Bulge test及奈米尺度高分子薄膜之機械性質量測

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研究生：	黃俊國 Chun-Kuo Huang
論文名稱：	Bulge test及奈米尺度高分子薄膜之機械性質量測 Bulge test and mechanical properties measurement of nano-structure polymeric thin films
指導教授：	蔡哲正 Cho-Jen Tsai
口試委員:
學位類別：	碩士 Master
系所名稱：	工學院 - 材料科學工程學系 Materials Science and Engineering
論文出版年：	2005
畢業學年度：	93
語文別：	英文
論文頁數：	59
中文關鍵詞：	高分子、薄膜、機械性質
外文關鍵詞：	bulge test, polymer, thin films, mechanical property
相關次數：	點閱：2 下載：0
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薄膜元件目前已廣泛的應用於許多領域，為了確保這些元件在長時間使用中不至於發生破壞的情形，這些薄膜材料的機械性質占了舉足輕重的地位。然而，隨著薄膜厚度的減少，較完備且經常被利用來量測材料機械性質的方法皆無法準確的量測出薄膜的性質，除此之外，對於軟性的材料，如高分子薄膜，量測的技術受到更大的挑戰。
Bulge test是一個針對薄膜的機械性質量測工具，它所使用的設備簡易，而且實驗所得到的資訊也相當豐富。受測的懸浮薄膜受到一均勻的壓力而向外鼓起，由所施加的壓力和薄膜鼓起高度的關係，可以得出一條壓力對鼓起高度的曲線，再經由曲線擬合和Vlassak等人所推導的公式，便可以求得薄膜材料的殘餘應力、彈性模數和Poisson ratio。
本論文主要是以bulge test針對奈米壓印過程中所使用的高分子薄膜進行量測，受測材料為Micro Resist Technology所生產的mr-I 8030(以PMMA為基底)，薄膜厚度從數十到數百個奈米。同時，我們也利用nanoindentation進行量測，並且將兩種量測技術所得到的結果作一個比較。由nanoindentation所得到的楊氏模數大約比由bulge test所量到的大了20%至50%，這樣的結果可能是由於nanoindentation在量測上會受到基材的效應，同時，在壓痕點下方的材料也會出現緻密化的情形，使結果出現了偏差。
Poisson ratio則是根據biaxial modulus和plane-strain modulus之間的關係所求得。實驗上可藉由正方形懸浮薄膜的bulge test來找出biaxial modulus，由長方形懸浮薄膜的bulge test來找出plane-strain modulus，而得到薄膜材料的Poisson ratio。

In last few decades, the applications of thin film have become more and more widely. In order to guarantee the long-term operation according to their specification, mechanical properties of thin film are highly desirable. Unfortunately, as the scale level of film structure decreasing, it becomes increasingly difficult to measure its mechanical properties.
Bulge test is a useful method for characterize mechanical properties in thin films. In bulge test, a pressure is applied to the backside of the thin film uniformly, making the free-standing thin film to deflect. By measuring the pressure applied and the deflection height of the thin film, a Pressure vs. deflection height curve can be obtained and mechanical properties of the film are determined from the curve fitting process. In bulge test, the accuracy of the measurement is significantly influenced by the sample geometry. The process of free-standing thin film fabrication will be described in this thesis. A big advantage of this test over other micromechanical test lies in the relatively simple stress-strain state in the sample since the stress state in the film is biaxial.
We apply bulge test to measure mechanical properties of polymeric thin film with thickness from several tenth to several hundredth nanometer. In this thesis, the polymeric thin film we tested is mr-I 8030 (Micro Resist Technology) which is used in nanoimprint lithography. The results are compared with data obtain by nanoindentation. The Young’s moduli measured by nanoindentation are about 20% to 50% greater than those measured by bulge test. This result can be viewed as the effect of substrate and the densification of thin film material under indent point.
We also introduce a method to estimate Poisson ratio of thin film material. Poisson ratio, ν, can be calculated from the relationship between biaxial modulus and plane strain modulus. This idea can be carried out by conducting bulge test on square and long rectangular free-standing thin films.

