How bismuth sulphide absorbs strongly without recombining quite so quickly

Bismuth sulphide can absorb light strongly while keeping the resulting electrons and holes available for longer than a purely direct semiconductor with comparable absorption. A team led by the University of Oxford has traced that behaviour to two nearby electronic transitions, one direct and one indirect, in a Nature study of Bi₂S₃ thin films.

The result offers a way to reduce a loss that is built into a good optical absorber. Electrons and holes can recombine through the reverse of the transition that created them, emitting light before their charge can be collected. Changing where the carriers settle after excitation can slow that recombination without requiring the material to become a weak absorber.

“Our work shows that this trade-off is not inevitable,” says Laura Herz, one of the study’s senior authors. The research establishes the mechanism in a film. Getting more electrical power from a solar cell will also depend on how well the charge travels through that film and crosses its contacts.

Absorption and recombination share the same transitions

A photon can provide the energy to promote an electron across a semiconductor bandgap, but it carries little momentum compared with the separation of states in the crystal’s band structure. In a direct transition, the initial and final states line up in crystal momentum, allowing absorption without another participant. An indirect transition usually needs a phonon to account for the momentum difference, making the process less probable.

That changes how much material is needed to absorb the light. It also changes how easily an electron can return and recombine with a hole, releasing a photon. A transition that readily absorbs light can provide an equally effective route back, once the occupation of the electronic states is taken into account.

The van Roosbroeck–Shockley treatment links absorption and radiative recombination through those occupations and the radiation field. Earlier Oxford work on methylammonium lead triiodide showed how the relevant absorption spectrum could account for radiative bimolecular recombination when the free carrier transitions and distributions were treated correctly. The absorption coefficient supplies part of that calculation; the populations of electrons and holes supply the rest.

Bi₂S₃ changes the population without losing the strong optical route.

Carriers can settle below the direct transition

The new study identifies an indirect transition roughly 40 meV below the direct one. Light can be absorbed through the strong direct route, after which carriers can occupy the lower energy states. Fewer are then available to recombine through the faster direct transition. The authors call this combination pseudo-direct.

At room temperature, 40 meV is small enough for thermal energy to redistribute carriers between the nearby states. At 300 K, kBT is about 25.9 meV, giving an illustrative Boltzmann factor of exp(−40/25.9), or approximately 0.21, for that separation.

It would be tempting to multiply a direct semiconductor’s recombination coefficient by 0.21 and stop there. That would treat the bands as two individual states, ignoring their densities of states and the distributions of both electrons and holes. The calculation indicates the energy scale over which temperature can change the population; it does not reproduce the paper’s recombination model.

This is also why the material can retain direct absorption while recombining more slowly. The photon excites a transition that is readily available, while the subsequent carrier distribution reduces the rate of the reverse process. Describing the material as simply direct or indirect would miss one half of that behaviour.

The evidence goes beyond one long decay

The researchers combined optical absorption, electronic structure calculations and temperature dependent carrier measurements. Their fit gives a separation of about 38 meV, close to the calculated value. At room temperature they extract a bimolecular recombination coefficient of approximately 5 × 10⁻¹¹ cm³/s, with their model giving about 75% suppression relative to the purely direct comparison case.

Varying temperature tests whether the carriers redistribute as the proposed band arrangement predicts. Changing the excitation density helps separate recombination processes that depend differently on the number of carriers present. Together those measurements give the model more to explain than a slow decay measured at one temperature after one laser pulse.

Defect related decay remains visible on longer timescales. The lower intrinsic recombination rate therefore sits alongside other routes by which the film can lose its excited carriers.

The coefficient does not specify a single lifetime

Bimolecular recombination depends on the product of electron and hole concentrations. If the excess densities are equal, its rate term is k₂n², where k₂ has units of volume per time. The instantaneous timescale associated with that term is 1/(k₂n), so a hundredfold increase in carrier density shortens the timescale a hundredfold even with the same material coefficient.

Using k₂ = 5 × 10⁻¹¹ cm³/s and n = 10¹⁶ cm⁻³ gives 2 µs. At 10¹⁸ cm⁻³ it gives 20 ns. These are calculations for an idealised bimolecular term, not measured Bi₂S₃ device lifetimes. Defect capture, interfaces and the actual carrier distribution will alter the observed decay.

A film excited by a short laser pulse can have a very different density from a cell operating continuously under sunlight. Its electrical boundary conditions are different too. A transient experiment can isolate a recombination mechanism without recreating the operating point of a photovoltaic device, which is why the coefficient cannot simply be assigned as a lifetime for a proposed cell.

The charge still has to reach a contact

Strong absorption can allow a thin active layer. In a simple single pass model, intensity falls as I(d) = I₀ exp(−αd), with reflection and interference left out. An absorption coefficient of 10⁵ cm⁻¹ gives a 1/e absorption depth of 100 nm at a wavelength where that coefficient applies. The number cannot be extended across the solar spectrum, especially near the absorption edge where α changes.

A thinner layer shortens the journey to a contact, provided the optical stack still captures enough light. Collection then depends on transport as well as on how long the carrier remains available. In a diffusion dominated description, L = √(Dτ), where D is diffusivity and τ is lifetime. Increasing τ extends the diffusion length, but poor transport can still prevent charge from reaching the collecting interface.

Trapping complicates the picture further. A long lived charge may remain detectable in a sample while being unable to move through the device on the timescale required to deliver current. Keeping charge present and getting it out are different physical requirements.

Adding contacts introduces electric fields, interfaces and further recombination paths. The contacts must collect the desired carrier selectively while blocking an easy loss route for the opposite carrier. A favourable decay in a bare film does not reveal how those interfaces will behave once the material is made into a junction.

Device transients also need careful interpretation. Krückemeier and colleagues’ work on transient photovoltage shows how extraction, recombination and capacitive effects can contribute to measured time constants. A slower electrical response can have several causes, so the time constant has to be linked to the process that produced it before being used as evidence of improved material performance.

From a lower recombination rate to more power

The reported 75% reduction applies to the recombination coefficient in the authors’ comparison. It is not a 75% increase in cell efficiency or an improvement that can be applied to an existing panel.

Shockley and Queisser’s detailed balance calculation describes an idealised junction through the balance of absorbed and emitted radiation. A material with several nearby bands has to be treated using those states and their populations; assuming a single direct transition would leave part of the recombination physics out of the comparison.

Occupying the lower states also gives up energy. The proposed advantage is to slow an unwanted recombination route at a relatively small energy cost, preserving more charge for collection without sacrificing strong absorption. How that affects the voltage and current together will depend on the assembled cell.

Measuring its current–voltage curve under a defined illumination spectrum would bring the competing losses into the same experiment. The collected current and open circuit voltage would reveal how much of the film’s reduced intrinsic recombination survives the journey through the absorber and its interfaces.

Sources

• Righetto and colleagues: Delayed electron–hole recombination in a pseudo-direct semiconductor, Nature, 28 October 2026
• University of Oxford: research announcement and Laura Herz quotation
• Davies and colleagues: absorption and bimolecular recombination, Nature Communications, 2018
• Krückemeier and colleagues: Quantifying Charge Extraction and Recombination Using the Rise and Decay of the Transient Photovoltage, Advanced Materials, 2023
• Shockley and Queisser: Detailed Balance Limit of Efficiency of p-n Junction Solar Cells, 1961