Height map

In an ideal electron beam writer system, the stage plane and sample plane should be normal to the incident electron beam. This enables a focused beam to remain in focus at any point on the sample surface. When the beam focus varies across the sample, the writing resolution and stitching errors also varies, as described here. To ensure that the beam is focused on the sample, some ebeam writers are equipped with a height detection system. A height detection system measures the sample height and adjusts the beam focus before exposing a pattern.

However, not all ebeam writers are equipped with a height detection system. These instruments are much more reliant on precision engineering and calibration in order to deliver accurate patterns. For these systems, it is prudent to characterize its capabilities in order to predict the feasibility of achieving certain patterns. Our height map measurements for several types of samples are found at the end of the page.

Focus mark calibration

When a new AE mark is installed, an engineer will calibrate the mark's height to match the sample height. Figure 1 shows a diagram of the stage, AE mark and cassette. Notice that in the diagram, the AE mark is not at the same level as the sample surface (the sample is in the cassette). During the automatic calibration that is performed before an exposure, the instrument focuses the beam on the AE Mark, not the sample surface.

Figure 1: A diagram of the stage, marks and cassette assembly

Figure 1: Diagram of the stage, marks and cassette assembly

The AE mark and sample height is calibrated by suspending a micrometer above the stage. The stage is moved so that either the AE mark or the sample is underneath the micrometer. Adjustments are made to the AE mark height and/or the cassette loading assembly in order to minimize the height disparity between the AE mark and the sample surface. It is also important that the BE mark and Au mark are also leveled with the AE mark and sample surface since these marks are used to calibrate the scan field and stigmatism respectively.

Piece holder cassette

The quality of the mark and sample height calibration is confirmed by measuring the beam focus value on the AE mark and sample. Two samples were prepared for the experiment. The sample is either a Si or SiO2 quarter that is covered with 100 [nm] gold particles. First, the sample is loaded (Load 1) into the piece holder cassette and the cassette is loaded into the instrument. The beam focus value is recorded on the AE mark and on 9 positions on the wafer (3x3 grid with a 7mm pitch). The beam focus value on the sample is acquired by focusing on the nanoparticles. After completing the measurement, the cassette was reloaded into the instrument by retracting from the stage and then inserted back onto the stage. The cassette was never removed from the system and the sample was never moved. Finally, the sample is loaded again (Load 2) as we did initially. This is performed by 2 different users. The instrument is calibrated for high resolution mode to facilitate imaging.

For the piece holder cassette, height maps were measured for a quarter wafer and a 1/2" x 1/2" chip. Focus values are recorded on a 3x3 grid with the top left corner corresponding to the top left corner of the wafer or chip. The grid spacing for the quarter wafer is 7 mm whereas the grid spacing for the chip is 4 mm.

SiO2 Quarter Wafer

Figure 2 shows the focus value map (height map) of the SiO2 sample measured by User A. The height map of Load 1 and Reload is not significantly different. The standard deviation of the difference is approximately 2.2 points, which is below a user's ability to focus on the nanoparticles -- a good user can focus on a nanoparticle within 5 focus value points. The difference in the height map of Load 1 and Load 2 has a standard deviation of approximately 5.6 points. The range of the focus value is 30 points.

Figure 2:  Height map of the SiO2 sample, User A

Figure 2: Height map of the SiO2 sample, User A

Figure 3 shows the height map of the SiO2 samples measured by User B. The standard deviation between Load 1 and Reload is approximately 5.1 points. The standard deviation between Load 1 and Load 2 is approximately 5.8 points.

Figure 3:  Height map of the SiO2 sample, User B

Figure 3: Height map of the SiO2 sample, User B

The focus values on the AE mark and the sample origin for Load 1, Reload and Load 2 is displayed in the table below. The focus value at the origin is smaller than the AE Mark by up to 62 points. This disparity is significant because the depth of field is approximately 7 points; a change in focus value of 10 points often adds a sufficient amount of blur when imaging the nanoparticles. Therefore, it is important to always focus on the sample surface before an exposure.

