1ｓｔ International Symposium on Thermal Design and Thermophysical Property for Electronics, June 18-20, 2008, TsukubaLight Pulse Heating Thermoreflectance Methods for Thermophysical Property
Measurements of Thin Films
Tetsuya BABA
Material Properties and Metrological Statistics Division, NMIJ, AIST
Tsukuba Central 3, 1-1-1, Umezono, Tsukuba, Ibaraki 305-8563, JAPANE-mail: t.baba@aist.go.jp
Reliable thermophysical property values of thin films are important to develop advanced industrial technologies such as
highly-integrated electric devices, optical disks, magneto-optical disks, and thermoelectric devices. In order to meet thisrequirement, the National Metrology Institute of Japan of the National Institute of Advanced Industrial Science andTechnology (NMIJ/AIST) has developed thermoreflectance methods by picosecond pulse heating and nanosecond pulse
heating under the same geometrical configuration to the laser flash method which is the standard method to measurethermal diffusivity of bulk materials. These light pulse heating methods observe one-dimensional heat diffusion acrosswell-defined length of the specimen thickness. Thermal diffusivity values across thin films were measured with small
uncertainty. Since the geometry is very simple, thermal diffusivity can be determined reliably with uncertainty
evaluation based on Guide to the Expression of Uncertainty in Measurement (GUM).

In addition, it is necessary to know a value of a boundary

1. INTRODUCTION
According to the ITRS (International Technology

thermal resistance between the layer as well as aRoadmap for Semiconductors) 2006 Update, the pace ofthermophysical property of each layer to understand internalchange in assembly and packaging has accelerated asheatpackaging is increasingly a limiting factor for both productsemiconductor device or storage media at high integration.

cost and performance. In order to reflect these rapid changes,

However, when multilayered films are measured with

“Package Substrate Physical Properties (Table 98) have been

conventional measurement methods, it is difficult to separatetransferofmultilayered

film

constitutingaupdated to incorporate additional parameters for thermal

contribution of thermal resistance between the layers fromproperties that are increasingly critical for higher temperature,

thermal conduction of each layer.

smaller form factor packages” in the assembly and packaging
part. It is also mentioned that one of the difficult challenges ≥2. LASER FLASH METHOD

32 nm is “Thermal-mechanical-electrical modeling for

There are varieties of thermal diffusivity measurement

interconnections and packaging” in the modeling andmethods by combination such as shape and dimension of thesimulation part and Difficult Challenges (Table 122) havespecimen, heating position, heating method of the specimen,

been updated as “Model thermal-mechanical, thermodynamicaand electronic properties of low κ, high κ, and conductors formeasurement method. It is common to measure a thermal

efficient in-chip package layout and power management, anddiffusivity by the laser flash method for specimens of

the impact of processing on these properties especially forthickness from several 100μm to several mm of metals,

interfaces and films under 1 micron dimension.” in theceramics, semiconductor, and s carbon materials etc. Then,modeling and simulation part.

thermal conductivity λ is calculated by equation λ=α c ρ from

In optical recording storage media, small area is heatedtemperature

measurement

position,atemperature

specific heat capacity c and density ρ [3-5].

by laser beam and it is recorded by changing state(magnetization, crystal phase or an amorphous phase) of the

Uniform pulse heating

Specimen

Thermometerarea. Therefore, control of a temperature change in record
media by pulse heating becomes key technology.
Thermal properties of such thin films do not agree withthose of bulk materials of same name / same composition.
Consequently, it is necessary to measure these thin films insitu as the shape of circuit elements or record media, or tomeasure thin film specimens which are synthesized to thedsame thickness by the same deposition method as the thinfilms in the vice [1, 2].

