Methodology for Bipolar Model Parameter Extraction. Tzung-Yin Lee and Michael Schröter February 5, TYL/MS 2/5/99, Page 1/34

Transcription

1 Methodology for Bipolar Model Parameter Extraction Tzung-Yin Lee and Michael Schröter February 5, 1999 TYL/MS 2/5/99, Page 1/34

2 Outline General Remarks Brief overview of TRADICA Parameter extraction flowchart Process-specific parameter extraction HICUM-specific parameter extraction SGPM-specific parameter extraction Model generation and verification Conclusion TYL/MS 2/5/99, Page 2/34

3 General Remarks Objectives - Concurrent engineering requires physics-based and predictive modeling strategy - Generation of scalable models Single transistor fitting - relies on a golden wafer which is typically very difficult to obtain, or is simply not available. - often results in unrealistic/nonphysical parameter values. - can only produce the simple equivalent circuit shown to the right due to lack of sufficient geometry related information. - usually provides a library with a very limited number of transistors, unless time and resource are unlimited. B C BCx r B i BC B i BE E E r E C BC C je C de C r CX i T C TYL/MS 2/5/99, Page 3/34

4 General Remarks (cont.) A process-based scalable approach - enables extraction of an accurate physics-based equivalent circuit (see fig. below) with a realistic representation of parasitic components. - maintains physical values of extracted parameters, therefore enabling later shift on the extracted parameters in accordance to process changes as well as statistical variation. - enables efficient model generation of transistors with different configurations. The process-based scalable methodology described in this presentation has been implemented as a Matlab toolbox called Bipax and used for production parameter extraction. B C BCx C BCx r Bx C js i SC i TS r Su C Eox C ds B* C jep i BEt C rbi r Bi C Su i BCi B i BEi E r E E S C BCi C jei i AVL C de C r CX i T T C P R th C th TYL/MS 2/5/99, Page 4/34

5 Brief overview of TRADICA - Model generation While initially being developed as a transistor dimensioning tool, TRADICA can also be used as a model generation and prediction tool [1]. TRADICA takes processspecific and modelspecific parameters as well PCM as geometry description to Data generate model parameters for transistors of various configurations, which are Design defined by emitter width Rules and length, number of emitter, base, and collector contacts (stripes), and their spatial arrangement. Process-specific parameters TRADICA Model parameters Model-specific parameters Transistor configurations Given specific parameters extracted from an arbitrary wafer, TRADICA can shift model parameters for wafers subject to various process variations based on respective process control monitor (PCM) data and analytical prediction equations. - Eliminating the need of a golden wafer - Enabling predictive and statistical modeling TYL/MS 2/5/99, Page 5/34

6 TRADICA Geometry Dimensions from Design Rules Base Emitter Base Collector l w b bpo b pm b E b sp silicide b EC b KB b KC b sil w sp n+ p+ poly p+ b SIC w ox w ox w Cx w Ci n-sic n-epi n+ sinker w jbl n+ buried layer b E +b EC b ch TYL/MS 2/5/99, Page 6/34

7 Process-specific parameters r SBi, r Ssp, r Spm, r Sil : pinched-base sheet resistance, base sheet resistance under spacer (link resistance), poly-on-mono sheet resistance, sheet resistance of silicided base. r KB, r KC, r KE, r Sbl : base, collector, emitter contact and buried layer sheet resistance C jei, V DEi, z Ei, α jei, C jep, V DEp, z Ep, α jep : C je related parameters C jci, V DCi, z Ci, V PTCi, C jcb, V DCb, z Cb, V PTCb, C jcp, V DCp, z Cp, V PTCp : C jc related parameters including punch-through voltages. C jsi, V DSi, z Si, C jsp, V DSp, z Sp : C CS related parameters γ C, γ B : Ratio of peripheral component to bottom component of specific collector and base currents δ C : Collector spreading angle Temperature coefficients and bandgap τ p /τ i : Ratio of peripheral component to bottom portion of the low-current transit time τ f. TYL/MS 2/5/99, Page 7/34

8 HICUM-specific parameters c 1, Q p, J ch, h fe, h fc, h jei, h jci : Transfer current parameters including GICCR HBT model extension J BEiS, m BEi, J REiS, m REi, J BCS, m BC : Base current parameters r Ci, V lim, V PT, V CEs : Critical current (I CK ) parameters τ, d τh, τ Bvl : Low-current transit-time parameters τ fe, g τfe : Emitter transit-time parameters τ hcs, α hc : Collector high-current transit-time parameters f AVL, q AVL : Avalanche current parameters J BEtS, α BEt : Tunneling current parameters A F, K F : Flicker noise parameters R th, C th : Parameters for self-heating α IT, α QF : Parameters for modeling NQS effect TYL/MS 2/5/99, Page 8/34

