Detection and identification of vacancy defects in antimony selenide

Domain: physics
Published: 2026-01-03
Editorial outcome: major_revision

Abstract
Antimony selenide (Sb2Se3) has an optimal bandgap and absorption coefficient for thin film solar cell applications and comprises earth abundant elements. The rate of increase in reported power conversion efficiencies has slowed due to a persistently large open circuit voltage deficit attributed to detrimental concentrations of point defects. Here we use depth-profiling positron annihilation lifetime spectroscopy to study Sb2Se3 crystals and thin films. The method is specific to neutral and negative charge states of vacancy-related defects. Both monovacancy and divacancy defects are identified in intrinsic and n-type samples but no monovacancy defects are detected in the p-type sample. Comparison of the experimental positron lifetimes with density functional theory calculated values provide evidence for the observation of Sb monovacancies in the –3 state and of Se monovacancies in the –2 state. The results are consistent with recent density function theory predictions that the Sb and the Se monovacancy defects both have accessible negative charge states.

Introduction
The global demand for sustainable, affordable, photovoltaic (PV) and thin film Sb2Se3 efficiency (PCE) greater than 20% motivates the search for suitable earth abundant PV materials1. The binary semiconductor Sb2Se3 has attracted particular attention due to its appropriate bandgap, 1.18 eV, high optical absorption coefficient and carrier mobility and the low toxicity and high natural abundance of the constituent elements. Antimony selenide solar cell PCEs have increased from, for example, 2.3% in 2014 to 7.6% in 2018, then from 9.2% in 2019 to 10.1% in 20222–5. But these values remain far from the detailed-balance limit of ~30%6. Performance of current Sb2Se3 cells is inhibited by the low values of open-circuit voltages, Voc, which are typically only ~40% of the bandgap value (i.e. ~50% of the Shockley-Queisser limit). This Voc deficit results from the presence of point and extended defects and associated carrier recombination7,8. Deep-level transient spectroscopy (DLTS) and temperature dependent admittance spectroscopy (TAS) measurements clearly show the presence of defects in monocrystalline and thin film Sb2Se3 4,9–13. These methods can identify charge transition energy levels within the bandgap due to defects, but they do not provide information on the chemical nature and local structure. This can only be inferred by comparison with density functional theory (DFT) calculations of charge transition levels for specific point defect types. Currently, there is no experimental identification of intrinsic point defects in Sb2Se3 using local structure sensitive spectroscopy methods. Here we report the detection of monovacancy and divacancy defects in Sb2Se3 crystals and thin films using the vacancy-related defect specific characterization technique positron annihilation lifetime spectroscopy performed using a depth-profiling high intensity positron beam.

Antimony selenide consists of strongly bonded quasi-one-dimensional (quasi-1D) [Sb4Se6]n ribbon units stacked together by weak van der Waals interactions forming an orthorhombic crystal structure (Fig. 1)14. This quasi-1D structure has the potential to enable structural reconstructions that result in a suppression of deep electronic states associated with grain boundaries, in stark contrast to other covalently-bonded semiconducting photovoltaics15,16. The low lattice symmetry results in two inequivalent Sb sites and three inequivalent Se sites within the ribbon units (Fig. 1). In consequence, the properties of the six intrinsic point defects, two monovacancies, VSe and VSb, two antisites, SbSe and SeSb, and two interstitials, Sei and Sbi, can vary with site, resulting in complex defect physics and chemistry.

First principles calculations provide essential insight on possible specific point defects, enabling determination of charge transition energy level positions, defect formation energies, and detailed local structure6,17–22. The defect formation energies then allow theoretical values for defect concentrations under given growth conditions to be calculated. This information, in turn, can enable detailed modeling of photovoltaic devices. However, it is desirable to validate the predictions of DFT against the results from point defect local structure sensitive experimental methods, for example, positron annihilation spectroscopy and electron magnetic resonance spectroscopy.

The defect formation energies and possible charge transition energy levels are determined by the nature of the bonding and local structural rearrangements of neighbour atoms adopted in the ground state configurations of the defects. Recently, it has been clearly shown that the assumed point defect ground state configurations commonly obtained from first-principles calculations can, in fact, be metastable arrangements22. The conventional approach starts from a high symmetry initial geometry and uses a gradient-based optimization algorithm which increments the neighbour atom positions seeking a minimum in the potential energy surface, but this may be a local minimum. A more sophisticated search procedure that involves increasing the number of nearest neighbour atoms that are displaced and that varies the amount of distortion, and that applies random perturbations to the coordinates of all the atoms in the supercell, has been developed22. In particular, it is found necessary to apply this approach for defects in materials with low-symmetry structures and flexible bonding environments, as exemplified by Sb2Se3 and Sb2S3 6,22. These studies cause significant changes in the predicted nature of the possible defect charge transition levels and their positions within the bandgap when compared to previous reports, and hence change the interpretation of the experimentally determined defect levels.

The removal of an Sb atom with its three donating electrons creates a neutral vacancy, V0Sb, but leaves three holes on the neighbour Se dangling bonds. Localization of three electrons at the vacancy compensate these and then results in a stable, fully ionized, V–3Sb charge state. Removing a Se ion results in a fully ionized V+2Se state6. Importantly, however, other charge states can be stabilized by the localization of excess charge at the vacancy site or through local atomic rearrangements, or a combination of both. Density function theory can provide detailed information on the nature of these processes and hence on the type and position of possible charge transition energy levels within the energy bandgap. The recent calculations applying the SHAKENBREAK approach to the monovacancy defects in Sb2Se3 find that both the Sb and Se vacancies are amphoteric6. It is reported that both monovacancy defects are stable in positive charge states for Fermi-level positions below mid-bandgap and that both have stable negatively charged states for positions close to the conduction band6. They also predict structural reconstructions involving either Se or Sb trimers that enable the stabilization of an abnormal positive +1 state for VSb or a –2 state for VSe, respectively6. Further, the Sb vacancies at the two possible sites (Fig. 1) are reported to both exhibit an unusually four-electron negative-U transition giving a +1/–3 level near midgap. The Se vacancy at site 2 exhibits a similar four-electron transfer, giving a +2/–2 transition level in the upper half of the bandgap. The Se vacancies at the other two sites exhibit two sequential two-electron negative-U transitions giving a +2/0 and 0/–2 pair of levels. In consequence, it is predicted that site-1 and site-3 Se monovacancies have an accessible neutral charge state for a narrow range of Fermi-level positions just above midgap6. By contrast, earlier DFT calculations predicted a more conventional ordering of charge transition levels within the bandgap where the Sb vacancies are stable in the −3 state for Fermi-level positions through almost the whole bandgap, with no accessible positive states, and where Se vacancies exist in positive charge states for Fermi-level positions lower in the bandgap but in the neutral charge state for level positions close to and above midgap and have no accessible negative charge states18–21. These differences in position and nature of the vacancy defect charge transition levels directly affect previous studies that rely on comparison with first-principles calculations to enable experimentally determined levels to be interpreted in terms of the presence or absence of specific vacancy defects9,23,24.

Vacancy defects that are stable in neutral or negative charge states can be detected and identified by positron annihilation spectroscopy25–27. These methods have unique specificity for vacancy, open volume, defects and have a sensitivity limit of approximately 1015 cm−3 and can estimate vacancy defect concentrations up to approximately 1019 cm−3 beyond which saturation positron trapping occurs25,26. Positron annihilation lifetime spectroscopy (PALS) enables the experimental detection of multiple positron states. Positrons implanted into perfect material enter a Bloch state and annihilate with a lifetime characteristic of the overlap between the positronic and electronic densities, termed the perfect lattice or bulk lifetime, τB. Missing atom sites present a trapping potential for positrons, but the local charge of the vacancy centre with respect to the lattice is also of critical importance in determining positron trapping. The Coulomb barrier presented by positively charged vacancy defects results in negligible trapping rates, while, in contrast, neutral or negatively charged vacancy defects are strong positron traps. Positron states localized at vacancy defects have lifetimes that are longer than that for the perfect lattice state due to the lower electron density at the missing atom site25–27. The lifetime of a positron state localized at specific vacancy defect is a characteristic of the particular defect type. Observation of both the perfect lattice state annihilations and longer lifetime defect localized state annihilation events enables the trapping to vacancy-related defects to be unambiguously established. Comparison of the experimentally determined lifetimes to those predicted by two-component DFT (TC-DFT) calculations for the positron states localized at specific vacancy–related defects can allow identification26,28. Moreover, positron lifetime measurements performed using a high intensity variable energy (VE) positron beam enable depth–profiling of vacancy–related defects from the near-surface down to depths of a few microns29,30.

Results
TC-DFT of the characteristic positron lifetime values
The positron lifetime values were calculated for annihilation from the perfect lattice state in Sb2Se3, and for states localized at neutral and negatively charged monovacancies and for possible divacancy defects. They were made using ABINIT with the PAW method28,31. Calculations were performed for the −3 charge state of the two possible Sb monovacancy defects and the predicted neutral and −2 charge states for the possible Se vacancies. These calculations started from the ground-state defect configurations obtained by Wang et al.6.

