Regional Approach Methods for SiGe HBT compact modeling

Transcription

1 Regional Approach Methods for SiGe HBT compact modeling M. Schroter 1),2) and H. Tran 2) 1) ECE Dept., University of California San Diego, La Jolla, CA, USA 2) Chair for Electron Devices and Integr. Circuits, Univ. of Technol. Dresden, Germany 6th HICUM Workshop, Heilbronn, June 12/13, 26 MS 1

2 OUTLINE Introduction Investigated Device Structures Overview on Regional Approach Methods Results and Discussion Conclusions MS 2

3 Introduction Introduction Bipolar transistor main application areas high-frequency/high-speed operation Circuit design constraints cost reduction (mask, re-spins..., yield prediction) some applications are close to the technology limit careful circuit optimization Process development and optimization evaluation of charge and delay components within device structure accurate physics-based modeling of charge storage effects MS 3

4 Introduction Existing methods for analyzing charge storage analytical solutions require strong simplifications of underlying semiconductor equations spatial partitioning into neutral region (NR) and space-charge region (SCR) by definition of abrupt boundaries (Regional Approach = RA) validity of results is limited to particular spatial and bias region device simulation yields detailed information on carrier and charge distributions no limitation of results w.r.t. certain spatial or bias regions however: no abrupt boundaries between spatial regions either desirable: charge storage components from device simulation as reference for analytical modeling this work: evaluation of possible RA options for device simulation MS 4

5 Investigated Device Structures Investigated Device Structures 1D device simulation: unit emitter area A E = 1μm 2 conventional emitter doping (CED) transistor: high-speed BJT, HBT version ad1lv_nge (dashed) ad2lv_ge (solid) with Ge(dotted) 1e L x 1e+2 1e+19 N [cm -3 ] 1e+18 1e+17 Ge(B) mole fraction 1e e x [μm] MS 5

6 Investigated Device Structures Device Structures low-emitter concentration (LEC) transistor: high-speed HBT version N [cm -3 ] mole fraction x [μm] L x MS 6

7 Investigated Device Structures High-frequency performance: transit frequency f T [GHz] symbols: a.c. lines: q.s V C E =.8V LEC CED HBT 4 2 BJT I C [ma] identical results for quasi-static and frequency dependent small-signal calculation partitioning of transit time based on carrier distribution MS 7

8 Overview on Regional Approach Methods Overview on Regional Approach Methods d.c. method(s) determination of NR-SCR boundary is based on static carrier distribution classical criterion for detecting point in SCR: majority carrier density < r * doping conc., with r << 1 works only for sufficiently low-injection does not work in center region of SCR (N but carrier densities remain finite) log(n, p, n) N n p N normalized boundary condition: x r = x N p n r p + n with r <(<) 1 N+p-n p+n NR x j SCR NR x works also for high injection search needs to start from neutral region designated as DCRA and used for comparisons problem: missing link to small-signal operation r x j x MS 8

9 Overview on Regional Approach Methods Small-signal based regional approaches link to small-signal measurements via relation between transit frequency and stored hole charge: 1 dq p = τ 2πf ec = T di C V C'E' differential hole charge from carrier variation: L x dq p = qa E p dx region boundaries detected from quasi-static small-signal carrier distribution next: comparison of 3 methods MS 9

10 Overview on Regional Approach Methods Regional Approach Methods: van den Biesen [6] popular for evaluating device simulation results replaces metallurgical boundaries by electrical boundaries: x m = xdp ( = dn) storage time partitioning: dq p di C V C'E' * = τ e τ ec * * + τ eb + τ b + τ bc + τ c minority carrier storage times, e.g.: τ b * = qa E x mc x me n I C V C'E' dx depletion region "charging times", e.g.: [cm -3 ] dρ 5 x me ad1lv_nge 1E-17*drho x mc V C E =.8V x me ( n p) τ eb = qa E I C V C'E' dx -5-1 no separation of NR and SCR -15 not suitable for compact modeling! x [μm] MS 1

