Inspection system for microelectronics BGA package using wavelength scanning interferometry

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1 Inspection system for microelectronics BGA package using wavelength scanning interferometry C.M. Kang a, H.G. Woo a, H.S. Cho a, J.W. Hahn b, J.Y. Lee b a Dept. of Mechanical Eng., Korea Advanced Institute of Science and Technology b Korea Research Institute of Standards and Science ABSTRACT Inspection and shape measurement of three-dimensional objects are widely needed in industries for quality monitoring and control. A number of visual or optical technologies have been successfully applied to measure three dimensional surfaces. Especially, the shape measurement using an interferometric principle becomes a successful methodology. However, those conventional interferometric methods to measure surface profile have an inherent shortcoming, namely π ambiguity problem. The problem inevitably happens when the object to be measured has discontinuous shape due to the repetition of interferometric signal with phase period of π. Therefore, in this paper, we choose as a shape measuring method Wavelength Shifting Interferometer(WSI) in which the absolute distance from the reference surface can be directly obtained from the amount of interferometric phase change. With the above advantage the coplanarity of ball grid array(bga) can be easily evaluated and inspected, which is the major factor in the BGA surface mounting technology. The WSI is basically composed of a Twyman Green Interferometry and a tunable laser source. The proposed WSI so far by other researchers suffer from low measurement resolution because of the methodological roughness in obtaining interferometric phase change. Therefore, we propose a new algorithm, which can obtain a small amount of even fractional phase change by sinusoidal function fitting. To evaluate the effectiveness of the proposed sinusoidal function fitting algorithm, a series of measurements is conducted for discontinuously shaped specimens which have various heights. The proposed algorithm shows much more enhanced measurement resolution than other existing conventional algorithms such as zero crossing algorithm and Fourier transform algorithm. To measure the three dimensional shape of ball grid array with WSI, a series of simulations was performed for a hemispherical ball model in which the diffuse surface conditions are considered. The simulation results show that the three dimensional shape of a ball can be measured using WSI for purpose of BGA product inspections. Keywords : wavelength shifting interferometer(wsi), phase change, sinusoidal function fitting, measurement, ball grid array(bga) 1. Introduction Three dimensional shape measurement techniques are widely needed in industries for product quality monitoring and control. A number of visual or optical methods have been developed for that purpose using moire and interferometry as non-contact and highly accurate measuring methods. However, those profilometries cannot measure a discontinuous height step caused by the phase ambiguity that is an inherent limitation of the monochromatic interferometry or the periodic fringe pattern projection method[1,]. Thus, to overcome this limitation, the additional mechanism which enables to scan reference mirror or to obtain a different fringe pattern is commonly used. Therefore, to avoid the complexity and expense caused by the additional mechanism, a wavelength scanning interferometer is suitable. The representative three dimensional measurement method is optical triangulation method using a laser and is successively applied to various measurement field. But it shows limited measurement accuracy because it is very Correspondence : hscho@lca.kaist.ac.kr ; WWW : ; Telephone : Optomechatronic Systems II, Hyung Suck Cho, Editor, Proceedings of SPIE Vol (01) 01 SPIE X/01/$15.00

