p a l l i e t a l . a r e n o t g i v e n), W ik i p e d ia g i v es 1.34 e V an d ab o u t 33 % (33.7 % in an o t h er p a ss a g e) an d 1.64/0.94 e V f or a tw o - j u n c t i o n ce l l (44 %) an d 1.83/1.16/0.71 e V f or t h r ee j u n c t i o n s (48 %), M e ma r i e t a l . u se 1.76 e V f or C s P b I_{3} d o t s an d g i v e an i d e a l g a p o f 1.73 e V, P_{in} = 1000.37 W / m^{2}, k_{B} T / q = 25.693 mV, e mi ss i o n in t o 2 π or, w i t h a mi r r or, π, s t e p ab sor pt an ce a s o n t h e e a r l i er p a g es$ $k_{B} : B o l t z mann co n s t an t$ $(co m p u t e d, π (2 π) : 0.94 e V 31.04 (30.16) %, V_{oc, r a d} 0.7112 (0.6934) V, J_{sc, r a d} 51.46 m A / c m^{2}; 1.0 e V 31.64 (30.82) %; 1.1 e V 33.00 (32.24) %; 1.3 e V 33.19 (32.57) %, 1.0456 (1.0278) V, 35.82 m A / c m^{2}; 1.335 e V 33.77 (33.16) %; 1.73 e V 28.61 (28.23) %; 1.76 e V 27.98 (27.62) %, 1.4763 (1.4585) V, 20.76 m A / c m^{2}; tw o - j u n c t i o n 1.64/0.94 e V 44.65 % an d t h r ee - j u n c t i o n 1.83/1.16/0.71 e V 47.22 % (2 π); t h e 42.3 % r ecor d a t 1.89/1.42/0.94 e V i s 0.910 o f i t s l imi t o f 46.47 %)$
Open-circuit voltage against the gap	$V_{oc} \approx \frac{E _{g}}{2 q}$	$Δ V_{n r} = V_{oc, r a d} - V_{oc} = \frac{k _{B} T}{q} ln \frac{1}{E Q E _{E L}}$	$V_{oc} : o p e n - c i r c u i t v o l t a g e, t h e p r a c t i c a l l imi t i s ab o u t ha l f t h e g a p in n e a r l y a l l d e v i ces an d S c h o tt k y ce l l s c ann o t e x cee d i t (G an es an e t a l .)$ $Δ V_{n r} : n o n - r a d ia t i v e l oss$ $E Q E_{E L} : e l ec t r o l u min esce n ce e f f i c i e n cy, t h e P b S ce l l s a r e t h e e n t r i es o f T ab l e 1 o f C hin t a p a l l i e t a l . w i t h an a ss u m e d g a p o f 1.3 e V (V_{oc, r a d} = 1.0278 V f or 2 π), t h e p er o v s k i t e d o t s ha v e 1.15 V an d ab o v e (W ik i p e d ia, p er o v s k i t e a r t i c l e) w i t h an a ss u m e d g a p o f 1.76 e V$ $k_{B} : B o l t z mann co n s t an t$ $(co m p u t e d : V_{oc} / E_{g} = 0.454 (0.59 V), 0.423 (0.55 V), 0.469 (0.61 V), 0.500 (0.65 V), 0.508 (0.66 V), 0.515 (0.67 V) an d 0.538 (0.70 V); t h e d e f i c i t E_{g} / q - V_{oc} i s 0.71 t o 0.60 V; f or 0.70 V Δ V_{n r} = 0.328 V an d E Q E_{E L} = 2.9 \times 1 0^{- 6}, f or 0.55 V 0.478 V an d 8.4 \times 1 0^{- 9}; t h e I R - o n l y ce l l (0.46 V) ha s 0.354 an d 0.568 V; f or 1.15 V a t 1.76 e V t h e r a t i o i s 0.653, t h e d e f i c i t 0.61 V, Δ V_{n r} = 0.309 V an d E Q E_{E L} = 6.1 \times 1 0^{- 6})$
Ideal fill factor	$F F_{0} = \frac{v - l n ( v + 0.72 )}{v + 1}$	$v = \frac{V _{oc}}{k _{B} T / q}$	$F F_{0} : f i l l f a c t or w i t h o u t r es i s t i v e l osses (ba c k g r o u n d k n o w l e d g e, a s o n t h e e a r l i er p a g es), o n e j u n c t i o n, t h e ce l l s a r e t h e e n t r i es o f T ab l e 1 o f C hin t a p a l l i e t a l ., t h e p er o v s k i t e d o t s a r e t h ose o f W ik i p e d ia (V_{oc} ab o v e 1.15 V, F F 80 t o 85 %)$ $k_{B} : B o l t z mann co n s t an t$ $(co m p u t e d : F F_{0} = 0.8262 f or 0.59 V an d 55.97 % i s 0.677 o f i t; 0.8304 f or 0.61 V an d 71.0 % i s 0.855; 0.8399 f or 0.66 V an d 74.6 % i s 0.888; 0.8467 f or 0.70 V an d 67.35 % i s 0.795; 0.8433 f or 0.68 V an d 70.89 % i s 0.841; f or 1.15 V F F_{0} = 0.8947 an d 80 t o 85 % i s 0.894 t o 0.950)$
Efficiency from the reported parameters	$η = \frac{V _{oc} J _{sc} F F}{P _{in}}, P_{in} = 100 mW/c m^{2}$	$J_{sc} = \frac{η P _{in}}{V _{oc} F F}$	$η : e f f i c i e n cy, V_{oc} in mV, J_{sc} in m A / c m^{2}, F F a s a f r a c t i o n (e f f i c i e n cy in p er ce n t = V_{oc} [mV] \cdot J_{sc} [m A / c m^{2}] \cdot F F /1000), t h e P b S e n t r i es a r e f r o m T ab l e 1 o f C hin t a p a l l i e t a l . (o n l y t h e 2010 r o w i s l ab e l l e d cer t i f i e d), t h e p er o v s k i t e d o t ce l l o f p v ma g a z in e (18.30 % cer t i f i e d, 18.37 % m e a s u r e d) g i v es n o V_{oc}, J_{sc} or F F, so t h e v a l u es o f W ik i p e d ia a r e u se d f or t h e c h ec k$ $(co m p u t e d : 2010590, 8.93, 55.97 % g i v e 2.95 % (2.94); 2014 8.49 % (8.55); 2016 10.52 % (10.60); 2022 15.51 % (15.45); 2023 13.30 % (13.30); 2024 13.27 % (13.24); 2025 13.32 % (13.40); t h e 2019 I R - o n l y r o w (0.46 V, 4.40, 58.1 %) g i v es 1.18 % a g ain s t 6.00 % p r in t e d; 1.15 V, 14 t o 15 m A / c m^{2} an d 80 t o 85 % g i v e 12.88 t o 14.66 %; 18.30 % n ee d s J_{sc} = 19.9 m A / c m^{2} (F F 0.80) or 18.7 m A / c m^{2} (F F 0.85) a t 1.15 V, w hi c h a r e 0.96 an d 0.90 o f t h e l imi t c u r r e n t o f 20.76 m A / c m^{2} a t 1.76 e V)$

