The Pennsylvania State University. The Graduate School. College of Engineering NANO-LEVEL CHARACTERIZATION OF THE SURFACE PROPERTIES OF

Transcription

1 The Pennsylvania State University The Graduate School College of Engineering NANO-LEVEL CHARACTERIZATION OF THE SURFACE PROPERTIES OF ENGINEERED SILICON WAFER A Thesis in Engineering Mechanics by Xiaoning Xi 2010 Xiaoning Xi Submitted in Partial Fulfillment of the Requirements for the Degree of Master of Science August 2010

2 The thesis of Xiaoning Xi was reviewed and approved* by the following: Bernhard R. Tittmann Schell Professor Thesis Advisor Samia A. Suliman Assistant Professor Sulin Zhang Assistant Professor Judith A. Todd P. B. Breneman Department Head Head of the Department of Engineering Science and Mechanics *Signatures are on file in the Graduate School

3 iii ABSTRACT Surface properties of silicon are the key parameter to the success of silicon direct bonding technique in the semiconductor industry. The hydrophilicity and the roughness of silicon surfaces processed with three typical surface treatments in the direct bonding technique were systematically evaluated by atomic force microscopy (AFM). HF-treated silicon surfaces used for hydrophobic bonding showed negligible dependence of adhesion forces on humidity. However, HF treatment resulted in a considerable increase of the roughness, suggesting that additional smoothing processes are desired. RCA 1 treated and thermal oxidized silicon surfaces, without roughness increase, exhibited substantial increases in adhesion forces when environmental humidity increased from 10% to around 60%. Further rise of humidity resulted in a drop of the adhesion force. Molecular dynamics simulations of the water layer absorbed on an oxidized silicon surface suggested that there is a densification in the water structure at the vicinity of the liquid-solid interface. Such a change in the atomic structure of the water layer, depending on its thickness, gives rise to the non-monotonic adhesion force humidity relationship on hydrophilic silicon surfaces. Based on this, a quantitative model to describe the relationship was introduced. Since hydrophilic treated surfaces exhibit strong adhesion forces over a wide range of humidity, the direct bonding should be done at a low humidity to reduce water bubble forming at the bonding interface during annealing process.

4 iv TABLE OF CONTENTS LIST OF FIGURES... vi ACKNOWLEDGEMENTS... vii Chapter 1 Introduction Background Object and project overview Scanning probe microscopy and atomic force microscopy Principle of AFM operation AFM operation modes Contact AFM mode Non-contact mode Intermittent-contact mode Force distance curve Molecular dynamics simulation Simulation cell Ensembles Force field and molecular models CLAYFF force field Molecular models of water Structure of silicon dioxide Chapter 2 Sample preparations and experiment setup Sample Treatments Chemical etching method Thermal oxidation Experiment Setup Chapter 3 Experiment result and discussion As-received silicon wafer surface HF treated silicon wafer surface OH treated silicon wafer surface Thermally oxidized silicon wafer surface Chapter 4 Molecular Dynamics Simulation Simulation method Simulation results Chapter 5 Theoretical modeling Chapter 6 Summary and Conclusions Chapter 7 Future works... 45

5 v LIST OF FIGURES Figure 1-1. Inter-atomic force vs. distance curve Figure 1-2. Contact and non-contact AFM images of a surface with a droplet of water Figure 1-3. Forces vs. distance curves in vacuum (top), air (bottom) Figure 1-4. A typical force vs. distance curve for the Auto probe M5 AFM in air Figure 1-5. Structure of water molecule Figure 1-6. Crystal structures of (a) silicon (b) β-cristobalite Figure 3-1. Adhesion forces vs. relative humidity (a) 3-d and 2-d images (b) of the asreceived silicon wafer surface. The surface image size is 1 1μm Figure 3-2. Adhesion forces vs. relative humidity (a) 3-d and 2-d images (b) of the clean HF treated silicon surface. The surface image size is 1 1μm Figure 3-3. Adhesion forces vs. relative humidity (a) 3-d and 2-d images (b) of the as clean OH treated silicon wafer surface. The surface image size is 1 1μm Figure 3-4. Adhesion forces vs. relative humidity (a) 3-d and 2-d images (b) of the thermally oxidized silicon wafer surface. The surface image size is 1 1μm Figure 4-1. Construction of the simulation system Figure 4-2. Structure (left) and oxygen-oxygen radial distribution function obtained from the simulation of pure water Figure 4-3. Final structure of the absorbed water layer from MD simulation. On the left is the side view of adsorbed layer. On the right is the chart representing the number of water molecules in the adsorbed layer at corresponding distance from the interface. The relationship between the number of water molecules and distance was fitted to an exponential equation Figure 4-4. Structures of (a) the first 1 Å thick of the absorbed water layer at the interface, (b) 1 Å thick of the absorbed water layer 30 Å away from the interface, (c) oxygen ions in β-cristobalite Figure 5-1. Thickness of the adsorbed water layer vs. relative humidity on OH treated silicon surface by IR spectra obtained by David and Jeong Figure 5-2. Schematics of the AFM tip position and ice-ice contact area as a function of relative humidity immediately prior to snap off Figure 5-3. Adhesion force between a silicon tip and OH treated silicon surface calculated by Eqs The experimental data are also displayed for comparison... 43

6 vi ACKNOWLEDGEMENTS I am heartily thankful to my supervisor, Dr. Bernhard Tittmann, whose encouragement, guidance and support enabled me to finish this project. It is my pleasure to thank those who made this thesis possible such as Jinjie Shi who helped me a lot with necessary sample process. I also would like to make a special reference to my husband Bu, who is always there to support me. Lastly, I offer my regards and blessings to all of those who supported me in any respect during the completion of the project such as Sahar, Matt, and Dr. Miyasaka.

7 Chapter 1 Introduction 1.1 Background As almost all electronic products nowadays contain semiconductor devices, the semiconductor industry has become the foundation of the digital innovation. The semiconductor industry is built on silicon materials. And in various areas of the industry, such as microelectromechanical systems (MEMS), microelectronics, and optoelectronics, there are frequent needs to integrate silicon based devices together. These materials integrations require welldeveloped techniques to perform silicon bonding 1,2. A number of techniques have been developed for this purpose, to bond silicon wafers or substrates together. These techniques can be categorized into anodic bonding, intermediate layer bonding, and direct bonding 3. The anodic bonding needs special equipment and the bonding quality is greatly influenced by the thicknesses of glass and oxide layer on the silicon wafer surface. Moreover, high voltages used in anodic bonding can potentially cause breakdown of oxide layers or a shift in threshold voltage. Intermediate layer bonding techniques have problems such as outgassing, low positioning accuracy, poor long-term reliability and uncertain bond quality. Comparing to these two types of methods, silicon direct bonding is of special interest since neither external force nor electrical field are needed. Additionally, direct wafer bonding is very suitable for heterogeneous integrations of dissimilar materials, such as building silicon-on-insulator (SOI) structures. Since SOI is becoming the mainstream technique for reducing transistor sizes on microchips down to 30nm, helping the semiconductor industry to extend Moore s Law 3, silicon direct bonding techniques have been receiving dramatically increased attentions recently.

