1. Theory

Definition: A perovskite-silicon tandem puts a wide-gap perovskite cell on a silicon cell of about 1.1 eV. The perovskite takes the photons above its gap (it absorbs below about 800 nm) and the silicon those below, up to 1100 nm (MDPI). In a two-terminal cell the two subcells are in series and their currents must match; in a four-terminal arrangement each cell has its own contacts and no matching is needed, at the price of extra electrodes and parasitic absorption (MDPI).
Gaps: MDPI gives a top gap window of 1.65 to 1.75 eV for current matching and calls 1.73 eV on 1.1 eV silicon a near-ideal pair; Wikipedia gives 1.6 to 1.8 eV. A 1.68 eV composition Rb $_{0.05}$ Cs $_{0.1}$ FA $_{0.85}$ Pb(I $_{0.75}$ Br $_{0.25}$ ) $_{3}$ gave a single-junction cell of 25.0 % with 1.31 V, and a tandem of 33.9 % (Nature Communications).
Silicon bottom cell: Silicon heterojunction cells dominate the best results; TOPCon and PERC bottom cells are also used (MDPI). The bottom cell of the Nature Communications tandem is a heterojunction cell with front pyramids of 600 to 800 nm and a rear texture of 700 to 800 nm, 20 mm by 20 mm, and the authors say that its modest efficiency limited the result. LONGi describes an asymmetric texture, fine at the front to help the perovskite deposition and large at the rear for passivation and infrared response (pv magazine).
Recombination junction: Indium tin oxide of 15 nm is used in the Nature Communications cell; thinner (1.7 nm) indium tin oxide, 5 nm indium zinc oxide (32.5 % certified) and 150 nm zinc tin oxide are reported (MDPI).
Halide segregation: Wide-gap perovskites for tandems have more than 20 % bromine; organic-cation compositions need 25 to 30 % for the same gap, and all-inorganic CsPb(I $_{1 - x}$ Br $_{x}$ ) $_{3}$ reaches about 1.7 eV with less than 20 % (MDPI). Under 2 suns the photoluminescence of the control film moved by about 35 nm in 80 minutes and that of the treated film negligibly (Nature Communications).
Records (efficiency tables, version 64): Green et al. list a two-terminal cell of 34.2 ± 1.0 % (LONGi, 1.0044 cm $^{2}$ , 1.990 V, 20.65 mA/cm $^{2}$ , 83.2 %, ESTI April 2024), a large cell of 28.6 ± 1.4 % (Oxford PV, 258.14 cm $^{2}$ total area, 1.909 V, 19.11 mA/cm $^{2}$ , 78.3 %, Fraunhofer ISE May 2023), a four-terminal module of 25.8 ± 2.1 % (LONGi, 2054 cm $^{2}$ , Fraunhofer ISE April 2024), perovskite/CIGS 24.2 ± 0.7 %, perovskite/perovskite 28.2 ± 0.5 % (30.1 ± 0.8 % in the notable exceptions) and perovskite/organic 23.4 ± 0.8 %.
Later records: LONGi announced 34.85 % (NREL, two-terminal, 16 April 2025, 1.97 V, fill factor 83.0 %) after 33.9 % in November 2023 and 34.6 % in 2024; the cell area was not given (LONGi; pv magazine). Fluxim also mentions an unconfirmed claim of about 35 % (ESTI).
Modules: Oxford PV reported 26.9 % for a 60-cell double-glass module (Fraunhofer CalLab, designated area just over 1.6 m $^{2}$ , June 2024) after 25 % for an industrial-size module in January 2024, and in September 2024 shipped 72-cell modules of 24.5 % to a US customer (Oxford PV; TaiyangNews).
Stability: The tandem of Nature Communications keeps 90 % for 1135 h at 65 C and 1 sun (encapsulated), against 95 % after 300 h in air, 95.43 % after 1000 h in nitrogen, 96 % after 1068 h and 89 % after 1000 h in other reports (MDPI).
Limits: MDPI gives 41 % for an ideal tandem and “approaching 46 %” for a two-terminal tandem, LONGi 43 % and Wikipedia 45.3 %; my calculation gives 44.39 % (45.15 % with a rear mirror) (computed).

