Working Group Bipolar (Tr..)

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1 Department of Electrical Engineering and Information Technology Institute of Circuits and Systems Chair for Electron Devices and Integrated Circuits Working Group Bipolar (Tr..) I T parameter extraction issues in HiCuM/L for very advanced HBTs M. Schroter, J. Krause Hamburg,

2 Outline 1 Introduction Doping profiles 3 Transit frequency 4 Parameter extraction 5 Extraction results 6 Results from device simulations M. Schroter, J. Krause IT parameter extraction issues in HiCuM/L for very advanced HBTs Slide /15

3 1 Introduction Currently, weight factors in the GICCR charge integral are assumed to be constant over bias. Depending on the extraction method experimental determination of the transfer current related model parameters Q p0 and c 10 may lead to issues for certain advanced devices. It is unclear whether this problem is caused by the method or the model formulation. exp( V B'E' V T ) exp( V B'C' V T ) exp( V I T c B'E' V T ) exp( V B'C' V T ) = 0 = c x 10 u Q p0 + h jei Q jei + h jci Q jci + Q ft, + Q r, T h g pdx x l with h g = μ nb n ib μ n ( x)n i ( x) Reproducing the issue by 1D device simulation allows to find the cause. M. Schroter, J. Krause IT parameter extraction issues in HiCuM/L for very advanced HBTs Slide 3/15

4 Doping profiles Two different reference profiles 500 GHz 300 GHz D [cm 3 ] Ge [%atom] D [cm 3 ] x [μm] x [μm] all investigations based on 1D DD device simulation indicated ft values are for 1D HD/MC simulation M. Schroter, J. Krause IT parameter extraction issues in HiCuM/L for very advanced HBTs Slide 4/15

5 3 Transit frequency Transit frequency 500 GHz 300 GHz f T [GHz] f T [GHz] f T V CE = (0.6, 0.8, 1.0, 1., 1.5)V M. Schroter, J. Krause IT parameter extraction issues in HiCuM/L for very advanced HBTs Slide 5/15

6 4 Parameter extraction 1st step: BE junction capacitance parameter extraction Q jei [fc/μm ] Q jei [fc/μm ] V [V] BE V [V] BE from extended HiCuM formulation, allows to analytically determine Q jei Note: C j,max is not directly measurable experimentally M. Schroter, J. Krause IT parameter extraction issues in HiCuM/L for very advanced HBTs Slide 6/15

7 4 Parameter extraction (cont d) nd step: c 10 and Q p0 extraction 7.5 analytical value numerical value linear fit 7.5 analytical value numerical value linear fit 7 7 Q jei [fc/μm ] 6.5 Q jei [fc/μm ] exp(v BE /V T )/ [μm /aa] c 10 exp( V BE V T ) Q jei h jei 0.65 V BE V BE 0.75 Q p exp(v BE /V T )/ [μm /aa] = V BC = 0V and very low h jei Slope and intercept of Q jei vs. exp(v BE /V T )/ represent auxiliary parameters c 10 =c 10 /h jei and Q p0 =Q p0 /h jei, resp. M. Schroter, J. Krause IT parameter extraction issues in HiCuM/L for very advanced HBTs Slide 7/15

8 4 Parameter extraction (cont d) Q p0 variation over V BE range (varied extraction intervals) Q p0 [fc/μm ] Q p0 [fc/μm ] V BE,max [V] V BE,max [V] Wide variation range of Q p0! Linear fit of Q jei vs. exp(v BE /V T )/ using increasing V BE interval with fixed starting point and V BE,max as final value M. Schroter, J. Krause IT parameter extraction issues in HiCuM/L for very advanced HBTs Slide 8/15

9 5 Extraction results Extracted model parameters parameter 500 GHz 300 GHz 100 GHz C jei ff/µm² ff/µm² ff/µm² V DEi V V V z Ei a jei Q p0,tech fc/µm² fc/µm² fc/µm² Q p0,rsbi fc/µm² fc/µm² 75.5 fc/µm² Q p0,extr fc/µm² fc/µm² fc/µm² c AC/µm AC/µm AC/µm 4 I S A/µm² A/µm² A/µm² h jci h jei Direct extraction gives too low or negative value for Q p0! M. Schroter, J. Krause IT parameter extraction issues in HiCuM/L for very advanced HBTs Slide 9/15

