Research on Defect Inspection Technology for Bump Height in Wafer-Level Packaging Based on the Triangulation Method

Abstract

With the advent of the era of big data and the vigorous development of consumer electronics, the demand for higher-speed processing capacity for gigantic amounts of data is increasing; this requires finer and far more numerous connections between dies as an essential component for connection and electronic communication between layers. The coplanarity of the height of micro bumps is crucial to ensure the reliability of the chip. The triangulation method has been widely used in various types of visual inspection applications over the past several years due to its high measurement accuracy and fast detection speed. In this paper, the application of triangulation technology is analyzed and used in micro bump height measurement. The measurement system proposed consists of a delicate design, a linearly arranged light projection module and a high-quality imaging module. Along the light stripe, multiple-height data of micro bumps are collected in a frame, and the full-field measurement is realized as the wafer is driven by the high-precision motional stage, following the optimal measurement route planned previously. In the scanning process, the images of the light strip projected on the top and bottom of the micro bumps are simultaneously acquired by the sophisticated micro vision system, and then the heights of micro bumps are calculated from a simple formula based on the geometry of the specimen and the system configuration. The experimental results demonstrate that the measuring deviation of the micro bump height has an accuracy of 1.5 μm.

1. Introduction

Wafer-level packaging is an important solution in the chip packaging process due to its advantages of high density, smaller package size and lower production costs. In this major process, bumps are crucial components, as the electrical connections between chips to ensure the transmission of information [1,2]. With a gigantic number of bumps deposited on a die or wafer, with greater than 2000 bumps per die, the coplanarity of the bump height becomes one of the most important parameters in the bumping process. The taller bumps may lead to strong stress, while the bumps with smaller height will cause insufficient connection during the bonding process. Both the situations mentioned above will result in the potential insecurity of chips. Additionally, these failure modes will become even more significant for the bumps with smaller dimension and height [3]. Therefore, it is essential to accurately measure the heights and coplanarity of bumps [4,5]. The traditional inspection method to measure bump height for small, intricate chips is that using a confocal microscope [6] and optical interferometry [7], which requires a series of repeated adjustments to control the light intensity, focusing position, incident angle, and other parameters. The methods mentioned above fail to meet industrial real-time measuring demand for online detection, as dozens of wafers need to be detected per hour in the packaging defect detection production line. Although this method has a high measuring accuracy, it is a costly and time-consuming solution that prevents companies from meeting the needs of high measuring speed in mass production. Meanwhile, it takes a lot of time to train workers in these methods and in routine maintenance, which means a major investment in engineering resources. Yongkai Yin [8] researched fringe projection with phase-shifting technology for three-dimensional measurement of micro solder bumps. However, the spherical geometry and textureless specular surface of bump caps causes the loss of phase information, which further results in huge measurement errors. Additionally, the phase unwrapping and phase matching require greater computation. In [9,10,11], the bump height was calculated from the shadow images of the bump; meanwhile, another image without a shadow was needed to fit the circle contour of the bump. Due to the different lighting conditions of these two images, images needed to be acquired successively at the same location in this method, meaning an inefficient operation in the inspection process. Mei Dong [12] pointed out that the coplanarity of the bump heights was only related to the top points of bumps, and not to the 3D contour profile. Consequently, the author proposed a conversion from the bump height calculation to the top point detection of bumps, and then the investigation of two planes and coplanarity calculated from two images based on the biplanar disparity matrix. In this way, explicit 3D reconstruction can be avoided. However, this method is sensitive to the wafer location and wafer title, and as a result, the measurement is highly dependent on the motion accuracy of the stage.

Triangulation technology has been used in the three-dimensional data acquisition of solder bumps in BGA packaging due to its high speed and high precision advantages. Reza Asgari [13,14] introduced the laser triangulation method in bump height measurement of micro bumps. It requires extremely complex algorithms to eliminate the speckle effect in the image due to exceedingly small laser spots.

