Numerical analysis of the 3ω-method

Transcription

1 Numerical analysis of the 3ω-method Comsol Conference, Stuttgart Manuel Feuchter, Marc Kamlah October 26, 2011 Institute for Applied Materials (IAM) KIT University of the State of Baden-Wuerttemberg and National Laboratory of the Helmholtz Association

2 Outline 1 Introduction 2 Functionality of 3ω-method 3 Geometry configurations 4 Numerical analysis 5 Outlook Manuel Feuchter, Marc Kamlah Comsol Conference 2011 October 26, /22

3 Introduction A Concept of the 3ω-method : The 3ω-method is an ac technique to determine the thermal conductivity of an amorphous solid. The 3ω-measurement is performed on a thin electrical conducting metal strip () deopsited on the sample surface. Literature: [Cahill & Pohl 1987], [Cahill 1990], [Lee & Cahill 1997], [Kim & Feldman 1999], [Borca-Tasciuc 2001], [Chen 2004], [Olson 2005]... Why do we work on the 3ω-method? Involved in DFG SPP Understanding size and interface dependent anisotropic thermal conduction in correlated multilayer structures. Goal: Minimize thermal conductivity in nanostructured thermoelectric materials. Reliable measurement technique is required. Manuel Feuchter, Marc Kamlah Comsol Conference 2011 October 26, /22

4 Functionality of 3ω-method Alternating current I..cos ω.. I ω Manuel Feuchter, Marc Kamlah Comsol Conference 2011 October 26, /22

5 Functionality of 3ω-method Alternating current I..cos ω.. I ω Joule heating P = R I 2 cos 2 =..cos 2ω.. P 2ω Manuel Feuchter, Marc Kamlah Comsol Conference 2011 October 26, /22

6 Functionality of 3ω-method Alternating current I..cos ω.. I ω Joule heating P = R I 2 cos 2 =..cos 2ω.. P 2ω Temperature amplitude T Analytic solution Resistance oscillation FE-Simulation R = R 0 + R 2ω Manuel Feuchter, Marc Kamlah Comsol Conference 2011 October 26, /22

7 Functionality of 3ω-method Alternating current I..cos ω.. I ω Joule heating P = R I 2 cos 2 =..cos 2ω.. P 2ω Temperature amplitude T Analytic solution Resistance oscillation FE-Simulation R = R 0 + R 2ω Modulated voltage U = I R V cosω cos2ω = cosω cos3ω ω 3ω Manuel Feuchter, Marc Kamlah Comsol Conference 2011 October 26, /22

8 Functionality of 3ω-method Alternating current I..cos ω.. I ω Joule heating P = R I 2 cos 2 =..cos 2ω.. P 2ω Temperature amplitude T Analytic solution Resistance oscillation FE-Simulation R = R 0 + R 2ω Modulated voltage U = I R V cosω cos2ω = cosω cos3ω U ω 3ω Manuel Feuchter, Marc Kamlah Comsol Conference 2011 October 26, /22

9 Functionality of 3ω-method Alternating current I..cos ω.. I ω Joule heating P = R I 2 cos 2 =..cos 2ω.. P 2ω Temperature amplitude T Analytic solution Resistance oscillation FE-Simulation R = R 0 + R 2ω Modulated voltage U = I R V cosω cos2ω = cosω cos3ω U ω 3ω Manuel Feuchter, Marc Kamlah Comsol Conference 2011 October 26, /22

10 Geometry configurations Classic geometry configuration: Heater is placed on top of (multi)layer- systems. Analytic solutions are available. Inverse geometry configuration: New possibilities to determine the thermal conductivity of nanostructured materials. Always the same - platform (A) as sample holder. Known system properties. Optimum reproducibility. No analytic solutions are available. A B C D E Manuel Feuchter, Marc Kamlah Comsol Conference 2011 October 26, /22

11 Strategy for nanostructured materials Manuel Feuchter, Marc Kamlah Comsol Conference 2011 October 26, /22

12 Finite Element Simulations COMSOL Multiphysics Heat conduction equation has to be solved in the time domain. Mathematic interface is used in the general form of the partial differential equation (PDEg). Example for 2d: 2 T h x 2 2 T s x 2 κ mx 2 T m x T h y T s y 2 1 D h T h t 1 D s T s t + κ my 2 T m y 2 + Q κ h = 0, = 0, ρ mc pm T m t = 0 Q = [ϱ 0 (1 + α (T T 0))]/(A) a y I0 2 1 (1 + cos(2ωt)) 2 b x κ n T s n h bc (T T 0) = 0 Manuel Feuchter, Marc Kamlah Comsol Conference 2011 October 26, /22

