CN110244527A - A Method for Optimizing Overlay Mark Shape and Measurement Conditions - Google Patents
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Abstract
Description
技术领域technical field
本发明属于光刻领域,更具体地,涉及一种套刻标记形貌和测量条件优化方法。The invention belongs to the field of photolithography, and more specifically relates to a method for optimizing the shape of overlay marks and measurement conditions.
背景技术Background technique
随着集成电路工艺的飞速发展,集成电路由小规模发展到极大规模,其关键尺寸(Critical Dimension,CD)也由微米级不断减小至今天的7nm节点。集成电路的制造过程包括材料制备、光刻、清洗、刻蚀、掺杂、化学机械抛光等多个工序,其中尤以光刻工艺最为关键。光刻工艺的主要指标有分辨率、焦深、关键尺寸、对准和套刻精度等。其中,套刻指的是当前光刻工艺层和前层工艺层的对准关系,一般要求套刻误差不大于关键尺寸的1/3,因此套刻误差的快速测量与精确评估是保证工艺及器件性能的关键。With the rapid development of integrated circuit technology, integrated circuits have developed from small scale to extremely large scale, and their critical dimensions (Critical Dimension, CD) have also been continuously reduced from micron level to today's 7nm node. The manufacturing process of integrated circuits includes multiple processes such as material preparation, photolithography, cleaning, etching, doping, and chemical mechanical polishing, among which the photolithography process is the most critical. The main indicators of the lithography process include resolution, depth of focus, key dimensions, alignment and overlay accuracy, etc. Among them, overlay refers to the alignment relationship between the current photolithography process layer and the previous layer process layer. Generally, the overlay error is required to be no more than 1/3 of the critical dimension. Therefore, the rapid measurement and accurate evaluation of the overlay error is to ensure the process and key to device performance.
Haiyong Gao等人在文献“Comparison study of diffraction-based overlayand image-based overlay measurements on programmed overlay errors”中总结,套刻测量方法大致可以分为两类:基于图形的套刻测量 (Image-Based Overlay,IBO)和基于衍射的套刻测量(Diffraction-Based Overlay,DBO)。韦亚一在文献《超大规模集成电路先进光刻理论与应用》中提到,为了测量前后工艺层的套刻误差,这两种方法都需要在相互套准的前后工艺层上的同一位置设计套刻标记,然后通过套刻测量设备对套刻标记进行测量,从而得到套刻误差测量结果。这些标记通常是在曝光区域的边缘,又叫“scribeline”或“kerf”区域。Haiyong Gao et al. summarized in the literature "Comparison study of diffraction-based overlay and image-based overlay measurements on programmed overlay errors" that overlay measurement methods can be roughly divided into two categories: image-based overlay measurement (Image-Based Overlay, IBO) and Diffraction-Based Overlay (DBO). Wei Yayi mentioned in the document "Advanced Lithography Theory and Application of VLSI", in order to measure the overlay error of the front and back process layers, both methods need to be designed at the same position on the front and back process layers that are registered with each other. Overlay marks, and then measure the overlay marks with overlay measuring equipment, so as to obtain overlay error measurement results. These marks are usually at the edge of the exposed area, also known as the "scribeline" or "kerf" area.
Jie Li等人在文献“Evaluating Diffraction-Based Overlay”中提到,DBO 方法主要包含eDBO和mDBO(model-based DBO)两种。对于mDBO方法,专利CN103472004B中提到,由于其需要大量构建套刻标记的正向光学特性模型,因而难以满足实际测量的时间需求。对于eDBO方法,专利 CN103454861B中提到该方法具有测量速度快,采样面积小的优点,同时消除了传统测量方法的许多误差项,如定位误差、焦面误差、像差因素和机械振动等。此外,中国专利CN200510091733,美国专利US7173699B2、 US7477405B2、US7428060B2和US6985232B2中均公开了这样的方法。Jie Li et al. mentioned in the document "Evaluating Diffraction-Based Overlay" that DBO methods mainly include eDBO and mDBO (model-based DBO). For the mDBO method, it is mentioned in the patent CN103472004B that it is difficult to meet the time requirement of actual measurement because it needs to construct a large number of forward optical characteristic models of overlay marks. For the eDBO method, the patent CN103454861B mentions that this method has the advantages of fast measurement speed and small sampling area, and at the same time eliminates many error items of traditional measurement methods, such as positioning error, focal plane error, aberration factors and mechanical vibration. In addition, Chinese patent CN200510091733, US patents US7173699B2, US7477405B2, US7428060B2 and US6985232B2 all disclose such methods.
eDBO方法基于套刻光学表征曲线的局部线性关系提取套刻误差。在套刻光学表征曲线200原点O处,套刻偏移量δ与光学表征量I近似呈线性关系:The eDBO method extracts the overlay error based on the local linear relationship of the overlay optical characterization curve. At the origin O of the overlay optical characterization curve 200, the overlay offset δ is approximately linear in relation to the optical characterization quantity I:
I=Kδ (1)I=Kδ (1)
其中,套刻偏移量δ和测量灵敏度K均为未知量,难以通过单次测量确定二者的数值。为此,eDBO通过引入已知套刻偏移量的方式,以差分法实现套刻误差的提取。Among them, the overlay offset δ and the measurement sensitivity K are both unknown quantities, and it is difficult to determine their values through a single measurement. For this reason, eDBO realizes the extraction of overlay error by differential method by introducing known overlay offset.
