Modeling high-speed SiGe-HBTs with HICUM/L2 v2.31

Transcription

1 Modeling high-speed SiGe-HBTs with HICUM/L2 v2.31 A. Pawlak, M. Schroter, A. Mukherjee, J. Krause Chair for Electron Devices and Integrated Circuits (CEDIC) Technische Universität Dresden, Germany 12th HICUM Workshop, Newport Beach, CA (USA), 212 MS 1

2 Outline Introduction HICUM equivalent circuit Transfer current Mobile charges Vertical NQS-effects Lateral NQS-effect Noise modeling Self-heating Experimental results MS 2

3 Introduction Introduction Experimental results... from DOTFIVE project (3 different process generations of 3 different technology partners) from characterizing other process types (production, high-voltage) => observation of a variety of physical effects some effects were difficult to describe with physics-based model parameters with existing v2.24 => motivation for extension to v2.31 heavy use of BTE, HD, DD device simulation for model development => final verification always on experimental results => this presentation: overview and details on v2.31 extensions MS 3

4 HICUM equivalent circuit HICUM equivalent circuit, Q BCx B Q js,, Q BCx R Bx i jsc i jbcx QdS B * S i TS C rbi R* bi C su C i jbci B Q jci R su Q jei S intrinsic transistor R Cx Q i r AVL i T Qf C thermal network ΔT j T C BEpar1 i jbep C BEpar2 Q jep i BEtp i jbei E R E i BEti P R th C th V nc noise correlation E V nb vertical NQS effects Q f,nqs I nc = 2qI T 1S. V nc I nb = 2qI jbei 1S. V nb Q f,qs τ f α Qf R=τ f 2 T b1 =1+jωτ f B f (2α qf -α IT ) noiseless intrinsic T b2 =jωτ f α IT T b1 V nb T b2 V nc transistor 1S. V nc i T,qs τ f V C1 V C2 τ f α IT V C1 τ f i T,nqs =V C2 α IT 3 R=τ f MS 4

5 Transfer current Transfer current... in HICUM is based on the GICCR From 1D drift-diffusion-transport equation: V BEi V BCi exp V T exp V T I T = c l W h j h v h g pdx Weight functions h j and h v are 1 in the 1D case, c is a bias independent constant. Weight function h g reads h g ( x) = 2 μ nr n ir, with "r" as reference region 2 μ n ( x)n i ( x) Reference region in HICUM is the neutral base: h k = 2 μ n ( x B )n i ( xb ) px ( ) dx 2 k μ n ( x)n i ( x) px ( ) dx k k represents the various regions in the transistor MS 5

6 Transfer current Transfer current related charge Actual charge in the transistor is divided into zero-bias, depletion and mobile charge component: Q p = qa E px ( ) dx = Q p + ΔQ j + ΔQ m Transfer current expression from GICCR: with weighted hole charge c 1 I T = exp exp = i Tf i Tr Q pt V BEi and weighted mobile charge (h f newly introduced in v2.3) V T V BCi =, Q rt = τ r i Tr => Transfer current is directly related to charges defined from small- and large-signal behavior V T Q pt = Q p + h jei Q jei + h jci Q jci + Q ft + Q rt ΔQ j Q ft h f τ f i Tf + h fe ΔQ Ef + ΔQ Bf + h fc ΔQ Cf MS 6

7 Transfer current h g GICCR allows taking into account material composition Si BJT Doping (cm 3 ) Low-current weight factors h g SiGe HBT h Si SiGe jei h jci 1 2 h jei h jci h jei.2 1. h jci Doping (cm 3 ) x (µm) x (µm) h g h f,h fb 1 21 h 1 h 2 fc fe h fc x (µm) Doping (cm 3 ) High-current weight factors Si SiGe h fe h fc h f.98 5 h fb (base as reference region) h g h fe h f,h fb x (µm) Doping (cm 3 ) MS 7

8 Transfer current Normalized transconductance g m /(I C /V T ) can be used to identify device non-ideality and to compare technologies experimental observation: drop in normalized transconductance already at low to medium injection for some technologies. experimental data 1D device simulation 1 1 g m V T /I C f T /f max =7/1 GHz f T /f max =25/3 GHz f T /f max =3/5 GHz.75 HICUM/L2 v2.2 HICUM/L2 v J C (ma/µm 2 ) g m V T /I C no Ge Box Ge Weak Ge gradient Strong Ge gradient J C (ma/µm 2 ) cannot be described with simple (bias independent) reverse Early voltage models From 1D device simulation: effect is directly related to Ge grading in BE-SCR => explicitly included in v2.3:, exp( u) 1 h jei = h jei u = a u hjei ( 1 ( V BEi V DEi ) z Ei) MS 8

