Enhanced P-type conductivity in Sb₂Se₃ through alkali and alkaline earth metal doping

Abstract

Antimony selenide (Sb₂Se₃) has recently received much attention as a potential candidate for light absorbers in thin-film photovoltaic technologies because of its earth abundance, nontoxicity, and promising electrical and optical properties. Treatments with alkali and alkaline earth elements have been shown to enhance the performance of conventional thin-film solar cells. In this study, we employ hybrid density functional theory to investigate the electronic structures and defect properties of Sb₂Se₃ doped with alkali and alkaline earth elements in comparison to those of native undoped Sb₂Se₃. Our results indicate that undoped Sb₂Se₃ exhibits slight p-type conductivity and semi-insulating property under Se-rich and Se-poor conditions, respectively, consistent with experimental observations. The calculations further reveal that potassium, magnesium, and calcium act as acceptor dopants in a Se-rich environment, improving the p-type conductivity by preferentially forming antisite defects, whereas sodium has a negligible impact. Notably, calcium substitution at Sb site shows the lowest formation energy and a shallow transition energy level, significantly enhancing p-type conductivity. Given its earth abundance, eco-friendliness, and nontoxicity, thus, calcium presents a promising p-type dopant for improving the conductivity and efficiency of Sb₂Se₃-based devices.

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Introduction

Antimony selenide (Sb₂Se₃) has recently received a great deal of attention as a potential light-absorbing material for thin-film photovoltaic technologies due to its earth abundance, nontoxicity, and favorable electrical and optical properties, including an appropriate bandgap (1.1–1.3 eV) and high absorption coefficient (>10⁵ cm⁻¹ in the visible region).^1–4 These characteristics position Sb₂Se₃ as a sustainable alternative to conventional photovoltaic materials and a promising candidate for efficient solar cells. Sb₂Se₃ features a unique one-dimensional (1D) nanoribbon structure with an orthorhombic unit cell, where the ribbons covalently connected along the c-axis are held together by weak van der Waals interactions. This structure results in large spacing between the nanoribbon chains and multiple nonequivalent atomic sites, leading to complicated intrinsic defect properties.^5–12 In addition, these nanoribbons provide anisotropic charge transport properties, where carrier mobility depends on their preferential orientations. When the nanoribbons are well-oriented along the c-axis, Sb₂Se₃ demonstrates intrinsically inert grain boundaries and favorable charge transport properties.^5,13 These attributes are critical for photovoltaic applications, as they minimize recombination losses at grain boundaries. Recently, the power conversion efficiency of Sb₂Se₃-based solar cells has exceeded 10% through vapor deposition or chemical bath deposition techniques,^14,15 yet this is still far below the theoretical limit of 26%.^16,17 This indicates the significant potential for further improvements through the development of effective doping strategies, minimization of intrinsic defects, and/or optimization of device structures and crystal growth conditions.

Density functional theory (DFT) calculations are extensively employed to study the electronic, optical, and structural properties of crystalline semiconductors used in solar cell applications.^18,19 Hybrid functionals incorporating nonlocal Hartree–Fock (HF) exchange are particularly effective in accurately reproducing the bandgap of materials, making them a preferred choice for describing the electronic structures and defect chemistry of such materials.^11,20,21 Zhou et al. demonstrated through DFT calculations that Sb₂Se₃ ribbons with well-oriented grain boundaries exhibit no significant surface reconstruction.⁵ Additionally, DFT approaches have been employed to investigate the properties of intrinsic defects in Sb₂Se₃ supercells^6–8,10 and evaluate the effects of extrinsic doping to identify suitable p-type and n-type dopants for Sb₂Se₃.^9,22,23

Introducing alkali elements, such as sodium and potassium, has been shown to significantly enhance the power conversion efficiency of CZTS^24,25 and CIGS^26–28 solar cells by improving surface and interface properties. Similarly, alkaline earth metal treatment (MgF₂ or CaF₂) have been reported to improve the conductivity and device performance of CIGS solar cells.^29–31 Since commercial soda-lime silicate glass contains Na, Mg, and Ca,³² these elements can diffuse into the active layers of solar cells during high-temperature growth, potentially affecting the device performance.