Area Scaling and Stability

Name	Formula	Related Formulae	Variables/Constants
Area and measurement scaling	$\frac{η _{A}}{η _{s ma l l}}$	$\frac{η _{s t e a d y}}{η _{cer t}}$	$η_{A} : e f f i c i e n cy o f t h e l a r g er ce l l$ $η_{s ma l l} : e f f i c i e n cy o f t h e s ma l l cer t i f i e d ce l l, p v ma g a z in e g i v es 15.60 % f or a ce l l o f 1 c m^{2}, 18.30 % cer t i f i e d, 18.37 % m e a s u r e d, 17.85 % s t e a d y s t a t e an d 17.68 % a v er a g e, an d n o a r e a f or t h e s ma l l ce l l; C hin t a p a l l i e t a l . l i s t a P b S m o d u l e o f 12.6 c m^{2} (13.40 %, ambi g u o u s)$ $(co m p u t e d : 15.60/18.30 = 0.852 an d 15.60/18.37 = 0.849; 17.85/18.30 = 0.975; 17.68/18.37 = 0.962; 18.30/18.37 = 0.996; 18.1/18.3 = 0.989; t h e P b S r ecor d 15.45 % i s 0.844 o f 18.30 %)$
Retention under storage	$R (t) = \frac{η ( t )}{η ( 0 )}$	$t_{25} = 25 years = 219000 h$	$R : r e t ain e d f r a c t i o n, W ik i p e d ia s a y s t ha t t h e Z n O / P b S ce l l o f M I T (8.55 % cer t i f i e d, 9.2 % in t h e l ab or a t or y) w a s s t ab l e f or m or e t han 150 d a y s in ai r w i t h o u t e n c a p s u l a t i o n an d e x p ec t s co mm er c ia l m o d u l es t o k ee p 90 % o f t h e ini t ia l e f f i c i e n cy (n o m e a s u r e d r e t e n t i o n i s g i v e n f or t h e q u an t u m - d o t ce l l s), C hin t a p a l l i e t a l . g i v e n o T_{80}; t h e T or o n t o n - t y p e ce l l s c a l l e d ai r - s t ab l e w er e ma d e in an o x y g e n - f r ee e n v i r o nm e n t (W ik i p e d ia)$ $(co m p u t e d : 150 d a y s a r e 3600 h, 0.0164 o f 25 y e a r s; t h e p er o v s k i t e ce l l o f p a g e 89 w a s t es t e d f or 4500 h, t h e or g ani c ce l l o f p a g e 91 f or 1200 h an d t h e d y e ce l l o f p a g e 92 f or 1000 h)$