8 2 There are basically two types of silicon direct bonding techniques: hydrophilic direct bonding and hydrophobic direct bonding. Traditional silicon direct bonding is done with the aid of hydrophilic surfaces. Surfaces of silicon wafers are modified to be hydrophilic by a series of surface treatments. The two surfaces are then brought into close contact. The bonding is formed via the OH formed on the hydrophilic surfaces at room temperature. The bonded silicon wafers are annealed above 1000 C to strengthen the bonding and diffuse the interface. Stronger bonds of Si-O-Si and Si-Si form when annealing. During this process, water present in the interface decomposes into bubbles, which weakens the bonding strength. The amount of water present between the surfaces is related to their wetting properties. The silicon direct bonding can also be done with the same procedure on hydrophobic surfaces to decrease the water molecules present between the surfaces. For both methods, the bonding quality is mainly affected by the cleanliness, uniformity and smoothness of the wafer surface 4,5. However, treatments to modify the surface hydrophobicity can seriously alter theses surface properties. For instance, surface roughness usually deteriorates after chemical hydrophobic treatments. Therefore, understanding the surface properties after various surface treatments, especially the surface hydrophilicity and roughness, is critical to improve both the hydrophilic and hydrophobic silicon direct bonding techniques. Analyses of the hydrophilicity of silicon dioxide have been done previously to understand hydrophilic silicon surfaces but discrepancies exist among literatures 6,7. There is also a lack of a systematic analysis of wetting properties and surface roughness changes after various surface treatments.

9 3 1.2 Object and project overview The considerations discussed above prompted us to conduct a systematic study of hydrophilicity and surface roughness of silicon wafer after different common surfaces treatments used in the semiconductor industry. Surface properties were evaluated utilizing Atomic Force Microscopy (AFM) with nano-scale resolutions. Molecular Dynamics (MD) simulations of the atomic structure of the absorbed water layer were conducted to understand the wetting property on oxidized, hydrophilic silicon surfaces. Based on experimental data and simulations, a mathematic model of the wetting property was then introduced. Results in this thesis are expected to provide better understandings of silicon surface properties and guidances for conducting surface treatments in the silicon direct bonding. 1.3 Scanning probe microscopy and atomic force microscopy Scanning Probe Microscopy (SPM) is a family of microscopies that conduct surface measurement by scanning a fine probe over the sample surface. The development of SPM techniques has greatly facilitated the advancement of nanotechnologies, by enabling innovative research tools such as studying surface properties at atomic scale, 3-D surface topography mapping and even manipulating individual atom. The first instrument in the scanning probe microscopy (SPM) family, called scanning tunneling microscopy (STM), was developed by G. Binnig and his co-workers at IBM Zurich Research Laboratory in STM can observe the surface in atomic scale but it can only be used on conductive samples. Later, other types of SPM were developed to probe nonconductive surfaces based on molecular forces between a tip and the sample surface. Nowadays, various types of SPM not only allow the visualization of topography in nanometer scale but also

10 4 can detect other surface properties based on the physic-chemical interaction between the detection tip and material surface. The SPM family now includes STM, Atomic Force Microscopy (AFM), Lateral Force Microscopy, Magnetic Force Microscopy, Electric Force Microscopy and so on. Among these techniques, AFM is most commonly used fot imaging surfaces of both insulating and conductive samples with nano/sub-nano resolution. AFM was invented by Binnig, Quate and Gerber in AFM can image topography and obatin information of structural and dynamic feature of surfaces at micrometer to nanometer levels. Most AFM can work in air, liquid or vacuum environment to gather three dimension topographic images of the sample surface without special sample preparations. This technique can be applied to different types of materials including semiconductors 10,11, biological systems and polymers 11, Another important usage of AFM is to study the force spectroscopy, i.e., measuring forces as a function of distance This allows the study of inter and intramolecular forces, and has become one of the most promising and interesting research areas made available by SPM 22. In a word, AFM has become a powerful tool in the development of microsystems and nanotechnology. AFM has been proven to be an effective tool for quantitative studies of various surface properties, and has been used in some studies to measure surface adhesion forces 6,7,23,24. In this work, adhesion forces were measured on silicon surfaces treated with typical treatments used in silicon direct bonding techniques. Quantitative data have been gathered to investigate adhesion forces and their humidity dependence resulted from different surface treatments. The surface roughness of treated samples was also investigated using AFM to provide references for silicon direct bonding techniques.

11 Principle of AFM operation AFM uses a sharp tip, usually a few microns long and less than 100 angstroms in diameter, to probe the sample surface. The tip is loaded at the free end of a μm long cantilever. The position of the cantilever is controlled by a piezoelectric scanner. When the tip is brought to near the sample surface, the force between the tip and sample cause the cantilever to bend. When the tip scans vertically on the surface, change of force causes the deflection of the cantilever. The deflection is measured using laser light reflected off the back of the cantilever onto a position-sensitive photodiode detector and recorded by a computer to generate force spectroscopy. There is also a feedback loop causing the piezoelectric scanner to retract or extend to control the deflection. When the tip scans across the sample surface, this feedback loop can keep the force between the tip and sample constant by retracting and extending the cantilever. By recording the retraction and extension of the cantilever, a map of the surface topography can be obtained AFM operation modes Different available imaging modes are available: contact mode, non-contact mode, intermittent contact mode 25. The most widely used is the contact mode (C-AFM). In this regime, the AFM tip is in intimate repulsive contact with a surface. In order to understand these modes, forces between the tip and sample surface need to be studied first. Among the several forces that contribute to the deflection of the AFM cantilever, the main force is the interatomic force, called van der Walls force. It is dependent on the distance between the tip and the sample. The relationship is showed in Figure 1-1.

