Ultrafast self-trapping of photoexcited carriers sets the upper limit on antimony trisulfide photovoltaic devices

Antimony trisulfide (Sb2S3) is considered to be a promising photovoltaic material; however, the performance is yet to be satisfactory. Poor power conversion efficiency and large open circuit voltage loss have been usually ascribed to interface and bulk extrinsic defects By performing a spectroscopy study on Sb2S3 polycrystalline films and single crystal, we show commonly existed characteristics including redshifted photoluminescence with 0.6 eV Stokes shift, and a few picosecond carrier trapping without saturation at carrier density as high as approximately 1020 cm−3. These features, together with polarized trap emission from Sb2S3 single crystal, strongly suggest that photoexcited carriers in Sb2S3 are intrinsically self-trapped by lattice deformation, instead of by extrinsic defects. The proposed self-trapping explains spectroscopic results and rationalizes the large open circuit voltage loss and near-unity carrier collection efficiency in Sb2S3 thin film solar cells. Self-trapping sets the upper limit on maximum open circuit voltage (approximately 0.8 V) and thus power conversion efficiency (approximately 16 %) for Sb2S3 solar cells.


Supplementary Note 1. Characterization of single crystal quality
The Transmission X-Ray Laue photograph of the needle shaped Sb 2 S 3 single crystal is shown in Fig. S3a. It reveals that the obtained sample was a single crystal owing to the presence of Laue cones. In addition, the calculation result of lattice parameters a = 11.26, b = 11.33, and c = 3.85 Å with high indexing rate (92.1%, 94.7% and 89.5%, respectively), indicates high crystalline quality.
We employed the space charge-limited current (SCLC) with device structure of Ag/Sb 2 S 3 /Ag to calculate the trap state density through the following equation: 1 where ε 0 is the vacuum permittivity, ε r (= 7) is the relative dielectric constant of the Sb 2 S 3 , V TFL is the onset voltage of trap filling limited (TFL) region (see Fig. S3b), q is the elemental charge and L is the distance between two electrodes (0.5 cm). According to the equation, trap density of Sb 2 S 3 single crystal was calculated to be 6.8 × 10 9 cm -3 , which is a very low value. As a comparison, the trap density in MAPbI 3 single crystal was calculated to be 3×10 10 ~ 3×10 11 cm -3 . 2

Supplementary Note 2. Estimate Huang-Rhys parameter based on Stokes shift
The coupling between photoexcitation and lattice phonons leads to the broad and Stokes shifted PL. Therefore, we can estimate the Huang-Rhys parameter S, which describes carrier phonon coupling, based on the Stokes shift E Stokes by 3

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Based on the absorption spectrum and PL, E Stokes ~ 600 meV. Previous coherent phonon measurement on Sb 2 S 3 indicates a longitudinal optical phonon mode with a frequency of 63.74 cm-1 (~ 7.9 mV) couples to photoexcitation strongly. Based on these values, the Huang-Rhys parameter S was calculated to be 38.5, which is much larger than CdSe (1), 4 ZnSe (0.31), 5 CsPbBr 3 (3.22) 6 but similar to Cs 2 AgInCl 6 (38.7) 7 and NaCl (30) 8 where STE have been demonstrated.

Supplementary Note 3. Temperature dependent PL intensity of Sb 2 S 3 single crystal flake and thermal quenching modeling
To further confirm deeply trapped STE, we performed a temperature dependent PL measurement on Sb 2 S 3 single crystal flake. The integrated PL intensity as a function of temperature is plotted in Fig. S6a where is the lifetime of STE and 0 is the effect scattering time for thermally activated STE to upper band edge state. The latter is usually much faster than former and we choose 0 ⁄ = 10 4 in our simulation (this number does not affect the trend).

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The simulated temperature dependent PL intensity for different E a is shown in Fig.   S6b. Comparing experimental and simulated results indicates E a s for STE is larger than 400 meV, which is constant with ~ 0.6 eV Stokes shift.

Supplementary Note 4. Rate equation model for two-step carrier trapping process
In the two-step carrier trapping process, 11 where 0 is initial photoexcited carrier density.
The transient absorption signal of free carrier contains contribution from both electron and hole as ∝ + (1 − ) and their relative contribution is inversely proportional to their effective masses. For Sb 2 S 3 , hole effect mass is generally larger than electron thus <0.5. The free carrier decay kinetics at different densities ( Fig. 4b in main text) can be best replicated with ~ 0.2, ~ 0.6 ps -1 and ~ 6×10 -21 cm -3 ps -1 .