Kevin T. Turner

Friction laws at the nanoscale.

Macroscopic laws of friction do not generally apply to nanoscale contacts. Although continuum mechanics models have been predicted to break down at the nanoscale, they continue to be applied for lack of a better theory. An understanding of how friction force depends on applied load and contact area at these scales is essential for the design of miniaturized devices with optimal mechanical performance. Here we use large-scale molecular dynamics simulations with realistic force fields to establish friction laws in dry nanoscale contacts. We show that friction force depends linearly on the number of atoms that chemically interact across the contact. By defining the contact area as being proportional to this number of interacting atoms, we show that the macroscopically observed linear relationship between friction force and contact area can be extended to the nanoscale. Our model predicts that as the adhesion between the contacting surfaces is reduced, a transition takes place from nonlinear to linear dependence of friction force on load. This transition is consistent with the results of several nanoscale friction experiments. We demonstrate that the breakdown of continuum mechanics can be understood as a result of the rough (multi-asperity) nature of the contact, and show that roughness theories of friction can be applied at the nanoscale.

Tensile testing of polysilicon

Tensile specimens of polysilicon are deposited on a silicon wafer; one end remains affixed to the wafer and the other end has a relatively large paddle that can be gripped by an electrostatic probe. The overall length of the specimen is less than 2 mm, but the smooth tensile portion can be as small as 1.5×2μm in cross section and 50μm long. The specimen is pulled by a computer-controlled translation stage. Force is recorded with a 100-g load cell, whereas displacement is recorded with a capacitance-based transducer. Strain can be measured directly on wider specimens with laser-based interferometry from two small gold markers deposited on the smooth portion of the specimen. The strength of this linear and brittle material is measured with relative ease. Youngs modulus measurement is more difficult; it can be determined from either the stress-strain curve, the record of force versus displacement or the comparison of the records of two specimens of different sizes. Specimens of different sizes—thicknesses of 1.5 or 3.5 μm, widths from 2 to 50 μm and lengths from 50 to 500 μm—were tested. The average tensile strength of this polysilicon is 1.45±0.19 GPa (210 ±28 ksi) for the 27 specimens that could be broken with electrostatic gripping. The average Youngs modulus from force displacement records of 43 specimens is 162±14 GPa (23.5 ±2.0×103 ksi). This single value is misleading because the modulus values tend to increase with decreasing specimen width; that is not the case for the strength. The three methods for determining the modulus agree in general, although the scatter can be large.

Method for Characterizing Nanoscale Wear of Atomic Force Microscope Tips

Atomic force microscopy (AFM) is a powerful tool for studying tribology (adhesion, friction, and lubrication) at the nanoscale and is emerging as a critical tool for nanomanufacturing. However, nanoscale wear is a key limitation of conventional AFM probes that are made of silicon and silicon nitride (SiNx). Here we present a method for systematically quantifying tip wear, which consists of sequential contact-mode AFM scans on ultrananocrystalline diamond surfaces with intermittent measurements of the tip properties using blind reconstruction, adhesion force measurements, and transmission electron microscopy (TEM). We demonstrate direct measurement of volume loss over the wear test and agreement between blind reconstruction and TEM imaging. The geometries of various types of tips were monitored over a scanning distance of approximately 100 mm. The results show multiple failure mechanisms for different materials, including nanoscale fracture of a monolithic Si tip upon initial engagement with the surface, film failure of a SiNx-coated Si tip, and gradual, progressive wear of monolithic SiNx tips consistent with atom-by-atom attrition. Overall, the method provides a quantitative and systematic process for examining tip degradation and nanoscale wear, and the experimental results illustrate the multiple mechanisms that may lead to tip failure.

Modeling of direct wafer bonding: effect of wafer bow and etch patterns

Direct wafer bonding is an important technology for the manufacture of silicon-on-insulator substrates and microelectromechanical systems. As devices become more complex and require the bonding of multiple patterned wafers, there is a need to understand the mechanics of the bonding process. A general bonding criterion based on the competition between the strain energy accumulated in the wafers and the surface energy that is dissipated as the bond front advances is developed. The bonding criterion is used to examine the case of bonding bowed wafers. An analytical expression for the strain energy accumulation rate, which is the quantity that controls bonding, and the final curvature of a bonded stack is developed. It is demonstrated that the thickness of the wafers plays a large role and bonding success is independent of wafer diameter. The analytical results are verified through a finite element model and a general method for implementing the bonding criterion numerically is presented. The bonding criterion developed permits the effect of etched features to be assessed. Shallow etched patterns are shown to make bonding more difficult, while it is demonstrated that deep etched features can facilitate bonding. Model results and their process design implications are discussed in detail.

Shear-enhanced adhesiveless transfer printing for use in deterministic materials assembly

This letter describes the physics and application of an approach to transfer printing that utilizes targeted shear loading to modulate stamp adhesion in a controlled and repeatable fashion. Experimental measurements of pull-off forces as functions of shear and stamp dimension reveal key scaling properties and provide a means for comparison to theory and modeling. Examples of printed structures in suspended and multilayer configurations demonstrate some capabilities in micro/nanoscale materials assembly.

