In this study, the structural, electronic, elastic, mechanical, and optical properties of a new Zintl phase K2AgAs ternary semiconductor compound have been investigated by the first-principles method using the plane-wave self-consistence field method. A triangulation of different exchange-correlation functionals, including local density approximation-LDA-PZ, generalized gradient approximation (GGA)-Q2D, GGA-BLYP, GGA-Perdew–Burke–Ernzerhof (PBE), GGA-PBESol, and GGA-revPBE, have been utilized to predict the properties of the material. The computed structural properties predicted that the K2AgAs compound is thermodynamically stable, and the lattice parameters are consistent with the reported experimental values. The electronic properties show that the bandgap ranges between 0.6645 and 1.1915 eV, while the conduction and valence bands are formed mainly through the hybridization of the As-2p, Ag-2p and Ag-3d, As-2p states, respectively, with other states making minimal contribution. From the calculation of elastic properties, K2AgAs were predicted to be mechanically stable. Notably, K2AgAs has been predicted to absorb light within the ultraviolet-visible regime. Owing to their good thermodynamic and mechanical stability, wide coverage of absorption in the UV-Vis region of the solar spectrum, and narrow bandgaps, K2AgAs can be formed/synthesized and applied as the active photoactive material in solar cells and other photovoltaics.

Metallic and semiconductor materials are essential components of electronic and optoelectronic devices, enabling advances in telecommunications, consumer electronics, healthcare, military applications, transportation, and clean energy applications in multivariate sectors.1–3,3 The aforementioned applications have been realized through the rapid growth of material science and technology where an extensive series of nanostructures and nanocomposites have been fabricated.4,5 However, by altering the chemical makeup of these nanostructures and nanocomposites, we can tweak their inherent qualities, create new features, and thereby increase the material’s efficiency or open up new application areas.4 Different elemental combinations forming binary, ternary, and even quaternary compounds have been investigated in the past;6–10 nonetheless, ternary compounds with A2BX configurations have created a niche of interest among researchers since the last few decades.11–13 

Maabed et al.14 studied the ternary K2CuP and K2AgP by exploring the physical properties of polar intermetallic phases of the materials, where during their study the structural electronic, and optical properties were investigated revealing that the material has indirect bandgap, possess covalent Cu–P, Ag–P bonding as well as wide ranging photon energy absorption in the ultraviolet. In an experimental study for similar structures, Yamada et al.,15 investigated a novel Plumbite Na2MgPb ternary compound, where an observed abrupt change in resistivity was attributed to αβ and βγ phase transition, their observations were theoretically corroborated by density functional theory (DFT) methods. In their treatise, other intermetallic ternary compounds of the form A2BX (A = Li, Na, K; B = Zn, Cg, Hg; X = Si, Ge, Sn, Pb) have been described with further description in references therein.15 In a closely related material, Na2MgSn was also investigated by Wang et al.16 for its thermal conductivity properties and thermoelectric applications.

In an effort to develop a novel material with low thermal conductivity for thermoelectric applications, Zhang et al.17 reported on K2CdX (X = Sn, Pb), where several properties were analyzed using first-principles methods, and their results demonstrated an alternative paradigm for investigating the interplay of structure and chemical bonding on transport properties. In the past decade, ternary compounds formed from the electropositive elements (group IA = Li, Na, K, Rb, Cs), pnictogen (group VA = N, P, As Sb, Bi), and coinage metal element (group IB = Cu, Ag, Au) have been an area of great interest.12,14,18–20 This class of compounds are known as Zintl phase compounds. The materials belonging to the classical Zintl concept were mostly binary compounds, and as research intensified in this area, more complex compounds were discovered beyond the binary structure, this pushed the initial definition describing them to be obscured.21 Therefore, Schafer et al. proposed a more general definition that takes many elements into account.22 In this study, the ternary semiconductor K2AgAs was investigated for its structural, elastic, mechanical, and optical properties for application in optoelectronics. To the best of our knowledge, this material has only been synthesized experimentally18 where its structure was predicted, but there exists no theoretical investigation about it, and therefore this forms the basis of our motivation as well as its potential for application in the optoelectronic sectors.7,9 Similar ternary compounds, which have been synthesized and analyzed experimentally, include Na2CuP, K2AgBi, and K2AgSb.18 

