Didier CELI, 22 nd Bipolar Arbeitskreis, Würzburg, October 2009

Transcription

1 HICUM/L0 v1.2: Application to Millimeter Wave Devices Didier CELI, 22 nd Bipolar Arbeitskreis, Würzburg, October 2009

2 Outline Purpose ariation of reverse Early effect with the evolution of technologies New features in HICUM/L0 version 1.2 Parameter extraction Application to very advanced HBTs The dark side of HICUM/L0 Summary 1/39

3 Purpose Evaluation of the new HICUM/L0 version (1.2) applied to mmw devices developed in the framework of DOTFIE [1] f T = 250GHz f max = 300GHz This new HICUM/L0 revision is very promising and corrects many limitations of HICUM/L0 and HICUM/L2 versions. Possibilities and limits of this new model. 2/39

4 AR variation vs. technologie performance (HBTs) Normalized collector I CN = I C I S e BE T current vs. BE I C /[I S.exp( BE / T )] / AR Simulation Simulation Simulation Simulation Simulation f T = 45 GHz AR = 3.5 f T = 70 GHz AR = 2.2 f T = 160 GHz AR = 1.4 f T = 220 GHz AR = 1.05 f T = 250 GHz AR = BE [] Using the SGP formulation, the slope of the normalized collector current give directly an estimation of the effective reverse Early voltage AR I CN 1 BE = AR 3/39

5 Comments We can observe an important decrease of AR with the increase of the transit frequecy f T It is not due a lower base doping profile, on the contrary, it is due to the shape of the EB doping profile and to the grading factor of the Germanium at the EB junction [2]. Today, this very important effective reverse Early effect (low AR ) cannot be accurately described in all existing models SGP Negative collector current in high-injection ( BE > AR ) due to the simplified formulation of the reverse Early effect BE AR HICUM/L0 v 1.12 The reverse Early effect is defined using a non-ideality factor M CF. Drawbacks (i) offset on the output characteristics [2] (M CR must be equal to M CF, non-physical), (ii) wrong temperature behavior [4]. HICUM/L2 v 2.23 Transfer current parameter extraction issue (negative Q P0 ) [5], [6]. Impossibility to take into account the high slope of the normalized colletor current [7]. A workaround was proposed in [8] used an artificial split of the BE capacitance across the base resistance (only valid if R BI is enough small) with dedicated parameters for the dc capacitance (I T modeling) [aa] Measurement Simulation exp C BE ( ) T BE [] I Measurement Simulation BE [] IC exp( BE T ) 0 HICUM default [7] HICUM workaround [7] [aa] 4/39

6 What is new in HICUM/L0 [3]? New added parameters High-injection effects Name Description Default Range Unit Scaling factor A HQ F IQF Smoothing factor to decorelated DC and AC high-injection effects (I CK ) Flag for turning on voltage ( BC ) dependence of forward knee current (I QF ) 0 [-0.9:10] or Effective reverse Early effect Name Description Default Range Unit Scaling factor ER Effective Early effect a zero bias ]0: [ - DEDC Effective BE buit-in potential for DC transfert current 0.9 ]0:10] - Z EDC Effective BE grading exponent for DC transfert current 0.5 ]0:1[ - - A JEDC Effective BE capacitance ratio (maximum to zero-bias) for DC transfert current 2.5 [1: [ - - Temperature effects Name Description Default Range Unit Scaling factor Z ETAIQF Thermal coefficient for I QF 0 ]- : [ - Z ETARTH Thermal coefficient for R TH 0 ]- : [ - 5/39

7 Transfer current New transfer current formulation according to C. Thiele dissertation [9] Correction of the negative transconductance (g m ) issue at high-current densities [10] HICUM/L0 v1.12 (lines) and v1.2 comparison (circles) (QUCS simulations [11]) BC =0.5, 0, /39

8 Reverse Early effect Reverse Early effect In order to overcome the limitation of the M CF factor [2], [4] - Offset on IC(CE) characteristics if M CF not equal to M CR - Temperature dependence in HICUM/L0 v1.2 the concept of reverse Early voltage has been re-introduced using (low currents, BC =0) BE T I I S e e C = = = Q 1 + h je C je h je0 + TE je Q p0 I S BE T Q p0 I S BE T e TE ER with ER TE Q p0 h je C JE0 = = constante Q je = = transition voltage BEi in first approximation (SGPM) C je0 The reserve Early effect in now bias dependent thanks to the transition voltage TE which is function of BEi via the model parameter DE, Z E, A JE In version 1.2 of HICUM/L0, in order to take into account the possible bias dependence of the weight factor h je [6], in advanced HBTs, 3 model parameters, DEDC, Z EDC, A JEDC have been added to model the bias dependence of TE in dc [13]. 7/39