This work aims to provide a new system for micro bump height measurement based on the triangulation method, in order to provide bump height metrology with high speed and precision. The triangulation method explained in this study is a linear stripe with the ability to measure multiple 3D bump height along the scan line. The results of an application study of 50 μm bump height and 100 μm bump pitch are reviewed. The repeatability of the bump inspection was tested, and the results showed that the measuring deviation of the bump height is within 1.5 μm.

2. Methodology

As shown in Figure 1, the basic measuring principle of triangulation is formed by a light projector, an imaging lens and a detector. A linear light stripe beam is projected onto the measured surface at a certain angle, and the detector collects the reflected light from different positions, shown as plane $A$ and plane $B$. The deviation of the different positions on the detector is calculated and the height difference between plane $A$ and $B$ can be deduced. For the height measurement of the micro-bump on the wafer, the height difference between the top of the bump and the wafer surface is calculated using the triangulation method.

Different incident and receiving angles are selected according to the reflectivity of the measured object. As is shown in Figure 2, the main bump geometry used in wafer-level packaging is a cylinder pillar with a spherical cap of radius $r$. Cu and Ni are typical bumping materials, and SnAg alloys are also adopted as one of the material compositions due to their excellent mechanical properties and precise control of the composition during electroplating [15,16]. Due to their metal material properties, both the hemispherical surface and the wafer surface have the property of high reflectivity. As a result, the light projector and the detector are symmetrically distributed to receive reflected light from the shiny measured area, as shown in Figure 3.

To improve the measuring speed, A linear light stripe is used instead of light spot. When the light beam is projected simultaneously onto the top of the bump and the surface of the wafer with neglected light width, as shown in Figure 3, the height from the top of the bump to the surface of the wafer is easily deduced, and can be stated in Equation (1).

(1)$\begin{array}{ll}y& =(x/\beta )/\sin (2\theta )\cos (\theta )\\ & =x/(2\beta \sin \theta )\end{array}$

In the equation above, $y$ is the height of the bump, while $x$ is the distance between different light strips detected on the CCD or CMOS detector caused by reflected light from different surfaces. The parameter $\beta$ is the magnification of the imaging system, and $\theta$ is the angle between the incident light and the normal wafer surface.

However, in practical situation, the beam width cannot be ignored, and it cannot be projected onto the top of the bump with its light bar center coinciding with the highest point of the bump exactly, as is shown in Figure 4. Affected by the width of the beam from the light projector, the beam reflected from the surface of the wafer forms a long strip on the detector. As part of the light is blocked by the bump, the shadow of the bump forms a concave arc in the long strip. As long as the direction of the light is invariable, the distance from the point $T$, which is located on the top of the bump, to the line tangent to the sphere and parallel to the projected line, is constant. Due to the symmetry of the light path, the distance from the point $T^{\prime }$, formed by the reflected light ray from the very top of the bump, and the point $S^{\prime }$, formed by the reflected light ray corresponding to the incident light ray tangent to the sphere of the bump, is constant on the image plane too. When the light projector moves along the $x$ axis, the distance between the two points remains invariant. So, a mathematical model of bump height measurement which is insusceptible to the position and width of light strip is proposed, according to the geometrical relationship mentioned above. The bump height of the bump can be stated in Equation (2).

(2)$h=\frac{x^{\prime }-r(1-\sin \theta )}{2\beta \sin \theta }$

In this formulation, $x^{\prime }$ is the distance from $T^{\prime }$ to $S^{\prime }$, while $r$ is the radius of the concave arc formed on the image plane. Limited to the numerical aperture of the imaging system, the reflected light from the top area of the bump forms a light spot on the imaging device, with $T^{\prime }$ as the center of the light spot. Therefore, the height of the bump can be calculated based on the parameters mentioned above.

The parameter $k$ is assumed to be stated in Equation (3); thus, $h$ can be expressed in Equation (4).