11 Overview on Regional Approach Methods Regional Approach Methods: FRA (1/3) region boundaries from peaks of ( p- n) Note: BC SCR boundaries cannot be detected from CE short distribution! need BE short instead collector related regions are trickier high-current effects => injection zone Ge drop causes barrier => additional peaks [cm -3 ] ρ V C E =.8V dv C E = SCR edges of BC junction: ρ ( x c, x C, c ) = x V B'C' V B'E' = ( max, min) region widths neutral base: w B = min{ x c, x jc } x e BC SCR: w BC = x Cc x c injection width: w i = max{ x c x jc, } ρ [cm -3 ] w E x e x c x C,c dv B E = x [μm] MS 11

12 Overview on Regional Approach Methods Regional Approach Methods: FRA (2/3) separation into BE and BC voltage change: dq p Q p = = V B'E' V C'E' dv B'E' Q p V B'E' V B'C' dv B'E' + Q p V B'C' V B'E' dv B'C' dv B E = dv B C minorities: m = p, p < n minority charge dq m = qa E mdx n, n p w hole charge partitioning: dq p = dq j + dq m depletion charge dq j = dq p dq m = qa E ( n p) dx w( p < n) consistent with q.s. definition of f T MS 12

13 Overview on Regional Approach Methods minority carrier storage time components from accumulated storage time: m τ m ( x) = qa E I C space-charge modulation in BC SCR: ( ρ) C ce = qa E = cross-coupled capacitance L x x mc x Full regional approach (3/3) V B'E' V C'E' V B'C' dξ dx 12 1 τ m (x) [ps] ad1lv_nge vcep8 w i w BE w B w BC profile I C high I C low I peak f T total value: τ f = τ m ( L x ) C ce g mi x je x jc x [μm] depletion capacitances: x me ( ρ) C jei = qa E V B'E' V B'C' dx ( ρ) C jci = qa E L x x mc V B'C' V B'E' dx MS 13

14 Overview on Regional Approach Methods Regional Approach Methods: DTRA [11] proposed for evaluation of device simulation results SCR boundary defined as 5% difference between accumulated carrier storage times x n p τ n ( x) = qa E dξ, τ I p ( x) = qa E C I C V C'E' x V C'E' dξ storage times include depletion charge contributions (C j /g m ) does not allow reliable detection of BC SCR end boundary detection difficult at high injection correction of τ E (2/3)τ E based on non-quasi-static operation ignored here τ(x) [ps] ad1lv_nge vcep8 dp(dashed) τ p I C low τ n I C high I peak f T x [μm] V C E =.8V MS 14

15 Results and Discussion Results and Discussion BJT storage time components (V C E =.8V) ad1lv_nge TE, TBE vce.8 τ [ps] τ B τ BC x τ C τ [ps] τ E o τ BE FRA DTRA DCRA 3 3 τ E 2 1 τ B τ BC τ C (FRA) I C [ma] τ C neutral base: τ B differs significantly; discontinuous for DTRA due to Kirk effect BC SCR: τ BC similar for FRA & DTRA, but too small for DCRA (τ m only) BE SCR: τ BE differs significantly, discontinuous for DCRA (no x e detection) neutral collector: τ C not detected by DCRA and DTRA 2 1 τ BE τ BE τ E I C [ma] MS 15

16 Results and Discussion CED HBT storage time components (V C E =.8V) τ B o τ BE FRA DTRA DCRA 1.5 τ E τ BC τ [ps] 1.5 τ [ps] 1 x τ C 1.5 τ BE τ B τ B.5 τ BC τ C I C [ma] I C [ma] τ E neutral base: τ B more consistent; DTRA does not detect carrier jam properly BC SCR: τ BC similar for FRA & DTRA; difference at low I C due to C jci /g m in DTRA BE SCR: τ BE more consistent; DTRA and FRA similar neutral collector (τ C ): small injection zone is detected by FRA, not by DTRA, DCRA MS 16

17 Results and Discussion LEC HBT storage time components (V C E =.8V) τ [ps] + τ B o τ BE FRA DTRA DCRA τ [ps] τ E τ BC τ B 1 τ BC.5 τ BE I C [ma] I C [ma] τ E neutral base: τ B dominates, detected fairly consistently for all methods BC SCR: τ BC identical for FRA & DTRA, increase due to barrier BE SCR: τ BE similar for DCRA and FRA; DTRA includes C jei /g m (low I C ) neutral collector (τ C ) and emitter (τ E ): negligible due to barriers MS 17

