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We develop a modified thin film model with adjustable ratio of the illuminated surface areas for accurate reflectivity calculation of deep via structures. We also propose a method combining a half oblate spheroid model and a reflectance modulation algorithm for extraction of via bottom profile from the measured reflectance spectrum. We demonstrate the use and enhancement of an existing wafer metrology tool, spectral reflectometer by implementing novel theoretical model and measurement algorithm for through-silicon via (TSV) inspection. Our non-destructive solution can measure TSV profile diameters as small as 5 μm and aspect ratios greater than 13:1. The measurement precision is in the range of 0.02 μm. Metrology results from actual 3D interconnect processing wafers are presented.
©2010 Optical Society of America
1. Introduction
Semiconductor device packaging technology is rapidly advancing, in response to the demand for thinner and smaller electronic devices. Three-dimensional chip stacking that uses through-silicon vias (TSV) is a key technical focus area, and the continuous development of this novel technology has created a need for non-contact characterization [1]. With a large via opening (≥ 30 um), it is possible to measure the via’s critical dimension (CD) and depth with optical imaging techniques. An imaging-based system with a high magnification objective lens (50-100x) and a large focus travel distance is the ideal tool for these measurements [2,3]. The maximum measurable depth increases with the via’s CD opening, and decreases with the objective’s numerical aperture (NA). As the via diameter decreases, the aspect ratio increases, there are few known non-contact measurement techniques that are suitable for in-line inspection. Infrared microscopy can be used for a growing range of applications due to the IR transparency of silicon and other semiconductors [4]. Usually infrared microscopy is used for backside measurement, as it can penetrate a polished silicon surface. However, the resolution of an IR microscope (typically ≥ 1 um) is coarser than a comparable optical microscope, since a larger wavelength of light is used.
Reflectometry technology has gained wide acceptance in semiconductor manufacturing processes for monitoring the linewidth and profiles of 2D and 3D structures [5,6]. The technology advantage of normal incidence measurements is that they are inherently more stable and accurate for scatterometry applications. The concept is orders of magnitude less susceptible to errors caused by incidence angle variations when used in high oblique angle systems. In most Front-End-of-Line (FEOL) and Back-End-of-Line (BEOL) applications, the total height or depth of the target structures is relatively small, typically less than one micrometer. RCWA theory is commonly used for modeling in reflectometry, and it can achieve optical responses with very high accuracy; however, the calculation is quite time consuming [7]. Masahiro Horie et al developed UV-reflectometry for fast trench-depth measurement. They calculated reflected light by comparing the area ratio of the complex amplitude reflectivity returned by top surface and trench regions [8,9]. Recently, there is a growing demand for measuring much deeper via structures, ranging to tens of micrometers. As a result, reflectometer-based metrology for TSV is a key challenge, since high aspect ratio features are more difficult to measure with conventional approaches. And more, since the wafer backside would be thinned down to expose the metal filled TSV either before or after wafer bonding process in most 3D interconnect processing; thus not only TSV depth but also bottom profile measurement are important for process control. The via depth information gives us an idea of how thick of the wafer must be reduced from the backside; and the via bottom profile information further indicates extra thinning thickness to reach entirely via opening for proper bonding.
At present, there is a great deal of activity – including many patent applications – directed toward the improvement of TSV processes so that the via structure has a desirable bottom shape [10,11]. However, due to their compact size and high aspect ratio, many structures have parts that cannot be visually examined or analyzed using standard microscope procedures without being destroyed [12]. Usually a photoresist is coated and patterned on the dielectric layer to form a via opening. The following plasma etch process creates an opening through the dielectric that has a diameter D. Zhang et al. [10] mentioned the via bottom is composed of a flat bottom portion and a rounded bottom corner that connects to the sidewall. However, it is only suitable for describing large size via bottoms. A key feature of small diameter high density TSVs (HDTSVs) is that the etch process generates an entirely curved via bottom with no flat portion.
In this paper, we propose a method combining a half oblate spheroid (a rotationally symmetric ellipsoid with major axis length a and minor axis length b) model and a reflectance modulation algorithm for extraction of via bottom profile from the measured reflectance spectrum. The bottom profile can range from a perfect flat disk (minor axis length b = 0) to a half round spheroid (b = a, a is the major axis length). We report the first measurement results from various TSV samples, including isolated deep vias with larger CDs and HDTSV arrays with small CDs. We demonstrate the use and enhancement of an existing wafer metrology tool, spectral reflectometer by implementing novel theoretical model and measurement algorithm for through-silicon via (TSV) inspection. Our non-destructive solution can measure TSV profile diameters as small as 5 μm and aspect ratios greater than 13:1. The measurement precision is in the range of 0.02 μm. Metrology results from actual 3D interconnect processing wafers are presented.