典型的eDBO套刻标记俯视图见300所示,301和304用来测量X方向上的套刻误差,302和303用来测量Y方向上的套刻误差。以X方向为例,待求套刻误差为ε,在两个套刻标记单元301、304上分别引入了已知套刻偏移量+D和-D,对应剖面图见图3(b)和3(c),则两个单元总的套刻偏移量δ±分别为D+ε和-D+ε。因此根据式(1)两个套刻标记单元的光学表征量分别如下式:A top view of a typical eDBO overlay mark is shown at 300 , 301 and 304 are used to measure the overlay error in the X direction, and 302 and 303 are used to measure the overlay error in the Y direction. Taking the X direction as an example, the overlay error to be obtained is ε, and the known overlay offsets +D and -D are respectively introduced into the two overlay marking units 301 and 304, and the corresponding cross-sectional view is shown in Figure 3(b) and 3(c), the total overlay offset δ ± of the two units is D+ε and -D+ε respectively. Therefore, according to the formula (1), the optical characterization quantities of the two overlay marking units are as follows:
I+=K(D+ε) (2)I + =K(D+ε) (2)
I-=K(-D+ε) (3)I - =K(-D+ε) (3)
则套刻误差ε为:Then the overlay error ε is:
因此,只需对套刻标记单元301和304分开测量得到I+、I-,就可以通过上式得到套刻误差ε。考虑到实际套刻测量中噪声△I的影响,式(2)、 (3)改写为:Therefore, only the overlay marking units 301 and 304 need to be measured separately to obtain I + , I − , and the overlay error ε can be obtained through the above formula. Considering the influence of noise △I in the actual overlay measurement, formulas (2) and (3) are rewritten as:
I+=K(D+ε)+△I+ (5)I + =K(D+ε)+△I + (5)
I-=K(-D+ε)+△I- (6)I - =K(-D+ε)+△I - (6)
因此,实际测量得到的套刻误差值如下式:Therefore, the overlay error value obtained by actual measurement is as follows:
用σm(套刻表征光学量I的仪器测量噪声标准差)替代式(7)中的△I++△I-,并忽略分母中的△I+-△I-即得到eDBO方法的重复性测量精度σ:Replace △I + +△I - in formula (7) with σ m (the standard deviation of the instrument measurement noise that characterizes the optical quantity I overlaid), and ignore △I + -△I - in the denominator to obtain the repetition of the eDBO method Sexual measurement accuracy σ:
可见测量灵敏度K和仪器的噪声水平共同决定了套刻误差的重复性测量精度。It can be seen that the measurement sensitivity K and the noise level of the instrument jointly determine the repeatability measurement accuracy of the overlay error.
eDBO方法的关键在于套刻偏移量δ∈[-D+ε,D+ε]范围内近似满足式(1)中的线性关系假设。然而,套刻光学表征曲线是周期性的奇函数(见 201),因此表征曲线的非线性会引入套刻偏移量表征误差Δδ1(见202),影响测量准确度μ。此外,套刻标记其他非对称因素会使套刻光学表征曲线平移而引入套刻偏移量表征误差Δδ2(见203),这也会影响测量准确度μ。The key to the eDBO method is that the overlay offset δ∈[-D+ε, D+ε] approximately satisfies the linear relationship assumption in formula (1). However, the overlay optical characteristic curve is a periodic odd function (see 201), so the nonlinearity of the characteristic curve will introduce the overlay offset characterization error Δδ 1 (see 202), affecting the measurement accuracy μ. In addition, other asymmetric factors of the overlay mark will translate the overlay optical characteristic curve and introduce an overlay offset error Δδ 2 (see 203), which will also affect the measurement accuracy μ.
套刻误差表征曲线不仅取决于套刻标记的形貌,而且与测量条件(如测量波长、入射角、方位角)相关,因此为实现重复性精度高、准确度高、鲁棒性好的套刻误差测量,有必要研究一种eDBO套刻标记形貌和测量条件优化方法。The overlay error characterization curve not only depends on the shape of the overlay mark, but also is related to the measurement conditions (such as measurement wavelength, incident angle, azimuth angle), so in order to achieve high repeatability, high accuracy, and good robustness In order to measure the engraving error, it is necessary to study a method for optimizing the morphology and measurement conditions of eDBO overlay marks.
发明内容Contents of the invention
针对现有技术的以上缺陷或改进需求,本发明提供了一种套刻标记形貌和测量条件优化方法,其目的在于,同时考虑套刻标记形貌优化与测量条件优化配置,以套刻误差重复性测量精度σ和准确度μ为两个优化目标,得到鲁棒性良好的多个帕累托最优结果,由此解决现有套刻误差测量重复性精度低、准确度低、鲁棒性差的技术问题。Aiming at the above defects or improvement needs of the prior art, the present invention provides a method for optimizing the shape of the overlay mark and the measurement conditions. Repeatability measurement accuracy σ and accuracy μ are two optimization objectives, and multiple Pareto optimal results with good robustness are obtained, thereby solving the problem of low repeatability, low accuracy, and robustness of existing overlay error measurement. Poor technical issues.