In the case of the divacancies, we performed a full search of stable geometries by combining different first-neighbour Sb and Se monovacancies in varying charge states. The initial structures were generated by removing pairs of Sb and Se atoms from the inequivalent sites, then the neighbour atoms were displaced using the SHAKENBREAK algorithm22. The structure was then relaxed within the DFT calculation. The resulting divacancy binding and formation energies are shown in Fig. 2 (also see Supplementary Note 1). The −1 and −3 charge states of the two divacancies VSb(1)VSe(2) and VSb(2)VSe(1) in the short-bond configuration exhibit the lowest binding and formation energies. The resulting calculated positron state lifetime values for monovacancy and relevant divacancy defects in Sb2Se3 are given in Table 1 (Also see Supplementary Table 1).

A perfect lattice (bulk) positron lifetime, τb, of 257 ps was obtained. The resulting positron densities for the perfect lattice state and for the positrons state localized at V–3Sb(1) are shown in Fig. 3. The calculated monovacancy localized positron state lifetimes are well separated from the bulk lifetime (Table 1), they were found to lie in the range 302 ps to 332 ps while the values for the most stable divacancies spanned the range 325 ps to 343 ps (Also see Supplementary Note 1).

Significant differences in the lifetimes for vacancy defects at the different possible inequivalent sites were observed. The lifetime for the −3 charge state of the Sb monovacancy was found to be 314 ps for site-2 but increased to 330 ps for the more open configuration at site-1. The resolution of positron lifetime spectroscopy is limited, hence, if Sb vacancies are present at both sites it would be expected that the experimental lifetime spectrum would exhibit a single lifetime component due to trapping at these defects that would be the weighted average of the contributions from the two sites and hence would have a lifetime value intermediate between 314 ps and 330 ps.

Lifetime values were also calculated for positron states localized at the proposed neutral and −2 charge states for the Se vacancies at site-1 and site-3 and for the −2 charge state for the site-2 Se vacancy starting from the geometries reported by Wang et al.6. The resulting Se vacancy −2 state lifetimes span from 302 ps for site-1 to 311 ps for site-2 (Table 1). The lifetime values for the neutral charge states of the site-1 and site-3 Se vacancy were notably longer at 329 ps and 332 ps, respectively.

These calculations provide evidence that positron lifetimes in the approximate range 300–310 ps indicate trapping to −2 state Se monovacancies, lifetimes in the approximate range 315 to 330 ps are consistent with trapping to −3 charge state Sb monovacancies. However, lifetimes around 330 ps are also consistent with the less probable neutral state of the Sb monovacancy. The positron states of the most stable divacancy defect (VSb(1)VSe(2)) have a lifetimes of 343 ps and 338 ps for the −1 and –3 charge states, respectively.

Variable energy positron lifetime spectroscopy measurements
These were performed on a series of single crystals prepared by Bridgman melt growth and included samples with p-type, intrinsic, and n-type conductivities32,33 (Supplementary Table 2). Measurements were also made on n-type Sb2Se3 thin films deposited using closed-space sublimation (CSS) and thermal evaporation (TE). Positron lifetime spectra were measured using different positron implantation energies. Typically, 4 keV, either 6 or 8 keV, and either 14, 16 or 17 keV energies were used and example positron implantation profiles are shown in Fig. 4a. For the 4 keV implantation energy almost all positrons are stopped in the top 150 nm and the mean implantation depth is ~63 nm, for 8 keV all are implanted to depths less than 450 nm and the mean depth is ~209 nm, while for 16 keV the mean depth is ~511 nm and almost all are implanted depths down to 1100 nm (Fig. 4a).

The experimental positron lifetime spectra were deconvolved assuming a finite number of discrete lifetime states. Fig. 5 shows examples spectra with fits for a p-type, Sn-doped, Sb2Se3 crystal and an n-type CSS thin film. Almost all the spectra measured fitted to three lifetimes, see Supplementary Tables 3 and 4 and Fig. 4, with the first lifetime component having a value less than or approximately equal to the TC-DFT calculated perfect lattice lifetime of 257 ps while the second component lifetime value was normally in the range 301(7) ps to 354(1) ps, consistent with trapping to monovacancy and or divacancy defects. The third component typically had a lifetime in the range 0.6–6 ns with an intensity less than 4% and is due to a small fraction of positrons forming positronium (Ps) (Supplementary Note 3). The standard trapping model predicts that when positrons are trapping to a population of vacancy defects, the first lifetime components should have a value less than the perfect lattice lifetime: this is termed the reduced bulk lifetime component, and its lifetime value and intensity systematically decrease with increasing trapping to vacancy defects (Supplementary Note 3)25,26. Observation of a spectrum component with a lifetime value greater than the perfect lattice lifetime, but less than the minimum Ps lifetime (~550 ps), unambiguously demonstrates positron trapping to neutral or negatively charged vacancy-related defects.

The lifetime components obtained by fitting the spectra from a p-type Sb2Se3:Sn crystal, and from two Sb2Se3 crystals exhibiting intrinsic conductivity, are given in Supplementary Table 3 and are shown in Fig. 4b. The spectra measured from the p-type crystal were dominated by a first lifetime component comparable to, or shorter than, the TC-DFT calculated positron lifetime of 257 ps for the perfect lattice state (Table 1). The 8 and 14 keV spectra yielded a first lifetime of 260 ps and 261 ps, respectively, with an intensity of ~95% consistent with almost all positrons annihilated from the perfect lattice state. However, it was only for the near-surface spectrum, where positrons are implanted to a mean depth of 63 nm (4 keV, Fig. 4a), that a vacancy-related defect component was detected. This had a lifetime value of 343(8) ps (I2 = 38(5)%) (Fig. 4b, Supplementary Table 3) but the spectrum was dominated by the first component at 239(4) ps (I1 = 62(5)%), the reduced bulk lifetime component. Assuming the values in Table 1 are accurate, the observation of a component with a lifetime greater than ~330 ps requires the presence of vacancy defects larger than monovacancies. Further, the defect lifetime of 343(8) ps is in agreement with the TC-DFT calculated value for the most stable divacancy defect configuration (VSb(1)VSe(2))–1 providing evidence for positron trapping to vacancy-related defects dominated by divacancies.

For the p-type crystal, positron trapping to vacancy-related defects was only observed in the near-surface (4 keV) spectrum, where the mean implantation depth was ~63 nm. The spectra measured using 8 keV and 14 keV were dominated by perfect lattice annihilations (Fig. 4b) indicating an absence of trapping to monovacancy or divacancy defects. The result is consistent with either vacancy-related defects restricted to only a narrow near surface region and being in neutral or negative charge states, or with a more uniform, deeper, distribution of defects but with those below the top layer existing only in positive charge states. Variable energy x-ray photoelectron spectroscopy measurements have been performed on a similar p-type Sn-doped crystals and demonstrated the presence of n-type inversion layer below ~13 nm34. The existence of this layer would be consistent with the observation of positron trapping to divacancy defects only for the 4 keV spectrum, assuming these defects are neutral or negative for Fermi level positions close to or above midgap but positively charged for Fermi level positions in the lower half of the bandgap. First principles calculations predict the monovacancy defects in Sb2Se3 exhibit this behaviour6, and Fig. 2a predicts the divacancy defects are not stable for Fermi level positions towards the VBM.

The positron lifetime results from the two nominally stoichiometric Sb2Se3 crystals that exhibited intrinsic conductivity (Supplementary Table 2) are also shown in Fig. 4b (Supplementary Table 3). The 8 keV spectrum from crystal A, where all positrons implanted to depths less than or equal to ~450 nm (Fig. 4a), was dominated by trapping to a vacancy-related component with a lifetime of 316(4) ps (I2 = 71(3)%). Comparison with the TC-DFT calculated values (Table 1) shows it to be significantly smaller than the divacancy lifetimes and to be comparable to the value for V–3Sb(2), providing evidence for the presence of monovacancy defects. However, the 14 keV spectrum from crystal A was dominated by annihilations from the perfect lattice state but with minority component with a lifetime 467(11) ps (I2 = 15(1)%) longer than that predicted for divacancy defects, providing evidence for the presence of a low concentration of larger multivacancy cluster defects within the top micron of the sample. The 6 keV spectrum from intrinsic conductivity crystal B also showed positron trapping to vacancy-related defects, while the 17 keV spectrum was again dominated by annihilations from the perfect lattice state. For crystal B the lifetime of the defect component observed in the sub-450 nm region was 344(3) ps (I2 = 57(2)%), longer than that observed for crystal A, and is consistent with positron trapping to the most stable divacancy defect configuration (VSb(1)VSe(2))–1 (Table 1). Nevertheless, the higher implantation energy spectra from both intrinsic conductivity crystals, which probe the top ~1200 nm, yielded spectra dominated by annihilations from the perfect lattice state (Fig. 4b and Supplementary Table 3).

