WO2022088336A1 - 一种测量薄膜不同方向应力梯度的方法 - Google Patents
一种测量薄膜不同方向应力梯度的方法 Download PDFInfo
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- 239000010409 thin film Substances 0.000 title claims abstract description 28
- 238000000034 method Methods 0.000 title claims abstract description 23
- 238000004088 simulation Methods 0.000 claims abstract description 25
- 238000012360 testing method Methods 0.000 claims abstract description 23
- 239000010408 film Substances 0.000 claims description 27
- 238000005259 measurement Methods 0.000 abstract description 5
- 238000004364 calculation method Methods 0.000 description 4
- 239000000463 material Substances 0.000 description 3
- 239000011159 matrix material Substances 0.000 description 2
- 230000009286 beneficial effect Effects 0.000 description 1
- 230000014509 gene expression Effects 0.000 description 1
- 239000004065 semiconductor Substances 0.000 description 1
- 238000010998 test method Methods 0.000 description 1
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01L—MEASURING FORCE, STRESS, TORQUE, WORK, MECHANICAL POWER, MECHANICAL EFFICIENCY, OR FLUID PRESSURE
- G01L5/00—Apparatus for, or methods of, measuring force, work, mechanical power, or torque, specially adapted for specific purposes
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01L—MEASURING FORCE, STRESS, TORQUE, WORK, MECHANICAL POWER, MECHANICAL EFFICIENCY, OR FLUID PRESSURE
- G01L5/00—Apparatus for, or methods of, measuring force, work, mechanical power, or torque, specially adapted for specific purposes
- G01L5/0047—Apparatus for, or methods of, measuring force, work, mechanical power, or torque, specially adapted for specific purposes measuring forces due to residual stresses
Definitions
- the invention relates to the field of semiconductor devices, in particular to a method for measuring stress gradients of thin films in different directions.
- the commonly used method for measuring the stress gradient is to set up a series of single-ended fixed cantilever beam structures of different lengths, then measure the warpage of the ends of the beams with different lengths, and then bring the formula into the calculation to obtain the stress gradient.
- This method usually assumes that the magnitude of the stress gradient of S11 (normal stress in the X-axis direction) or S22 (normal stress in the Y-axis direction) is the same.
- the purpose of the present invention is to provide a method for measuring the stress gradient of a thin film in different directions, which is used to solve the problem of large deviation in the measurement results in the prior art.
- a method for measuring stress gradients in different directions of a thin film comprising the steps of:
- the slope equivalent coefficient K X1 based on the S11 stress gradient and the slope equivalent coefficient K X2 based on the S22 stress gradient of the film in the first direction are obtained by simulation;
- the slope equivalent coefficient K Y1 based on the S11 stress gradient and the slope equivalent coefficient K Y2 based on the S22 stress gradient of the film in the second direction are obtained by simulation;
- the stress gradients in the first direction and the second direction of the thin film are calculated according to the K X1 , K X2 , K Y1 , K Y2 , and K 1 , K 2 .
- the stress gradient in the first direction is:
- the stress gradient in the second direction is:
- the step of obtaining the slope equivalent coefficient K X1 of the thin film based on the S11 stress gradient in the first direction includes:
- cantilever beams of different lengths are set in the first direction, different S11 stress gradients are applied to different cantilever beams in the first direction, and the end of the cantilever beam is respectively obtained according to the S11 stress gradient.
- the step of obtaining the slope equivalent coefficient K X2 of the thin film based on the S22 stress gradient in the first direction includes:
- cantilever beams of different lengths are set in the first direction, different S22 stress gradients are applied to different cantilever beams in the first direction, and the end of the cantilever beam is respectively obtained according to the S22 stress gradient.
- the step of obtaining the slope equivalent coefficient K Y1 of the thin film based on the S11 stress gradient in the second direction includes:
- cantilever beams with different lengths are set in the second direction, different S11 stress gradients are applied to different cantilever beams in the second direction, and the end of the cantilever beam is respectively obtained according to the S11 stress gradient.
