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A line scan interferometer, which comprises a visible supercontinuum source coupled to Fourier domain Michelson interferometer, is used to obtain 3D images of ~300 μm high solder balls on a semiconductor die with 125 nm axial and 15 μm lateral resolution. The ability to measure curved surfaces enables the determination of solder ball shape defects in addition to ball height. We show that the maximum measurable angular tilt from the sample surface normal for a given source power depends on the surface roughness of the sample. As an example, we demonstrate height measurement over +/−20 degrees from the normal on the solder balls and over +/−60 degrees on a rough steel ball bearing sample.
©2010 Optical Society of America
1. Introduction
We demonstrate a line scan system with 125 nm axial (z) and 15 μm lateral (x-y) resolution for 3D inspection of curved surfaces. The system comprises of a visible super-continuum (SC) laser coupled to a Fourier domain Michelson interferometer via cylindrical optics. While the broad bandwidth (600-700 nm) of the SC source is responsible for the high axial resolution [1], the high laser average output power ~5mW enables the measurement of curved surfaces that reflect most light in a direction away from the receiver. The combination of sub-micron resolution and angular measurement capability make the system suitable for inspection of solder ball grid arrays used in the semiconductor industry.
Reduction in size of semiconductor devices has led to an increased density of chips on a wafer. Consequently, conventional wire leads that extend outside the integrated circuit’s physical dimensions are being replaced by solder ball grid arrays that can directly be flip-chip bonded with an external circuit. The reliability of electrical contact depends on the shape and size of solder balls deposited on the chip, and, thus, inspection of the balls is important for quality control [2]. Current 2D inspection techniques using machine vision can measure ball diameter and location, but provide no information regarding the height of different balls. 3D methods such as laser triangulation and confocal microscopy have been used to measure the ball height, but they do not provide any shape information [2]. Recent work by Ohta et. al. [3,4] has also shown 3D measurement of tilted and curved surfaces with ~1 m stand-off distance and 1.5 μm axial resolution using an all-fiber integrated point-scan interferometer operating at 1.55 μm. In comparison, the SC based line scan technique demonstrated in this paper enables determination of top shape of the ball by measuring the 3D profile over a +/−20 degree angle from the vertical axis of the ball with 125 nm axial resolution. Thus, this method enables the measurement of individual ball heights along with the ability to detect defective ball shapes.
The different sections in the paper are organized as follows. We begin by describing the optical layout of the line scan interferometer and the setup for generating the visible supercontinuum source in section 2. Next, in section 3, we determine the performance metrics of the system by using calibrated samples to measure the system’s axial and transverse resolution, axial measurement range, sensitivity and angular measurement capability. Section 4 describes the measurements performed on a ball grid array sample to determine individual ball heights and detect different types of shape defects. Finally, we discuss the limitations of the system and the scope for improvement in section 5 before summarizing the results in section 6.
2. Experimental setup
2.1 Fourier domain line scan interferometer
Figure 1 illustrates the optical layout for the line scan interferometer. While the setup resembles a conventional point-scan FD-OCT system, the introduction of a cylindrical lens and replacement of a 1D array with a 2D CCD camera enables the measurement along an entire line instead of a single point with each camera image [5]. The interferometer layout was modeled using ZEMAX software to provide the best imaging performance using standard off-the-shelf optics. We use a visible supercontinuum laser as our light source for this experiment and describe it in further detail in section 2.3.
First, the light from the supercontinuum source is collimated to an 8 mm diameter beam using a 10X microscope objective. The collimated beam then passes through a 100 mm focal length plano-convex cylindrical lens CL1 followed by an equal focal length spherical achromatic doublet L1 separated from CL1 by 200 mm. This imaging geometry transforms the 8 mm circular beam at the input of CL1 to an 8 mm long (y-axis) by 15 μm wide (x-axis) line at the focal plane of lens L1. The positioning of the non-polarizing cube beam splitter just after lens L1 ensures that an identical focused line is generated in both the sample and reference arms. After reflection from the sample and reference mirror M2, the object and reference beams are re-combined at the beam splitter and produce an interference pattern. Variable neutral density filters ND1 and ND2 are used to adjust the balance between the light intensities in the two arms of the interferometer. In order to extract the sample height information from the interference pattern, it must be spectrally dispersed and imaged onto a camera.
