Surface Saturation Current Densities of Perovskite Thin Films from Suns-Photoluminescence Quantum Yield Measurements

We present a simple, yet powerful analysis of Suns-photoluminescence quantum yield measurements that can be used to determine the surface saturation current densities of thin film semiconductors. We apply the method to state-of-the-art polycrystalline perovskite thin films of varying absorber thickness. We show that the non-radiative bimolecular recombination in these samples originates from the surfaces. To the best of our knowledge, this is the first study to demonstrate and quantify non-linear (bimolecular) surface recombination in perovskite thin films.


Introduction
The photoluminescence quantum yield (PLQY) is an important optoelectronics measurement that can determine the implied photovoltaic quality of semiconductors [1], [2].PLQY measures the number of emitted photoluminescence (PL) photons, relative to the number of absorbed photons [3].Often, the PLQY is measured using a spectrometer [1], such that the spectral photon flux is obtained.When PLQY measurements are performed as a function of the light intensity or Suns (often named 'Suns-PLQY'), the excess carrier density, Δn, is varied providing information about the injection-dependence of the PLQY [1].
For lead-based perovskite thin films (PTFs), PLQY measurements have been used to quantify the implied open-circuit voltage, iVOC, and the iVOC deficit, ΔiVOC [1], [4]- [6].The iVOC represents the quasi-Fermi level splitting (QFLS), or the maximum possible open-circuit voltage that could be obtained if the film were converted into a solar cell [7], while ΔiVOC represents the loss in iVOC due to defect-mediated or non-radiative recombination [8].Suns-PLQY measurements have been used to quantify the non-radiative recombination of PTFs via extraction of the implied efficiency potential and ideality factor, nid [1], [9], [10].
One of the main limitations of state-of-the-art PTFs is non-radiative bimolecular recombination (NRBR) [11].NRBR refers to recombination which has the same injectiondependence or nid (nid = 1) as radiative bimolecular recombination but is mediated by defects, and hence does not produce photons (as expected in radiative recombination) [12].For context, the radiative recombination mechanism is described as "bimolecular" because each recombination event involves the recombination of a free electron with a free hole [13].NRBR in PTFs has been studied for more than half a decade, mostly using PLQY and/or time-resolved PL decay (TR-PL) measurements [11], [12], [14]- [18].However, the exact nature and spatial origin of NRBR remains elusive.Previous suggestions included trap-Auger recombination inside the bulk [12], [19], yet first principles calculations from Staub et al. demonstrated that the trap-Auger mechanism is unlikely as the required bulk defect densities, Nt, is much larger than the experimentally determined value (above 10 17 cm -3 compared to below 10 16 cm -3 ) [16].Brenes et al. subjected PTFs to light and atmospheric treatments and observed an increase in the PLQY and a concurrent decrease in the NRBR as determined from TR-PL [18].They proposed that the treatments passivate surface states thereby reducing NRBR, however, no supportive evidence has been provided.
In this study, we use Suns-PLQY measurements to quantify and determine the spatial origin of NRBR in state-of-the-art PTFs.Our analysis involves converting Suns-PLQY data to dark implied current density-voltage (iJ-V) curves and subsequent extraction of the recombination current parameter, J0, which we use to quantify NRBR.To validate the results, PTFs of the same composition but varying absorber thickness, W, were used.

