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Bandgap and Composition Design Explained | Perovskite Solar Cells

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Bandgap and Composition Design
— “mix it and you can dial in any value”, and the wall that lies beyond

One of the strengths of perovskites is that simply changing the ratio of halides or metals shifts the absorption edge continuously. Yet it turned out that widening the bandgap by adding bromine lets the composition separate under nothing more than illumination. This article starts by calculating the theoretical optimum ourselves, then lays out, in materials terms, the “dials” of composition design and where they run out.

Built from primary sources: our own calculation using the ASTM G173 standard spectrum (distributed by NLR), NLR (formerly NREL) and the efficiency tables, and peer-reviewed papers / Last updated September 2026

Conceptual image of a row of small plain glass pieces on a dark surface, each carrying a thin film whose colour shifts step by step from dark brown through reddish brown to orange
AI-generated concept image. An impression of the idea that changing the composition changes the range of light absorbed, and so the colour of the film. It does not show real samples or any actual correspondence between composition and colour.
What this article covers
  1. What the bandgap is, in three points
  2. Our calculation: what is the theoretical optimum in eV?
  3. What sets the bandgap: the orbitals of lead and iodine
  4. Three dials of composition design: X, B and A
  5. A materials engineer's view (1): mix Sn and Pb and the gap narrows below both ends
  6. The wall on the wide side: halides that separate under light
  7. Our calculation: how much voltage does a 1.74 eV cell lose?
  8. A materials engineer's view (2): designing not just the composition but its ability to stay mixed
  9. The values tandems call for
  10. Strengths, weaknesses and open issues
  11. Glossary / References / Claim-to-source audit
How claims are labelled in this article

Sourced = stated in published material or a peer-reviewed paper (link given)
Our calculation = a value this article derived from assumptions it states
Not yet confirmed = a plan or target with no confirmed track record
Structural readings and materials-design interpretations are marked separately as Commentary.

1. What the bandgap is, in three points

  • What it decides: the long-wavelength limit of the light a semiconductor can absorb. Photons with less energy than the bandgap Eg (eV) are not absorbed. In wavelength terms, λ (nm) ≈ 1240 ÷ Eg (our commentary)
  • Why there is an optimum: a narrower Eg collects more photons and so more current, but each photon yields less voltage. Shockley and Queisser derived the limiting efficiency under ideal conditions, allowing only radiative recombination, as a function of EgSourced
  • What perovskites allow: through the halide ratio, the bandgap of MAPb(BrxI1−x)3 has been reported to vary continuously over 1.6 to 2.3 eV, and that of FA-based compositions over 1.48 to 2.23 eVSourced
The single most important line in this article

A perovskite's bandgap is set by how it is mixed, but that mixture is not guaranteed to survive once light falls on it. Hoke and colleagues reported that when bromine-containing films were illuminated at around 1 sun, iodide-rich regions appeared in under a minute and the emission became pinned at 1.68 eVSourced. Composition design is two problems: making the target value, and keeping it (our commentary).

2. Our calculation: what is the theoretical optimum in eV?

We calculated the upper efficiency limit of an ideal single-junction solar cell from the standard solar spectrum. The spectrum is the ASTM G173-03 AM1.5G spectrum (global, on a 37° tilted surface) distributed by NLR (the National Laboratory of the Rockies, formerly the US National Renewable Energy Laboratory)Sourced.

Our calculation: the detailed-balance limit
  • Assumption: every photon above Eg is absorbed and yields one electron (step-function absorption)
  • Assumption: radiative recombination only (the ideal Shockley–Queisser condition). Cell temperature 25 °C (298.15 K). The dark current is taken from blackbody radiation at the same temperature
  • Assumption: the incident light is the ASTM G173 AM1.5G spectrum (about 1,000 W/m² when integrated)
  • Jsc is the integral of photons above Eg; the voltage is swept to find the maximum power point

Result: the limiting efficiency peaks at about 33.7% near Eg = 1.34 eVOur calculation. Shockley and Queisser's original 1961 paper treated the sun and the cell as blackbodies at 6000 K and 300 K and gave a maximum of 30% at 1.1 eVSourced. The values differ because this article uses a real spectrum that has passed through the atmosphere (AM1.5G).

Assumptions and limits: real cells add non-radiative recombination, reflection, parasitic absorption and resistive losses, and fall short of this value. Use it as a guide to which bandgap gives the highest ceiling.