- the step of obtaining the slope equivalent coefficient K Y2 of the thin film in the second direction based on the S22 stress gradient includes:
- cantilever beams of different lengths are set in the second direction, different S22 stress gradients are applied to different cantilever beams in the second direction, and the end of the cantilever beam is respectively obtained according to the S22 stress gradient.
- the step of obtaining the slope K 1 in the first direction of the film by the actual test includes:
- cantilever beams of different lengths are set in the first direction, and the end warping deflections of the cantilever beams of different lengths are measured;
- a relationship curve is obtained according to the warping deflection of the end of the cantilever beam and the length of the cantilever beam, and the slope K 1 is obtained according to the relationship curve.
- the step of obtaining the slope K 2 in the second direction of the film by the actual test includes:
- cantilever beams with different lengths are set in the second direction, and the end warping deflections of the cantilever beams with different lengths are measured;
- a relationship curve is obtained according to the warping deflection of the end of the cantilever beam and the length of the cantilever beam, and the slope K 2 is obtained according to the relationship curve.
- the beneficial effect of the invention is that the stress gradients of the film in different directions can be measured, and the deformation factor of the fixed end of the cantilever beam can be increased in the simulation, so that the test results are more accurate.
- This method does not involve Young's modulus (or stiffness matrix) and Poisson's ratio of anisotropic materials into the formula, which is simple to calculate and reduces the difficulty of testing.
- FIG. 1 is a flowchart of a method for measuring stress gradients in different directions of a thin film according to Embodiment 1 of the present invention.
- FIG. 2 is a flow chart of the specific implementation steps of the method for measuring the stress gradient of a thin film in different directions according to the first embodiment of the present invention.
- the present embodiment discloses a method for measuring stress gradients in different directions of a thin film, comprising the steps of:
- steps T1, T2, and T3 may be performed simultaneously, or may be performed in no particular order.
- the cantilever beam test method is used to test the stress gradient of the thin film, wherein the simulation can be performed through finite element simulation components, and the deformation factor of the fixed end of the cantilever beam is considered in the simulation. Beams are tested.
- S11 represents the principal stress in the X-axis direction
- S22 represents the principal stress in the Y-axis direction.
- the first direction may be the same as or different from the X-axis direction
- the second direction may be the same as or different from the Y-axis direction.
- the first direction and the X-axis direction are the same direction
- the second direction and the Y-axis direction are the same direction for description.
- step T4 the stress gradient in the first direction is:
- the stress gradient in the second direction is:
- the step of obtaining the slope equivalent coefficient K X1 of the thin film based on the S11 stress gradient in the first direction includes:
- a series of cantilever beams of different lengths are set in the first direction, different S11 stress gradients are applied to the cantilever beams of different lengths in the first direction, and the warping deflections of the ends of the cantilever beams of different lengths are obtained according to the S11 stress gradient, where , the value of the warping deflection at the end of the cantilever beam is a series of different values corresponding to the cantilever beam of different lengths;
- the relationship curve is obtained, and the relationship curve can be expressed as Among them, ⁇ nx1 is the warping deflection of the cantilever beam end under the S11 nx1 stress gradient, and L nx1 is the length of the cantilever beam.
- the slope can be calculated, and the slope equivalent coefficient can be obtained according to the slope. Specifically, different S11 stress gradients are taken as n for description.
- n stress gradients S11 nx1 will correspond to n different curves, and correspondingly obtain n different slopes K nx1 , and divide the slope K nx1 by the corresponding stress
- n equivalent slopes K nx11 will be obtained, and the average value of the n equivalent slopes K nx11 will be obtained to obtain the slope equivalent coefficient K X1 .