The positron lifetime results for the n-type crystal and thin film samples are shown in Fig. 4c and Supplementary Table 4. Three Sb2Se3 crystals grown from commercially supplied Sb2Se3 found to contain Cl contamination and to exhibit n-type conductivity were studied. Crystals Sb2Se3:Cl(A) and Sb2Se3:Cl(B) had been subjected to post-growth anneal in a Sb poor ambient. The 4 keV spectra from (A) and (B) returned a dominant lifetime component with values of 315(1) ps (I2 = 89(1)%) and 325(1) ps (I2 = 89(1)%), respectively, consistent with the presence of Sb monovacancies within the top 150 nm of the samples. However, the spectra measured at 8 keV and 14 keV gave dominant defect components with values of 306(1) ps (I2 = 88(1)%) and 305(1) ps (I2 = 88(1)%) for (A), while (B) returned 313(1) ps (I2 = 92(1)%) and 306(1) ps (I2 = 92(1)%), respectively. Comparing these experimental lifetime values to the TC-DFT calculated values in Table 1 provides evidence for dominant positron trapping to −2 charge state Se monovacancies in the region below the near surface layer.

The third crystal Sb2Se3:Cl(C) came from a different growth batch and was subjected to a post-growth anneal in a Se-poor environment (Supplementary Table 2). The 4 keV and 8 keV spectra were dominated by components with lifetimes of 311(3) ps (I2 = 82(1)%) and 303(3) ps (I2 = 79(2)%) again indicating dominant trapping to −2 charge state Se monovacancies. But the high energy (17 keV) spectrum was dominated by perfect lattice annihilation (258(3) ps, I1 = 98(1)%), providing evidence that the monovacancies were present only in the top ~450 nm of the sample.

An oxygen doped crystal, Sb2Se3:Cl,O, exhibiting n-type conductivity was also studied (Fig. 4c, Supplementary Table 4). The 4 keV near surface spectrum was dominated by a defect component with value 337(3) ps (I2 = 81(1)%) indicating the presence of divacancy defects. The 6 keV and 17 keV spectra, however, were dominated by components with values of 329(3) ps (I2 = 77(1)%) and 320(7) ps (I2 = 73(4)%), respectively. These values are consistent with positron trapping to −3 charge state Sb monovacancies, but the 329(3) ps value is also in agreement with calculated values for the site-1 and site-3 neutral charge state Se monovacancies and overlaps the divacancy defect range. However, it can also be noted that the observed n-type conductivity suggests the Fermi level in the should be above the 0/−2 charge transition levels for the Se monovacancies6.

A closed-space sublimation grown Sb2Se3 thin film and a thermally evaporated thin film were also studied. Both samples exhibited n-type conductivity due to Cl incorporation. The 4 keV and 16 keV spectra from the CSS thin film (Fig. 4c and Supplementary Table 4) were both dominated by a defect component with a lifetime of ~305 ps, consistent with trapping to −2 charge state Se monovacancies. The intensity of the component reduced from 86(1)% to 67(7)% with increasing implantation energy. The thermally evaporated film was only measured at 4 keV, the spectrum was dominated by a defect component with a lifetime of 354(1) ps. This is close to, but longer than, divacancy defect values, suggesting that trapping is dominated by divacancies but that there are also contributions from trapping to larger open-volume defects.

The dominant lifetime components from all the spectra measured are shown in Fig. 4d. There is a clear, systematic variation in the lifetime and intensity of the first component. The lifetime and intensity increase toward limiting values as the lifetime approaches ~260 ps. There is a concomitant decrease in the intensity of the second, vacancy-related defect, lifetime component. This behaviour is expected from the standard trapping model (STM) (Supplementary Note 3). The values of the bulk lifetime calculated from the experimental spectra using the STM are given in Supplementary Tables 3 and 4, and the average of these gave 260(6) ps. There is good agreement between this experimental value for the bulk, perfect lattice, state lifetime and the TC-DFT calculated value of 257 ps. There is also satisfactory agreement between the range of possible monovacancy lifetimes calculated by TC-DFT (Table 1) which span from 302 ps for V–2Se(3) to 330 ps for V–3Sb(1) and the lifetime values for the second vacancy-defect related component obtained from the large majority of the spectra measured which range between 301(7) ps and 329(3) ps (Fig. 4d). However, it can be noted that if the less stable VSb(2)VSe(1) divacancies (Fig. 2a) were present the calculated −1 and −3 state lifetime values of 328 ps and 325 ps, respectively (Table 1), would overlap with part of this range. Four spectra returned longer second lifetime values consistent with the TC-DFT calculated lifetime range for divacancy defects. These were measured using either 4 keV or 6 keV implantation energies for which all positrons were implanted to depths less than 150 nm or 300 nm, respectively.

Vacancy-related defect lifetime components with lifetime values in the range 301 ps to 313 ps were only observed from some of the n-type samples (Fig. 4c). The TC-DFT calculations attribute lifetimes in this range to positron states localized at −2 charge state Se monovacancies (Table 1). This is consistent with the recently proposed unusual amphoteric behaviour for the Se monovacancies at the three possible sites, all of which are predicted to have a charge transition level to the −2 charge state in the upper half of the bandgap6. Lifetime components with values in the range 315–329 ps were observed from n-type samples and an intrinsic conductivity crystal (Fig. 4). This is the lifetime range associated with the −3 charge state Sb monovacancies. For those spectra that return a component value consistent with the neutral Se vacancies it is not possible to differentiate between the different assignments based on lifetime measurements alone. However, it should be noted that the neutral charge states of the Se vacancies are predicted to be stable for only a narrow range of Fermi level positions just above midgap, while the −3 charge for Sb monovacancies is predicted for a wide range of level positions above midgap6

The detection of a reduced bulk lifetime component in measured spectra enables the rate of positron trapping to vacancy defects, κD, to be estimated (Supplementary Note 3). The vacancy defect concentration is related to the trapping rate, [V] = κD/μV, where μV is the defect specific trapping coefficient. The values of μV for negatively charged vacancy defects in various semiconductors have been reported to be in the range 25~0.1 × 1015–30 × 1015 s−1. Using the typical value of ~3 × 1015 s−1 the resulting estimated vacancy defect concentration obtained from the 8 keV spectrum from crystal Sb2Se3:(A) is ~1 × 1016 cm−3 while the 4 keV spectrum from crystal Sb2Se3:Cl(B) gives a value of ~4 × 1016 cm−3 (Supplementary Note 3).

Methods
Sample preparation
The Sb2Se3 single crystal and thin film samples are detailed in Supplementary Note 2 and summarized in Supplementary Table 2. The crystal samples were grown by the Bridgman method in evacuated quartz capsules, which had been back-filled with argon to a pressure of 400 Torr to suppress macroscopic gas bubble formation. Experiments were conducted on their (100) cleavage surfaces and for which the ribbons lie on the b-axis, i.e., parallel to the cleavage plane (using the Pnma setting of Space Group 62)35. All elemental and compound source materials were from Alfa Aesar. Crystals Sb2Se3 (A) and (B) were grown from source material that was formed in-house by direct combination of the elements (6N Sb and 5N Se) heated quartz capsules. The chlorine doped crystal (Sb2Se3:Cl) was commercially supplied Alfa Aesar 5N purity Sb2Se3, which has been shown to have unintentional chlorine doping at the level of ~4 × 1016 cm−3 rendering it n-type36. The oxygen doped sample (Sb2Se3:Cl,O) was formed by adding 5N Sb2O3 to 5N Alfa Aesar Sb2Se3 at the level of 0.01% by formula units (Sb2O3/Sb2Se3). Since the starting material also contained chlorine (see above), this sample may be considered to be co-doped with both chlorine and oxygen. It was also subjected to an extended annealing treatment to make it Sb-rich in order to encourage n-type conduction (isothermal heating with 55 at% Sb/45% Se at 340 °C for 336 hrs). Source material for a tin, doped selenium-rich crystal (Sb2Se3:Sn) was prepared by direct combination of the elements (6N Sb and 5N Se and Sn), with the tin being 0.01% of the antimony.

The Sb2Se3 thin films were formed by Close Space Sublimation (CSS) onto SnO2:F coated soda lime glass (Pilkington TEC15), the source material being Alfa-Aesar 5N Sb2Se3, i.e., chlorine doped, as above. The films were approximately 1500 nm in thickness. The thermally evaporated (TE) films were fabricated using similar source material placed in crucible in a chamber evacuated to 10−4 mbar and heated to high temperature to vapourise the source onto the same type of substrates. The TE films were approximately 800 nm in thickness.

Positron annihilation
Variable energy positron annihilation lifetime spectroscopy was performed using the PLEPS instrument on the NEPOMUC high intensity beamline at the Heinz Maier–Leibnitz Zentrum (MLZ) research reactor in Garching29,30. Spectra contained 4 × 106 counts. The spectra were fitted using the software package PALSfit Version 3.195 (Technical University of Denmark, Riso Campus)37. The timing instrument resolution function was determined using a SiC standard sample, which was described by three Gaussian functions; the resulting full-width half-maximum values varied from 210 ps to 280 ps for the measurements described.

