Browsing by Author "Horpenuk Andriy"

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    Features of simulation of characteristics of thermometric material Lu1–xZrxNiSb
    (Lviv Politechnic Publishing House, 2021) Krayovskyy Volodymyr; Pashkevych Volodymyr; Horpenuk Andriy; Romaka Volodymyr; Stadnyk Yuriy; Romaka Lyubov; Horyn Andriy; Romaka Vitaliy
    The results of modeling the thermometric characteristics of the semiconductor solid solution Lu1–xZrxNiSb, which is a promising thermometric material for the manufacture of sensitive elements of thermoelectric and electro resistive thermocouples, are presented. Modeling of the electronic structure of Lu1–xZrxNiSb was performed by the Korringa–Kohn–Rostoker (KKR) method in the approximation of coherent potential and local density and by the full-potential method of linearized plane waves (FLAPW). KKR simulations were performed using the AkaiKKR software package in the local density approximation for the exchange-correlation potential with parameterization Moruzzi, Janak, Williams in the semi-relativistic one taking into account the spin-orbit interaction. The implementation of the method in the Elk software package was used to perform FLAPW calculations. To check the limits of the existence of the thermometric material Lu1–xZrxNiSb, both methods were used to calculate the change in the values of the period of the unit cell a(x) in the range x = 0 – 1.0. It is shown that there is an agreement between the change in the values of a(x) Lu1–xZrxNiSb calculated by the FLAPW method and the results of experimental studies. The obtained result indicates higher accuracy of modeling of structural parameters Lu1–xZrxNiSb by the FLAPW method in comparison with the KKR method. To study the possibility of obtaining thermometric material Lu1–xZrxNiSb and to establish the limits of its existence in the form of a continuous solid solution, modeling of thermodynamic characteristics in the approximation of harmonic oscillations of atoms within the theory of DFT density functional for a hypothetical solid solution Lu1–xZrxNiSb, x = 0 – 1.0. The change in the values of the enthalpy of mixing ΔH and the total energy E Lu1–xZrxNiSb, x = 0–1.0, allows us to state that the thermometric material exists in the form of a solid substitution solution in the concentration range x = 0 – < 0.20. At higher conc exist. To understand the mechanisms of electrical conductivity of the thermometric material Lu1–xZrxNiSb, the methods of entry of impurity Zr atoms into the matrix of the basic semiconductor p-LuNiSb and their occupation of different crystallographic positions, as well as the presence of vacancies in them, were investigated. For this purpose, its electronic structure was modeled for different variants of the spatial arrangement of atoms and the presence of vacancies in crystallographic positions. It is shown that the most acceptable results of experimental studies are the model of the electronic structure of p-LuNiSb, which assumes the presence of vacancies in the crystallographic positions of 4a Lu atoms (~0.005) and 4c Ni atoms (~0.04). In this model of the spatial arrangement of atoms and the presence of vacancies at positions 4a and 4c, the LuNiSb compound is a semiconductor of the hole-type conductivity, in which the Fermi level eF is located near the level of the valence band eV. The kinetic characteristics of the semiconductor thermometric material Lu1–xZrxNiSb, in particular, the temperature dependences of the resistivity ρ(T, x) and the thermopower coefficient α(T, x) are modeled. It is established that at the lowest concentrations of impurity atoms Zr the Fermi level eF Lu1–xZrxNiSb passes from the bandgap to the conduction band eС. This is indicated by the negative values of the thermopower coefficient α(T, x) and the metallic conductivity type Lu1–xZrxNiSb. This changes the type of main current carriers from holes to electrons.