Considerable efforts have been made to improve the efficiency of Sb₂Se₃ solar cells through effective doping strategies.^{22,23,33–36} However, it is important to note that no systematic experimental or theoretical studies have yet addressed the impact of alkali and alkaline earth elements on Sb₂Se₃. Previous studies suggest that sodium and magnesium have negligible effects on device performance,^36,37 while potassium has been shown to enhance the solar cell efficiency.³⁸ Therefore, comprehensive investigation into the influence of these elements on the electrical conductivity of Sb₂Se₃ using DFT calculations is imperative.

In this study, we present computational results based on hybrid functional approaches to explore the effects of alkali and alkaline earth elements on the electronic properties of Sb₂Se₃ solar cells. We evaluate the electronic structures and intrinsic defect properties of defect-free Sb₂Se₃ (see Fig. 1) and subsequently analyze the extrinsic doping properties by incorporating Na and K as alkali metals and Mg and Ca as alkaline earth metals.

Fig. 1 Crystal structure of Sb₂Se₃ with labeled nonequivalent atomic sites: Sb₁ and Sb₂ for antimony and Se₁, Se₂, and Se₃ for selenium.

Computational methodology

We performed DFT calculations for antimony selenide with and without dopants using the generalized gradient approximation (GGA) within the framework of the projector-augmented wave (PAW) scheme, as implemented in the Vienna Ab Initio Simulation Package (VASP).^39–41 The crystal structure of Sb₂Se₃ was obtained from experimental data: a = 11.62 Å, b = 11.77 Å, c = 3.962 Å, and α = β = γ = 90°.⁴² The structure of a 1 × 1 × 3 supercell containing 60 atoms was optimized using the Perdew–Burke–Ernzerhof (PBE) functional with a 4 × 4 × 4 Monkhorst–Pack k-point grid, ensuring convergence of the total energy to less than 10⁻⁶ eV per atom and residual force to below 0.01 eV Å⁻¹. The plane-wave cutoff energy was set to 520 eV, and GD3BJ van der Waals corrections⁴³ were applied to account for interactions between Sb₂Se₃ nanoribbons. The hybrid Heyd–Scuseria–Ernzerhof (HSE) functional,⁴⁴ incorporating 25% HF exchange, was employed to evaluate total energies, band structures, and density of states (DOS). Band structure calculations used high-symmetry k-points: Γ (0.0, 0.0, 0.0), X (0.5, 0.0, 0.0), Y (0.0, 0.5, 0.0), and Z (0.0, 0.0, 0.5).

The defect formation energy of a specific defect α in charge state q, and the charge transition energy level (q/q′), were calculated as:

where E(α,q) and E(host) are the total energies of the supercell with and without the defect, respectively. n_i denotes the number of atoms of species i added to or removed from the supercell, corresponding to negative and positive values, respectively. μ_i is the elemental chemical potential and E_i is the energy of pure elemental phase of species i. E_f is the Fermi level referenced to the valence band maximum (VBM), which varies within the bandgap between the VBM and the conduction band minimum (CBM). ΔE_corr represents correction terms related to the supercell simulation that account for potential alignments and image charge effects, implemented in the sxdefectalign code.⁴⁵

We considered both interstitial and substitutional configurations for potential doping sites. For interstitial defects, five possible configurations were examined within the Sb₂Se₃ crystal structure. Following structural optimization, the most stable configuration corresponding to the lowest total energy was selected as the thermodynamically favored defect site.