13 Geometry import to generate mesh Example for 2d: Manuel Feuchter, Marc Kamlah Comsol Conference 2011 October 26, /22

14 Examples Placed material on top, ideal system: Two times, contact just over. To study the influence of material parameters on the temperature amplitude k 100k 1M k 100k 1M T [K] 0,2 0,15 0,1 D = κ ρ c p Dm 1 Dm 2 Dm 4 Dm 8 Dm 1/2 Dm 1/4 Dm 1/8 0,2 0,15 0,1 T [K] 0,12 0,1 0,08 0,06 D = κ ρ c p Dm 1 Dm 2 Dm 4 Dm 8 Dm 1/2 Dm 1/4 Dm 1/8 0,12 0,1 0,08 0,06 0,05 0,05 0,04 0,04 0,02 0, e+01 1e+02 1e+03 1e+04 1e+05 1e+06 1e+01 1e+02 1e+03 1e+04 1e+05 1e+06 Frequency fc [Hz] Frequency fc [Hz] Manuel Feuchter, Marc Kamlah Comsol Conference 2011 October 26, /22

15 Examples Thin layer on top: a layer b x d lay Bad conducting for a sensitivity in T. y d subs Contour shape analysis. By S. Wiedigen, project partner k 100k 1M k 100k 1M 4,5 4,5 4,0 dlay = 100 nm 4,0 4 dlay = 100 nm shape1 4 T [K] 3,0 2,0 STO layer dlay = 200 nm dlay = 400 nm dlay = 800 nm dlay = 1000 nm 3,0 2,0 T [K] 3,5 3 2,5 2 dlay = 100 nm shape2 dlay = 100 nm shape3 dlay = 100 nm shape4 3,5 3 2,5 2 1,5 1,5 1,0 1, ,5 0,5 0,0 0, e+01 1e+02 1e+03 1e+04 1e+05 1e+06 Frequency fc [Hz] How to enhance the sensitivity for change in κ lay? Frequency fc [Hz] Manuel Feuchter, Marc Kamlah Comsol Conference 2011 October 26, /22

16 Examples Thin layer on top: a layer b x d lay Bad conducting for a sensitivity in T. y d subs Contour shape analysis. By S. Wiedigen, project partner k 100k 1M k 100k 1M 4,5 4,5 4,0 dlay = 100 nm 4,0 4 dlay = 100 nm shape1 4 T [K] 3,0 2,0 PCMO layer dlay = 200 nm dlay = 400 nm dlay = 800 nm dlay = 1000 nm 3,0 2,0 T [K] 3,5 3 2,5 2 dlay = 100 nm shape2 dlay = 100 nm shape3 dlay = 100 nm shape4 3,5 3 2,5 2 1,5 1,5 1,0 1, ,5 0,5 0,0 0, e+01 1e+02 1e+03 1e+04 1e+05 1e+06 Frequency fc [Hz] How to enhance the sensitivity for change in κ lay? Frequency fc [Hz] Manuel Feuchter, Marc Kamlah Comsol Conference 2011 October 26, /22

17 Examples Application of heat sink: Heat sink: Good thermal conducting to attract heat. Full covering heat sink. a layer y b x heat sink d sink d lay d subs k 100k 1M 4,0 YSZ Heater- platform 4,0 3,0 3,0 T [K] 2,0 2,0 1,0 1,0 0,0 0, Frequency fc [Hz] Manuel Feuchter, Marc Kamlah Comsol Conference 2011 October 26, /22

18 Examples Application of heat sink: Heat sink: Good thermal conducting to attract heat. a layer b x heat sink d sink d lay Full covering heat sink. y d subs k 100k 1M 4,0 3,0 YSZ PCMO layer Heater- platform dlay = 400 nm 4,0 3,0 T [K] 2,0 2,0 1,0 1,0 0,0 0, Frequency fc [Hz] Manuel Feuchter, Marc Kamlah Comsol Conference 2011 October 26, /22

19 Examples Application of heat sink: Heat sink: Good thermal conducting to attract heat. a layer b x heat sink d sink d lay Full covering heat sink. y d subs k 100k 1M 4,0 3,0 YSZ PCMO layer Cu heat sink Heater- platform dlay = 400 nm dlay = 400 nm, sink 2000 nm 4,0 3,0 T [K] 2,0 2,0 1,0 1,0 0,0 0, Frequency fc [Hz] Manuel Feuchter, Marc Kamlah Comsol Conference 2011 October 26, /22

20 Outlook Heat flow analysis for 3d structures. Multiphysical coupling with respect to mechanical and dielectric properties. Bottom electrode configurations with additional s to measure Seebeck cross-plane. Manuel Feuchter, Marc Kamlah Comsol Conference 2011 October 26, /22

21 Acknowledgement: DFG for funding. Project partners from the University of Göttingen, Institute for material physics Group of C. Jooss and C. Volkert Supervisor M. Kamlah THANK YOU FOR YOUR ATTENTION! Manuel Feuchter, Marc Kamlah Comsol Conference 2011 October 26, /22

22 Manuel Feuchter, Marc Kamlah Comsol Conference 2011 October 26, /22

23 Attachment Alternating current I = I 0 cos(ωt) Joule heating P JH = P 0 2 (1 + cos(2ωt)) Temperature oscillation T(t) = T cos(2ωt + ϕ) Resistance oscillation R = R 0 + R cos(2ωt + ϕ) Modulated voltage U = I R U = I 0R 0 cos(ωt) + I 0 R 2 (cos(3ωt + ϕ) + cos(ωt + ϕ)) Manuel Feuchter, Marc Kamlah Comsol Conference 2011 October 26, /22