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    Study of thermometric material Er1-xScxNiSb. II. Experimental results
    (Lviv Politechnic Publishing House, 2021) Krayovskyy Volodymyr; Pashkevych Volodymyr; Horpenuk Andriy; Romaka Volodymyr; Stadnyk Yuriy; Romaka Lyubov; Horyn Andriy
    The results of a comprehensive study of the crystal and electronic structures, kinetic and energetic performances of the semiconductor thermometric material Er1-xScxNiSb (x = 0 – 0.1) are presented. Microprobe analysis of the concentration of atoms on the surface of Er1-xScxNiSb samples established their correspondence to the initial compositions of the charge, and the diffractograms of the samples are indexed in the structural type of MgAgAs. Because the atomic radius Sc (rSc = 0.164 nm) is smaller than that of Er (rEr = 0.176 nm), it is logical to reduce the values of the unit cell's period a(x) Er1-xScxNiSb, which correlate with the results of mathematical modeling. The temperature dependences of the resistivity ln(ρ(1/T)) contain high- and low-temperature activation regions, which are specific for semiconductors and indicate the location of the Fermi level in the bandgap, and positive values of the thermopower coefficient a (x, T) specify its position – near the valence band . This result does not agree with the results of modeling the electronic structure for its ordered version. The presence of a low-temperature activation region on the ln(ρ(1/T)) p-ErNiSb dependence with an activation energy = 0.4 meV indicates the compensation of the sample provided by acceptors and donors of unknown origin. A decrease in the values of the resistivity ρ(x, T) and the thermopower coefficient a(x, T) points to an increase in the concentration of holes in p-Er1-xScxNiSb in the area of concentrations x = 0 – 0.03. This is possible in a p-type semiconductor only by increasing the concentration of the main current carriers, which are holes. The fact of increasing the concentration of acceptors in Er1-xScxNiSb at insignificant concentrations of impurity atoms is also indicated by the nature of the change in the values of the activation energy of holes from the Fermi level to the valence band . Consequently, if in p-ErNiSb the Fermi level was at a distance of 45.4 meV from the level of the valence band , then at the concentration Er1-xScxNiSb, x = 0.01, the Fermi level shifted towards the valence band and was located at a distance of 13.6. Since the Fermi level reflects the ratio of ionized acceptors and donors in the semiconductor, its movement by x = 0.01 to the valence band is possible either with an increase in the number of acceptors or a rapid decrease in the concentration of ionized donors. At even higher concentrations of Sc impurity in p-Er1-xScxNiSb, x ≥ 0.03, low-temperature activation sites appear on the ln(ρ(1/T)) dependences, which is a sign of compensation and evidence of the simultaneous generation of acceptor and donor structural defects in the crystal nature. This is also indicated by the change in the position of the Fermi level in the bandgap of the semiconductor Er1-xScxNiSb, which is almost linearly removed from the level of the valence band : (x = 0.05) = 58.6 meV and (x = 0.10) = 88.1 meV. Such a movement of the Fermi level during doping of a p-type semiconductor is possible only if donors of unknown origin are generated. For a p-type semiconductor, this is possible only if the concentration of the main current carriers, which are free holes, is reduced, and donors are generated that compensate for the acceptor states. This conclusion is also confirmed by the behavior of the thermopower coefficient a(x, T) at concentrations x ≥ 0.03. The results of structural, kinetic, and energy studies of the thermometric material Er1-xScxNiSb allow us to speak about a complex mechanism of simultaneous generation of structural defects of acceptor and donor nature. However, the obtained array of experimental information does not allow us to unambiguously prove the existence of a mechanism for generating donors and acceptors. The research article offers a solution to this problem. Having the experimental results of the drift rate of the Fermi level as the activation energy (x) from the Fermi level to the valence band by calculating the distribution of the density of electronic states (DOS) sought the degree of compensation, which sets the direction and velocity of the Fermi level as close as possible to the experimental results. DOS calculations are performed for all variants of the location of atoms in the nodes of the unit cell, and the degree of occupancy of all positions by their own and/or foreign atoms. It turned out that for ErNiSb the most acceptable option is one that assumes the presence of vacancies in positions 4a and 4c of the Er and Ni atoms, respectively. Moreover, the number of vacancies in the position Er (4a) is twice less than the number of vacancies in the position Ni (4c). This proportion is maintained for Er1-xScxNiSb. Vacancies in the positions of Er (4a) and Ni (4c) atoms Er1-xScxNiSb are structural defects of acceptor nature, which generate two acceptor zones and in the semiconductor. The introduction of impurity Sc atoms into the ErNiSb structure by substituting Er atoms in position 4a is also accompanied by the occupation of vacancies by Sc atoms and a reduction in their number. Occupying a vacancy, the Sc atom participates in the formation of the valence band and the conduction band of the semiconductor Er1-xScxNiSb, acting as a source of free electrons. We can also assume that the introduction of Sc atoms into the structure of the compound ErNiSb is accompanied by a process of ordering the structure of Er1-xScxNiSb and Ni atoms occupy vacancies in position 4c. This process also, however, 2 times slower, leads to a decrease in the concentration of structural defects of acceptor nature. In this case, Ni, giving valence electrons, now act as donors.