9 High-injection effects A HQ The parameter A HQ has been added in order to better control the high-injection effects in dc mode (injection width). For that an effective critical current I CK* is defined as I CK I CK = A HQ A HQ can be positive or negative, in the range [-0.9:10]. If A HQ is positive, I CK* is lower than the critical current I CK, and the current gain fall-off arises at lower current densities. In the opposite, if A HQ is negative, the effective critical current I CK* is greater than the critical current I CK, and the current gain fall-off arises at higher current densities. 8/39

10 High-injection effects F IQF In HICUM/L0, the equivalent of the knee current I KF of the SGP model is the parameter I QF = Q P0 T F In fact, T F0 is not a constant, but depends on B C T F0 ( B C ) = T 0 ( B C = 0) + ΔT F ( B C ) Therefore, I QF can be written I QF ( B C ) Q P0 Q P0 Q P0 T 0 = = = T F0 ( B C ) T 0 ( B C = 0) + ΔT F ( B C ) 1 ΔT F( = B C ) In order to make I QF dependent or not on B C, the flag F IQF have been added in HICUM/L0 v1.2 I QF ( B C ) = I QF ΔT F B C 1 + F ( ) IQF T 0 If F IQF = 0, I QF is independent on B C. If F IQF = 1, I QF is voltage dependent. T 0 I QF ( B C = 0) ΔT F( B C ) T 0 Important remark As in the model, the default value of T 0 is ZERO, as soon as T 0 has not been extracted do not specify F IQF = 1 otherwise you will have a crash of the simulator: devided-by-zero. Warning, if you set T 0 to a small value (in order to avoid the division by zero), I QF could be also too small making after the dc parameter extraction impossible. 9/39

11 High-injection effects Effect of F IQF If F IQF is set to 1, the critical current I QF decrease if T F ( B C ) increase. Comments: If the variation of T F0 with B C is small (that is normally the case for high speed transistors with low B CEO ), the effect of F IQF is very small (and even not visible). 10/39

12 Temperature dependence In HICUM/L0 v1.2 the temperature dependence of the thermal conductivity [14] is introduced α T KT ( ) = K , for silicon K 0 = 1.48 W/cm.K and α = 4/3 T nom As the thermal resistance is inversely proportional to the thermal conductivity, and with some approximation, the thermal resistance can be written as T dev R TH ( T) = R TH T nom Z ETARTH Where T nom is the nominal temperature (temperature at which the model parameters are specified), T dev is the device temperature, R TH0 is the thermal resistance at the nominal temperature and Z ETARTH is the thermal exponent of R TH. T dev = T + ΔT, where ΔT is the temperature increase due to self-heating ΔT = P d R TH, with P d the total power dissipation This model has been tested and validated using QUCS [11] and NGSPICE [12]. The two simulators give the same results. 11/39

13 Temperature dependence The temperature increase, from a Gummel plot simulation at several BC, is plotted thanks to the HICUM thermal node. Simulation are performed for 3 values (-1, 0, 1) of Z ETARTH BC = -1.5 BC = -0.5 BC = 0 BC = /39

14 Implementation in EDA tools Simulator Release Date ADS 2009 Update 1 20 October 2009 Availble in early access ELDO AMS Available GoldenGate End of October 2009 HSPICE C Available NGSPICE 19 Available QUCS Available SPECTRE MMSIM Available 13/39

15 Parameter extraction Already discussed during the last ABK meeting [10] Focus on new Early formulation, 2 possible approaches Standard formulation using ac BE capacitance New formulation using dc BE capacitance 14/39

16 I S ER extraction (1) Standard formulation [10] The parameters of the BE depletion capacitance C JE comes from ac measurements (cold [S] parameters) In HICUM/L0 v1.2, the collector current at low BE and BC = 0 is given by BEi T I I S e C TE ER (1) The transition or depletion voltage TE is deduced from the BE depletion charge Q JE Q je DE TE C je0 1 Z Z E = = + A E DE je ( BEi j ) j = BEi in reverse and low forward modes j (2) TE TE is close to BEi at low BE From the expression of the collector current (1) we can deduce I S. ER BEi T e TE = I S ER ER I C At low current densities, the BE transition voltage TE vs. e (3) BEi T linear. The intercept allows to determine ER and then the slope I S I C is - ER ER I S = = intercept slope intercept e BEi T I C 15/39