Theory calculations
To support the experimental observations, two types of first-principles calculations were performed. To explore the stability of divacancies, we calculated their formation and binding energies using the SHAKENBREAK method22,38 and the hybrid PBE0 functional as implemented in CP2K39,40. These calculations were used to identify the lowest-energy geometries and charge states of the Sb–Se divacancies. Further computational details are provided in Supplementary Note 1. To allow for the interpretation of the positron annihilation lifetime measurements, we carried out two-component density functional theory (TC-DFT) calculations using the projector-augmented-wave method in ABINIT28,31. The electron–positron correlation was treated using the Boronski–Nieminen functional with the Barbiellini et al. gradient correction41,42 within the GGA-PBE framework. Lifetimes were obtained for the perfect lattice, the relevant Sb and Se monovacancies, and the lowest-energy divacancy configurations. Additional methodology information is given in Supplementary Note 1.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "In the submission, the authors report that vacancy-related defects in Sb2Se3 was studied by depth-dependent positron annihilation lifetime spectroscopy. They also calculated the positron lifetime of the associated defects. As a result, they provide the evidence for the observation of Sb monovacancies in the -3 state and of Se monovacancies in the-2 state. At first glance, the manuscript appears to be well written, but after careful reading, it was observed that some points require more detailed discussion and examination. The novelty required for publication in \"Nature Communications\" is also limited in the paper. As a result, it is recommend a rejection of this paper.\n1. The positron annihilation technique was used to detect the vacancy defects of Sb2Se3, and this gives us a better understanding of vacancy defects in Sb2Se3 materials. But the authors seem to have only tested for defects in Sb2Se3, lacking further scientific explanation of the different nature of defects in different samples, much less guidance on regulating defects in Sb2Se3.\n2. The authors do not provide any other results on the properties of the sample other than PALS tests, including specific test results on the type of conductivity, so we doubt whether the tested sample has the N-type, intrinsic, or P-type conductivity described by the authors. Authors should provide more information about the samples to ensure the authenticity and reliability of the study.\n3. It is also a question whether there really are Se vacancies in -2 states. Many theoretical calculations of the defects of Sb2Se3, including its sister material Sb2S3, indicate that the anionic vacancy defect is either positively charged or neutral, and only the reference 6 in your submission mentions that VSe is an amphoteric defect. How does the author explain this?\n4. The drawings in the manuscript need to be drawn more carefully. Both Picture 1 and Picture 2 seem to be a sceenshot taken directly from the software. Because the figure1 has a little horizontal line under the direction marker.\n5.In Line 42 of Page 2，the authors said “Antimony selenide solar cell PCEs have increased from, for example, 2.3% in 2014 to 7.6% in 2018, then from 9.2% in 2019 to 10.6 % in 20222-5”, but none of the solar cells in the articles you cited have an efficiency of 10.6%; The authors cited the wrong references.\n6. Why is the positron lifetime of neutral Sb vacancies not calculated in table 1?\n7. In line 407 of page 21, the authors mentioned that “Lifetime components in the range 337(3) ps to 354(1) ps (Fig. 3d) were observed from four of the samples and provide clear evidence for the presence of divacancy defects (Table 1).” Why there is no monovacancy defects but divacancy defects in the P-type sample, which goes against our common sense; There needs to be a sound scientific explanation.\n8. In line 327 of page 17 and line 338 of page 18, the name of the referenced figure is written incorrectly. Figure 3b should be Figure 3c.\n9. In line 291 of page 16, “The positron lifetime results from the two nominally stoichiometric Sb2Sb3 crystals that exhibited intrinsic conductivity (Supplementary Table 3) are also shown in Fig. 3b (Supplementary 292 Table 4).” The authors misspelled Sb2Se3 instead of Sb2Sb3.", "reviewer_2": "In this manuscript, the authors investigate and identify open volume defects with neutral and negative charges in different Sb2Se3 samples by the combination of positron annihilation lifetime spectroscopy and density functional theory. They claim the presence of monovacancy and divacancy in intrinsic and n-type samples, and the absence of monovacancy defects in p-type Sb2Se3. In my opinion, additional analysis and clarifications are needed to support the conclusions and make the work suitable for publication.\nBelow are specific comments for the authors to consider in revising the manuscript.\n1. The authors focus on vacancies, but the concentrations of antisites with open volumes may also be substantial in this material. Could they also contribute to the observed signals? It should be clarified in the text if the observed signal is due to a concentration-weighted average over all possible defect species and an assumption is made to only consider vacancies.\n2. The authors distinguished the monovacancy and divacancy by comparing the experimental positron lifetimes with the DFT results. However, the separation between calculated lifetimes between monovacancy and divacancy is vague. For unambiguous defect identification, additional techniques, such as Doppler broadening spectroscopy which offers insights into the local chemical environment of defects, could be beneficial.\n3. The positron lifetime is sensitive to the concentration of each defect species. Please discuss how robust the results are for changes in defect concentration by plotting a figure similar to Fig. 6a in Physical Review B, 2019, 99(6): 064108. I am concerned that the defect assignment may be influenced by this choice.\n4. The configurations and formation energies of divacancies appear to be absent from the report and should be included.\nMinor\n5. On the 32th line of page 2 the authors stated “The results are consistent with recent density function theory predictions that both the Sb and the Se monovacancy defects are amphoteric”. However, as the present study only considers neutral and negatively charged defects, so the conclusion of “amphoteric” cannot be drawn.\n6. Other points:\n• On the 126th line of page 6, “These methods have unique specificity for vacancy, open volume, defects and have a sensitivity limit of approximately 1015 cm-3”:\no These methods -> This method\no Please specify what the limit of 1015 cm-3 is for\no A citation should be added for the limit here\n• On the 160th line of page 7, combing -> combining\n• On the 9th line of SI, please correct the repetitive sentences\n• On the 35th line of SI, please cite for “the Standard Trapping Model (STM)”", "reviewer_3": "The manuscript “Detection and identification of vacancy defects in antimony selenide” by David J. Keeble and co-authors reports a major step forward in the identification of vacancy defects in antimony selenide, that is a highly promising rapidly emerging material for future generation solar cells, with reported lab record efficiencies above 10% achieved in the last few years. Keeble and co-authors convincingly demonstrate that the presence of Sb and Se monovacancies and divacancies can be uniquely resolved in Sb2Se3 by combining state-of-the-art positron annihilation lifetime spectroscopy studies and ab-initio calculations (including local relaxation of atoms due to the densities of the electrons and positron). These studies were performed at the expert level and support the conclusions well.\nThis paves the way to systematically examine the presence and concentrations of these point defects in Sb2Se3 layers tailored for application in solar cells, which is key to improve the current relatively modest open circuit voltages (around 50% of the Shockley-Queisser limit), related to the presence of point defects and extended defects leading to unwanted charge carrier recombination. The well-described research as well as the highly accessible explanation of the key concepts of positron annihilation spectroscopy and ab-initio calculations will make this work highly valuable generally for researchers working in the fields of semiconductor layers for solar cells or other applications where point defects play an important role in their functional properties.\nI recommend publication of this highly interesting manuscript in Nature Communications, after some minor revisions, as suggested in my (technical) comments listed below, have been considered by the authors.\nQuestions and Comments:\n1. Figure 2b, p. 10 (discussed on p. 8, line 165-167) shows the calculated positron density in the Sb(1) vacancy. Figure 1 on p. 4 suggests that the neighbouring Se(2) atom loses its single atomic bond. What happens with the Se(2) atom, does it go to an interstitial site or does it bind to another atom?\n2. Table 1, p. 9: The calculated lifetime associated with a neutral Se(2) monovacancy is missing. Is there a special reason why this was left out from the study?\n3. p. 11, lines 204-210: the ranges for discriminating between Se(2-) monovacancies, Sb(3-) monovacancies and divacancies are reported to within an accuracy of 1 ps. This is too accurate, since systematic experimental inaccuracies in the positron lifetime are around 3-5 ps [26]. Also systematic inaccuracies will exist for the calculated positron lifetimes of these point defects obtained from the ab-initio study. I would like to suggest to report more global ranges for discrimination of these defects: Se(2-) monovacancies ~300 to 310 ps, Sb(3-) monovacancies: ~315 to 330 ps, Se(0) monovacancies: around 330 ps, divacancies: ~330 to 350 ps. This leaves the conclusions well intact.\n4. Figure 3d, p. 13, and text on p. 18, lines 344-346: The single trapping model is applied in a highly convincing manner, not only evident by the extracted bulk (perfect lattice) positron lifetime that systematically falls in the range of 260(6) ps, but also demonstrated by the dependence of I_RB as a function of the reduced bulk lifetime tau_RB. I would like to suggest to plot, as a guide-to-the-eye, the function I_RB (tau_RB) = (tau_D/tau_B – 1)/(tau_D-tau_RB) * 100% of the single trap model, with tau_B=257 ps and tau_D = 320 ps (average value for the defects observed), that fits the measured the intensity I_RB very well for the relevant range in tau_RB of 100 to 257 ps.\nRemarks/suggestions on technical details:\n1. p. 2, line 44: V_oc ~ 40% of bandgap value is stated. It would be better to state that V_oc ~50% of Shockley-Queisser limit (since bandgap values cannot be reached theoretically, instead of the normally applicable Shockley-Queisser detailed balance limit).