UNIVERSITÉ LIBRE DE BRUXELLES
Ecole Polytechnique de Bruxelles
Service 4MAT
Small Scale Plasticity
With Confinement and Interfacial Effects
PhD student: Pouya HABIBZADEH
Promoter: Prof. Dr. Marie-Paule DELPLANCKE - OGLETREE
Co-Promoter: Prof. Dr. Stéphane GODET
Academic year: 2015/2016
Members of the Jury
Chairman
Prof. Dr. Thierry J. Massart, Université Libre de Bruxelles, Belgium Promoters
Prof. Dr. Marie-Paule Delplancke-Ogletree, Université Libre de Bruxelles, Belgium Prof. Dr. Stéphane Godet, Université Libre de Bruxelles, Belgium
Members
Prof. Dr. Daniel Kiener, Montanuniversität Leoben, Austria Prof. Dr. Herman Terryn, Vrije Universiteit Brussel, Belgium Dr. Peter Berke, Université Libre de Bruxelles, Belgium
Contact Information:
Pouya Habibzadeh
Université Libre de Bruxelles (ULB) Campus du Solbosch CP 165/63 50, av. F.D. Roosevelt 1050 Brussels, Belgium
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I wouldn't let a single day go by without saying to people I love, that I love them.
Gabriel García Márquez
Acknowledgments:
Finishing PhD thesis is definitely a significant personal challenge. But, it would not have been possible without the scientific, technical, and human contribution of many people.
I take this opportunity to express my profound gratitude and deep regards to my guide Prof. Dr. Marie-Paule Delplancke Ogletree for her exemplary guidance, monitoring and constant encouragement throughout the past years with her patience and knowledge. The blessing, help and guidance given by her time to time shall carry me a long way in the journey of life on which I am about to embark.
I also take this opportunity to express a deep sense of gratitude to Prof. Dr. Stéphane Godet for his cordial support, valuable information and guidance, which helped me in completing this task through various stages. I gratefully acknowledge Prof. Dr. Thierry Massart for his altruistic enthusiasm and sensible advices.
Besides my advisors, I would like to thank the rest of my jury members: Prof. Dr. Daniel Kiener for his help and valuable advice through e-mail and for generously agreeing to serve as external jury member of my thesis, despite his busy schedule and the long distance he had to travel. Special thanks also go to Prof. Dr. Herman Terryn and Dr. Peter Berke for their encouragement, insightful comments, and useful questions.
I would like to acknowledge Didier Robert for his support in the preparation of ultra-thin films, Gilles Wallaert for FIB training and Fikri Elghoulbzouri for training me in cathodic arc depositions well as a special thanks to Loïc Malet for his help in TEM characterizations.
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department for the valuable information provided by them in their respective fields. I am grateful for their cooperation during the period of my assignment.
From the EMAT group in Antwerpen University I would like to acknowledge Dr. Hosni Idrissi and Dr. Behnam Amin Ahmadi for all their help in TEM characterizations.
I also would like to thank my project mates: Patrycja Wnek and Mahdi Kazemi Hatami and my office mate Nenad Milenkovic, with whom I have spent 4 years. It was a pleasure to share our view on science and life.
I would like to thank my parents, whose education and encouragement, love and sincerity brought me to where I am standing now. All the support they have provided me over the years was the greatest gift anyone has ever given me; my brothers and my sister in-law for their constant encouragement without which this assignment would not have been possible.
Finally, to my precious Femke, for your help especially in the crucial moments we spent together, for your support in my scientific and daily life.
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List of Abbreviations
ACOM-TEM Automated Crystal Orientation Mapping in TEM
AFM Atomic Force Microscopy
Al Aluminum
Ar Argon
BCC Body Centered Cubic
BF Bright Field
C Carbon
CPU Central Processing Unit
Cr Chromium
Cu Copper
DC Direct Current
DLC Diamond like Carbon
DP Diffraction Pattern
EBSD Electron Backscattered Diffraction
EDX Energy Dispersive X-Ray Spectroscopy
eV electron Volt
FCC Face Centered Cubic
FFT Fast Fourier Transform
FIB Focused Ion Beam
Ga Gallium
H-P Hall-Petch
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nm nanometer
OIM Orientation Imaging Microscopy
PVD Physical Vapor Deposition
SEM Scanning Electron Microscopy
SiC Silicon Carbide
SPM Scanning Probe Microscope
TEM Transmission Electron Microscopy
TiN Titanium Nitride
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Abstract
The mechanical properties of crystalline metals are strongly affected when the sample size is limited to the micron or sub-micron scale. At these scales, the mechanical properties are enhanced far beyond classical predictions. Besides, the surface to volume ratio significantly increases. Therefore surfaces and interfaces play a big role in the mechanical properties of these micro-samples. The effect of different interfaces on the mechanical properties of micro-samples is not yet well understood. The aim of this project is to characterize, understand, and predict the effect of confinement on deformation mechanisms at micro-scale. In this study, micro-pillars were fabricated by Focused Ion Beam (FIB). Micro-pillars were homogeneously coated with thin films by magnetron sputtering and cathodic arc deposition. The mechanical properties of carbon-coated-, chromium carbon-coated-, naked-, annealed- and non-annealed micro-pillars were measured. Afterwards, the results of micro-compression tests and Automated Crystal Orientation Mapping on Transmission electron microscopy (ACOM TEM) were compared and led to some surprising new findings.
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Contents
Chapter 1 - Introduction
1.1 Introduction ... I-1 1.2 Aim and Main Tasks of the Thesis ... I-2 1.3 Materials Used in This Project ... I-3 1.4 Limitations at the Beginning of This Project ... I-3 1.5 The Structure of the Thesis ... I-5
Chapter 2 - Literature survey
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2.2.3 Coating Instruments Used ... II-24 2.2.3.1 Cathodic Arc Deposition ... II-24 2.2.3.2 Magnetron Sputtering ... II-26 2.2.4 Automated Crystallographic Orientation Mapping in a TEM ... II-27 2.3 Conclusions ... II-28
Chapter 3 - Experimental Instruments and Techniques
3.1 Sample Preparation ... III-1 3.1.1 Macroscopic Bulk Sample Preparation ... III-1 3.1.1.2 Electron Backscatter Diffraction ... III-3 3.1.2 Microscopic Sample Preparation ... III-3 3.1.2.1 Micro-Pillars Fabrication ... III-4 3.2 Micro Compression Test ... III-7 3.2.1. Optic Calibration with Large Radius Flat Punch Tip ... III-8 3.2.2 Scanning Probe Microscopy (SPM) ... III-9 3.2.3 Loading Procedure ...III-10 3.2.4 Conversion of Load-Displacement Curve to Stress Strain Curve ...III-12 3.3 TEM Sample Preparation ...III-13 3.4 Conclusions ...III-15
Chapter 4 - Uniaxial Compression of Copper Micro-pillars:
The Effect of Annealing
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5.2.4.1 Homogeneous Thickness of the Carbon Confined Layer ... V-26 5.2.4.2 Behavior of the Load-Displacement Curves ... V-26 5.2.4.3 ACOM TEM ... V-27 5.2.4.4 Comparison of Results of the Confined- and Naked Annealed Micro-pillars V-28 5.2.5 Conclusions ... V-31
Chapter 6 - Main Conclusions and Perspective for Future Work
6.1 Main Conclusions ... VI-1 6.2 Future Work... VI-4
References:
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1.1 Introduction
Micro- and nano- technologies have played a big role in the development of new devices, especially in the microelectronics industry. These new devices such as central processing units (CPU), cell phones, sensors, micro- and nano- electro mechanical systems, etc. require reducing component dimensions to the micro- and nano scale. Micro technology allows us to stack micro components into complicated devices, which have incredible high performance for different applications. The mechanical stability of micro components during the fabrication process and in service is one of the important issues in the development of these new devices. Plastic deformation or fracture of the micro components may cause disconnection of the communication between these micro components, leading to device failure.