- the step of obtaining the slope equivalent coefficient K X2 of the thin film based on the S22 stress gradient in the first direction includes:
- cantilever beams of different lengths are set in the first direction, different S22 stress gradients are applied to the cantilever beams of different lengths in the first direction, and the warping deflections of the ends of the cantilever beams of different lengths are obtained respectively according to the S22 stress gradient;
- ⁇ nx2 is the warping deflection of the cantilever beam end under the S22 nx2 stress gradient
- L nx2 is the length of the cantilever beam.
- the slope can be calculated, and the slope equivalent coefficient can be obtained according to the slope.
- different S22 stress gradients are taken as n for description.
- the n stress gradients S22 nx2 will correspond to n different curves, and correspondingly obtain n different slopes K nx2 , and divide the slope K nx2 by the corresponding stress
- n equivalent slopes K nx22 will be obtained, and the average value of the n equivalent slopes K nx22 will be obtained to obtain the slope equivalent coefficient K X2 .
- the step of obtaining the slope equivalent coefficient K Y1 of the thin film based on the S11 stress gradient in the second direction includes:
- cantilever beams with different lengths are set in the second direction, different S11 stress gradients are applied to different cantilever beams in the second direction, and the warping deflections at the ends of cantilever beams with different lengths are obtained according to the S11 stress gradient.
- the value of the end warping deflection is a series of different values corresponding to different lengths of cantilever beams;
- the relationship curve is obtained, and the relationship curve can be expressed as where ⁇ ny1 is the warping deflection at the end of the cantilever beam under the S11 ny1 stress gradient, and L ny1 is the length of the cantilever beam.
- the slope can be calculated, and the slope equivalent coefficient can be obtained according to the slope.
- the different S11 stress gradients are taken as n for description.
- the n stress gradients S11 ny1 correspond to n different curves, and correspondingly obtain n different slopes K ny1 , and divide the slope K ny1 by the corresponding stress Gradient S11 ny1 , n equivalent slopes K ny11 will be obtained, and the average value of the n equivalent slopes will be obtained to obtain the slope equivalent coefficient KY1 .
- the step of obtaining the slope equivalent coefficient K Y2 of the thin film based on the S22 stress gradient in the second direction includes:
- cantilever beams of different lengths are set in the second direction, different S22 stress gradients are applied to the cantilever beams of different lengths in the second direction, and the warping deflections at the ends of cantilever beams of different lengths are obtained according to the S22 stress gradient.
- the value of the warping deflection of the beam end is a series of different values corresponding to the cantilever beams of different lengths;
- the relationship curve is obtained according to the warping deflection at the end of the cantilever beam and the length of the cantilever beam
- This relationship curve can be expressed as where ⁇ ny2 is the warping deflection at the end of the cantilever beam under the S11 ny2 stress gradient, and L ny2 is the length of the cantilever beam.
- the slope can be calculated, and the slope equivalent coefficient can be obtained according to the slope.
- different S22 stress gradients are taken as n for illustration.
- the n stress gradients S22 ny2 correspond to n different curves, and correspondingly obtain n different slopes K ny2 , and divide the slope K ny2 by the corresponding stress Gradient S22 ny2 , n equivalent slopes K ny22 will be obtained, and the average value of the n equivalent slopes will be obtained to obtain the slope equivalent coefficient K Y2 .
- the step of obtaining the slope K 1 in the first direction of the film by actual testing includes:
- cantilever beams of different lengths are set in the first direction (i.e. X-axis direction), and the end warping deflections of cantilever beams of different lengths are measured by measuring instruments (such as laser measuring devices, Doppler measuring devices, etc.);
- the relationship curve can be obtained, and the relationship curve can be expressed as The slope K1 can be obtained from this relational curve.
- the step of obtaining the slope K2 in the second direction of the film by actual testing includes:
- cantilever beams with different lengths are set in the second direction, and the warping deflection of the cantilever beams with different lengths is measured;
- the relationship curve can be obtained, and the relationship curve can be expressed as The slope K 2 is obtained from this relationship.