(3)$k=\frac{1}{2\beta \sin \theta }$

(4)$h=k(x^{\prime }-r)+rk\sin \theta$

When the parameters $k$, $r$ and $\beta$ are calibrated, the height of the bump can be deduced.

The magnification of the imaging system $\beta$ can be calculated using a 2D calibration plate composed of circular marks in standard size for implementing the camera calibration. The incident angle $\theta$ is calculated from a pair of steps with known height formed by two reflecting planes. Additionally, the radius of the arc can be deduced by fitting the circle with edge points of the arc formed by the shadow of the bump. However, when the width of the light stripe is comparatively smaller than the diameter of the spherical cap of bump, the arc formed by the shadow of the bump in the image without the point S’ leads to larger fitting errors of the radius $r$. An efficient method to obtain the parameter $r$ is to detect the distance of point $P$ and point $Q$, which are both intersection points of line and arc formed by the shadow of the bump. As the light scans the wafer surface, the distance between the point $P$ and $Q$ changes. When the left edge of the light bar passes through the center point O in Figure 4, the distance reached its maximum. At this time, the distance of $P$ and $Q$ equals the diameter of the bump cap. Considering the magnification of the imaging system, $PQ$ equals $2\beta R$. Therefore, the radius $r$ can be deduced from the maximal value of $PQ$ and the calibrated parameter β.

Additionally, the coordinate of $T^{\prime }$ can be deduced by extracting the imaging point center of the laser spot. It is worth noting that due to the limitation of the entrance pupil of the receiving imaging system, only the reflected beam in a small circle (represented by DTC) at the top of the hemisphere can enter the receiving system, where $T$ is the vertex of the convex point. The light formed by the parallel light illuminating the hemispherical surface is reflected to the image detector at different angles through the receiving system. When the incident light fills the area of DTC, the center position of the light spot is represented by point T. However, as the light moves through the wafer, the light beam cannot always fill the area of DTC. When the light beam fills the area, the spot area is the largest. Only at this time can the coordinate of the point $T$ be extracted accurately. Therefore, the spot area size needs to be detected in real time. When the size reaches its maximum, the center coordinate can be extracted. As the light beam moves, it can be seen that the spot area can be kept at maximum when the light area covers the DTC area. As the light intensity distribution of light stripe is usually Gaussian distribution, the centroid extraction method is not adopted because the light distribution can affect the extraction accuracy; the circle fitting method is preferred. If the light intensity distribution is a uniform distribution, the centroid extraction method can be adopted.

The light beam cannot simultaneously cover the area of DTC while $PQ$ reaches its maximal length. So, the coordinate of $T^{\prime }$ and the length of $PQ$ can be recorded at different times, and the height of the bump can be calculated using the parameters mentioned above.

In addition, the bump height also affected the measurement accuracy. As shown in Figure 4, to accurately measure the height of the bump, it is necessary to collect high-definition pictures of the top and bottom of the bumps simultaneously. However, due to the limitation of the depth of field of the microscopic objective lens, when the height of the bump is too big, the top and the bottom of the bump cannot be within the depth of field of the lens simultaneously. So, the image of the top of the bump and the bottom cannot be obtained clearly, which will obviously affect the accuracy of bump height measurement. In order to minimize the influence of the bump height on the measurement accuracy, the angle θ is preferably set to 45°, so that the both the top and the bottom of the bump can be within the depth of field of the lens, which will guarantee good image quality.

3. System Configuration

According to the measurement methodology described above, a light bar with sharp edges is required. In the measurement system, the prolonged light bar is adopted so that the heights of multiple bumps are simultaneously calculated in a single scanning measurement process, which requires a linear structured light with high performance in the illumination intensity and intensity distribution along the length of the stripe. The intensity distribution can be altered when different light sources are used, while different imaging processing methods should be used accordingly.