At micro scale, the ratio of surface to volume significantly increases and plays a big role in the mechanical properties of these micro components. Also, in these devices there are multiple interfaces existing between the different elements. These interfaces may affect the mechanical properties of the micro components. Furthermore, in order to improve the mechanical properties of micro materials, different coatings can be used and the mechanical properties of the micro-material also can be dictated according to its confinement structure.
In order to design and produce reliable devices, appropriate material with well-defined mechanical properties should be selected. However, the mechanical properties at micro scale are far beyond classical predictions. Exploring and understanding the origins of these phenomena at small scale is necessary for micro-technology [1].
It is worthwhile to study the effect of different confinements with its different interfaces, on mechanical properties at micro scale. Therefore, new techniques and instruments are required to be developed to be able to understand the deformation mechanisms of confined materials at micro-scale.
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indentation in lower scale specimens. However, other methods have been developed for tensile tests [4], cantilever bending [5] and shearing [6]. These methods require a complex geometry and are not suitable for thin and homogenous coating, and therefore were not performed in this study.
In this study, we chose the micro-compression technique to determine the mechanical properties of micro-samples for it is known to not require complex geometric samples, which are not suitable for a uniform confined layer. Additional advantages of this method are simple setup, commercial availability, and experimental errors; such as tip shape, surface oxides, and misalignment are minimized [7]. Micro-compression testing has been widely employed by nano-indentation to determine the mechanical response of materials in the micrometer- and sub-micrometer scale [8]. The flow curve is extracted directly from load-displacement data considering the stress-state is nominally uniaxial.
The study of the mechanical properties of small-scale systems has not been fully developed, given that some of the tools for the fabrication and testing of samples have only recently become available. The mechanisms that occur during deformation are currently being studied.
1.2 Aim and Main Tasks of the Thesis
The aim of the project is to characterize, understand, and predict the effect of a different confinement on deformation mechanisms at micro scale with additional attention to interfaces. This study is part of a larger project, which focuses on the characterization of the fundamental deformation processes at lower scale and interacts with the modeling part. We have taken the opportunity to study the mechanical properties of a copper single-crystalline material at micro scale with both crystalline- and amorphous- coating.
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compared with that of micro-pillars submitted to different surface treatments, which correspond to different confinement conditions of the plasticity.
Focus Ion Beam (FIB) was used for fabricating the micro-pillars. Afterwards, thermal annealing was performed, resulting in considerably reduced artifacts. Later, the naked-and coated micro-pillars were compressed by nano-indentation. Subsequently; the compressed micro-pillars were characterized by Transmission Electron Microscopy (TEM).
1.3 Materials Used in This Project
In this study, the micro-pillars were fabricated on copper single crystal with {1, 1, 1} orientation. Carbon was deposited as amorphous coating, and chromium as crystalline coating.
Copper is frequently used in microelectronic devices. Properties such as good corrosion resistance, good strength and the ability to be polished to any desired texture make copper a good candidate for this project.
Chromium is also used often in microelectronic devices to solder different components. Choice of coating layers was also based on their crystalline structure (carbon: amorphous structure, chromium: BCC crystalline structure). In general the BCC structure has seldom been studied opposed to FCC materials. In addition, the interface between copper and selected coatings is sharp even at high deposition temperature due to their immiscibility with copper. Moreover, we also want to determine if these different interfaces are working as a dislocation barrier or as a dislocation source. All these particular properties and structures were determinant in the choice of coating material in this study.
1.4 Limitations at the Beginning of This Project
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The second challenge we had to deal with was regarding experimental techniques. FIB milling, which was performed in order to fabricate these micro samples, causes damage to the surface of these micro samples. Therefore, it is required that a new technique is established to prevent this. Besides the sample damage, there are other disadvantages that we need to consider when performing FIB milling, such as injection of dislocation loops and gallium ion implantation. When the sample dimension is reduced to the micro scale, the damage caused by FIB might be significant due to an increase of the ratio of damaged volume to the sample size. A new method should be developed to recover this damage layer [10] [11].
Determining the suitable sputtering condition is necessary to obtain a coated layer that has parallel slip systems to the substrate slip systems. This allows us to detect whether or not the difference in this crystalline structure causes a block of the dislocation to prevent it from escaping the surface.
There is no need for an additional interface between our micro sample and the confinement layer. It is essential to remove any contaminated layer before deposition of the confinement. We aim to develop a new method to remove all these undesired layers before sputtering. In this method we should carefully pay attention to not further damage the surface of the micro pillar.
We need to examine and determine how to deposit homogenous confinement all over the micro sample. This is important to be able to characterize and evaluate the differences of the mechanical properties of confined – and naked samples at micro scale. It’s essential for this homogenous layer to be as thin as possible because we do not want to study the effect of the composite on the mechanical properties. Therefore, development of a new technique is required to assure a thin and uniform coating on the micro samples. It is also required that the layer is strong enough to undergo the plastic deformation experiments, this was a big concern during the experiment. When comparing the non-confined samples to the confined samples we have to consider the oxide layer that forms on these samples because of the change in the crystalline structure on the surface.
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causes incorrect results. In a conventional nano-indentation it is very hard to verify if the flat punch tip is placed perpendicular on the micro-pillar before we run the test. Only after the test can we will be sure whether or not the deformed micro pillar was exposed to uniaxial force. Many unsuccessful results were obtained during these tests due to the misalignment force errors.
1.5 The Structure of the Thesis
This thesis concludes the study conducted during academic years 2011 till 2015 at the 4MAT laboratory of the Université libre de Bruxelles.
Chapter two is about the background and literature survey behind this study.