Abstract    ii
Table of contents    iv
List of Illustrations    vi
List of Tables    viii
Chapter 1. Introduction    1
1.1.    Thin films    1
1.2.    Techniques for characterizing mechanical properties of thin films    2
Cantilever beam test    2
Wafer curvature    3
Micro-tensile test    4
X-ray diffraction    4
Strain-induced elastic buckling instability for mechanical measurements (SIEBIMM)    5
Depth-sensing indentation    5
Bulge test    7
Chapter 2. The bulge test – a method to extract mechanical properties of the membrane    8
2.1.    Purpose of the bulge test    8
2.2.    Nomenclature    8
2.3.    The deflection of circular membranes    9
2.4.    Energy-minimization solution for a circular membrane    11
2.5.    Exact solution for the deflection of a pressurized circular membrane    15
No residual stress    17
Residual stress dominated regime    17
General case    18
Influence of bending stiffness    18
2.6.    Noncircular geometries    19
Infinitely long rectangular membranes    19
Square membrane    20
Generalized bulge equation    20
2.7.    Analysis for composite films    21
Chapter 3. System of Bulge Test    23
3.1.    Bulge test apparatus    23
The external chamber    23
The inner chamber    23
3.2.    The interferometer    26
Image analysis procedure    28
3.3.    Sample preparation    29
Deposition of silicon nitride    31
Photolithography    31
Reactive ion etching    32
Anisotropic wet etching    32
Sample mounting    33
Chapter 4. Results and discussion    34
4.1.    Silicon nitride thin films    34
Motivation    34
Bulge test results    34
Determination of Poisson ratio    35
4.2.    Bulge test on polymer films    38
Motivation    38
Bulge test results    39
Nanoindentation results    42
Chapter 5. Conclusions    45
Reference    46
Appendix: The results of bulge test    52
The result of SiNx film:    52
The results of polymeric films:    54

List of Illustrations
Fig. 1 1  The measurement of mechanical resonant frequencies of the cantilever beams    3
Fig. 1 2  The bending phenomenon of the substrate with residually-stressed thin film    3
Fig. 1 3  Micro-tensile test    4
Fig. 1 4  The load vs. indentation curve.    6
Fig. 1 5  The bulge test    7
Fig. 2 1  Model of spherical cap    9
Fig. 2 2  Edge constraint of a thin film window    10
Fig. 2 3  Large displacement of a plate    11
Fig. 2 4  The equilibrium for an element of the plate    12
Fig. 3 1  Bulge test apparatus    24
Fig. 3 2  A picture of the external chamber and the laser interferometer    25
Fig. 3 3  A close view of the internal chamber    25
Fig. 3 4  The setup of our interferometer    27
Fig. 3 5  (a), (b) The interference pattern of a well-aligned interferometer. (c) The interference pattern of a poorly-aligned interferometer.    27
Fig. 3 6  The image analysis software    28
Fig. 3 7  The variation of intensity vs. time steps    28
Fig. 3 8  The preparation of free-standing thin films    30
Fig. 3 9  The procedure of photolithography    31
Fig. 3 10  The free-standing thin film of silicon nitride with tensile residual stress.    33
Fig. 3 11  A SEM image of a single window    33
Fig. 3 12  The sample holder    33
Fig. 4 1  A typical pressure vs. deflection curve measured by bulge test.    34
Fig. 4 2  (a).The biaxial modulus of the etched layer shows almost no change with deviation in the whole thickness of the film. (b).The same result also observed in long rectangular membrane.    37
Fig. 4 3  Poisson ratio of silicon nitride    37
Fig. 4 4  Procedure of Poisson ratio calculation    38
Fig. 4 5  The thickness of polymeric film is measured by AFM.    39
Fig. 4 6  Bulge test data, with & without polymer (352nm)    40
Fig. 4 7  Bulge test data, with & without polymer (159nm)    40
Fig. 4 8  Bulge test data, with & without polymer (73nm)    41
Fig. 4 9  Biaxial modulus and Young’s modulus measured by bulge test    41
Fig. 4 10  Young’s modulus measured by nanoundentation and load-penetration curves corresponding to each of the load levels. (a). 2sec-2sec (loading-unloading) loading profile. (b). 2sec-10sec-2sec (loading-holding-unloading) loading profile. (c). 2sec-20sec-2sec loading profile.    43


List of Tables
Table 2 1  list of variables    8
Table 2 2  Coefficient for generalized bulge equation    21
Table 3 1  Nitride deposition parameters    31
Table 3 2  Photoresist spun parameters.    32
Table 3 3  Parameters for reactive ion etching of silicon nitride    32
Table 4 1  The mechanical properties of mr-I8030 measured by bulge test    42
Table 4 2  The mechanical properties of mr-I8030 measured by bulge test.    44

                                

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