2. Working Principle

Spectrum splitting: The perovskite converts the blue and green light at a voltage above 1.3 V, and the silicon converts the red and infrared at about 0.7 V, so the thermalisation loss of the high-energy photons falls (background knowledge). The ideal efficiency of a 1.12 eV cell is 32.73 % and that of a tandem 42 to 45 % (computed).
Current matching: For 1.68/1.12 eV the top cell could carry 23.06 mA/cm $^{2}$ and the bottom cell 20.75 mA/cm $^{2}$ , so the silicon limits the current and the measured 20.65 mA/cm $^{2}$ is 0.995 of it (computed). The matching point is a top gap of 1.729 eV; efficiency falls from 44.4 % there to 39.8 % at 1.65 eV and to 36.3 % at 1.60 eV (computed). A gap shift of 76 meV by halide segregation would therefore cost several points (computed, from the 35 nm shift).
Voltage: The measured 1.990 V is 0.894 of the radiative sum of 2.2248 V (computed, 1.68/1.12 eV assumed), and the deficit of 0.810 V is about 0.37 V for the perovskite and 0.44 V for the silicon cell and junction (computed). The fill factor is 0.943 of the ideal value (computed).
Interconnection: A recombination layer of ITO or IZO joins the cells with a small voltage drop; the layer must be transparent to the infrared that the silicon uses and thin enough not to shunt textured surfaces (MDPI; my reading).
Texture: Pyramids on the silicon increase the light path and reduce reflection, but the perovskite must cover them without pinholes (MDPI; pv magazine).
Two-terminal against four-terminal: The four-terminal tandem needs no matching and is 1.99 points higher at 1.68 eV in my model (computed), but it needs more electrodes and has parasitic absorption (MDPI); the module record read here is four-terminal (25.8 %).

3. Applications

Utility and rooftop modules: Oxford PV delivered 72-cell modules of 24.5 % to a US utility-scale customer in September 2024, and its 60-cell module of 26.9 % exceeds the 25 % of the best silicon modules of similar area (Oxford PV; TaiyangNews).
Higher power per area: Oxford PV claims 20 % more power than silicon modules of the same footprint (TaiyangNews); the module weighs less than 25 kg.
Retrofit of silicon lines: Silicon heterojunction, TOPCon and PERC cells serve as bottom cells (MDPI), so the existing silicon production can be reused (my reading).
Next steps: The all-perovskite and triple-junction stacks of Green et al. and Wikipedia (28.2 to 30.1 %, 35.3 % for perovskite-silicon triple) extend the principle (Green et al.; Wikipedia).