The interferogram is spectrally dispersed along the x-axis by passing the light through a 600 groves/mm transmission diffraction grating while achromatic doublet lenses L2 and L3 (both with 100 mm focal length) are used to image the wavelength resolved interferogram onto a 2048 x 2048 pixel CCD camera. Since L2 and L3 are identical lenses, the 8 mm long line on the sample is imaged 1:1 along the camera’s y-axis. Thus, while the CCD rows contain spatial information along the line (y-axis), the spectral information is contained along the CCD columns. Hence, a single image frame of the CCD provides height information along the entire line [6,7] and a complete 3D scan of the sample only requires a 1D translation of the sample along the x-axis.
2.2 Extraction of sample height from CCD images
The extraction of meaningful sample height data along the imaged line requires post-processing of the images acquired by the CCD camera. We used a 4 step algorithm to perform the required image processing analysis in Matlab. The detected spectrum as a function of frequency in each CCD row is given by [8]
The above equation represents the total intensity from three terms – only reference arm power, only sample arm power and interference between the sample and reference arms. However, the useful information about sample height information is only contained within the third interference term and the axial scan is obtained by taking the Fourier transform of this term. Thus, the first step in our algorithm is to remove the dominant DC term by performing a background image subtraction. This is accomplished by blocking the light in the sample arm and capturing an image with the light reflected from just the reference arm. This background image is then subtracted from each image before proceeding to the next step. In the 2nd step, we select a sub-frame from the entire 2048 x 2048 pixels image frame to define the spatial extent of the imaged line and the spectral range of the continuum to be used for processing. In our experiments, each row pixel corresponds to 7.4 μm of the line length while each column pixel represents a spectral bandwidth of 0.116 nm. We used 768 rows corresponding to the central 5.7 mm section of the 8 mm long line and 860 columns corresponding to the 100 nm wavelength range from 600 to 700 nm. We only used 100 nm of the available SC spectrum due to increased chromatic aberration from the cylindrical lens singlet for wider bandwidths.
The Fourier transform (FT) process requires equally sampled points in the frequency space while the light from the grating is spread across the CCD columns in equal wavelength increments. Thus, in step 3, the wavelength interferogram along each row is converted to a frequency interferogram and then re-sampled using a cubic-spline interpolation algorithm [9,10] to generate 1024 equally spaced points in the frequency domain. In the final step, the result is Fourier transformed to the z-space using a 32,768 point fast Fourier transform algorithm.
Since the samples we use are not multi layered biological tissues but instead metallic, we simplify our analysis by assuming that all reflections come from a single layer at the top of the sample surface. Under this assumption, the z position of the peak of the FT curve is assigned as the distance of the corresponding point on the sample from the interferometer zero delay position. Repeating this procedure for each row of the image produces a height profile of the sample along the imaged line (y-axis). By processing multiple images corresponding to different sample positions along the x-axis, we can build up a complete 3D map of the surface. An important precaution to take while performing this experiment is to always place the sample entirely on one side of the zero delay position. A sample surface that straddles the zero delay position would have ambiguous height measurements since the FD technique only measures the magnitude of the sample distance and not the sign.
2.3 Visible supercontinuum generation
This section briefly describes the visible supercontinuum laser source [11] used in the line scan system. A block diagram of the three stage laser is illustrated in Fig. 2 . The first stage comprises a 1553 nm DFB laser diode that is gain-switched to produce a 1 ns pulse at 400 kHz repetition rate. The pulses are amplified to 1.5 kW of peak power by a single mode Erbium doped fiber pre-amp followed by a cladding pumped Erbium-Ytterbium co-doped fiber power-amp. Next, the output from the power-amp is frequency doubled with 65% efficiency using a 10 mm long periodically poled lithium niobate (PPLN) crystal kept at 159.4°C.