18 Determination of compact model transit time Determination of compact model transit time Reciprocal f T and related storage times vs 1/I C for BJT standard transit time determination method τ f = τ f ( V BC ) + Δτ f ( I T, V ) BC slope is usually assumed to be caused by depletion caps improved method includes curvature (from V BE dependence of C je ) τ [ps] τ f τ mσ 1 2πf T ΣC j g m τ BE in reality: curvature and portion of offset caused by neutral charge in BE SCR /I C [1/mA] extracted C je always includes portion of neutral BE charge MS 18

19 Determination of compact model transit time Full regional approach: capacitances C [ff/μm 2 ] 3 ad1lv_nge CJE(diam), CCE(o), CME(+, axis2), CJC(sq), CMC(x) f T C ce BJT V C E =.8V C me C me [ff/μm 2 ] C jei 2 C jci C mc J C [ma/μm 2 ] BC depletion capacitances cross-coupled BE capacitance L x ρ C jci = qa E x mc V B'C' V B'E' dx ρ C ce = qa E L x x mc V B'E' V B'C' dx MS 19

20 Determination of compact model transit time Full regional approach: HBT capacitances C [ff/μm 2 ] V C E =.8V CED LECHBT f T C jei C me 1 8 C me [ff/μm 2 ] 6 4 C [ff/μm 2 ] V C E =.8V LEC LECHBT f T C jei C me C me [ff/μm 2 ] C jci C mc C ce 5 C jci 2 C ce J C [ma/μm 2 ] J C [ma/μm 2 ] C mc C jei dominates before, C me beyond peak f T stronger C me increase at high current densities due to barrier effect MS 2

21 Conclusions Conclusions several approaches for regional partitioning in Si-based HBTs have been investigated regarding their suitability for device simulation and compact modeling use d.c. carrier distribution based methods are unreliable small-signal quasi-static carrier distribution based methods: van den Biesen s scheme is not useful for compact modeling differential transit time approach (DTRA) is unreliable for BJTs, does not detect boundaries in the collector extended space-charge peak based regional approach (FRA) gives reliable physically reasonable results that can be linked directly to compact model development BE depletion charge always contains a portion of neutral charge MS 21

22 Conclusions Acknowledgments financial support from German Ministry of Research and Technology (DFG project SCHR695/1-2) Atmel Germany, Heilbronn, Germany ST Microelectronics, Crolles, France MS 22

23 Additional slides Additional slides p n+ sgn ( N) G improved (most recently): x SCR = x: r with r = G works for any discrete point (no search direction required) and all regions of operation r (,1) can be easily adjusted to depletion capacitance value MS 23

24 Full regional approach: results Full regional approach: results electron velocity, internal collector resistance internal collector resistance: 1 r Ci = A E carrier velocity: v jc = L x 1 x bcc dx qμ nci n w BC ( τ BC r Ci C jci ) τ BC includes collector charge modul. value close to physical (N C (x)!) v jc [1 7 cm/s], V B E [V] V C E =.8V ad1lv_nge BJT v jc V B E r Ci τ mσ J C [ma/μm 2 ] r Ci [Ωμm 2 ], τ mσ [ps] increasing J C : w BC increases (V c > V lim ) r Ci decreases E jc decreases v jc decreases MS 24

25 Full regional approach: results Full regional approach: results electron velocity, internal collector resistance v jc [1 7 cm/s], V B E [V] CED ad2lv HBT r Ci v jc V B E.1 τ mσ J C [ma/μm 2 ] V C E =.8V r Ci [Ωμm 2 ], τ mσ [ps] v jc [1 7 cm/s], V B E [V] LEC HBT v jc V B E r Ci τ mσ J C [ma/μm 2 ] V C E =.8V r Ci [Ωμm 2 ], τ mσ [ps] increasing J C : w BC decreases (V c < V lim ) r Ci increases E jc decreases v jc decreases MS 25

26 Full regional approach: results Full regional approach: bias dependent widths BJT MS 26

27 Full regional approach: results Full regional approach: bias dependent widths CED transistor MS 27

28 Full regional approach: results Full regional approach: bias dependent widths LEC transistor MS 28