- the stress gradient of the film in different directions can be measured, and at the same time, the deformation factor of the fixed end of the cantilever beam is considered in the simulation, so a more accurate measurement result can be obtained.
- the present method does not involve Young's modulus (or stiffness matrix) and Poisson's ratio of anisotropic materials when the measurement data is brought into the formula, the calculation is simple, and the measurement is also simple.
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Abstract
一种测量薄膜不同方向应力梯度的方法，包括步骤：通过仿真获取第一方向上薄膜基于S11应力梯度的斜率等效系数K X1、基于S22应力梯度的斜率等效系数K X2（T1）；通过仿真获取第二方向上薄膜基于S11应力梯度的斜率等效系数K Y1、基于S22应力梯度的斜率等效系数K Y2（T2）；通过实际测试获取薄膜第一方向上的斜率K 1以及第二方向上的斜率K 2（T3）；根据K X1、K X2、K Y1、K Y2、以及K 1、K 2计算薄膜第一方向、第二方向的应力梯度（T4）。该方法测量准确性更高，更简单。
Description
本发明涉及半导体器件领域，尤其涉及一种测量薄膜不同方向应力梯度的方法。
在MEMS领域，应力梯度普遍存在于器件结构中，引起结构变形，影响器件性能。
目前常用的测量应力梯度的方法为：设置一系列不同长度的单端固定悬臂梁结构，再测量不同长度梁的末端翘曲大小，再带入公式进行计算获得应力梯度。此方法通常假设S11(X轴方向正向应力)或S22(Y轴方向正向应力)的应力梯度大小是一致的。
然而，实际情况中，薄膜的S11或S22的应力大小往往不一致，因此导致上述计算方法不能获得准确的应力梯度。同时，根据理论公式
对于各向异性材料，需要对其等效杨氏模量E和泊松比v进行提取才能进行有效的计算，而这些都是很难进行提取的。再者，实际情况还要考虑悬臂梁固定部分的变形，而理论公式则是理想情况，不能考虑固定端变形情况。
因此，上述方法有待改进。
【发明内容】
本发明的目的在于提供一种测量薄膜不同方向应力梯度的方法，用于解决现有技术中测量结果存在较大偏差的问题。
本发明的技术方案如下：
一种测量薄膜不同方向应力梯度的方法，包括步骤：
通过仿真获取第一方向上薄膜基于S11应力梯度的斜率等效系数K
X1、基于S22应力梯度的斜率等效系数K
X2；
通过仿真获取第二方向上薄膜基于S11应力梯度的斜率等效系数K
Y1、基于S22应力梯度的斜率等效系数K
Y2；
通过实际测试获取薄膜第一方向上的斜率K
1以及第二方向上的斜率K
2；
根据所述K
X1、K
X2、K
Y1、K
Y2、以及K
1、K
2计算所述薄膜第一方向、第二方向的应力梯度。