9 Transfer current Transconductance at medium injection Stronger reduction of g m /(I C /V T ) could not be described with meaningful Q p values Need to keep physics-based value for Q p for accurate modeling of internal base (sheet) resistance => extract Q p from tetrodes rather than from transfer current. For graded Ge, weighted mobile charge is much larger than actual mobile charge (mostly concentrated in neutral base) => need to introduce h f : g m *V T /I C Q ft = h f τ f i Tf + h fe ΔQ Ef + ΔQ Bf + h fc ΔQ Cf.6 1D Device.5 h =3.9 f.4.7 h f =1.8 V (V) BE.9 1 => strongly improves g m modeling at medium bias Q min, Q min,t (fc) grad, Q min grad, Q min,t box, Q min box, Q min,t J (ma/µm 2 ) C MS 9

10 Temperature dependence of new weight factors... due to bandgap differences h jei also incl. movement of SCR boundaries.1 Transfer current 1 ΔV gbe V T h jei ( T) h jei ( T ) T ζ vgbe = exp 1 T, h jei a hjei T a hjei ( T) = a hjei ( T ) Medium-current weight factor High-current weight factor ΔV gbe V T ζ hjei T h f ( T) h f ( T ) T = exp 1 h fec (, ) ( T) = h fec, ( ) T V gb T V gec (, ) ( ) exp T V T T h f, h fe T ( C) Experimental results T ( C) 2 h f h fe MS 1

11 Transfer current Results Physics-based extensions in v2.3 and v2.31 Material composition related effects modeled explicitly by physics-based equations Takes into account temperature effects due to different bandgap values => Accurate transfer current modeling by GICCR with physics-based charges, weight factors, and parameters device simulation GICCR ideal (classical sol.) I T (ma) relative error (%) V B E (V) => New version has been successfully applied to several recent technologies MS 11

12 Mobile charges Mobile charges forward active bias mobile charge in HICUM corresponding transit time follows: Q f ccritical current I CK Q f = τ f + ΔQ Ef + ΔQ fh τ f = τ f + Δτ Ef + Δτ fh = i Tf τ f di T ' added parameter for better fitting to field dependence of mobility. τ f (ps) I /I C CK.8 Δτ fh Δτ Ef τ v ceff r Ci x+ x 2 + a I CK ickpt = v ceff V lim δ CK 1 δ CK 2 default δ CK =2 parameter allows better fitter for, e.g., pnp I CK (A) δ = 2. (default) CK δ = 1 (e.g. holes) CK V (V) CE MS 12

13 BC barrier effect BC barrier effect In HICUM v2.3, the collector heterojunction barrier effect is modeled. Barrier effect becomes more pronounced in advanced SiGe HBT generations Formation of barrier in conduction band strongly related to Kirk-effect in well-designed HBT => more rapid increase of transit time beyond I CK V C (V) ΔV cbar 15 1 I C.1 x.3 jc x (µm) 5 Ge (%) 1/(2πf T ) norm f T /f max =25/3 GHz f T /f max =3/5 GHz.5 1 J /J C CK Influence of heterojunction position on barrier effect Close to BC-junction -> related to Kirk-effect Far in the collector -> at too high (i.e. irrelevant) currents 1/(2πf T ) (ps) HBT, Δx Ge,C HBT, Δx Ge,C =3 nm HBT, Δx Ge,C =16 nm J (ma/µm 2 ) C MS 13

14 BC barrier effect Modeling the BC barrier effect Onset of barrier effect is still given by I CK (for a "well-designed" DHBT) barrier voltage (from bias dependent conduction band barrier): 2 ΔV cb V cbar i Tf I CK = exp with i bar = i bar + i2 bar + a cbar I cbar ΔV Cb (mv) simulation model J (ma/µm 2 ) C τ f (ps) τ f (ps) 2 15 V cbar I C /I CK τ f (ps) 15 1 a cbar New parameters: V cbar, I cbar, a cbar 5 I cbar I /I C CK I /I C CK MS 14

15 BC barrier effect New mobile charge formulation at high injection Include barrier related base and collector charge terms explicitly: Q f h, = ΔQ Ef + ΔQ Bf, b + ΔQ Bf c +, ΔQ Cf, c Q fh, c Barrier related base charge term calculated by a bias dependent barrier voltage. ΔQ Bf b ΔV C, = τ Bfvs i Tf exp V T 2 15 simul τ Bf,b τ fh,c with already existing τ Bfvs = ( 1 f τhc )τ hcs Δτ fh (ps) 1 τ Bf,b +τ fh,c Kirk-effect related transit times are "delayed" by the formation of the barrier: 5 ΔQ fh c, τ hcs i Tf w 2 ΔV C V Cbar = exp V T J C (ma/µm 2 ) => very accurate and flexible, and still backwards compatible MS 15