Under equilibrium growth conditions, there are a series of thermodynamic limits on the chemical potential.⁴⁶ To avoid precipitation of elemental dopant (X) and host elements (Sb and Se), first, their chemical potentials μ_i should satisfy:

μ_i ≤ 0 (3)

Second, the host material Sb₂Se₃ should remain stable, i.e.,

2μ_Sb + 3μ_Se = ΔH_f(Sb₂Se₃) = −1.39 eV (4)

where ΔH_f(Sb₂Se₃) denotes the formation energy of Sb₂Se₃ obtained at the HSE06-GD3DJ level of theory. To define Se-rich and Se-poor conditions, the chemical potentials of Se and Sb were adjusted. Under Se-rich conditions, μ_Se = 0 eV and μ_Sb = −0.7 eV, while μ_Se = −0.46 eV and μ_Sb = 0 eV under Se-poor conditions.

Finally, the formation of secondary phases between dopant and host elements should be prevented by satisfying:

aμ_X + bμ_Se < ΔH_f(X_aSe_b) or aμ_Sb + bμ_X < ΔH_f(Sb_aX_b) (5)

The formation energies of potential secondary phases were also calculated at the HSE06-GD3DJ level of theory, and the corresponding maximum chemical potential values of dopants under the two growth conditions of Sb₂Se₃ were determined (see Tables S1 and S2†).

Results and discussion

Undoped Sb₂Se₃

We evaluated the electronic structure of a defect-free Sb₂Se₃ supercell at the HSE06-GD3DJ level of theory. The calculated band structure (Fig. 2a) reveals that the VBM is located between Γ and X in reciprocal space along the a* axis, while the CBM is positioned between Γ and Z along the c* axis. This results in an indirect bandgap of 1.25 eV, consistent with experimental values of 1.2–1.3 eV.^14,47,48 The partial charge densities (Fig. 2b) indicate that the VBM is predominantly localized on Se atoms, while the CBM is distributed across both Sb and Se atoms. Furthermore, the projected DOS (Fig. 2c) shows that the VB primarily originates from selenium orbitals, while the CB exhibits mixed contributions from both antimony and selenium. Overall, these results align well with previous theoretical results.^7,9

Fig. 2 (a) Band structure, (b) partial charge densities of the CBM (top) and VBM (bottom), and (c) DOS of the Sb₂Se₃ supercell. In panel (a), the red and blue lines represent the VBM and CBM, respectively, with the Fermi level shifted to zero.

Intrinsic defect properties of Sb₂Se₃ were examined by calculating the formation energies and transition energy levels under Se-rich and Se-poor conditions. Three types of intrinsic defects were considered: vacancies (V_Sb and V_Se), antisites (Se_Sb and Sb_Se), and interstitials (Sb_i and Se_i) at all nonequivalent atomic sites. The Fermi level (E_f) was varied from zero (VBM) to the bandgap value of 1.25 eV (CBM). For each defect, the formation energies in its lowest-energy charge states were plotted with kinks indicating charge transition energy levels (q/q′), which correspond to ionization levels within the bandgap. Our calculation results show that the same defect at different atomic sites can have distinct formation energies and transition energy levels (see Fig. 3 and 4), consistent with previous theoretical studies.^7,8,10 Additionally, Table 1 provides a summary of our results for the intrinsic defect properties of Sb₂Se₃ and compares them with findings from previous theoretical studies.

Fig. 3 Formation energies of intrinsic defects in Sb₂Se₃ under Se-rich (left) and Se-poor (right) conditions as a function of the Fermi level (E_f). The dashed gray arrow indicates the Fermi level expected in Sb₂Se₃.

Fig. 4 Calculated transition energy levels of intrinsic defects within the bandgap of Sb₂Se₃. Red, green, and yellow bars represent acceptor, donor, and amphoteric defect levels, respectively. The dashed red and green lines, along with the gray box, indicate ionization levels within the bandgap, distinguishing shallow defect levels from deep defect levels.

