1. Theory

Definition: A halide perovskite solar cell uses an ABX $_{3}$ absorber, where A is methylammonium (MA), formamidinium (FA) or caesium, B is lead or tin and X is a halide (Wikipedia). The gap is tunable: 1.55 to 2.3 eV for MAPbX $_{3}$ , 1.48 to 2.2 eV for FAPbX $_{3}$ , about 1.7 eV for CsPbI $_{3 - x}$ Br $_{x}$ (over 21 %), and 1.24 to 1.41 eV for mixed (FAPbI $_{3}$ ) $_{1 - x}$ (CsSnI $_{3}$ ) $_{x}$ . The Shockley-Queisser optimum of 1.34 eV gives 33.7 %, and 1.55 eV about 31 % (Wikipedia).
Optoelectronic properties: The absorption coefficient is about 10 $^{5}$ cm $^{- 1}$ and the Urbach energy of MAPbI $_{3}$ about 15 meV (thesis). Bulk electron mobilities are 2 to 10 cm $^{2}$ /(V s) and diffusion lengths exceed 1 µm (Wikipedia), while the thesis gives 1 to 100 cm $^{2}$ /(V s) and lifetimes of 0.1 to 1 µs. Defect densities are 10 $^{9}$ to 10 $^{10}$ cm $^{- 3}$ in solution-grown crystals and 10 $^{15}$ to 10 $^{16}$ cm $^{- 3}$ in polycrystalline films; the optical permittivity of MAPbI $_{3}$ is about 6.5 and the static one about 30 (thesis).
Device structure: The stack is n-i-p or p-i-n, with or without a mesoporous scaffold; electron layers are TiO $_{2}$ , SnO $_{2}$ or ZnO, hole layers NiO $_{x}$ , CuSCN or spiro-OMeTAD, and the back contact is evaporated metal, screen-printed silver or carbon (Wikipedia). Films are made by spin coating, slot-die, blade, spray, inkjet and screen printing, or by evaporation; a roll-to-roll process reached 15.5 % for small cells and 11.0 % for serially connected modules in 2024 (Wikipedia).
Records (efficiency tables, version 64): Green et al. list a cell of 25.2 ± 0.8 % (Northwestern, 1.0347 cm $^{2}$ , 1.162 V, 26.39 mA/cm $^{2}$ , 82.0 %, Newport 2023), a thin-film cell of 26.7 ± 0.6 % (USTC, 0.0519 cm $^{2}$ , 1.193 V, 26.49 mA/cm $^{2}$ , 84.5 %, NPVM May 2024), a minimodule of 22.6 ± 0.5 % (Singfilm, 8 cells, 20.25 cm $^{2}$ , 1.169 V, 25.00 mA/cm $^{2}$ , 77.4 %), a module of 19.2 ± 0.4 % (SolaEon, 1027 cm $^{2}$ , 59.4 V, 0.4307 A, 77.1 %, NREL December 2023) and a large module of 15.0 ± 0.5 % (Microquanta, 7906 cm $^{2}$ , FhG-ISE January 2024). The tables mark these as initial performance or state that stability was not investigated.
Later claims: Fluxim lists 26.95 % (Soochow University and UNSW, 0.0583 cm $^{2}$ , 2025, NREL) as the record cell, and SolaEon reported 27.87 % (0.076 cm $^{2}$ , fill factor 87.61 %, NPVM, January 2026) as a laboratory-scale record without stability data. SolaEon also reported modules of 20.7 % over 0.72 m $^{2}$ (149 W) and 21.88 % over the illuminated 0.64 m $^{2}$ (140 W) in June 2025.
History: Wikipedia gives 3.8 % in 2009 and 27 % in 2025 for single-junction cells.
Stability protocols: ISOS defines dark (D), bias (V), thermal cycling (T), light (L), outdoor (O), light cycling (LC) and combined (LT) tests at levels 1 to 3, with 65 or 85 C for the second level and 85 % relative humidity for damp heat (ISOS consensus; Fluxim). T $_{80}$ of 1000 h is the usual benchmark (Fluxim).
Lead: Wikipedia quotes a lethal dose below 5 mg/kg body weight, leakage reductions of 84 % (resin coating), 96.1 % (sequestration coating) and 98 % (resin in carbon paste), and a 375-fold reduction with a self-healing epoxy encapsulation.