为实现上述目的,本发明提供了一种套刻标记形貌和测量条件优化方法,其特征在于,包括如下步骤:In order to achieve the above object, the present invention provides a method for optimizing the shape of overlay marks and measurement conditions, which is characterized in that it includes the following steps:
步骤101,确定套刻标记形貌结构和材料光学常数;Step 101, determining the overlay mark topography and material optical constants;
步骤102,根据步骤101确定的套刻标记形貌结构的参数和材料光学常数,以及设定的测量条件,通过解析或数值建模方法计算单个光学表征量I,通过连续改变套刻偏移量δ计算得到套刻光学表征曲线;所述套刻光学表征曲线表征光学表征量I和套刻偏移量δ的函数关系;Step 102, according to the parameters and material optical constants of the overlay mark determined in step 101, and the set measurement conditions, a single optical characteristic I is calculated by analytical or numerical modeling methods, and by continuously changing the overlay offset δ is calculated to obtain an overlay optical characterization curve; the overlay optical characterization curve represents the functional relationship between the optical characterization quantity I and the overlay offset δ;
步骤103,在所述套刻光学表征曲线的原点展开泰勒公式,得到套刻测量重复性精度σ和准确度μ的表达式;Step 103, expanding the Taylor formula at the origin of the overlay optical characterization curve to obtain the expressions of the overlay measurement repeatability precision σ and accuracy μ;
步骤104,从所述套刻标记形貌结构的参数和所述测量条件中选定待优化变量,以套刻测量重复性精度σ和准确度μ作为优化目标,采用多目标优化算法对所述待优化变量进行迭代选择,获取包含多组所述套刻测量重复性精度σ和准确度μ的帕累托优化结果。Step 104, select the variables to be optimized from the parameters of the topographic structure of the overlay mark and the measurement conditions, take the repeatability precision σ and accuracy μ of the overlay measurement as optimization objectives, and use a multi-objective optimization algorithm to optimize the The variables to be optimized are selected iteratively, and Pareto optimization results including multiple sets of overlay measurement repeatability precision σ and accuracy μ are obtained.
优选地,所述套刻标记形貌和测量条件优化方法还包括步骤105,对多个所述帕累托优化结果进行套刻误差提取仿真,验证各自对应的套刻测量重复性精度、测量准确度和鲁棒性,选择最优方案进行测量实验。Preferably, the method for optimizing the shape of the overlay mark and the measurement conditions further includes step 105, performing overlay error extraction simulation on a plurality of the Pareto optimization results, and verifying the repeatability accuracy and measurement accuracy of the corresponding overlay measurement degree and robustness, choose the optimal solution for measurement experiments.
优选地,所述套刻测量重复性精度σ和准确度μ的表达式为,Preferably, the expressions of the overlay measurement repeatability precision σ and accuracy μ are,
其中,σm为光学表征量的仪器测量标准差,D为设定的套刻偏移量, K为套刻灵敏度,ε为待测套刻误差值,Δa为其他非对称因素对光学表征量的影响,Among them, σ m is the instrument measurement standard deviation of the optical characterization, D is the set overlay offset, K is the overlay sensitivity, ε is the overlay error value to be measured, and Δ a is the impact of other asymmetric factors on the optical characterization Quantitative impact,
式中,I″(ξ+)为套刻光学表征曲线在δ=ξ+处的二阶导数值,I″(ξ-)为套刻光学表征曲线在δ=ξ-处的二阶导数值,ξ+∈[0,D+ε],ξ-∈[0,-D+ε]。In the formula, I″(ξ + ) is the second derivative value of the overlay optical characteristic curve at δ=ξ + , I″( ξ- ) is the second derivative value of the overlay optical characteristic curve at δ=ξ- , ξ + ∈ [0, D + ε], ξ - ∈ [0, -D + ε].
优选地,步骤103具体为,Preferably, step 103 is specifically,
根据泰勒公式将I+、I-修正为下式:According to Taylor's formula, I + and I - are corrected as the following formula:
其中,ΔI+、ΔI-为仪器测量噪声,I(0)为套刻光学表征曲线在原点的值;Among them, ΔI + and ΔI - are the measurement noise of the instrument, and I(0) is the value of the overlay optical characteristic curve at the origin;
根据式(13)和式(14),eDBO方法的测量误差△ε如式(15)所示:According to formula (13) and formula (14), the measurement error △ε of eDBO method is shown in formula (15):
用光学表征量的仪器测量标准差σm替换式(15)中的△I++△I-,得到所述套刻测量重复性精度σ和准确度μ的表达式(9)和表达式(10)。Using an optical characterization instrument to measure the standard deviation σ m to replace △I + + △I - in formula (15), the expression (9) and expression (9) and expression ( 10).
优选地,步骤102中,所述套刻标记形貌结构的参数包括顶层光栅的线宽CD1,底层光栅的线宽CD2,顶层光栅和底层光栅的周期Pitch,顶层光栅的壁高H1,底层光栅的壁高H3,中间薄膜层厚度与底层光栅壁高之和 H2,套刻偏移量δ,底层光栅左侧壁角LSWA和底层光栅右侧壁角RSWA;所述材料光学常数是指材料的复折射率。Preferably, in step 102, the parameters of the topography of the overlay mark include the line width CD 1 of the top grating, the line width CD 2 of the bottom grating, the period Pitch of the top grating and the bottom grating, and the wall height H 1 of the top grating , the wall height H 3 of the bottom grating, the sum H 2 of the thickness of the middle film layer and the wall height of the bottom grating, the overlay offset δ, the left wall angle LSWA of the bottom grating and the right wall angle RSWA of the bottom grating; the material optics The constant refers to the complex refractive index of the material.
优选地,步骤102中,所述测量条件包括测量入射角θ、方位角测量波长λ和偏振角Ψ的一种或几种的组合;所述光学表征量I是指反射率、椭偏参数或穆勒矩阵。Preferably, in step 102, the measurement conditions include measuring the incident angle θ, the azimuth angle Measuring one or more combinations of wavelength λ and polarization angle Ψ; the optical characterization quantity I refers to reflectivity, ellipsometric parameters or Mueller matrix.
