After FIB milling, atomic force microscopy (AFM) was used to examine the 3D profile and depth of the FIB-milled pattern. Optical experiments were used to measure the characteristics of the microlens. The results of the measurements and experiments are presented in this chapter.
4-1 Test Pattern Measurement
Test patterns for the FIB milling were designed to characterize the milled spot size, and the pixel number of the test pattern was 512×512. The FIB parameters, such as step size of each pixel, dwell time, passes, and Z-size, etc., were varied to reveal the characteristics of the milled spot. Herein, the step size means the distance between non-blank pixels in the bitmap figure. Dwell time is the time for which the ion beam stays on a pixel. Passes is the number of times the 24-bit bitmap file is scanned by the ion beam on the sample surface. Z-size is the expected depth of the pattern. The Z-size will be increased as dwell time or passes increases. In addition, the magnification and beam current of the FIB system determine the actual distance between pixels and the actual depth of each pixel. Herein, magnification is the ratio of the viewing area on the monitor screen to the scanned area on the sample. The SEM micrograph of the test pattern in the conditions of magnification as 480x and beam current as 0.3 nA is shown in Figure 4-1. Figure 4-2 shows the AFM measurement results of the FIB-milled test pattern. The profile of the ion-milled spot is shown in Figure 4-3.
Several relations between the measured results, such as “spot size”, “depth”, and
“distance”, etc., are discussed below. Herein, as Figure 4-3 shows, “spot size” means the diameter of the ion-milled spot, “depth” means the maximum depth of the spot profile, and “distance” means the actual distance between spots. The relation between
the beam current and “spot size” is shown in Figure 4-4. The milled spot size increases as the beam current or dwell time increases, as shown in the figure. The relation between the step size and “distance” is shown in Figure 4-5. The slope of the curves (a) and (b) in the figure is about 65 nm/step and 26 nm/step, respectively. As the figure shows, the actual distance correlates closely with the magnification and is independent of the beam current. When the magnification increases, the actual distance decreases concurrently. The relation between the dwell time and “depth” is shown in Figure 4-6. The ion-milled depth increases for either increased dwell time or beam current. Also, the milled depth is related to the magnification. In the conditions of the larger magnification and smaller step size, the actual distance will be smaller than the ion-milled spot size. Therefore, a larger depth will be induced by the overlap of the ion-milled spots. The relation between the step size and “depth” is shown in Figure 4-7. According to the trend of the curves, the sudden increase of the depth at small step size is caused by the overlap. From the discussion about the spot profile and overlap conditions, the gray-scale profile can be designed for the FIB process.
In summary, the characteristics of the FIB-milled spots were obtained through the test patterns. In order to achieve the desired depth and retain the better shape of the ion spot, the maximum dwell time and ion beam current of the FIB system are chosen as 1 msec and 0.5 nA, respectively. To avoid the overlap, blank pixels can be inserted into the bitmap, as will be considered as follows.
Figure 4-1: SEM micrograph of the test pattern. (Conditions: 480x and 0.3 nA)
Figure 4-2: AFM profile result of the test pattern.
100 μsec
300 μsec
600 μsec
1000 μsec
Dwell Time
30 20 15 7 Step Size
Figure 4-3: Diagram of the spot profile.
Spot Size v.s. Ion Current (1200x)
1.50E-07
0 200 400 600 800 1000 1200
Ion Current (pA)
Figure 4-4: Ion-milled spot size versus beam current for various dwell time for 1200x magnification.
Distance v.s. Step Size (480x)
Distance v.s. Step Size (1200x)
3.00E-07
Figure 4-5: Actual distance versus pixel step size for various beam current for (a) 480x and (b) 1200x magnification.
Distance (m) Distance (m)
Step Size
Depth v.s. Dwell Time (480x)
0 2000 4000 6000 8000 10000 12000
Dwell Time (0.1usec)
Depth v.s. Dwell Time (1200x)
0.00E+00
0 2000 4000 6000 8000 10000 12000
Dwell Time (0.1usec)
Figure 4-6: Depth versus dwell time for various beam current for (a) 480x and (b) 1200x magnification.
Depth v.s. Step Size (1200x & 1nA)
Figure 4-7: Depth versus pixel step size for various dwell time for 1200x magnification and beam current of 1 nA.
