公开(公告)号：US09127927B2

公开(公告)日：2015-09-08

申请号：US13712734

申请日：2012-12-12

申请人： Jonathan Iloreta ,  Paul Aoyagi ,  Hanyou Chu ,  Jeffrey Chard ,  Peilin Jiang ,  Mikhail Sushchik ,  Leonid Poslavsky ,  Philip D. Flanner, III

发明人： Jonathan Iloreta ,  Paul Aoyagi ,  Hanyou Chu ,  Jeffrey Chard ,  Peilin Jiang ,  Mikhail Sushchik ,  Leonid Poslavsky ,  Philip D. Flanner, III

IPC分类号： G06F17/16 ,  G01B11/30 ,  G06F7/00 ,  G06F17/40 ,  G06F19/00 ,  G01B11/00 ,  H01L21/66 ,  G01B11/24 ,  G03F7/20

CPC分类号： G01B11/00 ,  G01B11/24 ,  G01B11/30 ,  G01B2210/56 ,  G03F7/70625 ,  G06F7/00 ,  G06F17/16 ,  G06F17/40 ,  G06F19/00 ,  H01L22/12

摘要： Provided are optimized scatterometry techniques for evaluating a diffracting structure. In one embodiment, a method includes computing a finite-difference derivative of a field matrix with respect to first parameters (including a geometric parameter of the diffracting structure), computing an analytic derivative of the Jones matrix with respect to the field matrix, computing a derivative of the Jones matrix with respect to the first parameters, and computing a finite-difference derivative of the Jones matrix with respect to second parameters (including a non-geometric parameter). In one embodiment, a method includes generating a transfer matrix having Taylor Series approximations for elements, and decomposing the field matrix into two or more smaller matrices based on symmetry between the incident light and the diffracting structure.

摘要翻译： 提供了用于评估衍射结构的优化散射测量技术。 在一个实施例中，一种方法包括相对于第一参数（包括衍射结构的几何参数）计算场矩阵的有限差分导数，计算相对于场矩阵的Jones矩阵的分析导数，计算 相对于第一参数的Jones矩阵的导数，以及相对于第二参数（包括非几何参数）计算Jones矩阵的有限差分导数。 在一个实施例中，一种方法包括生成对于元素具有泰勒级数逼近的传递矩阵，并且基于入射光和衍射结构之间的对称性将场矩阵分解为两个或更多个较小的矩阵。

公开(公告)号：US20130158948A1

公开(公告)日：2013-06-20

申请号：US13712734

申请日：2012-12-12

申请人： Jonathan Iloreta ,  Paul Aoyagi ,  Hanyou Chu ,  Jeffrey Chard ,  Peilin Jiang ,  Mikhail Sushchik ,  Leonid Poslavsky ,  Phillip D. Flanner, III

发明人： Jonathan Iloreta ,  Paul Aoyagi ,  Hanyou Chu ,  Jeffrey Chard ,  Peilin Jiang ,  Mikhail Sushchik ,  Leonid Poslavsky ,  Phillip D. Flanner, III

IPC分类号： G01B11/00 ,  G06F17/16

CPC分类号： G01B11/00 ,  G01B11/24 ,  G01B11/30 ,  G01B2210/56 ,  G03F7/70625 ,  G06F7/00 ,  G06F17/16 ,  G06F17/40 ,  G06F19/00 ,  H01L22/12

摘要： Provided are optimized scatterometry techniques for evaluating a diffracting structure. In one embodiment, a method includes computing a finite-difference derivative of a field matrix with respect to first parameters (including a geometric parameter of the diffracting structure), computing an analytic derivative of the Jones matrix with respect to the field matrix, computing a derivative of the Jones matrix with respect to the first parameters, and computing a finite-difference derivative of the Jones matrix with respect to second parameters (including a non-geometric parameter). In one embodiment, a method includes generating a transfer matrix having Taylor Series approximations for elements, and decomposing the field matrix into two or more smaller matrices based on symmetry between the incident light and the diffracting structure.