Experimental Methods
To prepare the perovskite Cs0.05FA0.79MA0.16Pb(I0.83Br0.17)3precursor solution, cesium iodide (CsI, Sigma-Aldrich), formamidinium iodide (FAI, GreatCell Solar Materials), lead iodide (PbI2, TCI), methylammonium bromide (MABr, GreatCell Solar Materials), and lead bromide (PbBr2, Sigma-Aldrich) were stoichiometrically weighed and dissolved in a mixed solvent of N,Ndimethylformamide (DMF, TCl) and dimethyl sulfoxide (DMSO, Alfa Aesar) (4:1 v/v) with different concentrations: 1.1 M (thick perovskite layer), 0.74 M (intermediate layer), and 0.5 M (thin layer).Glass substrates were sequentially cleaned with detergent, deionised water, acetone, and isopropanol.After that, the cleaned glass substrates were treated with ultraviolet ozone (UVO) for 15 mins and then transferred into a nitrogen-filled glovebox.The precursor solution was spin-coated on the substrates at 2,000 rpm for 20 s, followed by 6,000 rpm for 30 s.During the spin-coating, 100 µl chlorobenzene (Sigma-Aldrich) was quickly dispensed 5 s prior to the end of the spin-coating process.The films were then annealed at 100 °C for 10 min on a hot plate, producing a dense perovskite film as indicated by secondary electron microscopy (SEM) images.For brevity, this PTF composition is denoted "Br17".Suns-PLQY measurements were carried out inside an integrating sphere (15 cm diameter, LabSphere), flushed with nitrogen gas.A green laser (LD-515-10MG, Roithner Lasertechnik) with a full-width-half-maximum (FWHM) spot size of ~778 µm was directed into the sphere via a small entrance port.An optical fiber collected the emission from the exit port of the sphere and guided it to the spectrometers (AvaSpec-2048x64TEC, Avantes).The spectral response was calibrated using a calibration lamp (HL-3plus-INT-Cal, Ocean Insight), giving a relative uncertainty of about ±3% in the spectral range of the PL emission (1.24 eV to 2.06 eV or 600 nm to 1,000 nm).Raw measured spectra were converted to power spectra by normalising for integration time.The integration time was 0.2 s for most of the measurements.The PLQY was determined using the method described by de Mello et al. [3].The samples were placed at an angle of 15° with respect to the laser beam to avoid specular reflectance toward the entrance port.To stabilise both the spectral PL magnitude and shape, the samples were light-soaked at an intensity of ~30 Suns for 3 min, after which the Suns-PLQY measurements were performed.Spectroscopy ellipsometry (SE) was used to determine the spectral absorptivity and thickness of the PTFs.An ellipsometer (M2000, J. A. Woollam) was used to measure the complex refractive index of the PTF on glass in the wavelength range of 210 to 1,000 nm.The ratio of the change in the polarisation of the light reflected from the sample was measured in ambient air at incident angles of 55°, 65°, and 75° to establish a model for the room temperature optical constants of the Br17 PTF.For this purpose, the computer software WVASEVR [ref] was used.To add an extra constraint on the ellipsometry fits, the experimental transmission spectrum of the measured samples, taken using a spectrophotometer (Lambda 1050, Perkin Elmer), was simultaneously fitted alongside the SE data.The curve fits are presented in S1 of the Supplementary Information (SI).The transfer matrix method (TMM) is used to calculate the PTF spectral absorptivity [20].The thicknesses determined from the spectroscopy ellipsometry and transmission (SE/T) are summarised in Table 1.

Analysis Methods
The PLQY is defined as the ratio of emitted PL photons to the absorbed excitation photons: where ϕPL(ℏω, Jrec) is the emitted absolute spectral PL photon flux (cm -2 •s -1 •eV -1 ) and ϕex is the absorbed excitation photon flux (cm -2 •s -1 ).ϕPL is a function of the photon energy, ℏω, and is specified at a particular value of ϕex.The Jrec, represents the current density due to the net generation (recombination) rate of excess charge carriers and is given by: Jrec = q•ϕex.It is noted that PTFs exhibit a significant fraction (~50%) of emission from the glass edges due to radiative recombination photons scattering from the non-planar PTF surface and waveguiding into the glass [21].Therefore, this analysis requires that Suns-PLQY measurements be performed inside a 4π integrating sphere [3].
Subsequently, the radiative-limited implied voltage, iVOC,rad, can be determined from iVOC and PLQY [8]: iVOC,rad represents iVOC when no non-radiative recombination is present.Jrec plotted as a function of iVOC represents the dark iJ-V curve of the PTF: Jrec(iVOC) = iJ(iV), where iJ(iV) is the implied dark current-density as a function of the implied voltage.The iJ-V curve can be decomposed into the iJ-V curves due to radiative (iJrad) and non-radiative (iJnr) recombination, respectively: Jrec plotted as a function of iVOC,rad represents the radiative dark iJ-V curve: Jrec(iVOC,rad) = iJrad(iV).As the radiative recombination has a nid of unity, the radiative dark iJ-V curve can be modelled as: where J0,rad is the radiative recombination parameter (A•cm -2 ) [26].If NRBR is the dominant non-radiative recombination mechanism, iJnr(iV) is: where J0,nr is the recombination parameter associated with NRBR (A•cm -2 ).Combining Equations ( 5) and ( 6), iJ(iV) can be expressed as: By varying W, one can determine the spatial origin of J0,nr.Accounting for NRBR at the surfaces and inside the bulk [26], J0,nr can be expressed as: where J0,s and J0,bulk,nr are the non-radiative saturation current densities for surface and bulk NRBR, respectively.Bbulk,nr is the NRBR coefficient [11], [12], [15], [18], and ni is the intrinsic carrier density [27].