2. TSV samples and Instrumentation
2.1 TSV Samples Detail
Three different groups of TSV samples from actual 3D interconnect processes were studied. These TSV targets included:
- 1. Deep Via (≥ 80 μm) with large CD (≥ 30 μm)
- 2. HDTSV with small CD (≤ 5 μm) and high aspect ratio (≥ 13)
- 3. HDTSV with a hard mask on top of it
2.2 Reflectometer Configuration
The TSV structures were measured by an unmodified Nanometrics 9010B reflectometer tool, the reflectance spectrum is measured in the broadband wavelength range 375 nm to 780 nm. It is a normal incidence system with a small aperture (4X) and low NA (0.035), primarily developed for thin film thickness and optical CD (OCD) measurements. The normal incidence measurement largely relies on the interference between light scattered from different locations on the target structure. To measure the via depth, the light reflected from the top and bottom of the via target structure must interfere with each other. The reflectance spectrum typically has regular oscillation over a large wavelength range. The limiting factor in this case is the pixel resolution of the charge-coupled device (CCD) detector, which is about 0.6 nm at the upper wavelength limit of 780 nm.
3. Theoretical model
3.1 Theoretical model of the reflectance spectrum
Consider the case of a high aspect ratio silicon via as shown in Fig. 1(a) . The via structure is modeled as a film with adjustable ratio of the illuminated surface areas. We examine the case where the light waves reflecting off the top silicon surface interfere constructively with the waves reflecting from the via bottom surface. To get constructive interference, the two reflected waves have to be shifted by an integer multiple of wavelengths. This must account for the extra distance traveled by the wave traveling down and back from the via bottom.
Fig. 1 Theoretical modeling of reflectance spectrum for via depth 30.00 and 30.25 μm. The spectrum for via depth 30.00 μm is well separated with the one for 30.25 μm
The original reflectance intensity from the sum of the two reflected beams is I. The components of the electrical field reflectances E1 and E2 must be combined using their proper phase angle difference as shown in Eq. (1). E1 and E2 are the electrical field reflectances from the silicon surface and the via bottom surface respectively. The via depth is d, and the wavelength is λ.
We use a modified thin film model which the portion of the illuminated top surface and via bottom areas is taken into account for the reflectance calculation. It is an attractive modeling tool as it allows for a complex via structure to be modeled as a film stack with each layer having an effective illumination portion. Assume the ratio coefficient α and (1-α) are the portion of the illuminated silicon top surface and the via bottom respectively. The modified reflectance intensity from the silicon surface and the via bottom surface is:
After modifying the electrical field reflectance, the simulated reflectance spectrum can be calculated using the Fresnel equation. According to the Fresnel equation, light in air that reflects off a silicon surface will undergo a 180° shift and its electrical field reflectance will be multiplied by a reflecting factor, rsi+.
Figure 1(b) shows the theoretical modeling of the reflectance spectrum for via depths of 30.00 and 30.25 μm. The spectra for the two via depths are well separated from each other. The illuminated surface areas of the silicon surface and the via bottom surface is 81% and 19% of the total surface area respectively. The refractive index of silicon varies with the wavelength range (6.706 @ 375 nm to 3.696 @ 780 nm).
Figure 2 shows another case, in which a high aspect ratio silicon via has an oxide hard mask on top of it; interference can occur if three reflected light waves (2, 3, & 4) interfere constructively. The illuminated surface areas of the oxide surface and the via bottom surface is 81% and 19% of the total surface area respectively. The refractive index nsi > noxide > nair. The optical path difference (opd) of the reflected light waves 4 and 3 from the top and bottom of the oxide film is
Fig. 2 Theoretical modeling of reflectance spectrum for via depth 30.00 with 1 μm oxide hard mask on top of it. The ratio of the illuminated surface areas of the silicon surface and the via bottom surface is 81% to 19% in this simulation case.