In the final stage, the frequency doubled output from the PPLN at 776.5 nm is coupled into a 3m long photonic crystal fiber using a 20X microscope objective to generate the continuum spectrum shown in Fig. 3 . While the total SC spectrum extends from 500 – 1200 nm, the line scan interferometer design only utilizes 100 nm of the SC spectrum from 600 – 700 nm to minimize the effects of chromatic aberration caused by the cylindrical lens. After collimating the output from the PCF using the 10X objective described in Section 2.1, we measured the average power in this spectral region to be 5 mW using a 600 nm long pass and 700 nm short pass filter.
3. System calibration
3.1 Transverse and axial resolution
In this section, we determine the system resolution along each linear axis. Along the x-axis, we define the resolution as the 1/e2 width of the line shaped focus at the sample surface. We determined this value to be ~15 μm using a razor edge scan to sample the beam profile. First, we selected the wavelength range of 600-700 nm using filters and used an aperture to select a 1 mm long section at the center of the 8 mm long line. Next, a power meter was placed behind the aperture while a razor edge was scanned along the x-axis of the beam. Thus, we obtained an integrated curve of the beam power along the x-axis from which the 1/e2 Gaussian full width could be deduced.
The resolution along the y-axis is determined by the imaging geometry of the interferometer design. Since lenses L2 and L3 in Fig. 1 have an equal focal length of 100 mm, the 8 mm long line on the sample surface is imaged with a magnification ratio of 1:1 along the CCD’s y-axis. Thus, the y-resolution of the system is now simply defined as being equal to the camera pixel size of 7.4 μm.
The z (axial) resolution of the system is related to coherence length of the light source used, which in turn depends on the optical bandwidth. The theoretical value of the coherence length for a light source with a Gaussian spectrum is given by [3]-
where λ0 is the center wavelength and Δλ is the full width at half maximum of the source spectrum. However, for a light source with a rectangular spectrum such as our visible SC, the multiplicative factor in Eq. (2) ~0.60. In our system, we have λ0 = 650 nm and Δλ = 100 nm which gives lcoh ~2.54 μm. The coherence length of the SC source was also determined experimentally by placing a flat silver mirror in the sample arm at a distance of 50 μm from the zero delay position and obtaining the z-profile (Fig. 4 ) at the center of the line. The experimentally measured coherence length is defined as the FWHM of the peak and was determined to be ~2.50 μm which is in good agreement with the theoretical value.The relationship between the axial (z) resolution and coherence length depends on the nature of the sample under test. For a tissue sample in an OCT setup, the two values are defined as being equal due to the multiple reflections from different layers. However, unlike OCT, we are not trying to determine the layers within the sample but instead determine the 3D shape of the sample surface. As described earlier in section 2.2, we assume that all reflections from a metallic sample arise from a single layer and we assign the peak location of the FT curve as the sample height measured from the zero delay position. Under this assumption, the location of the peak of the curve can be super-resolved to much better than the nominal 3 dB width [3]. In our system, we achieved a factor of 20 improvement and thus define the axial resolution to be 1/20th of the measured coherence length i.e. 125 nm.
Finally, we verified our estimate of the axial resolution by measuring a calibrated step height standard coated with aluminum. Figure 5 shows a 3D view of the 1mm x 1mm sample as measured with our line scan interferometer with a clearly resolved step in the middle. We measured the step height as 125.2 nm +/− 17.7 nm. The error bar was obtained by determining the standard deviation of the heights in each individual plane of the step and calculating the square root of the sum of their squares to estimate the standard deviation of the step height measurement. The experimentally observed value is in close agreement with the 131.0 nm measured by a calibrated Dektak stylus profilometer.