Important Questions

Ques: What is the quantum-dot record: 15.45, 18.1, 18.30 or 18.37 %?

pv magazine reports 18.30 % certified and 18.37 % measured for a perovskite-dot cell (October 2025), and Chintapalli et al. give 18.1 % certified for FAPbI $_{3}$ -MAI dots. Their PbS table has a highest value of 15.45 % (2022), and only its 2010 row is labelled certified, although the text says that dot cells reach ‘over 18 %’. Ganesan et al. quote 13.23 % for CsPbI $_{3}$ dots in 2018, and Wikipedia’s perovskite article gives 18.30 % as a 2024 value. The values agree if the 18 % belongs to perovskite dots and 15.45 % to PbS (computed ratio 0.844). The 18.30 and 18.37 % are one cell, with a ratio of 0.996 (computed). The date of 2024 or 2025 is not settled. For PbS 15.45 % is uncertified, so 13.4 % is the safer PbS value (my reading). Reference: pv magazine, ‘Perovskite quantum dot solar cell achieves record-breaking efficiency of 18.3%’ (8 October 2025); Chintapalli, Li and Thon, ‘PbS colloidal quantum dot photovoltaics: progress towards infrared and flexible applications’, Chem. Commun. 61, 14073-14086 (2025); Ganesan, Houtepen and Crisp, ‘Quantum Dot Solar Cells: Small Beginnings Have Large Impacts’, Applied Sciences 8(10), 1867 (2018); Wikipedia, ‘Perovskite solar cell’ (quantum-dot passage).

Ques: Do the parameters of the 18.3 % cell add up: 14 to 15 or about 19 mA/cm2?

Wikipedia’s perovskite article gives a voltage above 1.15 V, a current of 14 to 15 $mA/c m^{2}$ and a fill factor of 80 to 85 % for the perovskite-dot cell. These give 12.88 to 14.66 % and cannot give 18.30 % (computed). At 1.15 V, 18.30 % needs 19.9 $mA/c m^{2}$ for a fill factor of 0.80 or 18.7 $mA/c m^{2}$ for 0.85, which are 0.96 and 0.90 of the limit current of 20.76 $mA/c m^{2}$ at 1.76 eV (computed, gap assumed from Memari et al.). The pv magazine article gives no Voc, Jsc or fill factor and states that the 1 cm $^{2}$ cell has 15.60 %, 0.852 of the certified value (computed). The current in Wikipedia is therefore probably a value for an older cell, or a mistake (my reading). Memari et al. give 14.61 % (abstract) and 14.85 % for a simulated baseline. Reference: Wikipedia, ‘Perovskite solar cell’ (quantum-dot passage); pv magazine, ‘Perovskite quantum dot solar cell achieves record-breaking efficiency of 18.3%’ (8 October 2025); Memari et al., ‘Comprehensive guidance for optimizing the colloidal quantum dot (CQD) Perovskite solar cells: experiment and simulation’, Scientific Reports 13, 16675 (2023).

Ques: Is the PbS cell record 13.4 or 15.45 %, and does the table add up?

Chintapalli et al. list 15.45 % (2022, 0.66 V, 31.50 $mA/c m^{2}$ , 74.6 %, with a perovskite monolayer) as the highest PbS cell, and 13.2 to 13.4 % for 2023 to 2025. The product of the 2022 row is 15.51 % and that of the 2025 row 13.32 % against 13.40 % (computed, rounding). The 2019 infrared-only row gives 1.18 % against 6.00 % printed, probably a different measurement basis. The text says that the TBAI and MAI ligands gave more than 10 % in 2015, and the table has 10.60 % in 2016. Ganesan et al. give 11.6 % for PbS in 2018, and Compound Semiconductor 7 % certified in 2012. Because only 2010 is labelled certified in the table, 13.4 % is the safer record and 15.45 % the best reported (my reading). Reference: Chintapalli, Li and Thon, ‘PbS colloidal quantum dot photovoltaics: progress towards infrared and flexible applications’, Chem. Commun. 61, 14073-14086 (2025); Ganesan, Houtepen and Crisp, ‘Quantum Dot Solar Cells: Small Beginnings Have Large Impacts’, Applied Sciences 8(10), 1867 (2018); Compound Semiconductor, ‘Record efficiency quantum dot PbS solar cells’ (21 August 2012).