12 6 Figure 1-1. Inter-atomic force vs. distance curve 25. Two distance regimes are marked on Figure 1-1. In the contact regime, the AFM tip is held a few angstroms from the sample surface, the force between the tip and the sample surface is repulsive; in the non-contact regime, the tip is held on the order of ten to hundreds of angstroms from the sample surface and the inter-atomic force between the tip and sample surface is attractive Contact AFM mode In the contact AFM mode, also known as repulsive mode, an AFM tip in brought to a few angstroms above the surface. The tip is attached to the free end of a cantilever with relatively low spring constant. This spring constant needs to be lower than the effective spring constant holding the atoms of the sample together 25. In Figure 1-1, at the right side of the curve the atoms are separated by a large distance. As the atoms are gradually closer to each other, they begin weakly attracting each other. This

13 7 attraction increases as the atoms are brought closer until the atoms are close enough for their electron clouds to resist each other electrically. This repulsive force weakens the attractive force as the inter-atomic distance decreases. The force becomes zero when the distance between the atoms reaches a few angstroms. Then the total force becomes repulsive and the atoms are in contact. As shown in the Inter-atomic force vs. distance curve, the slope of the curve is very steep in the contact regime. It means when the cantilever pushes the tip against the sample, the cantilever bends rather than forcing the tip atoms closer to the sample atoms. In the contact mode, the AFM can generate the topographic data in two different modes: constant-height or constant-force mode. Constant-height mode is often used for taking atomicscale images of atomically flat surfaces, where the cantilever deflections and thus variations in applied force are small. The constant-force mode is generally preferred for most applications. In constant-height mode, the height of the scanner is fixed as it scans. So the spatial change of the cantilever deflection can be used directly to generate the topographic data. In constant-force mode, the deflection of the cantilever is the input to a feedback loop to adjust the scanner up and down in the vertical direction to keep the cantilever deflection constant. In this case, the topography image is generated from the scanner's motion. With the cantilever deflection is held constant; the total force applied to the sample is constant. In the constant-force mode, the speed of scanning is limited by the response time of the feedback circuit, but the total force exerted on the sample by the tip is well controlled Non-contact mode In the non-contact (NC) mode, an AFM cantilever is vibrated near its resonant frequency (typically from 100 to 400 khz) with amplitude of a few tens of angstroms. Then it detects changes in the resonant frequency or vibration amplitude as the tip comes near the surface of a

14 8 sample, on the order of tens to hundreds of angstroms from the surface. This area is indicated on the van der Waals curve of Figure 1-1 as the non-contact regime. The resonant frequency of a cantilever varies as the square root of its spring constant. In addition, the spring constant of the cantilever varies with the force gradient loaded on the cantilever. The force gradient is the derivative of the force versus distance curve which changes with the tip-to-sample distance. Therefore, variations in the resonant frequency of a cantilever can reflect changes in the sample topography. Different from contact AFM, the NC AFM measures sample topography with little or no contact between the tip and the sample. Non-contact AFM can also be used to measure the topography of insulators and semiconductors as well as electrical conductors. Because the total force between the tip and the sample in the non-contact regime is so small, usually only N, so NC AFM mode causes little damage when studying soft or elastic samples and avoids contamination to the sample at the mean time. Figure 1-2. Contact and non-contact AFM images of a surface with a droplet of water 25. When scanning rigid samples, contact and non-contact images may look the same. However, if there are a few mono-layers of water on the surface, the images may look quite different. An AFM probe operating in the contact mode will penetrate the liquid layer to image

15 9 the underlying surface, while in the non-contact mode, the AFM will image the surface of the liquid layer (see Figure 1-2) as part of the topography of the sample surface. For NC AFM, the small total force is more difficult to measure than the force in the contact regime. Cantilevers used for NC-AFM must be stiffer or they can be pulled into contact with the sample surface. The small force values and the stiffer cantilevers make the NC-AFM signal very weak and therefore difficult to measure. Thus, a sensitive, AC detection scheme is used for the NC-AFM operation Intermittent-contact mode Intermittent-contact atomic force microscopy (IC-AFM), also known as tapping contact AFM is similar to NC-AFM. The difference is that for IC-AFM the vibrating cantilever tip is closer to the sample so that when vibrating the tip just barely hits, or "taps" the sample. The IC- AFM operating region is indicated on the van der Waals curve in Figure 1-1. Similiarly with the NC AFM, for the IC-AFM the cantilever's oscillation amplitude changes with the tip-to-sample spacing. Measurement of these changes will generate the image of the topography Force distance curve There are several features of the AFM that make it suitable for force mapping, such as the sensitivity of the displacement, small tip-to-sample contact area and the ability to operate under various conditions 26. With commercially available cantilevers, the AFM can be used to measure forces accurately down to approximately 10 pn 27. It is possible to investigate the complicated inter- and intra-molecular interactions, magnitudes and time-dependence of rupture forces, the mechanical properties of molecules and so on 18, To evaluate how the force measuring

16 10 experiments are realized, it is necessary to understand how force-distance curves are generated and what information they can provide for the tip-sample interaction. An AFM force-distance curve (f-d curve) is a plot of tip-to-sample forces vs. tip-tosample distance. This technique can be used to analyze surface contaminants, viscosity, lubrication thickness, and local variations in the elastic properties of the surface. In fact, an f-d curve directly reflects the deflection of the cantilever versus the extension of the piezoelectric scanner, measured using a position-sensitive photo detector. Other than the van der Waals force, variations in the local elastic properties, contaminants and lubricants, as well as the thin layer of water on the sample surface in air, can affect the measurement of f-d curves. In experiments, f-d curves are quite complex and vary especially with different samples. The f-d curves in Figure 1-3 are simplified ones, just for discussion and understanding of the curve.

17 11 Figure 1-3. Forces vs. distance curves in vacuum (top), air (bottom) 25. At the left side of the curve, the scanner is fully retracted and the tip is far away from the sample surface, so there is no force and the cantilever is un-deflected. As the scanner extends, the tip approaches the surface, so it experiences an attractive van der Waals force until it snaps onto the surface (point a). At this time the cantilever suddenly bends slightly towards the surface. As the tip moves further, the cantilever deflects away from the surface, approximately linearly (region b). At the right end of the plot the scanner is in full extension, and then the scanner begins to retract. The cantilever deflection retraces the same curve as the scanner pulls the tip away from the surface.