In Chapter three, the material, equipment and techniques, which were used in this study, are described.
The effects of the annealing of micro-pillars are discussed in chapter four. Furthermore, the traces of slip systems on compressed naked micro-pillar are imaged by scanning electron microscopy (SEM) and transmission electron microscopy (TEM).
Chapter five deals with the effects of crystalline- and amorphous confinement on the mechanical properties of micro-pillars. Moreover, the different micro-pillar confinement techniques are discussed in detail.
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Chapter Overview
This chapter is divided into two sections. In the first section, a literature review about the plasticity theory, micro plasticity and dominant hardening mechanisms in micro plasticity is presented. The second section deals with introduction of the main instruments and techniques used in this study.
2.1 Theory
2.1.1 Crystalline Material
The scientific definition of a crystalline material is a material where the atoms exhibit a long-range order and symmetry. It means that an atom binds to its attached atoms in the exact same way as the next atom binds to the one after that. Hereby creating a repetitive and symmetric 3D structure called a lattice. The smallest coherent building block of the lattice is the unit cell, which is formed by the combination of atoms. Figure 2.1 shows a unit cell in the space lattice [12]. In contrast, amorphous materials have a short-range order of the atoms and there is no reoccurring structural unit cell detected in their structure.
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Most metallic materials have a crystalline structure, which has defects. These defects are classified as mentioned in the following, depending on their spatial extension;
• Point defects • Line defects • Planar defects • Bulk defects
Point defects occur when one or a few atoms have been displaced, exchanged, added or removed from their equilibrium position. Linear defects are called dislocations, which are very important in this study; they are introduced in section 2.1.2.1. Many defects can be in a planar classification such as grain boundary and material interfaces. Bulk defects form on a much bigger scale than the other crystal defects for example larger voids and inclusion of a second phase particle.
2.1.2 Plastic Deformation
By applying a force to the metallic materials that is greater than their elastic limit, we will observe a deformation even after releasing the load. This so-called plastic behavior can be explained by looking to the underlying atomic structure of the sample.
The stretching and compression, without breaking the inter-atomic bond causes elastic deformation in the crystal network. By increasing force over the elastic limit, some inter-atomic bonds will break. After the rupture, the inter-atomic bonds are reorganized in the lattice, followed by the introduction and subsequent movement of lattice defects, which mediate plastic deformation.
2.1.2.1 Dislocation
In 1926, Frenkel suggested that the strength of metals should be on the order of
where G is the shear modulus; however, experiments give values several orders of magnitude smaller than the value for the yield stress of polycrystalline metals [14]. This difference was explained by the theories of dislocation by Orowan, Polanyi and Taylor in 1934.
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movement of these defects in the crystal lattice, which is called “slip”, triggers the plastic deformation. Dislocations move along the slip planes (these planes are described in the following section) and the stress acting along this plane (resolved shear stress) drives this dislocation movement.
If there are no obstacles to the motion of dislocations in the crystal lattice, the crystal will deform elastically under an applied stress, but when the critical resolved shear stress for motion of dislocation reaches the specific value, the dislocations will move according to the applied stress. Afterwards, another plane will be activated and this process will be repeated until the shear of the crystal is completed.
This perfect mechanism is inexistent in all metals because there are several obstacles preventing dislocation movements. Most famous amongst these obstacles are grain boundaries, which block the dislocation movement. Slip plane is terminated at and by these obstacles and there is no possibility for dislocation movement under the same applied stress. This leads to dislocation pile-up at these obstacles until the stress is increased sufficiently, then slip is activated in a different slip plane, so that the plastic deformation can continue [15].
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2.1.2.2 Slip System
As mentioned earlier, plastic deformation occurs when applied force is higher than the elastic limit and at this point the dislocations move along in slip systems. In material science, slip systems are defined as the set of symmetrically slip planes and slip directions along which dislocation motion occurs.
Depending on the type of crystallographic lattice, different slip systems exist in the material. Normally, slips occur on planes, which have the greatest number of atoms per unit area and in the direction, which has the most atoms per unit length. Therefore, the slip planes have the highest density of atoms and the slip direction is the shortest lattice translation vectors. A critical resolved shear stress is needed to start a slip. Slip is one of the most important mechanisms for crystal deformation [17] [18]. Below, the two slip-systems in the crystallographic lattice used in this study are explained.
Slip Systems in Face Centered Cubic (FCC) Crystals
Slip in FCC crystal occurs along the {111} planes, which have the highest density of atoms (figure 2.3), and along the <1-10> directions, which have the most atoms per length (figure 2.4). Each of the four close-packed planes has three separate close-packed directions, so it gives 12 slip systems.
Figure 2.3: Four different (111) planes in the family of {111} FCC planes.
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Slip in Body Centered Cubic (BCC) Crystals
Slips in BCC crystals occur along the planes, which have the highest density of atoms as well; but, unlike FCC structure, there is no truly close packed plane in BCC structure. Therefore, slip systems in this crystalline structure cannot be activated easily like in FCC structure. BCC materials can have up to 48 slip systems. There are six planes in the {1, 1, 0} family and each plane has two <1, 1, 1> directions which have the most atoms per length (12 slip systems). In addition, 24 {1, 2, 3} and 12 {1, 1, 2} planes with one direction < 1, 1, 1> (36 slip systems) [19].
{1, 1, 0} 6 planes <1,1,1> 2 directions {1,1,2} 12 planes <1,1,1> 1 direction {1, 2, 3} 24 plane <1,1,1> 1 direction
Figure 2.5: Slip systems in BCC crystal.
2.1.2.3 Schmid Factor
Slips occur under applied force, when the shear stress in the slip direction reaches its critical value. Figure 2.6 shows a single crystal specimen with cross sectional area A, subjected to uniaxial load F (tensile or compressive). Slip plane normal and the slip direction are oriented at the angle ∅ and λ, with respect to the loading axis.
The load F can be resolved along the slip direction to give a shear force Fcos λ, acting in the slip direction. The resolved shear stress τ on the slip plane and toward the slip direction is the shear force (F cos λ) divided by the area of the slip plane ( ∅) so that
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Figure 2.6: Tensile stress along the axis of a cylindrical single crystal samples with cross-sectional area A [20].
The condition for the initial plastic deformation on first activated slip system is given by Schmid law. Plastic flow will take place when the resolved shear stress τ along the slip direction in a slip plane reaches a critical value τ :
σ cos λ cos ∅ Mσ τ (2.2)
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2.1.3 Small Scale Plasticity
As we mentioned earlier, plastic deformation in metals with a crystalline structure is encouraged by the glide of dislocations on slip systems. In most materials several obstacles exist to impede the movement of dislocations. The dislocations interact with these barriers and this leads to size effects in a way that the characteristic length scale of the material determines the mechanical properties of the material [14] [22].
