The role of crystallographic orientation on the forces generated in ultra-precision grinding of anisotropic materials such as monocrystalline silicon

This work presents a system of measuring grinding forces in precision applications. Several experiments demonstrate the performance in monitoring diamond wheel dressing, detecting workpiece contact, and process monitoring. The system appears promising for monitoring precision wafer grinding since this approach provides excellent sensitivity, high signal resolution, and good bandwidth. INTRODUCTION Ultra-precision grinding is a subset of precision machining where sub-micrometer geometric form errors and nanometer-level surface finishes are obtained using fixed abrasives and machine tools with high static and dynamic stiffness, high-resolution controls, and environmental isolation systems. For example, manufacturers of silicon wafers and precision optics often require tenth-wave form error and nanometer surface finish. The literature documents a comprehensive exploration of the properties and behavior of silicon and crystallographically similar diamond. Both materials show directionally-dependent behavior including preferred orientations for best results with various material removal processes [1,2,3]. For example, Wilks and Wilks showed that diamond polishing rates vary when working the crystal in different directions [4]. Furthermore, silicon turned with single point tools shows radial spokes of damage in the directions predicted to be the most difficult by Wilks and Wilks. Blackley et al. explained the orientation dependent machining damage in silicon by examining the variation in resolved tensile stress on the {111} slip planes [5]. The anisotropy of monocrystalline silicon causes machining properties like the critical chip thickness, or the ductile-to-brittle-cutting transition depth, to vary with the crystal orientation. Furthermore, the orientation of the crystal lattice during grinding plays a very significant role in the wafer form and surface quality. Recent wafer processing research focused on the roles of each of these components to analytically predict wafer shape and quality. For example, Pei et al. has done extensive research in understanding the geometrical parameters of the workpiece chuck shape, the wafer shape and the process parameters (work speed, wheel speed, feed rate, abrasive grit size, coolant geometry) for fine grinding [6]. FIGURE 1. The silicon unit cell. The crystal structure of silicon (diamond cubic at room temperature) is shown in Figure 1. The structure of the crystal lattice and atomic arrangement are extremely important in understanding the anisotropy of silicon because it affects its mechanical, electrical, chemical and optical properties. The mechanical anisotropy is especially influential on the orientationdependent results obtained when machining silicon and other crystalline materials. FIGURE 2. Modulus variation as a function of crystal orientation. One example of the anisotropy in the mechanical properties of silicon is found in the elastic modulus variation. The variation of the elastic modulus on individual crystal planes is found by taking slices of the three-dimensional surface through the origin of the crystal axes. Figure 2 also shows the elastic modulus variation on the cubic face of monocrystalline silicon. On the cubic crystal plane (001 plane), a 4-lobed pattern emerges in the elastic modulus variation. This variation mirrors the atomic structure on the (001) crystal face shown in Figure 1, and a pattern repeating every 90° is evident. As expected, the direction with the highest atomic density yields the highest elastic modulus. EXPERIMENTAL SETUP Figure 3 shows the hardware designed specifically for measuring forces in the normal and tangential directions during cylindrical grinding. The design features an aerostatic spindle (Professional Instruments 4R TwinMount) with a frameless, brushless, DC motor (MCS) and a 1024 count rotary encoder (Heidenhain) for synchronized data acquisition. Four high-resolution capacitive displacement sensors (1 mV/nm, Lion Precision C1-C) are used to measure the relative motion between the spindle rotor and stator. This arrangement allows the calculation of both radial and axial loads without compromising the structural loop stiffness of the machine tool. All experiments were carried out on a two-axis grinding machine (Moore CNC 450) with a programmable resolution of 0.1 micrometers. During experiments, an oil-based coolant is applied as a mist using pressurized air. The sensing area of the capacitance probes is kept clean and dry by the positive air pressure flowing through the air bearing spindle. FIGURE 3. CNC machine configuration for silicon grinding experiments. The spindle instrumentation measures the relative motion between the work spindle stator and rotor. The axial, radial, and tilt stiffnesses are known for the spindle, so the force calibration values can be computed directly by real-time analysis software. An additional consideration is that the capacitance sensors target a rotating steel surface with 100 nm form error. The software removes this form