Bandgap and the single-junction efficiency limit (our calculation) AM1.5G (ASTM G173), 25 °C, detailed-balance model with radiative recombination only 30%20%10%0% 1.01.21.4 1.61.82.0 2.2 Bandgap (eV) 1 2 3 4 Marked points (limit) 1.25 eV: 33.1% Range of Sn–Pb mixtures 1.34 eV: 33.7% (maximum) Optimum in our calculation 1.48 eV: 32.4% Reported value for FAPbI3 1.74 eV: 28.4% For Si tandem top cells Note: spectrum is ASTM G173-03 as distributed by NLR [Ref. 2]. The curve and point values are all our calculation, not published. Note: what each bandgap represents follows Hao et al. [Ref. 7], Eperon et al. [Ref. 5] and McMeekin et al. [Ref. 8].
Fig. 1 Drawing that includes our calculation (vector drawing). The AM1.5G spectrum is ASTM G173-03 as distributed by NLR [Ref. 2]; the approach follows Shockley and Queisser [Ref. 1]. The curve and the point efficiencies (33.7% and the rest) were calculated by this article and are not published figures. The small wiggles in the curve come from atmospheric absorption bands in the spectrum.
Eg (eV)Absorption edge (nm)Current ceiling Jsc (mA/cm²)Efficiency limitLink to the text
1.2599237.633.1%Sn–Pb mixtures (Section 5)
1.3492535.033.7%Optimum in our calculation
1.4883829.732.4%FAPbI3 (Eperon et al.)
1.5580027.331.5%Around MAPbI3 (Eperon et al., Hao et al.)
1.7471321.428.4%Top cell for Si tandems (McMeekin et al.)
2.0062014.622.9%Bromine-rich compositions

Wavelengths, currents and efficiencies are all Our calculation (assumptions in the box above). The pairing of compositions and bandgaps in the right-hand column uses values reported in the papers [Refs. 5, 7 and 8].

3. What sets the bandgap: the orbitals of lead and iodine

From photoelectron spectroscopy and calculations, Umebayashi and colleagues reported that in CH3NH3PbI3 the top of the valence band consists mainly of σ-antibonding states of Pb 6s and I 5p, and the bottom of the conduction band mainly of σ-antibonding states of Pb 6p and I 5sSourced. In other words, the band edges are built by the B site (lead) and the X site (iodine); the organic cation on the A site does not contribute directly to them (our commentary).

The band edges are made of B and X orbitals (conceptual) Top = conduction band, bottom = valence band. The vertical gap is the bandgap. Only relative sizes are shown Reference: MAPbI3 X replaced by Br B replaced by Sn Conduction band: Pb 6p + I 5s Valence band: Pb 6s + I 5p Eg about 1.55 eV wider Edge moves to shorter wavelengths narrower Edge moves to longer wavelengths Note: orbitals from Umebayashi et al. [Ref. 3]; widening with Br and narrowing with Sn from Hoke et al. [Ref. 6] and Hao et al. [Ref. 7]. Note: the figure does not show which band edge moves by how much. Band positions and gaps are schematic, not real energies. Note: about 1.55 eV is the value for MAPbI3 given by Hao et al. [Ref. 7].
Fig. 2 Concept diagram (vector drawing). The orbital make-up of the band edges follows Umebayashi et al. [Ref. 3]; the direction in which substitution widens or narrows the bandgap follows Hoke et al. [Ref. 6] and Hao et al. [Ref. 7]. Band positions and spacing are schematic and do not represent actual energy levels.

4. Three dials of composition design: X, B and A

DialWhat changesReported effectSource
X (halide)I to Br ratioContinuous tuning over 1.6 to 2.3 eV in MAPb(BrxI1−x)3. More Br moves the absorption edge to shorter wavelengthsHoke et al.
X (halide)I to Br ratio in FA compositions1.48 to 2.23 eV in FA lead trihalides. A planar cell of 14.2% with 1.48 eV FAPbI3Eperon et al.
X (halide)I to Br ratio in MA compositionsColour changes covering almost the whole visible range. Cell efficiency of 12.3%Noh et al.
B (metal)Sn to Pb ratioDoes not follow a straight line between the end members (MAPbI3 1.55 eV, MASnI3 1.35 eV); mixtures fall below 1.3 eV. Absorption extends to about 1,050 nmHao et al.
A (cation)Choice of MA or FA, and adding CsSwitching MA to FA narrows the gap to the FA minimum of 1.48 eV (Eperon et al.). FA0.83Cs0.17Pb(I0.6Br0.4)3 gives about 1.74 eV with a photostable compositionEperon et al. / McMeekin et al.
A and BFour iodides: MA or FA with Sn or PbDirect gaps spread over 1.25 to 1.75 eV. Sn–Pb solid solutions form across the whole composition rangeStoumpos et al.