摘要翻译： 提供了用于评估衍射结构的优化散射测量技术。 在一个实施例中，一种方法包括相对于第一参数（包括衍射结构的几何参数）计算场矩阵的有限差分导数，计算相对于场矩阵的Jones矩阵的分析导数，计算 相对于第一参数的Jones矩阵的导数，以及相对于第二参数（包括非几何参数）计算Jones矩阵的有限差分导数。 在一个实施例中，一种方法包括生成对于元素具有泰勒级数逼近的传递矩阵，并且基于入射光和衍射结构之间的对称性将场矩阵分解为两个或更多个较小的矩阵。

公开(公告)号：US07190453B1

公开(公告)日：2007-03-13

申请号：US10945167

申请日：2004-09-20

申请人： Paul Aoyagi ,  Philip D. Flanner, III ,  Leonid Poslavsky

发明人： Paul Aoyagi ,  Philip D. Flanner, III ,  Leonid Poslavsky

IPC分类号： G01J4/00 ,  G01B11/28

CPC分类号： G01N21/211 ,  G01B11/0641

摘要： A method of determining the actual properties of a film stack. An incident beam of light is directed towards the film stack, such that the incident beam of light is reflected from the film stack as a reflected beam of light. The actual properties of the reflected beam of light are measured, and properties of the film stack are estimated. A mathematical model of the film stack is solved with the estimated properties of the film stack to yield theoretical properties of the reflected beam of light. The theoretical properties of the reflected beam of light are compared to the actual properties of the reflected beam of light to yield a cost function. The estimated properties of the film stack are iteratively adjusted and the mathematical model is iteratively solved until the cost function is within a desired tolerance. The estimated properties of the film stack are reported as the actual properties of the film stack. A method based on analytical derivatives, and not numerically computed derivatives, of solutions to Maxwell's equations that are at least partially expressible as complex exponential matrices is used to iteratively adjust the estimated properties of the film stack.

摘要翻译： 确定薄膜叠层的实际特性的方法。 入射光束被引向胶片堆叠，使得入射光束作为反射光束从胶片堆叠反射。 测量反射光束的实际性质，并估计膜堆的性质。 利用膜堆的估计性质来解决膜堆的数学模型，以产生反射光束的理论性质。 将反射光束的理论性质与反射光束的实际特性进行比较，以产生成本函数。 迭代地调整膜堆的估计性质，并且迭代地求解数学模型，直到成本函数在期望的公差内。 膜叠层的估计性质被报告为薄膜叠层的实际特性。 使用基于分析导数而不是数值计算的导数，将至少部分地表示为复指数矩阵的麦克斯韦方程的解的方法迭代地调整膜堆的估计性质。

公开(公告)号：US07362686B1

公开(公告)日：2008-04-22

申请号：US11000771

申请日：2004-12-01

申请人： Paul Aoyagi ,  Philip D. Flanner, III ,  Leonid Poslavsky

发明人： Paul Aoyagi ,  Philip D. Flanner, III ,  Leonid Poslavsky

IPC分类号： G11B7/00 ,  B32B9/00

CPC分类号： G01B11/06

摘要： A method of determining actual properties of layered media. An incident beam of light is directed towards the layered media, such that the incident beam of light is reflected from the layered media as a reflected beam of light. The actual properties of the reflected beam of light are measured, and properties of the layered media are estimated. A mathematical model of the layered media is solved with the estimated properties of the layered media to yield theoretical properties of the reflected beam of light. The mathematical model is solved using a diagonal T matrix algorithm. The theoretical properties of the reflected beam of light are compared to the actual properties of the reflected beam of light to yield a cost function. The estimated properties of the layered media are iteratively adjusted and the mathematical model is iteratively solved until the cost function is within a desired tolerance. The estimated properties of the layered media are reported as the actual properties of the layered media.

