# Ab Initio High-Pressure Study of Semiconductor-Metal Phase Transition of the Chalcogenide Compound KPSe6

Authors: P. O. Jomo; C. O. Otieno; P. W. O. Nyawere
Journal: Advances in Condensed Matter Physics
 (2020)

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## Abstract

We report the results of pressure-induced semiconductor-metal phase transition of the semiconducting chalcogenide compound KPSe6 under high pressure using the ab initio methods. The ground-state energy calculations were performed within density functional theory and the generalized gradient approximation using the pseudopotential method with plane-wave basis sets. The projector augmented-wave (PAW) pseudopotentials were used in our calculation. The optimized lattice parameters were found from total energy calculations as 13 Bohr, 1.6 Bohr, and 1.8 Bohr for cell dimensions one, two, and three, respectively, which are in good agreement with experimental calculations. At zero pressure, the material portrayed a semiconducting property with a direct bandgap of ≈1.7 eV. As we subjected the material to pressure, the band gap was observed to reduce until it disappeared. The phase transition from the semiconductor to metal was found to occur at ∼45 GPa, implying that the material underwent metallization as pressure was increased further.


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## Body

## 1. Introduction

In the recent past, research on the effect of pressure on structural phase transformations and characteristics of materials by calculations from first principles have attracted much attention since they give an insight into the nature of solid-state theories [1, 2], and also assist in determining values of essential parameters for industrial applications [3]. For example, the structural, electrical, and optical properties of group III–V semiconducting compounds have been studied extensively [1, 3–5].Most elements do undergo structural phase transitions as pressure is induced [6–9]. When a material is subjected to compressional forces, its electronic band structure changes [10, 11] which further results in a change in its structural properties [10, 12–14]. This often leads first to the formation of low-symmetry complex structures which at higher pressure then transform into high-symmetry close-packed structures [6, 8, 13]. Besides, the delocalization of bonding electrons under pressure reduces the differences between the chemical properties of the elements and their crystal structures [15]. As a result, numerous new allotropes of the elements have been discovered [16].Structural studies of chalcogenides under high pressure up to 52 GPa have been carried out experimentally by using X-ray diffraction method [9]. For example, CaS, CaSe, and CaTe alkaline-earth chalcogenides undergo a structural phase transition at a pressure of 40 GPa, 38 GPa, and 33 GPa, respectively [9, 14]. The study of crystalline materials under pressure in material physics gives very important and useful material properties [1, 6, 9, 10, 12, 13, 17]. Subjecting a material to high pressure leads to a reduction of interatomic spacing which in turn affects the crystal structure and electronic orbitals [1, 18–23]. Likewise, high pressure can result in the formation of new material with different features from the initial material [24].Chalcogenide glasses are based on selenium, tellurium, and the addition of other elements such as arsenic, germanium, antimony, gallium, and potassium [3, 25]. They are well known for their advantages, such as a wide transmittance range (1–12 μm) [3], low intrinsic losses in the mid-IR [26], low phonon energy [27], and the absence of free-carrier effects [3, 28–30]. KPSe6 as a chalcogenide has attracted much interest because of its promising abilities in technological applications such as thin films and optical fibers [3, 25, 27, 30, 31]. KPSe6 crystallizes in the polar orthorhombic space group Pca21 [3, 26, 32]. This compound is a semiconductor at zero pressure with a direct bandgap of 1.883 eV [3, 26, 31, 33]. We aimed at investigating the behavior of KPSe6 under very high pressure.We arrange this paper in the following order: we explain the details of the calculation in Section2, Section 3 discusses the results, and conclusions are in Section 4.


