Sn doping induced intermediate band in CuGaS₂

Abstract

Sn doped CuGaS₂ has been investigated as an intermediate band (IB) material. Our results indicate that Sn doping can indeed induce IBs in the band gap of CuGaS₂ and the optical absorption and solar energy utilization are greatly enhanced due to the existence of the IBs. Though all Sn doped structures concerned are dynamically stable, we found that under thermal equilibrium growth conditions, the CuGaS₂ should be moderately doped to maintain its stability over a chemical potential region in order to achieve novel optoelectronic IB materials growth.

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1 Introduction

To keep up with social development and energy demands, solar cells have been the subject of a great amount of attention. The development of solar cells has gone through three generations from crystalline silicon solar cells and thin film solar cells to the third generation solar cell. Crystalline silicon solar cells have been successfully applied and batch produced, but their production cost remains high. Thin film solar cells such as CdTe and Cu(In,Ga)Se₂ contain toxic and rare-earth elements, so are not environment-friendly. What is more, the previous two generations of solar cells have been developing slowly over recent years and their conversion efficiency has been hovering at around 25%. Thus, a ‘green, environment-friendly, new conceptual and high efficiency’ third generation solar cell has been proposed.¹

One idea for efficiency improvement is to extend the solar cell response^1,2 by introducing several energy states due to defects, lying within the forbidden band gap of the host semiconductors. In order to suppress undesirable non-radiative recombination in the cell,^3,4 sufficient impurities (larger than 10¹⁹ cm⁻³) should be added to the host semiconductor. In this condition, the strong interaction of the impurities will lead to the formation of an impurity band rather than isolated defect energy levels, namely, the intermediate band (IB). The partially filled IB has amphoteric behavior,⁵ both providing and accepting electrons, which could decrease non-radiative recombination.

Unlike the traditional single band gap semiconductor absorption layer in solar cells, where only photons whose energy is larger than the band gap can be absorbed, an inserted impurity band in the band gap can create additional paths for electron transitions by absorption of two extra low energy photons from the IB to the conduction band (CB) and from the valence band (VB) to the IB, leading to a higher photocurrent.

The partially filled IB needs to have the right carrier occupancy to satisfy the requirement that the transitions both into and out of the IB are strong. Moreover, it needs to be isolated to avoid photo-voltage degradation. As a consequence, the use of IB materials could promise a high conversion efficiency. Theoretically, under the ideal conditions, the intermediate band solar cell can reach an upper efficiency of 63.2% with black body illumination from the detailed balance limit theory calculation,¹ which largely exceeds the efficiency of the Shockley–Queisser single-junction solar cell (40.7%)⁶ and tandem solar cell (57.1%). The efficiency will be extended to nearly 80%, by further increasing the number of IBs.⁷ Both theoretical and experimental reports have verified that IB materials could effectively increase optical absorption.^8–16

Recently, I–III–VI₂ type ternary compounds with a chalcopyrite structure have gained much attention. CuIn_1−xGa_x(S,Se)₂ thin film solar cells show an efficiency of higher than 20%.^17,18 CuGaS₂,¹⁹ with a band gap of 2.43 eV, is also an ideal IB host material,^20–25 since it has been reported that the optimum band gap for photovoltaic energy conversion in Cu-based chalcopyrite solar cells is 2.41 eV with an IB located at 0.92 eV from the CB or VB.²⁶ Besides, Cu₂ZnSn(S,Se)₄ is chosen as a substitute for CuIn_1–xGa_x(S,Se)₂ to achieve an indium-free thin film material. In Cu₂ZnSn(S,Se)₄, Sn plays an important role and the Sn-5s orbital contributes to the conduction band.²⁷ There are also experiments showing that Sn doped chalcopyrites exhibit IB characteristics, but there is a lack of systematic theoretical investigations.^28,29

In this work, we employ a screened-exchange hybrid density functional Heyd–Scuseria–Ernzerhof (HSE06) in the density functional calculation of the electronic structure and optical properties of Sn-doped CuGaS₂. The HSE06 calculated band gap of CuGaS₂ is 2.25 eV, in good agreement with the experimental measurement 2.43 eV.³⁰ Our results show that Sn-doped CuGaS₂ exhibits a good IB concept with partially filled IB states appearing in the forbidden band gap. Accordingly, the optical absorption range is largely red-shifted and the optical absorption intensity is enhanced compared with the host CuGaS₂. As the doping concentration increases, the band dispersion as well as the optical absorption becomes stronger. Meanwhile, the Sn doped structures are dynamically stable and phase stability analysis suggests that moderate Sn doping in CuGaS₂ can enable stable IB material growth. Thus, our results explicitly indicate that moderate Sn doping in CuGaS₂ can be used to achieve potential IB materials for photovoltaic applications.