Figure 1 Principle of the laser flash method

0.5

0.1388
0.0

t1/2

0.0

0.2

0.4

0.6

Time，t τ

0.8

1.0

Amplitude of output signal, K

Temperature rise，T/ΔT

1.0

29

(a)
28
27
26
25
-20

after pulse heating
When thermal diffusivity is measured with the laser flash
method, front face of a planar specimen kept at constanttemperature is pulsewise heated uniformly as shown in figure
1. Heat diffuses one-dimensionally from a heated specimen

Deviation, %Figure 2 Temperature change of specimen rear face

10
5
0
-5
-10

0

20

40

60

80

0

20

40

60

80

(b)

-20

Time, ms

front face to rear face and temperature of the whole specimen
finally becomes uniform. Because speed of a temperaturechange of specimen rear face is in proportion to a thermal
diffusivity and is in inverse proportion to the square of
thickness of specimen, a thermal diffusivity is calculated bythickness of specimen and heat diffusion time [3-5].

Figure 3 Transient temperature curve of IG-110
specimen: (a) experimental data, (b) deviationfrom the theoretical curve.
transient temperature curve, and the thermal diffusivity is
calculated. Conventional standard data analysis algorithm is

The following condition is assumed as ideal:
1) Duration of the laser pulse is negligibly short comparedwith the heat diffusion time.

the half time method where the time reaching half of the
maximum temperature rise value is determined frommeasured curve, and calculates thermal diffusivity from the2) Specimen is adiabatic to the environment.

following equation: [3]3) Specimen front face is heated uniformly.
4) Temperature change of specimen rear face is measured

α = 0 . 1388 d 2 t1 2

(2)

precisely.
5) Specimen is dense, uniform, and opaque.
6) Change of thermal diffusivity by temperature rise of
specimen after pulse heating is negligibly small.
Under the assumption mentioned above, when front faceof a plate of thermal diffusivity α , specific heat capacity

c , density ρ , thickness dis heated pulsewise withuniform energy density, temperature change of the specimen
rear face is expressed by the following equation:∞⎡⎛
2 t ⎞⎤T (t ) = ΔT ⋅ ⎢1 + 2∑ (−1) n exp⎜ − (nπ ) ⎟⎥
τ ⎠⎦
⎝
n =1
⎣

3. HIGH SPEEDLIGHT PULSE HEATINGTHERMOREFLECTANCE METHODS
3.1 Nanosecond light pulse heating
thermoreflectance method
1) Front face heating / front face detection
Picosecond thermoreflectance method was developed tomeasure thermal diffusivity of subnanometer thick thin films
by Paddock and Eesley [6]. The optical reflection intensity of(1)

where Δ T = Q / C , Q is the total energy absorbed by
the specimen, C is the heat capacity of the specimen,

τ = d 2 α is the characteristic time of heat diffusion acrossthe temperature detection light is detected by photodiode.
Since reflectivity of material surface changes dependent on
the surface temperature, the change of specimen front facetemperature can be observed by the change of reflected light
amplitude. This temperature measurement method with thetemperature change of such a reflectivity is called as

the specimen. Graph of equation (1) is shown in figure 2.
When 0.1388 times of the characteristic time passed afterthermoreflectance method [7]. Thermal diffusivity ofpulse heating, specimen rear face temperature reaches half ofcalculated from the cooling rate of the surface temperature

the maximum temperature rise. The characteristic time isdetermined by fitting theoretical curve to the rear facesubmicrometer thin films perpendicular to the surface wasand the penetration depth of the heating light.

On the other hand, for the specimen of 100 nm thick, thePump laser beam
Probe laser beam

temperature change speed decreases around 30 ps after pulse
heating as show by black line and deviates from theProbe laser
heating area

Pump laser
heating area
- 50μmφtemperature change of the 500 nm thick specimen. Because
the thermal diffusivity of glass substrate is much smaller than
the thermal diffusivity of aluminium thin film, the heatdiffusion to the substrate is suppressed when the heat arrives
at the interface between the thin film and the substrate.
As shown by blue line in figure 5, for the specimen of 50
nm thick, the temperature change only for the inside of theThin film 50 nm – 500nm

thin film cannot be observed because of heat diffusion to thesubstrate just after pulse heating.
Area of a diameter of several 10 μm on thin film front

Substrate – 1mm

face is heated by the picosecond laser beam and the same
position is irradiated by the probe beam. Then, the history offront face temperature is observed by the conventional
thermoreflectance method.