In our illumination model, a high-power metal arc lamp is used as the light source, which not only ensures the high illumination intensity required due to the reduction of exposure time during the fast scanning process, but also improves the measurement accuracy, as its incoherent property can effectively minimize the speckle effect caused by traditional coherent light sources. The light beam passing through the optical fiber is truncated by a precision slit aperture, which is manufactured by etching on thin glass coated with an opaque coating; a light stripe with the same shape of the slit aperture is formed. Strict quality requirements for the width and edges of the slit ensure the quality of light stripe. As shown in Figure 5, a slit aperture with a length of 30 mm and a width of 0.05 is installed with optic fiber. Subsequently, a set of optical filters are used to cut off the infrared ray to protect the wafer surface coating from the infrared light. Finally, passing through a group of lenses consisting of a collimating lens and a flat apochromatic microscope objective, an optimal light stripe is formed, and a narrow powerful line with a length of 2 mm and width of 0.025 mm is focused on the measured wafer surface.

A microscope imaging optical path with fixed magnification composed of an apochromatic microscope objective and a tube lens, with focus length $f_{objective}=40\mathrm{mm}$ and $f_{tube}=200\mathrm{mm}$, respectively, was used.

The reflected light from the wafer surface is recorded by a plane array camera. The shift of the reflected light strip from the top of bumps and the wafer surface in the image implies the height variations of the measured bumps. Combined with the system parameter calibration, the bump heights will be accurately calculated on a computer workstation according to Equation (3), as described above.

Figure 5 shows the schematic diagram of the bump height measurement system. The illuminating model is arranged at 45° relative to the wafer surface, and the imaging model is symmetrically disposed to ensure reliable data of the whole measurement range is gathered, in view of short depth of focus of the microscope.

To achieve the full field bump height measurement of the whole wafer, a scanning path generating algorithm was researched based on the field of view and wafer size. As shown in Figure 6. The parameter $W$ represents the scanning step. The row numbers of the scanning path $N$ are determined by the diameter of the wafer D and scanning step $W$:

(5)$N=D/W$

The length of scanning path of each row Li is determined by Equation (6):

(6)$L_{\mathrm{i}}=2\sqrt{{\left(\frac{D}{2}\right)}^2-{\left(\frac{D}{2}-i\ast W\right)}^2}\left(i=-\frac{N}{2},-\frac{N}{2}+1,-\frac{N}{2}+2,\cdots ,\cdots ,\frac{N}{2}-1,\frac{N}{2}\right)$

The scanning path of each row is prolonged to align the turning point with that of the next row, thereby forming a continuous scanning path. In addition, another critical parameter is the sampling interval. High measurement accuracy can be obtained in a small-step scanning model, as smaller sampling intervals mean more bump data and finer resolution of measurement. On the contrary, rapid scanning in large-step models achieves a relatively low accuracy.

During the scanning process, each image contains multiple bump shadows. As a result, image segmentation is needed to obtain different bump height parameters.

The wafer is placed on a stage of vacuum absorption driven by a four-axis high precision motion platform. Inspection of all micro bumps on the whole wafer is realized by back-and-forth scanning, driven by the high-precision motion platform. The camera captures raw image data when it receives the trigger signal that is generated based on the position information of the stage and the parameters of scanning step. Additionally, the wafer is moved in the direction perpendicular to the strip line, as shown in Figure 7.

To process the huge amount of data in the detected images, a parallel computing model based on the computing platform composed of FPGA, GPU and CPU is used to achieve scanning of the whole wafer. As shown in Figure 8, the image data acquired from the imaging module are first processed in the first image-processing module, composed of FPGAs in real time, in which image pre-processing algorithms such as image filtering and image segmentation are completed. Then, the image data are simplified and compressed in the second processing module, in which the analysis and statistics of the light stripe data and a rough estimate of the bump height are finished through exploiting the high-parallel capacity of the CPU+ GPU platform. The simplified data are further analyzed in the third module, and the height of the bump is accurately calculated according to the calibrated parameters. In the experiment, 100% 3D scanning of a 200 mm wafer containing approximately three million bumps can be accomplished in 30 min, which represents a throughput of nearly two wafers per hour.