优选地,步骤104中,选定的待优化变量为,套刻标记形貌结构参数中所有参数的任意组合与测量入射角θ、方位角测量波长λ和偏振角Ψ中的一个或多个的任意组合。Preferably, in step 104, the selected variables to be optimized are any combination of all parameters in the topographic structure parameters of the overlay mark and the measured incident angle θ, azimuth angle Any combination of one or more of wavelength λ and polarization angle Ψ is measured.
优选地,所述解析或数值建模方法采用严格耦合波分析、有限元方法、边界元方法或者有限时域差分法。Preferably, the analytical or numerical modeling method uses rigorous coupled wave analysis, finite element method, boundary element method or finite time domain difference method.
优选地,所述多目标优化算法采用多目标粒子群算法、多目标进化算法或多目标遗传算法。Preferably, the multi-objective optimization algorithm adopts a multi-objective particle swarm optimization algorithm, a multi-objective evolutionary algorithm or a multi-objective genetic algorithm.
总体而言,通过本发明所构思的以上技术方案与现有技术相比,能够取得下列有益效果:Generally speaking, compared with the prior art, the above technical solutions conceived by the present invention can achieve the following beneficial effects:
1、本发明提供的基于eDBO的优化方法,通过解析或数值建模方法计算得到表征光学表征量I和套刻偏移量δ的函数关系的套刻光学表征曲线,通过套刻光学表征曲线和泰勒公式展开得到套刻测量重复性精度σ和准确度μ的表达式,该表达式同时考虑了套刻光学表征曲线的非线性、仪器测量噪声以及其他非对称因素对eDBO方法的影响。然后以套刻测量重复性精度σ和准确度μ作为优化目标,采用多目标优化算法对所述待优化变量进行迭代选择,获取帕累托优化结果。本发明同时考虑了套刻标记形貌优化与测量条件优化配置,从而使得套刻误差测量在精确度和准确度方面有更好的表现,实现了高重复性测量精度、高测量准确度和鲁棒性好的套刻误差测量。1. The optimization method based on eDBO provided by the present invention calculates and obtains the overlay optical characterization curve representing the functional relationship between the optical characterization quantity I and the overlay offset δ through analytical or numerical modeling methods, and obtains the overlay optical characterization curve through the overlay optical characterization curve and Taylor's formula is expanded to obtain the expressions of overlay measurement repeatability precision σ and accuracy μ, which take into account the influence of nonlinearity of overlay optical characterization curve, instrument measurement noise and other asymmetric factors on eDBO method. Then, taking the overlay measurement repeatability precision σ and accuracy μ as optimization objectives, a multi-objective optimization algorithm is used to iteratively select the variables to be optimized to obtain Pareto optimization results. The present invention simultaneously considers the overlay mark shape optimization and measurement condition optimization configuration, so that the overlay error measurement has a better performance in terms of precision and accuracy, and realizes high repeatability measurement accuracy, high measurement accuracy and robustness. Overlay error measurement with good stickiness.
2、本发明根据测量重复性精度σ和准确度μ两个指标提供了多个帕累托优化结果。考虑实际加工、测量过程的影响,可通过仿真进一步对优化结果进行套刻测量重复性精度、测量准确度和鲁棒性验证,选择满足需要且鲁棒性良好的方案,保证优化结果在实际测量过程中的有效性。2. The present invention provides multiple Pareto optimization results according to the two indicators of measurement repeatability precision σ and accuracy μ. Considering the influence of the actual processing and measurement process, the optimization results can be further verified by overlay measurement repeatability accuracy, measurement accuracy and robustness through simulation, and a solution that meets the needs and good robustness can be selected to ensure that the optimization results are consistent with the actual measurement results. effectiveness in the process.
3、多目标优化算法对套刻测量重复性精度σ和准确度μ两个优化目标同时进行迭代选择,最终得到多组所述套刻测量重复性精度σ和准确度μ的帕累托优化结果。优化结果同时考虑了套刻光学表征曲线的非线性、仪器测量噪声以及其他非对称因素对eDBO方法的影响,重复性测量精度和准确度更好,鲁棒性更好。3. The multi-objective optimization algorithm iteratively selects the two optimization objectives of overlay measurement repeatability accuracy σ and accuracy μ at the same time, and finally obtains multiple sets of Pareto optimization results of the overlay measurement repeatability accuracy σ and accuracy μ . The optimization results also take into account the nonlinearity of overlay optical characterization curves, instrument measurement noise and other asymmetric factors on the eDBO method, and the repeatability measurement accuracy and accuracy are better, and the robustness is better.