18 12 In air, the retracting curve is often different because a monolayer or a few monolayers of water exist on many surfaces. As the scanner pulls away from the surface, the water holds the tip in contact with the surface longer, bending the cantilever strongly towards the surface (region c). The scanner keeps retracting and the tip springs free at the snap-back point (point d). This snapout displacement is dependent on several factors such as the tip size, and the nature of the surface and thickness of the water layer. As the scanner continues to retract after the snap-back point, the cantilever remains undeflected as the tip is moved far away from the surface. In a typical f-d curve, the force applied after the tip makes contact with the surface can provide a measurement of the stiffness of the sample. And the force required to pull the sample up from the surface is a measure of the adhesion force between the tip and the sample. And this force is what we focused on in our research work. Figure 1-4 is a typical force distance curve for Auto probe M5 AFM in air. The curve represents the force experienced by the cantilever vs. the vertical position of the scanner. The distance between the zero line and point a gives the magnitude of the adhesion force for each set of experiments. Figure 1-4. A typical force vs. distance curve for the Auto probe M5 AFM in air 25.

19 13 The most interesting regions of the force distance curve are two non-contact regions, containing the snap-in contact and the snap-out contact. The non-contact region in the approach curve gives information about attractive (van der Waals force) or repulsive forces (van der Waals in some liquids, double-layer, hydration and steric force) before contact; this discontinuity occurs when the tip-sample force exceeds the spring constant of the cantilever (pull-on force). The noncontact region in the withdrawal curve contains the snap-out contact, a discontinuity that occurs when the cantilever s spring constant is greater than the tip-sample adhesion forces (pull off force). A convenient way to precisely measure forces is to convert them into deflections of a spring, according to Hooke s law: Eq. 1-1 Where the acting force F, is determined by the cantilever deflection and the spring constant of the cantilever. Although the spring constants for the cantilevers are usually given by the manufacturer, the actual spring constant may vary from this value by an order of magnitude. Therefore, it is necessary to determine the spring constant experimentally. There are three mainly used method which involve determining: (i) the resonant frequency of the cantilever before and after adding a small mass to the tip 31, (ii) ascertaining the unloaded resonant frequency with knowledge of the cantilever s density and dimensions 32, or (iii) thermal fluctuation of the cantilever 33. In equation (l), the acting force leads to a total bending z of the cantilever due interaction with the surface. The real probe sample distance is then given by: Eq. 1-2 Where z is the distance between the sample surface and position of the cantilever and z is the sum of the cantilever deflection and sample deformation. Since we do not know in advance the cantilever deflection and the sample deformation, the distance that can be controlled is the

20 displacement of the piezo tube. Therefore, the raw curve obtained by AFM should be called deflection displacement curve rather than force-distance curve Molecular dynamics simulation Molecular dynamics (MD) is a computer simulation technique to dynamically simulate an atomic system. Dynamic behaviors of atoms in the system are updated over discrete time intervals, which are called time steps (usually at the level of s). Interatomic forces at each time step can be calculated with empirical interatomic potential models or quantum mechanics, while velocities and positions of atoms are usually governed by classic Newton s Law. MD simulations have been proven to be able to not only reproduce the structure and properties of various types of materials, but also provide distinct insights to the structure-property relationship. For this reason, it has been increasingly used in the past decade to study material related problems otherwise too difficult to investigate experimentally. MD simulation sets up a simulation cell which contains a number of atoms. The atoms are usually considered as point charges. Interactions between atoms are determined from the potential energy. The potential energy is most commonly determined from empirical short-ranged potentials and long-ranged Coulombic interactions, both of which are the functions of the separation between particular atoms. Forces are then derived from gradients of potential energies with respect to interatomic distances. The total force on each atom can be obtained by summing up all the forces exerted on it. According to Newton s 2 nd law, the acceleration of each atom in the system can be calculated. The velocity and coordinates of the atoms in the system are then calculated with initial values and lead the atoms to move over a very small time step. After the time step, a new cycle of computation begins with the new atomic coordinates and velocity. The time step used in MD simulation is at the order of femtosecond (10-15 second). As the typical

21 15 atomic thermal vibration is at the order of second, the choice of femtosecond level time step ensures that fast atomic motions can be probed properly in the simulation. A MD simulation may consist of up to several million time steps therefore the total simulated time can be on the order of pico- and nano- second Simulation cell The choice of simulation cell size depends on many factors. Usually the larger the simulation cell is, more features of the simulated material can be reproduced and more realistic the simulation would be. Also simulation cell size must be large enough to avoid boundary condition artifacts. Boundary conditions in MD simulations are often treated by choosing fixed values at the edges, or by employing periodic boundary conditions, all of which would cause artifacts if the cell size is too small. However, the cell size is limited by the computing power and time. Larger cell size includes more atoms and therefore requires more in computational time and power. In a word, the simulation cell size should be chosen based on the research purpose and available computation resources. But it must be, at least, sufficient large to reproduce structure features interested in the simulation and avoid boundary condition artifacts Ensembles In an MD simulation different statistical mechanical ensembles have different definition of temperature, volume and energy in the system. The canonical (NVT) ensemble has a constant number of atoms (N), volume (V), and temperature (T), while the system s energy can be variable. The microcanonical (NVE) ensemble has constant system energy but the temperature is allowed to change. The isothermal-isobaric (NPT) ensemble has a fixed system pressure while the

22 16 system s volume is fluctuate. Because the atoms in the system will move due to the forces governed by the potential energy equations, atom velocities will change, thus the temperature may change. In an ensemble with constant temperature, a thermostat is required to maintain the temperature. In addition to a thermostat, a barostat algorithm will be applied to keep the pressure constant in the NPT ensemble. There are many thermostats available based on different algorithms. In this study, different ensembles were used based on required simulation conditions. Berenson thermostat algorithm was used for buck/ surface simulation through the study. Details of the algorithm please refer to reference Force field and molecular models The degree of precision of the MD simulation is mainly dependent on the potential energy ensemble used. Potential energy is a key parameter in MD simulation. Short range potential energy equations prescribe the energy between atoms separated with a given distance. Potential models were first developed to study gas and crystalline materials There are several different potential models to describe the structure of silica and silicate CLAYFF force field In this study, a general force field, CLAYFF 42, developed for the simulation of hydrated mineral systems and their interfaces with aqueous solutions, was used. CLAYFF is based on an ionic (nonbonded) description of the metal-oxygen interactions associated with hydrated phases. All atoms are represented as point charges and are allowed complete translational freedom within this force field framework. Metal-oxygen interactions are based on a simple Lennard-Jones (12-6) potential combined with electrostatics. The empirical parameters are optimized on the basis of