Table 1 Summary of calculated intrinsic defects in Sb₂Se₃ under Se-rich and Se-poor conditions in comparison with previous DFT studies

Defect	Defect type	Activation E (eV)	ΔEf (eV)	Ref.	Activation E (eV)	ΔEf (eV)
Se-rich		Our work		Other DFT results
SeSb	Amphoteric	SeSb1: VBM + 0.73	1.1	8	SeSb1: VBM + 0.70	∼1.0
		SeSb2: VBM + 0.51	1.2		SeSb2: VBM + 0.62
	Acceptor			7	SeSb1: VBM + 0.55	∼1.0
Sei	Neutral		1.4
VSe	Donor	VSe1: VBM + 0.34	1.9	7 and 10	VSe1: VBM + 0.20	∼2.0
		VSe2: VBM + 0.83	2.0		VSe2: VBM + 0.80
		VSe3: VBM + 0.74	2.0		VSe3: VBM + 0.65
0.5
Se-poor		Our work		Other DFT results
VSe	Donor	VSe1: VBM + 0.34	1.4
		VSe2: VBM + 0.83	1.6	7	VSe2: VBM + 0.80	∼1.0
		VSe3: VBM + 0.74	1.5	8	VSe3: VBM + 0.81	∼1.4
SbSe	Donor	SbSe1: VBM + 0.26	1.2	7	SbSe1: VBM + 0.18	∼1.0
	Amphoteric	SbSe2: VBM + 0.57	1.0	8	SbSe2: VBM + 0.52	∼1.1
	Donor	SbSe3: VBM + 0.57	1.1
Sbi	Donor	VBM + 0.82	<2.0	8		<1.5

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As shown in Fig. 3, V_Sb1 and V_Sb2 has higher formation energies than other defects, indicating that V_Sb defects are not easily formed and occur at low concentrations within the lattice. The formation energy of V_Sb decreases as transitioning from the neutral state to the anionic state, confirming that V_Sb acts as an acceptor defect. Conversely, V_Se behaves as a donor defect, losing electrons as it changes from the neutral state to the doubly positively charged state. The formation energies of V_Sb and V_Se vary with growth conditions, increasing and decreasing, respectively, when the environment shifts from Se-rich to Se-poor conditions.

Antisite defects, such as Sb_Se and Se_Sb, are amphoteric, acting as either donor or acceptor defects depending on the position of the Fermi level. This behavior is consistent with previous theoretical findings.^8,10 The calculated (−/+) transition energy levels of Se_Sb1 and Sb_Se2 are 0.73 eV and 0.51 eV above the VBM, respectively (see Fig. 3 and Table 1). Among the interstitial defects, the anion interstitial defect (Se_i) has a lower neutral formation energy than the cation interstitial defect (Sb_i). Se_i remains electrically neutral across most of E_f range, contributing minimally to conductivity, as it does not significantly alter the charge carrier concentration. In contrast, Sb_i acts as a donor defect but has a relatively high formation energy, limiting its concentration.

Low-energy defects result in higher defect concentrations within the material. To ensure that these defects generate free carriers contributing to electrical conductivity, their transition levels should be shallow, i.e., close to either the VBM for acceptor defects or the CBM for donor defects. The calculated transition energy levels of intrinsic defects in Sb₂Se₃ indicate that most donor and acceptor defects are deep (see Fig. 4). This explains why native antimony selenide exhibits intrinsic-like conductivity behavior. While the (−/0) transition energy level of V_Sb is shallow, its multiple transition levels suggest that it may act as a recombination centers, detrimental to solar cell performance.