We will get constructive interference when
where refractive index noxide(λ) is a function of λ. Another optical path length difference between the reflected light waves 4 and 2 from the top oxide and bottom of the TSV structure is Δr’opd = 2nairdvia. We will get constructive interference when Δr’opd = 2dvia = mλ, m = 1, 2, 3…, where nair = 1 and λ is the wavelength in air. The reflectance spectrum oscillates at two distinct frequencies—high frequency features correspond to the deep via, and low frequency features result from the oxide hard mask. According to the Fresnel equation, the light path 2 in air, reflecting from the bottom Si surface, will undergo a 180° shift and its electrical field reflectance will be multiplied by a reflecting factor, rSi +. The light path 3 off the silicon surface undergo a 180° shift and transmitted through the oxide film will undergo an phase shift, and its electrical field reflectance will be multiplied by the transmitting factor tox +(transmitting from air into oxide), reflecting factors, rSi ++(reflecting from silicon surface in oxide medium), and the transmitting factor, tox -(transmitting from oxide into air). The light path 4 in air, reflecting off the top of the oxide film, will undergo a 180° shift and its electrical field reflectance will be multiplied by reflecting factors, rox +. The combined reflectance spectrum can be calculated by adding the individual reflectance spectrum of reflecting light path 2, 3 and 4. The refractive index of silicon varies with the wavelength range (6.706 @ 375 nm to 3.696 @ 780 nm). The refractive index of oxide is a constant 1.46 over our measured wavelength range.3.2 Theoretical model of the via bottom profile
A key feature of a small diameter HDTSV is that the etch process generates a curvature at the via bottom. Figure 3(a) shows the cross-sectional view of a 5 μm via hole; the bottom area is composed of a slow ascent portion starting from the bottom center and following with a steep ascent portion connects to the sidewall corner. We provide a half oblate spheroid model, shown in Fig. 3(b); the bottom profile can range from a perfect flat disk (minor axis length b = 0) to a half round spheroid (b = a, a is the major axis length). Since the oblate spheroid has a polar axis shorter than the diameter of the equatorial circle, it can be simply described by the lengths of its two perpendicular principal axes (major axes, axial length a) and its one minor axis (axial length b).
Fig. 3 (a) Cross-sectional view of 5 μm via hole; the bottom is composed of a slow ascent portion in the center area and a steep ascent portion connects to the sidewall corner. (b). Oblate spheroid model for the HDTSV via bottom profile
Although the bottom of small diameter via is curved, a great portion of light incident on the curved bottom surface was scattered and cannot be reflected back to the top surface. An attenuated interference spectrum is still possible obtained because the depth variations around bottom center area are quite small which can be physically considered as a flat surface for reflecting partial normal incidence light waves back to the top surface. We assume the bottom effective area with a diameter e which depth variations inside this area are small enough and beyond the depth resolution limit of the measuring tool as schematically shown in Fig. 4 .
Fig. 4 Schematic of via cross section view (left) and top view (right). The bottom effective area with a diameter e which depth variations inside this area are beyond the depth resolution limit Δdvia
The relationship between the via depth resolution (Δdvia) and the detector pixel resolution (Δλ) which can be derived from 2dvia = mλ [Eq. (5)] is:
The depth resolution decreases with the total depth of the structure, but it improves with the upper limit of the wavelength. A pixel resolution of 0.6 nm is typical for an NI-OCD system.
Besides accounting for the ratio of the illuminated surface areas (substrate top and via bottom), we propose a novel idea of modulating the amplitude of the high frequency oscillation on a low frequency carrier oscillation to be a via bottom profile model. The further attenuation on the high frequency amplitude reveals the ratio of the effective area to the totally bottom area that could partially returning normal incidence light back to the top surface. Taking the nominal via diameter as the horizontal, transverse diameter (≡ 2a) at the oblate equator in Eq. (6); the vertical, conjugate radius b can be obtained if one set of (x, y) on the oblate trajectory is known. If (0, 0) is the center of the oblate spheroid, the radius e of the effective bottom area and its relative postion to the center equatorial plane (≡ -b + Δdvia) are used as one set of x and y in Eq. (6) respectively.
Thus the decreasing effective radius e is because of the increasing vertical radius b, also the smaller amplitude of high frequency oscillations are observed.
Figure 5 shows the simulated reflectance spectrum from an HDTSV structure with a major axis length a = 5 um and the minor axis length b varying from 0 to 0.5a. The via depth is assumed to be 30.00 um with a 1 um oxide hard mask (same as Fig. 2). The depth resolution Δdvia of 30 nm @ 600 nm derived from Eq. (7) are used in this simulations. The illuminated surface areas of the oxide surface and the via bottom surface is roughly 81% and 19% of the total surface area respectively when the minor axis length b equal to 0(entirely flat bottom). The attenuation ratio of high frequency amplitude is taken as the area ratio of the effective area and the total bottom area (square of the e to a ratio). The effective area radius derived from Eq. (8) and the corresponding amplitude attenuation of high frequency oscillations are listed in Table 1 .
