A DFT study of structural and electronic properties of copper indium ditelluride Cu m-1In m Te2 m-2 with m = 2-5 neutral and anion clusters

Abstract

In this work, the electronic and structural properties of Cu _m-1In _m Te_2m-2 neutral and anion clusters are studied. The simulations are carried out using the QUANTUM ESPRESSO/PWSCF package, based on the density functional theory (DFT) principle, which employs a pseudo-potential with a plane wave basis set. Geometry optimization starting from several initial candidate structures was performed for each cluster size to determine the number of possible minimum-energy isomers for each size. The results show that the lowest-energy structures are cubic, ranging from cluster m = 2 to 5, and resemble the chalcopyrite structure. The geometry of neutral and anionic cases exhibits a structural change, including distortion and a transition from two-dimensional to one-dimensional. By considering energetics, i.e. HOMO-LUMO gap, binding energy, ionization potential and electron affinity, the relative stability of Cu _m-1In _m Te_2m-2/(Cu _m-1In _m Te_2m-2)^- was measured. From the most stable energy structures, CuIn₂Te₂/(CuIn₂Te₂)^- were found to have enhanced chemical stability relative to their neighbours. They are a magic-number species. The binding energy and HOMO-LUMO gap of CuIn₂Te₂/(CuIn₂Te₂)^- clusters show the most significant value, which indicates high chemical stability. The adiabatic ionization potential of the cluster decreases monotonically, showing favor for metallic character as cluster size increases. Both clusters' vertical/adiabatic detachment energies also show a slight odd-even oscillation with an increasing tendency as a function of cluster size. This indicates that the successive increase in metallic atoms results in a decrease in nonmetallic favor. We also analyse the partial charge density of the optimized geometries for both anion and neutral clusters. The numerical value indicates that these clusters, including photovoltaic solar cells and other devices, make a significant contribution to semiconductor design.

Fig. 1. Optimized geometry of neutral CuInTe₂ (a) and anion (CuInTe₂)⁻ (b) clusters with corresponding relative energy ΔE, with respect to the lowest energy structure. Clusters with higher energy are labelled as (b) and (c) in increasing order. The total energy is normalized to the energy of the lowest energy cluster.

Fig. 2. Optimized geometry of neutral Cu_m−1In_mTe_2m−2 (A) and anion (Cu_m−1In_mTe_2m−2)⁻ (B) (m = 2) clusters with corresponding relative energy ΔE, with respect to the lowest energy structure. Clusters with higher energy are labelled as (b) and (c) in increasing order. The number in front signifies the size of the m unit, and the total energy is normalized to the energy of the lowest energy cluster.

Fig. 3. Optimized geometry of neutral Cu_m−1In_mTe_2m−2 (A) and anion (Cu_m−1In_mTe_2m−2)⁻ (B) (m = 2) clusters with corresponding relative energy ΔE, with respect to the lowest energy structure. Clusters with higher energy are labelled as (b) and (c) in increasing order. Number in front signifies size of m unit and total energy is normalized to the energy of the lowest energy cluster.

Fig. 4. Optimized geometry of Cu_m−1In_mTe_2m−2 (A) and (Cu_m−1In_mTe_2m−2)⁻ (B) (m = 4) clusters with corresponding relative energy ΔE, with respect to the lowest energy structure. Clusters with higher energy are labelled as (b) and (c) in increasing order. The number in front signifies the size of the m unit, and the total energy is normalised to the energy of the lowest energy cluster.

Fig. 5. Optimized geometry of neutral Cu_m−1In_mTe_2m−2 (A) and anion (Cu_m−1In_mTe_2m−2)⁻ (B) (m = 5) clusters with corresponding relative energy ΔE, with respect to the lowest energy structure. Clusters with higher energy are labelled as (b) and (c) in increasing order. Number in front signifies size of m unit and total energy is normalized to the energy of the lowest energy cluster.

Fig. 6. (a) Binding energy (eV) as a function of cluster size and (b) H–L gap energy (eV) as a function of cluster size of Cu_m−1In_mTe_2m−2 for m = 2–5 neutral clusters.

Fig. 7. Binding energy (eV) for first isomers of anion (Cu_m−1In_mTe_2m−2)⁻ for (m = 2–5) clusters as a function of cluster size m.

Fig. 8. H–L gap (eV) for first isomers of anion (Cu_m−1In_mTe_2m−2)⁻ for (m = 2–5) clusters as a function of cluster size m.

Fig. 9. Vertical and adiabatic detachment energy of Cu_m−1In_mTe_2m−2 for (m = 2–5) clusters as a function of cluster size m.

Fig. 10. Adiabatic ionization potential of Cu_m−1In_mTe_2m−2 for (m = 2–5) clusters as a function of cluster size m.

Fig. 11. Partial charge density plots of the HOMO−1, HOMO, LUMO and LUMO+1 orbitals of (CuIn₂Te₂) (above) and (CuIn₂Te₂)⁻ (below). Subsurface plots are at 1/5th of the maximum value.

Fig. 12. LDOS and energy levels of CuIn₂Te₂ clusters. The Fermi level is shifted to the zero of the energy axis. The discrete spectra are broadened by a Gaussian of width 0.01 eV.