Based on piezoelectric constitutive equations and Bragg law. we proposed an extended model, in which the piezoelectric coupling factor determined by the elastic, dielectric and piezoelectric constants is introduced, to evaluate the residual stress in ferroelectric thin film with X-ray diffraction (XRD). Pb(Zr_(0.52)Ti_(0.48))O_3 thin films with thickness 0.05, 0.5, and 1.0 mum were grown on Pt/Ti/ Si(001) by pulsed laser deposition (PLD) at the substrate temperature 650 deg C and oxygen pressure 40 Pa. D500 goniometer and sin~2 psi method were used to measure the residual stress in PZT thin films. The origin of residual stress was theoretically discussed from the epitaxial stress, intrinsic stress, thermal stress, and transformation stress. The results show that the theoretical results are closer to the experimental results evaluated by the extended model, and the residual compressive stress evaluated by the extended model is larger than that evaluated by the conventional model due to the consideration of the piezoelectric coupling effects.
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机译:基于压电本构方程和布拉格定律。我们提出了一个扩展模型,其中引入了由弹性、介电和压电常数决定的压电耦合因子,以评估X射线衍射(XRD)铁电薄膜中的残余应力。在衬底温度650 °C、氧压40 Pa O_3采用脉冲激光沉积(PLD)方法在Pt/Ti/Si(001)上生长了厚度为0.05、0.5和1.0 mum的Pb(Zr_(0.52)Ti_(0.48))薄膜,采用D500测角仪和sin~2 psi法测定了PZT薄膜的残余应力。从外延应力、内禀应力、热应力和转变应力三个方面对残余应力的起源进行了理论论述。结果表明,理论结果与扩展模型评估的实验结果更接近,并且由于考虑了压电耦合效应,扩展模型评估的残余压应力大于常规模型评估的残余压应力。
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