Fig. 5 Simulated spectrum from HDTSV with varying minor axis length b from 0 to 0.5a (a: major axis length). Via depth is 30.00 μm with 1 μm oxide hard mask on top of it
Table 1. effective area radius and the corresponding amplitude attenuation
4. Measurement algorithm and results
4.1 Theoretical Model Fit
Figure 6(a) shows a model fitted for a nominal 80 μm deep TSV structure. The via CD is around 30 μm, approximately the same size as the illumination beam spot. We carefully moved the illumination beam spot so that two-thirds of it overlay the via hole and one third of it overlay the top of the Si surface. The ratio of the spot in the hole to the spot on the Si surface is around 55% [Fig. 6(b)]; thus, the incidence of illumination was optimal for collecting as much intense interference spectrum as possible from the TSV structure. The oscillation from the via depth is particularly obvious in the long wavelength region. A good fit to the experimental spectrum was obtained using the theoretical model with a depth of 80.54 μm. Also, because the frequency of the oscillation is proportional to the via depth, it is easy to transform the reflectance spectrum to the frequency spectrum using an inverse Fourier Transform (FT) calculation. Figure 7(b) shows the FT frequency spectrum which is directly calculated from the experimental data in Fig. 7(a). The FT analysis result reveals the via depth to be 81.48 μm, which agrees with the model fitted result within 1 μm discrepancy. The direct measurement and FT analysis approach is reliable and practical for measuring very deep vias, since it can handle the difficulty of separating the dense peaks and valleys of the high frequency oscillations.
Fig. 6 (a) Model fitting for a nominal 80um depth TSV structure. (b) Schematic of illumination beam spot which is two third inside the via hole and one third on top of the Si surface, the ratio of spot in hole to spot on Si surface is around 55% .
Fig. 7 (a) Experimental reflectance spectra with depth of 80.54 um.(b) Fourier transform of the reflectance spectra with peak value at 81.48 um.
Figure 8 shows the model fit to the measured spectrum of a high aspect ratio HDTSV array structure. The via CD is around 5 μm, and the via pitch is around 10 μm. The incidence of illumination covered the periodic array structures, and an average interference spectrum was obtained. An excellent fit to the experimental spectrum was obtained using a theoretical model with a depth of 65.08 μm. The measurement precision is better than 0.20 μm over multiple measurement results. The uniformity of the TSV depth is better than 3.16 μm from multiple site (A, B, C) measurement results (Fig. 9 ).
Fig. 8 Model fitting to the reflectance spectrum of high aspect ratio HDTSV array structure. The via CD is around 5 μm, via pitch is around10 um, via depth is 65.08 μm.
Fig. 9 The measurement precision is better than 0.20 μm from multiple times measurement results. The uniformity of TSV depth is better than 3.16 μm from multiple sites measurement results.
Figure 10(a) shows an experimental spectrum from an HDTSV array structure with a thin oxide hard mask on top of it. The via CD is around 5 μm, and the via pitch is around 10 um. The illuminated areas of the oxide surface and the via bottom surface is roughly 81% and 19% of the total surface area respectively. The low and high frequency oscillations were extracted using a spectrum processing algorithm, and were fitted with the modeling spectrum as shown in Figs. 10(b) and 10(c), respectively. The fit with the longer wavelength range (≥ 650 nm) is more meaningful for high frequency oscillation features, because the existing spectrometer has insufficient resolution for resolving dense oscillations over a shorter wavelength range. Figures 10(b) and 10(c) show an excellent model fit to the two individual reflectance spectra and their associated hard mask thicknesses, at 596 nm and a via depth of 37.16 μm, respectively. A cross-section SEM result shows good agreement (Fig. 11 ).
Fig. 10 (a) Experimental reflectance spectra from a HDTSV array structure with thin oxide hard mask on top of it. The via CD is around 5um (b) Theoretical model fitting to the low frequency features with oxide hard mask thickness of 596 nm. (c) Theoretical model fitting to the high frequency features with via depth of 37.16 nm.
Fig. 11 Left: cross section SEM result of top oxide layer. Middle: cross section SEM result of deep via structure. Right: top view of HDTSV sample with nominal CD 5 um, pitch 10 um, illumination spot around 30 um.
Figure 12(a) shows the HDTSV experimental spectrum that is fit with the model reflectance spectrum structure having minor axis length b = 0.52a. The via depth of 37.16 μm and the top oxide layer of 0.596 um (as mentioned in Fig. 10) were used as modeling parameters. The depth resolution for a nearly 40 um deep structure is considered to be 40 nm @ 600 nm [600 nm is about the wavelength resolution limit of our spectrometer for resolving dense oscillations as observed in Fig. 10 (a)]. We carefully attenuated the amplitude of the high frequency oscillation until the best fit was obtained at an attenuation ratio 3.9% which is corresponding to the effective bottom area radius equal to 600 nm. The coordinate of the effective circular area range, as shown in Fig. 12(b), can be expressed as (600, -b + 40) nm. Thus, the relationship between the major and minor axis lengths can be obtained from Eq. (8):
Fig. 12 (a) HDTSV experimental spectrum fitting with the modeling reflectance spectrum structure with minor axis length b = 0.52a. The via depth of 37.16 um and top oxide layer of 0.596 um. (b) The coordinate of effective circular area as shown in Fig. 10(b) can be expressed as (600, -b + 40) nm.