## 2. Computational Details

The study was done using the density functional theory (DFT) [34] by employing for the exchange-correlation functional, the generalized gradient approximation of Perdew–Burke–Ernzerhof [34–36] based on Plane Wave self-consistent field (PWscf) and Ultrasoft pseudopotential (USPP) method. Pressure increase was implemented as follows: starting with the relaxed unit cell, we modified the input file whereby we changed the “calculation” type from “scf” to “vc-relax” and then introduced two new segments; the first segment is called “&ions’ while the second one is called ‘&cell.” Under the first segment, the ion dynamics were set to damp while under the second segment, we entered the target pressure (Kbar) that we wanted to subject our cell to [35]. The new atomic positions obtained were then used to calculate the electronic structure properties of KPSe6 as at that pressure. The ab initio calculations are implemented in the Quantum Espresso simulation package [36], and pseudopotentials were taken from the Quantum Espresso database. For pseudopotentials, the valence electrons are 2s for K, 2p for P, and 2p for Se. The valence wave functions were expanded in a plane wave basis set truncated at a kinetic energy of 25 Ry (340 eV). At ambient conditions, KPSe6 crystallizes in the polar orthorhombic space group Pca21 [3, 26, 32]. The structure has three species of atoms as potassium K, phosphorous P, and selenium Se. The primitive unit cell of the chalcogenide compound KPSe6 has a total of 32 atoms: 4 potassium atoms, 4 phosphorous atoms, and 24 selenium atoms. Figure 1 shows the optimized crystal structure of KPSe6.Figure 1
The optimized crystal structure of KPSe6 at zero pressure as viewed using the crystalline and molecular structure visualization program (XCrySDen). The obtained crystal structure is orthorhombic and is in good agreement with the general crystal structure [32].


## 3. Results and Discussion

### 3.1. Structural Optimization

In this section, we report the graphical representation of the optimized lattice parameters and kinetic energy cutoff (ecut) for our chalcogenide compound KPSe6. The following graphs of Figure 2 represent how the optimized lattice parameters were obtained. The minima in the graphs represent the ground-state energy which corresponds to the accurate parameter to be used for the calculations.Figure 2
(a) A convergence curve for cell dimension one which gives ∼13.0 Bohr, (b) the optimized value for cell dimension two is ∼1.6 Bohr, and (c) the optimized value for cell dimension three is ∼1.8 Bohr. These optimized values were used in subsequent calculations.
(a)
(b)
(c)The ground-state calculation for the optimized kinetic energy cutoff (ecut) was performed, and the graph is plotted as shown in Figure3. The kinetic energy cutoff optimized value was ∼25 Ry. This was the value used for the rest of the calculations.Figure 3
A representative convergence curve for total energy versus kinetic energy cutoff. The optimized energy cutoff at the minima was ∼25 Ry as shown.


### 3.2. Electronic Structure Properties

Calculations of the band structure, partial density of states, and density of states of the compound KPSe6 are here reported. In order to determine the band structure properties, we used the following high symmetry points of Γ(0,0,0), X(1/2,0,0), Y(0,1/2,0), Z(0,0,1/2), T(0,1/2,1/2), U(1/2,0,1/2), S(1/2,1/2,0), and R(1/2,1/2,1/2) [16,37,38]. A direct bandgap of ∼1.7 eV was obtained at zero pressure and the gap formed around the T-symmetry. This result is in agreement with the experimental value of 1.883 eV [3, 26, 37, 39] and is within the error bar range [37]. The underestimation is caused by the occupied states being lower in energy as compared to the unoccupied states [39, 40]. The bands and curves for the density of states for this compound are as presented in Figure 4.Figure 4
(a) The electronic band structure and the density of states. The band structure and density of states show a very close similarity as seen above. (b) The curves represent the partial density of states and how each atom contributes to either the valance band or conduction band. It can be noted that Se 2(p) states contribute more to the valence band compared potassium and selenium, while P 2(p) states contribute more to the conduction band.
(a)
(b)


