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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Numerical approach x λe2 Ф(t) (ρC)e2 λe0 (ρC)e0 e2 (ρC)e1 λe1 z (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

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

Geometrical approach April 8, 2005 MOS-AK, Strasbourg

RTH calculation April 8, 2005 MOS-AK, Strasbourg

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

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

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

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

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

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

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