Tandem Limits and Current Matching

Name	Formula	Related Formulae	Variables/Constants
Series connection and current matching of a two-terminal tandem	$V = V_{t o p} + V_{b o t}, J = min (J_{t o p}, J_{b o t})$	$J_{t o p} = q \int_{E_{g, t}}^{\infty} Φ d E, J_{b o t} = q \int_{E_{g, b}}^{E_{g, t}} Φ d E$	$V_{t o p}, V_{b o t} : v o l t a g es o f t h e p er o v s k i t e an d s i l i co n ce l l s$ $J : co mm o n c u r r e n t d e n s i t y$ $Φ : p h o t o n f l ux o f t h e A M 1.5 G s p ec t r u m$ $E_{g, t}, E_{g, b} : g a p s o f t h e t o p an d b o tt o m ce l l s, t h e s t e p ab sor pt an ce (t h e t o p ce l l t ak es e v er y p h o t o n ab o v e i t s g a p, t h e s i l i co n e v er y p h o t o n b e tw ee n t h e tw o g a p s) i s m y m o d e l a ss u m pt i o n, M D P I g i v es a c u r r e n t - ma t c hin g w in d o w o f 1.65 t o 1.75 e V f or t h e t o p g a p$ $(co m p u t e d w i t h t h e p v l ib A M 1.5 G s p ec t r u m o f 1000.37 W / m^{2} : f or 1.68/1.12 e V t h e p h o t oc u r r e n t s a r e 23.06 an d 20.75 m A / c m^{2}, f or 1.73/1.12 e V 21.67 an d 22.14, f or 1.75/1.12 e V 21.06 an d 22.75, f or 1.65/1.12 e V 24.05 an d 19.76 an d f or 1.80/1.12 e V 19.65 an d 24.16; t h e p h o t oc u r r e n t ab o v e 1.12 e V i s 43.81 m A / c m^{2})$
Detailed-balance efficiency of a two-terminal tandem	$η_{2 T} = max_{J} \frac{J [ V _{t o p} ( J ) + V _{b o t} ( J ) ]}{P _{in}}$	$V_{i} (J) = \frac{k _{B} T}{q} ln (\frac{J _{i} - J}{J _{0, i}} + 1)$	$J_{0, i} : r a d ia t i v e d a r k c u r r e n t (e mi ss i o n in t o 2 π or, w i t h a r e a r mi r r or, π), P_{in} = 1000.37 W / m^{2}, k_{B} T / q = 25.693 mV, t h e m o d e l i s t h e o n e o f t h e I I I - V m u l t i - j u n c t i o n p a g e, an d t h e s i l i co n g a p o f 1.12 e V i g n or es A ug er r eco mbina t i o n an d t h e in d i r ec t g a p (a ss u m e d), t h e e x t r a c t s g i v e l imi t s o f 41 % an d^{'} a pp r o a c hin g 46 %^{'} (M D P I), 43 % (L O N G i) an d 45.3 % (W ik i p e d ia)$ $k_{B} : B o l t z mann co n s t an t$ $(co m p u t e d, 2 π (π) : 1.68/1.12 e V 42.11 % (42.84 %); t h e b es t t o p g a p f or a 1.12 e V ce l l i s 1.729 e V w i t h 44.39 % (45.15 %); 1.73/1.10 e V 44.20 %; b y t o p g a p w i t h 1.12 e V b e l o w : 1.55 e V 32.04 %, 1.60 e V 36.25 %, 1.65 e V 39.79 %, 1.70 e V 43.43 %, 1.75 e V 44.02 %, 1.80 e V 42.41 %, 1.90 e V 38.52 %; a s in g l e 1.12 e V ce l l g i v es 32.73 %)$
Efficiency of a four-terminal tandem	$η_{4 T} = \frac{P _{t o p} + P _{b o t}}{P _{in}}$	$P_{k} = max_{V} V [J_{p h, k} - J_{0, k} (e^{q V / k_{B} T} - 1)]$	$P_{t o p}, P_{b o t} : ma x im u m p o w er s o f t h e tw o in d e p e n d e n tl y w i r e d ce l l s$ $J_{p h, k} : p h o t oc u r r e n t o f ce l l k (ab o v e E_{g, t} f or t h e t o p ce l l an d b e tw ee n E_{g, b} an d E_{g, t} f or t h e b o tt o m ce l l), n o c u r r e n t ma t c hin g i s n ee d e d b u t e x t r a e l ec t r o d es an d p a r a s i t i c ab sor pt i o n a r e (M D P I), 2 π e mi ss i o n an d s t e p ab sor pt an ce a s ab o v e$ $k_{B} : B o l t z mann co n s t an t$ $(co m p u t e d, t o p / b o tt o m / t o t a l : 1.60 e V 30.14/13.31/43.45 %; 1.68 e V 28.98/15.12/44.10 %; 1.75 e V 27.83/16.63/44.45 %; 1.80 e V 26.86/17.70/44.55 %; t h e o pt im u m i s 44.58 % a t 1.81 e V; t h e f o u r - t er mina l v a l u e a t 1.68 e V e x cee d s t h e tw o - t er mina l o n e b y 1.99 p o in t s)$