### 3.3. Pressure-Induced Phase Transition

It is established that the bandgap of a material depends on the magnetic field, temperature, and pressure [39]. We examined how pressure affects the bandgap. According to Gulyamov [17, 23, 39], the pressure band gap relation is given by(1)EgP=Eg0−βP,where β represents the pressure coefficient which defines the shift in the position of the valence and conduction bands with variation in pressure [1, 18]. The Fermi level pressure dependence is given by [39](2)EFP,T=EgP2+34KTlnmhme,where EF represents the Fermi energy, T is the absolute temperature, Eg gives the energy gap, me∗ is the mass of an electron, and mh∗ is the mass of the hole. A graph showing the relationship between Fermi energy and pressure is as shown in Figure 5.Figure 5
Induced pressure dependence of the Fermi energy. There is a continued increase in Fermi energy with increased pressure, provided the structure has not undergone distortion [6, 41].On inducing pressure, the number of charge carriers with respect to the density of state increased which in turn enhanced the availability of more electrons responsible for electrical conductivity [17, 42, 43]. As we introduced more pressure, there was an overlap between the valence band and the conduction band which was attributed to the broadening of the bandwidth of the 2s and 2p atomic orbital [20]. This was because of their strong interaction with neighboring atoms that created wider bands than the energy gap, thus availing electrons to the conduction band [41]. The phase transition from the semiconductor to metal was found to occur at ∼45 GPa. Therefore, it was an indication that pressure can lead to the semiconductor-metal transition [42]. The changes in the band structure and density of state at different pressure in relation to Fermi energy are described using Figure 6.Figure 6
Calculated pressure-dependent band structures and density of states for the compound KPSe6 at (a) 20 GPa, (b) 30 GPa, (c) 40 GPa, and (d) 45 GPa. The bandgaps are ∼1.18 eV at 20 GPa (a), ∼1.05 eV at 30 GPa (b), ∼0.50 eV at 40 GPa (c), and 0.00 eV at 45 GPa (d).
(a)
(b)
(c)
(d)The variation of bandgaps for pressure calculations was also plotted as shown in Figure7.Figure 7
A plot of the calculated band gaps versus the pressure of the chalcogenide compound KPSe6.The crystal structure was stable and not distorted at high pressure; this showed that the material can withstand high compressional forces and thus can be used for various high-pressure industrial applications. The crystal structures at various pressures are as shown in Figure8.Figure 8
Crystal structures for KPSe6 at pressure (a) 0 GPa, (b) 20 GPa, (c) 30 GPa, (d) 40 GPa, (e) 45 GPa, and (f) 50 GPa, respectively, as viewed using crystalline and molecular structure visualization program (XCrySDen). The crystal structure remained undistorted as pressure was increased. This implies that the structure remained stable and that there was no structural phase transition.
(a)
(b)
(c)
(d)
(e)
(f)The bond lengths and bond angles were investigated as well at various pressure intervals using crystalline and molecular structure visualization program (XCrySDen). It was observed that the bond lengths reduced as more pressure was induced while the bond angles decreased and then increased as from 40 GPa as shown in Table1 and Figure 9.Table 1
Shows a structural analysis of KPSe6 in terms of bond lengths and bond angles at various pressure intervals.
KPSe6 structure analysis
Pressure (GPa)
Bond length (Å)
Bond angle (°)
K-Se
P-Se
Se-Se
K-Se-P
0
2.8002
1.9284
1.9703
83.030
20
2.8460
2.1322
2.2821
85.293
30
2.7130
2.0643
2.2234
84.275
40
2.6131
2.0090
2.1729
83.822
45
2.5707
1.9858
2.1526
84.094
50
2.5317
1.9627
2.1290
84.285Figure 9
A plot of pressure versus bond lengths of the atoms. The green curve shows the variation of the bond length between potassium and selenium while the blue curve is for the phosphorous-selenium bond lengths, and the maroon curve shows the variation of the bond length between one selenium atom and another selenium atom. It was observed the bond length increased up to 20 GPa after which it reduced with further application of pressure.The stability of the material is supported by the pressure-dependent study of band structures of KPSe6 with respect to its enthalpy, volume, and density as calculated and analyzed in Figures 10(a)–10(c).Figure 10
(a) A study on the effect of pressure on the enthalpy of the material. Pressure and enthalpy of the compound were found to be directly proportional. (b). A plot of the volume of the crystal against pressure. An inverse relationship was obtained as shown above. (c). A plot of the calculated density of the compound versus pressure. As more pressure was introduced into the system, the density of KPSe6 increased as well. This implies that the stability of the chalcogenide compound KPSe6 improved as pressure increased [17].
(a)
(b)
(c)