摘要翻译： 确定分层介质实际属性的方法。 入射光束被引向分层介质，使得入射光束作为反射光束从分层介质反射。 测量反射光束的实际特性，估算分层介质的性质。 分层介质的数学模型通过分层介质的估计性质来解决，以产生反射光束的理论特性。 使用对角T矩阵算法求解数学模型。 将反射光束的理论性质与反射光束的实际特性进行比较，以产生成本函数。 迭代地调整分层介质的估计性质，并且迭代地求解数学模型，直到成本函数在期望的公差内。 分层介质的估计性质被报告为分层介质的实际性质。

公开(公告)号：US07345761B1

公开(公告)日：2008-03-18

申请号：US10945166

申请日：2004-09-20

申请人： Paul Aoyagi ,  Philip D. Flanner, III ,  Leonid Poslavsky

发明人： Paul Aoyagi ,  Philip D. Flanner, III ,  Leonid Poslavsky

IPC分类号： G01J4/00

CPC分类号： G01N21/8422 ,  G01B11/0625 ,  G01N21/211

摘要： A method of determining actual properties of layered media. An incident beam of light is directed towards the layered media, such that the incident beam of light is reflected from the layered media as a reflected beam of light. The actual properties of the reflected beam of light are measured, and properties of the layered media are estimated. A mathematical model of the layered media is solved with the estimated properties of the layered media to yield theoretical properties of the reflected beam of light. The mathematical model is solved using at least one of a modified T matrix algorithm and a Z matrix algorithm. The theoretical properties of the reflected beam of light are compared to the actual properties of the reflected beam of light to yield a cost function. The estimated properties of the layered media are iteratively adjusted and the mathematical model is iteratively solved until the cost function is within a desired tolerance. The estimated properties of the layered media are reported as the actual properties of the layered media.

摘要翻译： 确定分层介质实际属性的方法。 入射光束被引向分层介质，使得入射光束作为反射光束从分层介质反射。 测量反射光束的实际特性，估算分层介质的性质。 分层介质的数学模型通过分层介质的估计性质来解决，以产生反射光束的理论特性。 使用修改的T矩阵算法和Z矩阵算法中的至少一个来解决数学模型。 将反射光束的理论性质与反射光束的实际特性进行比较，以产生成本函数。 迭代地调整分层介质的估计性质，并且迭代地求解数学模型，直到成本函数在期望的公差内。 分层介质的估计性质被报告为分层介质的实际性质。

公开(公告)号：US20140358476A1

公开(公告)日：2014-12-04

申请号：US14293809

申请日：2014-06-02

申请人： Mark Backues ,  Paul Aoyagi ,  Leonid Poslavsky

发明人： Mark Backues ,  Paul Aoyagi ,  Leonid Poslavsky

IPC分类号： G01B11/24

摘要： Automatic determination of Fourier harmonic order for computation of spectral information for diffraction structures described. An embodiment of a method includes automatically determining a Fourier harmonic order for computation of spectral information for periodic structures, wherein the determination of the Fourier harmonic order is based at least in part on the pitches in each of multiple directions of the periodic structures, material properties of the periodic structures, and characteristics of the periodic structures in which the materials are contained; and computing the spectral information for the periodic structures based at least in part on the determined Fourier harmonic order.

摘要翻译： 自动确定用于计算衍射结构的光谱信息的傅里叶谐波次序。 一种方法的实施例包括自动确定用于计算周期性结构的光谱信息的傅里叶谐波次序，其中，傅里叶谐波次序的确定至少部分地基于周期性结构的多个方向中的每一个的间距，材料特性 的周期结构，以及包含材料的周期性结构的特征; 以及至少部分地基于所确定的傅里叶谐波顺序来计算所述周期性结构的频谱信息。

公开(公告)号：US07375828B1

公开(公告)日：2008-05-20

申请号：US11137165

申请日：2005-05-25

申请人： Paul Aoyagi ,  Leonid Poslavsky

发明人： Paul Aoyagi ,  Leonid Poslavsky

IPC分类号： G01B11/28

CPC分类号： G01B11/0625

摘要： A method of determining actual properties of layered media. An incident beam of light is directed towards the layered media, such that the incident beam of light is reflected from the layered media as a reflected beam of light. The actual properties of the reflected beam of light are measured, and properties of the layered media are estimated. A mathematical model of the layered media based on a modal function expansion is solved with the estimated properties of the layered media to yield theoretical properties of the reflected beam of light. The eigenvalues of the modal functions are computed recursively by recasting the eigenvalue equation in the following form: βni+1=F(βni) where βni=the eigenvalue of the ith recursion and F is a function such that βn=F(βn) is mathematically identical to the eigenvalue equation.