优选的，所述第一方向的应力梯度为：
所述第二方向的应力梯度为：
优选的，所述获取第一方向上薄膜基于S11应力梯度的斜率等效系数K
X1的步骤包括：
在所述仿真测试中在所述第一方向设置不同长度的悬臂梁，对该第一方向上的不同悬臂梁施加不同的S11应力梯度，根据所述S11应力梯度分别获取所述悬臂梁末端翘曲挠度；
根据所述悬臂梁末端翘曲挠度和所述悬臂梁的长度获取关系曲线；
根据所述关系曲线，得到所述斜率等效系数K
X1。
优选的，所述获取第一方向上薄膜基于S22应力梯度的斜率等效系数K
X2的步骤包括：
在所述仿真测试中在所述第一方向设置不同长度的悬臂梁，对该第一方向上的不同悬臂梁施加不同的S22应力梯度，根据所述S22应力梯度分别获取所述悬臂梁末端翘曲挠度；
根据所述悬臂梁末端翘曲挠度和所述悬臂梁的长度获取关系曲线；
根据所述关系曲线，得到所述斜率等效系数K
X2。
优选的，所述获取第二方向上薄膜基于S11应力梯度的斜率等效系数 K
Y1的步骤包括：
在所述仿真测试中在所述第二方向设置不同长度的悬臂梁，对该第二方向上的不同悬臂梁施加不同的S11应力梯度，根据所述S11应力梯度分别获取所述悬臂梁末端翘曲挠度；
根据所述悬臂梁末端翘曲挠度和所述悬臂梁的长度获取关系曲线；
根据所述关系曲线，得到所述斜率等效系数K
Y1。
优选的，所述获取第二方向上薄膜基于S22应力梯度的斜率等效系数K
Y2的步骤包括：
在所述仿真测试中在所述第二方向设置不同长度的悬臂梁，对该第二方向上的不同悬臂梁施加不同的S22应力梯度，根据所述S22应力梯度分别获取所述悬臂梁末端翘曲挠度；
根据所述悬臂梁末端翘曲挠度和所述悬臂梁的长度获取关系曲线；
根据所述关系曲线，得到所述斜率等效系数K
Y2。
优选的，所述实际测试获取薄膜第一方向上的斜率K
1的步骤包括：
在实际测试中在第一方向上设置不同长度的悬臂梁，测量所述不同长度悬臂梁的末端翘曲挠度；
根据所述悬臂梁末端翘曲挠度和所述悬臂梁的长度获取关系曲线，根据所述关系曲线得到所述斜率K
1。
优选的，所述实际测试获取薄膜第二方向上的斜率K
2的步骤包括：
在实际测试中在第二方向上设置不同长度的悬臂梁，测量所述不同长度悬臂梁的末端翘曲挠度；
根据所述悬臂梁末端翘曲挠度和所述悬臂梁的长度获取关系曲线，根据所述关系曲线得到所述斜率K
2。
本发明的有益效果在于：可以测量薄膜不同方向的应力梯度，且可以在仿真中增加悬臂梁固定端的变形因素，使得测试结果更加准确。本方法带入公式中不涉及到各项异性材料的杨氏模量(或刚度矩阵)和泊松比，计算简单，降低了测试的难度。
为了更清楚地说明本发明实施例或现有技术中的技术方案，下面将对实施例或现有技术描述中所需要使用的附图作简单地介绍，显而易见地，下面描述中的附图仅仅是本发明的一些实施例，对于本领域普通技术人员来讲，在不付出创造性劳动的前提下，还可以根据这些附图获得其他的附图。
图1为本发明实施例一的测量薄膜不同方向应力梯度的方法流程图。
图2为本发明实施例一的测量薄膜不同方向应力梯度的方法具体实施步骤流程图。
为了便于理解本发明，下面将参照相关附图对本发明进行更全面的描述。附图中给出了本发明的较佳的实施例。但是，本发明可以通过许多其他不同的形式来实现，并不限于本文所描述的实施例。相反地，提供这些实施例的目的是使对本发明的公开内容的理解更加透彻全面。