2 Computational details

The tetrahedrally coordinated semiconductor CuGaS₂ has a chalcopyrite structure with a space group of I4̄2d. To investigate the doping properties, a supercell approach is used by replacing one Ga atom with one Sn atom in a 64-atom cell, which corresponds to a 1.5625 at% dopant concentration, as shown in Fig. 1.

Fig. 1 2 × 2 × 2 supercell of CuGaS₂ with Sn dopant.

Our calculations are performed within density functional theory (DFT)³¹ with the projector augmented wave (PAW)³² scheme, as implemented in the Vienna ab initio Simulation Package (VASP) code. For the exchange correlation functional part, since relaxation using HSE06 is time-consuming and has no significant effect on the final properties in our tests, the Perde–Burke–Ernzerhof (PBE)³³ version of the generalized gradient approximation (GGA) is used for the structure’s full relaxation, and the hybrid non-local exchange–correlation functional of Heyd–Scuseria–Ernzerhof (HSE06) is used to calculate the electronic structure and optical properties. The ionic coordinates are fully relaxed until the total energy is changed within 10⁻⁵ eV per atom and the Hellmann–Feynman force on each atomic site is less than 0.01 eV Å⁻¹. In the HSE06 (ref. 34 and 35) functional, 30% of the screened Hartree–Fock (HF) exchange is mixed with the PBE exchange functional and the screening parameter is set to 0.2 Å⁻¹. The cutoff energy for the plane-wave basis set is 300 eV, and a 2 × 2 × 2 Γ-centered Monkhorst–Pack³⁶ k-point mesh is used in both the PBE and HSE calculations.

In the optical property calculations, random phase approximation (RPA) with no local field effects has been used, and only interband and direct transitions have been considered from the contribution out of 600 electronic bands.

3 Results and discussion

3.1 Structural and electronic properties

The optimized structure of the host CuGaS₂ compound presents the average bond lengths of Ga–S and Cu–S to be 2.32 Å and 2.31 Å, which are consistent with previous theoretical and experimental results.³⁷ Doping Sn into the host CuGaS₂ leads to changes in both the lattice parameter and bond lengths, which vary at different doping concentrations. As shown in Table 1, the lattice constant is directly proportional to the doping concentration, obeying the Vegard’s law. The changes of the Sn–S bond length are featured with the 4 first-neighboring S atoms moving outwards from Sn with average bond lengths of 2.60 Å, much larger than that of Ga–S in Sn doped CuGaS₂. Consequently, Sn doping induces lattice expansion. The characteristics of structure change in Sn doped CuGaS₂ indicate that the Sn dopant mainly alters the local geometry around the Sn ions.

Table 1 Lattice parameters (in Å), main band gap and average sub-band gap (in eV) divided by the Fermi level of different concentrations of Sn doped CuGaS₂. E_VB–IB and E_IB–CB denote the sub-band gap values from the VB to the IB and from the IB to the CB

Sn (%)	a	c	E′g	EVB–IB	EIB–CB
0	5.37	10.62	2.25	—	—
6.25	5.39	10.70	2.33	1.47	0.86
12.5	5.41	10.77	2.56	1.37	1.19
25	5.43	10.96	2.70	1.29	1.41

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The HSE06 calculated band structure of host CuGaS₂ shows a direct band gap of 2.25 eV at the Γ point, which is larger than that obtained from previous DFT computational results using the LDA/GGA scheme (0.68–1.25 eV ^12,37–39) and close to the experimental value of about 2.43 eV. The good band gap agreement indicates that the application of the HSE hybrid functional successfully overcomes the limitations of DFT in the underestimation of the band gap. The corresponding valence band maximum is contributed by the Cu-3d and S-3p states and the conduction band minimum is derived from the Ga-4s and S-3p states.