10 5 Extraction results (cont d) Forward gummel V BC = 0V simulated modeled simulated modeled V [V] BE V BE [V] Despite of the negative/non-physical value obtained for Q p0, the fit in the gummel plot shows good conformance. M. Schroter, J. Krause IT parameter extraction issues in HiCuM/L for very advanced HBTs Slide 10/15

11 6 Results from device simulations Q p0h from DEVICE simulations Q p0h [fc/μm ] 50 Q p0 Q p0h [fc/μm ] Q p0 f T peak 0 f T peak V [V] BE V BE [V] Q p0h significantly larger than Q p0 distinctive bias dependence of Q p0h M. Schroter, J. Krause IT parameter extraction issues in HiCuM/L for very advanced HBTs Slide 11/15

12 6 Results from device simulations (cont d) weight factors from DEVICE simulations hje hjc hfe hfb hfc hp hje hjc hfe hfb hfc hp0 10 h h f T peak 10 0 f T peak most weight factors are fairly constant up to peak f T Q jei largest contribution in low-/medium bias range -> bias dependence of h jei relevant M. Schroter, J. Krause IT parameter extraction issues in HiCuM/L for very advanced HBTs Slide 1/15

13 6 Results from device simulations (cont d) calculation of Q jeih and h jei from internal quantities hjei const. value 0.4V < VBE < 0.7V hjei 8 6 const. value 0.4V < VBE < 0.7V V BE [V] ΔQ jeh Q jeih q A E h g ( Δp Δn) dx with h jei (V BE ) = Q jeih (V BE )/(Q jei (V BE ). h p0 ) V BE [V] x μ Bn nr n ir = = h x g = me μ n ( x)n i ( x) M. Schroter, J. Krause IT parameter extraction issues in HiCuM/L for very advanced HBTs Slide 13/15

14 7 Results from device simulations (cont d) Insertion in GICCR h jei (V BE ) h jei (V BE ) const. h jei V BE [V] V BE [V] Total weighted charge Q pt, = Q p0h + Q jeih low-/medium bias cond.: only Q jeih and Q p0h significant c 10 i T = ( V Q BE V T ) V BC V T c 10 ( qa E ) = V T μ nb n ib pt, [ exp exp( )] with const. h jei M. Schroter, J. Krause IT parameter extraction issues in HiCuM/L for very advanced HBTs Slide 14/15

15 8 Summary Extracting Q p0 from I C may not give accurate values. Ignoring the bias dependence of h p0 (or Q p0 ) and h jei obviously leads to the observed extraction issue. Pros and cons of existing compact GICCR formulation to be investigated and evaluated on advanced HBT: Keeping existing absolute charge term seems more favorable if bias dependence is mainly caused by Q p0h => otherwise h p0 (bias) mixed with bias dependence of other weight factors M. Schroter, J. Krause IT parameter extraction issues in HiCuM/L for very advanced HBTs Slide 15/15

16 9 Appendix 3rd Extraction step: h jci determination simulated modeled c 10 exp(v BE /V T )/I C [fc] c 10 exp(v BE /V T )/I C [fc] Q jci [fc/μm ] simulated modeled Q jci [fc/μm ] c 10 [exp(v BE /V T )]/I C plotted vs. Q jci is linear and the slope gives the auxiliary parameter h jci =h jci /h jei. h jei is currently set to 1 per default! M. Schroter, J. Krause IT parameter extraction issues in HiCuM/L for very advanced HBTs Slide 16/15

17 Appendix (cont d) Extraction of Q p0 from R SBi V CE = 0V linear fit V CE = 0V linear fit /r r /r r Q x j [C/μm ] Q x j [C/μm ] Q j = Q jei + Q jci vs. r = r SBi /r V CE = 0V 1 r Q j -- r = > Q p0 as the slope Q p0 M. Schroter, J. Krause IT parameter extraction issues in HiCuM/L for very advanced HBTs Slide 17/15

18 9 Appendix (cont d) Internal BC capacitance C jci [ff/μm ] C jci0 = ff/µm² V DCi = V z Ci = a jci = V PTCi = V C jci [ff/μm ] C jci0 = ff/µm² V DCi = V z Ci = a jci =.336 V PTCi = V V [V] BC V [V] BC M. Schroter, J. Krause IT parameter extraction issues in HiCuM/L for very advanced HBTs Slide 18/15

19 9 Appendix (cont d) from DEVICE REGAP postprocessor τ f τ f [ps] 10 τ f [ps] =0.356 ps, = ps τ 0500GHz, τ 0300GHz, M. Schroter, J. Krause IT parameter extraction issues in HiCuM/L for very advanced HBTs Slide 19/15