Fast, precise 3-D measurement of discontinuous step-structures fabricated on microelectronic products is essential for quality assurance of semiconductor chips, flat panel displays, and photovoltaic cells. Optical surface profilers of low-coherence interferometry have long been used for the purpose, but the vertical scanning range and speed are limited by the micro-actuators available today. Besides, the lateral field-of-view extendable for a single measurement is restricted by the low spatial coherence of broadband light sources. Here, we cope with the limitations of the conventional low-coherence interferometer by exploiting unique characteristics of femtosecond laser pulses, i.e., low temporal but high spatial coherence. By scanning the pulse repetition rate with direct reference to the Rb atomic clock, step heights of ~69.6 μm are determined with a repeatability of 10.3 nm. The spatial coherence of femtosecond pulses provides a large field-of-view with superior visibility, allowing for a high volume measurement rate of ~24,000 mm3/s.
© 2013 OSA
Microelectronic packaging is gaining more attention as customers’ demands for faster, smaller, lighter, thinner, and high performance electronic products grow rapidly [1,2]. Thus far, the ultimate packaging solution available is the flip chip assembly in which semiconductor chips are connected directly to printed circuit boards via solder bumps of a significant thickness reaching hundreds of micrometers [2,3]. Such discontinuous microelectronic step-structures are also essential for flat panel displays and photovoltaic products , but impose challenges in measuring the step height precisely in a fast way for quality assurance during manufacture. Conventional interferometric profilers using monochromatic lasers [5,6] widely used to test lenses and mirrors with nanometer precision are not suitable for profiling discontinuous surface features due to the 2π ambiguity in phase unwrapping  which limits the maximum step increase between two consecutive measuring points to half the wavelength.
Low-coherence scanning interferometry and time-domain optical coherence tomography relying on broadband light sources are free from the phase ambiguity in principle, as interferometric fringes are produced within a narrow range only when the optical path difference (OPD) between the reference and measurement arms approaches zero [8–12]. Despite the advantage, the low spatial coherence of broadband sources restricts the lateral field-of-view (FOV) usually to several square millimeters, while the interferometer design is required to be strictly symmetric and equal-path between the measurement and reference arms . Furthermore, it is not easy to improve the vertical scanning speed and range due to the practical limitations of micro-actuators available today. During the last decade, mode-locked femtosecond lasers have enabled remarkable progresses in precision spectroscopy [14,15], optical frequency metrology , and absolute laser ranging [17–23] owing to their unique temporal and spectral characteristics. They are now expected to open a new vista in the field of precision surface metrology as well, this time their exceptional coherence property, i.e., low in temporal but high in spatial term, plays an important role in achieving unprecedented performance in low-coherence 3-D profiling of large surfaces [24–29].
Here, we demonstrate a fast and precise profiling method of microelectronic step-structures by low-coherence scanning interferometry using femtosecond laser pulses. An unequal-path, non-symmetric interferometer system is configured such that the OPD between the reference and measurement arms are varied by scanning the repetition rate of femtosecond pulses. The scale of OPD variation is readily extended by adjusting the unbalanced length of the interferometer for a given scanning range of the pulse repetition rate. Furthermore, the high spatial coherence of femtosecond pulses provides higher visibility over a wide FOV. As a result, fast and precise 3-D profiling is accomplished with a high volume measurement rate being ~70,000 times faster than state-of-the-art low-coherence scanning interferometers.
2. Low-coherence interferometry by scanning the repetition rate of femtosecond pulses
Figure 1(a) shows the optical schematic of the low-coherence interferometer system configured in this investigation. A custom-built Er-doped fiber femtosecond laser of a 1560 nm center wavelength is used as the light source to generate a pulse train of ~100 fs duration at a repetition rate of 100 MHz with an average power of 280 mW. The generated pulse train is divided into two interferometer arms of different lengths; one is the reference arm of a long length made of a single-mode fiber (SMF) and a dispersion compensation fiber (DCF). The other is the measurement arm of a short length of only a single-mode fiber. The center wavelength of the original pulses is halved to 780 nm by use of a second-harmonic crystal (PPLN) so that the resulting interferometric fringes can be monitored with a digital camera operating in the visible and near infra-red range. The pulse repetition rate (fr) is scanned precisely with reference to the Rb atomic clock by elongating the cavity length of the femtosecond laser oscillator. Then the unbalanced optical delay of the unequal-path configuration converts the variation of fr to the OPD scanning between the reference and measurement pulses as illustrated in Fig. 1(b). Three different fr-scanning mechanisms with different tuning ranges and speeds are employed in series within the femtosecond laser oscillator: an electro-optic modulator (EOM) for 1.2 μm and 1 m/s; a PZT for 18 μm and 9 mm/s; and a motorized stage for 50 mm and 30 μm/s. When converted to actual OPD variation, the tuning range and speed induced by each scanning mechanism are magnified significantly as a function of the unbalanced length of the interferometer as plotted in Fig. 1(c).