23 17 known mineral structures, and partial atomic charges are derived from periodic DFT quantum chemical calculations of simple oxide, hydroxide, and oxyhydroxide model compounds with well-defined structures. Different from others work 19,43, a set of experimental crystal structure refinements of these model phases was incorporated to parameterize the empirical force field, rather than relying on quantum-mechanical calculations alone. The CLAYFF force field provides a general set of simple interatomic potentials that help understand the complex behavior of natural hydrated materials. Parameterization of CLAYFF using a set of simple structurally well-characterized hydrated phases allows good transferability of the force field parameters while maintaining full flexibility of all atoms and crystallographic cell parameters. CLAYFF accurately describes the bulk structures of a broad range of hydroxide and oxyhydroxide phases. The use of a simple nonbonded interaction potential to describe metal oxygen bonds and harmonic terms to describe water and hydroxyl bonding provides an efficient and accurate basis for simulating large systems involving thousands to millions of atoms Molecular models of water Water, though very common, has a unique molecular structure and some special properties. The asymmetry in the water molecule (Figure 1-5) creates a strong dipole moment, which gives rise to water s special properties, such as its anomalous thermal expansion and high surface tension. Much effort has been made to create adequate computational models of the water molecule so water structures and properties under different conditions can be simulated. These models include the widely used single point charge (SPC) model, TIP4P and a number of other models.

24 18 O H H Figure 1-5. Structure of water molecule. Single point charge (SPC) water model was developed by Berendsen 44 to represent water, hydroxyl, and oxygen-oxygen interactions. SPC model has partial charges centered directly on each of three atoms, and the short-range interactions represented by a simple Lennard- Jones term. Bond stretch and bond angle terms are introduced into the SPC water model using the expressions determined by Teleman to ensure full flexibility for the water and hydroxide components 45. By adding one or more charged dummy atoms into the simple water molecular model, more sophisticated models, for example, TIP4P (4 site model), TIP5P (5 site model), have been developed. Although SPC model is simpler, in comparison to these complex models, it is still widely used, not only because of its higher computational efficiency, but also because it has been proved in some occasions to be more accurate 46. For example, SPC has been successfully used in a variety of molecular simulations to evaluate water structure and properties 44,47-49 and for the interaction of water with hydroxide mineral surfaces 50,51. Therefore, SPC water model was used in this study.

25 Structure of silicon dioxide Silicon dioxide, also known as silica, has several polymorphic forms including amorphous silica, rhombohedral α-quartz which is the stable crystalline phase under normal condition and several other crystalline phases 52. Studies have shown that the structure of the thermal oxidized silicon surface usually is amorphous at long range However, since pure silicon has a cubic structure (Figure 1-6 (a)), a well-grown oxidized layer on its surface would have a cubic-related structure as well, at least within a short distance from the interface. Indeed, studies have found that the structure of the oxidized layer at the vicinity of the interface has a distorted cristobalite structure 56,57. For this reason, cubic cristobalite structure is chosen as the structure of the silicon dioxide layer in the simulations of this study. Furthermore, we believe the structure of the oxidized layer, though would affect quantitative results, is not a determinant factor in the adhesion force humidity relationship. Since the aim of simulations in this work is to provide a qualitative understanding, the ideal cubic structure, β-cristobalite (Figure 1-6 (b)), is chosen to reduce the complexity of potential models for our simulations. (a) (b) Figure 1-6. Crystal structures of (a) silicon (b) β-cristobalite.

26 Chapter 2 Sample preparations and experiment setup 2.1 Sample Treatments Chemical etching method Hydrofluoric acid solutions are widely used in the wet-chemical cleaning process to etch the films of silicon dioxide (SiO 2 ), silicon glasses and silicon nitride (Si 3 N 4 ) grown or deposited on Si wafer 58. There is always a very thin layer of native oxide on Si wafer, usually nm thick. It can be removed by a brief immersion into the diluted (typically 1:50 or 1:100) HF solution at room temperature. The surface wetting property will change from hydrophilic to hydrophobic when the oxide is removed. Research has been done to investigate the high degree of passivation of HF treated Silicon surfaces 59. These surfaces are now known to be oxide-free and passivated with H. The H-terminated surfaces are hydrophobic in nature and are not wetted by aqueous solutions. To prohibit the reoxidization of HF treated silicon surface 59, we immediately dry the surfaces with argon instead of rinsing them with water after taking the sample out of HF solutions and then keep the samples in a vacuum chamber. Mixture of HF and ammonium fluoride (NH 4 F) solutions which is known as buffered oxide etch (BOE or BHF) is used for pattern delineation etching of oxide and glass films. BOE has a more stable etching rate and reduces the loss of photo-resist polymer films 60. Surfactants can be added to improve the wetting characteristics or to decrease roughness of the Si surface 61. A commonly used BHF has volume ratio of NH 4 F (40wt%)- HF(49wt%). It contains only,

27 21 and very little free HF acid. The SiO 2 etching rate of is four or five times as fast as that for HF species in aqueous HF acid 62. Acidic or basic solutions mixed with H 2 O 2 are the other predominant way to passivate Si surfaces chemically by growing a thin layer of SiO 2. This is also the basis of the RCA standard clean developed by Kern in These clean processes leave a layer of 6-15 Å hydroxylated oxide on the Si surface, which prevents recontamination of the Si. Such surfaces are hydrophilic in nature and are easily wetted by aqueous solutions. The oxides left behind after these surface treatments are similar to the thermally grown oxides in some respects. The oxides tend to be ~10-15 Å thick, depending on the process temperature as well as the solution chemistry used 64. RCA standard clean contain two kinds of solutions: SC-1 and SC-2. These solutions have been widely utilized for over 40 years in fabrication of Si semiconductor devices. The originally composition of SC-1 solutions ranges from 5:1:1 to 7:2:1 parts by volume of H 2 O: H 2 O 2 :NH 4 OH: DI H 2 O is used and the H 2 O 2 is electronic grade 30 wt% H 2 O 2. The NH 4 OH is 27% (wt/wt% based on NH 3 ). The original composition for the SC-2 solution ranges from 6:1:1 to 8:2:1 parts by volume of H 2 O: H 2 O 2 : HCl. The H 2 O and H 2 O 2 are same with that mentioned above. The HCl concentration is 37 wt%. This is a standard silicon wafer cleaning method in wafer manufactory. For our experiment, to generate a thin layer of silicon oxide on the silicon wafer; we can just use RCA 1 solution 7. The exact compositions for both solutions are not critical for performance. Cleaning in either mixture is carried out at C for minutes and then rinsed in running DI water. There are some modifications of the RCA cleaning process: Reduction of the NH 4 OH concentration in SC-1 by a factor of 2-10 to reduce micro-roughening of the silicon surface and enhance particle removal 65 ; Dilution of SC-1 and SC-2 with DI H 2 O to various concentrations does not affect the cleaning performance 66.