All Sourced (Hoke et al. [Ref. 6], Eperon et al. [Ref. 5], Noh et al. [Ref. 9], Hao et al. [Ref. 7], McMeekin et al. [Ref. 8], Stoumpos et al. [Ref. 4]).

Bandgap ranges reported for each composition Bars = tuning ranges reported in the papers. Dashed lines = reference values used in the text 1.21.41.6 1.82.02.2 2.35 eV 1.34 optimum 1.68 segregation about 1.75: Si tandem top cell MAPb(Br,I)3 FAPb(Br,I)3 MASn(1−x)Pb(x)I3 <1.3 AMI3 (A = MA, FA / M = Sn, Pb) FA0.83Cs0.17Pb(I0.6Br0.4)3 about 1.74 eV Note: ranges reported by Hoke [Ref. 6], Eperon [Ref. 5], Hao [Ref. 7], Stoumpos [Ref. 4] and McMeekin [Ref. 8] and colleagues. Note: Sn–Pb mixtures are reported to go below 1.3 eV, but no lower bound is given, so that part is drawn pale. Note: 1.34 eV is our calculated optimum, 1.68 eV the emission under segregation, about 1.75 eV McMeekin et al.'s guide value.
Fig. 3 Concept diagram (vector drawing). Each composition's range places values reported in the papers [Refs. 4 to 8] on the horizontal axis; they were not measured under the same conditions. The 1.34 eV value comes from this article's calculation (Section 2). The pale part of the Sn–Pb bar is schematic, because no lower bound has been reported.

5. A materials engineer's view (1): mix Sn and Pb and the gap narrows below both ends

A materials engineer's view: a broken Vegard's law became a design tool

In designing alloys and solid solutions, the first rule of thumb that comes to mind is that mixing two components moves a property linearly between the two ends (Vegard's law). Hao and colleagues reported that the bandgap of CH3NH3Sn1−xPbxI3 does not run in a straight line between the end members, 1.55 eV (Pb) and 1.35 eV (Sn), and that the mixtures fall below 1.3 eVSourced. Absorption extends into the near infrared to about 1,050 nm, and the half-and-half Sn–Pb composition gave the broadest absorption and a short-circuit current of about 20 mA/cm²Sourced.

Narrower than either end is a value that linear interpolation can never produce. Applying the Section 2 calculation, the limiting efficiency at 1.25 eV is about 33.1%, higher than about 31.5% at 1.55 eVOur calculation. And in all-perovskite tandems, discussed in Section 9, the bottom cell needs a narrow bandgap, which is where this bowing pays off (our commentary).

Adding Sn, however, brings a different problem. Stoumpos and colleagues report that Sn compounds oxidise readily, becoming p-type through Sn⁴⁺ doping and showing metallic conductivitySourced. Freedom in the bandgap is bought at the price of chemical stability. See our explainer on tin-based perovskites for details.

6. The wall on the wide side: halides that separate under light

The most straightforward way to widen the bandgap is to add more bromine. Hoke and colleagues, however, started from earlier reports that in bromine-containing films the open-circuit voltage does not rise even though the bandgap widens (a voltage drop for x > 0.25), and set out to find the causeSourced.

  • What happened: under continuous illumination, MAPb(BrxI1−x)3 films with 0.2 < x < 1 developed a new emission peak at about 1.68 eV regardless of composition, which grew within a minute even at less than 1 sunSourced
  • Structurally: X-ray diffraction peaks split, suggesting separation into minority iodide-rich regions (x ≈ 0.2) and majority regions slightly richer in bromineSourced
  • Reversibility: after a few minutes in the dark, the emission, absorption and diffraction patterns returned to their original stateSourced
  • What it means: the authors propose that light moves halide ions, and that the narrower-gap iodide-rich regions act as recombination centres, pinning the emission and the open-circuit voltage at low valuesSourced
Under light the halides separate; in the dark they remix (conceptual) Each square = local composition. Darker = more iodide (narrower bandgap) light dark 1 Mixed state 2 Illuminated (<1 min) 3 A few minutes dark Uniform composition Sharp absorption edge Iodide-rich regions (x ≈ 0.2) Emission pinned near 1.68 eV Returns to the original mixed state (reversible) Note: each stage follows the report by Hoke et al. [Ref. 6] (MAPb(Br,I)3 films with 0.2 < x < 1). Note: the number, size and layout of the squares are schematic and do not show real domain sizes or distributions. Note: as the driving force, the authors hypothesise that photogenerated holes collect in the iodide-rich regions.
Fig. 4 Concept diagram (vector drawing). Each stage follows the description by Hoke et al. [Ref. 6]. The number and layout of the squares are entirely schematic and do not represent a real composition map or micrograph. The division into three stages is this article's own framing.

