3D SELF HEATING MODELING FOR ELECTRO- THERMAL CHARACTERISATION OF SiGe HBTs

Transcription

1 3D SELF HEATING MODELING FOR ELECTRO- THERMAL CHARACTERISATION OF SiGe HTs P-Y. SULIMA, J-L ATTAGLIA, T. IMMER, H. EKRICH, D. CELI 5 th European HICUM Workshop STMicroelectronics Crolles, France June 6-7, 5

2 Outline I. Introduction II. Modeling III. Measureent verification IV. Conclusions

3 Introduction SiGe heterojunction bipolar transistors (HT SiGe) technologies are of great iportance for the seiconductor arket to produce high speed devices :! Low cost and ature Technology! High RF perforances ( Ft, Ftax, current gain)! Low noise "High power effect : self heating High frequency perforance High current density " Modification of the electrical paraeters ( I ).V E perforances drop Work etter understanding and Modeling electrical devices : HT SiGe

4 Geoetrical structure NPN E C ulk Electrical représentation C Modeling Copact Models (Mextra, VIC, HICUM) based on the equation [] T ( M, t) ρc. + t ( λ( T ( M, t) ) T ( M, t) ) H T(M,t) Teperature [K] λ(t(m,t)) Heat conductivity [W - K - ] c Heat capacity [Jkg - K - ] ρ Density [kg -3 ] H Heat source : intrinsic transistor (Joule heat of phonons, electrons and holes, recobination heat, Peltier Thoson heat Theroelectric powers variation, radiation) P dis E THERMAL Network E R TH C TH Theral network sub circuit R P dis c Analytical solution ( T TH j T j CTH ( T j T t ( t) i ( t) v ( t) ce ab ) + R TH t Tab) RTH Pdis exp( ) RTHCTH [] G. K. Wachutka Rigorous therodynaic treatent of heat generation and conduction in seiconductor device odeling IEEE Transactions oncoputer Aided Design, Vol.9,N,Noveber 99 P dis ( t)

5 Modeling Copact Model Periodicity Upper layers Y c Xc E C E C E C ulk ulk Experient : X c and Y c Real geoetry : X c and Y c liited Model validation R TH C TH Siulation

6 Modeling Copact Model Hoogenization Scheatic cross section of the HT SiGe Transistor representation Layer Coposite SiO etal hoogenized Layer Deep trench and active transistor Layer 3 Substrate

7 Modeling Copact Model h e d 9,55µ e 5µ e s 3µ Layer E Junction Layer φ C Junction Layer 3 φ Transistor representation Layer Coposite SiO etal hoogenized Layer Deep trench and active transistor Layer 3 Substrate HT SiGe theral network Coposite SiO etal hoogenized paraeters λ d f ( e d, e λ Al Al, e λ W W, e λ SiO SiO ( ρ C ) g( e,( ρc ) e,( ρc ) e,( ρc ) e ) p d d p Al Al p W W ) p SiO SiO

8 Copact Model Modeling General resolution 3D Heat diffusion equation Heat generated C junction H Heaviside function ϕ ϕ ( t) [ H ( x) H ( x X )][ H ( y) H ( y Y )] e e Initial condition oundaries conditions Spatial periodicity x,y;xx c,yy c Analytical solution

9 Modeling Copact Model Θ el (M,t) Laplace +initial condition +boundaries condition Analytical solution Θ el ( x, y, z, t) Inverse Laplace transfor (Stehfest algorithe) Integral Fourier Transfor x Integral Fourier Transfor y Inverse Fourier transfor x and y And average teperature 5 5 Θ el ( α, β, z, p) n TH ( α, β, z, p) n Quadruples foralis Asyptotic value R TH, C TH

10 Modeling Copact Model Θ Θ Θ e e e d d d d h D C A D C A ψ ψ Θ Θ Θ s s s s s s s c c c c h D C A D C A ψ ψ Quadruples foralis ψ A Θ ; ; ψ ψ ψ ψ ψ Θ Θ + + ψ s ψ e

11 Modeling Copact Model Asyptotic behavior ) ( A p A TH Θ ψ ( ) TH TH R p Asyptotic theral resistance TH C TH p ) ( Asyptotic theral capacitance

12 Copact Model Modeling Volue source assuption C h S D ( ρc), e,, S ) ( e Se Asyptotic theral resistance Asyptotic theral capacitance TH Volue source ter ( p ) R TH TH ( p ) CTH RTH ( λd ( ρc) d + λs ( ρc) s ) + C R cs e λ

13 Measureents verification Five steps experiental verification General easureent set up

14 Measureents verification DC,855 3,85, VE (V),84,835,83 V CE Tsub( K) 3 35 V E,85 3,8, T sub ( K) 95,9,4,9,4 Pdiss(W) Calibration V E f(t i ) A e cte ; I b c te T sub f(p diss ) A e cte ; V E c te ; I b c te

15 Measureents verification DC 8,45E- 8,4E- 3 Transient 4,5,849 VE(V) 8,35E- 8,3E- Vce (V),5,847 Vbe (V) 8,5E-,5,845 8,E Tj( K),843 9,E-5,E-4 3,E-4 4,E-4 t (s) V E f(t j ) A e cte ; V E c te ; I b c te Measured V be f(t) A e cte ; V CE pulse[;]volts ; I b c te

16 Measureents verification Transient 6 5 DT(K) 4 Experiental "RC" network Tie(secondes) x DT(K) 4 3 "RC" network Experiental DT Pdis R TH ( e ( R TH t C TH ) ) Therogra :Tjf(t) ; A e 6,56µ²

17 Measureents verification Measureents 6 Copact Model DT(K) 4 Experiental Model Therogra Tjf(t) A e 6,56µ² teps (sec) x Model Experiental DT(K) teps(sec) teps (sec)

18 Coparison RC Network/Recursive Network Measureents perspectives Therogra Tjf(t) A e 5*3,6µ²

19 Conclusions Self Heating at a glance "Resolution of the heat equation in a real 3D HT SiGe by a new dynaic odel, with short calculations tie "Deterination of the theral network paraeters TH (R TH and C TH ) for standard self heating copact odels "Very good agreeent with experiental results "Siple theral copact odel to describe self heating phenoenon in electrical devices Soe perspectives Siulation for saller X C and Y C R TH C TH dependence of (X C, Y C ) Coupling phenoena structure "Developing the theral odel for HT SOI technology "Developent of the equivalent recursive network

20 Thanks for your attention 5 th European HICUM Workshop STMicroelectronics Crolles, France June 6-7, 5