Voltage, Fill Factor and Efficiency Checks

Name	Formula	Related Formulae	Variables/Constants
Voltage sum, deficit and voltage ratio	$Δ V = \frac{E _{g, t} + E _{g, b}}{q} - V_{oc}$	$r_{V} = \frac{V _{oc}}{V _{oc, t} + V _{oc, b}}$	$Δ V : d e f i c i t o f t h e t an d e m$ $V_{oc, t}, V_{oc, b} : r a d ia t i v e o p e n - c i r c u i t v o l t a g es o f t h e tw o ce l l s w i t h t h e i r o w n p h o t oc u r r e n t s, t h e ce l l s a r e t h e L O N G i e n t r y o f G r ee n e t a l . (1.990 V, 20.65 m A / c m^{2}, 83.2 %, 1.0044 c m^{2}) an d t h e L O N G i 34.85 % ce l l (1.97 V, 83.0 % f r o m p v ma g a z in e), w i t h g a p s o f 1.68/1.12 e V (a ss u m e d)$ $(co m p u t e d : t h e r a d ia t i v e v o l t a g es o f t h e tw o ce l l s a r e 1.3835 an d 0.8413 V f or 2 π (1.4014 an d 0.8591 V w i t h a mi r r or), s u m 2.2248 V (2.2604 V); t h e 34.2 % ce l l ha s Δ V = 0.810 V an d r_{V} = 0.894 (0.880); t h e 34.85 % ce l l ha s Δ V = 0.830 V an d r_{V} = 0.885 (0.871); t h e w i d e - g a p s in g l e - j u n c t i o n ce l l o f N a t u r e C o mm u ni c a t i o n s (1.68 e V, 1.31 V) ha s Δ V = 0.370 V an d r_{V} = 0.935 (mi r r or), so t h e t an d e m l oses ab o u t 0.44 V in t h e s i l i co n ce l l an d t h e j u n c t i o n)$
Ideal fill factor of the tandem	$F F_{0} = \frac{v - l n ( v + 0.72 )}{v + 1}$	$v = \frac{V _{oc}}{N k _{B} T / q}, N = 2$	$F F_{0} : f i l l f a c t or w i t h o u t r es i s t i v e l osses$ $N : n u mb er o f j u n c t i o n s, e q u a l v o l t a g es o f t h e tw o ce l l s an d an i d e a l i t y f a c t or o f 1 a r e m y a ss u m pt i o n s, t h e e x p r ess i o n i s ba c k g r o u n d k n o w l e d g e (a s o n t h e e a r l i er p a g es), t h e e n t r i es a r e f r o m G r ee n e t a l . an d t h e p a p er s q u o t e d$ $k_{B} : B o l t z mann co n s t an t$ $(co m p u t e d : t h e 34.2 % ce l l ha s F F_{0} = 0.882 an d 83.2 % i s 0.943 o f i t; t h e 34.85 % ce l l 0.881 an d 0.942; t h e 33.91 % ce l l o f N a t u r e C o mm u ni c a t i o n s 0.884 an d 0.941; t h e l a r g e O x f or d P V ce l l 0.879 an d 0.891; t h e 30.1 % a l l - p er o v s k i t e ce l l 0.891 an d 0.918)$
Efficiency from the reported parameters	$η = \frac{V _{oc} J _{sc} F F}{P _{in}}, P_{in} = 100 mW/c m^{2}$	$J_{sc} = \frac{η P _{in}}{V _{oc} F F}$	$η : e f f i c i e n cy, V_{oc} in mV, J_{sc} in m A / c m^{2}, F F a s a f r a c t i o n (e f f i c i e n cy in p er ce n t = V_{oc} [mV] \cdot J_{sc} [m A / c m^{2}] \cdot F F /1000), t h e e n t r i es a r e f r o m G r ee n e t a l . (tw o - t er mina l ce l l s), t h e N a t u r e C o mm u ni c a t i o n s p a p er an d p v ma g a z in e, w hi c h g a v e n o J_{sc} f or t h e 34.85 % ce l l$ $(co m p u t e d : L O N G i 1990, 20.65, 83.2 % g i v e 34.19 % (34.2); O x f or d P V 1909, 19.11, 78.3 % g i v e 28.56 % (28.6); p er o v s k i t e / C I GS 1768, 19.24, 72.9 % g i v e 24.80 % (24.2 \pm 0.7); p er o v s k i t e / p er o v s k i t e 2159, 16.59, 78.9 % g i v e 28.26 % (28.2), i t s minim o d u l e 2157, 14.86, 77.5 % g i v e 24.84 % (24.5), t h e 30.1 % ce l l 2200, 16.72, 81.8 % g i v e 30.09 % (30.1); p er o v s k i t e / or g ani c 2136, 14.56, 75.6 % g i v e 23.51 % (23.4); N a t u r e C o mm u ni c a t i o n s 2020, 20.22, 83.15 % g i v e 33.96 % (33.91) an d 2010, 20.2, 81.98 % g i v e 33.29 % (33.22); f or t h e 34.85 % ce l l J_{sc} = 34.85/ (1.97 \times 0.830) = 21.31 m A / c m^{2})$
Four-terminal module efficiency and module power	$η_{m o d} = \frac{\sum _{k} V _{k} I _{k} F F _{k}}{G A}$	$P = η_{m o d} G A$	$V_{k}, I_{k}, F F_{k} : v o l t a g e, c u r r e n t an d f i l l f a c t or o f t h e t o p an d b o tt o m c i r c u i t s$ $G : 1000 W / m^{2}$ $A : d es i g na t e d i l l u mina t i o n a r e a, t h e e n t r y i s t h e L O N G i f o u r - t er mina l m o d u l e o f G r ee n e t a l . (2054 c m^{2}, 110 an d 8.75 V, 0.40 an d 2.83 A, 75.4 an d 81.8 %, 25.8 \pm 2.1 %), t h e O x f or d P V m o d u l e ha s an a r e a j u s t o v er 1.6 m^{2}$ $(co m p u t e d : 110 \times 0.40 \times 0.754 = 33.18 W an d 8.75 \times 2.83 \times 0.818 = 20.26 W g i v e 53.43 W an d 26.01 % (25.8); 26.9 % o f 1.6 m^{2} i s ab o u t 430 W (O x f or d P V g a v e n o p o w er); 26.9/34.85 = 0.772 an d 24.5/26.9 = 0.911)$