2 difficult to lower a laser spot size below a certain limited value[1]. Moire method has been given much attention because of high measurement resolution even for considerably large measuring area. However, to enhance the measurement resolution, the grating used in the system should be scanned and accordingly an additional scanning mechanism, piezoactuator, is necessary. Moreover, it cannot measure the discontinuous shape because of phase ambiguity problem.[] Also, this problem happens in Monochromatic interferometry in spite of its high measurement accuracy.[3] Though white light scanning interferometer based on its short coherence length shows extremely high measurement accuracy, the complex mechanical system including piezo-actuator must be inevitably used for scanning a reference mirror.[4] Besides these interferometry, confocal microscope necessarily needs the scanning mechanism to move measurement stage or light source, too.[5] Considering the previous measurement methods, most of precise optical measurement methods need a scanning mechanism and it is difficult to measure discontinuously shaped objects. Recently, for the discontinuously shaped object many researches on wavelength scanning interferometer(wsi) have been carried out.[6] In WSI, the tunable laser enabling electrical scanning wavelength was used instead of a complex mechanical scanning system and the discontinuously shape object can be easily measured. Wavelength scanning interferometer was proposed at the first time by Takeda, M. et al.[7] as a three dimensional measurement method. In the research, Fourier transform method was used to obtain total phase change from measured laser light intensity signal and the relative large discontinuously shaped object from several millimeter to several centimeter was measured. Another researchers, Kuwamura, S. et al[6] measured the relative small object of several micrometer and used zero crossing method to obtain total phase change from measured laser light intensity signal. But these two methods cannot obtain the fractional phase change less than π and accordingly find the precise phase change. This problem makes the measurement accuracy of wavelength scanning interferometer lower seriously. In this paper, a new method, sinusoidal function fitting method, is proposed to improve accuracy of measurement and to show its effectiveness a series of measurement experiments is conducted. As the first step to measure surface profile of a BGA ball using WSI, we conduct a series of simulations in which the diffuse surface of each ball is modeled as a infinite number of very small specular facets oriented randomly with a normal Gaussian distribution. The detailed descriptions about measuring simulations for BGAs are given in section 5.. Wavelength scanning interferometry.1 Monochromatic interferometer The most representative and basically simple monochromatic interferometer is Twyman-Green interferometer as shown in Fig.1(a). In the electromagnetic wave theory, the reference light wave and the measuring light wave can be expressed as follows: = i( wt+φ r ) ur Ure (1) = i( wt+φ t ) ut Ute () where U r and U t respectively are the amplitude of the light wave reflected in a reference mirror and in a measured surface and φ r and φ t respectively are the phase of the light wave reflected in a reference mirror and in a measured surface. The interfered light wave can be expressed in the following equation u = u + u. (3) While the intensity of interference signal, I, is expressed by the following equation (4) r t I = u u = U + U + U U cos( φ φ ). (4) r t r t r t Let the phase difference of the reference wave and the measuring wave, φ φ, be φ, the height difference of the r t Proc. SPIE Vol

3 reference plane and the measuring surface point can be expressed as h φ = 4 π (5) λ where λ is the wavelength of the laser light. Object pixel u t : measurement light Reference mirror BS pixel 5um u r : reference light u= u + u m r CCD Tunable Laser Image on CCD camera (a) The measurement configuration (b) A captured image of a specimen by CCD camera Fig. 1 Twyman Green interferometer and image of discontinuously shape object Let us consider the surface profile be discontinuous as shown in Fig. 1(b). In this figure, the left side fringe image is obtained when Twyman-Green interferometer is applied to the discontinuously shaped object including the abrupt height difference of 5µm using a He-Ne laser source. Because the acquired fringe image is not continuous as a result, the object height cannot be obtained from equations, (4) and (5). This problem, well known as phase ambiguity[3], inevitably happens when the discontinuously shaped objects are measured based on a conventional interferometric principle. Therefore, to overcome the phase ambiguity, the many researches on wavelength scanning interferometer(wsi) are recently presented. In WSI, the absolute height information compared to the reference plane can be obtained from the measured phase change regardless of a shape discontinuity.. Measuring principle of wavelength scanning interferometry Wavelength scanning interferometer(wsi) is composed of a monochromatic interferometer system based on Twyman-Green interferometer and a tunable laser source instead of monochromatic laser in Fig. 1 (a). At every step of scanning wavelength, the CCD camera captures the image of object surface. The signal of the varying image during scanning laser wavelength is used to obtain the height of an object surface point corresponding to each cell of CCD camera. Because the laser wavelength is scanned, the equation (5) should be modified by equation (6). Generally, in a conventional tunable laser source an incremental wavelength, δλ=λ 1 -λ, is very small compared to laser wavelength, λ 1 or λ. Thus, the equation (6) can be rewritten as equation (7)[8]. 1 1 λ λ φ φ = 1 4πh 4 π 1 = h λ λ λλ 1 1 (6) 76 Proc. SPIE Vol. 4564