error automatically using the rotary encoder for synchronization. Data acquisition and analysis is carried out by custom LabWindows/CVI software with nearly real-time force feedback and a usable bandwidth of 150 Hz. The grinding experiments described below are on the outer diameter of cylindrical (100) silicon workpieces Ø150 mm by 10 mm thick. The results and approach are also applicable to face and contour grinding. The work spindle rotates at 500 RPM and the abrasive wheel spins at 3600 RPM. The diamond wheel is a Ø200 mm, 220 grit synthetic diamond wheel (Coors Ceramic SD 220). During the diamond wheel dressing experiments, the diamond wheel rotates at a much slower 400 RPM and a silicon carbide dressing wheel that is mounted in place of the workpiece rotates at 3000 RPM. During dressing and grinding the axial feed rate is 150 mm/min while the radial infeed varies and is reported individually for each experiment. EXPERIMENTAL RESULTS The first experiment demonstrates the importance and capability of real-time instrumentation in ultra-precision silicon wafer grinding. Because the typical material removal rates of a brittle material such as silicon are so low, the amount of energy generated in grinding is small and difficult to accurately detect. The same situation applies to diamond wheel dressing, which is notoriously time consuming because of the inherent strength of diamond wheels. While it is important that the grinding wheel be properly trued for use in precision grinding, the condition of the diamond wheel can be difficult to quantify. For example, a newly installed diamond grinding wheel will have a certain amount of eccentricity and out-ofroundness when mounted on the grinding spindle. It is difficult to quantify the wheel runout because of its rough surface. Diamond wheels are trued and dressed by a variety of methods depending on the particular application. In some situations, if the diamond wheel runout is large, it can take hundreds of passes of the dressing wheel to properly true the diamond wheel. Without adequate feedback, it is easy to stop the dressing operation to early and leave the diamond wheel out-of-true or to waste time dressing an already round wheel. The second experiment compares grinding forces under different wheel conditions, i.e., a dull wheel and freshly re-conditioned wheel while grinding a silicon sample. The upper time trace of Figure 4 shows the fluctuation in force that occurs as a worn and untrued wheel is used to grind the outer diameter of a silicon workpiece. The lower trace shows data taken with a properly trued wheel. Because the diamond wheel is now geometrically round and dressed so that the many abrasive grits are in a similar condition, the grinding force is more uniform and the once-per-revolution of the grinding wheel force is no longer seen in the inset. FIGURE 4. Time traces of grinding force with a untrued (upper) and trued (lower) wheel. Without the benefit of the force feedback it would be difficult or impossible to detect the higher force fluctuation of the untrued (worn) wheel. In the third experiment, we establish the correlation between the measured grinding forces and workpiece crystal orientation. In this experiment, a cylindrical (100) silicon workpiece was ground with a partially worn diamond wheel on the outer diameter. Figure 5 shows how the force data can be visualized over the geometry of the cylindrical workpiece. Although the figure has the familiar appearance of a form error measurement, these data show the fluctuation in grinding force obtained while grinding the outer diameter of the silicon. The forces have been essentially plotted over the cylindrical geometry and then unwrapped and also stretched as shown to make the figure. The left-hand surface shows the raw grinding force after low-pass filtering the measurement data with a cut-off frequency dictated by the instrument dynamics (150 Hz). This plot shows two interesting phenomena. The first is the regular, but asynchronous, lobing associated with the rotating grinding wheel that occurs approximately nine times per revolution. By counting in the workpiece diameter direction, the force fluctuates approximately nine times per revolution of the workpiece, which corresponds to the ratio of the grinding wheel speed to the workpiece speed. These lobes occurring at approximately nine times per workpiece revolution do not fall in neat lines along the length of the workpiece because the grinding wheel spindle does not rotate at a precise integer multiple of the workpiece spindle speed. The right-hand surface plot shows the same data, but with additional filtering to a low-pass frequency cutoff below the grinding wheel speed. Readily apparent is the characteristic four lobe pattern that occurs due to the anisotropy of the silicon crystal when machined on the outer diameter of the (100) face. Note that the four-lobe characteristic can be seen in the left-hand surface but it is partially concealed by the higher frequency grinding wheel force fluctuations. FIGURE 5. The variation in the grinding force measured on a particular pass of the rotating diamond wheel over the rotating silicon