需要说明的是，当元件被称为“固定于”另一个元件，它可以直接在另一个元件上或者也可以存在居中的元件。当一个元件被认为是“连接”另一个元件，它可以是直接连接到另一个元件或者可能同时存在居中元件。本文所使用的术语“垂直的”、“水平的”、“左”、“右”以及类似的表述只是为了说明的目的。
除非另有定义，本文所使用的所有的技术和科学术语与属于本发明的技术领域的技术人员通常理解的含义相同。本文中在本发明的说明书中所使用的术语只是为了描述具体的实施例的目的，不是旨在于限制本发明。本文所使用的术语“及/或、和/或”包括一个或多个相关的所列项目的任意的和所有的组合。
实施例一
参考附图1所示，本实施例公开了一种测量薄膜不同方向应力梯度的 方法，包括步骤：
T1、通过仿真获取第一方向上薄膜基于S11应力梯度的斜率等效系数K
X1、基于S22应力梯度的斜率等效系数K
X2；
T2、通过仿真获取第二方向上薄膜基于S11应力梯度的斜率等效系数K
Y1、基于S22应力梯度的斜率等效系数K
Y2；
T3、通过实际测试获取薄膜第一方向上的斜率K
1以及第二方向上的斜率K
2；
T4、根据K
X1、K
X2、K
Y1、K
Y2、以及K
1、K
2计算薄膜第一方向、第二方向的应力梯度。
需要说明的是，本实施例中，上述步骤T1、T2、T3可以同时进行，也可以不分先后的进行。
本实施例中，采用悬臂梁测试法对薄膜的应力梯度进行测试，其中，仿真可通过有限元仿真元件进行，在仿真中考虑悬臂梁固定端的变形因素，在实际测试中，采用实际结构的悬臂梁进行测试。
本实施例中，S11表示X轴方向主应力，S22表示Y轴方向主应力。其中，第一方向可与X轴方向相同，也可以不同，第二方向可与Y轴方向相同，也可以不同。本实施例以第一方向与X轴方向为同一方向、第二方向与Y轴方向为同一方向进行说明。
本实施例中，步骤T4中，第一方向的应力梯度为：
第二方向的应力梯度为：
如图2所示，本实施例中，获取第一方向(即X轴方向)上薄膜基于S11应力梯度的斜率等效系数K
X1的步骤包括：
在仿真中在第一方向设置一系列不同长度的悬臂梁，对该第一方向上 的不同长度悬臂梁施加不同的S11应力梯度，根据S11应力梯度分别获取不同长度悬臂梁末端翘曲挠度，其中，悬臂梁末端翘曲挠度的数值为一系列的与不同长度悬臂梁对应的不同数值；
根据悬臂梁末端翘曲挠度和悬臂梁的长度获取关系曲线，该关系曲线可以表达为
其中，δ
nx1为在S11
nx1应力梯度下的悬臂梁末端翘曲挠度，L
nx1为悬臂梁的长度。根据该关系曲线可计算出斜率，并根据斜率得出斜率等效系数。具体的，以不同的S11应力梯度为n个进行说明，n个应力梯度S11
nx1会对应n条不同的曲线，对应的获取n个不同的斜率K
nx1，用该斜率K
nx1除以相应的应力梯度S11
nx1，会得到n个等效斜率K
nx11，取n个等效斜率K
nx11的平均值获得斜率等效系数K
X1。
在本实施例中，获取第一方向上薄膜基于S22应力梯度的斜率等效系数K
X2的步骤包括：
在仿真中在第一方向设置不同长度的悬臂梁，对该第一方向上的不同长度悬臂梁施加不同的S22应力梯度，根据S22应力梯度分别获取不同长度悬臂梁末端翘曲挠度；
根据悬臂梁末端翘曲挠度和悬臂梁的长度获取关系曲线，该关系曲线可以表达为
其中，δ
nx2为在S22
nx2应力梯度下的悬臂梁末端翘曲挠度，L
nx2为悬臂梁的长度。
根据该关系曲线可计算出斜率，并根据斜率得出斜率等效系数。具体的，以不同的S22应力梯度为n个进行说明，n个应力梯度S22
nx2会对应n条不同的曲线，对应的获取n个不同的斜率K
