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The thermodynamic properties of ZnSe are obtained by using quasi-harmonic Debye model embedded in Gibbs-code for pressure range 0–10 GPa and for temperature range 0–1000 K. Helmholtz free energy, internal energy, entropy, Debye temperature, and specific heat are calculated. The thermal expansion coefficient along with Grüneisen parameter are also calculated at room temperature for the pressure range. It is found that internal energy is pressure dependent at low temperature, whereas entropy and Helmholtz free energy are pressure sensitive at high temperature. At ambient conditions, the obtained results are found to be in close agreement to available theoretical and experimental data.
Wide band gap semiconductors are very important due to their large number of applications in optical devices like light emitting diode, optical wave guide, solar cells, solid state lasers, and photodetectors. ZnSe is one member of the family of large band gap semiconductors which can crystallize in the cubic zinc blend structure at the ambient pressure and has a distinct property of reversible transformation thus being used in optical memory devices.[1] Thorough understanding of physical, chemical, and thermodynamical behavior is necessary for the device fabrication and their applications. The thermal property is considered to be one of the basic properties of material, which influences other properties like band gap variation with temperature.
In recent years, ZnSe has been widely studied both by theoretical and experimental ways for their structural, optical, and thermal properties.[2–4] Sarkar et al.[4] have studied Helmholtz free energy, entropy, and specific heat capacity at constant volume of ZnSe with variation of temperature using full potential linearized augmented plane wave (FP-LAPW) method in the framework of density functional theory (DFT) with generalized gradient approximation (GGA) as exchange and correlation functional. They concluded that the Helmholtz free energy decreases while entropy increases with increase in temperature. At low temperature, the specific heat shows T3-law, while at high temperature it approaches to the Dulong–Petit law. Lin et al.[5] employed Raman spectroscopy to determine
The first principle calculation of structural, vibrational, and thermodynamical properties of Zn-based semiconductors was performed by Yu et al.[7] and phonon dispersion curve along with phonon density of states was calculated using DFPT. The phonon contribution to entropy, internal energy, and specific heat at constant volume was determined within harmonic approximation.
Wang et al.[8] studied the linear expansion of ZnSe and its specific heat at constant pressure using quasiharmonic approximation with local density approximation as exchange correlation functional.
Dinesh et al.[9] studied the pressure-induced phase transition of ZnSe from zinc blend structure to rock salt structure. They determined the Debye temperature, Grüneisen parameter, thermal expansion coefficient, compressibility, force constant, and reststrahlen frequency of ZnSe in its zinc blend structure. Hamdi et al.[10] employed the DFPT within quasiharmonic approximation to study the pressure dependence of thermal expansion coefficient and specific heat at constant pressure along with vibrational and elastic properties.
The above literature survey shows that experimental and theoretical studies about thermodynamical properties under pressure with variation of temperature are insufficient. So we study the thermodynamic properties over a wide range of temperature and pressures in order to remove this deficiency. ZnSe is stable in the zinc blend phase up to pressure 11.04 GPa[11] at room temperature and transforms into wurtzite structure when heated above 1698 K.[12] The present study of pressure and temperature dependence of thermodynamical behavior of zinc selenide lies within the stability range of pressure and temperature: pressure range from 0 to 10 GPa and temperature range from 0 to 1000 K.
The optimized calculations are performed using DFT implemented in WIEN2k code[13] with FP-LAPW method. The generalized gradient approximation with Wu–Cohen (GGA-WC) parameterization[14] is used as exchange correlation functional. The core and valence states are separated by
The thermodynamic properties are determined by using quasi-harmonic Debye model which is implemented in Gibbs code.[15] The energy volume optimization data is used as input to determine the pressure and temperature dependence of Helmholtz free energy, internal energy, entropy, Debye temperature, and heat capacity. In the quasi-harmonic Debye model, the non-equilibrium Gibbs function
The equilibrium geometry is achieved by minimizing the Gibbs function with respect to volume of unit cell at constant pressure and temperature, i.e.,
By using minimizing condition in Eq. (
The Helmholtz free energy is important to determine the stability of a structure. A structure with more negative value of Helmholtz free energy will be considered more stable. The Helmholtz free energy at any temperature T can be written easily in the scope of standard thermodynamics as
The Helmholtz and internal energies are increasing with the increase of temperature. The internal energy is found insensitive to pressure above 200 K, while Helmholtz energy increases with pressure from 0 to 10 GPa. At low temperature limit,
The internal energy at 0 K is attributed to the existence of zero point motion and calculated
The Debye temperature is a key quantity in the quasi-harmonic Debye model, which is related to many properties like elastic constants, thermal expansion, melting temperature, and specific heat. The Debye temperature at zero Kelvin and zero Pascal is 390.53 K, which is close to the value 383 K reported in Ref. [9]. The effect of temperature and pressure on Debye temperature is displayed in Fig.
The Grüneisen parameter reflects the anharmonicity in the crystal, that is, how much phonon vibrations are deviating from harmonic oscillations. Table
The heat capacity at constant volume on the basis of Debye quasi-harmonic approximation as a function of temperature at different pressure is shown in Fig.
Figure
The effect of pressure on Debye temperature at T = 300 K is shown in Fig.
The pressure and temperature dependence of thermodynamic properties of zinc selenide in zinc blende phase have been calculated by using FP-LAPW+lo method in the framework of density functional theory and Debye quasi-harmonic approximation which are implemented in WIEN2k and Gibbs codes respectively. The Helmholtz free energy and Debye temperature are found to decrease with increasing temperature, but both have increasing behavior with rise of pressure, whereas internal energy and entropy of ZnSe have increasing trend with increase of temperature. The internal energy almost remains insensitive to pressure over most of the temperature range and entropy decreases with rise of pressure. The specific heat at constant volume approaches to classical limit at T = 300 K. The Grüneisen parameter and thermal expansion coefficient decrease with rise of pressure. The calculated thermodynamic properties are in good agreement with available theoretical and experimental data at ambient conditions.[7,19]
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