椭偏仪在位表征电化学沉积的系统搭建（十二）- 光学常数的提取与COMSOL Multiphysics

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椭偏仪在位表征电化学沉积的系统搭建（十二）- 光学常数的提取与COMSOL Multiphysics

2.3光学常数的提取

2.3.1建立光学模型

通过椭偏测试得到包含整个池体的参数ψ和Δ，这时要想提取CU₂O的光学常数及生长速率就需要进行建模拟合。首先把整个池体看成多层膜结构，光从空气中依次经过ITO、溶液、CU₂O以及Au衬底，zui后反射回到椭偏仪的出射臂，zui终信息被接收。在物理层面将池体简化为四层膜的模型，即ITO/溶液/CU₂O/(Au/Si)，如图2-3(a)所示。根据拟合需要可以对结构模型进行调整，如：ITO和溶液混合层/CU₂O/(Au/Si)的三层膜模型，如图2-3(b)所示。

图2-3光学模型示意图(a)四层；(b)三层

数据分析中用的是全局误差zui小化(GEM)数据分析法，数据分析程序如图2-4所示。其中光学模型选用上述的层状模型，拟合模型用Lorentz Oscillator+Drude模型和有效介质模型(EMA)。

图2-4数据拟合分析程序

2.3.2 Film Wizard

Film Wizard拟合软件是椭偏仪专用数据处理软件，可以实现椭偏谱的拟合与数据的提取。在建立好拟合模型后就可以使用该软件进行拟合，拟合步骤如下：

1.数据转换，即把椭偏仪测试得到的数据格式(.dat)转换为FilmWizard软件可以识别的文件格式(.tar)；

2.打开Film Wizard软件新建一个项目，然后把建立好的多层模型写到新建的项目里；

3.导入数据，即把已知的基底和其他层的数据导入模型，再把要拟合层的数据导入模型；

4.选择拟合模型，Lorentz Oscillator+Drude模型或有效介质模型(EMA)；

5.拟合，选择需要改变的拟合参数，如厚度、振子数等，然后通过调节要拟合的参数进行拟合直至拟合误差达到要求。

6.当误差达到zui小后，导出拟合得到的数据n、k、等。

2.4 COMSOL Multiphysics

COMSOL Multiphysics被广泛应用到许多领域的科学研究和工程计算中，COMSOL Multiphysics在多物理场的全耦合方面十分专业，可以高效的进行科学及工程领域的各种物理场景模拟，并在良好的计算性能与出众的双向多场直接耦合模拟分析能力加持下实现高精度数值仿真。

我们应用了COMSOL软件对电化学沉积中的电极形状建模及电流密度分布的模拟。电化学模块下主要一次和二次电流分布、三次电流分布、电池接口、腐蚀变形几何、电镀变形几何接口。这里主要用到了电化学模块中的一次和二次电流分布接口中的一次电流分布，进行了一般稳态研究，其涉及到的方程有：

其中为电解质的电位，为电势。在模拟过程中通过给定参数的初始值，即可进相应的拟合，得到电解液电场分布及电流密度分布等。

了解更多椭偏仪详情，请访问上海昊量光电的官方网页：

https://www.auniontech.com/three-level-56.html

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