Under Se-rich conditions, the dominant defects appear to be Se_Sb1 and Se_Sb2, whereas Sb_Se2 and Sb_Se3 are prevalent under Se-poor conditions (see Fig. 3 and Table 1). Note that under thermal equilibrium conditions, E_f is pinned at the intersection of the lowest acceptor and donor formation energies.⁴⁹ Under Se-rich conditions, the acceptor and donor defects with the lowest formation energies are Se_Sb2⁻ and Se_Sb1⁺, respectively, whereas Sb_Se1⁻ and Sb_i³⁺ are the acceptor and donor defects with the lowest formation energies under Se-poor conditions, respectively. As a result, the expected E_f positions are 0.54 eV under Se-rich conditions and 0.63 eV under Se-poor conditions (see Fig. 3), which aligns closely with the experimental values of 0.52 eV and 0.60 eV, respectively.⁵⁰

These results suggest that undoped Sb₂Se₃ material is intrinsically weakly p-type under Se-rich conditions, whereas it is semi-insulating under Se-poor conditions. Thus, additional treatments, such as doping with alkali or alkaline earth elements, are able to further increase the conductivity and improve the solar cell performance of Sb₂Se₃. Both interstitial (X_i) and cationic substitutional (X_Sb) configurations for these dopants were considered (see Fig. 5).

Fig. 5 Illustrations of (a) antisite defects and (b) interstitial defects in Sb₂Se₃.

Sodium doping

The first alkali element investigated in this study is sodium. Sodium in interstitial positions (Na_i) acts as a donor defect, donating an electron when it transitions from the neutral state to the singly positively charged state. As a result, the formation energy of Na_i decreases as E_f shifts downward toward the VBM (see Fig. 6a). The +1 charged state of Na_i is energetically favorable across the entire range of E_f. In contrast, sodium substitution at cationic sites (Na_Sb) behaves as an acceptor defect, as substitution at Sb sites creates an electronic hole. The formation energy of Na_Sb decreases as E_f shifts upward toward the CBM. The −2 charged state of Na_Sb2 is energetically stable for most values of E_f. Notably, Na_Sb2 has a lower formation energy than Na_Sb1, indicating that the defect's formation energy depends on the specific atomic site. Overall, the lower formation energy of Na_i in the neutral state suggests that sodium preferentially occupies interstitial spaces between Sb₂Se₃ ribbons, consistent with prior experimental observations.³⁷

Fig. 6 Formation energies of alkali dopants, (a) Na and (b) K, in Sb₂Se₃ under Se-rich (left) and Se-poor (right) conditions as a function of the Fermi level (E_f) compared with the formation energies of the intrinsic defects represented by gray lines. The dashed gray and green arrows indicate the Fermi levels expected in the undoped and doped systems, respectively.

Under Se-rich conditions, the singly ionized donor defect Na_i⁺ has the lowest formation energy when E_f is less than 0.53 eV, whereas the doubly ionized acceptor defect Na_Sb2²⁻ dominates when E_f is greater than 0.53 eV (see the left side of Fig. 6a). Due to charge neutrality, the Fermi level is pinned near 0.53 eV, aligning closely with the Fermi level (0.54 eV) in undoped Sb₂Se₃. Thus, sodium doping has a negligible effect on conductivity under Se-rich conditions, leaving the weak p-type conductivity unchanged. These calculation results are consistent with experimental findings,³⁷ which support sodium doping minimally affects conductivity and device performance of Sb₂Se₃.

Under Se-poor conditions, the (0/+) transition energy level of Na_i lies above the CBM, classifying it as a shallow defect. Thus, Na_i is easily ionized, contributing to n-type conductivity. The competition between the lowest donor defect Na_i⁺ and the lowest acceptor defect Na_Sb2²⁻ positions Fermi level at approximately 0.76 eV, representing an upward shift of more than 0.1 eV toward the CBM relative to undoped Sb₂Se₃ (see the right side of Fig. 6a). This upward shift indicates that Na-doped Sb₂Se₃ under Se-poor conditions exhibits weak n-type conductivity. Moreover, calculated band structure confirms the absence of localized Na-related defect states within the bandgap of Sb₂Se₃ (see Fig. S1†). Therefore, sodium doping slightly enhances the n-type conductivity under Se-poor conditions.