Results and Discussion
Unless otherwise stated, all the presented measurement results are for the intermediate PTF.
Figure 1a illustrates the Suns-PLQY measurements, represented as ϕPL(ℏω), which cover nearly three orders of magnitude of ϕex.Throughout the wide range of Suns, we observed no changes in the shape of ϕPL(ℏω), indicating the reasonably stable composition of the studied PTFs.Additionally, the absence of low-energy shoulders in ϕPL(ℏω) suggests that phase segregation [28] does not have a significant macroscopic impact on the Suns-PLQY measurements of the investigated samples.
Figure 1b shows PLQY as a function of ϕex in Suns, where 1-Sun is defined as equivalent to a photogenerated current density JL, of 18.7 mA.cm -2 (see Section S2 of the SI).We observe the PLQY remains consistently within (25.2 ± 3.3) % over almost two orders of magnitude (ϕex > 0.2 Suns).The PLQY may be defined additionally to Equation (1) as the external radiative recombination rate (Rrad,ext) relative to the net recombination rate (Rtot): PLQY = Rrad,ext/Rtot [29].A plateau of the PLQY indicates that the dominant recombination mechanism has the same injection dependence as the radiative recombination.The difference between this plateau value and unity is attributed to non-radiative recombination.Thus, NRBR can be identified in Suns-PLQY as a plateau of the PLQY (PLQY < 1) with changing Suns.This constancy suggests that the dominant non-radiative recombination mechanism is indeed NRBR. Figure 2a demonstrates the application of Equation ( 3) to the 1-Sun ϕPL(ℏω) of the intermediate PTF (see also Section S2 of SI).The fitting region was carefully selected to ensure a high signal-to-noise ratio (SNR) and avoid the "edge artefact" caused by low-energy photons scattered at the film surfaces and guided towards the glass edges [21].This fitting region (1.57eV < ℏω < 1.67 eV), is indicated by the pair of black, dashed vertical lines.The fit quality appears to be good, reflected by the fitted iVOC and T uncertainties of only ±1 mV and ±0.7 K, respectively.We note that the fitting range from above determines a carrier temperature close to the room temperature of about (296.7 ± 2.5) K [(22.5 ± 2.5)°C].We provide an analysis of the fitting sensitivity in Section S3 of the SI.

Figure 2b
displays the back-calculated spectral absorptivity (red line), which exhibits good agreement with the measured spectral absorptivity (black pentagons) in the region unaffected by the edge artefact (ℏω > 1.57 eV).This procedure is repeated for each ϕPL(ℏω) curve to determine iVOC.The iVOC,rad values are determined using Equation (3) together with the determined iVOC and PLQY. Figure 3 illustrates the Suns-PLQY data represented as dark iJ-V curves, where black triangles (circles) represent the dark (radiative) iJ-V curve.A ΔiVOC of 30 mV at 1-Sun, caused by NRBR, is indicated by the dashed horizontal line.By fitting the dark radiative iJ-V curve, we obtain a J0,rad value of (12.2 ± 0.1) yocto-A.cm - (1 yocto = 10 -24 ) using Equation (6).Subsequently, utilising this J0,rad value and Equation ( 8), we determine a J0,nr value of (36.5 ± 0.5) yocto-A.cm - from the fit to the dark iJ-V curve.
It is important to note that the fitting region for the dark iJ-V curve is limited to iV > 1,200 mV.Below this threshold, the curve deviates from Equation ( 8), likely due to the contribution of other recombination mechanisms such as bulk Shockley-Read-Hall (SRH) [30].The dark iJ-V curve fits for the thick and thin PTFs are in Section S4 of SI.Table 2 lists the J0,nr values for PTFs of varying thickness, indicating a slight increase in J0,nr with increasing thickness (less than 33%, see Section S6 of the SI).If NRBR originates only from the bulk, one would anticipate a nearly tripled J0,nr when transitioning from thin to thick PTFs (469/160 nm ≈ 2.93).Conversely, if NRBR arises from the surfaces, J0,nr should be independent of the thickness.The observed modest increase in J0,nr with increasing thickness suggests the presence of a significant surface component combined with a relatively smaller bulk component of J0,nr.
While a bulk J0,nr component could be attributed to SRH recombination [30] from shallow bulk defects, we find that the required Nt is implausibly large (see Section S5 of SI).A simpler explanation is relatively minor differences in the SRH recombination parameters [31] among the PTFs of different thicknesses.For instance, a 33% variation in the interface defect density, Nit, with the thickness could account for the observed difference.Therefore, the most plausible cause of NRBR are defects at the surfaces, and in this context, the J0,nr parameter is equivalent to J0,s (surface recombination).It should be noted that J0,s represents the cumulative value across both PTF/air and PTF/glass surfaces.
It is important to note that if NRBR originated from the grain boundaries, the opposite trend would be expected between J0,nr and the grain boundary diameter, Dgb (also listed in Table 2, see Section S6 of the SI) [32], since the grain boundary area per unit volume of the film is inversely proportional to Dgb (see Section S6 of SI).Hence, we rule out grain boundaries as the possible spatial origin of J0,nonrad.
Typically, surface recombination in PTFs has been specified in terms of the surface recombination velocity, SRV (cm.s -1 ) [33], [34].SRV values are usually specified as injectionindependent values, meaning the surface recombination rate is linear with respect to Δn (monomolecular recombination).However, when the surfaces are highly charged, corresponding to strong accumulation or strong inversion, the electron and hole densities at the surfaces are highly asymmetric.This leads to an injection-dependent SRV more aptly parametrised by the surface saturation current parameter, J0,s [31] and surface recombination proportional to the electron-hole product (bimolecular recombination).We note that J0,s is a well-established parameter for crystalline silicon photovoltaics [35], routinely used to assess the surface passivation quality [31], [36].Regarding the origin of  0,s , we propose two possible mechanisms from the framework of SRH recombination [30].Both assume a single energy-level surface defect and involve a significant interface band-bending/photovoltage, ψs, leading to asymmetric electron and hole densities at the boundary [31].The first case is near band-edge donor (acceptor) states close to the conduction (valence) band-edge: is the capture coefficient with x = p (x = n) for a donor (acceptor), Nit is the interface state density (cm -2 ) and (Et -Ei) is the defect energy level referenced to the intrinsic level.We determine that Equation ( 10) is a reasonable approximation if the defect energy-level is within 50 meV of the valence (conduction) band-edge, corresponding to excess carrier densities of less than 10 17 cm -3 .This mechanism was previously proposed by Brenes et al [18].The second case is a mid-gap defect accompanied by a large surface charge, Qs [31]: where ε is the permittivity.Qs could be caused by the accumulation of mobile, charged ions near the surfaces [37].We performed surface photovoltage mapping on a Br17 sample with in-situ LS, revealing a positive ψs of several hundred meV.This indicates the presence of donor states at the surface, further reinforcing the hypothesis of a significant J0,s (see Section S8 of the SI).To distinguish which of these two mechanisms is relevant, the temperaturedependence of J0,s can be measured from temperature-dependent Suns-PLQY.Ignoring the temperature dependencies of cn, Qs, and ε, which are non-trivial, Equations ( 10) and ( 11) have distinct temperature dependencies of T 3/2 •exp(-[Eg(T) + 2•(Et -Ei)]/2kBT) and T 4 •exp(-Eg(T)/kBT), respectively.Note that Eg is the bandgap energy.