Figure 4

In this method, the thermal diffusivity can be calculated

Geometrical configuration of front faceheating / front face detection picosecond
thermoreflectance methodfrom the cooling rate after pulse heating. However, it is noteasy to make quantitative and reproducible measurement

First, NMIJ/AIST developed a system for measuring
thermal diffusivity of thin films system under front facebecause the cooling rate changes sensitively dependent on thecondition of thin film front face.

heating / front face detection configuration Figure 5 shows
the result which observed the change of the front facetemperature by the picosecond thermoreflectance method

Picosecond
Thermoreflectancemethod(Laser) Flash method

about three kinds of aluminium thin films of different

unify

thickness synthesized on a glass substrate [8].
For the specimen of 500 nm thick, the heat has not arrived
at the substrate within 120 ps after pulse heating in and thefront face temperature change represented by red line

High Speed Laser Flash Method

corresponds to internal heat diffusion of the aluminium thin

Normalized temperature increase

film.

High speed laser flash method

Conventional picosecond
thermoreflectance method

Rear heating / Front detection

Front heating / Front detection

Thermal diffusivity measurementwith small uncertainty
Applicable to thinner films

Applicable to nontransparent
substrate1
50 nm
100 nm
500 nm
0
0

20

40

60

80

Delay time (ps)Figure 6 Evolution of light pulse heating methods andadvantage and disadvantage of different
geometrical configurations

Figure 5 Thermoreflectance signals of three kinds ofdifferent thickness of aluminium thin film
synthesized on a glass substrate

Picosecond
Ti-Sapphire laser

CW Argon-ion laser

Thermaldiffusivity

Auto correlator

Lock-in Amp.
Optical delay line

PC
Polarizer
Reference signal
Specimen
Photo diode
Probe pulse
λ/2 plate
AO modulator
Pump pulse
Polarizer

Figure 7

Block diagram of the thermoreflectance thin film measuring system by picosecond pulsed laser heating

2) Rear face heating / front face detection
National Metrology Institute of JAPAN, AIST has

be measured by lock-in detection at modulation frequency ofheating light by an acoustic optic modulator.

developed rear face heating / front face detection picosecond

Figure 8 shows the temperature history curves of anlight heating thermoreflectance methods which are evolution

aluminium single-layered thin film of 100 nm thick and aof the conventional laser flash method and the picosecond

molybdenum single-layered thin film of 100 nm measured bythermoreflectance method [9-12]. Figure 7 shows the block

the picosecond light pulse heating thermoreflectancediagram of a measurement system. This configuration ismethod [9]. Both films were synthesized on a Pyrex glass

essentially equivalent to the laser flash method which is thesubstrate by magnetron DC sputtering method. Here, film

standard measurement method to measure the thermal

thicknesses are nominal values.

thin films can be calculated with small uncertainty from thethickness of a thin film and the heat diffusion time across athin film.
The temperature detection beam is focused to a spot
diameter of about 50 μm at the specimen front face just
opposite to the heating light focus position. The reflected
light intensity of the temperature detection light is in
proportion to the change of specimen front face temperatureand the change of the reflected light intensity is detected byphotodiode. The temperature coefficient of reflectivity for

Normalized thermoreflectancediffusivity of bulk materials. The thermal diffusivity of the

1.0

Al
Mo

0.5

0.0

-50

normal metal such as aluminium is small with 10-5/K order.

0

50

100

150

200

Time delay /ps

Since the transient temperature rise of the specimen front
face after picosecond pulse heating is smaller than a few
degrees, the thermoreflectance signal is much smaller thanthe offset level of the reflected light. Such a small signal canFigure 8

Thermoreflectance signals of aluminium andmolybdenum thin films of 100 nm thick byrear face heating / front face detection
picosecond thermoreflectance method

Since thermoreflectance signals are similar to thoseobserved by the laser flash method for bulk specimen
suggest, the heat energy transport of these metallic thinfilms of about 100 nm thick at room temperature intime scale of several 100 ps can be expressed by theclassic thermal diffusion equation .

diffusivity of materials ranging from thin films of several 10
nm thick to bulk specimens of several mm thick can bemeasured the light pulse heating methods under the same
geometrical configuration of one dimensional heat diffusion
after impulse heating as shown in figure 9.