The pulse repetition rate is inversely proportional to the cavity length (Lc) by fr = c/Lc with c being the speed of light. The unbalanced optical delay provided by the unequal-path interferometer magnifies a small variation of Lc to a large OPD scale (See Figs. 1(b) and 1(c)) [18,30–34]. When the resulting OPD is near m·Lc (where, m = 1, 2, 3 …), the mth pulse (Pm) meets the leading reference pulse (P0). The distance offset (ΔD) between Pm and P0 is expressed as a function of the repetition rate asFig. 1(c): 120 μm by the EOM, 1.8 mm by the PZT, and 5.0 m by the motorized stage with scanning speeds of 100 m/s, 0.9 m/s and 3.0 mm/s, respectively. This scheme permits covering meso-scale step-structures whose height ranges from several micrometers to hundreds of millimeters. The OPD scanning precision is directly traceable to the Rb atomic clock by phase-locked-loop (PLL) control of fr-scanning (See Fig. 2(c)). The error contribution by the slow drift in the unbalanced optical delay is confirmed to be minute in repeatability tests due to the relatively short scanning time over the step-heights. The frequency stability of the repetition rate was evaluated to be 2.9 × 10−12 at 1 s averaging in terms of Allan deviation. There is no scanning element used within the interferometer so as to avoid troublesome issues such as limited scanning speed, possible misalignment, and heat generation.
The near-infrared pulses centered at 1560 nm are wavelength-converted into 780 nm using a second harmonic generation PPLN crystal (See Figs. 2(e) and 2(f)). In the proposed design of Fig. 1(a), a single PPLN was used for wavelength-converting both the reference and measurement pulses simultaneously: both pulses propagated through the same PPLN but in the opposite direction. This common-path wavelength-conversion scheme permits cancelling out the wavefront error caused by the length variation of the PPLN when the measurement and reference pulses interfere. The optical delay was carefully designed for the measurement and reference pulses not to overlap inside the PPLN which could cause unexpected intensity modulation in generated second harmonics. The measurement pulses (blue beam in Fig. 1(a)) are directed to the target specimen and combined with the delayed reference beam (green beam in Fig. 1(a)) at the beam splitter. The resulting low-coherence interferograms are obtained with a high-speed (350 frames per second (fps)) CMOS camera (MV-D752-160-CL-8; PhotonFocus) using a macro-imaging lens (AF Micro Nikkor 105 mm; Nikon) with a magnification adjustable up to 1.
The resulting interferogram at the relative pulse delay of Δz ( = ΔD/2) can be written asFigs. 2(g) and 2(h). The interferogram appeared only within a short coherence length without any substantial parasitic noise. There was not any conceivable phase drift made by carrier-envelope-phase drift as well (See Fig. 2(h)). The sinusoidal carrier was clearly resolved inside the pulse envelope, which permits analyzing the interferogram with a suitable phase-shifting algorithm for higher precision.
3. Reconstruction of 3-D profile of large-stepped surfaces
In order to process the large amount of interferograms captured by a high-speed camera, the 3-D reconstruction algorithm should be arranged as simple as possible. In addition, the algorithm must be robust to any vibration or scanning nonlinearity. To satisfy these requirements, we configured a hybrid algorithm that combines the weighted centroid algorithm with the arbitrary bucket (A-bucket) algorithm [35,36]. First, the centroid algorithm determines the envelope peak of the low-coherence interferogram to overcome the 2π phase ambiguity; then, the A-bucket algorithm is employed to measure the phase peak (fringe peak) of the optical carrier around the envelope peak with a higher measurement precision . The A-bucket algorithm uses least-square fitting for the phase extraction, being capable of providing high robustness to vibration, scanning error, and system nonlinearity. The overall reconstruction process is illustrated in Fig. 3.
For the weighted centroid algorithm, the envelope function is assumed Gaussian and symmetrical about the maximum envelope peak. When the intensity difference (|ΔIk|) at two consecutive scanning depths (zk and zk-1) is smaller than a specified threshold value, it is considered that the reference and measurement pulses do not overlap, and the depth can be moved toward the next position (zk + 1). In order to compensate for unexpected distortions in the interferogram caused by fiber dispersion, surface roughness, and complex reflectance of the specimen, a weighting factor (w(z)) is introduced so that the surface height h(x,y) is computed as
4. Measurement of high step-structures
A standard step-height specimen of 69.6 μm (certified by KRISS (Korea Research Institute of Standards and Science)) was measured as an example (See Fig. 4) to demonstrate the measurement capability of the proposed method. Profiling high step-structures requires a large OPD scanning range; the repetition rate (fr) was tuned from 99.37902000 to 99.37942000 MHz with an increment of 0.04 Hz, which corresponds to 60 nm scan step. The number of digits of the repetition rate here presents the high scanning precision realized in the measurement. The scan step was determined to be less than the Nyquist sampling limit (780 nm (center wavelength) / 2 (double pass) / 2 (Nyquist sampling) = 195 nm) and the number of samples was determined by considering the maximum step-height. Resulting interferograms obtained at 350 fps are presented in Fig. 4(a); upper five interferograms are from the bottom surface and the lower five are from the top surface. The combined algorithm of Fig. 3 was used to reconstruct the 3-D profile map as shown in Figs. 4(b) and 4(c). The measurement repeatability was evaluated by repeating 15 measurements over five sample bumps; to 45.1 nm using the centroid algorithm only (See Fig. 4(d)) and to 21.4 nm with the combined algorithm. This confirms that the proposed system is capable of measuring high step-structures such as metal bumps, through-silicon-via holes, and column spacers used in microelectronic products or flat panel display industries. It is worthwhile to note that the measurement step height can readily be extended to 2.5 m by using the intra-cavity motor stage, for example, for absolute calibration of long standard gauge blocks of industrial length standards.