\n2. p. 6, line 127: a sensitivity limit of 10^15 cm^-3 is quoted, that in fact depends on the material and type of vacancy (10^16 cm^-3 for the neutral vacancy and 10^15 cm^-3 for the negatively charge vacancy in c-Si). It seems appropriate to state here that such defects can be evaluated in the range of ~10^15 cm^-3 to ~10^19 cm^-3 [26].\n3. p. 11, line 215-216: thermal evaporation (TE) is stated as one of the synthesis methods of the Sb2Se3 films, but this method is not specified in the Methods Section, p. 23, line 455. Also, the thicknesses of the films are not specified in the manuscript, while these are crucial for the interpretation of the positron lifetime results, with implantation energies ranging from 4 to 17 keV (up to 1000 nm depth).\n4. Fig. 3b, p. 13: the label 17 keV for Sb2Se3(B) should be 6 keV.\n5. p. 20, lines 380-383: vacancy concentrations in units of cm^-3s^-1 are specified, while in the Supplementary Information specific trapping coefficients mu_V in units of s^-1 are provided. Were the unit cell dimensions of Sb2Se3 applied to convert the dimensions? A typical value of ~6x10^-8 cm^-3s^-1 is used in the manuscript, while a typical value for mu_V of 6x10^15 s^-1 is stated in the Supplementary Information. The two values are not positioned in the same way within the ranges specified (for example a typical value of ~1.2x10^-7 cm^-3s^-1 is expected, based on the typical value for mu_V).\n6. Supplementary Information, p. 5, line 43: In equation (1), the – sign should be a + sign in the sum of the two terms.", "reviewer_4": "I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts."}, "author_response": "We thank the reviewer for their careful consideration of the manuscript and for their constructive comments and corrections. They have enabled us to produce a higher quality, more accurate, revised manuscript. We address each comment in the below response.\nResponse to the remarks of Reviewer #1\nThe positron annihilation technique was used to detect the vacancy defects of Sb2Se3, and this gives us a better understanding of vacancy defects in Sb2Se3 materials. But the authors seem to have only tested for defects in Sb2Se3, lacking further scientific explanation of the different nature of defects in different samples, much less guidance on regulating defects in Sb2Se3.\nThe reviewer is referred to Supplementary Table 3 and the ‘Methods: Sample preparation’ section for details of the methods of used for controlling and regulating the defects in Sb Se crystals. Here we explained that two methods were used for stoichiometric control: a) by weighing at the synthesis stage, with the stoichiometric ratios being given explicitly in column 3 of the table and b) by post-growth annealing under controlled vapour pressures of the elements as detailed in column 4.\nWhilst method a) is self-explanatory, method b) relies on the manipulation of the vapour-solid equilibrium position. Experimentally this amounts to controlling both the temperature of the material itself and the vapour pressure of the vapour species above it so as to encourage either anion or cation vacancies. (The vapour-solid equilibrium relation is reviewed in Piacente, V.; Scardala, P.; Ferro, D. Total vapour-pressure of solid Sb Se . Journal of Materials Science Letters 1992, 11 (12), 855-857. DOI: 10.1007/bf00730486.) Hence the materials tested and their stoichiometric condition were selected to give a broad range of point defect outcomes: This is consistent with the aim of the study was to experimentally determine the range, identity and charge states of vacancy defects in Sb Se for the first time.\nThe authors do not provide any other results on the properties of the sample other than PALS tests, including specific test results on the type of conductivity, so we doubt whether the tested sample has the N-type, intrinsic, or P-type conductivity described by the authors. Authors should provide more information about the samples to ensure the authenticity and reliability of the study.\nThe referee requests details of the measurement of conductivity type. We refer the referee to ref 36. The conductivity type was determined using the hot probe method with details of the method used described in ref 36. Where carrier concentrations are given in the text, they were measured using the Hall method, which also confirmed the carrier type. To further clarify the conductivity of the samples studied we have added a detailed description into Supplementary Note 2 and included the results from hot-probe measurements on the samples.\nIt is also a question whether there really are Se vacancies in -2 states. Many theoretical calculations of the defects of Sb2Se3, including its sister material Sb2S3, indicate that the anionic vacancy defect is either positively charged or neutral, and only the reference 6 in your submission mentions that VSe is an amphoteric defect. How does the author explain this?\nRef 6 (Wang XW, et al. Phys Rev B 108, 134102 (2023)) from the Walsh group is the first high quality DFT study to implement the more comprehensive search algorithm seek a global local structure minimum (also see Wang et al Joule 8 2105 (2024). We discuss this explicitly in the paragraph starting “The removal of an Sb atom….” on p5 and concluding on p6.\nThe drawings in the manuscript need to be drawn more carefully. Both Picture 1 and Picture 2 seem to be a sceenshot taken directly from the software. Because the figure1 has a little horizontal line under the direction marker.\nThe incorporated images in Fig.1 and in Fig. 2 were jpegs but the image files supplied for publication are full resolution eps files.\nIn Line 42 of Page 2，the authors said “Antimony selenide solar cell PCEs have increased from, for example, 2.3% in 2014 to 7.6% in 2018, then from 9.2% in 2019 to10.6 % in 20222-5”, but none of the solar cells in the articles you cited have an efficiency of 10.6%; The authors cited the wrong references.\nWe thank the reviewer for pointing out this typo, it should indeed have been 10.1% not 10.6%, this has been corrected.\nWhy is the positron lifetime of neutral Sb vacancies not calculated in table 1?\nBecause the available high quality density functional theory studies report that the Sb vacancies are not stable in the neutral charge state, they are negative-U centres, see e.g. Wang XW, et al. Phys Rev B 108, 134102 (2023). We discuss this explicitly by us in the paragraph starting “The removal of an Sb atom….” on p5 and concluding on p6.\nIn line 407 of page 21, the authors mentioned that “Lifetime components in the range 337(3) ps to 354(1) ps (Fig. 3d) were observed from four of the samples and provide clear evidence for the presence of divacancy defects (Table 1).” Why there is no monovacancy defects but divacancy defects in the P-type sample, which goes against our common sense; There needs to be a sound scientific explanation.\nThis is an important point. We make it very clear that we are not saying that there are no monovacancy defects in the p-type material but what we are saying is that if monovacancies are present they must be in positive charge states and hence cannot trap positrons. As we discuss in the manuscript, the study of Wang et al predicts that the Se and Sb vacancies will be in positive charge states in p-type material. We return to this point in our discussion.\nA lifetime consistent with the presence of divacancies is only observed in the 4 keV spectrum (see Supplementary Table 4) where positrons are implanting to depths below 150 nm. In the manuscript we give an explanation for this. Experiments have shown the presence of narrow inversion layer at the surface of the p-type sample hence vacancy-related defects in this region can exist in neutral or negative charge states and trap positrons.\nIn summary, we are not saying there are no monovacancies in the p-type sample and we do provide sound scientific explanations for why we are observing a minority divacancy lifetime component in the 4 keV spectrum from the p-type sample.\nIn line 327 of page 17 and line 338 of page 18, the name of the referenced figure is written incorrectly. Figure 3b should be Figure 3c.\nWe thank the reviewer, and these typos have been corrected.\nIn line 291 of page 16, “The positron lifetime results from the two nominally stoichiometric Sb2Sb3 crystals that exhibited intrinsic conductivity (Supplementary Table 3) are also shown in Fig. 3b The authors misspelled Sb2Se3 instead of Sb2Sb3.\nWe thank the reviewer, and this typo has been corrected.\nResponse to the remarks of Reviewer #2\nIn this manuscript, the authors investigate and identify open volume defects with neutral and negative charges in different Sb2Se3 samples by the combination of positron annihilation lifetime spectroscopy and density functional theory. They claim the presence of monovacancy and divacancy in intrinsic and n-type samples, and the absence of monovacancy defects in p-type Sb2Se3. In my opinion, additional analysis and clarifications are needed to support the conclusions and make the work suitable for publication.\nBelow are specific comments for the authors to consider in revising the manuscript.\n1. The authors focus on vacancies, but the concentrations of antisites with open volumes may also be substantial in this material. Could they also contribute to the observed signals? It should be clarified in the text if the observed signal is due to a concentration-weighted average over all possible defect species and an assumption is made to only consider vacancies.\nThe positron lifetime results presented are unambiguously due to open volume vacancy defects. The method is essentially blind to antisite or interstitial defects.\nWhile it is indeed true that an antisite defect in a negative charge state would result in a slight increase in positron density in the vicinity it does not strongly localise as it does at the site of a missing atom.\nThe positron density attracted to a negative antisite defect, or similarly any negatively charged substitutional acceptor, essentially samples an environment that is similar to the perfect lattice and yields a lifetime component with a value at or close to the bulk lifetime (see K. Saarinen, et al. Phys. Rev. B 39, 5287 (1989)). The presence of weak localisation at negative non-vacancy centres has been inferred from variable temperature measurements at low temperature due the departures from the normal standard trapping model behaviour due to these centres starting to complete more effectively with trapping to vacancies. However, even in this case it does not alter the lifetimes of any resolved vacancy defect trapping these will still have their characteristic values.\nIn the measurements presented here we are clearly observing vacancy trapping lifetimes, further the standard trapping model accurately describes the results (e.g. Fig 3d) which provides evidence that if there are antisite defects present they are not strongly influencing positron annihilation.