附图说明Description of drawings
图1是本发明较佳实施例中套刻标记形貌和测量条件优化方法流程图;Fig. 1 is a flow chart of an overlay mark topography and a method for optimizing measurement conditions in a preferred embodiment of the present invention;
图2(a)是本发明较佳实施例中典型套刻光学表征曲线与套刻偏移量间的局部线性关系;Fig. 2 (a) is the local linear relationship between typical overlay optical characteristic curve and overlay offset in a preferred embodiment of the present invention;
图2(b)是本发明较佳实施例中套刻光学表征曲线的非线性对套刻误差表征的影响;Fig. 2 (b) is the impact of the non-linearity of the overlay optical characterization curve on the overlay error characterization in a preferred embodiment of the present invention;
图2(c)是本发明较佳实施例中套刻光学表征曲线中套刻标记的其他非对称因素对套刻误差表征的影响;Fig. 2 (c) is the impact of other asymmetric factors of the overlay mark in the overlay optical characterization curve on the overlay error characterization in a preferred embodiment of the present invention;
图3(a)是本发明较佳实施例中典型eDBO套刻标记形貌俯视图;Figure 3(a) is a top view of the topography of a typical eDBO overlay mark in a preferred embodiment of the present invention;
图3(b)是本发明较佳实施例中引入设定套刻偏移量+D后的套刻标记单元剖面图;Fig. 3 (b) is a sectional view of the overlay marking unit after introducing the set overlay offset + D in the preferred embodiment of the present invention;
图3(c)是本发明较佳实施例中引入设定套刻偏移量-D后的套刻标记单元剖面图;Figure 3(c) is a cross-sectional view of the overlay marking unit after introducing the set overlay offset -D in a preferred embodiment of the present invention;
图4是本发明较佳实施例中每一套刻标记单元的剖面结构示意图;Fig. 4 is a schematic cross-sectional structure diagram of each overlay marking unit in a preferred embodiment of the present invention;
图5是本发明较佳实施例中套刻误差测量条件示意图;Fig. 5 is a schematic diagram of overlay error measurement conditions in a preferred embodiment of the present invention;
图6(a)是本发明较佳实施例中采用多目标优化算法求取帕累托最优结果的流程图;Fig. 6 (a) is the flow chart that adopts multi-objective optimization algorithm to seek Pareto optimal result in the preferred embodiment of the present invention;
图6(b)是本发明较佳实施例中优化前套刻误差的测量重复性精度与准确度;Fig. 6 (b) is the measurement repeatability precision and accuracy of the overlay error before optimization in a preferred embodiment of the present invention;
图6(c)是本发明较佳实施例中优化后套刻误差的测量重复性精度与准确度;Fig. 6 (c) is the measurement repeatability precision and accuracy of overlay error after optimization in the preferred embodiment of the present invention;
图7(a)是本发明较佳实施例中帕累托优化结果的重复性测量精度σ的鲁棒性;Fig. 7 (a) is the robustness of the repeatability measurement precision σ of Pareto optimization result in the preferred embodiment of the present invention;
图7(b)是本发明较佳实施例中帕累托优化结果的测量准确度μ的鲁棒性。Fig. 7(b) is the robustness of the measurement accuracy μ of the Pareto optimization result in the preferred embodiment of the present invention.
具体实施方式Detailed ways
为了使本发明的目的、技术方案及优点更加清楚明白,以下结合附图及实施例,对本发明进行进一步详细说明。应当理解,此处所描述的具体实施例仅仅用以解释本发明,并不用于限定本发明。此外,下面所描述的本发明各个实施方式中所涉及到的技术特征只要彼此之间未构成冲突就可以相互组合。In order to make the object, technical solution and advantages of the present invention clearer, the present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described here are only used to explain the present invention, not to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not constitute a conflict with each other.
本发明基于经验关系的衍射套刻误差测量方法(Empirical Diffraction-BasedOverlay,eDBO)提供了一种基于eDBO方法的套刻标记形貌和测量条件优化方法。该方法以套刻误差重复性测量精度σ和准确度μ为两个优化目标,得到了多个帕累托最优结果,接着还可以仿真验证优化结果的鲁棒性以进行筛选,筛选后得到的结果即为套刻标记形貌参数和测量条件的最终优化结果。The invention provides an empirical relationship-based diffraction overlay error measurement method (Empirical Diffraction-Based Overlay, eDBO), which provides an eDBO method-based method for optimizing the shape of overlay marks and measurement conditions. This method takes the overlay error repeatability measurement precision σ and accuracy μ as two optimization objectives, and obtains multiple Pareto optimal results. Then, the robustness of the optimization results can be verified by simulation for screening. After screening, The result is the final optimization result of overlay mark morphology parameters and measurement conditions.
首先,根据半导体制造的工艺,需要确定eDBO套刻标记的拓扑结构,即每一层结构形状(例如薄膜或光栅),以及对应材料的光学常数(折射率n和消光系数k)。在此基础上,通过诸如RCWA、FEM、BEM、FDTD 等建模方法,可建立正向光学特性模型,计算套刻光学表征曲线。其次,根据泰勒公式,可得到eDBO方法的套刻误差重复性测量精度σ和测量准确度μ的表达式,根据套刻光学表征曲线即可计算两者的近似数值。由于重复性测量精度和准确度都是套刻测量中非常重要的指标,并且这两个指标相关性较弱,因此需要采用多目标优化算法同时对两个指标进行优化。选择套刻标记的形貌参数以及测量条件作为待优化变量,以多目标优化算法为迭代策略,可得到帕累托最优测量重复性精度σ和准确度μ,这两个指标对应的套刻标记形貌参数和测量条件即为优化结果。First, according to the semiconductor manufacturing process, it is necessary to determine the topology of the eDBO overlay mark, that is, the shape of each layer structure (such as a film or grating), and the optical constants (refractive index n and extinction coefficient k) of the corresponding materials. On this basis, through modeling methods such as RCWA, FEM, BEM, FDTD, etc., the forward optical characteristic model can be established, and the overlay optical characteristic curve can be calculated. Secondly, according to the Taylor formula, the expressions of the overlay error repeatability measurement accuracy σ and measurement accuracy μ of the eDBO method can be obtained, and the approximate values of the two can be calculated according to the overlay optical characterization curve. Since repeatability measurement precision and accuracy are very important indicators in overlay measurement, and the correlation between these two indicators is weak, it is necessary to use a multi-objective optimization algorithm to optimize the two indicators at the same time. Select the shape parameters and measurement conditions of the overlay mark as the variables to be optimized, and use the multi-objective optimization algorithm as the iterative strategy to obtain the Pareto optimal measurement repeatability precision σ and accuracy μ. The corresponding overlay of these two indicators The marked morphology parameters and measurement conditions are the optimization results.