D. Kiener [22] clarified the influences of the internal- and external length scale on the mechanical properties of the materials. He mentioned that internal length scale, like the grain size or average particle spacing, and also internal strain inhomogeneities cause a block of dislocation motion and affect the mechanical properties. Also, he mentions that the external lengths scale affect the mechanical properties in terms of sample dimension. In the following, we explained the influences of these length scales on the mechanical properties.
2.1.3.1 Size Effect due to The Internal Length Scale
The plasticity in micro- and macro-scale can differ considerably. This difference was experimentally demonstrated in the 1950 by Hall [23] and Petch [24] for grain boundary strengthening in polycrystalline metals. Later, the Hall-Petch (H-P) relation was expanded to cover the strengthening effect of various types of boundaries of plastic deformation [25].
The Hall-Petch relation showed the effect of the grain size on the mechanical properties of polycrystalline metals and alloys. The following equation is showing the yield stress influence of the grain size DGB and it is introduced by the parameter .
σ = σ + kD !" (2.3)
Where σ is a certain shear stress required for gliding dislocation in a single crystal, and K is a constant individual for each material.
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on the dislocation mechanism of plastic deformation, when grain boundaries block the motion of dislocations.
The Hall-Petch relation is not observed for nanomaterials with grain sizes of several tens of nanometers to a certain extent. As grain sizes are reduced to approximately 40nm, they cannot accommodate multiple lattice dislocations. Other plastic deformation mechanisms engage at this scale such as grain boundary sliding, partial dislocation emission and absorption at grain boundaries [26] [27].
The hall-Petch relation is not valid below a grain size of 20nm. Decreasing the grain size at this scale causes softening of the nano-material. The mechanisms behind this reversal are poorly understood, but the researchers refer to grain boundary activation and deformation [15] [28]. Figure 2.7 shows the strength of polycrystalline materials in relation to the grain sizes.
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2.1.3.2 Size Effect due to The Internal strain inhomogeneities
In the past two decades numerous experimental observations showed evident size effects in the presence of strain gradients provoked by non-homogenous deformation. Stölken and Evans stated augmented bending strengths with reduced foil thickness, and multiple authors detected an increase of the nanohardness with reduced indentation depth [29] [30] [31] [22].
Non-homogenous deformation leads to the storage of geometrically necessary dislocations (GNDs) in the material, which inflicts a local gradient in strain. This mentioned gradient stands in direct correlation to the density of GNDs(ρ ) [32].
% =1' ()*)+, (2.4)
Where b is the Burgers vector, and * is the shear in the slip systems. The density of GNDs affects the Taylor hardening relation, which is explained in the following.
The effect of a strain gradient - on the flow stress σ of material in the deformation field is expressed by the equation 5 [31]:
.//
01 = 1 + 2 -
(2.5) Where 3 is the flow stress of the material with no strain gradient and 2 is a characteristic material length scale.
2.1.3.3 Size Effect due to The External length scale
In the past decade, the vast progress in fabrication processes with precise control of material critical dimensions and microstructures in the lower scale have led to an innovation in materials science, more specifically for structural materials.
Besides the classical strengthening techniques performed on bulk materials like solution strengthening, alloying, fiber reinforcement and cold-working, development of new material with higher mechanical properties can be achieved through structure control at the lower scale [28].
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dislocation would be present in a volume of 10μm8 [22]. One example is single crystal gold nano_pillar attained strength 50 times higher than their bulk form [34].
Each dislocation is surrounded by a stress field; this is due to the mismatch in the lattice. Back stress is caused by the interaction between the dislocations. By reducing the sample size, the interaction of dislocation induced back stress with the dislocation sources increases. The back stress of dislocation is inversely proportional to the sample size [35]. This interaction prevents the source from generating the dislocations and increases the flow stress [36].
The other mechanism contributing to an increase of the flow stress of the material at lower scale, which shifts plasticity into nucleation-controlled regime, is dislocation starvation. The initial mobile dislocation in this mechanism annihilates through the surface of the micro pillar, and leaves the crystal dislocation starved. Subsequently, in order to progress the plastic deformation, new dislocations have to be nucleated using a significant fraction of applied stresses [37].
Another mechanism, which is mainly referring to size effects at micro scale, is source exhaustion hardening. The general assumption of this mechanism implicates the emission of dislocation from a specific single source or a randomly distributed array of sources. These sources are activated in a discrete way; we are then able to assess the effect of the decreased sample size on the source lengths and their operation strengths. In this mechanism, the number of available dislocation sources is reduced because we decrease the sample size. In addition, the influence of the surface affects the operation of these dislocation sources, which is termed the starvation/exhaustion mechanism [38].
Other mechanisms responsible for the considerably higher flow stress found in the micro-samples are explained in the following.
2.1.3.3.1 Taylor Hardening
Taylor proposed that trapped dislocations hinder the movement of other dislocations and causes internal stress, so the flow stress increases to overcome the stress field caused by the surrounding dislocations.
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τ = 9μb;ρ< (2.6)
Where τ is the flow stress, 9 is numerical constant, µ is the shear modulus, b is the Burgers vector and ρ<is the density of dislocations [39].
2.1.3.3.2 Dislocation Pile-up
We mentioned earlier that the stress field, which surrounds each dislocation, is due to the mismatch in the lattice. The interaction between dislocations is called a back stress, which is derived from the stress fields around the individual dislocations.
During the plastic deformation process, many dislocations on the same slip plane are generated by dislocation sources (Frank-Reed). When a certain shear stress is applied to the material, dislocations glide along slip planes, as it is shown in figure 2.8.
Figure 2.8: Slip of an edge dislocation under influence of shear stress [40].
If the primary dislocation from the source is prevented from moving because of barriers such as interfaces, surface layer induced by FIB, oxidation, regions with high internal stress gradient and grain boundary, the other dislocations from the source will pile-up behind the blocked dislocation. As it is shown in figure 2.9, the barrier is at X=O, the shear stress (τ0) is applied on the sample, moreover dislocations are also interacting
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Figure 2.9: Dislocation pile-up behind the barrier [36].
Physics of Pile-up Formation
In 1952, Mott used dislocation source characterization in his theory. It was assumed that the source properties could be represented by two parameters: an activation stress σ and a position x [41]
.
This means that the source will generate dislocations if and only if the total stress at x is more than σ .σ#x ? @ σ (2.7)
Figure 2.10 shows how a dislocation pile-up forms out of a source. If the applied stress on the source is less than the source activation stress, no dislocation is generated. When the applied stress σ increases just above σ then one dislocation is formed, the dislocation moves under the applied stress until it is blocked by a barrier. Then back stress from the dislocation causes the stress at the source to drop below σ and no additional dislocations will be generated.