28 Thermal oxidation Thermal oxidation is a way to grow oxide layer on the surface of a Si wafer in microfabrication of semiconductor. With such a layer of oxide, the surface wetting property of Si surface is hydrophilic. The technique makes an oxidizing agent to diffuse into the wafer and react with it at high temperature. The oxide layer gained in this way is called high temperature oxide layer (HTO). The growth rate is often predicted by the Deal-Grove model 67. Thermal oxidation of silicon is usually carried out at a high temperature between 800 and 1200 C. It may use either water vapor or molecular oxygen as the oxidant, so called either wet or dry oxidation. Thermal oxide combines silicon substrate with oxygen supplied from the ambient. Therefore, the oxide layer grows not only up out of the wafer but also down into it unit thicknesses of oxide will be produced for every unit thickness of silicon consumed. 2.2 Experiment Setup A homemade environmental chamber with a hydrometer is constructed. The humidity change in the chamber can be sensitively monitored by the hydrometer. The humidity is controlled by water vapor and dry nitrogen gas. The temperature is maintained at 23±0.5 C for all the measurements and relative humidity is used. Measurements of adhesion force vs. humidity were done in the process of increasing of humidity in case when the humidity decrease in the chamber the water layer still remain on the sample surface. The cantilever is an important element of the AFM. Its performance is largely dependent on its mechanical properties. Commercial cantilevers are usually made of silicon or silicon nitride, both of which are covered with a native oxide layer of 1 2 nm thickness 68. The mechanical properties of cantilevers are characterized by the spring constant and the resonance

29 23 frequency. Silicon tips with appropriate higher force constant are used cover the complete range of forces measured in my experiment. My earlier experiment showed that silicon nitride tip with small force constant cannot detect the large force at higher humidity. Plus silicon tips are widely used to measure the adhesion force in previous studies of on silicon/silicon oxide surfaces 6,23. The thin adsorbed layer of silicon tip is also considered in the force calculation model later. During the measurement process, when getting the force constant curve, a smaller region of tip movement was set to reduce the wear of the tip. For example instead of the [-1, 1] region, a [-0.3, 0.2] period may be applied as long as the adhesion force presents itself. Adhesion force at corresponding humidity is the average of more than thirty measurement results.

30 24 Chapter 3 Experiment result and discussion 3.1 As-received silicon wafer surface (a) (b) Figure 3-1. Adhesion forces vs. relative humidity (a) 3-d and 2-d images (b) of the as-received silicon wafer surface. The surface image size is 1 1μm. Firstly the adhesion force vs. relative humidity on as-received sample surface is measured. The result, shown in Figure 3-1(a), suggests that the surface exhibits hydrophilic

31 25 property: the adhesion force has high dependence on relative humidity. The force first increases with the humidity, reaches at a maximum of 138nN at RH = 70% and then decrease with the further increase of humidity. Although surfaces of a clean pure silicon wafer should be hydrophobic, a thin native oxide layer, typically nm thick, forms on the silicon surfaces and changes the surface to hydrophilic. The thickness of the absorbed water layer on the hydrophilic surface increases with the humidity, which leads to the increase of adhesion force. More study will be introduced later to explain why the adhesion force decrease at higher humidity. From the topography image (b), we can see that the surface is quite smooth with roughness measured as 2.3 Å RMS.

32 HF treated silicon wafer surface (a) (b) Figure 3-2. Adhesion forces vs. relative humidity (a) 3-d and 2-d images (b) of the clean HF treated silicon surface. The surface image size is 1 1μm. The as-received silicon wafer was then treated with diluted HF. HF treatment removes the native oxide layer and leaves the surface hydrophobic. HF treatment is used for silicon wafer cleaning as well as the hydrophobic silicon direct bonding. Hydrophobic surfaces bonding has advantages as it can reduce the bubble on the interface formed by the absorbed water layers on the wafer surfaces which will weaken the bonding strength 69. Our experimental result in Figure 3-2(a) shows that a short time (5 minutes) of immersion into the diluted HF has effectively

33 27 reversed the surface to be hydrophobic. The adhesion force becomes much smaller (around 20nN) after the treatment and shows little change with the humidity. Without the aid from the humidity to the adhesion force, hydrophobic bonding can only be done by bringing two wafers extremely close so that Si-Si bonding can form directly. However the AFM result shows the surface roughness increases dramatically to 15.7 Å RMS after the treatment. Such high roughness prevents a large portion of the surfaces from close contact, therefore is detrimental for a high bonding strength. Although hydrophobic silicon direct bonding is promising, additional surface treatment is required to flatten the surface before direct bonding performance.

34 OH treated silicon wafer surface (a) (b) Figure 3-3. Adhesion forces vs. relative humidity (a) 3-d and 2-d images (b) of the as clean OH treated silicon wafer surface. The surface image size is 1 1μm. An alternative to perform direct bonding is to modify the silicon wafer surfaces to hydrophilic. The adhesion force between OHˉ absorbed on hydrophilic surfaces would aid the bonding, so the bonding can be done at room temperature 70. After annealing at high temperature, the hydrogen trapped between the surfaces diffused away as water, and Si Si bonding or Si O bonding is formed. There are two commonly used methods of hydrophilic treatment for silicon wafers: chemical washing and thermal oxidation. In RCA 1 washing, a thin layer of oxide is

35 29 generated. The oxides left after these surface treatments are similar to the thermally grown oxides in some respects. But for chemical etching method, the oxidation only happens at the interface of silicon and chemical solution, thus Si-Si direct bonding can be achieved. The force-humidity curve in Figure 3-3 has the similar tendency with that of the as received silicon wafer but shows more change on humidity. The adhesion force reaches at a maximum of 134 nn at RH= 50%. The topography image provides surface roughness as 1.9 Å RMS. Therefore, RCA 1 treatment effectively improve the wetting property of the as received silicon wafer without increasing the surface roughness. This kind of surface treatment is easy to conduct and is beneficial for bonding process.

