Prober's positioning errors
Two main parts of the prober are the forcer and the platen on which is moves. It is important to keep forcer motion accurate as it provides better probing results and greater throughput. Knowing this, it is very important to keep prober well calibrated. But before we can calibrate the prober we must understand what kind of problems and errors affect stepping accuracy. There are quite a few different issues associated with motion.
Information presented below is applicable to many types of motion systems. However all data has been obtained using EG 2001, EG 4080, EG 4090 and Probe Specialists' NexGen probers. It's application may vary for different types of probers and motion systems.
Cyclic error
If we look at the forcer/platen system closely we can find that it is actually a stepper motor. One can lift the forcer and look under it. There will be quite a few metal strips arranged in up/down and left/right directions. Those metal strips are the coils through which electrical current can flow. By controlling current we can control position of the forcer. Up/down coils allow movement in X direction whereas left/right coils allows movement in Y direction.
For the forcer to move, we need a second set of strips - reference strips. If we look closely at the platen we can notice that it looks like a grid. But instead of coils like the ones found on the forcer it has protruding columns. They are called "teeth". The distance between two adjacent teeth is 20 mils in both horizontal and vertical directions. We should note that the distance between two adjacent coils on the forcer is also 20 mils.
In order for the forcer to move we must change current flowing through its coils gradually. It is achieved by applying current in the form of sine wave. (stepper motor actually needs two (or four) sine waves to move but that is not so important right now). One period (cycle) of the wave will change our position by 20 mils because it will move us from one tooth to the next one. In terms of step motor it is called full step.
Probers however can move in what is called microsteps. They can move multiple smaller steps per one cycle of the wave. It is achieved by dividing the sine wave which drives the forcer into many little segments. Depending on the prober, one cycle of sine wave can consist of 200, 512 or 2048 steps. The more steps the more accurate system can potentially be.
Let's consider the case when our sine wave is divided into 200 segments. In theory, doing one step should move forcer by 1/200 of a full step or 20/200 (1/10) mils (20 mils is one full step - distance between adjacent teeth). In practice it is not the case. Disparity between theory and practice happens because: 1) distance between teeth is not 20 mils but 20 mils plus/minus some small value, 2) distance between coils on the platen is also different from ideal 20 mils, and 3) electrical current which we expect to set on coils is not exact. All that leads to the fact that microsteps are not equal to 1/10 of a mil.
Let's look at the consequences of that problem. We will use ideal sine waves to drive our forcer in say X direction. We will move the distance of 20 mils (one tooth) by 10 microsteps at a time and measure real displacement optically using digital camera and special software.
Values at Y axis of the graph represent differences between the measured position and estimated position. Units are microns. (1 micron is about 1/25 of a mil. So 25 microns are about 1 mil.) Values at X - represent step number.
Now let's move the distance of 60 mils (three teeth). We will step in the same 10 microstep increments.
Notice that shape of the curve repeats itself 3 times in this graph. If we measure this error between different spots on the platen, we will see that shape will be relatively the same. This type of error is called cyclic.
Now it is logical to assume that moving in positive X (or Y) direction and negative will produce the same cyclic error. As a matter of fact they may be different. Difference can be smaller or bigger and depending on the platen and forcer in question. It is very important to know that calibrating for only one direction will produce rather big errors when stepping in the opposite direction.
Another thing to consider is cyclic error drift. If we had a situation when the platen is ideal (all teeth are exactly 20 mils and they are all absolutely the same over entire length) then cyclic error would be exactly the same over the entire working region. (It actually would not be exactly the same as there are other factors which weight in like umbilical cord tension and temperature distribution, but we won't consider it here.) However platens have small variations from tooth to tooth which differ over the platen. Because of that cyclic error will also vary depending on the spot.
Variations will depend a lot on the platen itself. For example laser etched platens tend to perform better than chemically etched. But we will see variations even between platens which are made with the same technical process.
Linear error
One of the major sources of positioning error is so called "linear error". It is an error accumulated by forcer when travelling over large distance. Linear error is very complex in its nature and there is no simple way to describe it. However we can separate some major factors that come into consideration.
Orthogonality error
It is important to separate orthogonality error from alignment error. Let's say we have aligned a wafer under the bridge camera and measured our positioning error (also under the bridge camera).