Stability and Segregation

Name	Formula	Related Formulae	Variables/Constants
Photoluminescence shift and gap shift	$Δ E = h c (\frac{1}{λ} - \frac{1}{λ + Δ λ})$	$E = \frac{1239.84 eV nm}{λ}$	$Δ E : s hi f t o f t h e g a p$ $λ : w a v e l e n g t h o f t h e p h o t o l u min esce n ce p e ak$ $Δ λ : r e d - s hi f t, N a t u r e C o mm u ni c a t i o n s r e p or t s f or t h e 1.68 e V R b_{0.05} C s_{0.1} F A_{0.85} P b (I_{0.75} B r_{0.25})_{3} f i l m a r e d - s hi f t o f ab o u t 35 nm f or t h e co n t r o l an d a n e g l i g ib l e o n e f or t h e t r e a t e d f i l m a f t er 80 min u t es a t 2 s u n s$ $(co m p u t e d : 1.68 e V i s 738 nm, a s hi f t o f 35 nm m o v es t h e p e ak t o 773 nm, 1.604 e V, a d r o p o f 76 m e V; t h e t o p ce l l w i t h a 1.60 e V g a p w o u l d ha v e t h e c u r r e n t s 25.47 an d 18.34 m A / c m^{2} an d a t an d e m e f f i c i e n cy o f 36.25 % in s t e a d o f 42.11 %)$
Retention of a tandem under stress	$R (t) = \frac{η ( t )}{η ( 0 )}$	$T_{90} : R (T_{90}) = 0.90$	$R : r e t ain e d f r a c t i o n$ $T_{90} : t im e t o 90 %, t h e t an d e m o f N a t u r e C o mm u ni c a t i o n s r e a c h es T_{90} = 1135 h a t 1 s u n an d 65 C (I S O S - L - 2, e n c a p s u l a t e d, t r a c k in g a t 1500 mV), t h e w i d e - g a p ce l l T_{80} > 3200 h, M D P I l i s t s 95 % a f t er 300 h in ambi e n t ai r (u n e n c a p s u l a t e d), 95.43 % a f t er 1000 h in ni t r o g e n, 96 % a f t er 1068 h u n d er A M 1.5 G (e n c a p s u l a t e d) an d 89 % a f t er 1000 h u n d er co n t in u o u s l i g h t$ $(co m p u t e d : a l oss o f 10 % in 1135 h i s 0.0088 % p er h o u r; 95.43 % a f t er 1000 h i s 0.0046 % p er h o u r; 96 % a f t er 1068 h 0.0037 % p er h o u r; 89 % a f t er 1000 h 0.011 % p er h o u r; t h e s in g l e F A P b I_{3} ce l l o f p a g e 89 l os t l ess t han 1 % in 4500 h, b e l o w 0.0002 % p er h o u r)$

Important Questions

Ques: What is the perovskite-silicon record: 34.2, 34.6, 34.85 or 35 %?

