The electron beam writer exposes a pattern by scanning a gaussian beam to fill in the shapes. The diameter of the gaussian beam depends on the focal point of the beam and the position of the sample. Ideally, the beam should always be focused on the sample surface. In practice, the sample is not flat enough. The variable working distance is problematic because it affects the beam diameter, scan field rotation and scan field size.
For the 3 inch prime wafer, the SEMI specification for total thickness variation is 25 [μm]. The total thickness variation is a measure of the difference between the maximum and minimum thickness values across a wafer. A 3 inch prime wafer also has other specifications for flatness such as bow (40 [μm]) and warp (40 [μm]).
The actual surface flatness needs to be measured after the sample has been loaded into a cassette. This is called a height map. Figure 1 is the average height map for a quarter wafer in the piece holder cassette. The details of height map measurements is described in the sample height page. In general, the height map for each sample size and cassette is different, but it is repeatable. Therefore, once the height map is measured, it can be used to instruct the electron beam writer to compensate for focus errors on the sample.
Figure 1: Height map of a quarter wafer in the piece holder cassette
The beam size varies with the focus value. The autofocusing routine can be used to measure the beam size, as shown here. The size of the beam effects the resolution of the print. For example, we have printed 400 [nm], 200 [nm], 150 [nm] and 100 [nm] periodicity line gratings with 50% duty cycle. The patterns are printed on a sample consisting of Si/SiO2(500nm)/PMMA(115nm). The patterns are exposed at 400 [uC/cm2] using M4_A2_1nA (Mode 4, Aperture 2, 1 nA). The focus value is varied from -80 [points] to 80 [points]. The grating patterns are printed within 100 [μm] of each other to ensure negligible difference sample height.
Figure 2 is a plot showing the width of the exposed line patterns as a function of focus value. The minimum width for the line patterns are found at a focus value of 40 and 60. Below 40 points and above 60 points, the width of the line patterns increases. This trend is observed for all three sizes of gratings. It is also important to realize that the best focal value is approximately 50 [points] above the calibrated focus value. When performing calibration, the electron beam writer will focus on the AE mark which may not be on the same plane as the sample. Focusing on the sample is better than focusing on the AE mark, but remember that the sample is not flat.
Figure 2: Grating line width vs focus value of gratings exposed at 400 [uC/cm2]
Figure 3 is shows the grating width as a function of focus value when the pattern is exposed at 300 [uC/cm2]. At this dose, the focus value has a weaker influence on the pattern widths. In addition, it is possible to print 100 [nm] periodicity line gratings within a very small focus window.
Figure 3: Grating line width vs focus value of gratings exposed at 300 [uC/cm2]
The electron beam writer draws patterns on a 2D plan by deflecting the beam at an angle, as described here. The deflection calibration is performed on the BE mark, so if the sample is further away than the BE mark, then the same deflection will result in a wider scan. In addition, the scan field will also be rotated. The influence of focus on deflection errors can be investigated by printing the pattern shown in figure 4.
Figure 4 shows 12 grating patterns (200 nm pitch with 50% duty cycle) printed using M2_A2_1nA (Mode 2, Aperture 2, 1nA) at a dose of 350 μC/cm2. The patterns are designed such that half of each grating belongs in one field and the other half belongs in a different field. In addition, the gratings that crosses a vertical field boundary are horizontal lines and the gratings that crosses a horizontal field boundary are vertical lines. If there are any imperfections in stitching the fields, it will be revealed at the field boundaries where the patterns are expected to match.
Figure 4: This test pattern is used to characterize deflection and rotation error
Figure 5 shows the seams for vertical grating patterns at different focus points. As the focus point increases from -90 to +90, the patterns are initially overlapped and gradually moves apart. This is indicative of the field size shrinking as the focus value increases and, on the contrary, the field size increases as the focus value decreases. The focus value also affects the rotation of the field, which is revealed by the misalignment of the gratings. The rotation error is easily observed when looking at the edge of the gratings. In this experiment, the rotation error is approximately 0 at a focus value offset of 0. At positive focus value offsets, the rotation is counterclockwise; and at negative focus value offsets, the rotation is clockwise.
Figure 5: This series of images shows the deflection and rotation error vs focus value
After carefully analyzing the image and assuming a linear relationship between focus vs gain and rotation, we determined that:
High end electron beam writers are equipped with height compensation units that monitors the height of the sample surface and adjusts the focus before printing. For systems without height compensation hardware, it is possible program the adjustments if the height map of a sample is known.