The structural, electronic, elastic, mechanical, and optical properties of the K2AgAs ternary semiconductor compounds were computed using quantum espresso (QE)23 package within the density functional theory (DFT) framework.24–26 The local density approximation (LDA)27 and generalized gradient approximation (GGA)27 with Q2D,28 BLYP,29 Perdew–Burke–Ernzerhof (PBE),30 PBESol,31 and revPBE32 exchange correlation functionals were used to build the Khon–Sham Hamiltonian. The work was done with two types of pseudopotentials, the ultra-soft and norm conserving, both with nonlinear core correction and scalar relativistic type. The K2AgAs crystal structure file was obtained from the Materials Project database.33–35 For self-consistent calculations, a converged Monkhorst–Pack grid of 8 × 8 × 8 K-points in the first Brillouin zone and a plane-wave kinetic energy cut-off of 140 Ry were used. Geometry optimization for computing the ground-state structural properties was performed by minimizing the total energy with respect to volume and thereafter, Birch–Murnaghan equation of state was used for fitting the data following a similar procedure as reported elsewhere,36,37 this gave the optimized crystal lattice parameters. The final optimization to be performed was the variable cell optimization in order to have equilibrium relaxed positions of the atoms and bonds. The self-consistent field calculation was required before making calculations for electronic band structure, density of states, optical properties, elastic properties, as well as mechanical properties. The calculations for the projected density of states were preceded by non-self-consistent field calculations.

The crystal structure of a K2AgAs semiconductor ternary compound was first reported in an experimental study by Savelberg and Schaefer.18 In their findings, the material was noted to exhibit an orthorhombic crystal system belonging to space group C222 and point group mmm. The experimental lattice parameters were obtained as a = 10.02 Å, b = 7.92 Å, and c = 6.02 Å, with unit cell volume of 477.7 Å3. This crystal type features a potassium (K) atom bonded to four arsenic (As) atoms and a silver (Ag) atom bonded to two As atoms in 4- and 2-coordinate geometries, respectively. The K–As and Ag–As bond lengths are determined in this study to be 3.55 and 2.54 Å, respectively, which are consistent with the previous reports.18 The geometry of the K2AgAs crystal structure is shown in Fig. 1.

FIG. 1.

Crystal structure of orthorhombic ternary K2AgAs compound.

FIG. 1.

Crystal structure of orthorhombic ternary K2AgAs compound.

Close modal
In the orthorhombic representation, the total energy of the K2AgAs crystal was minimized with respect to the lattice parameters, based on six correlation functionals. The Birch–Murnaghan (BM) equation38 [Eq. (1)] was employed to fit the minimized energy vs volume values to obtain the ground-state structural properties given in Table I,
EV=Eo+9VoBo16VoV2313BoI+VoV2312×64VoV23.
(1)
Here, E(V) refers to the total energy at a particular volume, whereas Eo, Vo, Bo, and BoI denote the equilibrium energy, equilibrium volume, bulk modulus, and first-pressure derivative, respectively. The computed lattice parameters of K2AgAs using different exchange-correlation functionals were in the range of 18.10–19.37 a.u. with a mean value of 18.77 a.u., this value is consistent with the experimental value 18.94 a.u. reported in other work.39 The thermodynamic stability of the K2AgAs ternary compounds was investigated by computing the enthalpies of formation, as shown in Table I. In this study, the enthalpy of formation was calculated from the ground state minimum energy of the compounds and constituent elements according to the relationship given in the literature.40 That is, the enthalpy of formation ∆Hf (Rydberg) of the K2AgAs compound at zero temperature and pressure is given as
ΔHfK2AgAs=EK2AgAsEmin2EKEminEAgEminEAsEmin,
(2)
where EK2AgAsEmin is the total minimum energy of the compound, while EXEmin (X = K, Ag, As) is the minimum energy for the specific element forming the compound.
TABLE I.

