# Thermal characterization of Au-Si multilayers using 3

```PHYS 211A
Thermal characterization of Au-Si
multilayers using 3-omega method
Sunmi Shin
Materials Science and Engineering Program
1
thermal conductivity
• Fourier’s Law of heat conduction:
Q &times;t
k=A &times; DT
Q: input power
∆T: temperature difference
t: thickness
A: cross-sectional area
What is the weaknesses?
• Long thermal equilibrium time
• Errors due to black body radiation
2
What is 3-omega measurement?
Nano lett., 14, 2448-2455 (2014)
3
How to extract thermal conductivity [1]
I = I 0 sin(w t)
Apply AC current
I 02 R I 02 R
P = [ I 0 sin(w t)] R =
+
cos(2w t)
2
2
2
 Heat generates a temperature fluctuation.
DT = TDC + T2w cos(2w t + f )
 R is influenced by temperature oscillation.
R(T ) = R(T0 )(1+ aDT )
1 dR
a=
R dT
Temperature coefficient of resistance (TCR)
R(T ) = R(T0 ) &eacute;&euml;1+ aTDC + a T2w cos(2w t + f )&ugrave;&ucirc;
4
How to extract thermal conductivity [2]
1
1
&eacute;
&ugrave;
V = IR = I 0 R0 &ecirc;(1+ aDTDC )cos(w t) + a DTAC cos(w t + f ) + a DTAC cos(3w t + f ) &uacute;
2
2
&euml;
&ucirc;
1
V3w = I 0 R0a T2w
2
T depends on k.
k can be extracted from V3ω vs ω.
Slope of the curve on logscale
 Indicative of k
Measured
3ω voltage
How?
5
Thermal conductivity with 1D heat conduction
P = -kA
P&ograve;
r1
r2
dT2w
dr
A = p rl
Heated region: semi-circle
T2
dr
= -kp l &ograve; dT2w
T1
r
DT2w
P
r2
=ln
kp l r1
1
V3w = I 0 R0a T2w
2
f2
V ln
dR
f1
k=
4p lR02 (V3w ,1 - V3w ,2 ) dT
3
0
V03a
k=
4p lR0 S
r=
1
D
=
q
4p f
1/q: thermal penetration depth
f: input frequency
D: thermal diffusivity of the specimen
Slope of the curve
6
Application: Au-Si multilayers with ultralow k
• Highly dissimilar interfaces lower the thermal conductivity.
DTR ~ 1.6
DTR ~ 18.7
Nano lett., 14, 2448-2455 (2014)
Debye temperature ratio (DTR): 3.9
Phy. Rev. B 73, 144301 (2006)
7
Heater
Film
Substrate
Film
Heater
Substrate
Nano lett., 14, 2448-2455 (2014)
8
Measured thermal conductivity of Au-Si multilayers
Nano lett., 14, 2448-2455 (2014)
9
Thank you!
10
```