In order to verify the measurement accuracy of the measurement method for micro bump height proposed in this paper, the following experimental setup was designed and established, as shown in Figure 9. Microbumps with a nominal height of 50 μm on a 200 mm wafer were measured.

4. Experiment

The estimation of measurement accuracy is performed by comparison with the measured values from a commercial instrument. SENSOFAR-S-neox is a high-precision 3D profiler based on white light interference, with 5 nm vertical resolution with 5 mm vertical measuring ranges. The heights of 16 micro bumps obtained using the proposed methods and Nikon instrument are shown in Table 1. In this experiment, the heights of five bumps (nominal height 50 μm) located on a column were measured point by point using the Sensofa instrument the proposed method with the system setup mentioned above, respectively. The corresponding measurement results were recorded in Table 1. The experimental results showed that the measurement accuracy of this method is within 1.5 μm compared with commercial instruments.

Repeated measurement experiments were carried out for a specific bump to verify the stability of the measurement device proposed in this paper. The bump was measured ten times, and the measurement results are shown in Table 2. The average value of ten measurements was 49.68 microns and the standard deviation is 0.82 microns.

5. Conclusions

In this study, a new method based on the triangulation method combined with bump geometry parameter analysis was proposed for measuring bump height, in which an incoherent light is used to reduce the influence of the speckle effect, and the refined designs and assembly of an optical system of illumination and imaging models ensured the acquisition of the high-quality real-time images. A line-scanning model was also adopted in order to accomplish measurement of the whole wafer by scanning along the optimized scanning path driven by the high-precision motion platform. The experimental results showed that the measurement accuracy was within 1.5 μm, and the repeatability measurement accuracy could reach 0.82 μm, which can meet the needs of industrial bump height measurement. The method proposed in the paper can not only be used in measuring the height of bumps, but may also be used in measuring the height difference between planes and spheres or arcs, as well as the height displacement between different surfaces of different shapes.

Author Contributions

Conceptualization, F.M. and Z.Z.; Methodology, Z.Z., Y.K. and C.C.; Software, F.M. and Y.K.; Validation, C.C. and D.W.; Investigation, F.M.; Writing—Original Draft Preparation, D.W. and X.Z.; Supervision, W.Z. All authors have read and agreed to the published version of the manuscript.

Data Availability Statement

Not applicable.

Conflicts of Interest

The authors declare no conflict of interest.

Footnotes

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

Figures and Tables

Figure 1. The measuring principle of triangulation.

Figure 2. The main structure and the material composition of a typical bump.

Figure 3. The shape of the bump and the surface of the wafer.

Figure 4. The measuring principle of the height of the bump.

Figure 5. Schematic of the experimental setup for height measurement of micro bumps on a wafer.

Figure 6. Scanning path generation algorithm.

Figure 7. Schematic diagram of scanning path.

Figure 8. Image data processing flow.

Figure 9. Photograph of the experimental setup.

Table 1

Comparison of measurement results of proposed method with SENSOFAR instrument.

Bump Number	Height Measured by SENSOFAR, A(μm)	Height Measured by Proposed Method, B(μm)	Biases between A and B(μm)
1	49.37	50.74	1.37
2	49.44	49.73	0.29
3	49.84	49.07	0.77
4	49.88	48.43	1.45
5	49.95	49.25	0.70

Table 2

Repeatability of measurements taken 10 times for each micro bump.

No. Times of Repetitive Measurement	Height Measured (μm)	Average Value (μm)	Standard Deviation (μm)
1	49.78	49.68	0.82
2	51.39
3	50.06
4	50.45
5	50.00
6	48.91
7	48.72
8	49.12
9	49.16
10	49.25

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