A new transit time extraction algorithm based on matrix deembedding techniques

Transcription

1 27 A new transit time extraction algorithm based on matrix deembedding techniques C. Raya, N. Kauffmann, D. Celi, T. Zimmer

2 State of art Method Result Introduction T F importance: - T F physical information from S parameters - T F necessary to extract all high injection model parameters - T F more convenient than using F T (Effects of transit time and capacitances decoupled) - Less computational effort for extraction / optimization Brief review of a few existing methods: - Conventional method based on 1/(2.π.F T ) - Methods based on de-embedding techniques Objective: - Accurate transit time extraction including the saturation at high injection - Focus on the deep saturation region especially for advanced BiCMOS technologies - Figures of merit to help improve extraction strategy (e.g. T BVL & D TH extraction, capacitance behavior in the forward region) 1/25

3 State of art Method Result Outline I State of art II Improved Transit time extraction method III Extraction Results IV - Conclusion 2/25

4 State of art Method Result I State of art

5 State of art Method Result Conventional method: tangent method 1 1 τ cor = TF + ( C BC. ( 1+ 1 β ) + C BE). 2πf.F g req t m ( r r ).C.( 1 1 ) τ = + + β cor E CX BC with g m Ic m C.VT 1 2πf req.f t τ 6 cor 5 4 TF 3 TF 2 TF = TF + TF VT Ic 3/25

6 State of art Method Result Conventional method: tangent method T F Tf extracted Verilog-A Code Robust at low injection, although it gives effective extracted parameters T F extraction not accurate especially at high injection and in the saturation region Bad g m approximation I TF Vbc=.6V,.4V,.2V, V, -.5V, -1V, -1.5V 4/25

7 State of art Method Result M. Malorny, M. Schröter Analytical method for calculating elements of an arbitrary equivalent circuit, MIXDES 24, Poland, pp Z. Huszka A Pragmatic Yet Accurate Transit Time Extraction Method for HICUM, Private communication T F Tf extracted Verilog-A Code Methods based on de-embedding techniques Good determination of g m and g Accurate T F extraction The saturation involves a small error for the high injection region. Requires a very good accuracy of the capacitances C BE and C BC I TF Vbc=.6V,.4V,.2V, V, -.5V, -1V, -1.5V The new suggested method is an improvement of this approach 5/25

8 State of art Method Result II Improved transit time extraction method

9 State of art Method Result Strategy: Access to the T F dependent main circuit S r su S HICUM small signal schematics C js g jsc Its c su C r CX C C BCx1 C BCx2 g jbcx C ds B C r bx BEpar1 g jbep C rbi g jbci B * B C jci C jei I AVL C dc gm.v B E g P T j C th C BEpar2 C jep g jbet r bi* g jbei E r E C de T F = f(y 11,Y 12 ) R th E Access to the T F dependent circuit by deembedding techniques requires to determine: The temperature The internal nodes Calculate all bias dependant components of the small signal circuit 6/25

10 State of art Method Result II Improved transit time extraction method Approximation of the internal temperature Approximation of the internal nodes B, B*, E, C, E, S Component calculation of the equivalent small signal circuit Full deembedding by matrix calculation Transit time extraction

11 State of art Method Result Temperature Extraction from S-parameters measurement => Small signal => C th could be neglected T j F LSH = P=Ic meas. P T j [ C] T j =T ambient + P.R th C th F LSH =1 F LSH = I TF P Ic meas.(v CE -R E.(Ic meas +Ib meas )-R CX.Ic meas ) P 1 =Ib meas.(v BE -R E.(Ic meas +Ib meas) ) P 2 =Ic meas.(v CE -R E.(Ic meas +Ib meas )-R CX.Ic meas ) P 3 =R E.(Ic meas +Ib meas )² P P 1 +P 2 +P 3 Temperature approximation Verilog-A Code 7/25

12 State of art Method Result Approximation of the internal nodes C r CX C Ic meas V C =V C -r CX (T j ).Ic meas B r BX Ib meas B* V B *=V B -r BX (T j ).Ib meas E Ie r E E Ie Ibmeas + Ic meas (Structure RF common emitter => Ie is not measured) V E =V E +r E (Tj).(Ib meas +Ic meas ) S r SU Is? S For V BC <.5V the substrate current (Is is not measured) is low (V SS V). V S is assumed equal to V S (involving an error on the calculation of V S C and V S B* ) B* Ir bi* r bi*? B Ir bi* =Ib meas -I jbcx -I jbep -I ts -T UNODE.I BEtp V B =V B* - I rbi*.r bi* r bi* calculated for a self-consistent algorithm 8/25

13 State of art Method Result II Improved transit time extraction method Approximation of the internal temperature Approximation of the internal nodes B, B*, E, C, E, S Component calculation of the equivalent small signal circuit Full deembedding by matrix calculation Transit time extraction

