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, 30.10.008
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
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
Doping profiles Two different reference profiles 500 GHz 300 GHz 10 1 0.8 10 1 0.4 D [cm 3 ] 10 0 10 19 0.4 0. 0.16 0.1 Ge [%atom] D [cm 3 ] 10 0 10 19 0. 0.16 0.1 10 18 0.08 10 18 0.08 0.04 0.04 10 17 0 0.01 0.0 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11 0 x [μm] 10 17 0 0.05 0.1 0.15 0. 0.5 0.3 0.35 0.4 0 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
3 Transit frequency Transit frequency 500 GHz 300 GHz 400 50 350 300 00 50 150 f T [GHz] 00 150 f T [GHz] 100 100 50 50 0 10 10 1 10 0 10 1 10 f T vs. @ V CE = (0.6, 0.8, 1.0, 1., 1.5)V 0 10 10 1 10 0 10 1 10 M. Schroter, J. Krause IT parameter extraction issues in HiCuM/L for very advanced HBTs Slide 5/15
4 Parameter extraction 1st step: BE junction capacitance parameter extraction 17 13 16 1.5 15 1 14 11.5 Q jei [fc/μm ] 13 1 11 Q jei [fc/μm ] 11 10.5 10 10 9.5 9 9 8 8.5 7 0 0. 0.4 0.6 0.8 1 V [V] BE 8 0 0. 0.4 0.6 0.8 1 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
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 ] 6.5 6 6 5.5 0.034 0.035 0.036 0.037 0.038 0.039 exp(v BE /V T )/ [μm /aa] c 10 exp( V BE V T ) Q jei h jei 0.65 V BE 0.75 0.65 V BE 0.75 Q p0 5.5 0.011 0.01 0.013 0.014 0.015 0.016 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
4 Parameter extraction (cont d) Q p0 variation over V BE range (varied extraction intervals) 8.5 0 8 7.5 0.5 7 1 Q p0 [fc/μm ] 6.5 6 5.5 Q p0 [fc/μm ] 1.5 5.5 4.5 4 3 3.5 0.65 0.7 0.75 0.8 V BE,max [V] 3.5 0.65 0.7 0.75 0.8 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
5 Extraction results Extracted model parameters parameter 500 GHz 300 GHz 100 GHz C jei0 7.8440 ff/µm² 8.1670 ff/µm² 6.431 ff/µm² V DEi 0.7996 V 0.9488 V 0.9119 V z Ei 0.145 0.616 0.107 a jei.1410 1.6030 1.5060 Q p0,tech 6.130 fc/µm² 35.186 fc/µm² 78.603 fc/µm² Q p0,rsbi 6.753 fc/µm² 33.75 fc/µm² 75.5 fc/µm² Q p0,extr 4.6647 fc/µm² -.576 fc/µm² 8.665 fc/µm² c 10 3.06 10-31 AC/µm 4.996 10-31 AC/µm 4 5.766 10-31 AC/µm 4 I S 6.564 10-17 A/µm² -1.163 10-16 A/µm² 6.6544 10-17 A/µm² h jci 0.0886 0.737 10-3 1.053 h jei 1.0 1.0 1.0 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
5 Extraction results (cont d) Forward gummel plot @ V BC = 0V 10 10 1 simulated modeled 10 10 1 simulated modeled 10 0 10 1 10 10 0 10 1 10 3 10 10 4 0.65 0.7 0.75 0.8 0.85 0.9 0.95 V [V] BE 10 3 0.65 0.7 0.75 0.8 0.85 0.9 0.95 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
6 Results from device simulations Q p0h from DEVICE simulations 150 10 100 100 80 Q p0h [fc/μm ] 50 Q p0 Q p0h [fc/μm ] 60 40 Q p0 f T peak 0 f T peak 0 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 V [V] BE 0 0.65 0.7 0.75 0.8 0.85 0.9 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
6 Results from device simulations (cont d) weight factors from DEVICE simulations 10 4 10 3 hje hjc hfe hfb hfc hp0 10 3 10 hje hjc hfe hfb hfc hp0 10 h h 10 1 10 1 10 0 f T peak 10 0 f T peak 10 1 10 10 0 10 1 10 10 0 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
6 Results from device simulations (cont d) calculation of Q jeih and h jei from internal quantities.6 14.4. 1 10 hjei 1.8 1.6 1.4 const. value 0.4V < VBE < 0.7V hjei 8 6 const. value 0.4V < VBE < 0.7V 1. 1 4 0.8 0.4 0.5 0.6 0.7 0.8 0.9 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 ) 0.4 0.5 0.6 0.7 0.8 0.9 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
7 Results from device simulations (cont d) Insertion in GICCR 10 10 10 0 10 0 10 10 4 10 10 4 10 6 h jei (V BE ) h jei (V BE ) ------ const. h jei 10 8 0.4 0.5 0.6 0.7 0.8 0.9 1 V BE [V] 10 6 0.4 0.5 0.6 0.7 0.8 0.9 1 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
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
9 Appendix 3rd Extraction step: h jci determination 13.5 13.48 13.46 simulated modeled 4.355 c 10 exp(v BE /V T )/I C [fc] 13.44 13.4 13.4 13.38 c 10 exp(v BE /V T )/I C [fc] 4.3545 4.354 13.36 13.34 13.3 0.8 0.6 0.4 0. 0 0. 0.4 0.6 Q jci [fc/μm ] 4.3535 simulated modeled 0.8 0.6 0.4 0. 0 0. 0.4 0.6 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
Appendix (cont d) Extraction of Q p0 from R SBi 1.8 1.6 V CE = 0V linear fit 1.8 1.6 V CE = 0V linear fit 1.4 1.4 1. 1. 1/r r 1 0.8 1/r r 1 0.8 0.6 0.6 0.4 0.4 0. 0. 0 0 0. 0.5 0 0.5 1 1.5.5 3 Q x 10 14 j [C/μm ] 0. 0.5 0 0.5 1 1.5.5 3 Q x 10 14 j [C/μm ] Q j = Q jei + Q jci vs. r = r SBi /r SBi0 @ 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
9 Appendix (cont d) Internal BC capacitance C jci [ff/μm ] 0 18 16 14 1 10 C jci0 = 4.739 ff/µm² V DCi = 0.867 V z Ci = 0.6166 a jci = 3.886 V PTCi = 1.8155 V C jci [ff/μm ] 8 7 6 5 4 C jci0 = 3.4011 ff/µm² V DCi = 0.7664 V z Ci = 0.3885 a jci =.336 V PTCi = 3.4343 V 8 6 3 4 3 1 0 1 V [V] BC 1 3 1 0 1 V [V] BC M. Schroter, J. Krause IT parameter extraction issues in HiCuM/L for very advanced HBTs Slide 18/15
9 Appendix (cont d) from DEVICE REGAP postprocessor τ f 0 10 18 9 16 8 14 7 1 6 τ f [ps] 10 τ f [ps] 5 8 4 6 3 4 1 0 0 10 0 30 40 0 0 5 10 15 0 =0.356 ps, =0.5769 ps τ 0500GHz, τ 0300GHz, M. Schroter, J. Krause IT parameter extraction issues in HiCuM/L for very advanced HBTs Slide 19/15