4. ANALYSIS OF MULTILAYERED FILM AND
BOUNDARY THERMAL RESISTANCE

3.2. Nanosecond light pulse heating
thermoreflectance method

Thin films constituting light heating phase change storage

Initially, the electrical delay method was developed tomedia, transparent conductive films, and interlayer dielectric

expand the observation time of the picosecond light pulseof semiconductor device are semitransparent to visible light,

heating thermoreflectance method longer for measurements

near infrared light whereas metallic thin films areof thicker films [12]. Since the pulse duration can be longer

nontransparent to these lights. Consequently both faces of thethan picosecond and the repetition period of pulses is flexible,

film are coated with metal thin film for surface heating bynanosecond pulse laser can be used for light pulse heating

heating laser beam and surface temperature detection by

thermoreflectance method [2, 11]. For the pump pulse, pulse

probe laser pulse based on the thermoreflectance method.

duration is 2 ns and pulse interval is 20 μs with intensity

Therefore, analysis of heat diffusion across three layer thinmodulation of 1 kHz by an acoustic optical modulator.

films on substrate must be considered on order to calculate

Typical size and shape of the specimen are a disk of 10 mmthermal diffusivity of the thin film sandwiched by metal thinin diameter or a square of 10 mm on each side. The specimen

films.

is irradiated from bottom to the rear face of the specimen by

It is necessary to know boundary thermal resistancethe heating beam and the reflected light of the probe beam is

between the layer as well as thermophysical property of eachdetected by a photodiode. The thermoreflectance signals arelayer of multilayered film to understand internal heat transfer

detected using a lock-in amplifier. In this system it is possibleof multilayered films constituting a semiconductor device or

to measure the thermal diffusivity of thin films with thickness

storage. However, when multilayered films are measured

up to several micrometers.

with conventional measurement methods, it is difficult to

After the laser flash method and high speed light pulse
heating

thermoreflectancemeasure thermal conductivity of each layer and thermal

methods(thepicosecond

and

the

nanosecond

In this section, the response function method that isthermoreflectance method) have been established, thermal

general technique to analyze heat diffusion of such athermoreflectancemethodBulk materials
10-2

resistance between the layers separately.

Thin plates and coatings
10-4

10-3

Thin films
10-6

10-5

10-8

10-7

Heat diffusion length / m(l )Laser flash method
Nanosecond thermoreflectance method
Picosecond thermoreflectance method(Electrical delay)
Picosecond thermoreflectance method(Optical delay)
Heat diffusion time / s

(τ )

100

10-2

10-4

10-6

10-8

10-10

10-12

（Thermal diffusivity, α = 1×10 −5 m 2s −1 , τ = l 2 α ）Figure 9 Observable heat diffusion time and observable thickness of the specimen covered with four types of lightpulse heating methods when the thermal diffusivity is 10-5m2s-1

multilayer films is described [13 - 15].
Following symbols are used in this section:

t:time, ξ :Laplace parameter, d :thickness,
α :thermal diffusivity, b : thermal effusivity,by the following equation:
∞
∞⎡
⎛
⎛
n
2 t ⎞ ⎞⎤A = ∫ ⎢1 − ⎜⎜1 + 2∑ (− 1) exp⎜ − (nπ ) ⎟ ⎟⎟⎥ dt0τ ⎠ ⎠⎦
⎝
n =1
⎣ ⎝

(4)

T (t ) :temperature,

⎡1
⎤ τ
τ
= lim ⎢ −cosech ξτ ⎥ =ξ →0 ξξ⎣⎦ 6~
T (ξ ) :Laplace transform of temperature,Thus, the heat diffusion time ” τ ” is calculated from theq (t ) :heat flux density,

areal heat diffusion time ” A ” and the thermal diffusivity is

q~ (ξ) :Laplace transform of heat flux density,

τ = d 2 α :heat diffusion time across film or layer.

calculated as α = d 2 τ , where d is the thickness of thethin film.
4.3 Two-layer thin film

4.1 Areal heat diffusion time
The areal heat diffusion time is defined as the area

Heat diffusion across a multi-layer thin film issurrounded by the horizontal line at the height of thesystematically analyzed by the response function method [2,maximum temperature rise and the transient temperature