7. Our calculation: how much voltage does a 1.74 eV cell lose?

McMeekin and colleagues reported a cell using FA0.83Cs0.17Pb(I0.6Br0.4)3 with an optical bandgap of about 1.74 eV, an open-circuit voltage of 1.2 V, over 17% on a small area and 14.7% on 0.715 cm²Sourced. We compare that voltage with the open-circuit voltage of the same ideal model used in Section 2.

Our calculation: the open-circuit voltage “loss”
  • Open-circuit voltage in the ideal model: with Eg = 1.74 eV, AM1.5G, 25 °C and radiative recombination only, about 1.46 VOur calculation
  • Gap to the reported value: 1.46 − 1.2 = about 0.26 V, i.e. about 82% of the ideal (1.2 ÷ 1.46)Our calculation
  • Gap to the bandgap: 1.74 − 1.2 = 0.54 VOur calculation

Assumptions and limits: the ideal open-circuit voltage is calculated on the same assumptions as Section 2. The reported 1.2 V is the value stated in the paper's abstract; this article does not separate out whether segregation occurred or how much it contributed. How much of the gap is due to halide segregation cannot be told from this calculation.

A cell with a bandgap of about 1.74 eV: voltages compared (includes our calculation) Bar length = voltage (V). The higher the bar, the closer to the theoretical ceiling Eg/q 1.74 V Ideal-model Voc about 1.46 V Reported Voc 1.2 V about 82% of the ideal Note: 1.74 eV and 1.2 V from McMeekin et al. [Ref. 8]; about 1.46 V and 82% are our calculation (Section 2 assumptions). Note: bars drawn at 1 V = 250 px. The breakdown of the gap (segregation, interfaces, defects and so on) is not shown.
Fig. 5 Drawing that includes our calculation (vector drawing). The 1.74 eV and 1.2 V are published values from McMeekin et al. [Ref. 8]. The ideal-model open-circuit voltage (about 1.46 V) and the ratio (about 82%) were calculated by this article and are not published figures. The breakdown of the difference is not shown.

8. A materials engineer's view (2): designing not just the composition but its ability to stay mixed

A materials engineer's view: an unusual solid solution that phase-separates under light

Phase separation in a solid solution normally takes heat treatment or long holding times. In halide perovskites, however, the composition separates at room temperature, under nothing more than light, within a minute, and remixes after a few minutes in the darkSourced (Hoke et al.). Diffusion this fast shows how easily halide ions move through the lattice (our commentary).

The phenomenon turns composition design into a two-stage task.

  • Stage one: choose a composition that gives the target bandgap (the dials of Section 4)
  • Stage two: make sure the composition stays mixed during operation (crystallinity, A-site composition, treatment of defects and grain boundaries)

McMeekin and colleagues demonstrated a 1.74 eV material in a mixed FA–Cs system that is “highly crystalline” and compositionally photostableSourced. Its bromine fraction is 0.4, inside the range where Hoke and colleagues observed segregation (0.2 < x < 1)Sourced. One reading is therefore that keeping bromine at or below 0.2 is not the only answer; at the same bromine fraction, behaviour can change with crystal quality and the A site (our commentary).

The lesson for materials suppliers is that a composition sheet (what, at what percentage) does not by itself make a material specification. If the same nominal composition can differ in its ability to stay mixed depending on precursor purity, crystallisation conditions and additives, then the stability of the emission spectrum and diffraction under illumination needs to be considered as an incoming-inspection metric (our commentary). The mechanism by which ions move is covered in our explainer on ion migration and degradation.

