1.Hubei Key Laboratory of Manufacture Quality Engineering, Hubei University of Technology, Wuhan 430068, China 2.State Key Laboratory for Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan 430074, China
Abstract:Optical scatterometry, as a fast, low-cost, and non-contact measurement instrument, is widely used in the profile characterization of nanostructure in the semiconductor manufacturing industry. In general, it involves two procedures, i.e. the forward optical modeling of sub-wavelength nanostructures and the reconstruction of structural profiles from the measured signatures. Here, the general term signature means the scattered light information from the diffractive grating structure, which can be in the form of reflectance, ellipsometric angles, Stokes vector elements, or Mueller matrix elements. The profile reconstruction process is an inverse problem with the objective of optimizing a set of floating profile parameters (e.g., critical dimension, sidewall angle, and height) whose theoretical signatures can best match the measured ones through regression analysis or library search. During solving the inverse problem, the refractive index and distinction coefficient of the material of nanostructure are assumed to be constants and they are generally fixed. This assumption is valid for most of the materials in semiconductor industry, but not for certain materials that are very photosensitive. That is, the optical constants of photosensitive materials may vary with the illumination time of the incident light beam in spectroscopic ellipsometer, and the error caused by the variation of optical constants propagates to the final extracted results of structural profiles, which should not be neglected, especially for high precision and accuracy metrology.Experiments performed on SiO2 and polymethyl methacrylate (PMMA) thin films are conducted and demonstrate that the extracted geometric parameters and optical constants of SiO2 film do not change with illumination time increasing, while the twenty groups of values of extracted refractive index n and distinction coefficient k of PMMA resist film vary obviously, and the difference between the extracted maximum and minimum film thickness has reached 40.5 nm, which to some extent illustrates that the above assumption is not valid for PMMA resist, so that the incident light beam of spectroscopic ellipsometer has a great influence on the extracted film thickness. Further, simulations based on a three-dimensional PMMA grating also indicate that the error of optical constant has considerably transferred to the extracted profile parameters. This finding is of significance for improving the accuracy of nanostructure characterization in optical scatterometry. Keywords:optical scatterometry/ photoresist nanostructure/ polymethyl methacrylate/ optical constant
其中, An, Bn和Cn描述折射率的色散; KAmp(K振幅)和eExponent (指数)项描述消光系数色散的形状; λBandedge一般设为定值400 nm. 模型中的An, Bn, Cn, KAmp和eExponent均为待定系数. 对于样品表面的粗糙结构, 采用麦克斯韦尔-加内特等效介质模型(maxwell-garnett effective medium approximation, MGEMA)[32]将其近似为一层均匀且各项同性的薄膜进行处理. 在此基础上, 将入射条件和基底硅的光学常数等设为已知值, 利用LM迭代算法分别对20组椭偏测量数据进行待测参数逆向求取, 并采用均方根误差(mean squared error, MSE)[33]来衡量测量与模型计算数据之间的拟合程度, 待测参数包括d1和r1, 光学常数模型参数$n(\infty) $, Eg, Ai, Bi和Ci. 图4为SiO2厚度d1及其表面粗糙层厚度r1的20组拟合值; 图5分别展示了第1, 5, 10, 15和20次所提取得到的各波长下折射率n1与消光系数k1值, 以及文献[34]中的SiO2光学常数变化曲线. 图 4 拟合得到的20组SiO2膜厚d1及其表面粗糙度等效膜厚r1 (a) r1; (b) d1; (c) MSE Figure4. Extracted results of the thicknesses of SiO2 film h1 and equivalent surface roughness r1: (a) r1; (b) d1; (c) MSE.
图 5 拟合得到的第1, 5, 10, 15和20组SiO2薄膜光学常数n1和k1的计算值, 以及文献[34]给出的折射率与消光系数 (a) n1; (b) k1 Figure5. Extracted results of the optical constants n1 and k1 of SiO2 film calculated by Cauchy model and the ones from Ref. [34]: (a) n1; (b) k1.
表1对比PMMA仿真光栅3个待测形貌参数的拟合值与真实值 Table1.Comparison of these three true dimensions and the extracted results of the simulated PMMA grating.
图 9 在入射角θ = 65°、方位角φ = 0°的入射条件下, PMMA光刻胶仿真光栅的模型计算Mueller矩阵光谱与“测量”光谱之间的拟合曲线 Figure9. Fitting results of the calculated and the “ellipsometer-measured” Mueller matrix elements at the incidence and azimuthal angles fixed at θ = 65° and φ = 0°.