9 SGPM-specific parameters JS, NF, BF: Collector current and current gain parameters VAF, VAR: Early voltages JKF: Knee current density JSE, NSE: Base recombination current parameters TF, XTF, VTF, ITF: Transit-time/f T parameters apo, JRB: Parameters for modeling the internal base resistance EG: Bandgap AF, KF: Flicker noise parameters PTF: Excess phase (non-quasi-static effect in transfer current) TYL/MS 2/5/99, Page 9/34

10 Process control monitors for predictive modeling Except δb E and δw C all the parameters listed here are the percentage changes relative to their values in the base-line process. δb E : emitter width change [µm] δr Sbi : internal base sheet resistance change [%] δρ Ci : internal collector sheet resistance change [%] δn Cx : external collector doping change [%] δw C : internal collector thickness change [µm] δr Spm : poly-on-mono sheet resistance change [%] δr Sbl : buried-layer sheet resistance change [%] δr E : emitter resistance change [%] δρ su : substrate sheet resistance change [%] TYL/MS 2/5/99, Page 1/34

11 Bipolar Parameter Extraction Flowchart Preparation & Measurements Extraction of Process-specific param Extraction of HICUM transit time param Extraction of HICUM DC param Extraction of SGPM param Model generation, e.g. Library Verification of DC and f T characteristics and spot-freq y-parameters - Collect design rules - Collect SEM/TEM pictures - Perform Measurements - Extraction of resistance and capacitance related parameters - Check scaling - Determine collector spreading angle - Extraction of transit time parameters - Extraction of HICUM collector and base current related parameters - Extraction of SGPM collector and base current related parameters - Optimization to obtain f T related parameters - Use TRADICA to generate model parameters - Tune extrinsic base resistance - Tune transit time parameters (on transistors with different configurations simultaneously) Verification of frequency sweep y-parameters Verification of high-freq noise and distortion - Tune NQS parameters: excess phase... (on transistors with different configurations simultaneously) - Check RF related performance (on transistors with different configurations simultaneously) TYL/MS 2/5/99, Page 11/34

12 Process-specific parameter extraction - Base silicide and poly sheet resistance Use two 3- (or 4-) terminal contact chain structures with different lengths, l 1 and l 2. short structure A long structure A Correct current spreading by subtracting current of short structure from that of long one. Obtain corrected resistance between terminals A and B, R AB, and terminals B and C, R BC B l 1 l 2 b sil B b sil b pm1 b sil b sil b pm2 A B C TYL/MS 2/5/99, Page 12/34

13 Process-specific parameter extraction - Base silicide and poly sheet resistance (cont.) Calculate the base poly sheet resistance as = l and silicide sheet resistance as l, where = is the length difference of the long and short structures. 2b pm2 R BC r pm l r Ssil = l l b 2 l 1 sil R BC R AB r pm 2( b pm2 b pm1 ) A similar structure with b pm = can be used to extract the specific base contact resistance (and the silicide sheet resistance). TYL/MS 2/5/99, Page 13/34

14 Process-specific parameter extraction - Collector contactsinker resistance and buried-layer sheet resistance Use two 4-terminal collector contact chain structures with different lengths, l 1 and l 2. Correct current spreading by subtracting current of short structure from that of long one. short structure long structure 4-terminal collector contact chain structure A B C D collector Oxide contact n n+ Sinker b 2 b 1 Buried layer TYL/MS 2/5/99, Page 14/34

15 Process-specific parameter extraction - Collector contactsinker resistance and buried-layer sheet resistance (cont.) Force current through terminals A and D, measure voltage at B and C, resulting in AD resistance, that contains no contact and sinker contribution. Buried layer sheet resistance is then = ( ). Measure resistance directly between B and C giving. The combined specific contact-sinker resistance is then = ( b KC l) in [ Ω µm 2 ]. R BC r Sbl AD R BC l b1 R BC = AD R BC + 2RKC AD R BC R BC r KC 2 TYL/MS 2/5/99, Page 15/34

16 Process-specific parameter extraction - Base pinch resistance Use enclosed structures to ensure current flowing under the emitter [2]-[5]. Emitter By using two structures with different lengths (l E ), the corner and fore-side current crowding can be canceled ( = ). l l E2 l E1 Base Base Base l E Measure bias-dependent total resistance R for test structures with various emitter widths (b E ). b E Base Emitter Base Collector Buried layer TYL/MS 2/5/99, Page 16/34

