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We have proposed and demonstrated a novel method to measure depths of through silicon vias (TSVs) at high speed. TSVs are fine and deep holes fabricated in silicon wafers for 3D semiconductors; they are used for electrical connections between vertically stacked wafers. Because the high-aspect ratio hole of the TSV makes it difficult for light to reach the bottom surface, conventional optical methods using visible lights cannot determine the depth value. By adopting an optical comb of a femtosecond pulse laser in the infra-red range as a light source, the depths of TSVs having aspect ratio of about 7 were measured. This measurement was done at high speed based on spectral resolved interferometry. The proposed method is expected to be an alternative method for depth inspection of TSVs.
©2012 Optical Society of America
1. Introduction
With the advent of smart electronics such as smart phones and smart pads, the basic components of such devices, semiconductors, are required to be smaller and to have multiple functions. According to the traditional semiconductor process based on the optical lithography, it is not easy to implement narrow linewidths of sub wavelength size even with a well patterned mask because of the diffraction limit of light [1, 2].
Recently, the three-dimensional packaging method has been suggested as a novel alternative manufacturing method, this method can achieve high density by vertically stacking wafers that are fabricated by the existing manufacturing process. For the 3D packaging process, new inspection methods as well as corresponding manufacturing processes should be suggested and demonstrated. One of the important processes is to produce through silicon vias (TSVs), which are very fine and deep holes used for electrically connecting the stacked wafers vertically. For this, the depth of the TSVs should be measured and controlled after they are created, because a short hole could lead to an electric disconnection between stacked wafers [3–6].
As TSVs are high-aspect ratio holes, and light cannot reach to the bottom surface of TSVs, it is very difficult to measure their depths precisely by using conventional optical metrological methods. On the other hand, scanning electron microscopes (SEMs) or tunneling electron microscopes (TEMs) provide a depth value as well as a profile of the cross section; however, the sections of a wafer desired to be measured in principle should be cut [7]. Some researchers have tried to measure depths of TSVs using infrared (IR) microscopes [8], diffraction phenomenon [9] and X-ray microscopes [10]. However, these method had practical limitations in terms of measurement resolution, measurement uncertainty, and measurement speed.
In this paper, a novel method for measuring the depths of TSVs is suggested and demonstrated based on spectral resolved interferometry. By adopting the optical comb of a femtosecond pulse laser in the near IR range as a light source, the depths of TSVs could be measured without any damage because IR light can partially propagate into a silicon wafer. Moreover, the depths can be measured in a very short time because the measuring process does not require a mechanical or electrical scanning mechanism which is usually essential in the existing measurement techniques. The spectrum analysis of the interference signals can lead these high speed measurements [10]. In addition, the depths can be measured with the traceability to the length and time standards because the optical comb in use was stabilized and locked to an atomic reference clock. The wide spectral bandwidth and pulse-to-pulse interference of the femtosecond pulse laser allow the flexibility of system installation with improvement of measurement resolution [11,12].
2. Basic principle of spectral resolved interferometer
The period of an interference signal in the spectral domain depends on the optical path difference, L. When the optical path difference increases, the interference signal becomes dense and narrow in the frequency domain. The intensity of the interference spectrum can be expressed as [11],
where, I(f,L) is the intensity of the interference spectrum, f is the optical frequency, L is the optical path difference, I0(f) is the spectrum of the light source, c is the speed of light, and φ(f,L) is the phase.To determine the period of the interference spectrum, the obtained spectrum is Fourier-transformed. The resulting Fourier spectrum can be expressed as
where, F is the frequency of the interference spectrum, which equals L/c, and is the delta function. The resulting Fourier spectrum has three different peaks: the first term represents the spectrum of the light source, the second and the third terms contain the information of the optical path difference, L. To extract the information of the desired optical path difference, only the second term of Eq. (2) is selected, it is then inverse Fourier-transformed.The inverse Fourier-transformed term, Í (f), can be expressed in terms of phase. By taking the logarithmic function, the phase term can be extracted as
where, Im{} takes the imaginary part of the complex number. Finally the optical path difference, L can be determined by Eq. (4). If the light propagates in a silicon wafer, its refractive index should be considered for determining the optical path difference, L.3. Experimental setup and results
The optical comb of a femtosecond pulse laser (M-comb, Menlosystem) having a spectral bandwidth of ~40 nm was adopted as the light source. It has a center wavelength of 1565 nm with equal mode spacing of 250 MHz. The repetition rate was stabilized with a rubidium reference clock, whose stability was 10−12 at 10 s. The frequency stability was good enough for dimensional metrology in laboratory conditions. Since the mode spacing is too narrow to be detected, it was extended to 25 GHz by using a Fabry-Perot etalon (FPE). The IR light of the femtosecond pulse laser can partially propagate into a silicon wafer, and then be reflected from the bottom surface of the TSV. Figure 1 shows the spectrum of the light source. The optical spectrum analyzer can obtain the spectrum with a wavelength resolution of 0.02 nm, which corresponds to ~2.5 GHz in frequency.
Fig. 1 Spectrum of the femtosecond pulse laser: (a) full spectrum of the femtosceond pulse laser and (b) the optical comb of the femtosecond pulse laser with a Fabry-Perot etalon having a free spectral range of 25 GHz.
