1. science
2. physics
3. optics

Femtosecond laser pulses for fast 3-D surface
profilometry of microelectronic step-structures
Woo-Deok Joo,1 Seungman Kim,1 Jiyong Park,1 Keunwoo Lee,1 Joohyung Lee,1
Seungchul Kim,1 Young-Jin Kim,1,2 and Seung-Woo Kim1,*
1
Ultrafast Optics for Ultraprecision Group, Department of Mechanical Engineering, Korea Advanced Institute of
Science and Technology (KAIST), Science Town, Daejeon, 305-701, South Korea
2
[email protected]
*
[email protected]
Abstract: 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 Optical Society of America
OCIS codes: (120.3180) Interferometry; (120.6650) Surface measurements, figure; (140.7090)
Ultrafast lasers; (140.4050) Mode-locked lasers; (140.3510) Lasers, fiber.
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1 July 2013 | Vol. 21, No. 13 | DOI:10.1364/OE.21.015323 | OPTICS EXPRESS 15323
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1. Introduction
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 [4], 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
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Received 2 May 2013; revised 12 Jun 2013; accepted 13 Jun 2013; published 19 Jun 2013
1 July 2013 | Vol. 21, No. 13 | DOI:10.1364/OE.21.015323 | OPTICS EXPRESS 15324
unwrapping [7] 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
[13]. 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 [16], 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 stepstructures 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).
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Received 2 May 2013; revised 12 Jun 2013; accepted 13 Jun 2013; published 19 Jun 2013
1 July 2013 | Vol. 21, No. 13 | DOI:10.1364/OE.21.015323 | OPTICS EXPRESS 15325
10
8
10
7
10
6
10
5
10
4
10
3
10
2
10
1
10
Δfr = 1.70 MHz (Motor stage)
Δfr = 600 Hz (PZT);
Δfr = 40 Hz (EOM)
0
200
400
600
800
1000
Fig. 1. Low-coherence scanning interferometer using femtosecond pulses for 3-D profilometry
of microelectronic step-structures. (a) Optical configuration of unequal-path interferometry. (b)
Relative time shift between the reference and measurement pulses during the repetition rate (fr)
scanning. (c) The OPD scanning range vs. the unequal-path length for three different fr-tuning
ranges: PZT (piezoelectric ceramic), EOM (electro-optical modulator), and motorized stage.
Abbreviations are; SMF: single-mode fiber, DCF: dispersion compensating fiber, DM:
dichroic mirror, PPLN: periodically poled lithium niobate, Lc: cavity length of the laser
oscillator.
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 as
 Δf