2. Working Principle

Absorption and collection: A film of 0.3 to 0.5 µm absorbs most of the light (95 % at 300 nm and 99 % at 460 nm for $α$ = 10 $^{5}$ cm $^{- 1}$ , computed), and the carriers diffuse several micrometres (0.5 to 16 µm for the stated mobilities and lifetimes, computed) to the selective layers, so the film is thinner than the diffusion length and the collection is efficient.
Defect tolerance: The valence band maximum is antibonding, defect levels are shallow and the deformation potential is low, so defects have a small effect on the optoelectronic behaviour, and the thesis adds that room-temperature self-healing may keep the densities low.
Voltage: The 26.7 % cell has 1.193 V; for a gap of 1.50 to 1.55 eV (assumed) the deficit is 0.307 to 0.357 V and the cell has 0.93 to 0.97 of the radiative voltage with a mirror, an external radiative efficiency of 0.03 to 0.21 (computed). The GaAs record has a deficit of 0.293 V (page 86).
Fill factor and current: The fill factor is 0.941 of the ideal value and the current 0.91 to 0.97 of the limit (computed), so the voltage and the fill factor leave about 0.84 of the radiative efficiency (computed).
Ions and hysteresis: Mobile ions (migration energies 0.1 to 0.9 eV, halides about five times more than MA or Pb) make the current-voltage curve depend on the scan speed, and the ion density can grow by two orders of magnitude in aged devices (Zhu et al.; Fluxim). Tables therefore use stabilised measurements; the hysteresis index of the good cells read here is below 1 % (computed).
Degradation: Heat decomposes the organic cations (MAPbX $_{3}$ below 100 C, FAPbI $_{3}$ stable for 60 minutes at 150 C, CsPbI $_{3}$ to about 390 C), light and halide segregation reduce the voltage by about 10 % in the first hour above 20 % bromine, reverse bias shunts the cell, and moisture speeds the change of the CsPbI $_{3}$ $α$ phase to the $δ$ phase (Wikipedia; Zhu et al.).
Operation: A DMPESI-treated FAPbI $_{3}$ cell kept more than 99 % of its efficiency over 4500 h of tracking at 1 sun in nitrogen, lost less than 5 % in 100 thermal cycles and 1000 h of damp heat (Nature Energy 2023).

3. Applications

Single-junction modules: SolaEon, Microquanta and Singfilm modules of 15 to 22 % (Green et al.; SolaEon), made by solution and printing methods such as slot-die, blade and screen printing (Wikipedia).
Tandem top cells: A gap of 1.6 to 1.8 eV suits a silicon bottom cell (Wikipedia), and a low-gap tin-lead absorber of 1.24 to 1.41 eV can serve as a bottom cell of an all-perovskite stack (my reading); the next page treats the perovskite-silicon tandem.
Flexible and roll-to-roll cells: The roll-to-roll process gave 15.5 % for small cells and 11.0 % for modules (Wikipedia).
Lead management: Coatings and encapsulation reduce the lead leakage by 84 to 98 % or 375-fold, and recycling of devices returned 21.9 ± 1.1 % average against 22.1 ± 0.9 % for fresh ones (Wikipedia).