Green et al. (version 64) list 34.2 ± 1.0 % for LONGi (ESTI, April 2024, 1.0044 $c m^{2}$ ). LONGi reports 33.9 % in November 2023, 34.6 % in 2024 and 34.85 % certified by NREL on 16 April 2025 (1.97 V, 83.0 %, area not given). The date of the 34.6 % is June 2024 in the LONGi release and September 2024 in pv magazine, which links it to a Nature paper. MDPI says 34.9 % certified in 2025 but its table stops at 33.89 % and Fluxim mentions an unconfirmed claim of about 35 %. These are successive records of one group, so 34.2 % is the value at the time of the table, and 34.85 % is the more likely current certified figure. The current density implied is 21.31 mA/ $c m^{2}$ (computed), but no area is stated, so the comparison with 34.2 % is open. 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); LONGi news release ‘34.85%! LONGi Breaks World Record for Crystalline Silicon-Perovskite Tandem Solar Cell Efficiency Again’ (16 April 2025); pv magazine Australia, ‘Longi achieves 34.85% efficiency for two-terminal tandem perovskite solar cell’ (22 April 2025); ‘A Review on Perovskite/Silicon Tandem Solar Cells: Current Status and Future Challenges’, Energies 18(16), 4327 (2025) (page cut off in Section 3.2); Fluxim, ‘Highest Perovskite Solar Cell Efficiencies (2026 Update)’; Wikipedia, ‘Perovskite solar cell’.

Ques: Is the tandem limit 41, 43, 45.3 or 46 %?

MDPI gives 41 % for an ideal tandem in its introduction and ‘approaching 46 %’ for a two-terminal tandem in its second section, LONGi cites 43 %, and Wikipedia gives 45.3 % for a perovskite-silicon tandem. The conditions are not stated. My detailed-balance calculation for AM1.5G at 298.15 K, with a 1.12 eV silicon cell and the best top gap of 1.729 eV, gives 44.39 % for emission from both faces and 45.15 % with a rear mirror (computed). The 45.3 % agrees with the mirror case, and 46 % is close to it. The values of 41 and 43 % probably include realistic silicon, because Auger recombination lowers the silicon limit to about 29.4 % (MDPI) from my 32.73 % (computed). I take 44 to 45 % as the detailed-balance limit and 41 to 43 % as the practical one (my reading). Reference: ‘A Review on Perovskite/Silicon Tandem Solar Cells: Current Status and Future Challenges’, Energies 18(16), 4327 (2025) (page cut off in Section 3.2); LONGi news release ‘34.85%! LONGi Breaks World Record for Crystalline Silicon-Perovskite Tandem Solar Cell Efficiency Again’ (16 April 2025); Wikipedia, ‘Perovskite solar cell’; Solar Cell Fundamentals page of this vault.

Ques: What is the best top-cell gap: 1.65-1.75, 1.68 or 1.73 eV?

MDPI gives a window of 1.65 to 1.75 eV for two-terminal current matching and 1.73 eV as the near-ideal partner of 1.1 eV silicon, but its table also lists 1.62, 1.63 and 1.8 eV, outside the window. Wikipedia gives 1.6 to 1.8 eV, Nature Communications uses 1.68 eV and the records in the table use 1.68 and 1.69 eV. My model gives the best top gap as 1.729 eV for a 1.12 eV silicon cell, with 44.39 %, against 42.11 % at 1.68 eV, because the silicon limits the current at 1.68 eV (20.75 against 23.06 $mA/c m^{2}$ , computed). The loss is 2.3 points, but a wider gap needs more bromine and more segregation, so 1.68 eV is a compromise, and 1.73 eV is the ideal. Real silicon has a higher optimum. Reference: ‘A Review on Perovskite/Silicon Tandem Solar Cells: Current Status and Future Challenges’, Energies 18(16), 4327 (2025) (page cut off in Section 3.2); ‘Uniform phase distribution of wide bandgap perovskite for high-performance perovskite-silicon tandem solar cells’, Nature Communications (2025), DOI 10.1038/s41467-025-66480-7; Wikipedia, ‘Perovskite solar cell’.

Ques: Is the record tandem voltage 2.04, 2.02, 1.99 or 1.92 V?