Focus Value
User A User B
AE Mark Sample Origin AE Mark Sample Origin
Load 38630 38610 38591 38551
Reload 38633 38613 38602 38555
Replace 38624 38613 38604 38542
Average 38629 38612 38599 38549
Standard Deviation 4.6 1.7 7 6.7

Figure 4 compares the average height map between User A and User B for the SiO2 sample. The standard deviation of the difference of the two height map is approximately 7.4 points or approximately 1 [μm]. The maximum range in the focus value is 30 points or approximately 3 μm, which is an incredible amount of mechanical repeatability. For small samples loaded into the piece holder cassette, the sample height is quite flat and there is little that can be done to improve it. However, it is important that the user focuses on the sample before each exposure because it varies significantly from time to time.

Figure 4:  Average height map of the SiO2 sample, User A vs User B

Figure 4: Average height map of the SiO2 sample, User A vs User B

Si Quarter Wafer

Figure 5 shows the height map of the Si sample measured by User A. The difference in the height map of Load 1 and Reload has a standard deviation of approximately 13.2 points, which is significantly different than the SiO2 sample. For the Load 2 measurement, the user did run into a strange problem where it was impossible to focus on any nanoparticle within a 2 mm range for the particular measurement position. The image appears very stigmatic. The user moved to previous positions and had no problem focusing, so it is not an instrument problem. In general, the results for User A for the Si and SiO2 sample are quite similar.

Figure 5:  Height map of the Si sample, User A

Figure 5: Height map of the Si sample, User A

User B was not able to gather a complete data set for Si before a 1 week trip. It is known from previous experience that in 2 weeks, the focus drifts and there may be other differences associated with the instrument. Nonetheless, User B was still able to make a single measurement. Figure 6 compares the average height map of User A and the single height map of User B for the Si sample. The disparity is not much different from for the SiO2 sample shown in Figure 4.

Figure 6:  Average height map of the Si sample, User A vs User B

Figure 6: Average height map of the Si sample, User A vs User B

SiO2 1/2"x1/2" chip

Figure 7 shows the height map of a SiO2 1/2"x1/2" chip measured by User A. The chip is placed at the corner of the quarter wafer region of the piece holder cassette. Measurements of the focus value is performed on a 3x3 grid with a 4 mm pitch. The origin of the measurement is at stage coordinate (62800,37800), which is near the top left corner of the chip. The difference in the height map of Load 1 and Reload has a standard deviation of approximately 3.3 points, whereas the standard deviation for Load 1 and Load 2 is 12.0 points. Surprisingly, the focus points vary by up to 140 points! If focus is a concern, do not use a chip sized sample on the piece holder.

Figure 6:  Height map of the Si sample, User A

Figure 7: Height map of the Si sample, User A

3 inch Wafer Cassette

Focus value measurements for the 3" wafer cassette is performed on a 22 mm x 22 mm grid centered on the wafer.

SiO2 Wafer

Figure 8 shows the height map of the SiO2 wafer measured by User A. The height map of Load 1 and Reload is not significantly different. The standard deviation of the difference is approximately 0 points. The difference in the height map of Load 1 and Load 2 has a standard deviation of approximately 9.5 points. The range of the focus value is 80 points.

Figure 7:  Height map of the 3 inch SiO2 wafer, User A

Figure 8: Height map of the 3 inch SiO2 wafer, User A

Figure 9 shows the height map of the SiO2 samples measured by User B. The standard deviation between Load 1 and Reload is approximately 5.0 points. The standard deviation between Load 1 and Load 2 is approximately 9.3 points.

Figure 8:  Height map of the 3 inch SiO2 wafer, User B

Figure 9: Height map of the 3 inch SiO2 wafer, User B

Figure 10 compares the average height map between User A and User B for the Si wafer, which looks nearly identical. The standard deviation of the difference of the two height map is merely 6.0 points, which is less than 1 μm. However, the range in the focus value is upwards of 80 points! Fortunately, the shape of the height map is consistent among the two users, so it may be possible to compensate by preprogramming the height map.

Figure 4:  Average height map of the SiO2 sample, User A vs User B

Figure 10: Average height map of the 3 inch SiO2 wafer, User A vs User B

Si Wafer

Figure 11 shows the height map of the Si wafer measured by User A. The height map of Load 1 and Reload is not significantly different. The standard deviation of the difference is approximately 3.4 points. The difference in the height map of Load 1 and Load 2 has a standard deviation of approximately 5.6 points. The range of the focus value is 92 points.