5. Fast step measurements
The fr-scanning using an EOM offers high-speed measurements of surface profiles without any mechanical movement (even in the oscillator as well as in the low-coherence interferometer) and provides low noise interferogram due to the higher locking bandwidth. A step-height of 1.13 μm was measured by scanning the repetition rate from 99.38000000 to 99.38002000 MHz with an increment of 0.02 Hz (30 nm scan step) with the unbalanced magnification factor (m) of 100 (See Fig. 5). Figures 5(b) and 5(c) show the result of 3-D height map along with sectional profiles. The repeatability was measured 10.3 nm (1-σ) for 15 consecutive measurements. The EOM scanning speed reaches ~1 MHz, which is limited by the used electric amplifier not by the EOM itself. Nevertheless, it is still much faster than mechanical scanning devices or state-of-the-art digital cameras. The overall processing time was shorter than the frame rate using a GPU-based parallel processing . Therefore, the EOM is expected to enable fast surface measurements up to several MHz when a sufficiently fast frame-rate camera is used together.
6. Wide FOV measurements
The high spatial coherence of femtosecond laser pulses permits expanding the lateral FOV of a single measurement to a significant size simply by changing the illumination optics. Conventional broadband light sources suffer from substantial power losses during the spatial mode filtering usually implemented through a small-sized pinhole. In principle, femtosecond pulses can be expanded to several meters without power loss thanks to their high spatial coherence . In our experiments, the FOV was exemplarily expanded to a 14.5 mm diameter and a 3-D step-structure was measured as shown in Fig. 6(a). The beam size of the current apparatus was restricted by the used collimator aperture, not by the spatial coherence or average power. It is also worthwhile to note that traditional low-coherence interferometers require large-sized beam splitters, reference mirrors, and scanning mechanics for large FOVs, which leads to the overall system complexity, optics deformation, and low scanning speed. Whereas, the proposed system design is free from these requirements, because the high spatial coherence enables the non-symmetric design as well as unbalanced configuration of OPD scanning (See Fig. 6(b)).
Even though not attempted in our current experiments, the lateral FOV could be further extended to cover a full semiconductor wafer of a 300 mm diameter using small-size interferometer optics . This would allow the volume measurement rate to reach 24,021 mm3/s ( = π·(300/2 mm)2 × 1 μm (step size) × 350 fps (camera frame rate in use)). The measurement performance is about 70,000 times higher than those of existing low-coherence interferometers (~0.35 mm3/s). The volume measurement rate is ultimately restricted by the frame rate of the cameras available today. Otherwise, the volume measurement rate could be extended to a maximum of 6,358,500 with a PZT ( = π·(300/2 mm)2 × 100 (multiplication factor) × 0.9 mm/s (PZT scan rate)) and 7,065,000,000 mm3/s using an EOM ( = π·(300/2 mm)2 × 100 (multiplication factor) × 1,000 mm/s (EOM scan rate)).
To summarize, we demonstrated that femtosecond laser pulses can be used as a light source for fast and precise 3-D profilometry of microelectronic step-structures. Low-coherence optical path length (OPD) scanning was realized by varying the repetition rate of femtosecond pulses through the unbalanced optical delay provided between the measurement and reference arms. A fast OPD scanning speed of 100 m/s was achieved for a 120 μm range using an electro-optic modulator (EOM) with the scanning precision being traceable to the Rb atomic clock. The lateral field-of-view (FOV) of a single measurement was extended to a 14.5 mm without significant wavefront errors due to the high spatial coherence of the femtosecond laser. All these measurement capabilities offered by using femtosecond pulses are well-suited for fast 3-D profiling of large step-structures widely used in microelectronic products such as semiconductor packaging, flat panel displays and photovoltaic devices.
This work was supported by the National Honor Scientist Program, the Space Core Technology Program, the Global Research Network Program, and the Basic Science Research Program (2010-0024882) funded by the National Research Foundation of the Republic of Korea.
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