13-18]. Figure 11 shows a cascade connection of quadra-pole

response curve at the rear face after pulse heating as shown inmatrices to represent heat diffusion across a two-layer thin

figure 10 [2, 16 -18]. Based on the response function method,

film. In Laplace transformed space, the heat flux flowing into
the layer 1 from outside is expressed as “ q~ (ξ ) ”, thethe areal heat diffusion time is calculated by the following
equation (3) when the temperature is normalized by the( )maximum temperature rise Tmax = 1 b τ :

[

]

∞
⎡1
~ ⎤
A = ∫ 1 − b τ ⋅ Tr (t ) dt = lim ⎢ − b τ ⋅ Tr (ξ )⎥(3)0ξ →0 ξ
⎦⎣~where ξ is a Laplace parameter and Tr (ξ ) is Laplacetransform of Tr (t ) defined by∞~
Tr (ξ ) = ∫ Tr (t ) exp(− ξt ) dt .

Normalized thermoreflectance01

temperature of the open face of the layer 1 is expressed as~“ T1 (ξ ) ”, the heat flux penetrating through the boundary fromthe layer 1 to the layer 2 is expressed as “ q~ (ξ ) ”, the2temperature at the boundary between the layer 1 and 2 is~expressed as “ T 2 (ξ ) ”, and the quadra-pole matrix of the~layer 1 is expressed as “ S1 (ξ ) ”. They are related by thefollowing equation if the boundary thermal resistance isnegligibly small [13,15]:⎡ q~2 (ξ ) ⎤ ~⎡ q~1 (ξ )⎤
=
⋅
S
(
)
ξ
1
⎢T~ (ξ ) ⎥⎢T~ (ξ ) ⎥
⎣ 2 ⎦
⎣ 1 ⎦

A2b

1

(5)

Each component of this equation is expressed as follows:
A2

A2b-A2(~T2 (ξ ) = −

0

)

(

)

~
q~2 (ξ ) = cosh ξτ 1 ⋅ q~1 (ξ1 ) − b1 ξ ⋅ sinh ξτ 1 ⋅ T1 (ξ )

(

)

(

(6)

)

1
~
⋅ sinh ξτ 1 ⋅ q~1 (ξ1 ) + cosh ξτ 1 ⋅ T1 (ξ ) (7)b1 ξSimilarly, the heat flux flowing from the layer 2 tooutside is expressed as “ q~ (ξ ) ”and the temperature of the
3

-50

0

50

100 150 200 250 300
Delay time /ps
Figure 10 Area surrounded by the maximum
temperature rise line and the temperature
response at the specimen rear face after thepulse heating

4.2 Single layer thin film
The transient temperature response at rear face of anadiabatic mono-layer thin film is identical to equation (1)which is the theoretical solution for the laser flash thermal
diffusivity measurement under the ideal condition given byParker et. al. Thus, the areal heat diffusion time is expressed~
open face of the layer 2 is expressed as “ T3 (ξ ) ” in Laplace~transformed space. Then, the pair of q~3 (ξ ) and T3 (ξ ) are~ (ξ ) and T~ (ξ ) by inverse of therelated to the pair of q22~

quadra-pole matrix of layer 2 “ S2 (ξ ) ”.

q~ (ξ ) ⎤⎡q~2 (ξ ) ⎤ ~−1 ⎡ 3
ξ
S
(
)
=
⋅
~
2
⎢T (ξ ) ⎥⎢T~ (ξ ) ⎥
⎣ 2 ⎦
⎣ 3 ⎦

(

(8)

)

(

)

~
q~2 (ξ ) = cosh ξτ 2 ⋅ q~3 (ξ ) + b2 ξ ⋅ sinh ξτ 2 ⋅ T3 (ξ )~T2 (ξ ) =

(

)

(

)

1
~
⋅ sinh ξτ 2 ⋅ q~3 (ξ ) + cosh ξτ 2 ⋅ T3 (ξ )
b2 ξ

(9)
(10)

1

When b2 →0 and τ 2 → 0 , equation (13) converges to2

1~
T3b (ξ ) =
⋅

(
)
)