17 Process-specific parameter extraction - Base pinch resistance (cont.) Extract the bias-dependent base sheet resistance values from the slopes of the fitted lines at different V BE. The external base link resistance can be determined from the extrapolated value,, where R KB, R bx = R KB + R sil + R pm + R link R sil, R pm, and R link are the base contact, silicide, poly-on-mono, and link resistance, respectively. rsb (ohm) The extrapolation of total base resistance 15 Jan BE/dLE 5 Bias dependence of Rsbi and Rsbx 4 rsbi, rsbx (ohm) 3 2 ratio= VBE (V) TYL/MS 2/5/99, Page 17/34

18 Process-specific parameter extraction - Emitter contact resistance Extract the emitter series and thermal resistance for transistors of various sizes using the simultaneous r E -R TH extraction method [6]. Plot r E vs. 1/A E to obtain the specific emitter contact resistance (in [ Ω µm 2 ] ) from the slope. Emitter resistance can also be extracted using the modified opencollector method [7], in which selfheating effect is insignificant. RE (ohm) /prj/rfbipolar/b25/b69223/w12/3v/d3: r E = [Ohm*um 2 ] Simultaneous r E -r TH extraction r E vs. 1/A E RE vs T=25., 75., /AE (1/um 2 ) R th vs. 1/A BC Rth vs T=25., 75., 125. Rth ( o C/W) /ABC (1/um 2 ) TYL/MS 2/5/99, Page 18/34

19 Process-specific parameter extraction - C je and C EOX Components to be considered: C jei A E, C jep P E, and C EOX P E, i.e. = + + C BE A E C jei P E ( C jep C EOX ) Measured test structures: a large area transistor, measured with CV meter, and several long-stripe transistors with different P/A ratios, measured with s-parameter technique. Obtain C jei for each bias from the zero x-axis intercept and C jep from the slope. Optimization to obtain the corresponding parameters. C BE [F] C jep [F] C jei [F] 1.5 x 1 14 Bottom peripheral separation of C BE P E /A E 6 x V BE [V] 1.5 x V BE [V] TYL/MS 2/5/99, Page 19/34

20 Process-specific parameter extraction - C jc and C COX Components to be considered: C jci A BC, C jcp P BC, and C COX P BC, i.e. = + + C BC A BC C jci P BC ( C jcp C COX ) Measured test structures: a large area transistor, measured with CV meter, and several long-stripe transistors with different P/A ratios, measured with s-parameter technique. Obtain C jci for each bias from the zero x-axis intercept and C jcp from the slope. Optimization to get the corresponding parameters. C BC [F] C jci [F] C jci [F] x 1 15 Bottom peripheral separation of C BC P BC /A BC x V BC [V] 6 x V BC [V] TYL/MS 2/5/99, Page 2/34

21 Process-specific parameter extraction - C CS Components to be considered: and, i.e. Measured test structures: a large area transistor, measured with CV meter, and several long-stripe transistors with different P/A ratios, measured with spotfrequency s-parameter technique. Obtain C jsi for each bias from the zero x-axis intercept and C jsp from the slope. Note that P CS can be larger than the value from design rules (or mask) due to additional contributions at the perimeter (depending on process). Optimization to obtain the corresponding parameters. C jsi A CS C jsp P CS C CS = A CS C jsi + P CS C jsp TYL/MS 2/5/99, Page 21/34

22 Extraction of transit-time from f T Extract τ f from f T [8] 2 1/2πf T vs. 1/I C Plot 1/(2πf T ) versus 1/I C. Extract low current τ f, τ f, from the intercept of the straight lines at low current with y axis and applying 1 τ f = ( R 2π f CX + R E )C C CB T g m τ f., giving Obtain τ f at high current densities from the difference between the straight lines and 1/(2πf T ) data. Then the transit-time as a function of I C and V CE can be obtained as τ f ( I C, V CE ) = τ f + τ f ( I C, V CE ). 1/2πf T [ps] τ F [ps] /I [1/mA] C τ f τ f τ f 5 τ f I [ma] C TYL/MS 2/5/99, Page 22/34

23 HICUM-specific parameter extraction - Transit-time Extract τ f vs. V CE from low-current τ f. (cf. next page) Extract I CK vs. V CE from, e.g., τ f inflection points [9]. τ F [ps] τ F vs J C, AE=.45um x 14.um I CK I C /AE [ma/um 2 ] 3 f T vs J C, AE=.45um x 14.um 25 2 f T [GHz] I C /AE [ma/um 2 ] TYL/MS 2/5/99, Page 23/34