16 Vertical NQS-effects Vertical NQS-effects HICUM includes mobile charge and transfer current related NQS effects => modeled using polynomial approximation and separate networks charge delay and input admittance transfer current delay and transconductancea Q f,nqs V C1 Q f,qs i T,qs τ V C2 f τ α R=τ f τ f f α Qf IT V C1 τ f i T,nqs =V C2 α IT 3 R=τ f Mag(Y 11 /Y 11 (f )) simulation mag simulation phase no NQS 2 inverted polynomial Phase(Y 11 ) ( ) Mag(Y 21 /Y 21 (f )) 1.9 simulation mag simulation phase no NQS inverted polynomial Phase(Y 21 ) ( ) f/f T f/f T => Good agreement in small-signal and large-signal simulation MS 16

17 Lateral NQS-effect Lateral NQS-effect... caused by high-frequency emitter current crowding theoretical solution only for small-signal case (and negligible DC current crowding) => simple capacitance parallel to R Bi : C RBi = f CRBi ( C jei + C jci + C dei + C dci ) Verilog-A only allows adjunct network with charge definition: Q RBi = C RBi V RBi or Q RBi = f CRBi ( Q jei + Q jci + Q dei + Q dci )? latter leads to strong overestimation of the charge, current and admittance present solution ONLY valid for small-signal operation and not too high frequencies Do NOT use for large-signal operation!! => still under investigation Feedback from circuit design? Q RBi (fc) C RBi B* R Bi B V RBi Q RBi =C RBi V RBi Q RBi =f CRBi (Σ Q) J C (ma/µm 2 ) MS 17

18 Lateral NQS-effect Problems with implementation of lateral NQS-effect... caused by undesired derivatives small-signal form of Q RBi = C RBi V RBi in Verilog-A leads to dq RBi dt dc ( RBi V RBi ) dv RBi = = C dt RBi dt + dc RBi dv RBi V RBi dt dv RBi theoretical solution => undesired derivative from Verlog-A implementation constraints Also: undesired derivatives result in large overhead of compiled code since dc RBi /dv RBi internally requires the calculation of the derivatives of all nonlinear capacitances (incl. for C dei and C dci ) alternatives are presently under investigation not present in smallsignal theory MS 18

19 Noise modeling Noise modeling New noise correlation model in v2.31 is valid at all frequencies physically connected to NQS effects => can use same delay time and assoc. parameters V nb noise correlation I nb = 2qI jbei I nc = 2qI T 1S. V nb 2 T b1 =1+jωτ f B f (2α qf -α IT ) noiseless intrinsic T b2 =jωτ f α IT T b1 V nb T b2 V nc transistor V nc 1S. V nc 1S. V nc NF min (db) HICUM meas no corr HD BTE RC delay f (GHz) Additional flicker noise contribution for emitter resistance R E 2 K I A fre E fre = f I re 4kT R E MS 19

20 Self-heating Self-heating intra-device thermal coupling (self-heating) described by single-pole network dissipated power: P = f(i T, V CEi, I BE, I BC, R B, R E, R CX, I AVL ) Based on observations of experimental data and solution of heat transport equation: P R th ΔT j C th T T R th ( T) = R th ( T ) ζ Rth T R th (K/mW) w E =13nm w E =1.5µm model R th (K/mW) Parameter extraction.5 Numerical simulation T ( C) 1.85 measured model T ( C) Temperature node also allows modeling of inter-device thermal coupling MS 2

21 Summary on V2.31 extensions Summary on V2.31 extensions list of new model parameters and flags Parameter Def. Description δ CK 2 Fitting factor for I CK a hjei Parameter describing the slope of h jei (V BE ) r hjei 1 Smoothing parameter for h jei (V BE ) at high voltage. ΔV gbe Bandgap difference between base and BE-junction, used for h jei and h f. ζ hjei 1 Temperature coefficient for a hjei. ζ VgBE 1 Temperature coefficient for h jei. h f 1 Weight factor for the low current minority charge. V cbar Barrier voltage, = turns the model off. a cbar.1 Smoothing parameter for barrier voltage. i cbar Normalization parameter, = turns the model off. ζ rth Temperature coefficient for R th FLCONO High-frequency noise correlation flag Kf re R E flicker noise coefficient Af re 2 R E flicker noise exponent factor TYPE 1 Flag for npn (1) and pnp (-1) transistors MS 21