Now let's imaging that we have perfectly aligned wafer under the bridge camera and measuring position error in the probing area. For one system we have measured error displayed in the picture 1. For the other - on the picture 2.
Notice that we can plot straight lines through the dots on both pictures. It's easy to notice that lines on both pictures are at an angle to their respective coordinate axes. It means that as forcer moves in one direction only (say X) it actually moves in two directions (X and Y). This type of error is called orthogonality error.
Before drawing any conclusions about the magnitude of orthogonality error it is important to remember one thing: when we are measuring error in the microscope area chuck can be at a different Z height than when we are aligning wafer (or a glass mask) under the bridge camera. It must be noted that as chuck travel's up and down, it can rotate ever so slightly. This small rotation can translate in perceived positioning error. So it is advisable to conduct all measurement using the same chuck Z height in both bridge and probing areas.
To differentiate between true orthogonality error and errors caused by misalignment or warpage we should measure angles between plotted lines and coordinate axes for both X and Y. If angles are the same it means that there are some errors due to aforementioned reasons (picture 1). If angles are different than we can call it orthogonality error (picture 2).
Warpage
As it was mentioned before platen is comprised of the features called "teeth" which are 20 mills apart from each other. They form rows and columns which cover the entire platen surface. When forcer moves around it counts on the fact that all teeth are exactly 20 mills apart from each other. In reality however it is not always the case.
Due to manufacturing process or wear-and-tear of the platen teeth are not evenly spaced across it. In different regions of the platen distances between the teeth can vary. If we are to step across the platen and measure positioning errors, we will see that there are regions where errors are particularly apparent. If we plot these errors on the graph we can notice that these regions are "warped".
Warpage error is unique to the platen. Each one of them has its own special regions and requires special calibration.
Temperature expansion error
It is well known that materials' volume changes with the temperature. It happens due to intra-molecular interaction which changes with temperature. Basically the bigger the temperature the bigger is the volume of the material. It brings us to the interesting fact that distance between teeth of 20 mills is only achievable at a certain temperature. As it changes so will the distance!
Usually platen is calibrated at 20 degrees Centigrade (20 C). It means that at 20 C distance between teeth will be exactly 20 mils. Linear temperature expansion of the steel is 13.5 u/(m*K). It means that it will change by 13.5 microns over 1 meter of distance when temperature changes by 1 degrees Centigrade (or 1 degree Kelvin).
Temperature expansion of the platen means that forcer will actually cover more (or less) distance depending on the actual temperature of the platen. This in turn may lead to positioning error if not properly accounted for. Fortunately temperature expansion is very predictable and very easy to compensate. All probers have built in compensation mechanism to account for this phenomenon. Unfortunately temperature expansion is not really uniform across the platen hence cannot be described by just one temperature which prober uses for position correction. This problem arises from the fact that forcer tends to spend more time in the center of the probing/bridge region. As a result center part of the region heats up more than outer parts. However the temperature sensor is located on the very edge of the platen which has yet a different temperature. As a result, the prober compensates for a little bit different amount of error than it should.
Another thing to consider when compensating for temperature expansion is the actual temperature of the wafer (or glass mask). Obviously it can be very different from the nominal 20 C or from the temperature of the platen. Thus temperature expansion of the wafer should be accounted separately and it is imperative to know it exactly.
It is highly recommended to perform measurement and calibration process on the stabilized system in (preferably) temperature stable environment. Systems should be warmed up for few minutes before calibration. Also temperature expansion coefficients of the silicon (or glass) should be taken into account.
Umbilical cord
Umbilical cord is a patch of wires that go from the prober to the forcer. These wires provide power and allow prober to control forcer's movement. It is important to note that stiffness of this patch cord is very crucial to the accurate positioning of the system.
Umbilical cord influences the positioning accuracy of the forcer. Tension created by it changes the actual position. It exerts pressure on the forcer which results in a very small rotation. The results would be similar if we just press with a finger on the side of the forcer. Rotation of the forcer results in the effective position displacement of the wafer during the probing. Amount of displacement is proportional to the rotation angle and the distance from the center of the chuck to the probing location. Naturally it is minimal in the center and maximal at the edges of the wafer.
Umbilical cord error is non-linear and there are regions on the platen where it's influence it negligibly small. However there are regions where errors introduced by the patch cord can be more than 10 microns.
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