1

)

ξ ⎡b1b3 R12 ξ sinh ξτ 1 sinh( ξ τ 3 ) ⎤~S1 (ξ )
q~1 (ξ )⎢⎢+ b1 sinh ξτ 1 cosh( ξ τ 3 )⎢⎢⎣+ b3 cosh ξτ 1 sinh( ξ τ 3 )((~
S2 (ξ )

q~2 (ξ )

⎥
⎥
⎥
⎥⎦

(15)

Replacing a pair of b3 and τ 3 with a pair of b2 and τ 2 ,~~substituting T3b (ξ ) to Tr (ξ ) in equation (3), andq~3 (ξ )normalizing by the maximum temperature rise, the areal heatdiffusion time is expressed by the following equation:~
T1(ξ )~
T3 (ξ )~
T2 (ξ )(

Figure 11 Cascade connections of quadra-pole matrices
to represent heat diffusion across a two-layer
thin film~ (ξ ) = 1 and q~ (ξ ) = 0 to equations (6),Substituting q31~(7), (9), and (10), T 3 ( ξ ) is expressed as follows:1~T3 (ξ ) =
⋅

(11)

⎢
⎥
⎣⎢b2 cosh( ξτ 1 ) sinh( ξτ 2 ) ⎦⎥to12

= A2 +
where

(16)

12

b1 τ 1 + b2 τ 2

A2 is the areal heat diffusion time of a two-layer

figure 10 [2, 16]. From equation (16), the boundary thermalξ ⎡b1 sinh( ξτ 1 ) cosh( ξτ 2 ) + ⎤Substituting

b1b2 R12τ 1 τ 2thin film without boundary thermal resistance as shown in1~~
Tr (ξ ) = T3 (ξ )

)

⎡1
⎤
~
A2b = lim ⎢ − b1 τ 1 + b2 τ 2 ⋅ T3b (ξ )⎥ξ →0 ξ
⎦⎣equation(3)

andnormalize by the maximum temperature rise, the areal heat

resistance is expressed as follows:

R12 =
where

b1 τ 1 + b2 τ 2
b1b2 τ 1 τ 2( A2b − A2 )(17)

A2 and A2b are explained in figure 10.

diffusion time across the adiabatic two-layer thin film is

5. THIN FILM THERMOPHYSICAL PROPERTYREFERENCE MATERIAL AND TRACEABILITY

expressed as follows [2, 16]:

(

)

⎡1
~ ⎤
A2 = lim ⎢ − b1 τ 1 + b2 τ 2 ⋅ T3 (ξ )⎥ξ →0 ξ
⎣
⎦
=

b1τ 1

32

+ 3b2τ 1τ 2

12(

+ 3b1τ 1 τ 2 + b2τ 2
12

6 ⋅ b1 τ 1 + b2 τ 2

The high-speed laser flash method in extended definition
32

(12)

)

mentioned above can be generally used and popular after
commercial instruments are available and traceability to thenational standard and /or the international standard isestablished.
The national standard of the laser flash method was

4.4 Three-layer thin film
Similarly, temperature response of the rear face of athree-layer thin film in Laplace transformed space after apulse heating to the front face is expressed by the following
equation [13,14,15]:b~
T4 (ξ ) = 2 ⋅(ξ ⎡b1b3 sinh ξτ 1 sinh( ξτ 2 ) sinh( ξ τ 3 )⎤⎥⎢⎢+ b1b2 sinh ξτ 1 cosh( ξ τ 2 ) cosh( ξ τ 3 ) ⎥⎥⎢2⎢+ b2 cosh ξτ 1 sinh( ξτ 2 ) cosh( ξ τ 3 ) ⎥⎥⎢⎣⎢+ b2 b3 cosh ξτ 1 cosh( ξτ 2 ) sinh( ξ τ 3 )⎦⎥

( )
( )
( )

(13)

R=

λcρ

=

b ξ

= lim
d →0

Measurement,

GUM"