Figure 2 shows the optical layout of the overall measurement system. The pulse train emitted by the femtosecond pulse laser is delivered into the interferometer part through the FPE by a single mode optical fiber. A Michelson type interferometer was installed with an objective lens having a magnification of 20 in the measurement arm. The focused light in the measurement arm was reflected from the top surface and bottom surface of the TSV. In the reference arm, the light was collimated, and then reflected from the metal-coated mirror. The optical path differences between the reference mirror and the two surfaces of the TSV make the interference spectra containing two different dominant periods. The optical spectrum analyzer (AQ9370C, Yokogawa) can obtain the interference spectra with 8196 sampling points in the wavelength range of 1545 nm to 1585 nm. The wavelength resolution was fixed at 0.02 nm. Each spectrum can be obtained within 1 s. In addition, when blocking the reference arm, the measurement system can operate in confocal microscope mode with a photo-detector. This mode was very useful to find the locations that needed to be measured. This mode was also used to check the focusing point of the objective lens. To scan the sample laterally, a three-axis PZT-driven stage having a motion range of 90 μm × 90 μm × 90 μm was exploited.
Fig. 2 Optical layout of the TSV depth measurement system (FPE: Fabry-Perot etalon, BS: beam splitter, OL: objective lens, CL: collimation lens, FL: focusing lens, C: optical coupler, PD: photo-detector, OSA: optical spectrum analyzer).
The sample has many TSVs, as shown in Fig. 3(a) ; the TSVs diameter and depth are about 20 μm and ~150 μm, respectively. The aspect ratio was more than 7. The sample was fabricated by a conventional deep-etching process. To observe the cross-section with SEM, the sample was cut along the axis of one TSV. Figure 3(b) shows the SEM image of the TSV. The depth was estimated to be 145 μm.
Fig. 3 Measurement sample having TSVs: (a) top view of the TSVs (b) cross-section view of the TSV measured by SEM.
The interference spectrum obtained by an optical spectrum analyzer has one or two dominant periodic signals depending on the location in the sample. At the bottom surface and the top surface of the TSV, the interference spectrum had one dominant periodic signal, which corresponds to the optical path difference between the reference mirror and the top surface or the bottom surface. However, at a position near the edge between the top surface and the bottom surface, the interference spectrum had two periodic signals, whose amplitudes changed relative to the measuring location. Therefore, the Fourier transform of the interference spectra had two peaks at near edges as shown in Fig. 4(b) , or one peak at both the top surface and the bottom surface as shown in Fig. 4(a) and Fig. 4(c). For a small diameter of a TSV, the refractive index should be considered carefully because the light can propagate in a silicon wafer more than in the air.
Fig. 4 Fourier transform of the interference spectrum at: (a) the top surface; (b) the near edges; (c) the bottom surface of the TSV.
The obtained cross-section of the TSV is shown in Fig. 5(a) . The bottom line can be observed very clearly. At the edge, there are some fluctuations due to the diffraction effect. It should be noted that the scales of horizontal and vertical axes in the figure are not equal. The measurement length was 50 μm, with a lateral step of 0.5 μm. The average depth of the TSV was 144.86 μm, with a standard deviation of 0.03 μm in 10 repeated measurements. The combined uncertainty can be estimated roughly as less than 200 nm (k=1) from the uncertainty budget in our previous work [11].
Fig. 5 Measurement results. (a) profile of the TSV obtained by the suggested method. (The scale on each axis is not equal.). (b) three-dimensional profile of the TSV.
To define the depth of the bottom surface, the center part of length 10 μm was selected for analysis in order to avoid the influence of any rounding of the corners. Two 10 μm-length lines at the right and left sides on the top surface were chosen with the same offset of 15 μm from the center line of the hole in order to avoid the diffraction effect at the edge. According to the ISO guidelines [13, 14], the step height, 2h is found by fitting the Eq. (5) by the method of least square to the profile, z(x).
The unknowns α, β represent the slope and the intercept of the fitted line, respectively, and δ takes the value +1 in regions A and B and the value −1 in region C in Fig. 5(a). The depth of the TSV, D, is twice of the estimated value, h. The portions to be used for determining the depth of the TSV are those shown as A, B and C in Fig. 5(a). Table 1 shows the measurement results of the TSV. To show a 3D view of the TSV, the image was obtained in the area of 25 μm × 25 μm with a lateral step of 0.5 μm. In Fig. 5(b), it can be observed at both the bottom surface and the top surface at the same time.
Table 1. Measurement Results of the TSV Depths (unit: μm)
4. Summary
The fabrication of TSVs is essential to electrically connect the vertically stacked wafers for the 3D semiconductor packaging process. However, the inspection of the TSVs is not an easy task because they have fine and deep holes. Conventional optical methods cannot be used to determine the depth of TSVs due to the diffraction effect at the edge and stray light in the fine holes. In this paper, for precision depth measurements of the TSVs at high speed, a novel technique was suggested and demonstrated based on spectral resolved interferometry with the optical comb of a femtosecond pulse laser used as the light source. By analyzing the interference spectra, it was possible to obtain the depths and profiles of the TSVs. In repeated measurements, the average depth of TSVs having the diameter of 20 μm was 144.86 μm with a standard deviation of 0.03 μm. 3D profiles of the TSVs were also constructed. It is expected that this technique will be used for metrological tools for development of the 3D semiconductor packaging process as well as in other areas that require depth measurements of holes with high aspect ratio.
Acknowledgments
This work was supported in part by the National Program: Development of Application Technologies of Physical Measurement Standards (2012), KRISS.
References and links
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