Potassium doping

The second alkali metal we studied is potassium. The formation energies of K-related defects in K-doped Sb₂Se₃ are presented in Fig. 6b alongside the formation energies of native defects in the undoped system. Similar to sodium, the doubly ionized acceptor defect K_Sb2²⁻ and singly ionized donor defect K_i⁺ determine the doping effect of potassium under both Se-rich and Se-poor conditions. However, the impact of the K-doping on electrical conductivity depends on the growth conditions.

Under Se-rich conditions, the acceptor defect K_Sb2 has a lower formation energy than the donor K_i in the neutral state, indicating that potassium doping introduces electronic holes and increases the hole carrier concentration. K_Sb2²⁻ is the most stable defect when E_f is greater than 0.44 eV, while K_i⁺ is the most stable defect when E_f is below 0.44 eV. This places E_f at 0.44 eV, approximately 0.1 eV closer to the VBM compared with the undoped system. These results suggest that potassium doping enhances p-type conductivity. This finding is in good agreement with the experimental observations, where KOH treatment of Sb₂Se₃ films increased hole concentrations and shifted the VBM close to E_f.

Under Se-poor conditions, the neutral formation energy of K_i is lower than that of K_Sb2, meaning that potassium primarily acts as a donor defect by preferentially forming K_i. The (0/+) transition energy level of K_i lies above the CBM, confirming its classification as a shallow defect. K_i produces additional free electrons, influencing n-type conductivity and positioning E_f at 0.67 eV above the VBM. Band structure calculations also reveal that potassium hybridizes well with host material without introducing localized defect levels (see Fig. S1†). Thus, K-doped Sb₂Se₃ exhibits slight n-type conductivity under Se-poor conditions.

Magnesium doping

Next, we discuss the impact of alkaline earth elements on the conductivity of Sb₂Se₃. Magnesium is examined as the first alkaline earth atom. The neutral donor defect Mg_i has a significantly higher formation energy than the acceptor defects Mg_Sb1 and Mg_Sb2 under both Se-rich and Se-poor conditions (see Fig. 7a). This suggests that magnesium more likely substitutes at cationic antimony sites rather than occupying interstitial positions between atomic nanoribbons. Among the acceptor defects, Mg_Sb2 has a lower energy than Mg_Sb1, making it the more stable defect. Mg-related acceptor defects are located below the VBM, generating free hole carriers and potentially enhancing p-type conductivity. Band structure calculations confirm that Mg doping does not introduce defect states within the bandgap (see Fig. S1†), consistent with experimental reports.³⁶

Fig. 7 Formation energies of alkaline earth dopants, (a) Mg and (b) Ca, in Sb₂Se₃ under Se-rich (left) and Se-poor (right) conditions as a function of the Fermi level (E_f) compared with the formation energies of the intrinsic defects represented by gray lines. The dashed gray and green arrows indicate the Fermi levels expected in the undoped and doped systems, respectively.

Experimental data indicates that Mg doping in Sb₂Se₃ films results in only minor changes in the mobility and device performance, leading to its characterization as an inert dopant.³⁶ However, our calculations show that Mg preferentially forms the acceptor defect Mg_Sb2. Under Se-rich conditions, E_f is positioned at approximately 0.41 eV, while under Se-poor conditions, it lies at 0.53 eV. These values represent a downshift of approximately 0.1 eV compared undoped Sb₂Se₃ system under both conditions. This shift suggests that Mg doping at Sb sites could enhance p-type conductivity by increasing the free hole concentration, particularly under Se-rich conditions. The discrepancy with experimental results is attributed to the possibility that Mg may not diffuse sufficiently into the active material to substitute for Sb sites. This limited substitution could explain the observed inert behavior of Mg doping in enhancing carrier mobility and device performance. Note that further experimental investigations are warranted to better understand the precise role of Mg doping in Sb₂Se₃.