Computed ground-state lattice parameters, bulk modulus, equilibrium volumes, and enthalpies of formation of the K2AgAs ternary compound using various correlation functionals.

Lattice parameter ao (a.u.)Bulk modulus Bo (GPa)Equilibrium volume (a.u.)3Enthalpy of formation ∆Hf (Ry)
LDA 18.2719 9.5 6100.26 −440.239 07 
Q2D 18.1046 12.1 5934.24 −442.598 05 
BLYP 19.3720 5.2 7269.87 −443.835 49 
PBE 18.9865 6.2 6844.40 −444.784 74 
PBESol 18.5902 7.5 6424.73 −898.978 27 
revPBE 19.2732 5.4 7159.19 −445.052 04 
Other work 18.9351    
Lattice parameter ao (a.u.)Bulk modulus Bo (GPa)Equilibrium volume (a.u.)3Enthalpy of formation ∆Hf (Ry)
LDA 18.2719 9.5 6100.26 −440.239 07 
Q2D 18.1046 12.1 5934.24 −442.598 05 
BLYP 19.3720 5.2 7269.87 −443.835 49 
PBE 18.9865 6.2 6844.40 −444.784 74 
PBESol 18.5902 7.5 6424.73 −898.978 27 
revPBE 19.2732 5.4 7159.19 −445.052 04 
Other work 18.9351    

The computed values of the enthalpy of formation using all six correlation functionals were less than zero, implying that the K2AgAs ternary compound is thermodynamically stable and can be synthesized,41 

The nature and size of the bandgap of the K2AgAs ternary compound were determined from the band structure plots [Figs. 2(a)2(f)]. The X-Γ symmetry points in the computed band structures appeared at different points of the valence band maxima and conduction band minima. This implies that the compound under investigation had an indirect bandgap. The bandgap sizes predicted using LDA-PZ, GGA-Q2D, GGA-BLYP, GGA-PBE, GGA-PBESol, and GGA-revPBE exchange correlation functionals were 0.941, 0.664, 1.136, 1.086, 1.022, and 1.191 eV, respectively. The bandgaps obtained using LDA and Q2D exchange-correlation functionals were found to be underestimated compared to those obtained using the other functionals. This is in agreement with other reports that LDA underestimates the bandgap of materials.42 The specific electronic contributions to the formation of the valence and conduction bands are investigated through calculation of the projected density of states (pdos)43 [Figs. 2(a)2(f)]. In this investigation, it was found that the hybridization of the As-2p and Ag-3d states dominates the formation of the valence band in the K2AgAs ternary compound, while the hybridization of the Ag-2p and As-2p states dominated the formation of the conduction band. All other states, including Ag-1s, As-1s, K-1s, K-2s, K-3p, and K-4p, contributed less to the formation of the valence and conduction bands.

FIG. 2.

(a) Band diagram and density of states for K2AgAs semiconductor compound with a bandgap of 0.941 eV obtained by LDA-PZ functional. (b) Band diagram and density of states for K2AgAs semiconductor compound with a bandgap of 0.6645 eV obtained by GGA-Q2D functional. (c) Band diagram and density of states for K2AgAs semiconductor compound with a bandgap of 1.1368 eV obtained by GGA-BLYP method. (d) Band diagram and density of states for K2AgAs semiconductor compound with a bandgap of 1.0866 eV obtained by GGA-PBE functional. (e) Band diagram and density of states for K2AgAs semiconductor compound with a bandgap of 1.1915 eV obtained by GGA-revPBE functional. (f) Band diagram and density of states for K2AgAs semiconductor compound with a bandgap of 1.0228 eV obtained by GGA-PBESol functional.

FIG. 2.