Absorption, Transport and Limit

Name	Formula	Related Formulae	Variables/Constants
Absorptance and film thickness	$a = 1 - e^{- α d}$	$d_{f} = \frac{- l n ( 1 - f )}{α}, a_{mi r r or} = 1 - e^{- 2 α d}$	$a : ab sor pt an ce o f o n e p a ss$ $α : ab sor pt i o n coe f f i c i e n t$ $d : f i l m t hi c k n ess$ $f : t a r g e t ab sor b e d f r a c t i o n$ $a_{mi r r or} : ab sor pt an ce w i t h a p er f ec t r e a r mi r r or (a ss u m e d), t h e t h es i s r e a d h er e g i v es α \approx 1 0^{5} c m^{- 1} an d s a y s t ha t ab o u t 300 nm ab sor b 99 % o f u n co n ce n t r a t e d s u n l i g h t, W ik i p e d ia s a y s t ha t a f i l m o f ab o u t 500 nm ab sor b s t h e w h o l e v i s ib l e s p ec t r u m (n o v a l u e o f α)$ $(co m p u t e d w i t h α = 1 0^{5} c m^{- 1} (a s in g l e v a l u e, a ss u m e d f or t h e w h o l e s p ec t r u m) : 230 nm ab sor b 90 %, 300 nm 95.0 %, 460 nm 99 %, 500 nm 99.3 %; 300 nm w i t h a mi r r or 99.75 %)$
Urbach edge	$α (E) = α_{0} exp (\frac{E - E _{g}}{E _{U}}), E < E_{g}$	$E_{U} = (\frac{d l n α}{d E})^{- 1}$	$α_{0} : v a l u e a t t h e g a p$ $E_{U} : U r ba c h e n er g y, t h e t h es i s g i v es ab o u t 15 m e V f or M A P b I_{3}, 19 m e V f or M A P b B r_{3} an d C s P b B r_{3} cr y s t a l s, 36 m e V f or a s p in - co a t e d C s P b B r_{3} f i l m, an d f or co m p a r i so n 11 m e V f or s i l i co n, 8 m e V f or G a A s an d 25 m e V f or C I GS (t h e G a A s p a g e u ses 6.7 m e V f r o m M i l l er e t a l .)$ $(co m p u t e d : t h e ab sor pt i o n f a l l s t o 0.264 o f i t s v a l u e a t t h e g a p 20 m e V b e l o w i t an d t o 1.3 \times 1 0^{- 3} a t 100 m e V b e l o w i t f or 15 m e V, a g ain s t 0.082 an d 4 \times 1 0^{- 6} f or 8 m e V an d 0.449 an d 0.018 f or 25 m e V)$
Diffusion length	$L = D τ, D = μ \frac{k _{B} T}{q}$	$τ^{- 1} = τ_{r a d}^{- 1} + τ_{t r a p}^{- 1} + τ_{A ug er}^{- 1}$	$L : d i f f u s i o n l e n g t h$ $D : d i f f u s i o n coe f f i c i e n t$ $μ : m o bi l i t y$ $τ : l i f e t im e, t h e t h es i s g i v es μ \approx 1 t o 100 c m^{2} / (V s) an d τ \approx 0.1 t o 1 μ s; W ik i p e d ia g i v es 2 t o 10 c m^{2} / (V s) f or t h e e l ec t r o n s o f b u l k f i l m s an d a d i f f u s i o n l e n g t h ab o v e 1 μ m; Z h u e t a l . q u o t e 700 n s (a l l - in or g ani c) an d 2900 n s (h y b r i d)$ $k_{B} : B o l t z mann co n s t an t$ $(co m p u t e d w i t h k_{B} T / q = 25.693 mV : D = 0.0257 c m^{2} / s f or 1 c m^{2} / (V s) an d 0.257 f or 10; μ = 1, τ = 0.1 μ s g i v es L = 0.51 μ m; μ = 10, τ = 1 μ s g i v es 5.1 μ m; μ = 100, τ = 1 μ s g i v es 16 μ m; μ = 10 w i t h 13 n s (t h e q u an t u m - d o t f i l m o f W ik i p e d ia) g i v es 0.58 μ m an d w i t h 700 n s 4.2 μ m)$
Exciton binding energy	$E_{b} = 13.6 eV \frac{μ ^{*}}{m _{0} ε _{r}^{2}}$	$μ^{} = \frac{m _{e}^{} m _{h}^{}}{m _{e}^{} + m _{h}^{*}}$	$E_{b} : bin d in g e n er g y o f a W anni er e x c i t o n$ $μ^{} : r e d u ce d ma ss$ $ε_{r} : r e l a t i v e p er mi tt i v i t y, t h e t h es i s g i v es ab o u t 30 m e V f or C s P b B r_{3}, ab o u t 350 m e V f or C s_{4} P b B r_{6}, a s t a t i c p er mi tt i v i t y o f ab o u t 30 an d o pt i c a l v a l u es o f ab o u t 4 (C s P b B r_{3}), 4.5 (M A P b B r_{3}) an d 6.5 (M A P b I_{3}); W ik i p e d ia s a y s o n l y t ha t t h e e n er g y i s s ma l l; μ^{} = 0.104 m_{0} f or M A P b I_{3} i s a ss u m e d (ba c k g r o u n d k n o w l e d g e)$ $(co m p u t e d : 33 m e V f or ε_{r} = 6.5 an d 1.6 m e V f or ε_{r} = 30)$
Radiative limit at perovskite gaps	$V_{oc, S Q} = \frac{k _{B} T}{q} ln (\frac{J _{sc}}{J _{0}} + 1)$	$J_{0} = \frac{2 Ω q}{c ^{2} h ^{3}} \int_{E_{g}}^{\infty} \frac{E ^{2} d E}{e ^{E / k_{B} T} - 1}$	$Ω : so l i d an g l e o f e mi ss i o n (2 π f or b o t h f a ces, π w i t h a r e a r mi r r or), t h e m e t h o d i s t h e o n e o f t h e S o l a r C e l l F u n d am e n t a l s p a g e (A M 1.5 G, 1000.37 W / m^{2}, 298.15 K), W ik i p e d ia g i v es 33.7 % a t 1.34 e V an d ab o u t 31 % a t 1.55 e V, t h e g a p s o f t h e r ecor d ce l l s a r e n o t in t h e so u r ces an d 1.50 t o 1.55 e V i s m y a ss u m pt i o n$ $k_{B} : B o l t z mann co n s t an t$ $(co m p u t e d, mi r r or (b o t h f a ces) : 1.34 e V g i v es 33.76 % (33.15 %); 1.50 e V 32.15 %, 1.2329 V, 28.97 m A / c m^{2} (31.64 %, 1.2151 V); 1.53 e V 31.83 %, 1.2611 V, 27.99 m A / c m^{2} (31.34 %, 1.2433 V); 1.55 e V 31.50 %, 1.2797 V, 27.26 m A / c m^{2} (31.02 %, 1.2619 V); 1.60 e V 30.58 %, 1.3264 V, 25.47 m A / c m^{2} (30.14 %, 1.3086 V))$