3.2 Sensitivity
The sensitivity of the system is a measure of the smallest reflectivity of the sample arm that produces a minimum detectable SNR = 1. The theoretical expression for shot noise limited sensitivity in the Fourier domain configuration is given by [12],
where Psample is the sample arm power returning to the detection arm, η is the efficiency of the spectrometer system, τi is the camera integration time, h is the Planck’s constant and ν is the center frequency of the light. While the above equation was obtained for a point-scan system, it is still valid for our line scan system provided we redefine Psample as the sample arm power returning to the detection arm towards each individual CCD row and not the entire camera. With an ideal reflector in the sample arm, we measured 0.5 mW power returning to the detection arm and imaged across ~1000 CCD rows resulting in Psample ~0.5 μW. The spectrometer efficiency η was determined to be 0.20, the integration time was set to 100 μs and the center wavelength was 650 nm. Thus, the theoretically expected sensitivity is SNRFD = 75.1 dB.The sensitivity of the system was also determined experimentally by using a weak reflector in the sample arm. A 99% reflectivity mirror was placed in the sample arm with a 10 dB neutral density filter in front of it to provide a total of 20 dB attenuation to the light in the sample arm. The mirror was placed at varying distances from the interferometer zero delay position and the height along the line was measured for each position using the technique described in section 2.2. Figure 6 shows the obtained FT z-space curves at the center of the imaged line for the different positions of the sample arm mirror.
We calculate the system sensitivity at a given position of the sample by adding the SNR of the corresponding curve (20 times the log ratio of the peak to the standard deviation of the noise floor) to the known attenuation of the sample arm [13]. At z = 100 μm, the SNR is measured as 50.4 dB, resulting in a system sensitivity of 70.4 dB. We attribute the deviation of 4.7 dB from the theoretically expected value largely due to excess relative intensity noise in the SC source above the shot-noise limit. In addition, numerical sampling errors and mechanical vibrations in the interferometer setup also contribute to the degraded system sensitivity.
3.3 Axial measurement range
The axial measurement range in a Fourier domain system is limited by the finite spectrometer resolution. The axial position of the sample is encoded as a function of the periodicity of the interference fringes. The wavelength separation between adjacent fringe maxima decreases as the sample distance from the zero delay position increases. The maximum measurable range is reached when the fringe period becomes less than 2 pixels wide. The theoretical maximum measurement range for an FD-OCT system is given by [6]
where δλ is the spectrometer resolution. In our system, the 100 nm wide spectrum centered at 650 nm is spread across 860 horizontal pixels (columns) to give δλ = 0.116 nm. This gives a maximum measurement range zmax = 910 μm and is consistent with the experimentally obtained data shown in Fig. 6. We observe a characteristic depth dependant decrease in system sensitivity due to increase in sampling errors at longer delays attributed to finite spectrometer resolution [12]. At the far end of the measurement range near z = 900 um, the sensitivity is almost 32 dB lower than the maximum obtained near the zero delay position.3.4 Angular measurement range
The angular measurement range of the line scan system depends on a combination of source power, camera exposure time and sample surface finish. Utilizing the full dynamic range of sample reflectivities that can be measured by the system requires that the strongest reflection from the sample produce an interference signal just below the camera saturation. On the other hand, the weakest detectable reflection must be above the system sensitivity. As per the analysis performed in [14], the maximum sample signal and dynamic range of sample reflectivities is given by,
where Nsat is the number of photoelectrons that saturate one camera pixel, Nref is the number of photoelectrons generated by the reference arm signal, γ = Nref / Nsat and N is the number of wavelength pixels. Figure 7 below shows the curves for variation of dynamic range and Ns,max/Nsat versus γ for our system (camera well depth Nsat = 40,000 and N = 860). Since our measured system sensitivity was −70.4 dB and the strongest reflection from any of our samples was – 4 dB, we operated at a reference arm power corresponding to γ = 0.25 resulting in a DR = 66.3 dB.The following procedure was used with each sample to ensure optimal use of the above dynamic range. First, the camera exposure was set to the lowest possible setting of 20 μs. The reference arm was blocked, and the sample was positioned at the location of the strongest reflection. In the optimum situation, we must ensure that the strongest reflection from the sample equals the maximum allowable sample reflection for a given γ. From Fig. 7, we observe that for γ = 0.25, we should have Ns,max = 0.25 Nsat. In order to meet the above condition, the exposure time of the camera was increased until the strongest reflection from the sample had a signal level of 64 gray levels (25% of the saturation value of 256 gray levels). Finally, the sample arm was blocked and the ND filter in front of the reference arm mirror was adjusted until this reflection also had a value of 64 gray levels, thereby ensuring that we set γ = 0.25.