The back stress from the first dislocation is compensated by increasing the applied stress, and more dislocations are generated and blocked by the obstacle. This process continues as the applied stress increases. Once the increased stress at the obstacle reaches a critical value, yielding occurs. If the sources parameters and the barrier strength are known then the yield can be calculated by using the appropriate dislocation density [42].
Figure 2.10: In the left picture double-ended pile-up is shown and in the right picture the single-ended pile-ups is shown fortwo different positions of the Frank-Read source, as proposed by
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The number of dislocations in the pile-up depends on the back stress effect on the source. Thus, the dislocation population N is a function of the applied stress σ and the source characteristic σ and a position x . When more dislocations are added tothe pile-up, the tail of the pile-up approaches the dislocation source. There is a region between the pile-up tail and the source, which is called dislocation free region.
At the limit d→∞, when the dislocation at the end is far away from the source, the back stress of an infinite grain size is negligible. On the other hand, when d decreases, the tail of the pile-up approaches the source, and then the number of dislocations will be limited in the pile-up because of the back stress force. Consequently, the local force acting on dislocation pile-up is decreased, so it is necessary to increase the external load for dislocation pile-up.
In figure 2.11, the single ended pile-up is shown and the source is considered to be located at the left boundary, x=0. The first dislocation which is blocked at the grain boundary is at the right, x=d. The point where the pile-up terminates is at 9 ϵ (0, d). The dislocation density is found by enforcing the equilibrium condition that the Peach-Kohler force vanishes throughout the pile-up. This condition for screw dislocation is [42]:
0 BC"DPV .G9<HIJJ JMKL<JM1 σ xϵ(9, d) (2.8)
Where µ is the shear modulus, PV is the principal value of the integral, n (x) is the dislocation density to be determined and σ , which is the applied stress, is a constant.
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Equation 2.8 was solved by Leibfried 1951, Eshelby 1949, Hirt and Lothe 1982, the resulting density is:
n(x) =2σμb (x − 9)
! "
(d − x)!" xϵ(9, d) (2.9)
Equation 2.9 should be solved for the unknown 9 and was accomplished as Mott in 1952 assumed that the source requires the threshold stress (σ ) for generating dislocation.
σ(x = 0) = σ (2.10)
Where σ (x) is the total stress at point x, to find σ (x), first we have to find σS(x), the stress at x resulting from the dislocations was given by Hirth and Loth in 1982.
σS(x) = −σ (1 −(9 − X) ! " (d − X)!") (2.11) σ(x) = σ + σS(x) = σ (9 − X) ! " (d − X)!" (2.12)
Substituting equation 2.12 into 2.10 and solving for 9 gives us:
9 = (σ ,σ "d (2.13)
With 9 known, the density is calculated and gives us the number of dislocations:
N = V n(x)d(x) =< πσ (d − 9)μb
9
(2.14)
II-15 σC = Nσ =πσ (d − 9)σ
"
μb
(2.15)
When 9 from equation 2.13 is substituted, equation 2.15 is solved for σ .
σ = (μbσπd + σC ", ! "
(2.16) Where σ is the applied stress, μ the shear modulus, b the Burgers vector, σC the strength of the interface, d the grain size or critical length scale and σ is the source strength.
In equation 2.16, by decreasing d to the lower scale, the applied stress should be higher to overcome the back stress from dislocation pile-up to reactive the dislocation sources, thus dislocation pile-up has a significant role at lower scale plasticity.
2.1.3.3.3 Dislocation Nucleation
Dislocation sources generate dislocations for plastic slip. If the number of dislocation sources is reduced due to the small sample volume or absence of defects in a single crystal, other sources, which are located in unfavorable slip systems, are required to be activated. Therefore, higher flow stress is required to activate them [43].
2.1.3.3.4 Forest Hardening
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2.2 Introduction of Instruments and Techniques
2.2.1 Focused Ion Beam
Focused ion beam systems have been used in studies of materials and for technological applications for approximately twenty years. High-resolution imaging and flexible micromachining could be obtained with this technique. FIB is similar to a scanning electron microscope (SEM), except for the beam source. FIB works with an ion beam that could be operated at low beam current for imaging and high beam current for site specific sputtering or milling. On the other hand, SEM operates with an electron beam. The dual beam system (SEM/FIB) allows SEM observations of a specimen while machining of the sample by FIB. The configuration of the column is shown in figure 2.12. In FIB, when ions interact with the surface of the samples, secondary electrons are generated by their impact and are used to obtain high spatial resolution images. Generally gallium ions are used during milling; this allows precision machining of the samples under high- or low current. Modern FIB systems can reach a 4nm imaging resolution. In addition, coarse milling by use of a higher primary current allows us to mill a lot of material; fine milling by use of a lower current enables us to perform precise milling down to a submicron scale [45] [46].
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2.2.1.2 Pillar Fabrication by FIB
Focused gallium ion beam is increasingly used for making micrometer and sub-micrometer size pillars for the measuring of mechanical properties at small scale. As mentioned above, FIB is used to mill away the material. By changing the current, voltage, and the method of scanning the Ga+ beam, the amount of material milled away
can be controlled.
Uchic et al. first introduced a micro-compression test in order to measure the mechanical properties of materials at small scale [8]. In this method micro-pillars are fabricated by FIB and their mechanical properties are measured under uniaxial compression. Shan et al. extended this method to electron transparent range [48]. Kiener et al. fabricated copper micro-pillars for the determination of mechanical properties of copper at the micrometer scale. They used copper single crystals with a <110> {111} orientation. First, the copper single crystal was cut with a diamond saw to achieve a {111} surface with a {110}-side face along a <112> edge. Afterwards, both perpendicular planes were electro-polished in order to etch away the deformed layer, which was created during the cutting process. Moreover, the side faces were polished using an alumina suspension with a 1µm grain size to reduce the FIB milling time. The final polishing resulted in a 5µm-deformed layer, which was then removed by FIB with 30KV Ga+ ions. Figure 2.13 shows the orientation of the sample with respect to the
copper single crystal.
Figure 2.13: correlation between the sample dimensions and the crystal directions for micro-pillars [49].
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Finally, they were milled by 100pA to reduce the damage caused by the ion milling. Figure 2.14b shows a tilted SEM image of a micro-pillar along the sample edge. One of the methods that they used to minimize the tapering was to tilt the sample by 54° and mill using grazing incident ions. The advantage of this method is that the side planes are parallel to the specimen axis and no tapering occurs [49].
Figure 2.14: FIB fabricated micro-pillar samples (a) FIB image of the top view of a pre-form b) Tilted SEM view of a pillar after final milling with grazing ion impact. The TiN top layer is marked by an arrow [49].