4 φ φ 1 4 π h δλ (7) λ When the wavelength is scanned from λ 1 to λ N with a constant wavelength increment, δλ, the relationship between wavelength and phase is given by 1 1 φ φ = 1 4π h λ λ φ φ = i i 1 4π h + λ λ i i φ φ = 1 4 π h. N N λ λ N 1 N (8) The total phase change can be derived as λ φ = φ1 φn 4πh = K h (9) λ λ λ = λn λ1, K = 4 π. λ (10) where K is given as a constant after a measuring experiment. According to the equation (9), the height of a measurement point can directly be obtained from the total phase change. As the height of the measurement point increases, the total phase change increases and, in other words, the frequency of periodically changing light intensity at a measurement point increases. This simple measuring principle is one of the most important advantages of a WSI compared to other conventional interferometry. Consequently, because the total phase change of the interferometric intensity directly gives the absolute height information of the measurement point, even the discontinuous surface profile can be easily measurable in WSI. While the fringe images of the conventional interferometry are spatial, the measured signal in WSI shows a temporally varying a sinusoidal function form during scanning laser wavelength. 3. Phase measuring algorithm In WSI, measuring accuracy of the object height directly depends on the accuracy of obtaining total phase change from the light intensity temporally varying during scanning laser wavelength. The algorithms developed so far can be summarized by two methods, Fourier transform and zero-crossing. 3.1 Fourier transform Technique Fourier transform is used to obtain the frequency of temporally and periodically varying interferometric signal because at a given wavelength scanning range the total phase change is proportional to the frequency. The mathematical form of discrete Fourier transform can be expressed by X k 1 1 N i( π kr/ N) x e r N r = 0 = (11) Proc. SPIE Vol

5 where N is the number of measurement and χ r is the intensity of the measured light. To investigate the Fourier transform method in more details, the real experimental data was processed as shown in Fig.. The light intensity is measured by a CCD camera at each laser wavelength scanning step in Fig. (a) and the Fourier transformed signal is shown in Fig. (b). The peak signal at a specific frequency of horizontal axis denotes that the frequency of the measured interferometric signal can be easily found in Fig. (b). The normalized frequency obtained by discrete Fourier transform is given in discrete values as shown in equation (1). Since the obtained frequency directly denotes the height of a measured object point, the intervals of discrete frequency have a serious influence on the measurement accuracy in WSI. To achieve more accurate measurements, the refined frequency value between the discrete frequency values is needed. But it is difficult in discrete Fourier transform because of the limited number of signal measurements or wavelength scanning steps. 1 1,,..., N N N N (1) Peak frequency (a) The measured light intensity signal (b) The Fourier transformed signal Fig. Wavelength scanning interferometer signal and Fourier transformed signal 3. Zero Crossing Algorithm Kuwamura et al. [6] proposed zero-crossing algorithm in WSI to obtain the height of an object surface point in real time. In this method, we count the number of times when the values of measured light intensities cross the mean value of measured light intensities during scanning the laser wavelength in Fig.3. Let the number of crossing be N, the total phase change at a measured point is calculated by the following equation, φ = ( N 1) π. (13) Intensity I mean Scanning start Measured phase shift Scanning end Wave length, λ Real phase shift Fig. 3 Zero crossing method 78 Proc. SPIE Vol. 4564

6 Though the height of a measurement surface point can easily calculated by the above equation, the total phase change can be measured only with phase increment, π. Therefore, the phase change less than π cannot measured in this method and the measurement accuracy becomes very low. 3.3 Sinusoidal function fitting method As shown in the above two methods, the frequency interval in discrete Fourier transform and the measurable phase change increment are main limits to enhance measurement accuracy in WSI. So, this paper proposes a new sinusoidal function fitting method, in which the measured light intensity signal are assumed as a sinusoidal function and its parameters are obtained by well known least square method. Let us assume a measured signal, y i, as shown in Fig. (a) to be a sinusoidal function. Then the error function can be expressed as equation, N 1 t = 0 (( ( cos( ) ) t ) ) E = y a b t c + d (14) where the a,b,c,d are the constant parameters. The values of these parameters which minimize the error function are found by taking partial derivatives of E with respect to all the parameters according to equations (3.11) and (3.1). E E E E = 0, = 0, = 0, = 0 a b c d (15) The resulting nonlinear equations are iteratively solved by well known Newton-Rhapson method. The actual measured signal and the approximated sinusoidal function are compared in Fig. 4. It shows that the signal is so accurately approximated that even the fractional phase change less than π can be easily calculated. Sinusoidal function fitting method Measured signal Fig. 4 The measured light intensity signal and approximated signal by sinusoidal function fitting method 4. Surface profile Measurement for the discontinuously shaped object 4.1 WSI measurement system configuration Fig.5 shows the schematic drawing and real photographic image of WSI system configuration WSI for surface profile measurement. We used a dye laser as a tunable laser source, which is a RING type model made by Coherent Inc. and its tunable wavelength ranges from 570nm to 590nm. This laser is optically pumped by another laser, which is Ar ion laser of Beamlok model made by Spectra Physics Inc. and has 6W optical output power. The tuned laser wavelength is confirmed by a wavemeter, which are made by Burleigh Inc. and can very precisely measure with accuracy of 0.001nm. The CCD camera is a SFA-01ED model made by Samsung Electronic Inc., which has pixels of 640*4. Proc. SPIE Vol