Voltage, Fill Factor and Efficiency Checks

Name	Formula	Related Formulae	Variables/Constants
Voltage deficit and voltage ratio	$Δ V = \frac{E _{g}}{q} - V_{oc}$	$r_{V} = \frac{V _{oc}}{V _{oc, S Q}}, r_{J} = \frac{J _{sc}}{J _{sc, ma x}}, r_{η} = \frac{η}{η _{S Q}}$	$Δ V : d e f i c i t$ $r_{V}, r_{J}, r_{η} : f r a c t i o n s o f t h e r a d ia t i v e v o l t a g e, c u r r e n t an d e f f i c i e n cy, t h e ce l l i s t h e 26.7 % e n t r y o f G r ee n e t a l . (U S T C, 0.0519 c m^{2}, 1.193 V, 26.49 m A / c m^{2}, 84.5 %, N P V M 5/24), w i t h a g a p o f 1.50 t o 1.55 e V an d a mi r r or (b o t h a ss u m e d)$ $(co m p u t e d : Δ V = 0.307, 0.327, 0.337 an d 0.357 V f or 1.50, 1.52, 1.53 an d 1.55 e V; r_{V} = 0.968, 0.953, 0.946 an d 0.932 (0.982, 0.967, 0.960 an d 0.945 f or b o t h f a ces); r_{J} = 0.914, 0.935, 0.946 an d 0.972; r_{η} = 0.830, 0.835, 0.839 an d 0.848; t h e G a A s r ecor d ha s Δ V = 0.293 V an d r_{V} = 0.973)$
External radiative efficiency	$V_{oc} = V_{oc, r a d} - \frac{k _{B} T}{q} ∣ ln ERE ∣$	$ERE = exp (- \frac{V _{oc, r a d} - V _{oc}}{k _{B} T / q})$	$V_{oc, r a d} : r a d ia t i v e l imi t o f t h e s am e g a p$ $E R E : e x t er na l r a d ia t i v e (l u min esce n ce) e f f i c i e n cy, t h e r e l a t i o n i s t h e o n e o f t h e G a A s p a g e, an d t h e g a p an d t h e mi r r or a r e a ss u m e d$ $k_{B} : B o l t z mann co n s t an t$ $(co m p u t e d f or 1.193 V : E R E = 0.212, 0.102, 0.071 an d 0.034 f or 1.50, 1.52, 1.53 an d 1.55 e V w i t h a mi r r or an d 0.423, 0.204, 0.141 an d 0.068 f or b o t h f a ces; t h e G a A s r ecor d ha s 0.30)$
Ideal fill factor	$F F_{0} = \frac{v _{oc} - l n ( v _{oc} + 0.72 )}{v _{oc} + 1}$	$v_{oc} = \frac{q V _{oc}}{n k _{B} T}$	$F F_{0} : f i l l f a c t or w i t h o u t r es i s t i v e l osses$ $v_{oc} : n or ma l i se d v o l t a g e, n = 1 (a ss u m e d), t h e e x p r ess i o n i s ba c k g r o u n d k n o w l e d g e (a s o n t h e H I T an d G a A s p a g es)$ $k_{B} : B o l t z mann co n s t an t$ $(co m p u t e d : t h e 26.7 % ce l l (1.193 V) ha s F F_{0} = 0.898 an d 84.5 % i s 0.941 o f i t; t h e 25.2 % ce l l (1.162 V) ha s 0.896 an d 82.0 % i s 0.916 o f i t)$
Efficiency from the reported parameters	$η = \frac{V _{oc} J _{sc} F F}{P _{in}}, P_{in} = 100 mW/c m^{2}$	$η_{c h ec k} = \frac{V _{oc} J _{sc} F F}{1000}$ $Δ η = η_{p r in t e d} - η_{c h ec k}$	$η : e f f i c i e n cy, V_{oc} in mV, J_{sc} in m A / c m^{2}, F F a s a f r a c t i o n (η_{c h ec k} i s in p er ce n t : t h e 1000 t u r n s mV in t o V, an d 1 mW / c m^{2} i s 1 p er ce n t o f P_{in}), t h e e n t r i es a r e f r o m t h e e f f i c i e n cy t ab l es (v er s i o n 64) o f G r ee n e t a l . an d t h e S o l a E o n r e p or t$ $(co m p u t e d : 1193, 26.49, 84.5 % g i v e 26.70 % (26.7); 1162, 26.39, 82.0 % g i v e 25.15 % (25.2); t h e minim o d u l e 1169, 25.00, 77.4 % g i v es 22.62 % (22.6); f or t h e 27.87 % ce l l (F F = 87.61 %, n o V oc or J sc p r in t e d) t h e p r o d u c t V_{oc} J_{sc} = 31.81 mW / c m^{2}, f or e x am pl e 1.200 V w i t h 26.5 m A / c m^{2} (a ss u m e d J_{sc}), an d 27.87/31.83 = 0.876 o f t h e 1.53 e V l imi t)$
Module efficiency from voltage, current and area	$η_{m o d} = \frac{V _{oc} I _{sc} F F}{G A}$	$η_{m o d, r e l} = \frac{η _{m o d}}{η _{ce l l}}$	$η_{m o d} : m o d u l e e f f i c i e n cy$ $V_{oc}, I_{sc} : m o d u l e v o l t a g e an d c u r r e n t$ $F F : f i l l f a c t or$ $G : 1000 W / m^{2}$ $A : d es i g na t e d i l l u mina t i o n a r e a, t h e e n t r i es a r e f r o m G r ee n e t a l . (S o l a E o n 1027 c m^{2}; M i cr o q u an t a 7906 c m^{2}) an d f r o m t h e S o l a E o n r e p or t (0.72 m^{2})$ $(co m p u t e d : 59.4 V, 0.4307 A, 77.1 % g i v e 19.72 W an d 19.21 % (19.2); 206.05 V, 0.752 A, 76.5 % g i v e 118.5 W an d 14.99 % (15.0); 149 W o n 0.72 m^{2} i s 20.7 % an d 140 W o n 0.64 m^{2} i s 21.88 %; t h e r a t i os t o t h e 26.7 % ce l l a r e 0.719 (19.2), 0.562 (15.0) an d 0.847 (22.6 minim o d u l e a g ain s t 26.7))$