W.D Nix et al. also used a FIB to fabricate sub-micrometer pillars of gold. They used a {001} oriented gold single crystal disc for pillar fabrication. First, they chose 3000pA current of Ga+ ions to mill out a carter in their sample by FIB and left a 4µm diameter
“island” in the center. By fabricating the pillar in a crater, they made sure that the indenter tip is in contact only with the pillar. Later, smaller currents and various tilt angles were used to get a fine structure of pillars. Figure 2.15 shows FIB gold pillars by W.D Nix et al. [11].
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Sriram et al. also made sub-micrometer copper pillars to investigate the load carrying capacity in twin boundaries [50]. They cut samples into a 1mm² and 100µm thick foil with a diamond saw then polished it down to 20µm. Later, the sample was mounted on an L-Shaped holder to put it into the FIB equipment. First of all a straight edge was milled at 2000pA to a depth of 1µm. Afterwards, the sample was repositioned in the FIB to get a perpendicular ledge to the beam. Ion beam current was progressively reduced from 3000pA to 300pA for making ledges and rough pillars. Rough pillars had a 2.5µm diameter and a 3µm length. For the finishing operation 10pA current was used. The final pillar has a diameter ranging from 120 to 140nm with aspect ratio of 1:3 to 1:5. Figure 2.16 shows SEM images of the process of making pillars by Sriram et al [51].
Figure 2.16: (a–e) SEM images of process of making pillars using FIB. (a) Triangular shaped film mounted on L holder; (b) FIB milling of platform to create pillars. (c) Sequence of rough pillars milled on the platform. (d)
10 Rough pillars milled. (e) Finished individual pillar [50].
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Table 2.1 shows the parameters for fabrication of FCC gold nano-pillars with diameter around 400nm [1]. Figure 2.17 shows the steps employed by Woo Lee.
Step Current (pA) Rin (μm) Rout (μm)
1 300 3 15 2 100 2 4 3 100 1 2.5 4 30 0.7 1.2 5 30 0.5 0.9 6 10 0.3 0.6 7 10 0.25 0.35 8 10 0. 23 0.27
Table 2.1: FIB parameters for the fabrication of 400nm gold nano-pillar [1].
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2.2.2 Micro Compression
The nano-indentation technique was developed to measure the mechanical properties of hard thin film and other near surface treatments in the early 1980s [52]. It has increasingly been used over the past three decades for measuring the mechanical properties of materials. This method is mostly used for the characterization of materials at micro- or nano scale and consequently for the development of nano- and micro electro mechanical systems [53]. Uniaxial deformation like micro-compression test is the easiest way to study of the plastic behavior, when the sample dimensions are reduced to the fundamental length scale for dislocation-based plastic flow.
Uchic initially used a conventional nano-indentation device with a flat-punch indentation tip to perform conventional uniaxial compression tests. Then micro-samples from single crystal, poly-crystal, intermetallic- and metallic glasses were milled by FIB and their mechanical properties were determined by a micro compression test. The applied forces at the micro newton scale and displacement measurement at the nanometer scale are plotted on graphs to draw load-displacement curves. The mechanical properties of materials can be interpreted from these curves [54]. Size dependent strengthening, intermittent and stochastic flows have frequently been observed by this technique [55] [8] [28].
Issues in Micro-Compression Test Result
When the mechanical properties of the micro-compression test are evaluated, the following items should be considered[7]:
• Size effect: The sample size effect in micro-compression is still under debate, with two major discussions considering dislocation starvation and source truncation. According to the previous experiments, the smaller pillars are mechanically stronger under compression.
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the micro-pillar is deformed. Later, the increase in the micro-pillar cross section and its hardening in the deformed volume cause a plastic deformation in the lower part of the micro-pillar. Consequently, this tapering should be considered when the mechanical properties for a tapered micro-pillar are discussed [7]. • Strain rates: the strain rate dependence of the flow stress is low for FCC
materials at room temperature [7]. Edington investigated bulk copper single crystal. For variation of the strain rate from 6.5×10-5 s-1 to 1.2×103 s-1 the shear
stress was increased by about 8MPa [58]. D. Kiener et al. performed micro-compression tests for copper {111} on a copper needle with different strain rates, which resulted in a flow stress that was lower by one order of magnitude. Therefore, the differences could be attributed to the scatter typically observed in lower scale mechanical experiments. Regarding the interpretation on strain rate dependence in micro-compression test, systematic tests should be carried out over a large range of strain rates and temperatures.
• Friction between flat punch tip and top surface of micro-pillar: Friction occurs between the flat punch tip and the top surface of micro-pillar. Raabe et al. noted that by increasing the friction coefficient, clear friction effects on the compression micro-pillar sample could be seen [59]. Friction also causes a multi-axial stress state and an increase of shear stress on the top surface of a micro-pillar.
• FIB induced surface damage: The most common damage due to FIB milling is the formation of an amorphous structure on the surface of samples. These damaged layers contain Ga+ resulting from Ga+ implantation [39]. Auger Electron
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response of the micro-pillar during the micro-compression test. Chapter four discusses how we can minimize the FIB induced surface damage.
• Buckling: Buckling elastic or plastic is common in a compression test and it is an even bigger concern in micro-compression tests. Consequently, it is important to know the detailed mechanisms of buckling for the micro-pillars and the different factors, which could contribute to such buckling. Elastic Euler buckling will not happen even with Al micro-pillars as long as the aspect ratio is below 25 [60]. Micro-compression tests conducted by a nano-indenter with conventional optical microscope makes precise force alignment challenging. When the force is misaligned with the micro-pillar’s axis, it results in a multi-axial loading (in contrast to desired uniaxial loading), leading to a drop in reaction force and the compressive force breaking down to a shear force and uniaxial components. Nowadays, the micro-compression tests are carried out by in-situ equipped with nano-indenters, which are mounted inside a SEM chamber. This technique allows accurate positioning of micro-pillars and indenter tip due to the higher resolution of in-situ SEM imaging compared to the conventional nano-indenters, which are equipped with optical microscope [7].
• Oxide layer: Even if the micro-pillars are immediately transferred into the nano-indenter after fabrication, prevention of oxide layer formation on micro-pillars is impossible. This layer acts as a confined layer, hence the micro-pillars are not naked and as an effect they represent different micro-compression curves. Moreover, chemical interaction of the oxide layer with the sample material has an impact on the material properties of the tested sample [61].
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2.2.3 Coating Instruments Used
In this study to modify the mechanical properties of the micro sized samples and to study the role of interfaces at micro-scale, thin films will be deposited on a copper single crystal.
We study the modification of the mechanical properties of micro scale materials by confinement and not by combining materials to form an overall structure that is different than the sum of the individual components. Consequently, the coating should be as thin as possible to maximally reduce the development of composite. Nevertheless, the coating layer should be strong enough for good adherence when the samples are deformed.
Carbon as an amorphous layer and chromium as a crystalline layer were chosen as confinement layers; pulsed vacuum arc technique is used for carbon deposition and magnetron sputtering for chromium deposition.