36 Thermally oxidized silicon wafer surface (a) (b) Figure 3-4. Adhesion forces vs. relative humidity (a) 3-d and 2-d images (b) of the thermally oxidized silicon wafer surface. The surface image size is 1 1μm. The other kind of hydrophilic treatment method is thermal oxidation. This method is usually used in the direct bonding for the SOI devices, because it will grow a layer of electron insulating silicon dioxide on the surface. The force-humidity curve in Figure 3-4 show that this treatment also successfully leaves the clean silicon surfaces to be hydrophilic. The trend of forcehumidity curve is similar to those of the other two hydrophilic sample surfaces except the maximum is higher (212 nn at RH= 60%). And the roughness value 1.4 Å RMS is significantly

37 31 lower than the HF treated surface. Therefore, although thermal oxidation has higher requirement to process, it is an effective way to do surface preparation for direct bonding. It should be noticed that even at low relative humidity (20%~30%) the hydrophilic surfaces have larger adhesion forces than the hydrophobic surfaces. The amount of water trapped between the surfaces at this humidity region is less than that at higher humidity. Therefore hydrophilic silicon direct bonding should be performed at low environmental humidity, and this would be helpful to reduce the bubble generation in annealing process. For the hydrophobic surface, the result is quite straightforward, so there is no necessity for further study. For all the hydrophilic surfaces studied in this work, adhesion force has strong dependence on humidity and the curve shows that the force doesn t always increase with the humidity increase. Adhesion force initially increases, reaches a maximum and decreases thereafter. It has been proven that the thickness of the absorbed water layer on hydrophilic surfaces increases with the humidity 6. The traditional theory cannot explain the decrease of adhesion forced at higher humidity with thicker adsorbed layer. To explain this special phenomenon happened to hydrophilic surfaces, MD simulation and a new force model are introduced in next two chapters.

38 32 Chapter 4 Molecular Dynamics Simulation I believe the nano/sub-nano structure of the absorbed water layer is the key to explaining the adhesion force humidity relationship on oxidized, hydrophilic surfaces. Therefore, to have a better understanding of the structure, molecular dynamics simulation was conducted to simulate the adsorbed water layer on oxidized silicon surface. 4.1 Simulation method DL_POLY , a general molecular dynamics simulation package, was used to perform the simulation tasks in this study. CLAYFF 42 force field was used to define the interatomic and inter-molecule potentials, including the potential between (1) oxygen ions in water molecules, (2) ions in silicon dioxide, (3) oxygen ions in water molecules and ions in silicon dioxide. The cut-offs used in this study are 12 Å for short-ranged potentials and 15 Å for all interactions. The step size in this study is 1 femto-second. The simulation procedure is described as below. A liquid water system was simulated first. The system is a cubic box containing 1026 SPC water molecules. The simulation was conducted at room temperature (293K) and normal pressure (1 atmosphere) for 0.3 nano-second (ns). The statistics of the system properties were collected for every 0.06 ns. The density was calculated with the average volume of the final 50,000 steps. Pure silicon dioxide with β-cristobalite structure was also simulated. A simulation system containing 1000 SiO 2 formula units (5*5*5 β-cristobalite unit cells) was first relaxed at 0K to ensure the structure was reproduced. The system was then simulated at 293K under 1 atm. for 0.1

39 33 ns to obtain cell parameters at room temperature. Cell parameters were obtained by averaging cell parameters from the last 40,000 steps. An absorbed water layer on silicon dioxide was then simulated. The construction of the simulation system is illustrated in Figure 4-1. The size of the simulation cell is 3.64*3.64*25 nm. Periodical boundary condition was applied along x, y, z directions. The large size along z direction is to keep enough empty space to avoid boundary condition artifacts. A layer of β- cristobalite silicon dioxide was placed in the center of the simulation box. The silicon dioxide layer has a thickness of 5 unit cells, and ions in the layer of bottom 3 unit cells were fixed at positions of the ideal β-cristobalite structure. Cell parameters were set to these obtained from the pure silicon simulation at room temperature. Since the periodical boundary condition was broken in the thickness direction, charges on the upper and lower surfaces of the silicon dioxide layer must be balanced to remove the dipole moment on the system. This is done by randomly selecting half of surface oxygen ions and placing them on the corresponding sites on the other surface water molecules were then added on top of the silicon dioxide layer. A NVT ensemble was used and the temperature was kept at 293K. The system was simulated for 0.2 ns and the final structure was analyzed.

40 34 Water Silicon Dioxide Figure 4-1. Construction of the simulation system. 4.2 Simulation results Properly reproductions of the liquid water and silicon dioxide structure are essential for the simulation of the absorbed water layer on the silicon dioxide surface. Therefore results from the simulations of pure liquid water and silicon dioxide were examined first. The simulation of pure liquid water showed that equilibrium was achieved very soon, within the first 5,000~10,000 steps. System properties, such as temperature, pressure and configurational energy, showed minimal fluctuations after the initial equilibrating period. The density obtained from the average of the final 50,000 steps, g/cm 3, agrees with the experimental value of the liquid water density at room temperature, g/cm The structure and radial distribution function (Figure 4-2) showed typical liquid structural characteristics.

41 35 Figure 4-2. Structure (left) and oxygen-oxygen radial distribution function obtained from the simulation of pure water. The simulated pure silicon dioxide retained cubic, β-cristobalite structure both after 0K relaxation and at room temperature. The simulated cell parameter is Å, which agrees reasonably well with the reported parameter of Å 73. With the information gathered from above simulations, a simulation of a layer of water on a β-cristobalite silicon dioxide surface was then conducted. The method is described in the last section. When water molecules were added onto the silicon dioxide surface, the intermolecular distance was kept large to avoid the collision of ions. This results in an initial density of the water layer that is larger than that of the pure water. Therefore a densification process was observed immediately after the simulation started. During the process, water molecules were observed to move towards the silicon surface, resulting in an increase in the water layer density. No further densification was observed after 100,000 steps, and the system was equilibrated for another100, 000 steps. A layer of water with around 4 nm thickness absorbed onto the silicon dioxide surface was obtained at the end, as shown in Figure 4-3.