最后,还可以对多个优化结果进行套刻误差提取仿真验证。仿真包括模拟半导体工艺中的加工工艺误差、测量条件不确定性,以及测量的随机噪声,来验证不同优化结果的性能及其鲁棒性,根据具体需要选择套刻标记形貌和测量条件进行测量实验。Finally, it is also possible to perform overlay error extraction simulation verification on multiple optimization results. The simulation includes simulating the processing error in the semiconductor process, the uncertainty of the measurement conditions, and the random noise of the measurement to verify the performance and robustness of different optimization results, and select the overlay mark shape and measurement conditions for measurement according to specific needs experiment.
以下结合附图和实例对本发明提供的套刻标记形貌和测量条件优化方法进行进一步详细的说明。The method for optimizing the overlay mark appearance and measurement conditions provided by the present invention will be further described in detail below with reference to the accompanying drawings and examples.
图1展示了本发明提供的套刻标记和测量配置优化方法的处理流程100。本发明实施例将以三层套刻标记400为例,来具体阐述本发明提供的方法的具体操作流程:FIG. 1 shows a processing flow 100 of an overlay mark and measurement configuration optimization method provided by the present invention. The embodiment of the present invention will take the three-layer overlay mark 400 as an example to specifically illustrate the specific operation process of the method provided by the present invention:
(1)确定套刻标记结构及材料光学常数(1) Determine the overlay mark structure and material optical constants
本实施例提供的套刻标记结构俯视图如图3(a)所示,套刻标记300 包含四个单元,水平光栅单元302、303用于测量Y方向的套刻误差,竖直光栅单元301、304用于测量X方向的套刻误差。其中,每个单元的垂直光栅方向的剖面图都如图4所示。其底层为Si光栅层(梯形凸起),中间层为SiO2薄膜层,顶层为光刻胶光栅(方形凸起),基底为Si。其中套刻标记剖面形貌结构的参数如下,CD1表示顶层光刻胶光栅的线宽,CD2表示底层Si光栅层的线宽,Pitch表示光栅的周期,H1表示顶层光刻胶光栅的壁高、H3表示底层Si光栅层的壁高,H2表示中间薄膜层厚度与底层光栅层壁高之和,δ表示套刻偏移量,LSWA和RSWA分别表示底层光栅左右侧壁角。套刻标记剖面形貌结构的参数不仅限于上述列举的参数,本领域普通技术人员可根据实际需要进行设置,在此不一一穷尽列举。此外,还需通过测量手段得到材料光学常数。材料光学常数是指材料的复折射率,即折射率和消光系数。The top view of the overlay mark structure provided by this embodiment is shown in FIG. 304 is used to measure the overlay error in the X direction. Wherein, the cross-sectional view of each unit vertical to the grating direction is shown in FIG. 4 . The bottom layer is a Si grating layer (trapezoidal protrusions), the middle layer is a SiO2 thin film layer, the top layer is a photoresist grating (square protrusions), and the base is Si. Among them, the parameters of the cross-sectional morphology of the overlay mark are as follows, CD 1 represents the line width of the top photoresist grating, CD 2 represents the line width of the bottom Si grating layer, Pitch represents the period of the grating, H 1 represents the top layer photoresist grating Wall height, H 3 represents the wall height of the bottom Si grating layer, H 2 represents the sum of the thickness of the middle film layer and the wall height of the bottom grating layer, δ represents the overlay offset, LSWA and RSWA represent the left and right side wall angles of the bottom grating, respectively. The parameters of the cross-sectional topography of the overlay mark are not limited to the parameters listed above, and those skilled in the art can set them according to actual needs, and they are not exhaustively listed here. In addition, the optical constant of the material needs to be obtained by measurement means. The material optical constant refers to the complex refractive index of the material, that is, the refractive index and the extinction coefficient.
(2)确定套刻光学表征曲线的计算方法(2) Calculation method for determining overlay optical characterization curve
根据步骤(1)得到的套刻标记形貌参数和材料光学常数,以及图5中500 中测量入射角θ、方位角测量波长λ,偏振角Ψ,即可通过解析或数值建模方法计算单个光学表征量I。通过连续改变套刻偏移量δ即可计算套刻光学表征曲线。According to the overlay mark morphology parameters and material optical constants obtained in step (1), and the incident angle θ and azimuth angle measured in 500 in Fig. 5 By measuring the wavelength λ and the polarization angle Ψ, a single optical characteristic I can be calculated by analytical or numerical modeling methods. The overlay optical characterization curve can be calculated by continuously changing the overlay offset δ.
可以利用的建模方法包括严格耦合波分析(RCWA)、有限元方法 (FEM)、边界元方法(BEM)或者有限时域差分法(FDTD)等。光学表征量I包括反射率、椭偏参数,穆勒矩阵中的任一个。Available modeling methods include Rigorous Coupled Wave Analysis (RCWA), Finite Element Method (FEM), Boundary Element Method (BEM) or Finite Difference Time Domain (FDTD). The optical characterization quantity I includes any one of reflectivity, ellipsometric parameters, and Mueller matrix.