17 Results TE [] I S = A M CF = ER = I C /[I S.exp( BE / T )] I S = A M CF = ER = [exp( BE / T )]/I C [1/aA] I S = A M CF = ER = BE [] I C [A] BE [] Comments Despite the fit was good at low and medium current densities, the value of ER (too small) and I S (too large) are not physical. Moreover, the accuracy at high-currents is not good and cannot be adjusted with the high-injection parameters. 16/39

18 I S ER extraction (2) Second approach using dc BE junction capacitance [13] First step: determination of the dc BE capacitance The parameters of the BE junction capacitance (used only in dc) come from dc measurements from the collector current at low and medium current densities and BC = BEi T I S e Q I C JE as we can write that allows to calculate Q JE from dc measurements TE = I TE C I S e C JE0 Q JE ER BEi T Q JE C JE0 ER I e = S C JE0 I C ER C JE0 From Q JE it is now easy to determine C JEdc, the dc BE capacitance from its derivative BEi T ER C JEdc BEi d T e dq I C JE C JE0 ER I = = S d BEi d BEi BEi d T e I C d BEi BEi BEi T I e C T di e C T d BEi = = I C BEi T BEi T BEi T e 1 1 di C e 1 dln( I I C T I C d C ) e 1 = BEi I C T d = k BEi I C T 17/39

19 Therfore C JEdc can be calculated from C JEdc dq JE BEi T C d JE0 ER I e 1 = = S k BEi I C = T C JE BEi Z EDC DEDC (4) Second step: determination of the dc BE capacitance parameters DEDC, Z EDC and A JEDC (5) from (4) we can write at low forward BEi BEi T e k I C T = 1 ( ER I S ) C BEi Z EDC 1 BEi Z EDC DEDC DEDC (6) DEDC and Z EDC are determinated as for a junction capacitance (linear regression, at low forward BEi, taking the logarithm of (6)) A JEDC, is optimized at higher BEI (before high current effects) 18/39

20 Results of dc BE capacitance parameter extraction 5 Normalized C jbedc Capacitance Remarks BE [] Often (why?) Z EDC is greater than 0.5 and even close to 1, whereas A JEDC is always greater than 5. Same observation in [15], [8] WARNING: Z EDC cannot be equal to 1 otherwise TE is not defined. We have chosen to limit Z EDC to TE Q je C je0 = = DEDC j Z Z EDC + A EDC DEDC jedc ( BEi j ) 19/39

21 BEi T Third step: determination of I S and ER Once DEDC, Z EDC and A JEDC are known, I S and ER are determined as for the standard approach, from linear regression of TE vs. e. I C I S I= S = A M CF = ER ER = DEDC = 0.78 Z EDC = 0.99 A JEDC = TE [] Comments [exp( BE / T )]/I C [1/aA] We can remark that this measured characteristic is more linear than the one obtained with ac capacitance parameters I S and ER are also more physical 20/39

22 Results I C /[I S.exp( BE / T )] I S = A M CF = ER = I C [A] I S = A M CF = ER = BE [] BE [] Contrary to the standard approach (ac BE capacitance), now the fits of the normalized collector current and of the forward Gummel plot are perfect. Without the workaround proposed by Z. Huszka in [8], it is not possible to obtain the same accuracy with HICUM/L2. No solution with SGP model (necessity to use a non-ideality factor N F not equal to 1) Same issue with the other advanced BJT models (MEXTRAM, BIC), where the bias dependence of the reverse Early effect is based on the ac BE capacitance parameters. 21/39

23 Transistion voltage TE vs. BE Knowing the low collector current dc parameters, it is now possible to plot the transition voltage TE vs. BE (2) in oder to again validate the new model features and the extracted parameters From measurements, TE can be easy deduced (only valid at low BE ) from the expression of the collector (1) current using BEi T TE = ER I S e I C TE is simulated from Q JEdc /C JE I S = A ER = Limit of the TE determination TE [] TE = BE BE [] 22/39