24 HICUM-specific parameter extraction (cont.) - Lowcurrent transit-time parameters Low-current transit-time τ f parameters (τ, d τh, and τ bvl ) are obtained through optimization of the τ f vs. V CE curve. Geometry scaling of τ f is realized through the ratio of peripheral component to bottom portion of the low-current transit time τ f, τ p /τ i [1]. τ F [ps] Fitting of τ f τ F vs V CEi, AE=.42um x 14.4um w12/3v/d3/ 16 Dec V [V] CEi TYL/MS 2/5/99, Page 24/34

25 HICUM-specific parameter extraction (cont.) - Critical current I CK and high-current transit-time parameters I CK parameters (r Ci, V lim, V PT, and V CEs ) are obtained through optimization of the I CK vs. V CE curve. Geometry scaling of I CK is realized through the collector spreading angle δ C. δ C can be obtained by comparing the I CK values extracted from transistors with different emitter sizes at a given V CE [1]. Then perform optimization to obtain high-current transit time parameters (τ Ef, g τfe, τ hcs, α hc ). I CK [A] Fitting of I CK ICK fit V [V] CEi TYL/MS 2/5/99, Page 25/34

26 HICUM-specific parameter extraction - DC characteristics parameters Extract Q p from r Sbi vs. bias Extract c1 at low collector current density (e.g. VBE=.6...7V), where the influence of series resistance is negligible. Extract I ch from high collector current Extract I BEi and m BEi from medium base current Extract I REi and m REi from very low base current region Extract h jci from forward Early effect Geometry scaling is realized through γ C and γ B (ratio of peripheral component to bottom component of specific collector and base currents) J C, J B [ma/um 2 ] J C /J B Gummel plot V BE (V) Current gain I C /I B J [ma/um 2 ] C TYL/MS 2/5/99, Page 26/34

27 SGPM-specific parameter extraction - DC and Transittime parameters Because SGPM couples f T characteristics with intrinsic current-voltage characteristics, transport parameters need to be extracted first. Extraction of SGPM transport parameters is similar to that of HICUM. SGPM f T parameters TF, XTF, VTF, and ITF are obtained from optimization, which is often a lengthy process. Geometry scaling is realized through γ C and γ B (ratio of peripheral component to bottom component of specific collector and base currents) and δ C (collector spreading angle). TYL/MS 2/5/99, Page 27/34

28 Model verification Model verification is performed simultaneously on transistors with different configurations to confirm the accuracy of the scalable model generation. Model verification can also be used to tune parameters which can not be precisely determined from previous steps (e.g. parameters for NQS effect). For design of RF applications, verification of a model should include - DC characteristics: Gummel plot, transconductance g m, output conductance g o. -f T vs. J C at different V CE - freq=constant vs. J C at different V CE - y-parameters vs. frequency for different bias conditions - Temperature dependence - Noise (low and high frequencies) - Distortion A process-based scalable parameter extraction methodology and its result when applied to industrial high-speed bipolar process are presented. For more results please refer to the material presented to the Compact Model Council CMC on Dec. 1, 1998 [11]. TYL/MS 2/5/99, Page 28/34

29 HICUM - DC Verification J C, J B [ma/um 2 ] Gummel plot G m V BC =, -1, -2 V G m [ms/um 2 ] V BC =, -1, -2 V V BE (V) J C [ma/um 2 ] J C [ma/um 2 ] J C vs V CE plot I B =4, 8, 12, 16, 2 µa V CE [V] 5 G m /I C 12 Current gain 1 G O (di C /dv CE ) G m /J C [1/V] J C /J B V BC =, -1, -2 V G O [ms/um 2 ] I B =4, 8, 12, 16, 2 µa 1 V BC =, -1, -2 V J [ma/um 2 ] C 1 J [ma/um 2 ] C V (V) CE TYL/MS 2/5/99, Page 29/34

30 HICUM - f T verification Model verification hic@ft HICUM f 3V/d3/Q T characteristics p 4x14 (16 Dec 1998) A E =.4µmx14µm Model verification hic@ft HICUM f 3V/d3/Q 1 p1x14 T characteristics (16 Dec 1998) A E =1.1µmx14µm f T f T VCE=.5,.8, 1.5, 3. V 25 VCE=.5,.8, 1.5, 3. V f T [GHz] f T [GHz] J C [ma/um 2 ] J C [ma/um 2 ] τ f τ f τ f [ps] 15 τ f [ps] J [ma/um 2 ] C J [ma/um 2 ] C TYL/MS 2/5/99, Page 3/34