Stability and Ageing

Name	Formula	Related Formulae	Variables/Constants
Stability metric and extrapolation	$T_{80} : η (T_{80}) = 0.80 η (0)$	$T_{80}^{e x t} \approx \frac{20 %}{loss rate}, loss rate = \frac{Δ η}{Δ t}$	$T_{80} : t im e t o 80 % o f t h e ini t ia l e f f i c i e n cy (T_{90}, T_{97} an d so o n a r e d e f in e d in t h e s am e w a y in Z h u e t a l .), l oss r a t e : l in e a r r a t e (a ss u m e d), F l ux im c a l l s T_{80} = 1000 h t h e s t an d a r d b e n c hma r k, t h e t a r g e t i s 20 t o 25 y e a r s, a D M P E S I - t r e a t e d F A P b I_{3} ce l l l os t l ess t han 1 % in m or e t han 4500 h o f ma x im u m - p o w er - p o in t t r a c k in g (1 s u n, N_{2}, r oo m t e m p er a t u r e, u n e n c a p s u l a t e d), w i t h an e x t r a p o l a t e d T_{80} ab o v e nin e y e a r s$ $(co m p u t e d : 1 % in 4500 h g i v es 20 % in 90000 h (10.3 y e a r s o f co n t in u o u s i l l u mina t i o n); nin e y e a r s a r e 78840 h; 25 y e a r s a r e 219000 h, or 43800 h a t 1 s u n i f 1 s u n i s f i v e t im es t h e a v er a g e i r r a d ia t i o n o f a p an e l (Z h u e t a l .), so 4500 h a r e 0.103 o f i t (a ss u m e d d ose sc a l in g))$
Hysteresis index	$H I = \frac{η _{r e v} - η _{f w d}}{η _{r e v}}$	$η_{s t ab} at V_{m p} until \frac{dJ}{d t} < 0.07 %/ min$	$H I : h y s t er es i s in d e x$ $η_{r e v}, η_{f w d} : e f f i c i e n c i es f r o m t h e r e v er se an d f or w a r d v o l t a g e s w ee p s$ $η_{s t ab} : s t abi l i se d e f f i c i e n cy, G r ee n e t a l . m e a s u r e t h e 26.7 % ce l l w i t h a t e n - p o in t s w ee p an d a co n s t an t bia s u n t i l t h e c u r r e n t c han g es b y l ess t han 0.07 %/ min, F l ux im s a y s t ha t s w ee p s ab o v e 1000 V / s f r eez e t h e i o n s$ $(co m p u t e d : t h e D M P E S I ce l l ha s 23.32 % (r e v er se) an d 23.14 % (f or w a r d), H I = 0.77 %, an d 23.3 % s t abi l i se d; t h e S o l a E o n m o d u l e ha s 25.47 % (r e v er se) an d 25.27 % (s t abi l i se d), 0.79 %)$
Acceleration of ageing	$A F = (\frac{I}{I _{r e f}})^{0.7} exp [\frac{E _{a}}{k _{B}} (\frac{1}{T _{r e f}} - \frac{1}{T})]$	$t_{u se} = A F t_{t es t}$	$A F : a cce l er a t i o n f a c t or$ $I : l i g h t in t e n s i t y$ $E_{a} : a c t i v a t i o n e n er g y$ $T : t e m p er a t u r e in k e l v in, t h e e x p o n e n t 0.7 o f t h e l i g h t t er m i s q u o t e d b y Z h u e t a l . f or M A P b I_{3}, w h o g i v e i o n mi g r a t i o n e n er g i es o f 0.1 t o 0.9 e V (0.29 t o 0.1 e V u n d er l i g h t); t h e v a l u e o f E_{a} b e l o w i s a ss u m e d$ $k_{B} : B o l t z mann co n s t an t$ $(co m p u t e d : 85 C a g ain s t 25 C g i v es 26.1 f or 0.5 e V, 1.9 f or 0.1 e V, 7.1 f or 0.3 e V an d 354 f or 0.9 e V; 65 C w i t h 0.5 e V g i v es 10.0; t h e l i g h t t er m i s 5.0 f or 10 s u n s a g ain s t 1 s u n an d 3.1 f or 1 s u n a g ain s t 0.2 s u n)$
Phase transition temperatures	$T (^{\circ} C) = T (K) - 273.15$	$Δ T = T_{o p} - T_{c}$	$T : t e m p er a t u r e$ $T_{c} : t r an s i t i o n t e m p er a t u r e$ $T_{o p} : o p er a t in g t e m p er a t u r e, W ik i p e d ia r e p or t s f or M A P b I_{3} an or t h or h o mbi c p ha se a t l o w t e m p er a t u r e, a t e t r a g o na l o n e a t 162 K an d a c u bi c o n e a t 327 K (m y r e a d in g o f t h e e x t r a c t), Z h u e t a l . g i v e an o p er a t in g r an g e o f - 40 t o 75 C w i t h 65 C a s t h e u s u a l l imi t$ $(co m p u t e d : 162 K i s - 111.2 C an d 327 K i s 53.9 C, so a p an e l a t 65 C l i es 11 K ab o v e t h e c u bi c t r an s i t i o n o f M A P b I_{3})$

Important Questions

Ques: What is the perovskite single-junction record: 26.7, 26.95, 27 or 27.87 %?