24 Effective reverse Early voltage vs. BE Using the same concept than in the SGP model for modeling the Early effect, it is possible to define an effective reverse Early voltage ER* and to plot its dependence with BE (only valid at low BE ) BEi T I S e I C TE ER = I S BEi T e BEi ER 1.2 I S = A ER = that leads to the value of ER* From simulation ER = BEi ER TE From measurements ER BEi = = ER TE BEi I S e I C BEi T ER [] * Limit of the ER* determination BE [] Decrease of ER* vs. BE It is the first time that such characteritic is shown 23/39

25 Comments on possible g m non-linearity Strange behavior have been reported by CEDIC [15] on the transconductance g m using dc BE capacitance This behavior has been not observed (or seen) on measurements of avanced HBTs (DOT- FIE). ery good correspondence between simulations and experimental data for the first, second and third derivatives. To be clarified... 24/39

26 Comments on possible g m non-linearity Experimental results: I C and I B vs. BC = 0 and first derivative 1/ T 1/ T 25/39

27 Comments on possible g m non-linearity Experimental results: second and third derivatives 26/39

28 Final results ery good accuracy obtained for modeling both dc and ac characteristics in a wide range of currents and voltages, even far from the f T peak. f T [GHz] BC = 0.50 BC = 0.30 BC = 0.15 BC = 0.00 BC = BC = BC = BE [] I C [ma] I C [ma] CE [] Transit time parameter extraction: idem HICUM/L2 [16] High-currents dc parameters extraction see [10] 27/39

29 f T vs. constant BE It is the first time that these characteristics are shown with a such accuracy f T peak f T [GHz] BE = BE = BE = BE = BE = BE = BE = Low current region Breakdown region BC [] ery high current region S aturated region 28/39

30 Forward Gummel plot The current gain fall-off can be accurately described thanks to the CjEdc capacitance added in HICUM/L0 version 1.2 for modeling the reverse effective Early voltage. ery good behavior at high current densities. The curve fitting is facilitated with the introduction of the temperature dependence of R TH Forward Current Gain BC = 0.5 BC = 0 BC = -0.5 C JEdc I C [A] BC = 0.5 BC = 0 BC = I B [A] I C [A] BE [] 29/39

31 Comments These results demonstrate the capabilities of the new HICUM/L0 version (1.2) modeling, with a very good accuracy, advanced HBTs devices dedicated to millimeter wave applications. Despite these very good results, the work is not finished and the most difficult part, for a modeling engineer, is now to defined a simple extraction flow in order to obtain, every time, independently on who will perform the extraction, these kind of results. The definition of this extraction flow is not so obvious due to the difficulty to used direct methods for the extraction of high-current parameters. This is mainly because of the strong impact of the self-heating in this region In consequence global optimizations are needed with many loops in dc and ac in order to obtain this kind of result. And at the end, if the extraction is performed several time, today the results (accuracy and model parameter values) are never the same. f T [GHz] BC = 7.5E-01 BC = 3.0E-01 BC = 1.5E-01 BC = 0.0E+00 BC =-1.5E-01 BC =-3.0E-01 BC =-5.0E I C [ma] T [ o C] 30/39

32 Comments Now our goal is to find and to clearly define the shortest way (extraction flow) to obtain both reliable (physical and accurate) and reproducible HICUM/L0 parameters with the minimum of loops and go backs. The extraction of HICUM/L0 parameters is facilitated w.r.t HICUM/L2 due the de-coupling between dc and ac model equations. In HICUM/L0 it is possible to extracted dc parameter without to have to know the transit time parameters (extracted from f T characteristics). This de-coupling between dc and ac characteristics, is in fact not total because dc characteristics at high currents depend slightly on the critical current I CK, which can be obtained only (to my knowledge) from f T measurements. 31/39

33 The dark side of HICUM/L0 Normalized collector current temperature dependence I C /exp( BE / T ) [fa] T = 27 o C I C /exp( BE / T ) [fa] T = 125 o C I C /exp( BE / T ) [fa] N. Derrier BE [] T = -40 o C BE [] N. Derrier N. Derrier BE [] Despite the very good results at room temperature, the temperature behavior of the collector current at low and medium current densities is not good. One of the causes is the thermal coefficients (TC) of the dc capacitance which are the same than those of ac capacitance. They are not adapted to describe the temperature dependence of the effective reverse Early voltage. Possible solution (?) add TC for dc capacitance parameters. 32/39