## 3.1. Structural Optimization

In this section, we report the graphical representation of the optimized lattice parameters and kinetic energy cutoff (ecut) for our chalcogenide compound KPSe6. The following graphs of Figure 2 represent how the optimized lattice parameters were obtained. The minima in the graphs represent the ground-state energy which corresponds to the accurate parameter to be used for the calculations.Figure 2
(a) A convergence curve for cell dimension one which gives ∼13.0 Bohr, (b) the optimized value for cell dimension two is ∼1.6 Bohr, and (c) the optimized value for cell dimension three is ∼1.8 Bohr. These optimized values were used in subsequent calculations.
(a)
(b)
(c)The ground-state calculation for the optimized kinetic energy cutoff (ecut) was performed, and the graph is plotted as shown in Figure3. The kinetic energy cutoff optimized value was ∼25 Ry. This was the value used for the rest of the calculations.Figure 3
A representative convergence curve for total energy versus kinetic energy cutoff. The optimized energy cutoff at the minima was ∼25 Ry as shown.


## 3.2. Electronic Structure Properties

Calculations of the band structure, partial density of states, and density of states of the compound KPSe6 are here reported. In order to determine the band structure properties, we used the following high symmetry points of Γ(0,0,0), X(1/2,0,0), Y(0,1/2,0), Z(0,0,1/2), T(0,1/2,1/2), U(1/2,0,1/2), S(1/2,1/2,0), and R(1/2,1/2,1/2) [16,37,38]. A direct bandgap of ∼1.7 eV was obtained at zero pressure and the gap formed around the T-symmetry. This result is in agreement with the experimental value of 1.883 eV [3, 26, 37, 39] and is within the error bar range [37]. The underestimation is caused by the occupied states being lower in energy as compared to the unoccupied states [39, 40]. The bands and curves for the density of states for this compound are as presented in Figure 4.Figure 4
(a) The electronic band structure and the density of states. The band structure and density of states show a very close similarity as seen above. (b) The curves represent the partial density of states and how each atom contributes to either the valance band or conduction band. It can be noted that Se 2(p) states contribute more to the valence band compared potassium and selenium, while P 2(p) states contribute more to the conduction band.
(a)
(b)