(a) Band diagram and density of states for K2AgAs semiconductor compound with a bandgap of 0.941 eV obtained by LDA-PZ functional. (b) Band diagram and density of states for K2AgAs semiconductor compound with a bandgap of 0.6645 eV obtained by GGA-Q2D functional. (c) Band diagram and density of states for K2AgAs semiconductor compound with a bandgap of 1.1368 eV obtained by GGA-BLYP method. (d) Band diagram and density of states for K2AgAs semiconductor compound with a bandgap of 1.0866 eV obtained by GGA-PBE functional. (e) Band diagram and density of states for K2AgAs semiconductor compound with a bandgap of 1.1915 eV obtained by GGA-revPBE functional. (f) Band diagram and density of states for K2AgAs semiconductor compound with a bandgap of 1.0228 eV obtained by GGA-PBESol functional.

Close modal
The K2AgAs ternary semiconductor compound adopts an orthorhombic crystal structure with space group C222 and point group mmm. This crystal system features nine independent elastic constants, namely, C11, C12, C13, C22, C23, C33, C44, C55, and C66.44 According to the Born criteria,44 this orthorhombic crystal system must satisfy the following necessary and sufficient conditions for mechanical stability:
C11>0;C11C22>C122,C11C22C33+2C12C13C23,C11C232C22C132C33C122>0,C44>0;C55>0;C66>0.
(3)

The computed elastic constants in Table II satisfy the stability conditions given in Eq. (3), implying that the compound under investigation is mechanically stable. Other mechanical properties, including the bulk modulus (B), shear modulus (G), Young’s modulus (E), and Poisson’s ratio (n), as shown in Table III, were obtained from the Voigt–Reuss–Hill approximation.45 

TABLE II.

Elastic tensor in GPa for K2AgAs orthodromic crystal structure.

C11C12C13C22C23C33C44C55C66
LDA 39.59 4.70 1.98 32.39 14.91 33.82 19.89 5.91 4.69 
PBE 43.54 7.61 4.50 37.79 18.41 38.09 19.35 5.96 5.67 
PBESol 44.18 6.95 3.77 37.86 17.85 38.59 20.28 6.39 5.71 
BLYP 42.13 8.13 5.26 36.87 19.11 36.36 18.54 5.31 5.21 
revPBE 42.37 7.33 4.75 35.41 17.66 35.80 18.72 5.50 5.40 
Q2D 38.58 5.68 2.95 36.07 16.61 36.26 19.57 6.42 5.21 
C11C12C13C22C23C33C44C55C66
LDA 39.59 4.70 1.98 32.39 14.91 33.82 19.89 5.91 4.69 
PBE 43.54 7.61 4.50 37.79 18.41 38.09 19.35 5.96 5.67 
PBESol 44.18 6.95 3.77 37.86 17.85 38.59 20.28 6.39 5.71 
BLYP 42.13 8.13 5.26 36.87 19.11 36.36 18.54 5.31 5.21 
revPBE 42.37 7.33 4.75 35.41 17.66 35.80 18.72 5.50 5.40 
Q2D 38.58 5.68 2.95 36.07 16.61 36.26 19.57 6.42 5.21 
TABLE III.

Voigt–Reuss–Hill average mechanical properties, bulk modulus B, Young’s modulus E, shear modulus G, Pugh’s ratio B/G, Poisson’s ratio n, and Debye temperature.

BEGB/GnθD (K)
LDA 16.47 24.94 10.04 1.64 0.2421 170.82 
PBE 19.97 26.96 10.60 1.88 0.2712 178.28 
PBESol 19.70 27.82 11.03 1.77 0.2608 180.42 
BLYP 19.86 25.19 9.80 2.03 0.2847 172.15 
revPBE 19.20 25.55 10.02 1.92 0.2742 173.99 
Q2D 17.82 26.20 10.47 1.70 0.2512 175.53 
BEGB/GnθD (K)
LDA 16.47 24.94 10.04 1.64 0.2421 170.82 
PBE 19.97 26.96 10.60 1.88 0.2712 178.28 
PBESol 19.70 27.82 11.03 1.77 0.2608 180.42 
BLYP 19.86 25.19 9.80 2.03 0.2847 172.15 
revPBE 19.20 25.55 10.02 1.92 0.2742 173.99 
Q2D 17.82 26.20 10.47 1.70 0.2512 175.53 