\n2. The authors distinguished the monovacancy and divacancy by comparing the experimental positron lifetimes with the DFT results. However, the separation between calculated lifetimes between monovacancy and divacancy is vague. For unambiguous defect identification, additional techniques, such as Doppler broadening spectroscopy which offers insights into the local chemical environment of defects, could be beneficial.\nWe agree with the reviewer, they highlight one of the significant outcomes from this manuscript. We demonstrate the viability of future coincidence Doppler broadening spectroscopy (CDBS) measurements. The observation of the perfect lattice positron lifetime in p-type samples will enable future studies to obtain precision CDBS ratio spectra. Further TC-DFT calculations are also required to enable this future study.\n3. The positron lifetime is sensitive to the concentration of each defect species. Please discuss how robust the results are for changes in defect concentration by plotting a figure similar to Fig. 6a in Physical Review B, 2019, 99(6): 064108. I am concerned that the defect assignment may be influenced by this choice.\nThe statement “The positron lifetime is sensitive to the concentration of each defect species” is not in general correct, it requires a specification of which positron lifetime is being discussed. It is only true if the lifetime being referred to is the average positron lifetime, τ(or a reduced bulk lifetime).\nThe average positron lifetime is critically dependent on concentration of each defect species present since τ=∑Iτ and the defect concentrations determine the intensities. The positron state lifetimes i i i for specific vacancy-related defects are independent of defect concentration and are characteristic of the local environment of the defect.\nUnzueta et al (PRB 99 064108) were only able to report average lifetimes for there rather complex Heusler alloy samples. It seems they were unable to deconvolve their experimental spectra. These had modest statistics (3E6) and required subtraction of source correction components. In consequence, the only way they are able to attempt to infer defect concentrations was to assume they could use the standard trapping model (STM) expression [ V ]=( 1τµ )  (τ−τ ) (τ −τ)  but they were B V B V also forced to use their TC-DFT calculated values for both τ and the value defect lifetime τ (and B V to assume the was only one positron trapping defect). Their Fig. 6a is just the textbook plot of the STM showing the variation of τwith vacancy defect concentration for the one-defect case. It was only possible for them to infer possible defect concentration ranges by mapping their only experimental τ values to the predictions from the above formula using their theoretical τ and τ values as seen B V in their Fig. 6b and Fig. 6c.\nWe are in a much more fortunate position. Our spectra have higher statistics and more importantly do not require source correction. In consequence we can deconvolve our lifetime spectra as shown in our Fig. 3 (and in the detailed tables in the Supplementary Information). We determine an experimental value for τ (Fig. 3d) and indeed happen to find the TC-DFT calculated value agrees with B the experimental value. We directly determine an experimental vacancy defect lifetime from the deconvolution which provides direct evidence that we are dominantly in the one-defect case. The results show we are not in, or close, to the saturation trapping region and so can directly use the STM expression [ V ]=µκ where for us κ is exclusively determined by the experimental values V V V obtained from the deconvolution (see Supplementary Note 3 Eq. 3); this is in stark contrast to the situation of Unzueta et al.\nThe STM calculated concentration estimate we report is not sensitive to concentration in the same manner that mean lifetime is sensitive to concentration as reported in Unzueta et al (PRB 99 064108) Figs 6b and 6c. The defect component lifetime is intrinsically independent of concentration, of course its intensity and the values of the reduced bulk lifetime and its intensity are concentration dependent – this is what allows us to calculate the concentration.\n4. The configurations and formation energies of divacancies appear to be absent from the report and should be included.\nThis manuscript describes the first experimental positron lifetime spectroscopy study of vacancy-related defects in Sb Se and the necessary supporting two-component density functional theory (TC- 2 3 DFT) calculations that enable interpretation. In contrast to ‘conventional’ DFT studies the primary focus of TC-DFT is the calculation of the positron parameters. These calculations use the output geometries from the Wang et al (2023) study (kindly shared by the authors) as initial inputs for the positron density and further structural relaxation optimisations. We are not reporting a full density function theory study of monovacancy and divacancy defects in this manuscript. Motivated by the clear experimental observation of divacancies in certain samples reported here we do indeed plan a future combined theory and experimental study of divacancy and larger defects which would enable the calculation of formation energies and configurations, but this is outwith the scope of this study.\nMinor\n5. On the 32th line of page 2 the authors stated “The results are consistent with recent density function theory predictions that both the Sb and the Se monovacancy defects are amphoteric”. However, as the present study only considers neutral and negatively charged defects, so the conclusion of “amphoteric” cannot be drawn.\nWe agree with the reviewer and amphoteric has been omitted in the revised manuscript.\n6. Other points:\n• On the 126th line of page 6, “These methods have unique specificity for vacancy, open volume, defects and have a sensitivity limit of approximately 1015 cm-3”:\n• These methods -> This method\n• Please specify what the limit of 1015 cm-3 is for\n• A citation should be added for the limit here\nThe reason for the use of the plural is that the statement “These methods have unique specificity for vacancy, open volume, defects and….” is true for all positron annihilation spectroscopy methods positron lifetime, Doppler broadening spectroscopy and 2DACAR. The paragraph was aimed at a general audience; it starts with general statements before focusing on the method used here, positron lifetime spectroscopy.\nThe sensitivity limit is explicitly discussed in Reference 25 and is stated in Ref 26, we have now added these citations at the appropriate point.\nThe reviewer asks us to specify what type/s of open volume vacancy defect the approximate concentration sensitivity limit of 1015 cm-3 applies. This question has a rather complex and technical answer which due to the constraints of word count and of clarity for the non-specialist we did not articulate further. The standard positron trapping model (See Supplementary Note 3) states the trapping rate, κ, of positrons to an open volume defect is given by κ = µ[V] where [V] is the defect V V V concentration and µ is the defect-specific positron trapping coefficient. The sensitivity limit depends V on the experimental limitations of measuring κ. In the simplest experimental situation of one positron V trapping defect type then the sensitivity limit comes from the ability to detect and measure the intensity the defect lifetime component. The lower sensitivity limit for defect concentration is then given by product [V] = κ /µ, and hence also on the value of µ. The method has the best sensitivity for min Vmin V V vacancy defects with the largest defect-specific positron trapping coefficients. Negatively charged vacancy defect will have a higher value than a neutral vacancy, the coefficient for a vacancy cluster defect can increase with increasing size, up to a certain point. The issue is our knowledge of the µ V values is addressed in Supplementary Note 3.\n• On the 160th line of page 7, combing -> combining\nCorrection made.\n• On the 9th line of SI, please correct the repetitive sentences\nThe two sentences have been reworded.\n• On the 35th line of SI, please cite for “the Standard Trapping Model (STM)”\nReference 5 is now cited.\nResponse to the remarks of Reviewer #3\nThe manuscript “Detection and identification of vacancy defects in antimony selenide” by David J. Keeble and co-authors reports a major step forward in the identification of vacancy defects in antimony selenide, that is a highly promising rapidly emerging material for future generation solar cells, with reported lab record efficiencies above 10% achieved in the last few years. Keeble and co-authors convincingly demonstrate that the presence of Sb and Se monovacancies and divacancies can be uniquely resolved in Sb2Se3 by combining state-of-the-art positron annihilation lifetime spectroscopy studies and ab-initio calculations (including local relaxation of atoms due to the densities of the electrons and positron). These studies were performed at the expert level and support the conclusions well.\nThis paves the way to systematically examine the presence and concentrations of these point defects in Sb2Se3 layers tailored for application in solar cells, which is key to improve the current relatively modest open circuit voltages (around 50% of the Shockley Queisser limit), related to the presence of point defects and extended defects leading to unwanted charge carrier recombination. The well-described research as well as the highly accessible explanation of the key concepts of positron annihilation spectroscopy and abinitio calculations will make this work highly valuable generally for researchers working in the fields of semiconductor layers for solar cells or other applications where point defects play an important role in their functional properties. I recommend publication of this highly interesting manuscript in Nature Communications, after some minor revisions, as suggested in my (technical) comments listed below, have been considered by the authors.\nQuestions and Comments:\n1. Figure 2b, p. 10 (discussed on p. 8, line 165-167) shows the calculated positron density in the Sb(1) vacancy. Figure 1 on p. 4 suggests that the neighbouring Se(2) atom loses its single atomic bond. What happens with the Se(2) atom, does it go to an interstitial site or does it bind to another atom?\nThe primary purpose of our Figure 2b was to clearly demonstrate to a non-positron audience the positron localisation at vacancy-type defects. The precise details of the local structure of the site-3 – 3 charge Sb monovacancy is better illustrated in Wang et al (PRB 108 134102) FIG.2(a) (and more clearly in their supplementary information Figure 1(b)). We thought it was not appropriate for us to go any further than we have into the level of local structural detail performed and described by Wang et al. There is a movement of the neighbour toward the vacancy site (Wang et al SI section S2).\n2. Table 1, p. 9: The calculated lifetime associated with a neutral Se(2) monovacancy is missing. Is there a special reason why this was left out from the study?