ΔD = m c(τ f − τ i ) = m c( f r−, 1f − f r−,i1 ) ≅ − m c ⋅  r 2  ,
f

r 
(1)
where fr,i is the initial, fr,f is the final value of the repetition rate; τi is the initial, τf is the final
value of the pulse spacing in time, and ∆fr is the difference between fr,i and fr,f realized in fr scanning. A 300 m long unbalanced optical path delay was installed in our experiments,
which provides a magnification factor (m) of 100; this optical delay was realized with a
186.45 m single-mode fiber (SMF-28, Corning) of a 16.7 ps/nm/km dispersion slope and a
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1 July 2013 | Vol. 21, No. 13 | DOI:10.1364/OE.21.015323 | OPTICS EXPRESS 15326
18.10 m dispersion-compensating fiber (LLWBDK, OFS) of a −172 ps/nm/km dispersion
slope at the wavelength of 1560 nm. Now, the repetition rate scanning enables an effective
OPD scanning in the interferometer as shown in Fig. 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.
Fig. 2. Management of the femtosecond light pulses. (a) Pulse duration measured by
interferometric autocorrelation is 90 fs at full-width-half-maximum (FWHM). (b) Optical
spectrum centered at 1560 nm. (c) Frequency stability of the repetition rate is 2.9 × 10−12 at 1-s
averaging in terms of Allan deviation. Inset: time trace of the repetition rate at 1-s sampling
rate. (d) Pulse duration of frequency-doubled reference pulses is 83 fs at FWHM. (e) Optical
spectrum of frequency-doubled reference pulses. (f) Optical spectrum of frequency-doubled
measurement pulses. (g) Low-coherence interferogram measured as a function of the repetition
rate. (h) Magnified view of the low-coherence interferogram near the envelope peak. The
sinusoidal carrier is clearly resolved inside the pulse envelope.
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
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1 July 2013 | Vol. 21, No. 13 | DOI:10.1364/OE.21.015323 | OPTICS EXPRESS 15327
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-CL8; 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 as
I ( Δz ) = I o ⋅  1 + γ (h − Δz ) ⋅ cos ( 2k ( h − Δz ) )  ,
(2)
where I0 denotes the background intensity, γ is the envelope function of the low-coherence
interferogram, h is the surface height of the specimen, and k is the wave-vector in the air. An
exemplary interferogram obtained by fr-scanning is shown in Figs. 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 [24]. 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.
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1 July 2013 | Vol. 21, No. 13 | DOI:10.1364/OE.21.015323 | OPTICS EXPRESS 15328
Fig. 3. 3-D profile reconstruction algorithm. The weighted centroid algorithm is combined
with the arbitrary bucket algorithm; the former locates the envelope peak of the low-coherence
interferogram to eliminate the 2π ambiguity and the latter determines the position of the phase
peak of the optical carrier signal with high precision. Abbreviations: Ixy: intensity at pixel (x,y),
zk : k-th scanning depth, ∆Ik : intensity difference between two consecutive scanning depths of
zk and zk-1, wk : weighting factor, Zc(x,y): surface height at pixel (x,y) determined by the
centroid algorithm, Num: numerator part of Zc, Den: denominator part of Zc, Zk,c: nearest zk to
Zc, Zf (x,y): final surface height at pixel (x,y).
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
  w( z ) ⋅ ΔI '( z )  ⋅zdz .
h ( x, y ) = 
  w( z ) ⋅ ΔI '( z) dz
2
2
(3)
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
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1 July 2013 | Vol. 21, No. 13 | DOI:10.1364/OE.21.015323 | OPTICS EXPRESS 15329
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 stepstructures 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.
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a
Δfr = 0.00 Hz
Δfr = 0.04 Hz
Δfr = 0.08 Hz
Δfr = 0.12 Hz
Δfr = 0.16 Hz
Interferogram
on bottom surface
fr,i = 99.37902000 Hz
Repetition rate scan
Δfr = 46.40 Hz
Δfr = 46.44 Hz
Δfr = 46.48 Hz
Δfr = 46.52 Hz
Δfr = 46.56 Hz
Interferogram
on top surface
b
A'
70
60
B'
C'
40
5
30
B
4
20
C
3
10
2
0
A-A'
300
Height (μm)
0
4
3
2
1
0
7
6
5
1
c
Height (μm)
50
A
B-B'
C-C'
200
100
0
1
2
3
4
5
6
7
d
Height deviation (nm)
X (mm)
100
+σ
0
-σ
-100
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Measurement Number
Fig. 4. Measurement of high step-structures. (a) Interferograms obtained during fr-scan using a
PZT. The repetition rate was varied from 99.37902000 to 99.37942000 MHz with a 0.04 Hz
increment (60 nm scan step). Upper five interferograms were taken from the top surface of the
specimen and the lower five interferograms from the bottom surface. (b) Reconstructed 3-D
profile showing step heights of ~69.6 μm. (c) Sectional profiles along lines A-A’, B-B’, and CC’. (d) Measurement repeatability over 15 consecutive measurements at five sample bumps
with the weighted centroid algorithm is 45.1 nm (1-σ). It scales down to 21.4 nm using the
combined algorithm of Fig. 3.
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1 July 2013 | Vol. 21, No. 13 | DOI:10.1364/OE.21.015323 | OPTICS EXPRESS 15331
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 [35]. Therefore, the
EOM is expected to enable fast surface measurements up to several MHz when a sufficiently
fast frame-rate camera is used together.
a
fr,i = 99.38000000 Hz
Δfr = 0.00 Hz
Repetition rate scan
Δfr = 0.04 Hz
Δfr = 0.08 Hz
Δfr = 0.12 Hz
Δfr = 0.16 Hz
Height (μm)
b
1.0
0
A'
0.1
B'
0.2
C'
0.3
A
B
0.6
C
6
0.4
0.2
0
0
0.5
1.0
1.5
c
0.8
A-A'
B-B'
C-C'
Height (μm)
5
4
3
2
1
0
0.0
0.5
1.0
1.5
d
Height deviation (nm)
X (mm)
+σ
20
0
-20
-σ
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Measurement number
Fig. 5. Rapid measurement. (a) Interferograms obtained during fr-scanning with an intra-cavity
EOM. The repetition rate was tuned with an increment of 0.02 Hz (30 nm scan step). (b)
Reconstructed 3-D height map showing ~1.13 μm step heights. (c) Sectional profiles along
lines A-A’, B-B’, and C-C’. (d) Measurement repeatability over 15 consecutive measurements
is 10.3 nm (1-σ).
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Received 2 May 2013; revised 12 Jun 2013; accepted 13 Jun 2013; published 19 Jun 2013
1 July 2013 | Vol. 21, No. 13 | DOI:10.1364/OE.21.015323 | OPTICS EXPRESS 15332
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 [24]. 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)).
Fig. 6. Step-height measurement over a large FOV. (a) Reconstructed 3-D profile of step
structures over a wide FOV of 14.5 mm in diameter. (b) A unbalanced non-symmetric lowcoherence interferometer design with an extended FOV: the high spatial coherence of
femtosecond laser pulses enables non-symmetric interferometer design and the repetitive
temporal coherence along with a long unbalanced optical delay provides a long range of OPD
scanning. As a result, a superior volume measurement rate could be achieved with the advent
of the high-speed multiple CCDs array [37]. Abbreviations are; L: lens, DCF: dispersion
compensating fiber, DM: dichroic mirror.
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Received 2 May 2013; revised 12 Jun 2013; accepted 13 Jun 2013; published 19 Jun 2013
1 July 2013 | Vol. 21, No. 13 | DOI:10.1364/OE.21.015323 | OPTICS EXPRESS 15333
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 [34]. 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)).
7. Conclusion
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.
Acknowledgments
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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Received 2 May 2013; revised 12 Jun 2013; accepted 13 Jun 2013; published 19 Jun 2013
1 July 2013 | Vol. 21, No. 13 | DOI:10.1364/OE.21.015323 | OPTICS EXPRESS 15334