The ductile or brittle nature of the K2AgAs ternary compound can be predicted using the Pugh’s ratio (B/G).46 Herein, B/G > 1.75 indicates ductility, while B/G < 1.75 portrays the brittle nature of a material.46 According to Table III, the predicted Pugh ratio values imply that the studied compound lies within the ductile domain. On the other hand, the Poisson’s ratio provides information about interatomic bonding within a material.47 A value of n > 0.25 depicts ionic bonding within a material.48 The computed values of n within the GGA portray ionic bonding within the K2AgAs. Furthermore, material incompressibility can be described using the B and G values.49 Within the GGA approximation, higher B values were predicted compared to the LDA approximation. The larger the value of B, the harder it becomes to compress the material. The material stiffness can also be predicted from the E value,49 where a high magnitude of E is a measure of greater stiffness. The E values computed within the LDA and GGA approximations in Table III provide a prediction of the stiffness of the K2AgAs. To study the mechanical anisotropic properties of the K2AgAs material in the elastic regime, a complete elastic matrix tensor analysis was performed after extracting the values forming the matrix following the elastic analysis and Born’s criteria.50 The spatial dependences of E, G, and n on the xy, xz, and yz planes are depicted in Fig. 3 for the GGA-PBE approximation as a representative analysis of the material. The green and blue lines in the 2D spatial dependence plots represent measures of anisotropy.50 The magnitude of the curvature of the lines predicts the degree of anisotropy. The more the curvature of the lines is toward the center, the more the anisotropy, while the closer the curvature is toward forming a circle, the weaker the anisotropy.50 Along the xy and xz planes, the spatial dependences of E and G show substantial anisotropy as compared to the yz planes, which is a behavior portrayed by most porous and soft materials.50 

FIG. 3.

Spatial dependence of (a) Young’s modulus, (b) shear modulus, and (c) Poisson’s ratio.

FIG. 3.

Spatial dependence of (a) Young’s modulus, (b) shear modulus, and (c) Poisson’s ratio.

Close modal
The prospects of materials for photovoltaic applications can be predicted based on their optical properties. The optical behavior of materials when subjected to electromagnetic radiations can be described by the complex function εω=ε1ω+iε2ω,51,52 where real ε1(ω) dielectric constant shows the polarization of radiation while imaginary ε2(ω) dielectric constant helps in the determination of the other angular frequency dependent optical properties, such as the refractive index n(ω), extinction coefficient k(ω), energy loss value L(ω), reflectivity R(ω), and absorption coefficient α(ω). These parameters are derived from the values obtained from ɛ1 and ɛ2 and given as follows:43,53,54
nω=ε12ω+ε22(ω)+ε12(ω)1/22,
(4)
kω=ε12ω+ε22(ω)ε12(ω)1/22,
(5)
Lω=ε2(ω)ε12ω+ε22(ω),
(6)
Rω=nω12+k(ω)2nω+12+k(ω)2,
(7)
αω=2ωε12ω+ε22ε1ω1/2.
(8)