MDPI’s table lists 2.04 V (2022) as the highest voltage and 2.0 V for the certified 32.5 % cell, while its text calls 1.92 V a record. Nature Communications gives 2.02 V (lab) and 2.01 V (certified), Green et al. 1.990 V for the 34.2 % cell and pv magazine 1.97 V for the 34.85 % cell. The 1.92 V is an older value, and 2.04 V belongs to a cell of lower efficiency, since a higher voltage does not guarantee a higher efficiency. The radiative sum for 1.68/1.12 eV is 2.2248 V (computed), so 1.99 V is 0.894 of it and 2.04 V would be 0.917 (computed). The values are most likely all correct for different cells, and the record cells have 1.97 to 2.02 V. A voltage record cell has a lower current (14.34 $mA/c m^{2}$ for the 2.04 V entry). Reference: ‘A Review on Perovskite/Silicon Tandem Solar Cells: Current Status and Future Challenges’, Energies 18(16), 4327 (2025) (page cut off in Section 3.2); ‘Uniform phase distribution of wide bandgap perovskite for high-performance perovskite-silicon tandem solar cells’, Nature Communications (2025), DOI 10.1038/s41467-025-66480-7; 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); pv magazine Australia, ‘Longi achieves 34.85% efficiency for two-terminal tandem perovskite solar cell’ (22 April 2025).

Ques: What module efficiency has been reached: 24.5, 25, 25.8, 26.9 or 28.6 %?

Oxford PV reported 25 % for an industrial-size module in January 2024, 26.9 % for a 60-cell module of just over 1.6 $m^{2}$ (Fraunhofer CalLab, June 2024) and 24.5 % for the 72-cell modules it shipped in September 2024. Green et al. list 28.6 ± 1.4 % for an Oxford PV cell of 258.14 $c m^{2}$ total area (May 2023) and 25.8 ± 2.1 % for a LONGi four-terminal module of 2054 $c m^{2}$ . The values refer to different sizes, cell counts and terminal schemes. The product of the module parameters gives 26.01 % (computed), within its uncertainty. A 60-cell record of 26.9 % is 0.772 of the 34.85 % cell, and the shipped product is 0.911 of the record module (computed). For commercial modules 24.5 % is the more likely level, and 26.9 % the demonstrated record. Reference: Oxford PV news release on the 26.9 % module (19 June 2024); TaiyangNews, ‘Oxford PV has started commercial delivery of its tandem solar modules’ (5 September 2024); 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: Is a two-terminal or a four-terminal tandem better?

MDPI says that a four-terminal tandem needs more electrodes, adds parasitic absorption and raises the cost, and the cell records of Green et al. and of LONGi are two-terminal, while the module record read here (25.8 %) is four-terminal. In my detailed-balance model the four-terminal value is 44.10 % at 1.68 eV against 42.11 % for two terminals, and the optima are 44.58 % (1.81 eV) and 44.39 % (1.729 eV) (computed). The difference at the practical gap comes from the current mismatch, not from the junction, and it vanishes at the matching gap. A two-terminal cell is cheaper to wire, and a four-terminal one tolerates changes of the spectrum and any gap (background knowledge). The sources give no direct comparison at equal conditions, and I consider two terminals more likely for products and four terminals for flexibility (my reading). Reference: ‘A Review on Perovskite/Silicon Tandem Solar Cells: Current Status and Future Challenges’, Energies 18(16), 4327 (2025) (page cut off in Section 3.2); 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); III-V Multi-Junction Solar Cell page of this vault.

Ques: How stable is a perovskite-silicon tandem: 300, 1000 or 1135 hours?

Nature Communications reports T $_{90}$ of 1135 h at 1 sun and 65 C for an encapsulated tandem (tracking at 1500 mV) and T $_{80}$ above 3200 h for the wide-gap single-junction cell. MDPI lists 95 % after 300 h in ambient air, 95.43 % after 1000 h in nitrogen, 96 % after 1068 h under AM1.5G (encapsulated) and 89 % after 1000 h of continuous light. The loss rates are 0.0167, 0.0046, 0.0037 and 0.011 % per hour for the MDPI results and 0.0088 for the T $_{90}$ (computed), about fourfold apart. The FAPbI $_{3}$ cell of page 89 lost under 1 % in 4500 h, so the wide-gap tandem is less stable. Silicon is expected to last 25 years, so about 1000 h is far from the target. The 96 % encapsulated result is the more likely best, and none has an outdoor test (the sources give none). Reference: ‘Uniform phase distribution of wide bandgap perovskite for high-performance perovskite-silicon tandem solar cells’, Nature Communications (2025), DOI 10.1038/s41467-025-66480-7; ‘A Review on Perovskite/Silicon Tandem Solar Cells: Current Status and Future Challenges’, Energies 18(16), 4327 (2025) (page cut off in Section 3.2); Perovskite Solar Cell page of this vault.

Ques: Which silicon bottom cell is best: heterojunction, TOPCon or PERC?