Ques: Is the voltage limited to half the gap: 0.65 or 0.70 V?

Ganesan et al. say that the practical voltage is about half the gap in nearly all devices and that Schottky cells cannot exceed it. Chintapalli et al. list 0.46 to 0.70 V. With an assumed gap of 1.3 eV the ratio is 0.423 to 0.538, so the 0.70 V cell is above the half-gap line (computed). The deficit is 0.60 to 0.75 V and the non-radiative loss 0.33 to 0.48 V, which is an electroluminescence efficiency of $2.9 \times 1 0^{- 6}$ to $8.4 \times 1 0^{- 9}$ (computed). The perovskite dots with 1.15 V at 1.76 eV have a ratio of 0.653 and a loss of 0.31 V (computed, gap assumed). The gap of the PbS cells is not given in the table, so the ratios depend on the assumption. The half-gap rule is a rough limit for PbS and is broken by perovskite dots (my reading). Reference: Ganesan, Houtepen and Crisp, ‘Quantum Dot Solar Cells: Small Beginnings Have Large Impacts’, Applied Sciences 8(10), 1867 (2018); Chintapalli, Li and Thon, ‘PbS colloidal quantum dot photovoltaics: progress towards infrared and flexible applications’, Chem. Commun. 61, 14073-14086 (2025); Wikipedia, ‘Perovskite solar cell’ (quantum-dot passage).

Ques: What gap should the dots have: 1.3, 1.34, 1.73 or 1.76 eV?

Ganesan et al. give an optimum of about 1.3 eV, and most cells use dots near it. Wikipedia gives 1.34 eV with a limit of about 33 % (33.7 % elsewhere). Memari et al. use 1.76 eV for CsPbI $_{3}$ dots in their model and give an ideal gap of 1.73 eV. Chintapalli et al. give PbS gaps of 0.6 to 1.7 eV in one section and 0.75 to 1.6 eV in another. My model has its maximum at 1.335 eV with 33.77 % for a rear mirror and 33.16 % for emission from both faces, which agrees with 33.7 % and 33 % (computed). At 1.73 and 1.76 eV the limits are 28.61 and 27.98 % (mirror, computed). The 1.73 eV comes from a simulation paper and not from a measurement. Reference: Ganesan, Houtepen and Crisp, ‘Quantum Dot Solar Cells: Small Beginnings Have Large Impacts’, Applied Sciences 8(10), 1867 (2018); Wikipedia, ‘Quantum dot solar cell’; Memari et al., ‘Comprehensive guidance for optimizing the colloidal quantum dot (CQD) Perovskite solar cells: experiment and simulation’, Scientific Reports 13, 16675 (2023); Chintapalli, Li and Thon, ‘PbS colloidal quantum dot photovoltaics: progress towards infrared and flexible applications’, Chem. Commun. 61, 14073-14086 (2025); Solar Cell Fundamentals page of this vault.

Ques: When does carrier multiplication start: 2, 2.4, 2.7 or 3 times the gap?

Ganesan et al. say that the onset needs more than twice the gap and that yields above 100 % were measured. Ma et al. report 2.4 ± 0.1 times for silicon nanocrystals with 2.6 excitons at 3.4 times, and an absorbed-photon efficiency above 100 % over about 2.7 times for PbS of 0.94 eV. Wikipedia gives about 3 times for PbS (Wyoming, 2010). The thresholds belong to different materials and the energy conservation limit is 2 times (background knowledge). For a gap of 0.94 eV an ideal staircase would add 39.9 % to the current, a single extra exciton above 2.7 times 11.2 % and above 3 times 5.7 % (computed). For 1.3 eV the gains are 14.1 %, 1.2 % and 0.1 % (computed). The sources give no gain measured in a full cell, and 2.4 to 3 times is the likely range (my reading). Reference: Ganesan, Houtepen and Crisp, ‘Quantum Dot Solar Cells: Small Beginnings Have Large Impacts’, Applied Sciences 8(10), 1867 (2018); Ma, Zhang and Meng, ‘Atomic Scale Investigation of Dye Sensitized Solar Cells: Interface Structure and Dynamics’ (arXiv 1406.3111); Wikipedia, ‘Quantum dot solar cell’.