We used two chrome steel ball bearing samples of identical size (3.17 mm diameter) but different surface finish to determine our system’s angular measurement capability. Sample #1 was left in its original high reflectivity polished state while sample #2 was roughened using a 240-grit sandpaper to provide enhanced diffused scatter. The ball bearing samples were scanned along the x-axis in 15 μm increments and the resulting CCD images were processed using the algorithm described in Section 2.2. Before plotting the results on a color coded height map, an additional step was performed to delete points on the ball with an insufficient SNR to accurately determine the ball height at that point. All points with an SNR < 10 dB in the FT z-space curve (as described in Section 3.2) were not assigned any color and are instead just plotted as a white pixel.
The 3D height maps obtained for the polished and roughened ball bearing samples are shown in Fig. 8a , 8b and 8c, 8d respectively. In the case of the polished ball, we were only able to measure over an angular range of +/− 20 degrees from the ball normal. We were unable to map out the ball bearing surface at steeper angles since the non-specular reflection from the ball surface at these angles was below the sensitivity limit of the system. On the other hand, we were able to obtain height information over +/− 60 degrees from the roughened sample due to the surface reflectance being more diffuse as opposed to specular. The difference in observable angular range between the two samples is due to the difference in reflectivity fall-off rates from the normal to off-normal angles. In the polished ball bearing, the reflectivity falls of much more rapidly in non-specular directions compared to the gradual decrease in the roughened ball. Table 1 below summarizes the performance metrics of the line scan system.
Fig. 8 (Color online) 3D scan of steel ball bearing – (a) Polished ball - top view, (b) Polished ball - side view, (c) Roughened ball - top view, (d) Roughened ball - side view.
Table 1. Performance metrics of line scan system
4. Experimental results – measurement of solder ball grid array
4.1 3D map of sample surface
After completing the characterization of the system’s performance metrics, we performed a 3D scan on a solder ball grid array sample. The sample consists of 75 spherical solder balls on a 4.5 mm x 5 mm silicon die. The solder balls are ~300 μm high and are positioned on a square gird with adjacent ball spacing (center to center) of ~500 μm. The sample was placed on a stepper motor and a Labview program was used to scan the sample along the x-axis in 15 μm increments. The program also controlled a frame grabber card that captured interference images from the CCD camera at a rate of 2 frames/sec resulting in a net linear scan rate of 30 μm/s. We acquired 300 images (4.5 mm) to cover the entire area of the die and then processed the images in Matlab using the algorithm described in section 2.2. Finally, we removed any horizontal and vertical tilt from the processed 3D image resulting from errors in the initial positioning of the sample.
The final obtained image in Fig. 9 shows the resulting 3D map of the sample with a leveled substrate and ball tops of different heights and shapes. The color bar shows the height of each pixel as measured from the interferometer zero delay plane. Locations on the sample which did not reflect sufficient light back towards the camera are shown in white as they did not produce a measurable interference pattern to extract a meaningful height value. While almost all points from the base of the sample could be measured, we could only measure +/− 20 degrees on most ball tops due to the mostly specular reflection from the shiny solder balls.