7 To trace the light from a tunable laser source, the laser diameter is enlarged to cover the measurement area of target plane by objective lens, pinhole and convex lens. The pinhole of 1µm diameter is set up to locate at the focal plane of objective lens and has a role of optical filter to enhance the spatial quality of laser beam. The enlarged and collimated laser beam out of convex lens goes to wedge window through mirrors, by which some part of laser is reflected to an photo detector. The measured signal of optical power on the photo detector is used for compensation of laser beam power. In a dye laser system, the compensation is very important because during scanning laser wavelength the laser power drifts so serious that the interferometric signal cannot accurately measured by CCD camera without the influence of the laser power drift. Then, the incident laser on the beam splitter is split into object surface and reference mirror. The two separate beam are reflected at the respective surfaces and united again through the beam splitter. The CCD camera can capture the image interfered by two laser beam and the interference signal detected each pixel gives us the information of object surface. Tunable dye laser Objective Object objective object pinhole mirror BS CCD Reference Mirror BS CCD camera A/D+PC pinhole Wedge window Lens Wedge window Lens Convex lens Convex lens Mirror Photo Detector mirro r mirro r Photo Diode (a) The schematic drawing (b) The photography Fig. 5 Schematic drawing and photography of experimental setup 4. Measurement experiments for a discontinuously shaped object In this section, experimental procedures and results are presented for the discontinuously shaped objects which are selected to show that WSI can be successively applied to obtain absolute height of arbitrary shaped object regardless of surface discontinuity. The measurements are performed for standard specimen of 5µm height difference made by Mitutoyo Inc. and specially machined specimen of µm height difference. The experimental procedure is the following 9 steps, (1) capture the interference image by CCD camera () scan laser wavelength to next value (3) continue step (1) and () for the predetermined scanning range (4) gather a series of the light intensity data on each pixel (5) compensate the light intensity data with the light power signal detected by photo diode (6) perform sinusoidal function fitting for the light intensity data (7) find the total phase change by least square method (8) find the height value on each pixel (9) reconstruct the object surface profile. The experiments are conducted for various scanning ranges of 8nm, 10nm, 1nm, 14nm. To compare the conventional Fourier transform method with the newly proposed sinusoidal function fitting method, the reconstructed surface profile using Fourier transform method are given for specimen of 5µm height difference and 14nm scanning range in Fig. 6. The result shows that Fourier transform method cannot distinguish two object planes of 5µm height Proc. SPIE Vol. 4564

