1. Self-heating investigation of bulk and SOI transistors
Pierre-Yvan Sulima, Hélène Beckrich, Jean Luc Battaglia, Thomas Zimmer
University of Bordeaux 1, France
ST Microelectronics
April 8, 2005
MOS-AK, Strasbourg

2. Preface This presentation deals Heat transfer is material dependant
with bipolar transistors
with heat transfer
but:
Heat transfer is material dependant
MOS & BJT => Si
Results are valid for MOS, too ?
So, this presentation may interest you
April 8, 2005
MOS-AK, Strasbourg

3. Outline Introduction: self-heating Measurement set-up
Self-heating modelling
Equivalent networks
Predictive model
Results, conclusion and perspectives
April 8, 2005
MOS-AK, Strasbourg

4. Introduction: macroscopic
Self-heating:
Heating of the device due to its power dissipation
Bipolar transistor:
P = IC VCE + IB VBE
DT = P ZTH
April 8, 2005
MOS-AK, Strasbourg

5. Introduction: impact Electrical Power -> T changes
Temperature variation
Mobility variation
E-gap variation
IC, IB variation
Electrical power variation
Feedback: convergence problems for electrical and physical simulators
Limit of operation in high power region
April 8, 2005
MOS-AK, Strasbourg

6. Measurement set-up: step 1
-> VCE(t):
Bipolar transistor
-> VBE(t):
April 8, 2005
MOS-AK, Strasbourg

7. Calibration: Measure VBE(T), step 2
IB = const
VCE = VCElow
Variation of T
27°C -> 50°C
Measure of VBE
April 8, 2005
MOS-AK, Strasbourg

8. Dynamic behaviour: Trise(time)
From VBE(t)
And VBE(T)
-> Trise (t)
New method which permits to take into account the temperature VCE=VCEmin => Mixdes05
April 8, 2005
MOS-AK, Strasbourg

9. Electrical modelling of Trise(t)
State of the art (VBIC, MEXTRAM, HICUM)
Results
April 8, 2005
MOS-AK, Strasbourg

10. New thermal self-heating model
The differential equation describing heat transfer is:
: thermal conductivity, [W/m°C]
c: specific heat, [J/kg°C]
: material density, [kg/m3]
T: temperature, [°C]
/c: thermal diffusivity, [m2/s]
April 8, 2005
MOS-AK, Strasbourg

11. Geometric presentation
Transistor, HBT
Schematic system representation with Cartesian co-ordinates
Schematic system representation with cylindrical co-ordinates: bidimensional axisymmetric geometry
April 8, 2005
MOS-AK, Strasbourg

12. Boundary & initial conditions
Initial condition: t=0,
April 8, 2005
MOS-AK, Strasbourg

13. Analytical problem resolution
Calculation of the thermal impedance
Trise(t) = Pdiss(t) ZTH(t)
Transform into the Laplace domain and solution of differential equation:
April 8, 2005
MOS-AK, Strasbourg

14. Comparison Standard New model Thermal impedance: Step response:
April 8, 2005
MOS-AK, Strasbourg

15. Results (1)
Comparison between the standard (double exponential) and new model
a 1E2B2C 0.5x10 µm device
April 8, 2005
MOS-AK, Strasbourg

16. Results (2)
Measurement for different Ib different power dissipation
a 1E1B1C 0.8x6.4 µm device
April 8, 2005
MOS-AK, Strasbourg

17. Equivalent networks Electrical-thermal networks for SPICE simulation
Represent the thermal impedance as accurate as possible
Have as few parameters as possible
The parameters have a physical meaning
April 8, 2005
MOS-AK, Strasbourg

18. Equivalent network - recursive parallel
Recursive parallel network
April 8, 2005
MOS-AK, Strasbourg

19. Results: recursive parallel
Recursive parallel network
N=10
RTH, R, C, k
4 parameters have to be determined
Independent of cell number
-10dB/dec
- 45°
April 8, 2005
MOS-AK, Strasbourg

20. Time domain Step response of the parallel recursive circuit
April 8, 2005
MOS-AK, Strasbourg

21. Predictive Modelling
Calculate the thermal impedance as a function of the layout data
Numerical approach
Geometrical approach
April 8, 2005
MOS-AK, Strasbourg

22. Numerical approach x λe2 Ф(t) (ρC)e2 λe0 (ρC)e0 e2 (ρC)e1 λe1z
(ρC)e1
λe1 x
HBT cross section: 3 layers:
back end (Isolation and metallization)
Active layer (intrinsic transistor + deep trench isolation)
Substrate
Resolving the Heat transfer equation with the specific initial and corner conditions
April 8, 2005
MOS-AK, Strasbourg

23. Results (RTH = f(emitter area))
Physical approach
Numerical calculation takes some minutes
Actually: some problems with CTH scaling
April 8, 2005
MOS-AK, Strasbourg

24. Geometrical approach
April 8, 2005
MOS-AK, Strasbourg

25. RTH calculation
April 8, 2005
MOS-AK, Strasbourg

26. Results: output characteristics
April 8, 2005
MOS-AK, Strasbourg

27. HBT on SOI Schematic Cross section TEM Cross section view
April 8, 2005
MOS-AK, Strasbourg

28. Results - Layout investigation:
Type
Active surface [µm2]
# E (emitter)
Active E-surface [µm2]
RTH [K/W] Q1
0.882 12
0.15*0.49
3100 Q2
0.8775 5
0.15*1.17
5400
Comparison to bulk Si: HBT SOI = 2 * HBT bulk (! Very rough estimation !)
April 8, 2005
MOS-AK, Strasbourg

29. Discussion Limit of the standard model
Development of a new accurate model
Resolution of heat transfer differential equation
Physical model
Representation with equivalent networks
The parallel recursive network is very accurate
4 parameters needed
Use in compact circuit modelling
April 8, 2005
MOS-AK, Strasbourg

30. Under work: predictive model
Numerical approach
Geometrical approach
Both approaches give good results
Calculation time
Usability
Methods applied to HBT on SOI
April 8, 2005
MOS-AK, Strasbourg

31. Perspectives Thermal coupling between transistors
Power device modelling
Layout optimisation
Investigation of the thermal behaviour of MOS transistors ? (cooperation)
Tools
Methods
Equations
Extraction methods
April 8, 2005
MOS-AK, Strasbourg

32. Thanks for your attention
The paper is open for discussion.
April 8, 2005
MOS-AK, Strasbourg