Preventing Nanoscale Wear of Atomic Force Microscopy Tips Through the Use of Monolithic Ultrananocrystalline Diamond Probes

Nanoscale wear is a key limitation of conventional atomic force microscopy (AFM) probes that results in decreased resolution, accuracy, and reproducibility in probe-based imaging, writing, measurement, and nanomanufacturing applications. Diamond is potentially an ideal probe material due to its unrivaled hardness and stiffness, its low friction and wear, and its chemical inertness. However, the manufacture of monolithic diamond probes with consistently shaped small-radius tips has not been previously achieved. The first wafer-level fabrication of monolithic ultrananocrystalline diamond (UNCD) probes with <5-nm grain sizes and smooth tips with radii of 30-40 nm is reported, which are obtained through a combination of microfabrication and hot-filament chemical vapor deposition. Their nanoscale wear resistance under contact-mode scanning conditions is compared with that of conventional silicon nitride (SiN(x)) probes of similar geometry at two different relative humidity levels (approximately 15 and approximately 70%). While SiN(x) probes exhibit significant wear that further increases with humidity, UNCD probes show little measurable wear. The only significant degradation of the UNCD probes observed in one case is associated with removal of the initial seed layer of the UNCD film. The results show the potential of a new material for AFM probes and demonstrate a systematic approach to studying wear at the nanoscale.

Comparison of Micro-Pin-Fin and Microchannel Heat Sinks Considering Thermal-Hydraulic Performance and Manufacturability

This paper explores the potential of micro-pin-fin heat sinks as an effective alternative to microchannel heat sinks for dissipating high heat fluxes from small areas. The overall goal is to compare microchannel and micro-pin-fin heat sinks based on three metrics: thermal performance, hydraulic performance, and cost of manufacturing. The channels and pins of the microchannel and micro-pin-fin heat sinks, respectively, have a width of 200 ¿m and a height of 670 ¿m. A comparison of the thermal-hydraulic performance shows that the micro-pin-fin heat sink has a lower convection thermal resistance at liquid flow rates above approximately 60 g/min, though this is accompanied by a higher pressure drop. Methods that could feasibly fabricate the two heat sinks are reviewed, with references outlining current capabilities and limitations. A case study on micro-end-milling of the heat sinks is included. This paper includes equations that separate the fabrication cost into the independent variables that contribute to material cost, machining cost, and machining time. It is concluded that, with micro-end-milling, the machining time is the primary factor in determining cost, and, due to the additional machining time required, the micro-pin-fin heat sinks are roughly three times as expensive to make. It is also noted that improvements in the fabrication process, including spindle speed and tool coatings, will decrease the difference in cost.

Mechanics of wafer bonding: effect of clamping

A mechanics-based model is developed to examine the effects of clamping during wafer bonding processes. The model provides closed-form expressions that relate the initial geometry and elastic properties of the wafers to the final shape of the bonded pair and the strain energy release rate at the interface for two different clamping configurations. The results demonstrate that the curvature of bonded pairs may be controlled through the use of specific clamping arrangements during the bonding process. Furthermore, it is demonstrated that the strain energy release rate depends on the clamping configuration and that using applied loads usually leads to an undesirable increase in the strain energy release rate. The results are discussed in detail and implications for process development and bonding tool design are highlighted.

Methods to Measure the Strength of Cell Adhesion to Substrates

Cell-substrate adhesion is a critical factor in the development of biomaterials for use in applications such as implantable devices and tissue engineering scaffolds. In addition, cell adhesion to the extracellular matrix is intertwined with a number of fundamental cell processes, and several diseases are characterized by cells with altered adhesion properties. While many approaches exist to characterize cell adhesion, only a fraction of the techniques provides quantitative measurements of the strength of adhesion by physically detaching cells through application of force or stress. In this review, the most commonly used techniques to measure the adhesion strength of cells adhered to substrates are summarized. These methods can be divided into three general categories: centrifugation, hydrodynamic shear and micromanipulation. For each method, the technique is described and its capabilities assessed. A comprehensive review of recent applications of the methods is given, and adhesion strength measurements performed using different techniques on fibroblasts, a commonly-studied cell, are compared. Finally, the strengths and drawbacks of the various techniques are discussed.

Predicting distortions and overlay errors due to wafer deformation during chucking on lithography scanners

Chucking of substrates with wafer shape and thickness variations results in elastic deformation that can cause significant in-plane distortions that lead to overlay errors in lithographic patterning. As feature sizes shrink, overlay errors due to the combination of wafer geometry and chucking become a larger fraction of the error budget and must be controlled. We use a finite element model and a lithographic correction postprocessing scheme to predict in-plane distortions that result from chucking wafers with shape variations. We then use the predictions of in-plane distortions at two different patterning steps to calculate the component of overlay error that arises from localized shape variations. Using the model, in-plane distortion and overlay errors due to chucking are examined for multiple wafers with different geometries. The results show that long spatial wavelength shape variations cause significant distortion, but can largely be mitigated through the use of simple first-order corrections that are applied in typical lithography scanners. In contrast, high-frequency spatial variations cause distortions that cannot be corrected and hence lead to meaningful overlay errors. The results provide fundamental insight into chucking-induced overlay errors and can serve as a basis for the development of higher order scanner correction schemes that explicitly account for the wafer geometry through high-density wafer shape measurements.