After doping CuGaS₂ with Sn, its electronic structure is significantly changed, as a consequence of structural changes. Partially filled and isolated IBs are introduced into the band gap at both high and low doping concentrations. Dispersion of the IB is obviously seen in Fig. 2, which is of great significance to the mobility and transfer of electrons. The electrons, excited from the VB to the upper empty IB states, can easily flow downwards due to the dispersion feature of the IB, and can then be excited to the CB. As the doping concentration decreases, the dispersion becomes weak. The values of the main band gap and average sub-band gap divided by the Fermi level are presented in Table 1. As the bond length change (increase) of Sn–S is larger than the change in the lattice constant, the interaction between the Ga and S atoms and the Cu and S atoms increased, leading to a little increase in the band gap. The band gap increase is larger for the high-concentration doped CuGaS₂, which is similar to Ti doped CuGaS₂.⁴⁰ By taking data from the sub-band gap and main gap, we estimated the proportion of solar energy that can be absorbed from the solar spectrum. The results show that after Sn doping, the solar energy utilization ratio now reaches 82.3%, 69.0% and 60.5% for the 6.25%, 12.5% and 25% Sn doping concentrations, respectively. In comparison with the original 26% of CuGaS₂, the solar energy utilization is greatly enhanced.

Fig. 2 Band structures of (a) 6.25% (b) 12.5% (c) 25% Sn doped CuGaS₂. The horizontal dashed line denotes the Fermi level.

In order to gain further understanding into the origin of the IB, we show the density of states (DOS) and projected density of states (PDOS) of the Sn doped CuGaS₂ system in Fig. 3. The IB is mainly contributed to from the hybrid states of S-3p, Sn-5s and Cu-3d. We also obtain the partial charge density of the intermediate band. Fig. 4 vividly shows that the charge density of the IB state is mainly located at the Sn dopant and the first neighboring S atoms, and a little at the neighboring second shell of Cu atoms. As previously mentioned, both the VB and CB of the host CuGaS₂ have a large contribution from the S-3p orbital. Meanwhile, the IB is formed mainly through the combination of S-3p and Sn-5s orbitals. Therefore, the optical absorption coefficient is expected to be large, benefiting from the additional effective electron transitions between the inter-bands.

Fig. 3 DOS and PDOS of Sn doped CuGaS₂. The vertical dashed line is the Fermi level.

Fig. 4 Partial charge density of the intermediate band in Sn doped CuGaS₂.

3.2 Optical properties

To reveal the effect of the partially filled IB on the optical absorption, which is undoubtedly a critical factor for IB materials, the absorption coefficient, which is closely connected with the complex dielectric function ε(ω) = ε₁(ω) + iε₂(ω), has been calculated. ε₂(ω) is an imaginary part and can be calculated from the momentum matrix elements between the occupied and unoccupied wave functions. ε₁(ω) is the real part and can be evaluated from ε₂(ω) through the Kramers–Kronig relationship.⁴¹ From ε₁(ω) and ε₂(ω), the other optical properties, such as the extinction coefficient κ(ω), the refractive index n(ω) and the absorption coefficient α(ω) can be evaluated. The absorption coefficient is expressed as the following equation:

The calculated absorption coefficients α(ω) of different concentrations of Sn doped CuGaS₂ are presented in Fig. 5(a)–(c) and compared with that of the host CuGaS₂. It can be found that in the case of the host, CuGaS₂, only one absorption peak appears at the theoretical value of the band gap at about 2.3 eV, and no absorption is observed in the energy region below 1.5 eV. After Sn is doped in CuGaS₂, except for the peak at 2.3 eV, additional absorption peaks appear, corresponding to the electron transitions from the VB to the IB or the IB to the CB. Our result is consistent with previous experimental observations.^28,29

Fig. 5 Optical absorption coefficients for CuGaS₂ (red dash-dot line) and Sn doped systems at (a) 6.25% (b) 12.5% (c) 25% doping concentration (blue solid line).

It is apparent that the absorption is largely enhanced in the lower energy region, and the absorption energy range is broadened, due to the formation of intermediate states in the band gap. At the low doping concentration, the enhancement is not very large because of the unfavorable electron occupancy in the IB, where the filled states greatly outnumber the empty states as seen in Fig. 2(a). At the high doping concentration, the enhancement effect is especially visible, which is consistent with the solar energy utilization ratio.

In a word, the Sn doped CuGaS₂ systems exhibit a two-step optical transition between the VB and the CB through the IB, thus leading to a substantially enhanced light absorption and extended absorption energy range.

3.3 Dynamical and phase stability

We have analyzed the dynamical stability of the Sn doped CuGaS₂ structure from the phonon calculations, seen in Fig. 6, where only one doping concentration is presented for simplicity. The absence of any imaginary frequency confirms the stability of the Sn doped CuGaS₂ material.

