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