42 36 Figure 4-3. Final structure of the absorbed water layer from MD simulation. On the left is the side view of adsorbed layer. On the right is the chart representing the number of water molecules in the adsorbed layer at corresponding distance from the interface. The relationship between the number of water molecules and distance was fitted to an exponential equation. The structure of the absorbed water layer was then analyzed. Starting from the silicon dioxide surface, the number of water molecules in every 1 Å thickness was counted to obtain data of water density versus distances from the silicon dioxide surface. Note that some water molecules were found to have diffused into the silicon dioxide and they were discarded in the counting. Water molecules within the top 5 Å thick of the water layer were also discarded because of the irregularity of the surface structure. The water density versus distance data was then fitted to an exponential equation so the fitted density could eventually approach a constant value, and is also shown in Figure 4-2. Similar density data were extracted from the result of the pure water simulation, which is also shown in the figure as dashed line. From Figure 4-2, it can be seen that the density of the water layer on the silicon dioxide surface is considerably larger than the density of pure water. This suggests that the surface Van der Waals force density would also be considerably larger for an absorbed water layer on silicon dioxide surface than the pure water. Same conclusions would also apply for the surface energy.

43 37 Furthermore, it can be seen, from Figure 4-2, that the water density increases dramatically when it becomes close to the silicon dioxide surface. This promoted us to have a closer look at the atomic structure of the water layer at the vicinity of the interface, and compare it to the structure at a distance from the interface. For this purpose, atomic structures of two 1 Å thick water layers, the first 1 Å layer at the interface and a layer 30 Å away from the interface, were compared, as shown in Figure 4-3 (a) and (b). (a) (b) (c) Figure 4-4. Structures of (a) the first 1 Å thick of the absorbed water layer at the interface, (b) 1 Å thick of the absorbed water layer 30 Å away from the interface, (c) oxygen ions in β-cristobalite. From Figure 4-4 (a) and (b) it can be seen that the atomic structure of the water layer at near interface is very different from that 30 Å away from the interface. Intermolecular distances at near interface are much shorter, and the arrangement of molecules is less random. Actually, the structure of water molecules at the near interface resembles that of oxygen ions in the silicon dioxide, which is also shown in Figure 4-4 (c). This is apparently resulted from the influence of silicon ions at the silicon dioxide surface. In a perfect silicon dioxide structure, every silicon ion bonds with 4 oxygen ions. Surface breaks the perfect structure and leaves vacant oxygen sites that can be filled by water molecules. Oxygen ions in water molecules bond with surface silicon ions at these sites, leading to the resemblance in structures. In a word, the atomic structure of water

44 38 layer at near interface is more solid-like than liquid-like. In the simulated structure, the water layer shows pronounced solid-like structure up to the first 5 Å from the interface, and gradually changes to liquid-like with increasing distance, accompanied by the decrease in density. The difference in the atomic structure would inevitably lead to differences in material properties such as surface energy. Experiments using attenuated-total-reflection infrared spectroscopy have shown the thickness of the absorbed water layer at room temperature is only about 7.5 Å at 30% relative humidity 6. Therefore the solid-like structure of the absorbed water layer and its properties must be accounted for when explaining the relationship between the adhesion force and humidity, especially at low humidity.

45 Chapter 5 Theoretical modeling Our experiment results show that adhesion force initially increases, reaches a maximum and decreases thereafter. Such phenomenon has been observed in earlier studies and theoretical attempts have been made to explain it. Xiao and Qian improved the model of capillary force and included the humidity dependence, but its prediction doesn t match the experimental results very well 7. It has been proven that the thickness of the absorbed water layer on hydrophilic surfaces increases with the humidity 6. Therefore the change of adhesion force dependence on the humidity indicates a change in the property of the absorbed water layer. Asay and Kim proposed a model, which treats the absorbed water layer at low humidity as ice 6. The structure of the absorbed water layer changes from ice to water which lowers the surface energy. This causes the change of adhesion force dependence on the humidity. This model, however, still cannot reproduce Xiao and Qian s experimental results, neither the various results in this work. We believe this is because that assuming ice structure for the water layer at low humidity is not adequate. The structure of such thin water layers should be greatly influenced by the solid surface structure. This can be seen by the different observations on thermal oxidation and RCA 1 treated surfaces in this work. RCA 1 treated surface doesn t have a dense layer of the hydrophilic oxide, therefore it has less ability to keep the absorb water layer as a solid-like structure. This causes the RCA 1 treated surface reaches a lower maximum at lower humidity. A model accounting for the differences between the solid surfaces would be more accurate and appropriate for a quantitative description of adhesion force humidity relation. The force model proposed by Asay and Kim in 2006 is so far the best model used for calculating the adhesion force on silicon dioxide hydrophilic surface. They considered the

46 molecular configuration of water in the adsorbed layer and divided it into three different parts: ice-like layer, transitional region, liquid layer. 40 Figure 5-1. Thickness of the adsorbed water layer vs. relative humidity on OH treated silicon surface by IR spectra obtained by David and Jeong 6. The dividing is shown in the Figure 5-1 above. At RH <30%, the adsorbed layer is icelike structure, the tip is separated from the ice-like water; In the RH of 30% 60% region, liquid water structure grows on top of the ice-like structure, both ice-like and liquid water structures coexist in the outmost layer. At RH>60%, liquid water structure dominates the outer region of the adsorbed layer. These three different parts are reflected in an important parameter in force calculation surface energy. They estimated the surface tension of the outmost water layer (γ surface ) to be ergs/cm 2 for RH <30%, 72.8 ergs/cm 2 for RH>60%, and a linear transition from to 72.8 ergs/cm 2 for the RH of 30% 60% region. The value for the surface energy of pure liquid water at room temperature is 72.8 ergs/cm The surface energy of ice like water is103.3 ergs/cm 2 75,76. The exact value of the silicon oxide surface energy is not known, but it is expected to be higher than 103 ergs/cm2. For this reason, the model works for RH > 5%. From the MD simulation results, we can see that regions are acceptable. As shown in Figure 5-1, when RH < 30%, the adsorbed layer is assumed to be ice like, the thickness of water

47 41 layer is less than around 8 Å. in the corresponding region of Figure 5-1, the structure of adsorption is different from liquid. When RH > 60%, the adsorbed layer is assumed to be liquid like, this is understandable through the corresponding region of Figure 5-1. Traditional theory considered the adhesion force contains two parts, the van der Waals force and the capillary force. In Asay and Kim s model, they also considered these two terms. But they are improved by considering the surface energy variation and geometry relationships of the adsorbed layers. Assuming that the adsorbed layer acts like a non-deformable layer, and the tip sample connection is like a sphere of radius R on a flat surface in vapor, we can write down the van der Waals force term (F vdw ). The overall contribution of F vdw to the total adhesion force is small. Eq. 5-1 In the Derjaguin approximation, n=4. R is AFM tip sphere radius Figure 5-2. Schematics of the AFM tip position and ice-ice contact area as a function of relative humidity immediately prior to snap off.