摘要翻译： 确定分层介质实际属性的方法。 入射光束被引向分层介质，使得入射光束作为反射光束从分层介质反射。 测量反射光束的实际特性，估算分层介质的性质。 基于模态函数展开的分层介质的数学模型用分层介质的估计性质来解决，以产生反射光束的理论性质。 模态函数的特征值通过以下列形式重新设计特征值方程来递归地计算：<？in-line-formula description =“In-line formula”end =“lead”？> beta β-in-line-formula description =“In-line Formulas”end =“tail “？”其中，第i个递归的特征值和F是使得β递归的特征值， 在数学上，SUB> = F（βN n N）与特征值方程相同。

公开(公告)号：US10481088B2

公开(公告)日：2019-11-19

申请号：US14293809

申请日：2014-06-02

申请人： Mark Backues ,  Paul Aoyagi ,  Leonid Poslavsky

发明人： Mark Backues ,  Paul Aoyagi ,  Leonid Poslavsky

IPC分类号： G01B11/24 ,  G01N21/47 ,  G01N21/956 ,  G01M11/02 ,  G01N21/21 ,  G03F7/20 ,  G06F17/40 ,  G06F19/00 ,  G06F11/30 ,  H05K13/08 ,  G01B11/30

摘要： Automatic determination of Fourier harmonic order for computation of spectral information for diffraction structures described. An embodiment of a method includes automatically determining a Fourier harmonic order for computation of spectral information for periodic structures, wherein the determination of the Fourier harmonic order is based at least in part on the pitches in each of multiple directions of the periodic structures, material properties of the periodic structures, and characteristics of the periodic structures in which the materials are contained; and computing the spectral information for the periodic structures based at least in part on the determined Fourier harmonic order.

公开(公告)号：US07760358B1

公开(公告)日：2010-07-20

申请号：US11669995

申请日：2007-02-01

申请人： Paul Aoyagi ,  Leonid Poslavsky

发明人： Paul Aoyagi ,  Leonid Poslavsky

IPC分类号： G01J4/00

CPC分类号： G01N21/8422 ,  G01N2021/8438

摘要： The above and other needs are met by a method of determining actual properties of a film stack by directing an incident beam of light towards the film stack, such that the incident beam of light is reflected from the film stack as a reflected beam of light. The actual properties of the reflected beam of light are measured, and properties of the film stack are estimated. A mathematical model of the film stack is solved with the estimated properties of the film stack, to yield theoretical properties of the reflected beam of light. The mathematical model is solved in part using a fast Z-matrix algorithm. The theoretical properties of the reflected beam of light are compared to the actual properties of the reflected beam of light, to yield a cost function. The estimated properties of the film stack are iteratively adjusted, and the mathematical model is iteratively solved, until the cost function is within a desired tolerance. The estimated properties of the film stack are reported as the actual properties of the film stack.

摘要翻译： 上述和其他需要通过一种通过将入射光束引导到薄膜叠层来确定薄膜叠层的实际特性的方法来满足，使得入射光束作为反射光束从薄膜叠层反射。 测量反射光束的实际性质，并估计膜堆的性质。 利用膜堆的估计性质来解决膜堆的数学模型，以产生反射光束的理论性质。 数学模型部分采用快速Z矩阵算法求解。 将反射光束的理论性质与反射光束的实际特性进行比较，以产生成本函数。 迭代地调整膜堆的估计性质，并且迭代地求解数学模型，直到成本函数在期望的公差内。 膜叠层的估计性质被报告为薄膜叠层的实际特性。