Ohmyoung Kwon
1
e-mail: omkwon@wow.hongik.ac.kr
Li Shi
Arun Majumdar
Department of Mechanical Engineering,
University of California,
Berkeley, CA 94720
Scanning Thermal Wave
Microscopy (STWM)
This paper presents a technique, scanning thermal wave microscopy (STWM), which can
image the phase lag and amplitude of thermal waves with sub-micrometer resolution by
scanning a temperature-sensing nanoscale tip across a sample surface. Phase lag mea-
surements during tip-sample contact showed enhancement of tip-sample heat transfer due
to the presence of a liquid film. The measurement accuracy of STWM is proved by a
benchmark experiment and comparison to theoretical prediction. The application of
STWM for sub-surface imaging of buried structures is demonstrated by measuring the
phase lag and amplitude distributions of an interconnect via sample. The measurement
showed excellent agreement with a finite element analysis offering the promising pros-
pects of three-dimensional thermal probing of micro and nanostructures. Finally, it was
shown that the resolving power of thermal waves for subsurface structures improves as
the wavelengths of the thermal waves become shorter at higher modulation frequencies.
DOI: 10.1115/1.1518492
Keywords: Electronics, Heat Transfer, Microscale, Microstructures, Nanoscale, Nonin-
trusive Diagnostics
1 Introduction
This paper presents a new non-destructive evaluation NDE
technique of imaging sub-surface structure on the sub-micrometer
scale using thermal waves. Although the atomic force microscope
AFM can examine surface structures with atomic resolution, it
does not generally yield any sub-surface information. As three-
dimensional micro and nanoengineered devices are developed in
the future, the demand for the NDE technique of micro- and nano-
structures is expected to grow. For example, with advances in
integrated circuit IC manufacturing technology, the minimum
feature size in ULSI circuits is becoming smaller and the number
of layers is increasing. This trend poses challenges in the diagno-
sis and study of the reliability physics of ULSI circuits. Hence,
there is a need for developing techniques to locate and character-
ize sub-surface defects in ULSI circuits buried in insulating
materials.
The propagation of thermal waves in a solid can be used to
study sub-surface structures at micro and nanometer scales. This
is because thermal waves propagate at much slower speeds than
sound waves which is commonly used in NDE at large scales.
Hence, for a given frequency, the wavelengths of thermal waves
are much shorter. When the surface of a one-dimensional semi-
infinite medium is modulated in a sinusoidal manner, the tempera-
ture fluctuation in the medium is given as 1
T x , t =T
0
exp -
/2 x cos
t -
/2 x (1)
where x is the distance from the surface, T
0
is the amplitude of the
surface temperature fluctuation, is the angular frequency, and
is the thermal diffusivity. From Eq. 1 the dispersion relation and
the wavelength of plane thermal waves are given as
v =2
f (2)
and
=2
/ f (3)
where v is the wave speed, f is the wave frequency, and is the
wavelength. At 100 kHz, the wave speed in Pyrex glass is about
0.9 m/s and the wavelength is about 9 m. Consequently, phase
lag of 1 deg corresponds to 25 nm of distance. If one had to use
ultrasonic waves of similar wavelengths, the frequencies required
would be in the range of 0.1–1 GHz, which is difficult to operate.
One must note, however, that the thermal waves decay exponen-
tially and the decay length is on the order of the wavelength.
Hence, features only a wavelength below a surface can be studied.
The phase lag and the amplitude of thermal waves depend on
the thermal diffusivity of the medium and the wave frequency 1.
Using this principle, extensive work has been done to obtain the
thermal properties of materials. This can be classified depending
upon whether thermal waves were generated by electrical 2–4
or optical heating 5–7 and/or upon whether the phase lag and
the amplitude were measured optically 5,6 or thermo-electrically
2,3,7. In these works, the focus was on extracting the material
properties and not for imaging. Therefore, most of the data were
obtained at a single point.
There have also been many efforts undertaken to image subsur-
face structures using photoacoustic microscopy and photothermal
wave microscopy 8. Photoacoustic microscopy PAM uses pho-
tothermally generated acoustic waves to investigate subsurface
structures and photothermal wave microscopy images thermal
wave propagation and scattering by subsurface defects using
probe beam. Thermoreflectance technique was also applied to im-
age amplitude and phase lag distributions in a resistor heated by
an alternating current 9. The same technique was applied to
perform reflectance microscopy on a biased MOSFET structure by
scanning its gate surface 10. Ocariz et al. 11 performed a the-
oretical study of the scattering of planar and spherical thermal
waves by a buried single infinite cylinder. They also measured the
amplitude and phase distributions using three different modulated
photothermal techniques: thermoreflectance, infrared radiometry,
and mirage 12,13. The resolution of these techniques is diffrac-
tion limited by the wavelength of the probe beam, which is ap-
proximately 1 m. To overcome this, STWM described here takes
advantage of the high spatial resolution 50 nm of recently
developed probes for the purpose of scanning thermal microscopy
SThM14.
Through a benchmark experiment, it is first shown that STWM
can image thermal wave propagation with sub-micrometer resolu-
tion. Then, STWM is used to measure the amplitude and phase lag
1
Current address: Department of Mechanical Engineering, Hong-ik University,
Seoul, Korea 121-791.
Contributed by the Heat Transfer Division for publication in the JOURNAL OF
HEAT TRANSFER. Manuscript received by the Heat Transfer Division December 17,
2001; revision received July 3, 2002. Associate Editor: D. Poulikakos.
156 Õ Vol. 125, FEBRUARY 2003 Copyright © 2003 by ASME Transactions of the ASME