2.2.3.1 Cathodic Arc Deposition
The cathodic arc deposition is a form of physical vapor deposition consisting of the following steps:
• An electric arc vaporizes the cathode • The vaporized material forms a plasma
• The coated layer is obtained by condensing the species of the low-pressure plasma on a substrate.
In this process, the deposited species have a high kinetic energy usually ranging from 20eV to 200eV [63]. The deposition parameters such as arc current, pressure, deposition time and substrate temperature can be controlled precisely; As a result, layers with excellent quality, dense, hard, and very low concentration of defects can be prepared.
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deposition. The titanium nitride was deposited to improve commercial characteristics of machining tools [66] [67].
Vacuum arc discharge forms in the vapors of the cathodic material. The cathode material is deposited on the substrate in ionized state with high energy. The plasma may be contaminated with macro particles of ions, which is prevented by employing a magnetic filter [65]. This magnetic filter is shown in the following schematic picture of the cathodic arc chamber.
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2.2.3.2 Magnetron Sputtering
Magnetron sputtering has been used for many years for the deposition of coatings, which have different properties such as hard, wear resistant coatings, low friction coatings, corrosion resistant coatings, and coatings with specific optical or electrical properties [69].
Magnetron sputtering technique is a physical and non-thermal procedure during which atoms are ejected from a solid target into the gas phase by reason of the bombardment by energetic ions and are deposited on a substrate. A gas (the most common sputtering gas is argon which is non-reactive) is blown in to the vacuum chamber (normally 10-3
mbar) to be ionized by the imposed electric field to make the plasma. Therefore, the coating layer will have the same material composition as the target, including the impurities of the system. Figure 2.19 shows the schematic of a D.C magnetron sputtering set up. The vacuum pumping system, the gas inlet system and the power supply system are connected to the chamber.
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Following the bombardment of the target by ionized gas, many interactions occur on the target surface such as x-ray emission, photon generation, ionized atoms, secondary electron emission, backscattering, and liberation of neutral atoms. This target bombardment by ionized gas causes an increase in temperature, thus a cooling system is required [71].
Following parameters can be adjusted to improve the coating layer with this technique: • Pressure
• Substrate temperature • Current
• Voltage to the target
• The distance between target and substrate • Bias on substrate
Changes of these parameters can influence the coating microstructure and mechanical properties. For example the distance between target and cathode or the pressure of the chamber controls the number of collisions along the target to substrate path.
By decreasing the pressure, the collisions between electrons and the gas molecules decrease and can affect the coating porosity, crystallinity and texture. The current density can influence the sputtering rate [72]. Also, applying a bias to the substrate (Anode) helps to accelerate the sputtering of electrons or ions on the substrate. This parameter could affect the layer growth [73].
2.2.4 Automated Crystallographic Orientation Mapping in a TEM
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In this technique, the sample is scanned by the electron beam in combination with the beam precession. Afterwards, diffraction patterns are obtained from different zones of the scanned sample. The collected diffraction patterns are compared with pre-calculated diffraction pattern templates by software with a cross-correlation method and the best match pattern gives us the local crystal orientation. [74].
2.3 Conclusions
• Literature review on the plasticity theory, micro plasticity and dominant hardening mechanisms in micro plasticity such as Taylor hardening, dislocation pile-ups, dislocation starvation, dislocation nucleation and forest hardening was performed.
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Chapter Overview
Measuring mechanical properties at the micro scale is a combination of art and science and requires lots of patience. Considering that micro-pillar samples cannot be seen with the naked eye, mechanical tests only allow an interpretation to be made on the basis of indirect observation in this study; thus making this a challenging topic.
At this scale, preparation of the samples requires a lot of attention as well as testing and characterization. In this chapter, the procedures for the preparation of samples, mechanical tests, and post characterization of the micro-pillars are described.
3.1 Sample Preparation
Sample preparation for micro-compression tests on micro-pillars are divided into macroscopic preparation (bulk sample) and microscopic preparation (micro-pillars) techniques. Below, we have outlined the various procedures.
3.1.1 Macroscopic Bulk Sample Preparation
Figure 3.1 shows a high purity single crystal copper (99.999%) with (1, 1, 1) orientation, which was used as a bulk sample in this study. Only this particular bulk sample was used throughout all tests to maintain the same material for all experimental work. The surface preparation method was identical for all samples. Electro-polishing was used to obtain a clean, defect free and similar surface condition for all samples. However, in order to avoid a wavy surface or local over-heating of the sample caused by excessive electro-polishing, an initial mechanical polishing was performed.
Mechanical Polishing Materials • AccuStop Apparatus
• 1000 and 2000 GRIT grinding paper • Superglue
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amount of material to be removed from the examination surface. The samples were attached to the AccuStop by a small amount of superglue; they were then grinded against the 1000 and 2000 GRIT grinding paper.
Electro-Polishing Materials • LectroPol-5 by Struers • Ultrasonic Machine • Phosphoric Acid 85%
The samples that were attached to the AccuStop were immerged into acetone and placed into an ultrasonic machine. By this we can separate the samples from the apparatus. The copper single crystal samples were then electro-polished according to the parameters given in table 3.1 in a commercial LectroPol-5 instrument from Struers.
Figure 3.1: Single crystal copper sample
geometry employed in this work. Figure 3.2:AccuStop sample holder.
Material Single Crystal copper
Voltage 24V
Time 20s
Electrolyte Phosphoric Acid 85% Area of sample 0.5cm²
Temperature 22°C
Flow Rate 13
Table 3.1: electro polished parameters for polishing copper single crystal.
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3.1.1.2 Electron Backscatter Diffraction
After polishing, the electron backscatter diffraction (EBSD) technique was used to characterize the crystallographic orientation of the bulk sample. Figure 3.3 shows the EBSD result for a copper single crystal and indicates a surface misorientation less than 10° to [111].
It should be considered that the material properties of the single crystal depend on the crystallographic orientation [76]. For this reason an identical crystallographic orientation is applied for all experimental work. In this way, the changes of the mechanical properties of micro-pillars will be due to the difference in the confinement, not due to the different crystallographic orientation.
Consistently, prior to the fabrication of a new series of micro-pillars on bulk samples, the crystallographic orientation of the bulk sample was examined by EBSD.
Figure 3.3: EBSD of bulk copper single crystal surface.
3.1.2 Microscopic Sample Preparation
The Classical method for micro-pillar fabrication is FIB milling. A dual beam Quanta 3D FIB system manufactured by FEI Company was used to mill the micro-pillars.
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protected by photoresist. This technique does not guarantee for the pillar to have a same size and shape for each fabrication due to the different chemical etching condition. As mentioned earlier it is crucial to use the same size and shape of micro-pillars in this study. Therefore all micro-pillars in this study were fabricated by FIB using the same conditions such as current, voltage, and time to obtain same size and same shape micro-pillars.
