# Air-Based Contactless Wafer Precision Positioning System
## 5 Wafer Sensing
### Linear Sensor Array  
A linear CCD has been selected to measure the edge position of the wafer. It consists of an array of pixels that measure the intensity of the light. The change from light to dark is used to find the edge of the wafer. The concept is shown in Figure 17. As discussed in the state of the art, [PERSON] had implemented CCD sensors but used a somewhat different concept where noise from stray light limited the performance [3].  
The selection of the CCD sensor is based on a trade-off between the resolution, sampling time, and range. The sampling time is limited by the available modules for the National Instruments CompactRio. The NJ9201 is used which supports 500 ks/s. The TCD1103 GFG has 1500 pixels of 5.5 um by 64 um on a 5.5 um center. It supports a data rate of 2 MHz. With 1500 pixels and a low integration time this results in a sampling rate of almost 1.3 kHz, and with the limitation of the 500 ks/s this is lowered to 320 Hz. High power cool white LEDs are used as the light source. The intensity of the light is tuned to maximize the dynamic range.  
Figure 16: Closed loop cross coupled frequency response of the actuators, from actuator reference position to measured position.  
In this paper, the sensor output is compared to a threshold. This threshold is used to detect the transition from light to dark. Instead, a threshold a sub-pixel interpolation method could also be used. Using this method it is possible to increase the resolution of the sensors to better than 0.05 of the pixel size, while at the same time reducing the effects of noise [17; 18; 19; 20]. Using the sub-pixel interpolation method the theoretic resolution of the chosen CCD could be as low as 0.11 \(\upmu\)m. However, to limit the calculation time on the FPGA, it was chosen to implement the threshold model. Figure 18 shows the output of the CCD sensor. The threshold is placed at 0.6. When the threshold is reached the pixel number corresponds to the position on the CCD where the shadow ends.  
When using a point light source, the measured position should be adjusted to get the real position. Figure 19 shows that the distance between the shadow and the wafer position is dependent on the position and height of the wafer. The wafer position is calculated  
Figure 17: Linear CCD sensor concept to measure the edge of a wafer.  
Figure 18: Output of the CCD sensor. It shows the edge of the wafer. The edge is a curve over 10 pixels.  
using Equation (3a). Because the height of the wafer is not fixed a disturbance could enter the system through a variation in the height. The size of the disturbance can be estimated by Equation (3a).  
The difference in fly-height is estimated to be in the order of micrometers. When minimizing the height between the wafer and CCD the disturbance is estimated to be within 0.1 of the pixel size for large movements, which is acceptable when using the threshold model, if sub-pixel interpolation is used it is better to remove the height by using a collimated light source or by adding another LED. With two LEDs, another data point is known which can be used to eliminate the height from the equation as shown in Equation (3b) [21].  
\[X_{w} =\frac{h_{ wafer}}{h_{led}}(x_{L1}-xs1)+s1 \tag{3a}\] \[X_{w} =\frac{x_{L2}x_{s1}-x_{L1}x_{s2}}{-x_{L1}+x_{L2}+x_{s1}-x_{s2}} \tag{3b}\]