4-2 Microlens and Mask Pattern Measurement
According to the information from the test pattern measurement, the FIB parameters for the milled patterns, i.e., the Fresnel microlens and gray-scale mask, are determined. The maximum dwell time and beam current are fixed to 1 msec and 0.5 nA as discussed above. To begin with, the microlens pattern had a diameter of 100 μm and the desired depth was about 528 nm. The step size was 1 in the bitmap. The FIB-milled pattern was measured by AFM, as shown in Figure 4-8. As the figure shows, the actual depth, about 24 nm, is too small and the milled profile loses the desired shape due to the overlap of the ion-milled spot.
0.00E+00
(a)
(b)
Figure 4-8: AFM measurement of the (a) middle region and (b) right-side region of the microlens pattern of diameter 100 μm.
Depth
The shallow milled depth was caused by the limited milling time allowed for each run. In this case, the depth problem can be solved by reducing the pattern diameter. The loss of fine structures in the outer rings in the milled pattern was caused by the overlapped ion spot. Therefore, blank pixels can be inserted in the bitmap figures for compensation. Figure 4-9 shows the measurement of a sample with a diameter of 50 μm and two inserted blank pixels. The whole profile of the pattern is shown in Figure 4-10. As the figures show, the profile is deeper than the non-compensated one and profile is closer to the design. But the depth of the pattern, about 88 nm, is still not enough, so the area of the milled region must be reduced again.
(a)
Figure 4-9: AFM measurement of the (a) middle region and (b) right-side region of the microlens pattern of diameter 50 μm.
(b)
Figure 4-9: (Continued) AFM measurement of the (a) middle region and (b) right-side region of the microlens pattern of diameter 50 μm.
Figure 4-10: AFM profile of the microlens pattern of diameter 50 μm.
For different magnification and pattern diameter, the total volume removed by the focused ion beam should be equal for the same dwell time and ion current. Based on this principle, the depth of the milled pattern can be roughly calculated as
2 2
1 1 2 2 removed
L × =d L ×d =V , (4-1) where L1 and L2 represent the pattern diameters in two different magnification, and d1
Depth
79.65 nm 88.32 nm
and d2 represent the corresponding depth of the FIB-milled patterns. The desired depth of the microlens and gray-scale mask is about 530 nm and 170 nm respectively;
the pattern diameter of the lens and mask can be calculated as 20 μm and 30 μm. To avoid the overlap caused by the reduced pattern diameter, seven blank pixels were inserted into the 20-μm microlens pattern and four blank pixels were inserted into the 30-μm gray-scale mask pattern. The AFM measurement results of the microlens are shown in Figure 4-11. Figure 4-12 shows the AFM measurement results of the gray-scale mask, and Figure 4-13 shows the whole profile of the mask. As the figures show, the depth of the gray-scale mask, about 211 nm, is a little larger than the desired depth, 170 nm; the depth of the microlens, about 525 nm, is close to the desired depth, 530 nm. So the pattern diameter of the mask should be tuned to match the design.
Besides, the height of the outer rings is decreased due to the overlap, so more blank pixels must be inserted into the bitmap figures.
Figure 4-11: AFM measurement of the microlens pattern of diameter 20 μm.
Depth
(a)
(b)
Figure 4-12: AFM measurement of the (a) middle region and (b) left-side region of the mask pattern of diameter 30 μm.
Depth
Figure 4-13: AFM profile of the mask pattern of diameter 30 μm.
The diameter of the third compensated patterns was 20 μm for the microlens and 35 μm for the gray-scale mask. In addition, ten blank pixels were inserted into the microlens pattern and six blank pixels into the gray-scale mask pattern. The 2D and 3D profile of the patterns are shown in Figure 4-14 and 4-15, respectively. The roughness analysis of the patterns is shown in Figure 4-16 to be about 3 to 4 nm, which is suitable for optical components. As the figures show, the depth of the microlens and mask was measured as 530 nm and 180 nm respectively, which is close to the desired value. But some overlap issues still cause the reduced height of the outer blazing rings. So, inserting more blank pixels must be considered to avoid the occurrence of the overlap. Figures 4-17 and 4-18 show the measured profiles of the nitride microlens and gray-scale mask compared with the designed 2D profiles, respectively.
