In this project I designed, fabricated, and tested a passive alignment mechanism that positioned silicon wafers relative to a MEMS-based atomic force microscope. The AFM was attached to a precision flexure-based stage that allowed for precise movement of the AFM chip. The aim of the overall project was to enable high-throughput nanometer scale inspection of sample features located at the same region on multiple wafers. The design objectives for the positioning mechanism were to achieve lateral positioning repeatability better than 10 μm and to allow for the setup of 90 samples per hour. The image to the right shows the final high-throughput inspection setup. The wafer alignment stage is coupled to the AFM stage by kinematic couplings with gravity as a preload.
The project began as a proposal for an undergraduate research course in the Spring of 2015, and I continued developing my work through the Summer and into the Fall of 2015. The project is sponsored by Professor Michael Cullinan as part of his Nanoscale Design and Manufacturing Lab. Funding is provided by a grant from the NASCENT center in Austin, TX.
Precision Passive Alignment
In my quest to determine the most effective means of precisely fixturing wafers I explored three precision techniques including kinematic couplings, kinematic averaging, and exact constraint design. Sub-micron repeatability is achievable with both kinematic averaging and kinematic couplings . Neither of these methods could be used to align wafers without significantly altering the geometry of the wafer so I chose to use exact constraint design and to explore the repeatability limits of a fixture using simple pin constraints.
Two pins are placed on the flat of the wafer and constrain one rotational and one translational degree of freedom. A third pin constrains a second translational degree of freedom, and the pins remain in contact with the wafer with the application of a nesting force. Determining the optimal location for the third pin and nesting force was a major focus of this project. Blanding describes a method for choosing a location for the nesting force utilizing a graphical method . He shows that the intersections between the line of action (LOA) of each constraint forms an instantaneous center of rotation (ICR) for the wafer. Application of the nesting force will result in a moment about one of the instantaneous centers if the wafer is not in contact with one of the three pins. The direction of this restoring moment should be such that it helps seat the wafer against all pins .
optimization for repeatability
In order to maximize the repeatability of the wafer alignment mechanism I deduced that the restoring moment about the non-infinite instantaneous centers of rotation should be maximized. First, I calculated the reaction forces at each pin using static analysis. I then utilized Mathematica to reduce these equations to a more palatable form and verified the results using Solidworks simulation. After verifying the reaction forces I proceeded to determine the moments about the instantaneous centers as a function of the angles ϕ and θ. By symmetry and choice of coordinate system I found that the two ICRs were equal in magnitude and opposite in direction.
Nesting Force Window
I created a Matlab script to determine the restoring moments about the ICRs as a function of the third pin angle and the nesting force angle WRT the horizontal axis. I limited the angle between the third pin and the x-axis to the region [-45°,80°] with the lower bound preventing interference with the right pin and the upper bound preventing over-constraint in the y-direction due to binding. The script generated a 3D plot which allowed me to visualize the restoring moment as a function of the third pin angle and nesting force angle. After limiting the resulting moments to those with a restoring action, I was left with the figure shown to the right. It was evident that the restoring moment is maximized as the third pin angle is moved towards its upper bound.
In order to test the validity of my nesting force window analysis I designed the stage to include multiple holes for the third pin location. The location for application of the nesting force was fixed to isolate the impact of varying the third pin location. The initial prototype utilized a prismatic flexure which was to provide a force of 10N. I created an excel spreadsheet that allowed me to vary parameters for the dimensions of the flexure that satisfied constraints for material thickness, length, required force and displacement, as well as safety factor. The spreadsheet can be found by clicking the picture below.
The stage utilizes three vee-blocks to interface with half-balls on the AFM metrology stage. The kinematic coupling ensures excellent positioning repeatability when the AFM metrology stage is removed and replaced relative to the wafer alignment stage.