\nWang et al do not find a stable neutral charge state for the site-2 Se monovacancy, their calculations show it to be a strange four-electron negative-U centre flipping from +2 to – 2, in consequence we did not have a local geometry to enable a calculation.\n3. p. 11, lines 204-210: the ranges for discriminating between Se(2-) monovacancies, Sb(3-) monovacancies and divacancies are reported to within an accuracy of 1 ps. This is too accurate, since systematic experimental inaccuracies in the positron lifetime are around 3-5 ps [26]. Also systematic inaccuracies will exist for the calculated positron lifetimes of these point defects obtained from the ab-initio study. I would like to suggest to report more global ranges for discrimination of these defects: Se(2-) monovacancies ~300 to 310 ps, Sb(3-) monovacancies: ~315 to 330 ps, Se(0) monovacancies: around 330 ps, divacancies: ~330 to 350 ps. This leaves the conclusions well intact.\nWe completely agree with the reviewer and have restructured the paragraph and modified the lifetime ranges as suggested.\n4. Figure 3d, p. 13, and text on p. 18, lines 344-346: The single trapping model is applied in a highly convincing manner, not only evident by the extracted bulk (perfect lattice) positron lifetime that systematically falls in the range of 260(6) ps, but also demonstrated by the dependence of I_RB as a function of the reduced bulk lifetime tau_RB. I would like to suggest to plot, as a guide-to-the-eye, the function I_RB (tau_RB) = (tau_D/tau_B –1)/(tau_D-tau_RB) * 100% of the single trap model, with tau_B=257 ps and tau_D = 320 ps (average value for the defects observed), that fits the measured the intensity I_RB very well for the relevant range in tau_RB of 100 to 257 ps.\nWe thank the referee for this suggestion and have added a guide to the eye line to Fig. 3d and have added the appropriate expression with a brief explanation to Supplementary Note 3.\nRemarks/suggestions on technical details:\n1. p. 2, line 44: V_oc ~ 40% of bandgap value is stated. It would be better to state that V_oc ~50% of Shockley-Queisser limit (since bandgap values cannot be reached theoretically, instead of the normally applicable Shockley-Queisser detailed balance limit).\nThe referee is correct about the SQ limit - even though most papers refer to Voc as a fraction of bandgap. For clarity we have therefore amended the manuscript to say it both ways.\nOriginal manuscript states: “low values of open-circuit voltages, V , which are typically only ~40 % of oc the bandgap value.”\nChanged to: ““low values of open-circuit voltages, V , which are typically only ~40 % of the bandgap oc value (i.e. ~50% of the Shockley-Queisser limit).”\n2. p. 6, line 127: a sensitivity limit of 10^15 cm^-3 is quoted, that in fact depends on the material and type of vacancy (10^16 cm^-3 for the neutral vacancy and 10^15 cm^-3 for the negatively charge vacancy in c-Si). It seems appropriate to state here that such defects can be evaluated in the range of ~10^15 cm^-3 to ~10^19 cm^-3 [26].\nIndeed, we were trying to keep this issue of sensitivity as simple as possible for the non-specialist reader. We have considered the reviewers helpful suggestion and modified the sentence adding references.\nChanged to: “These methods have unique specificity for vacancy, open volume, defects and have a sensitivity limit of approximately 1015 cm-3 and can estimate vacancy defects concentrations up to approximately 1019 cm-3 beyond which saturation positron trapping occurs25,26.”\n3. p. 11, line 215-216: thermal evaporation (TE) is stated as one of the synthesis methods of the Sb2Se3 films, but this method is not specified in the Methods Section, p. 23, line 455. Also, the thicknesses of the films are not specified in the manuscript, while these are crucial for the interpretation of the positron lifetime results, with implantation energies ranging from 4 to 17 keV (up to 1000 nm depth).\nWe have corrected these omissions in the revised text. The CSS film was approximately 1500 nm in thickness and the thermally evaporated film was 800 nm. A description of the thermally evaporated films has been added to the Methods section.\n4. Fig. 3b, p. 13: the label 17 keV for Sb2Se3(B) should be 6 keV.\nThe 17 keV label has been moved to the appropriate symbol and the symbol for the Sb Se (B) data 2 3 point corrected.\n5. p. 20, lines 380-383: vacancy concentrations in units of cm^-3s^-1 are specified, while in the Supplementary Information specific trapping coefficients mu_V in units of s^-1 are provided. Were the unit cell dimensions of Sb2Se3 applied to convert the dimensions? A typical value of ~6x10^-8 cm^-3s^-1 is used in the manuscript, while a typical value for mu_V of 6x10^15 s^-1 is stated in the Supplementary Information. The two values are not positioned in the same way within the ranges specified (for example a typical value of ~1.2x10^-7 cm^-3s^-1 is expected, based on the typical value for mu_V).\nWe thank the reviewer for bringing this to our attention. We had made an error on p20 lines 380-383. In this sentence we should have quoted defect specific trapping coefficient values per atom per second, rather than the volume specific values in units of cm-3s-1. For the semiconductor community there is a strong temptation to quote in units of cm-3s-1, but as we are making a general point here we should have used s-1.\nWe are quoting from Table 3.3 in Ref. 25 (Krause-Rehberg) and for negative charge state vacancies the range should strictly have been 0.1E15 to 30E15 s-1. However, Krause-Rehberg & Leipner go on to quote a more selected range of experimental values along with theory values in Table 3.4. The average of these values for negative vacancies ~ 3E15 s-1, this is a more probable value. We have modified the relevant text on p20 accordingly. We have also modified the text on p5 of Supplementary Note 3 to be consistent with the main text. We have used the 3E15 s-1 value and calculated the resulting per volume trapping coefficient values for both the Sb and the Se sites in Sb Se and obtain 2 3 an approximate average value of 1.6 x 10-7 cm3s-1. We have added text stating this in the modified Supplementary Note 3 and have changed the value of the two vacancy defect concentrations reported on p20 of the main text. This has resulted in a small reduction in these values compared to those given in the original manuscript.\n6. Supplementary Information, p. 5, line 43: In equation (1), the – sign should be a + sign in the sum of the two terms.\nThis typo has been corrected.\nWe again thank the reviewers for their thorough and careful consideration of the manuscript and for their constructive comments and corrections. New Density Functional Theory calculations have been performed and are included to address directly the question raised regarding the binding and formation energies of the possible divacancies. The postdoctoral associate who performed these extensive additional calculations has, in consequence, been added to the author list."}, {"round": 2, "reviewer_comments": {"reviewer_1": "This study applies the positron annihilation technology to the selenide antimony material system to detect the presence of vacancy defects. In the revision, the authors have properly addressed previous concerns. Regarding the analysis, I have minor suggestions to this study.\nIt might be necessary to provide some additional information to further support the conclusion. For instance, in Figure 4, the author has presented two spectra of positron annihilation lifetimes. Could you provide the original curves of the positron annihilation lifetimes in other cases and the corresponding results of the three-exponential fitting?\nIs the result of the three-index fitting of the lifetime of positron completely reliable? The authors mentioned that a longer positron lifetime (For example, 467 ns) indicates the presence of larger open volume defects, can it be considered that these are some holes present in the crystal? If this is the case, what is puzzling is that there are holes in the single-crystal samples, while the deposited film samples do not have any holes at all. This is highly contrary to common sense.\nApart from these issues, this study is indeed an interesting and novel one, and it holds significant importance for the future microscopic non-destructive detection of materials.", "reviewer_2": "While I appreciate that the authors have addressed Q1 and Q3 in sufficient technical detail, the evidence provided for divacancy identification (Q2 and Q4) remains insufficient. My concerns are as follows:\n1. Formation energy not discussed:\nThe manuscript does not include any estimate of the formation energy of the divacancy, nor does it reference prior work on its thermodynamic stability in Sb₂Se₃. Without this, it's difficult to evaluate whether such a defect is likely to form under the relevant growth or annealing conditions. Even if the calculated positron lifetime matches the experimental value, a divacancy with a high formation energy would likely exist only in negligible concentrations.\n2. Lifetime difference within uncertainty margins:\nGiven the close proximity of the calculated lifetimes, it is challenging to reliably distinguish the divacancy from the monovacancy based on positron lifetime alone. The lowest predicted divacancy lifetime is nearly indistinguishable from the highest monovacancy value, while the highest divacancy lifetime exceeds it by only about 20 ps. This difference falls well within the typical combined uncertainty of positron lifetime measurements and TC-DFT calculations, making it difficult to unambiguously attribute the longer lifetime component to a divacancy.\n3. Limited exploration of charge states and configurations:\nThe divacancy geometries were generated by directly combining two monovacancies. However, it is not clear whether other plausible divacancy configurations or charge states were considered. This limits the strength of the comparison between theory and experiment, as both the structure and charge state can significantly affect the formation energy and positron lifetime. I would expect at least a brief discussion of this aspect.\nOverall, these points suggest that the divacancy identification should be discussed with more caution, as the current wording suggests a level of certainty that the evidence does not fully support.", "reviewer_3": "The authors of the manuscript “Detection and identification of vacancy defects in antimony selenide” satisfactorily answered my questions and comments, explaining well their views and insights on these points. They carefully and properly revised the manuscript including the Supplementary Information. They addressed the comments of all reviewers. I recommend publication of this highly interesting manuscript in its current version in Nature Communications.\nMinor text suggestions:\n1. p. 7, line 144: “Here we report the detection of vacancy-related defects” (add ‘of’)\n2. p. 22, line 420: “In particular, this concerns the prediction of a stable” (add ‘this concerns’ to complete the sentence)\n3. Supplementary Information, p. 10, line 4: “in vacuum.6” (It concerns Reference 6 of the list of References on the same page)", "reviewer_4": "I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts."}, "author_response": "We address each comment in the below response.\nResponse to the remarks of Reviewer #1\nThis study applies the positron annihilation technology to the selenide antimony material system to detect the presence of vacancy defects. In the revision, the authors have properly addressed previous concerns. Regarding the analysis, I have minor suggestions to this study.\nIt might be necessary to provide some additional information to further support the conclusion. For instance, in Figure 4, the author has presented two spectra of positron annihilation lifetimes. Could you provide the original curves of the positron annihilation lifetimes in other cases and the corresponding results of the three-exponential fitting? Is the result of the three-index fitting of the lifetime of positron completely reliable?\nWe chose to illustrate the results of the fitting of the experimental lifetime spectra along with the fit and fit components using two typical spectra in Figure 5 (Figure 4 previously), the plots for all the spectra look very similar to these and so we have not shown them all. We do include all the best fit results, including all the relevant three-component fits, in Supplementary Tables 3 and 4. We have updated these tables to include the reduced chi-squared values for each to show that the values are within the typical accepted reliability range.\nThe authors mentioned that a longer positron lifetime (For example, 467 ns) indicates the presence of larger open volume defects, can it be considered that these are some holes present in the crystal? If this is the case, what is puzzling is that there are holes in the single-crystal samples, while the deposited film samples do not have any holes at all. This is highly contrary to common sense.\nThe lifetime for a divacancy in this material is ~340 ps. The lifetime of 467 ps is consistent with trapping to a multivacancy cluster containing more than two vacancies. If the open volume was the size of a nanovoid the lifetime value would be in positronium range of ~0.5 < τ < 142 ns (Supplementary o-Ps Note 3). We have changed the text to clarify this point; “..a low concentration of larger multivacancy cluster defects..”.\nApart from these issues, this study is indeed an interesting and novel one, and it holds significant importance for the future microscopic non-destructive detection of materials.\nWe thank the reviewer for their comments which have contributed to our improved revised manuscript and for their positive assessment of that manuscript.\nResponse to the remarks of Reviewer #2\nWhile I appreciate that the authors have addressed Q1 and Q3 in sufficient technical detail, the evidence provided for divacancy identification (Q2 and Q4) remains insufficient. My concerns are as follows:\n1. Formation energy not discussed:\nThe manuscript does not include any estimate of the formation energy of the divacancy, nor does it reference prior work on its thermodynamic stability in Sb₂Se₃. Without this, it's difficult to evaluate whether such a defect is likely to form under the relevant growth or annealing conditions. Even if the calculated positron lifetime matches the experimental value, a divacancy with a high formation energy would likely exist only in negligible concentrations.\nWe performed new extensive density functional theory calculations of the binding and formation energies of the possible divacancy configurations to address this point. The results are now included in the new Figure 2 and related new text in the manuscript (also see Supplementary Note 1). These show that VSb(1)VSe(2) divacancy has a binding energy of -0.81 eV and is predicted to have the lowest formation energy for Fermi level positions through most of the band gap. The subsequent TC-DFT calculations returned a positron state lifetime of 343 ps and 338 ps, for the -1 and -3 charge states (Table 1), respectively, in good agreement the experimental lifetimes (Fig. 4, Supplementary Tables 3 and 4). The VSb(2)VSe(1)-short configuration has a slightly lower binding energy while the other possible divacancy configurations have noticeably lower binding energies, more restricted ranges of stable Fermi level position, and higher formation energies (Fig. 2, Supplementary Note 1).\n2. Lifetime difference within uncertainty margins: Given the close proximity of the calculated lifetimes, it is challenging to reliably distinguish the divacancy from the monovacancy based on positron lifetime alone. The lowest predicted divacancy lifetime is nearly indistinguishable from the highest monovacancy value, while the highest divacancy lifetime exceeds it by only about 20 ps. This difference falls well within the typical combined uncertainty of positron lifetime measurements and TC-DFT calculations, making it difficult to unambiguously attribute the longer lifetime component to a divacancy.\nWhile there indeed systematic uncertainties in the TC-DFT calculations dependent on calculation method and approximations assumed the trend in lifetime values from perfect lattice to monovacancy to divacancy are normally reliable. In this work a centrally important result is the good agreement between the experimental perfect lattice state lifetime value of 260(6) ps which it unambiguously determined in this work and the TC-DFT calculated value of 257 ps. This provides strong supporting evidence that, possibly fortuitously, the method and approximations used are indeed yielding positron lifetime values appropriate for Sb Se . This point is clearly made in the manuscript. 2 3\nThe experimental positron lifetime results unambiguously exhibit lifetime less than 320 ps (301 ps to 316 ps) from ten of the spectra (Fig. 4, Supplementary Tables 3 and 4). Our updated divacancy TC-DFT calculations performed using the ShakeNBreak/DFT optimised ground state geometries return divacancy positron state lifetimes ranging from 320 ps to 343 ps (Supplementary Table 1). The 320 ps value is for the least probably, most unstable, divacancy configuration (Fig. 2). A proposal that attributes the experimental lifetimes in the range ~300-320 ps to divacancy defects would not seem reasonable.\nIn performing the DFT calculations for the divacancies at the suggestion of the reviewer it can be noted that we also performed check ShakeNBreak/DFT calculations for the monovacancy defects, the results for the ground state configurations were in very good agreement with those of Wang XW et al (PRB 108 134102) (see Supplementary Fig. 1). The TC-DFT calculated monovacancy positron state 2 lifetimes range between 302 ps and 332 ps (Table 1). The longer values of 329 ps and 332 ps are for the lower probability neutral charge state of the Se vacancy (PRB 108 134102 Fig. 1b). Our experimental positron lifetime results return a positron lifetime between 337 ps and 354 ps for four of the spectra, two of which give values of ~ 343 ps (Fig. 4, Supplementary Tables 3 and 4). These lifetimes are unambiguously longer than 332 ps and a proposal that attributes these defect lifetimes to monovacancy defects would not seem reasonable.\nAs discussed in the manuscript experimental lifetime components in the range ~320 ps to 329 ps returned in three of the spectra cannot be unambiguously attributed to monovacancy defects due to the overlap with between the VSb(3) value of 330 ps with the range for the less probably neutral VSe states and the lower binding energy divacancy configurations (Table 1, Supplementary Table 1). Nevertheless, given that the -3 charge states of the Sb vacancies have the lowest formation energies (PRB 108 134102 Fig. 1b, Supplementary Fig. 1) for possible positron trapping vacancy-related defects it would not seem unreasonable to postulate, as we do, that these experimental lifetimes are more probably attributable to Sb monovacancies.\n3. Limited exploration of charge states and configurations: The divacancy geometries were generated by directly combining two monovacancies. However, it is not clear whether other plausible divacancy configurations or charge states were considered. This limits the strength of the comparison between theory and experiment, as both the structure and charge state can significantly affect the formation energy and positron lifetime. I would expect at least a brief discussion of this aspect.\nWe now report full ShakeNBreak/DFT calculations that find the fully relaxed possible divacancy binding energies, formation energies, and local geometries, see answer to point 1.\nOverall, these points suggest that the divacancy identification should be discussed with more caution, as the current wording suggests a level of certainty that the evidence does not fully support.\nWe appreciated the reviewers concerns on this point which is why we undertook to perform an exhaustive set of new DFT calculations to carefully explore the feasibility of the possible divacancy configurations and then use these ground state structures for the TC-DFT calculations. We are grateful to the reviewer for guiding us down this path as it has resulting in a far stronger, more rigorous, manuscript. It turned out the agreement between the lowest energy, most probably, divacancy configuration and our experimental results was also significantly improved.\nResponse to the remarks of Reviewer #3\nThe authors of the manuscript “Detection and identification of vacancy defects in antimony selenide” satisfactorily answered my questions and comments, explaining well their views and insights on these points. They carefully and properly revised the manuscript including the Supplementary Information. They addressed the comments of all reviewers. I recommend publication of this highly interesting manuscript in its current version in Nature Communications.\nMinor text suggestions:\n1. p. 7, line 144: “Here we report the detection of vacancy-related defects” (add ‘of’)\nCorrection made.\n2. p. 22, line 420: “In particular, this concerns the prediction of a stable” (add ‘this concerns’ to complete the sentence)\nWe agree the English could be improved for this sentence, the subject – the DFT predictions – are referred to in the previous sentence and the repetition of prediction in the target sentence was also not ideal. In consequence we have modified the sentence to read “In particular, the existence of a stable –2 charge…..”.\n3. Supplementary Information, p. 10, line 4: “in vacuum.6” (It concerns Reference 6 of the list of References on the same page).\nCorrection made.\nWe thank the review for their knowledgeable and highly positive assessment."}, {"round": 3, "reviewer_comments": {"reviewer_1": "In this revision, the authors have well addressed my concerns, the manuscript is recommended for acceptance.", "reviewer_2": "I am satisfied with the response. The additions to the manuscript have made it a more substantial piece of work, and I am happy to recommend publication without further changes.", "reviewer_4": "I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts."}, "author_response": ""}]

Decision letter