Conclusions
In this study, we have successfully showcased a straightforward analysis approach utilising Suns-PLQY measurements to quantify non-radiative bimolecular recombination in semiconductor thin films, as well as identify its spatial origin.Notably, we demonstrated that NRBR in the studied PTFs arises from defects located at the surfaces, which can be effectively described by the J0,s parameter.We determined an average J0,s value of (35.6 ± 10.6) yocto-A.cm - across thicknesses ranging from 160 nm to 470 nm.We propose either band-edge surface defects or mid-gap surface defects coupled with large surface charge as plausible origins of J0,s, and suggest using temperature-dependent Suns-PLQY to determine the exact origin of J0,s.The application of this simple analysis technique holds potential for the characterisation of J0,s in perovskite compositions and other semiconductor materials.

Figure 2
Figure 2 (a) A linear transform of the 1-Sun ϕPL(ℏω), according to Equation (3) (black triangles) and linear curve fit (solid red line) used to extract iVOC and T. The error bars on the black triangles represent the measurement uncertainty.The shaded red regions represent the effect of the standard errors of iVOC and T on the fit.(b) Reference spectral absorptivity (black pentagons) and back-calculated spectral absorptivity from 1-Sun ϕPL(ℏω) (solid red line).The error bars on the measured spectral absorptivity represent the standard deviation of the absorptivity measured from either side of the PTF/glass stack.The shaded red regions represent the propagated uncertainty in the measured ϕPL(ℏω), and the curve-fitted iVOC and T.

Figure 3
Figure 3 Dark iJ-V curves for intermediate PTF.The red (blue) curve is a curve fit to the dark (radiative) iJ-V curve using Equation (8) [Equation (6)].The dashed line represents the 1-Sun JL, equal to 18.7 mA.cm -2 .The horizontal distance between the intersection of the dark iJ-V curves with this dashed line represents the 1-Sun ΔiVOC.

Table 1
Thicknesses of the PTF samples used in this study, as determined by SE/T.

Table 2
(8)nr values obtained from Equations (6) and(8).The asterisks indicate additional measurements on separate locations.W and Dgb values are included for completeness.The average uncertainty is calculated using