[19]

and

a

qualitysystemevaluation of homogeneity and stability of high density
isotropy graphite is under progress, The standard value ofthermal diffusivity of the graphite is to be determined withuncertainty evaluation based on GUM and will be supplied asa reference material in 2005.
NMIJ/AIST is also developing the standard of thin film
thermophysical property by the high-speed laser flash method
establish the national standard in 2005 for picosecond

Boundary thermal resistance is defined by:ξτ

based on “Guide to the Expression of Uncertainty inunder the same scheme as shown in Table 1. It is planned to

4.5 Boundary thermal resistanced 2 (λ cρ )diffusivity standard by the laser flash method was evaluatedcorresponding to ISO 17025 was constructed [5]. Now,1)established in 2002 by NMIJ/AIST. Uncertainty of thermal( )sinh ξτb ξ

thermoreflectance method. The national standard and thin
(14)

film reference material are developed and to be supplied in2008 for nanosecond thermoreflectance method.

Table 1 Program to develop thermal diffusivity standards
by light pulse heating methods planned by NMIJ/AIST
Observable
Light pulse heating methods Heat diffusion
Time

Planned year to start service
MetrologicalStandard

Reference
Material

FY2002

FY2005[6]

C. A. Paddock and G. L. Eesley, “Transient
thermoreflectance from thin metal films”, J. Appl.
Phys., AIP, Melville, vol.60, 1986, pp.285-290, 7.

[7]

A. Rosencwaig, J. Ospal, W. Smith, D. Willenborg,"Detection of thermal waves through opticalreflectance", Applied Physics Letters, vol.46, 1985,
pp.1013-1015.

[8]

N. Taketoshi, T. Baba, A. Ono, “Picosecond
thermoreflectance measurements of thermal diffusionin film/substrate two layer systems", Thermal
Conductivity24/Thermal Expansion 12, vol.24, 1999,
pp.289-302.

[9]N. Taketoshi, T. Baba and A. Ono, “Observation of heatdiffusion across submicrometer thin films using apicosecond thermoreflectance technique”, Jpn. J. Appl.
Phys., vol.38, 1999, L1268-1271, 11.

Laser flash method
Conventional
Application tothin plates andcoatings
Nanosecond
thermoreflectance method

1ms～10s
1μs～10ms

10ns～100μs

under
under
consideration consideration
FY2007

FY2008FY2005

underconsideration

Picosecond
thermoreflectance method
Electrical delay
Optical delay

100ps～10ns
10ps～1ns

6.SUMMARY
Thermoreflectance methods by picosecond pulse heating
and by nanosecond pulse heating have been developed under
the same geometrical configuration as the laser flash method
which is the standard method to measure thermal diffusivityof bulk materials. Thermal diffusivity values across thin films
were measured with small uncertainty. These high speed lightpulse heating thermoreflectance methods observe heatdiffusion time across well-defined length of the specimen
thickness under one-dimensional heat flow. Since thegeometry is very simple, thermal diffusivity can be
determined reliably with uncertainty evaluation based on
GUM [16]. NMIJ/AIST is engaged in research forestablishment of national standard, international standard forthermal diffusivity measurements of thin films.

REFERENCES
[1]

[2]

[3]

D. G. Cahill, K. E. Goodson, and A. Majumdar,”
Thermometry and thermal transport in micro/nanoscalesolid de-vices and structures”, J. Heat Transfer, ASME,
vol. 124, 2002, pp. 223-241, 4.
T. Baba, Proceedings of Workshop on Thermal
Investigations of ICs and Systems (Therminic 2004),
Sophia Antipolis, France, 29 September – 1 October
2004, pp. 241-249.
W. J. Parker, R. J. Jenkins, C. P. Butler and G. L.
Abbott,“Flash method of determining thermal
diffusivity, heat capacity, and thermal conductivity”
J. Appl. Phys., vol.32, 1961, pp1679–84

[4]

T.
Baba,
and
A.
Ono,
Meas.
Sci.
Technol., ”Improvement of the laser flash method to
reduceuncertainty
inthermaldiffusivity
measurements”, 12, 2001, pp.2046-2057.

[5]

M. Akoshima and T. Baba, “Thermal diffusivity
measurements of candidate reference materials by thelaser flash method”, Int. J. Thermophys., 26 (2005) pp.
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