nx2，用该斜率K
nx2除以相应的应力梯度S22
nx2，会得到n个等效斜率K
nx22，取n个等效斜率K
nx22的平均值获得斜率等效系数K
X2。
在本实施例中，获取第二方向上薄膜基于S11应力梯度的斜率等效系数K
Y1的步骤包括：
在仿真中在第二方向设置不同长度的悬臂梁，对该第二方向上的不同悬臂梁施加不同的S11应力梯度，根据S11应力梯度分别获取不同长度悬 臂梁末端翘曲挠度，其中，悬臂梁末端翘曲挠度的数值为一系列的与不同长度悬臂梁对应的不同数值；
根据悬臂梁末端翘曲挠度和悬臂梁的长度获取关系曲线，该关系曲线可以表达为
其中，δ
ny1为在S11
ny1应力梯度下的悬臂梁末端翘曲挠度，L
ny1为悬臂梁的长度。
根据该关系曲线可计算出斜率，并根据斜率得出斜率等效系数。具体的，以不同的S11应力梯度为n个进行说明，n个应力梯度S11
ny1会对应n条不同的曲线，对应的获取n个不同的斜率K
ny1，用该斜率K
ny1除以相应的应力梯度S11
ny1，会得到n个等效斜率K
ny11，取n个等效斜率的平均值获得斜率等效系数K
Y1。
在本实施例中，获取第二方向(即Y轴方向)上薄膜基于S22应力梯度的斜率等效系数K
Y2的步骤包括：
在仿真中在第二方向设置不同长度的悬臂梁，对该第二方向上的不同长度悬臂梁施加不同的S22应力梯度，根据S22应力梯度分别获取不同长度悬臂梁末端翘曲挠度，其中，悬臂梁末端翘曲挠度的数值为一系列的与不同长度悬臂梁对应的不同数值；
根据悬臂梁末端翘曲挠度和悬臂梁的长度获取关系曲线，
该关系曲线可以表达为
其中，δ
ny2为在S11
ny2应力梯度下的悬臂梁末端翘曲挠度，L
ny2为悬臂梁的长度。
根据该关系曲线可计算出斜率，并根据斜率得出斜率等效系数。具体的，以不同的S22应力梯度为n个进行说明，n个应力梯度S22
ny2会对应n条不同的曲线，对应的获取n个不同的斜率K
ny2，用该斜率K
ny2除以相应的应力梯度S22
ny2，会得到n个等效斜率K
ny22，取n个等效斜率的平均值获得斜率等效系数K
Y2。
在本实施例中，实际测试获取薄膜第一方向上的斜率K
1的步骤包括：
在实际测试中在第一方向(即X轴方向)上设置不同长度的悬臂梁，通过测量器械(如激光测量装置、多普勒测量装置等)测量不同长度悬臂 梁的末端翘曲挠度；
根据悬臂梁末端翘曲挠度和悬臂梁的长度获取关系曲线，该关系曲线可表达为
根据该关系曲线可得到斜率K1。
在本实施例中，实际测试获取薄膜第二方向上的斜率K2的步骤包括：
在实际测试中在第二方向上设置不同长度的悬臂梁，测量不同长度悬臂梁的末端翘曲挠度；
根据悬臂梁末端翘曲挠度和悬臂梁的长度获取关系曲线，该关系曲线可表达为
根据该关系曲线得到斜率K
2。
本实施例中，可以测量出薄膜不同方向的应力梯度，同时，在仿真中考虑了悬臂梁固定端的变形因素，因此可以得到更准确的测量结果。以及，本方法在测量数据带入公式中不涉及到各向异性材料的杨氏模量(或刚度矩阵)和泊松比，计算简单，测量也简单。
以上所述实施例的各技术特征可以进行任意的组合，为使描述简洁，未对上述实施例中的各个技术特征所有可能的组合都进行描述，然而，只要这些技术特征的组合不存在矛盾，都应当认为是本说明书记载的范围。
以上所述的仅是本发明的实施方式，在此应当指出，对于本领域的普通技术人员来说，在不脱离本发明创造构思的前提下，还可以做出改进，但这些均属于本发明的保护范围。