Fig. 6 Phonon dispersion curve and phonon density of states (PHDOS) for 6.25% Sn doped CuGaS₂.

In search of suitable growth conditions and the effect of doping on intrinsic defects, we carry out formation energy calculations for the Sn doped CuGaS₂ systems. The formation energy of a defect can be defined as

ΔH_f = E_doped − E_host + ∑n_Xμ_X, (2)

where E_doped is the total energy of the supercell containing the dopant, E_host is the energy of the same supercell CuGaS₂ in the absence of the dopant, X is the atom transferred to (n_X is positive) or from (n_X is negative) a chemical reservoir that has the chemical potential μ_X, and n_X is the number of atoms changed during the defect formation. Here, we define Δμ_X = μ_X − μ^bulk/gas_X to express the chemical potential of X relative to its chemical potential in the stable elemental bulk/gaseous state. The equation thus takes the form

ΔH_f = E_doped − E_host + ∑n_X(Δμ_X + μ^bulk/gas_X). (3)

There are some thermodynamic limits to the chemical potential of each constituent element (Δμ_X). (i) To maintain a stable CuGaS₂ compound, their summation is always equal to the calculated formation enthalpy, so

Δμ_Cu + Δμ_Ga + 2Δμ_S = ΔH_f(CuGaS₂),

(ii) to avoid the precipitation of elemental solids, the atomic chemical potentials should be bounded by:

Δμ_Cu ≤ 0, Δμ_Ga ≤ 0, Δμ_S ≤ 0,

(iii) the chemical potentials are further restricted by the formation of competing binary phases, so that

Fig. 7(a) shows the stability region (light green shaded area) for CuGaS₂ as a function of Δμ_Cu and Δμ_Ga, in the absence of impurities. When an impurity, i.e. Sn, is introduced into the host CuGaS₂ system, additional constraints will be further imposed on the chemical domain of CuGaS₂ to avoid the competing phases of SnS and SnS₂ by

Fig. 7 The stability region for (a) CuGaS₂ (light green shaded area) and (b) the impact of dopant Sn on the stability region of CuGaS₂.

Consequently, the constraint of SnS and SnS₂ as secondary phases will significantly reduce the stability region of the host CuGaS₂ (shaded area). On the other hand, as ΔH_f(SnS) and ΔH_f(SnS₂) are constants, the allowed chemical potential Δμ_S and thus Δμ_Cu and Δμ_Ga will strongly depend on Δμ_Sn.

The area with black slanted lines in Fig. 7(b) denotes the region where CuGaS₂ is unstable with respect to the formation of SnS or SnS₂, assuming Δμ_Sn = −0.6 eV.

When Δμ_Sn becomes less negative, i.e. the Sn content is higher, Δμ_S is required to be lower to avoid the formation of SnS or SnS₂, and thus the unstable area will expand. Under extremely Sn rich conditions, i.e. Δμ_Sn = 0,³⁹ the unstable area will cross over into the entire colored region. In fact, Δμ_Sn should be smaller than −0.26 eV to maintain a stable region.

In conclusion, the Sn doping content should be moderate in order to ensure a stable chemical potential region for growing Sn@CuGaS₂ IB materials.

4 Summary

Using first-principles methods, we studied the optoelectronic properties and the dynamical and phase stabilities of Sn doped CuGaS₂ at the Ga site. An intermediate band (IB) appears in the band gap of Sn doped CuGaS₂ for different doping concentrations. Benefiting from the three-photon process induced by the IB, the optical absorption coefficients are enhanced and the absorption energy ranges are largely extended in the Sn doped CuGaS₂ systems. Further, dynamical stability analysis indicates that Sn doped CuGaS₂ is stable. Above all, phase stability analysis suggest that under thermal equilibrium growth conditions, the Sn doping content should be moderate to avoid Sn-related competing secondary phases. Therefore, we point out that moderate Sn doping in CuGaS₂ can be used to generate IB materials.

Acknowledgements

This work has been supported by the Special Funds for Major State Basic Research Project of China (973) under Grant No. 2012CB933702 and the NSFC under Grant No. 11204310 and U1230202 (NSAF). The calculations were performed at the Center for Computational Science of CASHIPS, the ScGrid of the Supercomputing Center and the Computer Network Information Center at the Chinese Academy of Science.

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