Calcium doping

Finally, we consider calcium as the second alkaline earth metal. Given the lack of experimental studies on Ca doping, exploring the effects of calcium treatment of Sb₂Se₃ via computational approaches is valuable. The formation energy of the acceptor defect Ca_Sb2 is lower than that of the acceptor defect Ca_Sb1, reflecting the characteristic behavior of 1D semiconductor with nonequivalent atom environments (see Fig. 7b). Similar to magnesium, Ca_Sb2 has a much lower formation energy than a donor defect Ca_i under both Se-rich and Se-poor conditions, indicating that cationic substitution at Sb sites is the dominant doping type for calcium. Consequently, Ca doping is expected to increase the concentration free hole carriers, enhancing the p-type conductivity of Sb₂Se₃.

The Fermi level in Ca-doped system is predicted to be located at approximately 0.22 eV and 0.51 eV under Se-rich and Se-poor conditions, respectively (see Fig. 7b). These positions are determined by the dominance of the acceptor defect Ca_Sb2⁻ under both conditions, while Se_Sb1⁺ and Sb_i³⁺ are the lowest-energy donor defects for Se-rich and Se-poor conditions, respectively. Calcium doping downshifts E_f toward the VBM by approximately 0.3 eV under Se-rich conditions and 0.1 eV under Se-poor conditions, supporting an increase in p-type conductivity. Moreover, the (−/0) transition energy levels for Ca_Sb are shallow, with values of 0.09 eV and 0.03 eV for Ca_Sb1 and Ca_Sb2, respectively (see Fig. 8). These shallow transition levels indicate that Ca_Sb defects are easily ionized, promoting a higher concentration of free hole carriers while reducing carrier recombination rates. Overall, our calculations identify calcium as a highly promising p-type dopant for Sb₂Se₃.

Fig. 8 Calculated transition energy levels of alkali and alkaline earth dopants at different atomic sites within the bandgap of Sb₂Se₃. The red and green bars represent acceptor and donor defect levels, respectively. The dashed red and green lines, along with the gray box, indicate ionization levels within the bandgap, distinguishing shallow defects from deep defects. The Mg_Sb1 (−/0) and Mg_Sb2 (−/0) levels are shallow acceptor states in the VB, whereas Na_i (0/+), K_i (0/+), and Ca_i (0/2+) are shallow donor states in the CB.

Recent theoretical and experimental studies have proposed lead (Pb) as an effective p-type dopant in Sb₂Se₃.^22,33 For comparison, the formation energy of Pb_Sb2 under Se-rich conditions is 0.7 eV, comparable to that of Ca_Sb2 (0.8 eV). Both defects have lower formation energies than the intrinsic defects in Sb₂Se₃, making them likely to form. As a result, Ca potentially passivates the deep-level defects in Sb₂Se₃ that are detrimental to device performance. In addition, the (−/0) transition energy level of Pb_Sb2 under Se-rich conditions (0.15 eV) is deeper than that of Ca_Sb2 (0.03 eV). The lower formation energy of the Ca_Sb2 suggests a higher concentration of free carriers, and its shallower defect level promotes ionization and reduces recombination of free carriers. The band structure of the Ca-doped system shows no Ca-related defect levels within the bandgap; instead, defect states are hybridized with the VB and CB of the bulk material (see Fig. S1†). These findings highlight the effectiveness of Ca doping in enhancing the p-type conductivity of Sb₂Se₃.

The transition energy levels of alkali and alkaline earth dopants within the bandgap of Sb₂Se₃ are shown in Fig. 8. Compared with intrinsic defects, these dopants produce shallow donor defects (Na_i, K_i, Mg_i, and Ca_i) and shallow acceptor defects (Mg_Sb and Ca_Sb), although Na_Sb and K_Sb exhibit relatively deep levels. These results demonstrate that alkali and alkaline earth metal doping can introduce shallow, low-energy defects into Sb₂Se₃, thereby increasing the concentration of free carriers. Furthermore, band structures calculations confirm that these dopants do not introduce localized defect states within the bandgap (see Fig. S1†). This feature ensures easier ionization of these dopants, contributing positively to the electrical conductivity of Sb₂Se₃.