34 Temperature dependence issues Base and collector currents I B [A] T-bias leakage BE [] T = -40 o C T = -20 o C T = 0 o C T = 27 o C T = 50 o C T = 75 o C T = 100 o C T = 125 o C I C [A] N. Derrier N. Derrier T-bias leakage BE [] The temperature dependence of the ideal base current is well described. In the opposite, the temperature dependence of ideal part of the collector current in not correctly described. This issue exist not only in HICUM/L0 model but also in all bipolar models (SGP, HICUM/L2), where ER (T) is not well taken into account. This issue is critical for the accurate design of bandgap voltage reference circuits and must be solved in priority. 33/39

35 Phase excess Although there is no phase excess in HICUM/L0, the phase of h 21e is quite good in the range of measurement. Magnitude and phase of h 21e for BE from 0.75 to BC = Mag(h21) [db] Pha(h21) [deg] f [Hz] But warning, as the f T is very high (250 GH Z ), the effect of the phase excess is not really visible at frequencies below 100 GH Z Proposal: for a first order model, introduce a P TF parameter like in SGP model f [Hz] 34/39

36 Base resistance The bias dependence of R Bi depends on Q JE. But which Q JE model to use? Q JEdc or Q JEac In HICUM/L0 it is Q JEac 21 Q JEdc RBASE(IB) 21 Q JEac RBASE(IB) RBASE (Ohm) RBASE (Ohm) IB (A) IB (A) 35/39

37 Summary The new version 1.2 of HICUM/L0 have been tested for very advanced HBTs dedicated to mmw applications. Pro and cons A new model reference is born! ery good results obtained at room temperature in comparison with other tested models SGP and HICUM/L2. Easy parameter extraction thanks to an accurate decoupling between dc and ac behaviors. Implemented in most circuit simulators. First scalable model library available in DOTFIE PDK (July 2009). Temperature dependence MUST be improved (idem for HICUM/L2). Base resistance bias dependence model must be clarified. 36/39

38 Acknowledgements Thanks to every body who have participated to this project: To J. Beckner (IFX) who helped me to convince CEDIC to make official this new HICUM/L0 version. To C. Thiele (IFX) who has corrected and improved many weaknesses of the model. To M. Schröter and A. Mukherjee (CEDIC) for the A implementation. To Z. Huszka (AMS) for the fruitful discussions on model and parameter extraction. To Crolles teams (ST), process integration, RF characterization and device modeling teams. To EDA vendors and open source developers for their implementation of the code in circuit simulators. 37/39

39 References [1] [2] D. Céli, About Modeling the Reverse Early Effect in HICUM/L0, 6 th HICUM Workshop, Heilbronn, June [3] M. Schröter, A. Mukherjee, HICUM/L0 version 1.2: Release Notes, TuD, November [4] H. Beckrich-Ros, F. Pourchon, HICUM/L0 Temperature Modeling: Towards Improvement, 7 th HICUM Workshop, Dresden, June [5] D. Céli, C 10, Q P0 Extraction or Model Issue?, DOTFIE correspondance (dm154.08), August [6] M. Schröter, J. Krause, I T Parameter Extraction Issue in HICUM/L2 for advanced HBTs, 21 th Bipolar Arbeitskreis, Hamburg, October [7] XMOD, TuD, ST, HBT Models for ST Process, WP4 DOTFIE deliverable, August [8] Z. Huszka, E. Seebacher, IGICCR Part II: Full HICUM/L2 Extraction Flow wit Self-Heating, 21 th Bipolar Arbeitskreis, Hamburg, October [9] C. Thiele, Weiterentwicklung eines Kompaktmodells für Bipolartransistoren mit spezieller Beachtung des Hochstrombereichs und eines geringen Parameterextraktionsaufwands, Dissertation, Munich, June [10] D. Céli, HICUM/L0 v1.2; Parameter Extraction and alidation, 21 th Bipolar Arbeitskreis, Hamburg, October [11] [12] [13] Z. Huszka, D. Céli, Fixing Mon-Uniqueness of HICUM/L2 by Improved GICCR, private communication, November /39

40 [14]. Palankovski, R. Schultheis, S. Selberherr, Simulation of Power Heterojunction Bipolar Transistors on Gallium Arsenide, IEEE Trans. Electron Devices, ol. 48, N 6, pp , June [15] CEDIC, DOTFIE WP4 - Device and compact modeling, deliverable report 4.2.1, May [16] D. Céli, Step by Step Extraction of HICUM/L2 High-Current Parameters, 8 th HICUM Workshop, Böblingen, May /39