The second prototype made a number of improvements on the first prototype. The blade flexure used in the first prototype exhibited significant torsion and was prone to yielding. Thus, a compound double-parallelogram flexure was designed for the second prototype. In addition, the location of the nesting force application for the second prototype was modified to both increase the restoring moments for all pin positions as well as to align the coordinate system for the wafer with that of the AFM metrology setup. The stiffness of the flexure was found using the equation below:
I created a spreadsheet and optimized the length, thickness, and height of the flexural elements to produce a spring constant of 7.7 N/mm and verified the results of my calculations with a Solidworks FEA simulation. The results from my calculations were within 2% of the value predicted by FEA.
fabrication and assembly
The wafer alignment stages were manufactured from 6061-T6 Aluminum due to availability and ease of machining. I designed the stage to be machined using two processes. I created DXF files for the outline of the stage to be waterjet in the ME machine shop. I then squared up the rough shape on a manual CNC mill and used a fly cutter to ensure that the surface to be machined was flat. Finally, I generated toolpaths to machine features in the stage. My toolpaths included pockets for the vee-blocks, a large pocket for the wafer to sit in, and various drilling features. In order to create precision holes for press-fitting the pins I used a spotting drill followed by a conventional drill bit and fiinished with a reamer. Holes were deburred after each drilling process. The surface of the stage in contact with the wafer was to be as smooth and flat as possible. Initially, I planned to lap the surface, but I ultimately decided to decrease roughness by wet sanding the wafer pocket surface with progressively fine sand paper. The final manufacturing step was to place the stage on a heating plate set to 100°C and carefully place the vee-blocks and alignment pins in the holes.
All flexural elements were cut out on a waterjet machine. After much experimentation we found that the minimum element thickness achievable on the machine was 0.4 mm for a beam width of 10 mm. Flexures cut on the waterjet consistently exhibited non-uniform profiles with stiffness consistently less than what would be calculated based on calculations assuming rectangular cross-sections.
I utilized six capacitance probes to test the translational and rotational positioning repeatability of the wafer alignment mechanism. Translational displacement was measured using one probe for each axis. Rotation about each axis was measured using the difference in displacement measured between two parallel probes. All probes measured the distance from the end of the probe to a face on an aluminum block bonded to a wafer. All measurements were made relative to an arbitrary reference point which was set by the distance between the probes and the block on the wafer on the first repeatability trial. Images to the right show the test fixture from sketch to experiment
Analog output from the capacitance probes was connected to a DAQ system. I designed a LabVIEW VI to sample each probe 1000 times per second. The average value was then scaled to convert the voltage readings to displacement readings. The VI allowed for all of the probes to be zeroed before testing and was set to write the displacement measured by each capacitance probe to an excel file when a button was pressed.
The procedure for testing took place in the following steps. First, the wafer with the aluminum block was placed in the wafer alignment stage. The wafer was pressed against the pins and the flexure was carefully engaged to keep the wafer in contact with the pins. Next, the capacitance probe fixture was placed on top of the wafer alignment stage. The two stages were kinematically coupled to reduce error in the position of the capacitance probe stage relative to the wafer stage. With the wafer and the measurement stage in position, the VI was set to record the capacitance probe displacements. Finally, the measurement stage was removed from the wafer alignment stage and the wafer was removed from the wafer stage. The test procedure was repeated 50 times for each pin location to determine if there was a significant correlation between third pin angle and wafer positioning repeatability.
The results for both translational and rotational repeatability as a function of pin location are shown below. Repeatability is defined as the standard deviation of the displacements or rotations recorded for each pin. Graphs of repeatability as a function of trial indicate the presence of drift. Repeatability in the X-Y plane of the kinematic coupling between the wafer stage and measurement stage would likely be better than one micron without the drift. The coupling exhibited superb sub-micron repeatability in the z-direction. Results for translational and rotational repeatability were poor with the third pin located at an angle of 0º. All other pin locations exhibited sub-five micron repeatability in the X Y and Z directions with pin locations at θ=60º and θ=70º exhibiting repeatability on the order of one micron.