Finally, we summarize the defect properties of doped Sb₂Se₃ systems in comparison to those of the undoped material (see Table 2). Notably, under Se-rich conditions, systems doped with alkaline earth metals exhibit enhanced p-type conductivity compared with the undoped system. This improvement is primarily attributed to the presence of shallow, low-energy, and hole-generating acceptor defects, such as Mg_Sb2 and Ca_Sb2. Experimental investigations of calcium and magnesium doping in Sb₂Se₃ by our research team are currently underway.

Table 2 Comparison of the conductivity, Fermi level (E_f), and defect properties of Sb₂Se₃ under Se-rich conditions with respect to alkali and alkaline earth dopants

Se-rich	Sb2Se3	Na–SbSe2	K–Sb2Se3	Mg–Sb2Se3	Ca–Sb2Se3
Conductivity	p-Type	p-Type	p-Type	p-Type	p-Type
Ef expected (eV)	0.54	0.53	0.44	0.41	0.22
Hole-generating acceptors	SeSb2^−	NaSb2^2−	KSb2^2−	MgSb2^−	CaSb2^−
High-population deep donors	VSe2^2+, SeSb1^+	VSe2^2+, SeSb1^+	VSe2^2+, SeSb1^+	VSe2^2+, SeSb1^+	VSe2^2+, SeSb1^+

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Conclusions

Using hybrid DFT calculations, we investigated the impacts of alkali and alkaline earth elements on the electronic structure and defect properties of Sb₂Se₃. In line with recent experimental and theoretical studies,^10,50 our calculations confirm that the expected Fermi level for undoped Sb₂Se₃ are 0.52 eV and 0.63 eV under Se-rich and Se-poor conditions, respectively. These values indicate that the undoped Sb₂Se₃ has weak p-type conductivity under Se-rich conditions and semi-insulating behavior under Se-poor conditions, with a calculated indirect bandgap of 1.25 eV. The dominant intrinsic defects are Se_Sb1 and Se_Sb2 under Se-rich conditions and Sb_Se2 and Sb_Se3 under Se-poor conditions.

Our findings demonstrate that alkali (Na and K) and alkaline earth (Mg and Ca) elements introduce shallow defects in Sb₂Se₃ without creating harmful localized defect states within the bandgap. Sodium preferentially occupies interstitial positions, behaving as a donor defect. This enhances n-type conductivity under Se-poor conditions but has minimal effects under Se-rich conditions. Potassium doping varies with crystal growth conditions. K acts as an acceptor dopant by forming K_Sb2 under Se-rich conditions, while under Se-poor conditions, it behaves as a donor dopant by forming K_i.

Alkaline earth atoms Mg and Ca preferentially substitute at Sb sites, forming acceptor defects that significantly increase hole conductivity. Calcium, in particular, has the lowest formation energy and shallow (−/0) transition levels, comparable to those of Pb, a recently proposed p-type dopant. These results suggest that calcium, as a nontoxic and eco-friendly alternative, could be a potential p-type dopant that enhance hole carrier concentration in Sb₂Se₃.

Our comprehensive theoretical study provides valuable insights into the intrinsic and extrinsic defect properties of Sb₂Se₃ and highlights the role of alkali and alkaline earth metal doping in improving its conductivity and solar cell performance. Furthermore, the findings offer broader implications for understanding material properties of Sb₂Se₃ in applications beyond photovoltaics, including electrochemical cells and photocatalysis.

Data availability

The data supporting this article have been included as part of the ESI.†

Conflicts of interest

The authors declare that they have no conflicts of interest.

Acknowledgements

This research is supported by the Ministry of Trade, Industry and Energy (MOTIE) and the Korea Institute for Advancement of Technology (KIAT) through the International Cooperative R&D program (Project No. P0024567) and by the DGIST R&D Program of the Ministry of Science and ICT of Korea (25-ET-01). The authors are thankful for the use of the High-Performance Computing (HPC) clusters of the Supercomputing AI Education and Research Center at DGIST.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d4ta08978b

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