3.1.2.1 Micro-Pillars Fabrication
We chose to fabricate micro-pillars for the reason that their geometry is appropriate and advantageous for obtaining a homogenous, uniform confinement. Many other micro-samples, like tensile samples have complex geometry and are therefore not appropriate.
As we mentioned earlier, it is essential to start off with same size micro-pillars to be able to distinguish the effect of various confinements on the mechanical properties of these micro-pillars. In this order, FIB helps us to fabricate same size micro-pillars by applying the same parameters during each fabrication.
In this study, the FEI QUANTA 3D dual beam SEM/FIB, which is a dual-beam system equipped with an Ominiprobe was used. This FIB instrument supplies 30kV Ga+ ions
with currents ranging from 10pA to 20nA.
To ensure the high quality and uniformity of the micro-pillar, we have to gradually decrease the current and rotate the sample during the fabrication process. These steps should be applied for all micro-pillars in an identical way and condition.
Different concentric circular patterns used for producing micro-pillars are shown in figure 3.4; the accelerated Ga+ ion beam bombarded the area between the inner and
outer circles, thus the material inside the inner circle and outside the outer circle remains.
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Coarse Milling
To fabricate the micro-pillar that can be seen in figure 3.5, higher ion beam currents (1nA-0.5nA) were used for coarse milling while the preformed micro-pillar was surrounded by a large cavity (35µm -30µm). Coarse milling reduces the milling time; however it does not allow us to accurately shape the micro-pillar. For this reason we first start with coarse milling to reduce the fabrication time to then finish the shape by fine milling.
A large cavity surrounding the pillar was designed for the following reasons:
• Imaging of the sidewalls of micro-pillars before and after micro-compression. • Ensuring the flat punch tip in micro-compression by nano-indentation tests does
not touch any other surfaces than the micro-pillar. • Facilitating the coating process.
• Optical microscope in the nano-indenter system allows for simple location and identification of the micro-pillars [77].
Fine Milling
With the use of lower currents (100pA-30pA) fine milling was conducted. To minimize the tapering and create a homogenous border, several rotations of the samples were performed during the milling.
Table 3.2 shows the parameters used for FIB to fabricate copper micro-pillars in this study. In this table, Din shows the diameter of inner circle and Dout shows the diameter of
the outer circle in the patterns of figure 3.4.
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Figure 3.4: The concentric circular patterns are used for producing micro-pillars.
Figure 3.5: the SEM snapshots during the micro-pillar fabrication.
10µm 10µm
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Step Current (pA) Din (μm) Dout (μm) Time (minute)
1 1000 8 35 51
2 500 8 30 51
3 100 4 12 45
4 30 3.2 14.25 15
Table 3.2: The focused-ion beam parameters for the production of copper micro-pillars.
3.2 Micro Compression Test
Micro-pillars with 3µm diameters were compressed in the Hysitron TI 950 TriboIndenter nano- indentation system, which is equipped with a 10µm flat punch tip. The tip size was chosen about 3 times larger than the micro-pillar diameter allowing the micro-pillar’s surface to be fully indented by the tip. Figure 3.6 shows the SEM images of the indenter tip used in this study.
Figure 3.6: flat punch tip with 10μm diameter.
As shown in figure 3.7, the Triboindenter is divided into several parts such as: • The transducer
• The transducer controller • Separate data acquisition system
The Triboindenter software captures the voltage signal from the transducer and the microscope scanner enables the displacement control while capturing image using
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Scanning Probe Microscope (SPM) technique. The probe or indenter tip, which is screwed to the transducer, has been used for indenting and also for imaging [53]. This machine generally is used for depth-sensing indentation experiments with a sharp tip; however, in this study the same platform is applied to perform conventional uniaxial compression tests.
Figure 3.7: Tool Schematic Diagrams of the Hysitron Triboindenter tool [78].
3.2.1. Optic Calibration with Large Radius Flat Punch Tip
After mounting the flat punch tip on the transducer (as depicted in figure 3.7), the tip is optically calibrated. The calibration is normally performed on a single crystal aluminum or polycarbonate. A residual plastic deformation larger than 1µm is usually required for locating the feature by optical microscope [79]. This procedure is difficult to apply with a large radius flat punch tip as the displacements necessary to see the features optically could not be reached with the maximum normal force of the standard transducer and the given testing materials. Two steps were performed for optic calibration:
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Zoom calibration was performed in ten different zoom levels. Given the difficulty of the situation mentioned and the lengthy process, the zoom calibration was completed using the H-pattern method (figure 3.8). In the H-pattern method, indentation is performed 7 times in an H- shape. Then, the machine is calibrated optically through the center of the H- pattern.
Figure 3.8: the H pattern on an aluminum single crystal.
3.2.2 Scanning Probe Microscopy (SPM)
One of the advantages of the Hysitron system is the possibility of imaging before and after indentation. It works with a specially designed force transducer and the SPM imaging software. The resolution of the SPM image is not as good as with a dedicated AFM due to the bluntness of the tip [53]. Therefore this method was used to find micro-pillars by applying a 2µN force for imaging although the micro-micro-pillars were damaged during probe scanning. Consequently this method cannot be used in this study. Figure 3.9 shows a damaged micro-pillar by scanning probe microscopy.
Figure 3.9: damaged micro-pillar by scanning probe microscopy.
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3.2.3 Loading Procedure
The Hysitron nano-indenter transducers are designed based on force-control. The load function used in this study for the micro-compression test is shown in figure 3.10 and the obtained load displacement curve is shown in figure 3.11.
Thermal drift should be considered for small indentation made over long periods of time therefore a total time of twenty seconds was chosen for the loading- and unloading process.
Every running transducer has a characteristic electrostatic force constant (ESF). This constant relates the necessary electrostatic applied force to the subsequent tip displacement. The relationship between force and displacement is not linear over large displacement distances. Consequently, it is essential and critical to know and calibrate ESF before all tests. This calibration is done by Air indentation.
Therefore, in this study, air indentation was performed on all samples before performing the micro-compression test. Triboindenter software automatically measured the displacement rate and it also extracted the load displacement data. Figure 3.12 shows an annealed single crystal copper micro-pillar before and after indentation. During micro-compression testing, the micro-pillars sink under the force of the compression. Therefore the deformation is carried by the substrate instead of the micro-pillar, which leads to inaccurate measurements. This effect of sinking-in may be amplified for micro-pillars with large aspect ratio. Another parameter, which affects the micro-compression result, is tapering effect. An ideal micro-pillar is perfectly cylindrical; however a slight tapering forms for most micro-pillars that have been fabricated by FIB-milling [80]. When we have tapering, the deformation takes place on the upper part of the micro-pillar and affects the results.