Fig. 9 (Color online) 3D height map (microns) of solder ball grid array. Row and column numbers 1 to 9 are used to identify the grid position of the solder balls.
4.2 Ball heights and dynamic repeatability
The overall 3D map of the sample needs to be further processed to extract information regarding the height of each ball. We obtain the dynamic height repeatability of each ball by removing the BGA sample from the stepper motor stage at the end of each scan and then placing it in the sample holder again before the start of the next scan. Thus, for each independent scan performed in the above manner, vertical and horizontal tilt correction was performed to the height map before determination of ball heights. The simplest algorithm is to subtract the average substrate base height around each ball from the highest point on the corresponding ball. However, we found this algorithm lacked robustness when determining the dynamic height repeatability of each ball.
Thus, we decided instead to define the height of each ball as the average of the 9 highest pixels on each ball minus the average height of the surrounding flat base. While the new algorithm produced ball heights which were lower than the true heights of the ball, we significantly improved the repeatability of the measurements. We illustrate our results by using the above algorithm to perform a dynamic height repeatability test on a subset of the solder balls. Table 2 below shows the mean height and standard deviation obtained for the 9 balls in column 3 of the die after 10 independent scans of the same region. The overall dynamic repeatability of the height measurements is defined as the worst case standard deviation of ~167 nm. We believe the variations in the values of the standard deviation in the table below arise due to the relatively large pixel size (15 μm x-pixel and 7.4 μm y-pixel) compared to the ball size (~290 μm). Thus, repeated scans of the same ball produce different height results as each scan might sample slightly different regions on the ball due to differences in initial sample positioning. While the repeatability results were adequate for the intended application, we believe further improvements can be made to the repeatability using a better algorithm based on obtaining a best fit sphere for the points.
Table 2. Average solder ball heights (column 3 of the die) and standard deviation over 10 independent scans
4.3 Measurement of solder ball shape defects
In addition to determining ball height, the line scan system also enables the measurement of the solder ball top shape. While a normal ball has a round top, we can see from Fig. 9 that some balls have other shapes. We shall discuss examples of three of the most common defect types below. First, we look at the following two balls – Col 1 Row 9 and Col 2 Row 6. Both these balls are shown in orange on the color map indicating a lower height than most of the other balls which are in red. This defect is known as a flat top and looks like a ball that has been squished from the top. Thus, we get a distinct image with a large number of pixels on the ball with similar height distribution and lower average height than non defective balls.
The second type of defect consists of incomplete spheres such as the balls in Col 1 Row 1 and Col 2 Row 9. One way to indentify these defects is the occurrence of a large number of white pixels (due to absence of reflecting material resulting in low SNR) at the location of the top of the ball. In addition, the presence of two or more clusters of points separated by a discontinuity also indicates the presence of missing solder from the ball shape. Finally, the third type of defect as seen in the ball in Col 9 Row 8 represents a ball that is positioned at the incorrect grid location. This defect can be identified by determining the x-y position of the ball center and comparing its distance to the centers of neighboring balls. Figures 10a , 10b and 10c show the line scan 3D view of each type of defect while Figs. 11a , 11b and 11c show the corresponding 2D microscope image.
Fig. 10 (Color online) 3D view of solder ball defects – (a) Flat top, (b) Incomplete sphere, (c) Incorrect grid location.
Fig. 11 2D microscope view of solder ball defects – (a) Flat top, (b) Incomplete sphere, (c) Incorrect grid location.
5. Discussion
We have demonstrated that the angular measurement capability of the system depends on the sample surface roughness and optimum utilization of the system’s dynamic range. In our system, the limitation in the range of angles that could be measured for a given sample was based on two factors. First, we can see from Eq. (6) that the dynamic range of sample reflectivities that can be successfully measured for a given reference arm power is directly proportional to the camera well depth. Hence, by using a CCD camera with a larger well depth, we can increase the dynamic range and measure over a wider range of angles.
