The structural, electronic and thermoelectric properties of AZr_1-xM_xO₃ (A = Ba, Ca, Sr; M = Al, Cu, x = 0.25) without and with an oxygen vacancy (Vo) have been unveiled using the Perdew-Burke-Ernzerhof Generalized Gradient Approximation (PBE-GGA) functional along with Tran-Blaha modified Becke-Jonhson (TB-mBJ)approximation based on Density Functional Theory (DFT) in the framework of WIEN2k code for memristors applications. Moreover, isosurface charge density plots have been calculated by using Vienna ab initio Simulation Package (VASP) simulation code. The analysis of structural parameters reveals that substituting Zr⁴⁺ with Al³⁺ and Cu²⁺ causes the lattice distortion which tends to increase in the presence of Vo along with dopant. The study of band structure, density of states (DOS) and isosurface charge density plots predict the enhanced charge conduction and formation of conducting filaments (CFs) for all composites with dopant and/or Vo. Moreover, spin polarized density of states for Cu doped composites has also been calculated to confirm the large exchange splitting of Cu-3d states. The thermoelectric characteristics of considered composites have also been explored using the Boltztrap code to better explain the semi-classical Boltzmann transport theory. Thermoelectric parameters confirm the semiconductor nature of all composites, ensuring the compatibility for memristors and thermoelectric devices applications. In addition to this spin polarized thermoelectric behavior of Cu doped composites that ensure the contribution of spin down $(\downarrow )$ states of Cu for charge transport mechanism. The SrZrCuO₃+Vo composite is found most promising candidate followed by BaZrCuO₃ for memristors applications while, CaZrCuO₃ is found most suitable amongst studied composites for thermoelectric devices.

使用Perdew揭示了无氧空位（Vo）的AZr _1-x M _x O ₃（A = Ba，Ca，Sr; M = Al，Cu，x = 0.25）的结构，电子和热电性质-Burke-Ernzerhof广义梯度逼近（PBE-GGA）函数以及基于WYN2k代码的忆阻器应用中基于密度泛函理论（DFT）的Tran-Blaha修改的Becke-Jonhson（TB-mBJ）逼近。而且，等值面的电荷密度图已经通过使用计算出的维也纳从头算仿真程序包（VASP）仿真代码。结构参数分析表明，用Al ³⁺和Cu ²⁺代替Zr ⁴⁺会导致晶格畸变，在Vo与掺杂剂一起存在时晶格畸变趋于增加。能带结构，状态密度（DOS）和等表面电荷密度图的研究预测了所有掺杂物和/或Vo的复合材料的电荷传导增强以及导电丝（CF）的形成。此外，还计算了掺Cu复合材料的自旋极化态密度，以确认Cu-3d的大交换分裂状态。还使用Boltztrap代码探索了考虑的复合材料的热电特性，以更好地解释半经典的Boltzmann输运理论。热电参数确定了所有复合材料的半导体性质，从而确保了与忆阻器和热电设备应用的兼容性。除了这种自旋极化的Cu掺杂复合材料的热电行为，还可以确保自旋向下的贡献$（\downarrow ）$态的铜用于电荷传输机制。SrZrCuO ₃ + Vo复合材料被认为是最有前途的候选材料，其次是BaZrCuO ₃用于忆阻器应用，而CaZrCuO ₃被认为是最适合研究热电器件的复合材料。