Green et al. (version 64) list 26.7 ± 0.6 % for the USTC cell (0.0519 $c m^{2}$ , NPVM, May 2024). Fluxim gives 26.95 % for Soochow University and UNSW in 2025 (0.0583 $c m^{2}$ , certified by NREL) but also says 26.7 % in its text and FAQ, which contradicts its own table. Wikipedia gives 27 % in 2025, and SolaEon claims 27.87 % (0.076 $c m^{2}$ , fill factor 87.61 %, NPVM, January 2026) without voltage, current or stability data. The values are successive records on very small areas, not conflicting measurements. The product of the 27.87 % claim is 31.81 mW/ $c m^{2}$ for Voc times Jsc (computed). 27.87 % is the most recent figure but rests on a company report, so 26.95 % is the more likely best independently certified value in the sources, and 26.7 % the most reliable (my reading). Reference: Green, Dunlop, Yoshita, Kopidakis, Bothe, Siefer, Hinken, Rauer, Hohl-Ebinger and Hao, ‘Solar cell efficiency tables (Version 64)’, Prog. Photovolt. 32(7), 425-441 (2024); Fluxim, ‘Highest Perovskite Solar Cell Efficiencies (2026 Update)’; perovskite-info.com, ‘SolaEon reports 27.87% efficiency for single-junction perovskite solar cell’ (30 January 2026; credited to indexbox.io); Wikipedia, ‘Perovskite solar cell’.

Ques: Is the gap of MAPbI3 1.55 or 1.6 eV, and is the limit 31 or 33.7 %?

Wikipedia gives a range of 1.55 to 2.3 eV for MAPbX $_{3}$ and 1.48 to 2.2 eV for FAPbX $_{3}$ , a limit of 33.7 % at 1.34 eV and about 31 % at 1.55 eV; the thesis puts the gap of MAPbI $_{3}$ at about 1.6 eV with a limit of about 31 %. My calculation gives 31.50 % at 1.55 eV and 30.58 % at 1.60 eV with a mirror, 31.02 and 30.14 % for emission from both faces, and 33.76 % at 1.34 eV (computed). The 31 % belongs to 1.55 eV, and 1.6 eV corresponds to about 30.6 %, so the thesis value is a rounding (my reading). The record cells probably use FA-rich compositions near 1.5 eV, for which the limit is 31.6 to 32.2 %, but the sources do not give their gaps (computed, assumed). Reference: Wikipedia, ‘Perovskite solar cell’; Doctoral thesis on halide perovskite crystals, arXiv:1809.10949 (title not shown in the extract); Solar Cell Fundamentals page of this vault.

Ques: How large is the voltage deficit of the 26.7 % cell?

Green et al. give 1.193 V, 26.49 $mA/c m^{2}$ and 84.5 % for the USTC cell but not its gap. For 1.50, 1.53 and 1.55 eV (assumed) the deficit is 0.307, 0.337 and 0.357 V, and with a rear mirror the cell has 0.968, 0.946 and 0.932 of the radiative voltage (computed). The external radiative efficiency is then 0.21, 0.071 and 0.034, or twice as much for emission from both faces (computed). The GaAs record has a deficit of 0.293 V and an efficiency of 0.30 (page 86). The assumed gap changes the result by a factor of six, so the numbers are a range, not a measurement. A gap of 1.5 to 1.53 eV is the more likely for FA-rich films, which makes the cell lose about 0.3 V, similar to the best GaAs cell. Reference: Green, Dunlop, Yoshita, Kopidakis, Bothe, Siefer, Hinken, Rauer, Hohl-Ebinger and Hao, ‘Solar cell efficiency tables (Version 64)’, Prog. Photovolt. 32(7), 425-441 (2024); Gallium Arsenide (GaAs) Single-Junction Solar Cell page of this vault; Solar Cell Fundamentals page of this vault.

Ques: How thick must the absorber be: 300 nm, 500 nm or 460 nm?

The thesis gives an absorption coefficient of about 10 $^{5}$ $c m^{- 1}$ and says that about 300 nm of a lead-based film absorb 99 % of unconcentrated sunlight. Wikipedia says that a film of about 500 nm absorbs the whole visible spectrum and gives no coefficient. For a single pass and a constant coefficient of 10 $^{5}$ $c m^{- 1}$ , 300 nm absorb 95.0 %, 460 nm 99 % and 500 nm 99.3 % (computed). With a rear mirror, 300 nm absorb 99.75 % (computed), so the thesis figure is correct for a double pass or for a coefficient above 10 $^{5}$ $c m^{- 1}$ over most of the spectrum. The coefficient falls near the gap (Urbach energy about 15 meV), so a constant value overestimates the absorption of red light. Records use films of 500 to 700 nm in practice (background knowledge), so 460 to 500 nm is the more likely single-pass figure. Reference: Doctoral thesis on halide perovskite crystals, arXiv:1809.10949 (title not shown in the extract); Wikipedia, ‘Perovskite solar cell’.

Ques: Is the carrier lifetime of a perovskite 0.1-1 µs, 700 ns, 2.9 µs or 13 ns, and the diffusion length 0.5 or 5 µm?