The second factor that limits the measurement of weak reflections at steeper angles from the sample is the system sensitivity. As can be seen from Eq. (3), the system sensitivity can be increased by increasing the source power incident on the sample or the camera exposure time. While the above equation is only valid for a shot noise limited light source, the SC light source in our setup was generated by a modulation instability process and hence suffered from additional amplitude fluctuations [11]. We determined the noise of the SC source to be ~1.5x higher than the shot noise limit producing a degradation of 3.5 dB in the system sensitivity. However, in section 3.2, the difference between the theoretical and experimental sensitivity was measured as 4.7 dB. We believe the additional 1.2 dB degradation arises from numerical errors in the interferogram re-sampling process as well as mechanical vibration instabilities in the interferometer setup.
The problem of excessive noise can be solved by replacing the SC source with a low noise broadband super-luminescent diode (SLD). SLDs with a center wavelength of 825 nm, 60 nm of 3 dB bandwidth and >15 mW of single mode fiber coupled output power are already commercially available. While the SLD would offer near shot noise limited performance, the main drawback would be the reduction in the system’s axial resolution. While our 100 nm wide SC centered at 650 nm has a theoretical coherence length of 2.1 μm, the SLD based system would only have 5.7 μm of coherence length. Given an identical improvement factor using super-resolution, the SLD based system would have ~340 nm of z-resolution compared to the 125 nm of the current SC based system.
Finally, we determine the limitation in the scan speed of the system and investigate the potential for improvements. The system demonstrated in this paper measures a 5.7 mm x 15 μm area every 0.5s with a typical camera exposure time of 100 μs. Even though our camera is capable of 15 fps operation, our custom Labview program used to control the sample stepper motor and frame grabber card currently operates at just 2 fps. Thus, while we have sufficient source power to make measurements with just 100 μs of camera exposure time, the speed bottleneck arises from the extremely slow frame rate of the camera. In theory, we can achieve a 1000x improvement in speed using a 2,000 fps camera and still be limited by the frame rate and not a lack of SNR. Watanabe et. al. [15] have demonstrated a high speed line field FD-OCT system using a 1500 fps CMOS camera for in-vivo measurement of a human finger-tip.
Another way to increase speed with limited camera frame rates is to increase the line length incident on the sample surface. In our system, we had an 8 mm line incident on the sample of which only the central 5.7 mm was used for processing to ensure more uniform sample illumination intensity. The length of the line was determined by the imaging performance of the cylindrical lens CL1 in Fig. 1. While large diameter high performance spherical lenses are easily available off the shelf, obtaining an achromatic and diffraction limited performance cylindrical lens of >1” diameter requires expensive custom design and manufacturing. However, with a combination of longer line length and higher scanning speed, the system may potentially be suitable for rapid in-line inspection of bumped wafers.
6. Summary
In summary, we have demonstrated a visible supercontinuum based line scan FD interferometer with an axial resolution of 125 nm, lateral resolution of 15 μm and sensitivity of 70.4 dB. We used the above system for the simultaneous height and top shape measurement of ~300 μm high solder balls on a semiconductor die sample. By measuring over a +/− 20 degree angle down the ball tops, we were able to identify solder ball shape defects such as flat top, damaged center and incorrect location.
The ability to measure curved surfaces at large incidence angles depends strongly on the surface roughness of the sample and requires an optimization of reference arm power and camera exposure time to utilize the maximum dynamic range. We successfully demonstrated measurement over +/− 60 degrees on a rough 3.17 mm diameter steel ball bearing. The angular measurement range in our system for a given sample finish was limited by the intensity fluctuations of the SC source and the camera well depth. Finally, we determined that the commercial viability of a wafer inspection system requires an increase in scan speed of the system, which is currently limited by the camera frame rate.
Acknowledgements
This work was funded by Coherix Inc. and NIST under the Advanced Technology Program.
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