Thermal impedance calculations for micro-electronic structures. Bjorn Vermeersch Seminar Fysische Elektronica March 9, 2006

Transcription

1 Thermal impedance calculations for micro-electronic structures Bjorn Vermeersch Seminar Fysische Elektronica March 9, 2006

2 Overview Introduction Thermal characterization Numerical calculations Influence of substrate thickness Present and future work 2

3 Introduction General framework study of conductive heat transfer application to electronics is interesting & even indispensable: more & more thermal issues in chip design: small dimensions + dissipation (huge power densities) semiconductor behaviour highly T-dependent variable device characteristics, electrothermal coupling PhD : fundamental research (characterization and physical modelling of relevant phenomena) 3

4 Introduction Fundamentals k 2 T - C v T t heat flow heat storage = p heat source 4

5 Overview Introduction Thermal characterization Numerical calculations Influence of substrate thickness Present and future work 5

6 Thermal characterization General overview 6

7 Thermal characterization Thermal impedance Thermal resistance by definition: R th = Extended towards frequency domain: thermal impedance (in phasor notation): Z th ( jω) = T P ( jω) ( jω) T P 7

8 Thermal characterization Thermal AC sources and phasors oscillating power & temperatures (angular frequency ω) described by complex phasors in reality: AC components superimposed on DC bias thermal frequency response () t Pcos( ωt) P = T () t = Tcos( ωt ϕ) 8

9 Thermal characterization What makes Z th so useful? captures the entire dynamic thermal behaviour (thermal blueprint of the structure) + T = th π () t P() f Z () f exp( j2 ft)f d familiar: similarities with electrical impedance can be measured experimentally (see next slide) compact description if using Nyquist representation (see later) 9

10 Thermal characterization Measurement technique Z th jω P + 0 ( jω) = T() t exp( jωt)t d 10

11 Thermal characterization plot of Im[Z th ] versus Re[Z th ] Nyquist curves interesting properties (circular arcs) Nyquist = V.I.P. 11

12 Thermal characterization Experimental measurement Diode BZX-55-C7V5 in JEDEC DO-35 glass package Free convection cooling conditions 12

13 Thermal characterization Analogy with Debye relaxation Cole-Cole plot one single relaxation constant distribution of relaxation constants ε ε ε ε 0 = j ( ) ωτ α Z th ( jω) = n i = A i ( jωτ ) i 1 α i 13

14 Thermal characterization Diode Curve fitting 14

15 Overview Introduction Thermal characterization Numerical calculations Influence of substrate thickness Present and future work 15

16 Numerical calculations Boundary Element Method (1) 16

17 Numerical calculations Boundary Element Method (2) 17

18 Numerical calculations Boundary conditions Overview 18

19 Numerical calculations Boundary conditions Interfaces real material interface not perfectly smooth temperature drop over air filled cavities modelled by thermal contact resistance r c T T = r 1 2 c q 19

20 Overview Introduction Thermal characterization Numerical calculations Influence of substrate thickness Present and future work 20

21 Infl. of substrate thickness Purpose & setup illustrative introduction to the subject provides physical insight in thermal AC problems 21

22 Infl. of substrate thickness Thermal impedance for various H values 22

23 Infl. of substrate thickness High frequency behaviour high frequency arc not influenced by substrate thickness physical explanation: rule of thumb for AC sources charact. dimension of heated zone 1 / ω 23

24 Infl. of substrate thickness Thermal resistance (DC analysis) 24

25 Infl. of substrate thickness Heat spreading model R = R + th geo R bulk = = R geo H - L + k W L 2 kw 2 1 kw R geo + 2 H R 0 α 25

26 Infl. of substrate thickness Model Geometrical resistance 26

27 Infl. of substrate thickness Comparison: model vs. simulations R 0 = = = R MODEL geo 65.4 L kw 43.7 K/W ( ) 6 2 SIMULATIONS (curve fitting data) R 0 = 38K/W α = 1 kw 2 = ( ) 2 α = KW 1 m 1 = KW 1 m 1 27

28 Infl. of substrate thickness Extension: asymmetric cases 28

29 Infl. of substrate thickness Impedance for off-centre case 29

30 Overview Introduction Thermal characterization Numerical calculations Influence of substrate thickness Present and future work 30

31 Present and future work continuous tendency towards smaller & faster electronics (IMEC: CMOS 45nm) thermal phenomena occurring in extremely small scale of space & time 2 main issues: non-fourier conduction physical modelling of heat transfer in general nano heat transfer Effects of miniaturisation 31

32 Present and future work Non-Fourier conduction heat conduction = mechanical process limited to speed of sound (Silicon: v = 5x10 3 m/s = 5 nm/ps) Fourier Cattaneo/Vernotte r q = r k T r r r ( cf. J = σe = σ V) r q + τ gives rise to thermal wave effects r q t = r k T (Silicon: τ= 3.5 ps) 32

33 Present and future work Limits of classical theory macroscopic parameters (k, Cv) might lose their meaning for very small structures definition of temperature itself becomes obscure: measure for average energy nano-scale structure: limited number of atoms large temp. deviations to be expected may have large influence on electric characteristics; substantial increase of thermally induced noise not unlikely 33

34 Acknowledgements I d like to express my gratitude to for supporting the presented work. 34