The investigated optical properties of the K2AgAs ternary semiconductor compound using the GGA-PBE correlation functional are shown in Figs. 48, which has been used for the purpose of analyzing the properties of this material. The highest ε1(ω) peak is 18.75 at 2.1, as shown in Fig. 4. The light absorption capability was determined from the ε2(ω) peaks (Fig. 4). Here, the main ε2(ω) peak is 18.71, which appeared at 2.7 eV. These peaks arise from the transition of electrons from the valence to the conduction band.52 The depth of light penetration in a material is determined by its absorption coefficient. The calculated absorption coefficient of the K2AgAs material covers a wide range of energy values within the electromagnetic spectrum, including the ultraviolet–visible region. This absorption region is a desirable feature for photoactive materials in solar cells and other similar pn-junction devices. The optical transparency of a material is determined by its refractive index (Fig. 5). The n(ω) value obtained for K2AgAs material is 4.9 at 4.3 eV. R(ω) describes the surface behavior of a material. The R(ω) peaks are maximum in the ultraviolet–visible region and show an overall low reflectivity (Fig. 7). Because k(ω) measures the loss of light in the medium owing to absorption/scattering per unit volume, it portrays the same trend as R(ω). The energy loss function of electrons in a medium determines the energy loss of electrons through dispersion, scattering, and heating, as described by L(ω) in Fig. 6. The L(ω) peaks are minimal in the ultraviolet–visible regions and increase in the far-energy regions. The compound seems to display excellent absorption properties as it is seen in Fig. 8, the absorption is high from the visible region to the deep infrared region. Cumulatively, the optical properties of the K2AgAs ternary semiconductor compound show that it has low energy loss and optimal absorption in the ultraviolet-visible region, which endows it with potential applications in solar cells.

FIG. 4.

The dielectric constants epsilon 1 and epsilon 2 for K2AgAs compound.

FIG. 4.

The dielectric constants epsilon 1 and epsilon 2 for K2AgAs compound.

Close modal
FIG. 5.

The frequency dependent refractive index and extinction coefficient for K2AgAs compound.

FIG. 5.

The frequency dependent refractive index and extinction coefficient for K2AgAs compound.

Close modal
FIG. 6.

The frequency dependent energy loss function for K2AgAs compound.

FIG. 6.

The frequency dependent energy loss function for K2AgAs compound.

Close modal
FIG. 7.

The frequency dependent reflectivity for K2AgAs compound.

FIG. 7.

The frequency dependent reflectivity for K2AgAs compound.

Close modal
FIG. 8.

The frequency-dependent absorption for K2AgAs compound.

FIG. 8.

The frequency-dependent absorption for K2AgAs compound.

Close modal

In summary, the analysis of structural, electronic, elastic, mechanical, and optical properties of K2AgAs ternary compounds using LDA-PZ, GGA-Q2D, GGA-BLYP, GGA-PBE, GGA-PBESol, and GGA-revPBE exchange correlational functionals have been done. This compound has been predicted to be thermodynamically and mechanically stable, demonstrating its potential for formation or synthesis. Narrow bandgaps ranging between 0.6645 and 1.1915 eV have been determined, which are desirable for photoactive materials in solar cell applications. The formation of the bandgap has been demonstrated through the valence band and conduction band calculation of the density of states, which revealed that the conduction band is dominated by Ag-2p and As-2p orbitals, while the valence band is majorly formed through the hybridization of Ag-3d and As-2p states with other orbitals making minimal contribution. The lattice parameters have been found to collaborate values reported in the literature. The optical properties showed that the K2AgAs compound had low energy loss and high absorption in the ultraviolet and visible regions of the electromagnetic spectrum, giving the credence that the material is suitable as a photoactive layer material in solar cells. These properties cumulatively demonstrate that this compound can be used in photovoltaic applications.

The authors acknowledge the Partnership for Skills in Applied Sciences, Engineering and Technology (PASET)-Regional Scholarship Innovation Fund (RSIF) for supporting (M.M.), and RSIF Grant No. RSIF_RA_015 (R.M. and M.M.) for support, and the Center for High Performance Computing CHPC, RSA for HPC computing resources.

The authors have no conflicts to disclose.

Robinson Musembi: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Funding acquisition (equal); Investigation (equal); Methodology (equal); Project administration (equal); Resources (equal); Software (equal); Supervision (equal); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Mwende Mbilo: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Funding acquisition (equal); Investigation (equal); Methodology (equal); Project administration (equal); Resources (equal); Software (equal); Supervision (equal); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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