Conceptual image of plain square glass pieces laid out in a grid on a dark surface, each carrying a thin film whose colour steps from dark brown through reddish brown to orange
Fig. 6 AI-generated concept image. An impression of composition screening, in which samples with gradually changed compositions are laid out for comparison. It does not show any correspondence between colour, composition and bandgap, nor the appearance of real samples.

9. The values tandems call for

Separate from the single-junction optimum (about 1.34 eV in Section 2), tandems, which stack two cells, require a different bandgap for each of the upper and lower cells.

  • Tandems with silicon: McMeekin and colleagues put the optimum optical bandgap of a perovskite top cell paired with silicon at about 1.75 eVSourced. Efficiency tables Version 68 lists 35.2% (LONGi, measured by ESTI) for a two-terminal perovskite/silicon tandem cell of about 1 cm²Sourced
  • All-perovskite tandems: the bottom cell needs a narrow bandgap, and the Sn–Pb mixtures of Section 5 are candidates (our commentary). The same tables list two-terminal perovskite/perovskite tandems at 28.2% on 1.038 cm² and 30.1% on a small area of 0.0493 cm²Sourced

Tandems are covered in detail in our explainers on silicon–perovskite tandems and on all-perovskite tandems.

10. Strengths, weaknesses and open issues

AspectStrength (confirmed in primary sources)Weakness or issue
Tuning rangeContinuous tuning up to roughly 1.48 to 2.3 eV via the halide ratio (Eperon et al., Hoke et al.)Light-induced segregation on the bromine-rich side (Hoke et al.)
Narrow sideSn–Pb mixing goes below 1.3 eV, absorbing to about 1,050 nm (Hao et al.)Sn oxidation readily makes the material p-type (Stoumpos et al.)
Wide sidePhotostable about 1.74 eV with FA–Cs mixing (McMeekin et al.)Open-circuit voltage about 82% of the ideal modelOur calculation
Absorption edgeSharp, with an absorption coefficient above 1×10⁴ cm⁻¹ at 0.1 eV above the bandgap (Hoke et al.)At x = 0.5 the absorption onset is more gradual (Hoke et al.)

Each item is Sourced (source in brackets), except “about 82%”, which is our calculation. Sorting them into strengths and weaknesses is this article's own framing.

(1) Long-term compositional stability is not assessed in this article

The segregation reports described here are observations over minutes to tens of minutes. How the composition changes after years of illumination outdoors could not be established from generalisable primary sources within the scope of this article.

(2) Composition and colour do not map one to one

The colour of a film depends not only on the bandgap but also on thickness and scattering. Composition or bandgap cannot be judged from the colour of a film (our commentary).

The article in summary
  • The theoretical single-junction optimum is about 1.34 eV, at about 33.7%Our calculation
  • The band edges are built from lead and halide orbitals, so changing X and B moves the bandgapSourced
  • Mixing Sn and Pb gives a gap below 1.3 eV, narrower than either endSourced
  • With bromine mixed in, light separates the halides within a minute and pins the emission at 1.68 eVSourced
  • The 1.2 V open-circuit voltage of a 1.74 eV cell is about 82% of the idealOur calculation
  • Composition design has two stages: making the value and keeping it (our commentary)

11. Glossary

Bandgap (Eg)
The energy difference between the top of the valence band and the bottom of the conduction band. Light with less energy is not absorbed.
Shockley–Queisser limit
The upper efficiency limit of a single-junction solar cell under ideal conditions allowing only radiative recombination. A function of the bandgap.
AM1.5G
The standard spectrum (global) of sunlight that has passed through 1.5 times the thickness of the atmosphere. Defined in ASTM G173.
Short-circuit current density (Jsc)
The current that flows when the electrodes are shorted. Its ceiling is set by the number of photons that can be absorbed.
Open-circuit voltage (Voc)
The voltage when no current flows. The less recombination, the higher it is.
Vegard's law
The rule of thumb that properties of a solid solution, such as the lattice constant, change linearly with composition.
Bowing
A bandgap in a solid solution that sags away from the straight line. In Sn–Pb systems it falls below both ends.
Halide segregation
In mixed halides, the separation into iodide-rich and bromide-rich regions under illumination or other stimuli.
Optical bandgap
A bandgap determined from the onset of the absorption spectrum.
σ-antibonding state
A high-energy orbital state formed when two atomic orbitals overlap out of phase.
Tandem
A structure that stacks cells of different bandgap so that short- and long-wavelength light are converted by different cells.
Two-terminal
A tandem format in which the upper and lower cells are connected in series and the device has only two electrodes.