22 Experimental results Experimental results Technologies shown here ST B9MW with f T /f max = 2/3 GHz, A E = 1x.13x4.87 μm 2 IHP SGB25V with f T /f max = 75/95 GHz, A E = 1x.64x12.68 μm 2 IHP 5GHz with f T /f max = 3/5 GHz, A E = 8x.12x.96 μm 2 => Comparison over large bias, temperature, and geometry range MS 22

23 Experimental results I C, I B (A) I C, I B (A) ST B9MW technology Forward gummel characteristics for [-4, 27, 75, 125] C V BE (V) V BE (V).9 Forward current gain Forward current gain I C, I B (A) I C, I B (A) V BE (V) V (V) BE => very good agreement over wide bias and T range Forward current gain Forward current gain MS 23

24 Experimental results 3 ST technology (cont d) transit frequency for [-4, 27, 75, 125] C. 3 f T [GHz] 2 1 f T [GHz] I [ma/µm 2 ] C I C [ma/µm 2 ] 3 3 f T [GHz] 2 1 f T [GHz] I [ma/µm 2 ] C I C [ma/µm 2 ] => very good agreement over wide bias and T range MS 24

25 Experimental results 4 ST technology (cont d) Maximum oscillation frequency for [-4, 27, 75, 125] C. 3 f max [GHz] 2 f max [GHz] I /A [ma/µm 2 ] C E I C /A E [ma/µm 2 ] 3 3 f max [GHz] 2 1 f max [GHz] I /A [ma/µm 2 ] C E I /A [ma/µm 2 ] C E => good agreement over wide bias and T range MS 25

26 Experimental results 1 ST technology (cont d) Normalized transconductance for [-4, 27, 75, 125] C. 1 g m *V T /I C.5 g m *V T /I C.5 g m *V T /I C V [V] BE g m *V T /I C V [V] BE V BE [V] V BE [V] => very good agreement over wide bias and T range MS 26

27 Experimental results IHP SGB25V technology Temperature dependence of forward Gummel characteristics 1 meas model T J C, J B [ma/µm 2 ] V [V] BE => very good agreement over wide bias and T range MS 27

28 Experimental results IHP SGB25V technology (cont d) geometry scaling of transit frequency f T (GHz) meas model meas J (ma/µm 2 ) C J C (ma/µm 2 ) model 6 A A E = 1x.64x12.68 μm 2 E =1x.64x27.8 μm 2 f T (GHz) 4 f T (GHz) meas model 2 A E =1x.98x12.68 μm J C (ma/µm 2 ) => good agreement over geometry and wide bias range MS 28

29 Experimental results IHP 5GHz technology Temperature dependence of forward Gummel characteristics and transit frequency J C, J B [ma/µm 2 ] meas model f T [GHz] T = 15 C T = 27 C T = 5 C T = 75 C T = 1 C model V [V] BE J C [ma/µm 2 ] => very good agreement over wide bias and geometry range MS 29

30 Experimental results U (db) V BE =.75 V V BE =.8 V V BE =.9 V model power gain MSG (db) 1 1 f (GHz) IHP 5GHz technology (cont d) V BE =.75 V V BE =.8 V V BE =.9 V model 1 1 f (GHz) stability factor not stable below peak f T => reasonable agreement over frequency and wide bias range k meas model k V BE =.75 V V BE =.8 V V BE =.9 V model 1 1 f (GHz) J C (ma/µm 2 ) MS 3

31 Experimental results IHP 5GHz technology (cont d) Large-signal results for A E =.12 x 1μm 2 (4 in parallel) harmonic f = 8GHz 2 J C = 2.5mA/µm 2 V CE =1.3V P out (dbm) nd 3 rd P (dbm) in => very good agreement for dynamic characteristics MS 31

32 Summary and conclusions Summary and conclusions observation of various physical effects both in advanced technologies (during DOTFIVE project) and other technologies measured in our lab HICUM/L2 v2.31 extensions BC barrier effect & improved description of material composition in transfer current and g m BC barrier effect in mobile charge temperature dependence of new parameters and of thermal resistance HF noise correlation model valid up to very high frequencies miscellaneous: flicker noise addition in RE, optimized NQS effect VA implement., pnp flag access to variety of (production) technologies for modle verification is very important => otherwise difficult to make a model widely applicable throughout industry need better measurement capability for small- and large-signal model verification Goal for InP HBTs: extend HICUM/L2 add specific physical effects (as determined to be relevant) enable geometry scaling => circuit optimization and statistical modeling generate scalable HICUM/L and distributed HICUM/L4 automatically from L2 => offer unified and flexible HBT modeling strategy MS 32

33 Summary and conclusions Acknowledgments IHP, Frakfurt/Oder, Germany ST Microelectronics, Grenoble, France EU CATRENE project RF2THzSiSoC MS 33