31 HICUM: Spot-frequency y-parameters vs. freq=1.ghz Re(y11) [ma/v] 3V/d3/Q p 4x14 (16 Dec 1998) V CE =.5,.8, 1.5, 3. V 1 2 Re( y12) [ma/v] 1 2 Re(y21) [ma/v] Re(y22) [ma/v] J [ma/um 2 ] C J [ma/um 2 ] C J [ma/um 2 ] C J [ma/um 2 ] C 1 1 Im(y11) [ma/v] 1 Im( y12) [ma/v] 1 2 Im(y21) [ma/v] 1 1 Im(y22) [ma/v] J [ma/um 2 ] C J [ma/um 2 ] C J [ma/um 2 ] C J [ma/um 2 ] C TYL/MS 2/5/99, Page 31/34

32 HICUM: Frequency-sweep y-parameter verification /prj/rfbipolar/b25/b69223/w12/3v/d3 hic V BE =.86V V CE =.8V J C =.11549mA/um 2 J B =.8423mA/um Re(y11) [A/V] 1 8 Re(y12) [A/V] 1 1 Re(y21) [A/V] 1 2 Re(y22) [A/V] Freq [Hz] Freq [Hz] Freq [Hz] Freq [Hz].15 Im(y11) [A/V] x Im(y12) [A/V] 1 3 Im(y21) [A/V] 8 x Im(y22) [A/V] Freq [Hz] Freq [Hz] Freq [Hz] Freq [Hz] TYL/MS 2/5/99, Page 32/34

33 HICUM: Frequency-sweep s-parameter verification j V BE =.86V V CE =.8V J C =.11549mA/um 2 J B =.8423mA/um 2 1 Re(s11) [ ].2 Re(s12) [ ] 1 Re(s21) [ ] 1 Re(s22) [ ] Freq [Hz] Freq [Hz] Freq [Hz] Freq [Hz] Im(s11) [ ] Im(s12) [ ] 2 Im(s21) [ ] Im(s22) [ ] Freq [Hz] Freq [Hz] Freq [Hz] Freq [Hz] TYL/MS 2/5/99, Page 33/34

34 References [1]. M. schroter, H.-M. Rein, W. Rabe, R. Reimjann, A. Wassener, and A. Koldehoff, Physics- and process-based bipolar transistor modeling for integrated circuit design, to be published in IEEE J. Solid-State Circuits. [2]. H.-M Rein and M. Schroter, Experimental determination of the internal base resistance of bipolar transistors under forward-bias conditions, Solid-State Electron., Vol. 34, p , [3]. M. Schroter, Simulation and modeling of the low-frequency base resistance of bipolar transistors in dependence on current and geometry, IEEE Trans. on Electron Dev., Vol. 38, p , [4]. M. Schroter, Modeling of the low-frequency base resistance of single base contact bipolar transistors, IEEE Trans. on Electron Dev., Vol. 39, p , [5]. H.-M. Rein and M. Schroter, Base spreading resistance of square emitter transistors and its dependence on current crowding, IEEE Trans. on Electron Dev., Vol. 36, p , [6]. H. Tran, M. Schroter, D. J. Walkey, D. Marchesan, and T. J. Smy, Simultaneous extraction of thermal and emitter series resistance in bipolar transistors, p , 1997 BCTM. [7]. R. Gabl and M. Reisch, Emitter series resistance from open-collector measurements - influence of the collector region and the substrate pnp transistor, IEEE Trans. on Electron Dev., p , Vol. 45, No. 12, Dec [8]. H.-M Rein, Proper choice of the measuring frequency for determining f T of bipolar transistors, Solid-State Electronics, Vol. 26, p and p. 929, 1983 [9]. M. Schroter and T.-Y. Lee, Physics-based minority charge and transit time modeling for bipolar transistors, IEEE Trans. on Electron Dev., p.288-3, Vol. 46, No. 2, Dec [1]. M. Schroter and D. J. Walkey, Physical modeling of lateral scaling in bipolar transistors, IEEE J. Solid-State Circuits, Vol. 31, p , 1996, and Vol. 32, p.171, 1998 [11]. M. Schroter and T.-Y. Lee, HICUM: A Physical-Based Scalable Compact Bipolar Transistor Model, Presentation to the Compact Model Council, Dec. 1, TYL/MS 2/5/99, Page 34/34