12. References (primary sources)

  1. Shockley, Queisser “Detailed Balance Limit of Efficiency of p-n Junction Solar Cells”, J. Appl. Phys. 32, 510 (1961) https://doi.org/10.1063/1.1736034
  2. NLR (National Laboratory of the Rockies, formerly NREL) “Reference Air Mass 1.5 Spectra” (distributes the ASTM G173-03 tables) https://www.nlr.gov/grid/solar-resource/spectra-am1.5
  3. Umebayashi et al. “Electronic structures of lead iodide based low-dimensional crystals”, Phys. Rev. B 67, 155405 (2003) https://doi.org/10.1103/PhysRevB.67.155405
  4. Stoumpos, Malliakas, Kanatzidis “Semiconducting Tin and Lead Iodide Perovskites with Organic Cations: Phase Transitions, High Mobilities, and Near-Infrared Photoluminescent Properties”, Inorg. Chem. 52, 9019 (2013) https://doi.org/10.1021/ic401215x
  5. Eperon et al. “Formamidinium lead trihalide: a broadly tunable perovskite for efficient planar heterojunction solar cells”, Energy Environ. Sci. 7, 982 (2014) https://doi.org/10.1039/C3EE43822H
  6. Hoke et al. “Reversible photo-induced trap formation in mixed-halide hybrid perovskites for photovoltaics”, Chem. Sci. 6, 613 (2015) https://doi.org/10.1039/C4SC03141E
  7. Hao et al. “Anomalous Band Gap Behavior in Mixed Sn and Pb Perovskites Enables Broadening of Absorption Spectrum in Solar Cells”, J. Am. Chem. Soc. 136, 8094 (2014) https://doi.org/10.1021/ja5033259
  8. McMeekin et al. “A mixed-cation lead mixed-halide perovskite absorber for tandem solar cells”, Science 351, 151 (2016) https://doi.org/10.1126/science.aad5845
  9. Noh et al. “Chemical Management for Colorful, Efficient, and Stable Inorganic–Organic Hybrid Nanostructured Solar Cells”, Nano Lett. 13, 1764 (2013) https://doi.org/10.1021/nl400349b
  10. Green et al. “Solar cell efficiency tables (Version 68)”, Joule 10, 102494 (2026) https://doi.org/10.1016/j.joule.2026.102494