Ques: Is the sunlight above 3 eV under 1 % of the spectrum?

Wikipedia and Ganesan et al. say that impact ionisation in bulk semiconductors starts only above about 3 eV, which is under 1 % of the solar spectrum. My integration of the AM1.5G spectrum (1000.37 $W/ m^{2}$ ) gives 6.1 % of the power above 3.0 eV (413 nm) and 2.7 % of the photon current, 1.86 of 68.98 $mA/c m^{2}$ above 0.3 eV (computed). Only 0.10 % of the power lies above 3.9 eV. The under 1 % statement therefore fits about 3.9 eV and not 3 eV, and 6.1 % is six times larger than 1 % (my reading). For a dot of 1.3 eV the threshold of 2.6 eV has 14.8 % of the power above it (computed). Reference: Wikipedia, ‘Quantum dot solar cell’; Ganesan, Houtepen and Crisp, ‘Quantum Dot Solar Cells: Small Beginnings Have Large Impacts’, Applied Sciences 8(10), 1867 (2018).

Ques: Is the multi-exciton limit 44, 48, 65 or 66 %?

Wikipedia gives 44 % for a two-junction cell with 1.64 and 0.94 eV, 48 % for three junctions with 1.83, 1.16 and 0.71 eV, 66 % for hot-carrier cells, 65 % for the multiple-exciton cell of NREL (2005) and 86 % for an infinite stack, and notes the 42.3 % record at 1.89/1.42/0.94 eV. Ma et al. cite up to 66 % for the Ross-Nozik hot-carrier converter. My model gives 44.65 % and 47.22 % for the two sets of gaps and 46.47 % for the record gaps, so the record is 0.910 of its limit (computed, 2 $π$ emission, no concentration). The 65 and 66 % limits are for different concepts and are almost the same by chance; the 86 % needs the maximum concentration (background knowledge). The 44 and 48 % values agree with my values at one sun. Reference: Wikipedia, ‘Quantum dot solar cell’; Ma, Zhang and Meng, ‘Atomic Scale Investigation of Dye Sensitized Solar Cells: Interface Structure and Dynamics’ (arXiv 1406.3111); III-V Multi-Junction Solar Cell page of this vault.

Ques: How thick can the dot film be: 230 or 500 nm?

Ganesan et al. give a record minority-carrier diffusion length of about 230 nm (TMS-Cl treatment with partial fusion of the dots) and an optimized film thickness above 500 nm, almost twice that of other record devices, and say that the thickness is limited to the depletion width plus the diffusion length. A mobility of about 1 $c m^{2} /V s$ is the design rule for using carrier multiplication. For 1 $c m^{2} /V s$ , a diffusion length of 230 nm needs a lifetime of 20.6 ns, and for 0.01 $c m^{2} /V s$ the length is 22.7 nm at 20 ns (computed). The ratio 500/230 is 2.17 (computed), which means that the field of the depletion region must collect much of the film. Memari et al. simulate 100 to 350 nm. Reference: Ganesan, Houtepen and Crisp, ‘Quantum Dot Solar Cells: Small Beginnings Have Large Impacts’, Applied Sciences 8(10), 1867 (2018); Memari et al., ‘Comprehensive guidance for optimizing the colloidal quantum dot (CQD) Perovskite solar cells: experiment and simulation’, Scientific Reports 13, 16675 (2023).

Ques: How stable are quantum-dot cells: 150 days, 90 % or no data?

Wikipedia says that the ZnO/PbS cell of MIT (8.55 % certified, 9.2 % in the laboratory) was stable for more than 150 days in air without encapsulation, and that commercial modules are expected to keep 90 % of the initial efficiency, but it gives no measured retention for dot cells. The Toronto n-type cells called air-stable were fabricated in an oxygen-free environment. Chintapalli et al. say that mixed halides improve stability and call for outdoor tests, with no T $_{80}$ . The pv magazine article gives no stability. A period of 150 days is 3600 h and 0.0164 of 25 years (computed), against 4500 h for the perovskite cell, 1200 h for the organic cell and 1000 h for the dye cell on the earlier pages. Stability data for the record dot cells are missing (my reading). Pb and Cd dots add a toxicity concern (Wikipedia). Reference: Wikipedia, ‘Quantum dot solar cell’; Chintapalli, Li and Thon, ‘PbS colloidal quantum dot photovoltaics: progress towards infrared and flexible applications’, Chem. Commun. 61, 14073-14086 (2025); pv magazine, ‘Perovskite quantum dot solar cell achieves record-breaking efficiency of 18.3%’ (8 October 2025); Perovskite Solar Cell page of this vault.

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