8 difference and it proves not a suitable method. In the Fig. 6, the odd peaks at the center of reconstructed object surface are caused by sharp step profile, in which CCD camera cannot catch the correct light signal. So they can be regarded as a kind of meaningless measurement noise. The experimental results are presented in Fig. 7 for specimen of 5µm height difference and various scanning ranges of 8nm, 10nm, 1nm, 14nm using the proposed sinusoidal function fitting method. A pixel corresponds to 17µm distance at the object plane in this experimental setup. The reconstructed surface profiles show that the discontinuously shaped object is measurable with considering accuracy. The results for wider scanning wavelength range show more flat upper and lower object plane and give higher measurement accuracy. Furthermore, the result in Fig. 7(d) shows that the proposed method for narrower wavelength scanning range is superior to conventional Fourier transform method for wider range. Similarly, the experimental results for specimen of µm height difference and scanning ranges of 8nm, 14nm are shown in Fig.8. It is observed that the object with large height different planes can be easily reconstructed in WSI measurement system. µm ŸŒ Ÿ Ÿ ŸŒ ŸŒ Fig. 6 The reconstructed object shape of 5µm height difference by Fourier transform method Z Axis[um] Z Axis[um] Y Axis[pixel] X Axis[pixel] Y Axis[pixel] X Axis[pixel] (a) Wavelength scanning range : 14nm (b) Wavelength scanning range : 1nm Z Axis[um] Z Axis[um] Y Axis[pixel] X Axis[pixel] Y Axis[pixel] (c) Wavelength scanning range : 10nm (d) Wavelength scanning range : 8nm Fig. 7 The reconstructed object shape of 5µm height difference 4 X Axis[pixel] Proc. SPIE Vol

9 Y Axis[pixel] X Axis[pixel] Z Axis[um] Y Axis[pixel] X Axis[pixel] Z Axis[um] (a) Wavelength scanning range : 14nm (b) Wavelength scanning range : 8nm Fig. 8 The reconstructed object shape of µm height difference 5. Simulation of surface profile measurement of BGA 5.1 Surface model of BGA ball Thus, far we have presented the experimental results of measurement of specular objects with step height [11]. However, the measurement of BGAs shown in Fig. 9(a) requires the optical instrumentation conditions different from the one used previously. In this work, to explore the possibility of measuring the three dimensional surface profile of BGAs we conducted a series of the measurement simulations using the WSI system as the first research step. In measurements of BGAs, first of all, surface characteristics of a BGA ball different from those of the previous experiments should be considered. A metal surface shows various optical characteristics depending on surface roughness. The lead surface like BGAs generally shows diffuse characteristics while the precisely machined surface does specular characteristics. To simulate this we assume that the diffuse surface of each ball of BGA is composed of an infinite number of very small specular facets oriented randomly with a normal Gaussian distribution according to a previous research[9]. In the model, the ball has the shape of a sphere and each facet is assumed to have a very tiny rectangular size, 0.1µm 0.1µm, not to show any macroscopic irregularity. Fig. 9 (b) illustrates the assumed model for the simulation. The vector of each facet perpendicular to its surface deviates from an average normal vector, α, of neighboring facets as shown in Fig.9 (c). The normal vector, α, has the x, y components, α x and α y, respectively. Here, if we assume the two components to be random variables with standard deviation, σ, the probabilistic density distribution of α x and α y can be expressed as equation (16), ( αx + αy ) σ 1 P( αx, αy) = e (16) πσ where the value of the standard deviation, σ, should be determined by how much the object surface is diffused. Microfacets 0.1µm α : normal vector of micro facet z Micro facet surface normal vector ball y (a) BGA(Ball Grid Array) (b) Microfacets for modeling hemispherical (c) The normal vector of a microfacet diffuse surface of a single ball Fig. 9 The normal vector of a micro facet deviated from surface normal vector 5. Simulation procedure Simulation conditions are practically selected to simulate the measurement experiments stated in section 4 as realistic as possible. To measure a BGA ball, the discontinuously shaped object in this simulation is replaced by an 8 Proc. SPIE Vol. 4564

