Richert Damien, Morán-Meza José, Kaja Khaled, Delvallée Alexandra, Allal Djamel, Gautier Brice, Piquemal François
Laboratoire National de Métrologie et d'Essais (LNE), 78197 Trappes, France.
Institut National des Sciences Appliquées de Lyon, 69100 Villeurbanne, France.
Nanomaterials (Basel). 2021 Nov 17;11(11):3104. doi: 10.3390/nano11113104.
The importance of high dielectric constant materials in the development of high frequency nano-electronic devices is undeniable. Their polarization properties are directly dependent on the value of their relative permittivity. We report here on the nanoscale metrological quantification of the dielectric constants of two high-κ materials, lead zirconate titanate (PZT) and lead magnesium niobate-lead titanate (PMN-PT), in the GHz range using scanning microwave microscopy (SMM). We demonstrate the importance of the capacitance calibration procedure and dimensional measurements on the weight of the combined relative uncertainties. A novel approach is proposed to correct lateral dimension measurements of micro-capacitive structures using the microwave electrical signatures, especially for rough surfaces of high-κ materials. A new analytical expression is also given for the capacitance calculations, taking into account the contribution of fringing electric fields. We determine the dielectric constant values ε = 445 and ε = 641 at the frequency around 3.6 GHz, with combined relative uncertainties of 3.5% and 6.9% for PZT and PMN-PT, respectively. This work provides a general description of the metrological path for a quantified measurement of high dielectric constants with well-controlled low uncertainty levels.
高介电常数材料在高频纳米电子器件发展中的重要性是不可否认的。它们的极化特性直接取决于其相对介电常数的值。我们在此报告使用扫描微波显微镜（SMM）在GHz范围内对两种高κ材料锆钛酸铅（PZT）和铌镁酸铅 - 钛酸铅（PMN - PT）的介电常数进行纳米级计量量化。我们证明了电容校准程序和尺寸测量对组合相对不确定度的重要性。提出了一种新颖的方法，利用微波电特征校正微电容结构的横向尺寸测量，特别是对于高κ材料的粗糙表面。还给出了考虑边缘电场贡献的电容计算新解析表达式。我们在约3.6 GHz频率下确定PZT和PMN - PT的介电常数分别为ε = 445和ε = 641，其组合相对不确定度分别为3.5%和6.9%。这项工作提供了一条用于在低不确定度水平得到良好控制的情况下对高介电常数进行量化测量的计量路径的一般性描述。