## 3.3. Pressure-Induced Phase Transition

It is established that the bandgap of a material depends on the magnetic field, temperature, and pressure [39]. We examined how pressure affects the bandgap. According to Gulyamov [17, 23, 39], the pressure band gap relation is given by(1)EgP=Eg0−βP,where β represents the pressure coefficient which defines the shift in the position of the valence and conduction bands with variation in pressure [1, 18]. The Fermi level pressure dependence is given by [39](2)EFP,T=EgP2+34KTlnmhme,where EF represents the Fermi energy, T is the absolute temperature, Eg gives the energy gap, me∗ is the mass of an electron, and mh∗ is the mass of the hole. A graph showing the relationship between Fermi energy and pressure is as shown in Figure 5.Figure 5
Induced pressure dependence of the Fermi energy. There is a continued increase in Fermi energy with increased pressure, provided the structure has not undergone distortion [6, 41].On inducing pressure, the number of charge carriers with respect to the density of state increased which in turn enhanced the availability of more electrons responsible for electrical conductivity [17, 42, 43]. As we introduced more pressure, there was an overlap between the valence band and the conduction band which was attributed to the broadening of the bandwidth of the 2s and 2p atomic orbital [20]. This was because of their strong interaction with neighboring atoms that created wider bands than the energy gap, thus availing electrons to the conduction band [41]. The phase transition from the semiconductor to metal was found to occur at ∼45 GPa. Therefore, it was an indication that pressure can lead to the semiconductor-metal transition [42]. The changes in the band structure and density of state at different pressure in relation to Fermi energy are described using Figure 6.Figure 6
Calculated pressure-dependent band structures and density of states for the compound KPSe6 at (a) 20 GPa, (b) 30 GPa, (c) 40 GPa, and (d) 45 GPa. The bandgaps are ∼1.18 eV at 20 GPa (a), ∼1.05 eV at 30 GPa (b), ∼0.50 eV at 40 GPa (c), and 0.00 eV at 45 GPa (d).
(a)
(b)
(c)
(d)The variation of bandgaps for pressure calculations was also plotted as shown in Figure7.Figure 7
A plot of the calculated band gaps versus the pressure of the chalcogenide compound KPSe6.The crystal structure was stable and not distorted at high pressure; this showed that the material can withstand high compressional forces and thus can be used for various high-pressure industrial applications. The crystal structures at various pressures are as shown in Figure8.Figure 8
Crystal structures for KPSe6 at pressure (a) 0 GPa, (b) 20 GPa, (c) 30 GPa, (d) 40 GPa, (e) 45 GPa, and (f) 50 GPa, respectively, as viewed using crystalline and molecular structure visualization program (XCrySDen). The crystal structure remained undistorted as pressure was increased. This implies that the structure remained stable and that there was no structural phase transition.
(a)
(b)
(c)
(d)
(e)
(f)The bond lengths and bond angles were investigated as well at various pressure intervals using crystalline and molecular structure visualization program (XCrySDen). It was observed that the bond lengths reduced as more pressure was induced while the bond angles decreased and then increased as from 40 GPa as shown in Table1 and Figure 9.Table 1
Shows a structural analysis of KPSe6 in terms of bond lengths and bond angles at various pressure intervals.
KPSe6 structure analysis
Pressure (GPa)
Bond length (Å)
Bond angle (°)
K-Se
P-Se
Se-Se
K-Se-P
0
2.8002
1.9284
1.9703
83.030
20
2.8460
2.1322
2.2821
85.293
30
2.7130
2.0643
2.2234
84.275
40
2.6131
2.0090
2.1729
83.822
45
2.5707
1.9858
2.1526
84.094
50
2.5317
1.9627
2.1290
84.285Figure 9
A plot of pressure versus bond lengths of the atoms. The green curve shows the variation of the bond length between potassium and selenium while the blue curve is for the phosphorous-selenium bond lengths, and the maroon curve shows the variation of the bond length between one selenium atom and another selenium atom. It was observed the bond length increased up to 20 GPa after which it reduced with further application of pressure.The stability of the material is supported by the pressure-dependent study of band structures of KPSe6 with respect to its enthalpy, volume, and density as calculated and analyzed in Figures 10(a)–10(c).Figure 10
(a) A study on the effect of pressure on the enthalpy of the material. Pressure and enthalpy of the compound were found to be directly proportional. (b). A plot of the volume of the crystal against pressure. An inverse relationship was obtained as shown above. (c). A plot of the calculated density of the compound versus pressure. As more pressure was introduced into the system, the density of KPSe6 increased as well. This implies that the stability of the chalcogenide compound KPSe6 improved as pressure increased [17].
(a)
(b)
(c)


## 4. Conclusion

We have performed an ab initio theoretical and computational study of the chalcogenide compound KPSe6. The structural and electronic properties of the chalcogenide compound were investigated under high pressure. Results show that the volume and energy gap for this material decrease while the enthalpy, Fermi energy, and density increase as we increase pressure. This shows the conductivity of this material increases with increasing pressure. From these calculations, the bands of the chalcogenide KPSe6 overlap at a pressure of ∼45 GPa. This implies that the material has undergone a semiconductor-metal transformation with a potential application to high pressure.



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