(3)基于泰勒公式得到套刻测量重复性精度和准确度(3) Obtain the repeatability and accuracy of overlay measurement based on Taylor's formula
如图2(b)所示,套刻光学表征曲线201为周期性奇函数,因此其非线性会导致测量不准确(见图2(b)中202)。其次,因为套刻误差本质上是非对称因素中的一种,所以套刻标记在工艺过程中的其他非对称因素(如左侧壁角LSWA≠右侧壁角RSWA)也会使整个套刻光学表征曲线平移而使套刻误差测量结果不准确(见图2(c)中203)。这两个因素都会致eDBO方法存在测量准确度的问题。考虑前述套刻光学表征曲线的非线性和其他非对称因素,我们基于泰勒展开式将I+、I-修正为下式:As shown in FIG. 2( b ), the overlay optical characteristic curve 201 is a periodic odd function, so its non-linearity will lead to inaccurate measurement (see 202 in FIG. 2( b )). Secondly, because the overlay error is essentially one of the asymmetric factors, other asymmetric factors (such as the left wall angle LSWA≠right wall angle RSWA) of the overlay mark in the process will also make the entire overlay optical The translation of the characteristic curve makes the overlay error measurement result inaccurate (see 203 in Fig. 2(c)). Both of these factors can cause measurement accuracy problems with the eDBO method. Considering the nonlinear and other asymmetrical factors of the aforementioned overlay optical characteristic curve, we correct I + and I - to the following formula based on the Taylor expansion:
其中,ε为待测套刻误差值,D为设定的套刻偏移量,Δa为其他非对称因素对套刻光学表征量的影响,ΔI+、ΔI-为仪器测量噪声,I(0)为套刻光学表征曲线在原点(对应套刻偏移量为0)的值,一般为0,K为套刻灵敏度。I″(ξ+) 和I″(ξ-)分别为套刻光学表征曲线在ξ+、ξ-二阶导数值,由泰勒展开定理可知,ξ+∈[0,D+ε],ξ-∈[0,-D+ε]。Among them, ε is the overlay error value to be measured, D is the set overlay offset, Δ a is the influence of other asymmetric factors on the optical representation of overlay, ΔI + and ΔI - are the measurement noise of the instrument, I( 0) is the value of the overlay optical characteristic curve at the origin (corresponding to the overlay offset of 0), generally 0, and K is the overlay sensitivity. I″(ξ + ) and I″(ξ - ) are the second-order derivative values of the overlay optical characteristic curve at ξ + , ξ - respectively. According to the Taylor expansion theorem, ξ + ∈[0,D+ε], ξ - ∈[0,-D+ε].
根据式(13)和式(14),eDBO方法的测量误差△ε如式(15)所示:According to formula (13) and formula (14), the measurement error △ε of eDBO method is shown in formula (15):
式(15)中N+和N-如下式:N + and N - in formula (15) are as follows:
用σm(套刻光学表征量的仪器测量标准差)替换式(15)中的△I+-△I-,即可得到套刻误差的重复性测量精度σ和准确度μ:By replacing △I + -△I - in formula (15) with σ m (instrumental measurement standard deviation of overlay optical characterization quantity), the repeatability measurement precision σ and accuracy μ of overlay error can be obtained:
由于N+和N-不是一个确定值,在本实施例中,仅选取其平均值来计算σ和μ。Since N + and N − are not definite values, in this embodiment, only their average values are selected to calculate σ and μ.
表达式(9)、(10)优点在于同时考虑了套刻表征曲线的非线性、仪器测量噪声以及其他非对称因素对eDBO方法的影响。The advantages of the expressions (9) and (10) are that the influence of the nonlinearity of the overlay characteristic curve, the measurement noise of the instrument and other asymmetric factors on the eDBO method is considered at the same time.
(4)优化套刻标记形貌和测量条件(4) Optimizing overlay mark morphology and measurement conditions
由前述可知,σ和μ与套刻光学表征曲线相关,而套刻光学表征曲线由套刻标记结构形貌参数和测量条件通过光学模型计算得来,也即每组套刻标记结构形貌参数和测量条件对应每组确定的σ和μ。本实施例中,我们选择套刻标记剖面图(见图4中400)中Pitch、CD1、CD2,以及套刻测量条件示意图5的500中测量入射角θ、方位角测量波长λ作为优化变量,以σ和μ作为优化目标。本实施例中的优化变量仅用于解释本发明,其他的优化变量包括θ、λ、Ψ、Pitch、CD1、CD2的任意组合。It can be seen from the foregoing that σ and μ are related to the overlay optical characterization curve, and the overlay optical characterization curve is calculated from the overlay mark structure morphology parameters and measurement conditions through the optical model, that is, each set of overlay mark structure shape parameters and measurement conditions corresponding to each set of determined σ and μ. In this embodiment, we select Pitch, CD 1 , CD 2 in the overlay mark section view (see 400 in Figure 4), and measure the incident angle θ and azimuth angle in 500 of the overlay measurement condition schematic diagram 5 The measurement wavelength λ is used as an optimization variable, and σ and μ are used as optimization targets. The optimization variables in this embodiment are only used to explain the present invention, and other optimization variables include θ, Any combination of λ, Ψ, Pitch, CD 1 , CD 2 .
