Cerium dioxide (CeO₂), zirconium dioxide (ZrO₂) and tin dioxide (SnO₂) also known as ceria, are fascinating materials with a wide range of applications due to their unique properties. To investigate the doping response of La in of XO₂ (X = Ce, Zr, Sn) generalized gradient approximation (GGA-PBEsol) based on CASTEP (Cambridge Serial Total Energy Package) code with ultra-soft pseudo-potential (USP) plane wave method is used. The incorporation of La in pure material shows a significant reduction of band gap and enhances the conductivity of the material. The bandgap narrowing primes to the maximum optical absorption in the visible light region. To assess the mechanical stability, the elastic responses, including the bulk Poisson's ratios, and Young's modulus calculate the significant hardness and ductile nature of the materials. The nature of the materials for optoelectronic applications, such as solar cells, is evident in the optical characteristics, including real and fictitious components of the dielectric constant, refractive index, absorption, and energy loss function. The computation of the structural, electronic, mechanical, and optical responses validates its significance for optoelectronic applications.

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中文翻译：

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计算确定有前途的 XO2（X = Ce、Zr、Sn）中的 La 取代：用于光电应用的新兴材料

二氧化铈(CeO ₂ )、二氧化锆(ZrO ₂ )和二氧化锡(SnO ₂ )也称为二氧化铈，由于其独特的性质，是具有广泛应用的迷人材料。基于具有超软赝势 (USP) 平面的 CASTEP（剑桥串行总能量包）代码，研究 XO ₂ (X = Ce, Zr, Sn) 广义梯度近似 (GGA-PBEsol)中 La 的掺杂响应采用波浪法。在纯材料中掺入 La 可显着减小带隙并增强材料的电导率。带隙变窄导致可见光区域的最大光学吸收。为了评估机械稳定性，弹性响应（包括体积泊松比和杨氏模量）可计算材料的显着硬度和延展性。用于光电应用（例如太阳能电池）的材料的性质在光学特性中很明显，包括介电常数、折射率、吸收和能量损失函数的真实和虚构部分。结构、电子、机械和光学响应的​​计算验证了其对于光电应用的重要性。

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