Finally, the relation between the depth and pattern size, i.e., ion-scanned area, is shown in Figure 4-19. The measured data can be fitted by the curve
depth pattern size = c× , (4-2) where c is a constant and can be calculated as 1.9×102 μm3, as shown in the figure.
In summary, the Fresnel microlens in silicon nitride and the gray-scale mask for the microlens in AZ4620 are fabricated. The profile of the patterns is close to the design. In addition, the loss of fine structures can be overcome by inserting blank pixels into the bitmap figures.
235 nm 211.5 nm
(a)
(b)
Figure 4-14: 2D profile of the (a) microlens and (b) gray-scale mask.
Depth Depth
(a)
(b)
Figure 4-15: 3D profile of the (a) microlens and (b) gray-scale mask.
(a)
(b)
Figure 4-16: Roughness of the (a) microlens and (b) gray-scale mask.
Roughness Roughness
Figure 4-17: Comparison between the measured profile and designed profile for the silicon nitride microlens of diameter 20 μm.
Figure 4-18: Comparison between the measured profile and designed profile for the gray-scale mask of diameter 35 μm.
Thickness (nm) Thickness (nm)
Diameter (μm)
Diameter (μm)
* measured data
－ designed data
* measured data
－ designed data
Figure 4-19: Pattern size versus milled depth.
4-3 Optical Experiment
The Fresnel microlens was directly patterned in the silicon nitride film by the FIB system. Optical experiment was conducted to verify the performance of the microlens, as shown schematically in Figure 4-20. First, a proper distance was selected to ensure that the pattern of microlens is clearly displayed on the screen.
Then, the microlens or the objective lens was moved a certain distance to make the pattern on the screen shrink to a bright point, i.e., a focused spot. Therefore, the distance is the focal length of the microlens fabricated by the focused ion beam. After a series of optical experiments, the focal length was measured as about 12 μm, and the N.A. value of the microlens can be calculated as
1 10 μm
N.A. sin(tan ( )) 0.64 12 μm
= − ≈ . (4-3) Pattern Size (μm2)
Depth (nm)
* measured data
— fit curve
2 3
depth pattern size 1.9 10 μm× = ×
In addition, the screen was replaced by a CCD camera to check the profile of the focused spot. Figure 4-21 shows the image of the focused spot captured by the CCD camera. The intensity profile of the focused spot is shown in Figure 4-22, and the cross-section of the profile is shown in Figure 4-23, respectively. The FWHM (full-width at half-maximum) of the focused spot in the x-direction and y-direction can be calculated as about 0.64 μm and 0.66 μm, respectively. Therefore, the fabricated microlens is symmetric. The diffraction limit of a 0.64 N.A. lens is
0.5 0.5 0.633 μm
0.494 μm
N.A. 0.64
d λ ×
≈ = ≈ , (4-4) where λ is the wavelength of the laser used for the experiment, and N.A. is the numeric aperture of the microlens. Therefore, the numerical aperture, 0.64, of the fabricated microlens in silicon nitride is close to the specification, 0.65, of a DVD optical pick-up head. But the measured spot size of the focused spot is larger than the diffraction limit of the lens. The reason is that the height of the outer blazing rings is a little different from that of the design. The reduced height causes the reduction of the focusing ability.
Focal plane of the objective lens Objective lens
Figure 4-20: Schematic diagram of the optical measurement.
Screen
Figure 4-21: Image of the focused spot on the CCD camera.
Figure 4-22: Intensity profile of the focused spot.
0 0.2 0.4 0.6 0.8 1 1.2
20 15
10 5
0
25 30 15 20
5 10 0
μm μm
Relative intensity
y x
(a)
(b)
Figure 4-23: Cross-section of the intensity profile in (a) the x-direction and (b) the y-direction.
4-4 Summary
The relations between the FIB parameters, such as step size, dwell time, passes, and Z-size, etc., have been obtained through the test patterns. The profiles of the Fresnel microlens and gray-scale mask in silicon nitride fabricated by FIB milling has also been measured by AFM. Through the optical experiment, the numerical aperture of the fabricated microlens in silicon nitride is measured as 0.64, close to the specification of a DVD optical pick-up head. However, due to the reduced height of the outer rings, the measured spot size of the focused spot is larger than the diffraction limit of the lens.