10 object with hemispherical surface which is modeled as a collection of an infinite number of facets as mentioned in section 5.1. Each facet is assumed to reflect the laser light ray like a specular mirror when laser light is irradiated onto BGA ball surface. A part of numerous laser rays reflected on each facet goes toward CCD cell and the other does out of CCD cell as shown in Fig. 10(a). Each CCD cell can capture only the laser light rays entering onto it and can not these rays going out of CCD cell. In Fig. 10(a), the laser light rays,3 are measurable by CCD cell and the ray 1 is not. Considering this measurement scenario in such a manner, each CCD cell measures the summed intensity of all the laser light ray reached within it. At this stage, the path length of each laser light ray to be measured in CCD cells should be calculated to obtain the light intensity of the interfered laser ray with the reference laser light. The intensity signal measured in each CCD cell depends on the orientation of randomly distributed facets and the path length of numerous light rays reflected on them. Therefore, we cannot expect a kind of images of obvious laser interference fringes obtained for specular plane objects presented in section 4 and the practical images for diffuse objects show numerous speckles. However, it is well known that these speckles are general characteristics of diffuse surface in laser interferometry and include a kind of phase information [10]. The simulation procedures can be sequentially thought by the following steps ; (1) The laser light of spatially uniform intensity is irradiated over an object to be measured. () Each facet reflects the laser light in the opposite direction to the irradiation direction with respect to its random surface normal vector of equation (16). (3) After reflection in each facet, the laser light is divided into numerous light rays which have its own direction, respectively. (4) Among the numerous light rays, we calculate the intensity contributed by only the light ray that reaches CCD cell. (5) The optical path of each laser light ray is calculated to obtain the light intensity interfered with reference light. (6) In each CCD cell, we calculate the sum of the intensity of all the light ray reached it. (7) The signal value calculated in each CCD cell makes up a measuring image. (8) For laser wavelength scanning, steps (1) through (7) are repeated and the obtained image data are stored. (9) Perform steps (4)-(9) described in section 4. using equations (9), (10), (14) and (15), and reconstruct the object surface profile. 5.3 Simulation results Fig. 10(b) shows the acquired image of a lead ball of BGA at CCD camera by simulations. Because the average normal vectors of outer region of the ball surface deviate much from the CCD center line, the number of laser light ray irradiated on CCD cell from outer region is less than that from inner region. Therefore, the image of outer region Object facet 1 3 CCD cell Reference mirror Beam splitter laser (a) Schematic diagram of WSI simulation and path of laser light ray (b) The image of a lead ball composed of speckles Fig. 10 Schematic diagram of simulation procedure and the image of a lead ball Proc. SPIE Vol

11 becomes darker in the image. As a result, the partial surface within a limited range of average normal vector can be measured in this measurement configuration. The speckles of the image denote a properly assumed surface model since they are generally shown in interferometric measurement experiments for a diffuse surface. The previous measured specimen well show spatially periodic interferometer fringes shown in Fig. 1(b), but the object with diffuse surface shows an image full of speckles. From the obtained image the shape of a ball is reconstructed as shown in Fig. 11. In this figure, the measurable angle range of a ball is up to about ±40 deg. deviated from the CCD center line. The above resultant angle range is sufficient for inspection of a BGA ball since the height of the highest point of a ball practically is more important in inspections of BGA products than the shape information. In the meanwhile, the radius of the hemisphere shape of a ball is obtained with 3µm maximum error, which is within acceptable error range. The simulation results indicate that the three dimensional shape of BGA can be measured using the WSI system for purpose of BGA product inspections Conclusions (a) The reconstructed shape of a BGA ball (b) The measurable angle range of a BGA ball Fig. 11 The reconstructed hemispherical shape of a BGA ball In this paper, a method was proposed for more accurate measurement and the experimental measurement results showing its effectiveness were presented in comparison with conventional Fourier transform and zero crossing method. In the experiments, discontinuously shaped objects of 5µm and µm height difference were measured and the shape were reconstructed as a result. From the measurement results, the conventional methods could not measure the object of 5µm height difference but the proposed sinusoidal function fitting method could measure it even for smaller wavelength scanning range. It was confirmed by experiments that the more wider wavelength scanning range is used the more accurate measurement in WSI can be obtained. Thus, objects of simple shape having different height were so far measured using WSI, but this proposed method can be used for three dimensional measurements of more complex objects, for example, a BGA ball. To measure three dimensional shape of a BGA ball, in this paper, as the first research step we conducted a series of the measurement simulations using a WSI system and presented the measurement results of reconstructed hemispherical ball surface. To model the diffuse surface of a lead ball of BGA we assume that the diffuse surface are composed of an infinite number of very small specular facets of which the surface normal vectors are randomly orientated with a Gaussian distribution. Simulation results show that the proposed WSI system can be successfully applied to measurement and reconstruction of three dimensional shape of a BGA ball for purpose of BGA inspection. REFERENCES 1. Steven, 3D Vision System Analysis and Design, in Three Dimensional Machine Vision, Takeo Kanade Ed., H. Takasaki, Moire Topography, Applied Optics, Vol. 9, Proc. SPIE Vol. 4564

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