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PHYS 211A Thermal characterization of Au-Si multilayers using 3-omega method Sunmi Shin Materials Science and Engineering Program 1 Conventional steady-state system to measure thermal conductivity • Fourier’s Law of heat conduction: Q ×t k=A × 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 ) éë1+ aTDC + a T2w cos(2w t + f )ùû 4 How to extract thermal conductivity [2] 1 1 é ù V = IR = I 0 R0 ê(1+ aDTDC )cos(w t) + a DTAC cos(w t + f ) + a DTAC cos(3w t + f ) ú 2 2 ë û 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 Pò r1 r2 dT2w dr A = p rl Heated region: semi-circle T2 dr = -kp l ò 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 Temperature gradient within specimen 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