A method for extraction of power dissipating sources from

A method for extraction of power dissipating sources from interferometric thermal mapping measurements D. Pogany, M. Litzenberger, S. Bychikhin, E. Go...

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A method for extraction of power dissipating sources from interferometric thermal mapping measurements D. Pogany, M. Litzenberger, S. Bychikhin, E. Gornik Institute for Solid State Electronics Vienna University of Technology, Vienna, Austria G. Groos, M. Stecher Infineon Technology, Munich, Germany D. Pogany, ESSDERC’02, Firenze

Outline Motivation Background Extraction method Results Conclusions

D. Pogany, ESSDERC’02, Firenze

Motivation * Experimental access to temperature and current density inside devices important for device reliability physics * Relevant for ESD protection and power devices * Backside laser interferometry: useful tool for thermal mapping with ns time and µm space resolution

D. Pogany, ESSDERC’02, Firenze

Principle of backside laser interferometry ∗ λ=1.3µm: non-invasive * measuring phase shift * polished backside

4π  dn  [ ] ∆ϕ (t ) = ∆T (z ,t ) + α n ∆n (z ,t ) + α p ∆p (z ,t ) dz  ∫ λ  dT 

Thermal contribution (>0) Free-carrier contribution (<0) D. Pogany, ESSDERC’02, Firenze

When thermal effects dominate 4π dn L ∆ϕ ( x , y ,t ) = ∆T ( x , y , z ,t )dz ∫ λ dT 0 E 2 D ( x , y ,t ) =

λ cV

4π dn / dT

∆ϕ ( x , y , t ) [IEEE TED’02]

2D thermal energy density ∝ Phase shift E2D

- depends on power dissipation density and time - reflects all the previous heating in the device D. Pogany, ESSDERC’02, Firenze

Phase shift derivation: Integration of thermal diffusion equation  ∂ 2T ∂ 2T ∂ 2T ∂T ( x , y , z ,t ) cV = P3 D ( x , y , z ,t ) + κ  2 + 2 + 2 ∂t ∂y ∂z  ∂x ∂∆ϕ ( x , y , t ) 4π dn = P2 D ( x , y , t ) + ∂t λcV dT

κ  ∂ 2 ∆ϕ ( x , y , t )

 cV 

∂x 2

  

≈0

∂ 2 ∆ϕ ( x , y , t )  4π dn  + + 2 ∂y  λcV dT



L

0

 ∂ 2 ∆T ( x , y , z , t )   κ dz 2 ∂z  

L

P2 D ( x , y , t ) = ∫ P3 D ( x , y , z , t )dz 0

2D power dissipation density D. Pogany, ESSDERC’02, Firenze

Instantaneous 2D power dissipation density λ cV ∂∆ϕ ( x , y , t ) λ κ  ∂ 2 ∆ϕ ( x , y , t ) ∂ 2 ∆ϕ ( x , y , t )    P2 D ( x , y , t ) = − + 2 2 dn 4π dn 4π  ∂t ∂x ∂y  dT

4 se s Pha rad) hift (

P2D: extracted from time and space derivatives of measured phase signal

dT

3 2 1 0

po n io sit

p

n o i t osi

D. Pogany, ESSDERC’02, Firenze

* heterodyne interferometer [J. Elstat.2000, IEEE TED2002]

* 3ns @ 1.5µm resolution * 3-4µm thermal resolution (150ns)

3

Power density (mW/µm2)

+

4

SPT pn diode [email protected]

I=0.75A 25 20 15 10 5 0 -5

x=20µm y=0µm

0

2 1 0

Phase shift (rad)

Structure and method

250 500 750 1000

Time (ns)

D. Pogany, ESSDERC’02, Firenze

Experiments on ESD diode: ∆ϕ along the length

Phase shift(rad)

SPT pn diode [email protected]

3.5 3.0 t=100ns (a) 2.5 t=150ns 2.0 t=50ns 1.5 t=1µs 1.0 0.5 p+ 0.0 anode + cathode -0.5 z=0 p epi n-sinker -1.0 n buried layer -1.5 -2.0 z=L laser beam -2.5 -40 -20 0 20 40 60 80

Position along the x-axis(µm)

D. Pogany, ESSDERC’02, Firenze

Measurement results: ∆ϕ along the width 4

Phase shift(rad)

t=150ns 3 2

(b) t=1µs

+ digital filtering and derivation

1 0 -120 -90 -60 -30

0

30

60

90 120

Position along the y-axis(µm)

D. Pogany, ESSDERC’02, Firenze

t=50ns

2

Power density (mW/µm )

Extracted P2D

4

I=0.75A

2

Power density (mW/µm )

3

25 20 15 10 5 0 -5

x=20µm y=0µm

0

250

500

2 1 0

750 1000

Time (ns)

20 15 10

t=200ns

t=100ns

t=500ns

5 0 -5 -40

-20 0 20 40 60 80 Position along the x-axis (µm)

anode D. Pogany, ESSDERC’02, Firenze

4

I=0.75A

2

Power density (mW/µm )

3

25 20 15 10 5 0 -5

x=20µm y=0µm

0

250

500

2 1 0

750 1000

Time (ns)

Phase shift (rad)

Quantitative agreement

P2D=62.4W / 3300 µm2 total dissipated power

anode area

D. Pogany, ESSDERC’02, Firenze

dT λ κ dn 4π dT

 ∂ 2 ∆ϕ ( x , y , t )    2 ∂x  

Power density (mW/µm )

λ cV ∂∆ϕ ( x , y , t ) dn 4π ∂t

2

Insight into P2D extraction

20 t=100ns (a) 15 10 5 0 -5 20 TD term t=200ns SD term 15 10 (b) 5 0 -5 -60-40-20 0 20 40 60 80100

P2D>0

P2D=0

Position along the x-axis(µm) D. Pogany, ESSDERC’02, Firenze

Conclusions * Quantitative method for extraction of instantaneous 2D power dissipation density inside semiconductor devices * Experimentally verified on a ESD diode * Suitable for analysis of complex spatial and temporal dynamics in ESD protection and power devices (moving current filaments, etc. [APL 2002])

D. Pogany, ESSDERC’02, Firenze