13. Claim-to-source audit

Claim in the textBasisLabel
That the limiting efficiency under ideal conditions allowing only radiative recombination (the detailed-balance limit) was derived as a function of bandgap. That treating the sun and the cell as blackbodies at 6000 K and 300 K gave a maximum of 30% at 1.1 eVJ. Appl. Phys. paper (abstract). Reference 1 https://doi.org/10.1063/1.1736034Sourced
That the ASTM G173-03 AM1.5G spectrum (global, 37° tilted surface) is distributed by NLR. The renaming of NREL as NLRNLR “Reference Air Mass 1.5 Spectra” page and data. Reference 2 https://www.nlr.gov/grid/solar-resource/spectra-am1.5Sourced
That in CH3NH3PbI3 the top of the valence band consists mainly of σ-antibonding states of Pb 6s and I 5p, and the bottom of the conduction band mainly of σ-antibonding states of Pb 6p and I 5sPhys. Rev. B paper (abstract). Reference 3 https://doi.org/10.1103/PhysRevB.67.155405Sourced
That four iodides of MA or FA with Sn or Pb are direct-gap semiconductors with bandgaps between 1.25 and 1.75 eV. That Sn–Pb solid solutions form across the whole composition range. That Sn compounds oxidise readily, becoming p-type through Sn⁴⁺ doping and showing metallic conductivityInorg. Chem. paper (abstract). Reference 4 https://doi.org/10.1021/ic401215xSourced
That the bandgap of FA lead trihalides can be tuned from 1.48 to 2.23 eV. A planar cell of 14.2% with the 1.48 eV material. That MA-based bandgaps are about 1.55 eV or higherEnergy Environ. Sci. paper (abstract). Reference 5 https://doi.org/10.1039/C3EE43822HSourced
That the bandgap of MAPb(BrxI1−x)3 can be tuned from 1.6 to 2.3 eV. Earlier reports of a voltage drop for x > 0.25. That for 0.2 < x < 1 an emission peak at about 1.68 eV appears within a minute under illumination, independent of composition. The splitting of X-ray diffraction peaks and the suggested iodide-rich (x ≈ 0.2) regions. Reversible recovery after a few minutes in the dark. The hypothesis that iodide-rich regions pin the emission and open-circuit voltage. An absorption coefficient above 1×10⁴ cm⁻¹ at 0.1 eV above the bandgap, with a more gradual onset at x = 0.5. The hypothesis that holes collecting in iodide-rich regions drive segregationChem. Sci. paper (full text). Reference 6 https://doi.org/10.1039/C4SC03141ESourced
That the bandgap of CH3NH3Sn1−xPbxI3 does not follow Vegard's law between the end members (1.55 eV and 1.35 eV) and falls below 1.3 eV for mixtures. That absorption extends to about 1,050 nm. The broadest absorption and a short-circuit current of about 20 mA/cm² for Sn0.5Pb0.5J. Am. Chem. Soc. paper (abstract). Reference 7 https://doi.org/10.1021/ja5033259Sourced
That the optimum optical bandgap of a top cell for a tandem with silicon is about 1.75 eV. That FA0.83Cs0.17Pb(I0.6Br0.4)3 is highly crystalline and compositionally photostable, with an optical bandgap of about 1.74 eV, an open-circuit voltage of 1.2 V, over 17% on a small area and 14.7% on 0.715 cm²Science paper (abstract). Reference 8 https://doi.org/10.1126/science.aad5845Sourced
That compositional control of MAPb(I1−xBrx)3 gave colour changes covering almost the whole visible range, and that the most efficient cell reached 12.3%Nano Lett. paper (abstract). Reference 9 https://doi.org/10.1021/nl400349bSourced
Two-terminal perovskite/silicon tandem at 35.2% (0.9994 cm², LONGi, measured by ESTI). Two-terminal perovskite/perovskite tandems at 28.2% (1.038 cm²) and 30.1% on a small area (0.0493 cm²)“Solar cell efficiency tables (Version 68)”, Joule. Reference 10 https://doi.org/10.1016/j.joule.2026.102494Sourced
Limiting efficiencies for AM1.5G, 25 °C and radiative recombination only (maximum about 33.7% at 1.34 eV; 33.1% at 1.25 eV; 32.4% at 1.48 eV; 31.5% at 1.55 eV; 28.4% at 1.74 eV; 22.9% at 2.00 eV), the current ceilings and the absorption-edge wavelengths. The ideal open-circuit voltage of about 1.46 V at 1.74 eV, the gap of about 0.26 V and ratio of about 82% to the reported 1.2 V, and the 0.54 V gap to the bandgapOur calculation, using the ASTM G173 AM1.5G spectrum (Reference 2) and assuming step-function absorption, radiative recombination only and a dark current from 298.15 K blackbody radiation. Includes the numerical parts of Figs. 1 and 5 and the Section 2 tableOur calculation
The framing that, because the band edges are built from B and X orbitals, A does not contribute directly. Reading the breakdown of Vegard's law as a design tool. The two stages of making the value and keeping it. The reading that at the same bromine fraction behaviour can change with crystal quality and the A site. The idea of including stability under illumination in incoming inspection. That composition cannot be judged from colour. The sorting into strengths and weaknessesOur summary and commentary based on published content. Not views expressed by the authors of the papersCommentary
Compositional stability under long-term outdoor illumination. The share of the open-circuit voltage gap due to halide segregationNo generalisable primary source could be confirmed within the scope of this article, and our calculation cannot separate it out, so nothing is stated (our note)Commentary
That Figs. 1 to 5 are explanatory drawings, not real measured data, energy levels or micrographs. That the hero image and Fig. 6 are AI-generated imagesOur noteCommentary

Last updated 25 September 2026. Sources are limited to primary material (peer-reviewed papers, the standard spectrum distributed by NLR, and the efficiency tables). The theoretical efficiency limits and the open-circuit voltage comparison are our own calculations on stated assumptions. Long-term outdoor compositional stability, and the share of the open-circuit voltage loss due to halide segregation, are not stated because no primary source could be confirmed. The content of papers is limited to what could be confirmed in the abstract or the openly available full text. All figures are explanatory concept graphics. Figs. 1 to 5 are vector drawings; the hero image and Fig. 6 are AI-generated images, and none of them shows real measured data or the appearance of real samples.

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