The thesis gives mobilities of 1 to 100 $c m^{2} / (V s)$ , lifetimes of 0.1 to 1 µs and diffusion lengths of hundreds to thousands of nanometres. Wikipedia gives 2 to 10 $c m^{2} / (V s)$ for bulk electrons and a diffusion length above 1 µm, and 13 ns for passivated CsPbI $_{3}$ nanocrystal films. Zhu et al. quote 700 ns for all-inorganic and 2900 ns for hybrid films, and the thesis 4.4 and 30 ns for CsPbBr $_{3}$ crystals. With 25.693 mV the diffusion length is 0.51 µm (1 $c m^{2} / (V s)$ , 0.1 µs), 5.1 µm (10, 1 µs) and 16 µm (100, 1 µs) (computed); 13 ns with 10 $c m^{2} / (V s)$ gives 0.58 µm. The values refer to different materials and methods. For hybrid lead-iodide films 1 to 10 µm is the more likely range, and the 13 ns belongs to nanocrystals. Reference: Doctoral thesis on halide perovskite crystals, arXiv:1809.10949 (title not shown in the extract); Wikipedia, ‘Perovskite solar cell’; Zhu et al., ‘Long-term operating stability in perovskite photovoltaics’, Nat. Rev. Mater. (2023), PDF from light.utoronto.ca.

Ques: Is the stability benchmark 1000 h, 4500 h or 25 years?

Fluxim calls T $_{80}$ of 1000 h the standard benchmark and 20 to 25 years the target. Zhu et al. report record cells with T $_{80}$ above 1000 h, T $_{99}$ above 2000 h at 60 C and T $_{90}$ of 2000 h, and a Nature Energy 2023 study reports less than 1 % loss in more than 4500 h of tracking (1 sun, nitrogen, room temperature, unencapsulated) with an extrapolated T $_{80}$ above nine years. Green et al. mark their perovskite entries as initial performance. The conditions differ, so the values cannot be ranked. A linear extrapolation gives 10.3 years of continuous light (computed), and 4500 h are 0.103 of the 43 800 h that 25 years of outdoor use would correspond to at five times the average irradiation (computed, assumed). 4500 h in nitrogen is the best demonstration read here; the 25-year target is not yet shown. Reference: Fluxim, ‘Perovskite Solar Cell Stability: Comprehensive Guide, Testing ISOS Protocols, and Tools for Long-Term Reliability’; Zhu et al., ‘Long-term operating stability in perovskite photovoltaics’, Nat. Rev. Mater. (2023), PDF from light.utoronto.ca; ‘Multifunctional sulfonium-based treatment for perovskite solar cells with less than 1% efficiency loss over 4,500-h operational stability tests’, Nature Energy (2023); Green, Dunlop, Yoshita, Kopidakis, Bothe, Siefer, Hinken, Rauer, Hohl-Ebinger and Hao, ‘Solar cell efficiency tables (Version 64)’, Prog. Photovolt. 32(7), 425-441 (2024).

Ques: Does the record efficiency depend on the scan direction, and which value is more reliable?

Green et al. measure the USTC cell with a ten-point current-voltage sweep and a constant bias until the current changes by less than 0.07 %/min, and they state that stability was not investigated. The Nature Energy 2023 cell has 23.32 % in the reverse scan, 23.14 % forward and 23.3 % stabilised, a hysteresis index of 0.77 % (computed). SolaEon gives 25.47 % in reverse scan and 25.27 % stabilised for a module, 0.79 % lower (computed). Fluxim says that sweeps above 1000 V/s freeze the ions, which would hide hysteresis, and Wikipedia does not mention hysteresis. The reverse scan overstates the efficiency by about 0.2 points for these good devices, and the stabilised value is the more likely true one. Poor cells can differ much more (background knowledge). Reference: Green, Dunlop, Yoshita, Kopidakis, Bothe, Siefer, Hinken, Rauer, Hohl-Ebinger and Hao, ‘Solar cell efficiency tables (Version 64)’, Prog. Photovolt. 32(7), 425-441 (2024); ‘Multifunctional sulfonium-based treatment for perovskite solar cells with less than 1% efficiency loss over 4,500-h operational stability tests’, Nature Energy (2023); perovskite-info.com, ‘SolaEon reports 27.87% efficiency for single-junction perovskite solar cell’ (30 January 2026; credited to indexbox.io); Fluxim, ‘Perovskite Solar Cell Stability: Comprehensive Guide, Testing ISOS Protocols, and Tools for Long-Term Reliability’; Wikipedia, ‘Perovskite solar cell’.

Ques: What module efficiency has been reached: 15.0, 19.2, 20.7, 21.88, 22.6 or 25.27 %?