Claims (8)
- 一种测量薄膜不同方向应力梯度的方法，其特征在于，包括步骤：通过仿真获取第一方向上薄膜基于S11应力梯度的斜率等效系数K X1、基于S22应力梯度的斜率等效系数K X2；通过仿真获取第二方向上薄膜基于S11应力梯度的斜率等效系数K Y1、基于S22应力梯度的斜率等效系数K Y2；通过实际测试获取薄膜第一方向上的斜率K 1以及第二方向上的斜率K 2；根据所述K X1、K X2、K Y1、K Y2、以及K 1、K 2计算所述薄膜第一方向、第二方向的应力梯度。
- 根据权利要求1所述的测量薄膜不同方向应力梯度的方法，其特征在于，所述第一方向的应力梯度为：
所述第二方向的应力梯度为：
- 根据权利要求1所述的测量薄膜不同方向应力梯度的方法，其特征在于，所述获取第一方向上薄膜基于S11应力梯度的斜率等效系数K X1的步骤包括：在所述仿真中在所述第一方向设置不同长度的悬臂梁，对该第一方向上的不同悬臂梁施加不同的S11应力梯度，根据所述S11应力梯度分别获取所述悬臂梁末端翘曲挠度；根据所述悬臂梁末端翘曲挠度和所述悬臂梁的长度获取关系曲线；根据所述关系曲线，得到所述斜率等效系数K X1。
- 根据权利要求1所述的测量薄膜不同方向应力梯度的方法，其特征 在于，所述获取第一方向上薄膜基于S22应力梯度的斜率等效系数K X2的步骤包括：在所述仿真中在所述第一方向设置不同长度的悬臂梁，对该第一方向上的不同悬臂梁施加不同的S22应力梯度，根据所述S22应力梯度分别获取所述悬臂梁末端翘曲挠度；根据所述悬臂梁末端翘曲挠度和所述悬臂梁的长度获取关系曲线；根据所述关系曲线，得到所述斜率等效系数K X2。
- 根据权利要求1所述的测量薄膜不同方向应力梯度的方法，其特征在于，所述获取第二方向上薄膜基于S11应力梯度的斜率等效系数K Y1的步骤包括：在所述仿真中在所述第二方向设置不同长度的悬臂梁，对该第二方向上的不同悬臂梁施加不同的S11应力梯度，根据所述S11应力梯度分别获取所述悬臂梁末端翘曲挠度；根据所述悬臂梁末端翘曲挠度和所述悬臂梁的长度获取关系曲线；根据所述关系曲线，得到所述斜率等效系数K Y1。
- 根据权利要求1所述的测量薄膜不同方向应力梯度的方法，其特征在于，所述获取第二方向上薄膜基于S22应力梯度的斜率等效系数K Y2的步骤包括：在所述仿真中在所述第二方向设置不同长度的悬臂梁，对该第二方向上的不同悬臂梁施加不同的S22应力梯度，根据所述S22应力梯度分别获取所述悬臂梁末端翘曲挠度；根据所述悬臂梁末端翘曲挠度和所述悬臂梁的长度获取关系曲线；根据所述关系曲线，得到所述斜率等效系数K Y2。
- 根据权利要求1所述的测量薄膜不同方向应力梯度的方法，其特征在于，所述实际测试获取薄膜第一方向上的斜率K 1的步骤包括：在实际测试中在第一方向上设置不同长度的悬臂梁，测量所述不同长度悬臂梁的末端翘曲挠度；根据所述悬臂梁末端翘曲挠度和所述悬臂梁的长度获取关系曲线，根 据所述关系曲线得到所述斜率K 1。
- 根据权利要求1所述的测量薄膜不同方向应力梯度的方法，其特征在于，所述实际测试获取薄膜第二方向上的斜率K 2的步骤包括：在实际测试中在第二方向上设置不同长度的悬臂梁，测量所述不同长度悬臂梁的末端翘曲挠度；根据所述悬臂梁末端翘曲挠度和所述悬臂梁的长度获取关系曲线，根据所述关系曲线得到所述斜率K 2。
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