With the nominal via diameter a ≅ 2.5 μm, then b = 1.3 μm ( = 0.52a) can be obtained from Eq. (9). Thus, the via bottom profile is completely described.
Figure 13 shows the cross-section SEM result for the via bottom, b = 0.48a. There is acceptable agreement with our fitted model, b = 0.52a. The discrepancy might be caused by the bottom surface roughness which further attenuates the reflected light; thus, the effective area is slightly overestimated.
4. Summary
We have independently developed a modified thin film model and analysis method for measurements on high aspect ratio TSV structures. Depending on the 3D interconnect processing needs; solutions can be implemented for a large variety of TSV structures, including actual HDTSV arrays.
Metrology for TSV processing is a key challenge to maintaining and improving the overall yield in this new era of 3D integration. We demonstrated that existing reflectometer technologies can be used and enhanced to measure a high aspect ratio TSV depth and bottom profile. The theoretical model predicts the reflectance spectrum from the top and bottom Si surface sufficiently well; thus, it can be used to provide the necessary calibration between interference signals and via depth, with measurement sensitivity up to 0.01 um. A novel idea of modulating the amplitude of the high frequency oscillation is developed for half oblate via bottom profile modeling.
Our future work will focus on the measurements of HDTSVs with decreasing diameters and increasing aspect ratios. We will refine our current profile model by introducing a surface roughness effect, as well as the estimated uncertainty for the depth and profile obtained from the fitting. We also will explore a measurement solution for an oxide and seed Cu layer within the via structure.
Acknowledgment
The authors would like to thank Sum-Min Wang and Dun-Ying Shu at EOL/ITRI (Electronics and Opto-Electronics Research Laboratory/ Industrial Technology Research Institute) for 3D interconnect processing wafers support. We also would like to thank Michael Tu and Perry Liang at Nanometrics for their help on collecting reflectometer spectra.
References and links
1. ITRS Assembly & Packaging 2008.
2. P. de Groot and X. C. de Lega, “Valve cone measurement using white light interference microscopy in a spherical measurement geometry,” Opt. Eng. 42(5), 1232 (2003). [CrossRef]
3. J. H. Belk, and D. E. Hulsey, “ Non-contact hole depth gage”, US patent 2003/0107728 A1.
4. D. Marx, D. Grant, R. Dudley, A. Rudack, and W. H. Teh, “Wafer Thickness Sensor (WTS) for Etched Depth Measurement of TSV,” IWLPC-International Wafer-level packaging conference proceeding (2009).
5. Z. Liu, X. Zhang, J. Hu, and D. J. Roy, “Measurement of deep silicon trench profile using normal incidence optical CD metrology,” Proc. SPIE 5752, 1152–1160 (2005). [CrossRef]
6. C. A. Duran, A. A. Maznev, G. T. Merklin, A. Mazurenko, and M. Gostein, “Infrared Reflectometry for Metrology of Trenches in Power Devices,” IEEE/SEMI Advanced Semiconductor Manufacturing Conference, p. 175, (2007).
7. C. J. Raymond, M. Littau, R. Markle, and M. Purdy, “Scatterometry for shallow trench isolation (STI) process metrology,” Proc. SPIE 4344, 716–725 (2001). [CrossRef]
8. M. Horie, S. Shiota, S. Yamaguchi, et al.., “UV-reflectometry for fast trench-depth measurement,” Proc. SPIE 6922, 69223D (2008). [CrossRef]
9. S. Yamaguchi, and M. Horie, “Measuring Method and Apparatus for Measuring Depth of Trench Pattern,” US patent 2008/0049222 A1.
10. B. Chao, Z. Chun, H. Low, H. L. Lee, S. Y. Loong, and G. Guo, “Via electromigration improvement by changing the via bottom geometric profile,” US patent 7045455B2.
11. K. K. Kirby, “Methods for forming interconnects in microelectronic workpieces and microelectronic workpieces formed using such method,” US patent 7271482.
12. A. Kadyshevitch, C. Talbot, D. Shur, and A. G. Hegedus, “Contact Opening Metrology,” US patent 2007/0257191 A1.