Figure 10:  Height map of the 3 inch Si wafer, User A

Figure 11: Height map of the 3 inch Si wafer, User A

Figure 12 shows the height map of the SiO2 samples measured by User B. The standard deviation between Load 1 and Reload is approximately 8.3 points. The standard deviation between Load 1 and Load 2 is approximately 17.4 points.

Figure 11:  Height map of the 3 inch Si wafer, User B

Figure 12: Height map of the 3 inch Si wafer, User B

Figure 13 compares the average height map between User A and User B for the Si wafer, which looks nearly identical. The standard deviation of the difference of the two height map is merely 6.2 points, which is less than 1 μm. However, the range in the focus value is upwards of 110 points! As we observed with the SiO2 wafer, the shape of the height map is consistent among the two users, so it may be possible to compensate by preprogramming the height map.

Figure 12:  Average height map of the SiO2 sample, User A vs User B

Figure 13: Average height map of the 3 inch Si wafer, User A vs User B

4 inch Wafer Cassette

Focus value measurements for the 4" wafer cassette is performed on a 22 mm x 22 mm grid centered on the wafer.

4 inch Si Wafer

Figure 14 shows the height map of the 4 inch Si wafer measured by User A. The height map of Load 1 and Reload is not significantly different. The standard deviation of the difference is approximately 3 points. The difference in the height map of Load 1 and Load 2 has a standard deviation of approximately 13.5 points. The range of the focus value is 130 points.

Figure 14:  Height map of the 4 inch Si wafer, User A

Figure 14: Height map of the 4 inch Si wafer, User A

Figure 15 shows the height map of the Si samples measured by User B. The standard deviation between Load 1 and Reload is approximately 16.5 points. The standard deviation between Load 1 and Load 2 is approximately 17.0 points.

Figure 15:  Height map of the 4 inch Si wafer, User B

Figure 15: Height map of the 4 inch Si wafer, User B

Figure 16 compares the average height map between User A and User B for the 4 inch Si wafer, which looks similar. The standard deviation of the difference of the two height map is merely 16.5 points. However, the range in the focus value is upwards of 130 points! Fortunately, the shape of the height map is consistent among the two users, so it may be possible to compensate by preprogramming the height map.

Figure 16:  Average height map of the 4 inch Si wafer, User A vs User B

Figure 16: Average height map of the 4 inch Si wafer, User A vs User B

Conclusion

The sample loading system for the JBX-5500FS electron beam writer is quite impressive. There is no significant difference in the height map between users and samples. The variations in the height map has a standard deviation that is slightly less than the depth of focus of the beam. However, there is significant disparity between the focus at the AE Mark and the sample origin. It is wise to always focus on the sample to ensure optimal performance from the instrument.

The height map for the piece holder cassette using a quarter wafer is quite flat with a range of approximately 30 points. Focusing on the top left corner of the sample should be fine. On the contrary, the height map for the piece holder cassette using a 1/2"x1/2" chip is the least flat and it is not recommended for patterns that require a tight focus tolerance.

The height map for the 3 inch wafer cassette has a range of up to 110 points! The shape of the height map appears to be similar among two users and two different substrates. This confirms that the design of the cassette minimizes the sample's influence on the height map. However, the variations in the height map is quite severe and must be compensated in order achieve a uniform patterning performance across a 3 inch wafer.

The height map for the 4 inch wafer cassette has a range of up to 130 points! The shape of the height map appears to be similar among two users. The bump in the middle of the wafer is probably caused by the backing plate. Since the height map is repeatable, it is probably prudent to compensate for it by adjusting the focus.

The average height map for a chip, quarter wafer, 3 inch wafer and 4 inch wafer is shown in the interactive plots of Figure 17, 18, 19 and 20, respectively. The default perspective of the plot matches the perspective of the user looking down on the cassette. The coordinates (-x,-y) is top left and the coordinates (x,y) is bottom right.

Figure 17: Height map of a 1/2 inch x 1/2 inch chip in the piece holder cassette

Figure 18: Height map of a quarter wafer in the piece holder cassette

Figure 19: Height map of a 3 inch wafer in the 3 inch wafer cassette

Figure 20: Height map of a 4 inch wafer in the 4 inch wafer cassette