MDPI’s table shows heterojunction bottom cells with the highest efficiencies (33.89 % in 2024 with 1.98 V and 20.86 $mA/c m^{2}$ ), TOPCon cells at 31.32 % and 30.36 % (2025), 29.2 % and 28.2 %, a PERC cell of 28.81 % and an older back-surface-field cell of 21.19 %. The text and the table disagree on the type of two cited cells (one described as TOPerc is listed as heterojunction, another described as homojunction as TOPCon). Nature Communications uses a heterojunction cell and says that its quality limited the tandem. Heterojunction cells give high voltage and a flat surface (background knowledge) and are the more likely best bottom cell, with TOPCon close. The best silicon single-junction value is 27.81 % (LONGi HIBC, ISFH) or 27.8 % (MDPI) against 27.1 % in Wikipedia, so the 34.85 % tandem is 1.25 times the 27.81 % (computed). Reference: ‘A Review on Perovskite/Silicon Tandem Solar Cells: Current Status and Future Challenges’, Energies 18(16), 4327 (2025) (page cut off in Section 3.2); ‘Uniform phase distribution of wide bandgap perovskite for high-performance perovskite-silicon tandem solar cells’, Nature Communications (2025), DOI 10.1038/s41467-025-66480-7; LONGi news release ‘34.85%! LONGi Breaks World Record for Crystalline Silicon-Perovskite Tandem Solar Cell Efficiency Again’ (16 April 2025); Wikipedia, ‘Multi-junction solar cell’.

Ques: How much bromine and what gap shift are tolerable?

MDPI says that wide-gap perovskites for tandems have more than 20 % bromine, that organic-cation compositions need 25 to 30 % for the gap of 1.68 eV, and that all-inorganic CsPb(I $_{1 - x}$ Br $_{x}$ ) $_{3}$ reaches 1.7 eV with less than 20 %. Zhu et al. (page 89) state that segregation begins above about 20 % bromine, or 20 to 33 % in another passage. Nature Communications uses 25 % bromine with rubidium and caesium (1.68 eV), and the untreated film shifts its photoluminescence by about 35 nm in 80 minutes at 2 suns, which is 76 meV (computed). In my model a gap of 1.60 eV instead of 1.68 eV reduces the tandem from 42.11 to 36.25 % (computed). The 20 % figure is the onset threshold and 25 to 30 % the practical level for organic cations; the sources give no single limit. Reference: ‘A Review on Perovskite/Silicon Tandem Solar Cells: Current Status and Future Challenges’, Energies 18(16), 4327 (2025) (page cut off in Section 3.2); ‘Uniform phase distribution of wide bandgap perovskite for high-performance perovskite-silicon tandem solar cells’, Nature Communications (2025), DOI 10.1038/s41467-025-66480-7; Perovskite Solar Cell page of this vault.

Ques: How does the efficiency depend on the area: 1 cm2, 20 mm square or 258 cm2?

Green et al. give 1.0044 $c m^{2}$ for the 34.2 % cell and 258.14 $c m^{2}$ for the 28.6 % Oxford PV cell, LONGi gives no area for 34.85 %, MDPI lists 1 cm $^{2}$ cells of 29.3 and 28.4 %, and the Nature Communications paper reports a 20 mm by 20 mm silicon wafer without a separate active area. The wide-gap single-junction cell there is 0.108 $c m^{2}$ with a 0.0725 $c m^{2}$ mask. The efficiency falls from 34.2 % at 1 $c m^{2}$ to 28.6 % at 258 $c m^{2}$ and 26.9 % for a module (computed ratio 0.836 and 0.787 to the 34.2 %). The fill factor of the large cell is 0.891 of the ideal value, against 0.943 for the small one (computed), which suggests resistance and uniformity as the main causes (my reading). Mask areas are not cell areas, so the records are not directly comparable. 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); ‘Uniform phase distribution of wide bandgap perovskite for high-performance perovskite-silicon tandem solar cells’, Nature Communications (2025), DOI 10.1038/s41467-025-66480-7; ‘A Review on Perovskite/Silicon Tandem Solar Cells: Current Status and Future Challenges’, Energies 18(16), 4327 (2025) (page cut off in Section 3.2); LONGi news release ‘34.85%! LONGi Breaks World Record for Crystalline Silicon-Perovskite Tandem Solar Cell Efficiency Again’ (16 April 2025).

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Perovskite-Silicon Tandem Solar Cell