由于优化目标含σ和μ两者且待优化变量较多,因此需要采用全局搜索能力强的多目标优化算法进行优化变量迭代选择。常见的多目标优化算法有多目标粒子群算法(MOPSO),多目标进化算法(MOEA),多目标遗传算法(MOGA)等。本实施例选择多目标进化算法作为优化算法,多目标优化算法是全局优化算法,相对于局部优化算法有更好的优化效果。多目标优化算法对套刻测量重复性精度σ和准确度μ两个优化目标同时进行迭代选择,最终得到多组所述套刻测量重复性精度σ和准确度μ的帕累托优化结果。Since the optimization objective includes both σ and μ and there are many variables to be optimized, it is necessary to use a multi-objective optimization algorithm with strong global search capability for iterative selection of optimization variables. Common multi-objective optimization algorithms include multi-objective particle swarm optimization (MOPSO), multi-objective evolutionary algorithm (MOEA), and multi-objective genetic algorithm (MOGA). In this embodiment, the multi-objective evolutionary algorithm is selected as the optimization algorithm, and the multi-objective optimization algorithm is a global optimization algorithm, which has a better optimization effect than the local optimization algorithm. The multi-objective optimization algorithm iteratively selects the two optimization objectives of overlay measurement repeatability accuracy σ and accuracy μ at the same time, and finally obtains multiple sets of Pareto optimization results of the overlay measurement repeatability accuracy σ and accuracy μ.
如图6(a)所示,在多目标进化算法迭代开始之前,首先生成多组优化变量初始值,然后根据光学模型计算得到套刻光学表征曲线以得到优化变量初始值对应的σ和μ,接着根据多目标进化算法的优化策略(一般优先选择σ或μ值更小的优化变量)选择优化变量。为了保证优化变量的个数,通常还要在子代基础上进行一些变异以产生新的个体来维持每一代的个体数量以及个体多样性。每次迭代完成后,判断优化目标σ和μ是否已达到最优,若达到最优,则停止优化算法。As shown in Figure 6(a), before the iteration of the multi-objective evolutionary algorithm starts, multiple sets of initial values of the optimization variables are first generated, and then the overlay optical characterization curves are calculated according to the optical model to obtain the σ and μ corresponding to the initial values of the optimization variables. Then, the optimization variables are selected according to the optimization strategy of the multi-objective evolutionary algorithm (generally, the optimization variables with smaller values of σ or μ are preferred). In order to ensure the number of optimized variables, some mutations are usually performed on the basis of offspring to generate new individuals to maintain the number of individuals and individual diversity in each generation. After each iteration is completed, it is judged whether the optimization objectives σ and μ have reached the optimum, and if they are optimal, the optimization algorithm is stopped.
更具体地,对于本例中的套刻标记结构400,图6(b)和图6(c)分别表示了待优化变量在优化前和优化后对应的σ、μ值。可见在本例中,经过优化算法迭代选择,σ、μ的大小为原来的十分之一。图6(c)中,σ和μ对应的优化变量(θ、λ、Pitch、CD1、CD2)即为得到的优化结果。More specifically, for the overlay mark structure 400 in this example, Fig. 6(b) and Fig. 6(c) respectively represent the values of σ and μ corresponding to the variables to be optimized before and after optimization. It can be seen that in this example, after the iterative selection of the optimization algorithm, the size of σ and μ is one-tenth of the original size. In Figure 6(c), the optimization variables corresponding to σ and μ (θ, λ, Pitch, CD 1 , CD 2 ) are the obtained optimization results.
(5)优化结果仿真验证(5) Simulation verification of optimization results
在半导体制造过程中,难以保证优化结果中套刻标记形貌参数Pitch、CD1、CD2和测量条件θ、λ为理想值。所以还需要考虑实际加工、测量过程的影响来对优化结果进行套刻测量重复性精度、测量准确度和鲁棒性验证,以保证其在实际测量过程中的有效性。In the semiconductor manufacturing process, it is difficult to guarantee the overlay mark morphology parameters Pitch, CD 1 , CD 2 and measurement conditions θ, λ is an ideal value. Therefore, it is also necessary to consider the influence of the actual processing and measurement process to verify the repeatability accuracy, measurement accuracy and robustness of the optimization results to ensure its effectiveness in the actual measurement process.
更具体地,对于本例中的套刻标记结构400,图7(a)和图7(b)中的R分别表征了50个帕累托优化结果的重复性测量精度σ和测量准确度μ的鲁棒性。可见,有的优化结果难以抵抗加工工艺和实际测量条件的复杂影响,因此在实际应用中,需从帕累托优化结果中选择鲁棒性好的结果作为最终的优化结果,进行套刻误差测量实验。More specifically, for the overlay mark structure 400 in this example, R in Fig. 7(a) and Fig. 7(b) characterizes the repeatability measurement accuracy σ and measurement accuracy μ of 50 Pareto optimization results respectively robustness. It can be seen that some optimization results are difficult to resist the complex influence of processing technology and actual measurement conditions. Therefore, in practical applications, it is necessary to select the result with good robustness from the Pareto optimization results as the final optimization result for overlay error measurement experiment.
本领域的技术人员容易理解,以上所述仅为本发明的较佳实施例而已,并不用以限制本发明,凡在本发明的精神和原则之内所作的任何修改、等同替换和改进等,均应包含在本发明的保护范围之内。It is easy for those skilled in the art to understand that the above descriptions are only preferred embodiments of the present invention, and are not intended to limit the present invention. Any modifications, equivalent replacements and improvements made within the spirit and principles of the present invention, All should be included within the protection scope of the present invention.
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