Green et al. list 22.6 % for an 8-cell minimodule of 20.25 $c m^{2}$ , 19.2 % for the SolaEon module of 1027 $c m^{2}$ and 15.0 % for a Microquanta module of 7906 $c m^{2}$ ; the products check to 22.62, 19.21 and 14.99 % (computed). SolaEon reports 20.7 % over 0.72 m $^{2}$ (149 W) and 21.88 % over the illuminated 0.64 m $^{2}$ (140 W) in June 2025, and 25.27 % stabilised (25.47 % reverse scan) on a 0.72 m $^{2}$ sample in September 2025. The last cannot be the same module: 25.27 % of 0.72 m $^{2}$ would be 182 W against 149 W (computed). Efficiency falls with area, from 26.7 % at 0.05 $c m^{2}$ to 15.0 % at 0.79 m $^{2}$ . The certified full-area values of 19 to 22 % are the more likely module level, and 25.27 % probably refers to a smaller sub-area or a different basis (my reading). Reference: Green, Dunlop, Yoshita, Kopidakis, Bothe, Siefer, Hinken, Rauer, Hohl-Ebinger and Hao, ‘Solar cell efficiency tables (Version 64)’, Prog. Photovolt. 32(7), 425-441 (2024); perovskite-info.com, ‘SolaEon reports 27.87% efficiency for single-junction perovskite solar cell’ (30 January 2026; credited to indexbox.io).

Ques: How well can lead leakage be suppressed: 84, 96.1, 98 % or 375-fold?

Wikipedia gives a leakage reduction of 84 % for a resin coating and 98 % when the resin is used in carbon paste, a sequestration efficiency of 96.1 % for another coating, and a 375-fold reduction in leakage under simulated sunlight for a self-healing epoxy encapsulation. A 375-fold reduction is 99.73 % (computed), so the ordering is 84 < 96.1 < 98 < 99.7 %, but the measures and tests differ. It also quotes a solubility product of 4.4 × 10 $^{- 9}$ for the degradation products against about 10 $^{- 34}$ for CdTe, a ratio of 4 × 10 $^{25}$ (computed), a lethal dose below 5 mg/kg and a blood limit of 5 µg/dL (2003) said to be revoked in 2010; I could not verify the last. The encapsulated device is the more likely best case, and the percentages cannot be compared directly. Reference: Wikipedia, ‘Perovskite solar cell’.

Ques: What is the upper operating temperature: 65, 75 or 90 C?

Zhu et al. give an operating range of -40 to 75 C, call 65 C the usual upper limit but say the evidence suggests 70 to 75 C, call ageing above 95 C unrepresentative, and then set a limit below 90 C for FA-based perovskites. The ISOS levels use 65 or 85 C. MAPbX $_{3}$ decomposes below 100 C, FAPbI $_{3}$ is stable for 60 minutes at 150 C and CsPbI $_{3}$ up to about 390 C. Wikipedia places the tetragonal-cubic transition of MAPbI $_{3}$ at 327 K, which is 53.9 C (computed), so a panel at 65 C is 11 K above it. The statements concern different compositions and purposes. For modules in the field 65 to 75 C is the more likely limit, and 85 C is a test stress that FA-rich compositions can pass (my reading). Reference: Zhu et al., ‘Long-term operating stability in perovskite photovoltaics’, Nat. Rev. Mater. (2023), PDF from light.utoronto.ca; Wikipedia, ‘Perovskite solar cell’; ‘Consensus statement for stability assessment and reporting for perovskite photovoltaics based on ISOS procedures’, Nature Energy (2020).

Ques: Is the exciton binding energy of a lead halide perovskite about 30 meV, 33 meV or 2 meV?

The thesis gives about 30 meV for CsPbBr $_{3}$ and about 350 meV for Cs $_{4}$ PbBr $_{6}$ and links the small values to a high polarisability and a static permittivity of about 30; its optical permittivities are about 4 for CsPbBr $_{3}$ , 4.5 for MAPbBr $_{3}$ and 6.5 for MAPbI $_{3}$ . Wikipedia says only that the energy is small. With a hydrogenic model and a reduced mass of 0.104 $m_{0}$ (assumed) the binding energy is 33 meV for a permittivity of 6.5 and 1.6 meV for 30 (computed). The two permittivities describe different frequencies, since the lattice screens only at low frequency, so the exciton is more likely bound by 10 to 30 meV at room temperature and the carriers are mostly free (my reading). Neither source gives a value for MAPbI $_{3}$ directly. Reference: Doctoral thesis on halide perovskite crystals, arXiv:1809.10949 (title not shown in the extract); Wikipedia, ‘Perovskite solar cell’.

Ques: Is the Urbach energy of MAPbI3 15 meV, and how does it compare with GaAs at 8 or 6.7 meV?

The thesis gives about 15 meV for MAPbI $_{3}$ , 19 meV for MAPbBr $_{3}$ and for CsPbBr $_{3}$ crystals, 36 meV for a spin-coated CsPbBr $_{3}$ film, and 11, 8 and 25 meV for silicon, GaAs and CIGS. The GaAs page uses 6.7 meV from Miller et al., so the two values for GaAs differ by 1.3 meV. At 100 meV below the gap the absorption falls to 1.3 × 10 $^{- 3}$ of its value at the gap for 15 meV, 4 × 10 $^{- 6}$ for 8 meV and 3 × 10 $^{- 7}$ for 6.7 meV (computed). The tail of the perovskite is therefore about three orders higher in the sub-gap region, which adds to the voltage deficit (my reading). The thesis value is for a single compound and a reference, so 15 meV is the more likely figure for good iodide films, and 6.7 to 8 meV for GaAs. Reference: Doctoral thesis on halide perovskite crystals, arXiv:1809.10949 (title not shown in the extract); Gallium Arsenide (GaAs) Single-Junction Solar Cell page of this vault.

Quartz 5

Explorer

Perovskite Solar Cell