14 State of art Method Result Deembbedding Y Matrix Z Matrix Y A Matrix Y 1 Y [ Y] = [ Y] + [ Y1] [ Y] = [ Y] [ Y1] A A 1 A [ A] = [ A1].[ A] 1 [ A] = [ A1].[ A] Z Z 1 Z [ Z] = [ Z] + [ Z1] [ Z] = [ Z] [ Z1] 9/25

15 State of art Method Result Full deembedding B C BEpar1 C js C BCx1 C BCx2 g jbcx C ds r bx C BEpar2 g jsc g jbep C jep S Its C rbi B * B g jbet r bi* E r su c su g jbci g jbei r E E S C jci C jei C r CX Internal transistor (*) r bi* is deembeded as a passive resistance (r bi* is bias dependent) Different approaches available to compute r bi* : calculation, extraction, C A Step1 Y Step2 A Step3 Y Step4 Z Step5 Y Step6 A Step7 (*) Y Step8 1/25

16 State of art Method Result II Improved transit time extraction method Approximation of the internal temperature Approximation of the internal nodes B, B*, E, C, E, S Component calculation of the equivalent small signal circuit Full deembedding by matrix calculation Transit time extraction

17 State of art Method Result Y matrix (from HICUM Verilog-A code) ( ) π ( ) ( ) g + g + 2π.f. C + C + C + C g j.2..f. C + C gm gavl_c gavl_b j.2. π.f req. CdC + CdC_be g + gavl_c + j.2. π.f req.cdc avl_c avl_b req de de_bc dc_be dc avl_c req de_bc dc g avl_c B g avl_b.v B E C dc C Q = C. v + CdE _ bc. v f de B ' E ' B ' C ' Q = C. v + CdC _ be. v r dc B ' C ' B ' E ' C de j2p.freq.c dc_be.v B E g m.v B E g C C de dc Q = = v Q f f CdE _ bc B ' E ' v = ' ' B ' C ' cte vb C vb ' E ' = cte Q = = v Q r r CdC _ be B ' C ' v = ' ' B ' E ' cte vb E vb ' C ' = cte j2p.freq.c de_bc.v B C E 11/24

18 State of art Method Result g m & g determination R(Y 11 ) and R(Y 12 ) are too noisy and sensitive to the deembedding and the measurement accuracy. In general g m >> g avl_b + g avl_c and g >> g avl_c then g avl_b and g avl_c could be neglected: N.B.: Another solution is to determine a self-consistent expression for g and g m using: gavl _ b = K avl. gm + g ( ) g = K.g + g avl _ c avl a ( ) π ( ) ( ) g + g + 2π.f. C + C + C + C g j.2..f. C + C gm gavl_c gavl_b j.2. π.f req. CdC + CdC_be g + gavl_c + j.2. π.f req.cdc avl_c avl_b req de de_bc dc_be dc avl_c req de_bc dc g g ( ) ( ) R Y m 21 R Y 22 ( ) ( ) ( ) ( ) g = R Y + R Y m g = R Y + R Y /24

19 State of art Method Result C dc_be negligible ( 11) imag Y = C + C + C + C j.2. π.freq Rigorously de de _ bc dc dc _ be ( Y21) ( j.2..freq) ( Y22) ( j.2..freq) CdC _ be = imag π imag π However imag(y 22 ) is too sensitive to the substrate network, moreover C dc_be is low for V BC <.7V, then practically C dc_be is negligible. imag j.2. π.f ( Y11) req C + C _ + C de de bc dc 13/24

20 State of art Method Result T F from Imag(Y 11 ) imag j.2. π.f ( Y11) req CdE + CdE _ bc + C QF ITF QF QFF C = +. = + ( g + g ).T vb ' E ' vb ' C ' vb ' E ' ITF vb ' E ' vb ' C ' C de m F de _ bc I TF dc v B ' C ' v B ' C ' QF ITF Qf dtf QFF = +. = I + TF. g.tf vb ' C ' vb ' E ' vb ' C ' Tf B ' C ' B ' C vb ' E ' v I B ' E ' v dv v ' B ' E ' ITF ITF ( Y11) QFF QFF imag dtf = gm. TF + ITF. + C vb ' E ' vb ' C ' vb ' C ' vb ' E ' j.2. π.freq dvb ' C ' I TF I TF I TF dc ( Y11) 1 imag. g j.2. π.f Tf m req C dtf C = I + C dvb ' C ' TF. dc 14/24

21 State of art Method Result Determination of C from Imag(Y 12 ) at low injection imag( Y12) dt dq = + = + + j.2..f f FF CdE _ bc CdC ITF. g.tf CdC π req B ' E ' dvb ' C ' dvb ' C ' v ITF For the low injection region: Q v FF B ' C ' vb ' E ' i TF and g. TF Therefore: ( Y12) imag dtf = CdE _ bc + CdC ITF. + CdC = C j.2. π.freq dvb ' C ' imag ( Y12) At low injection region (before the Ft peak): C j.2. π.f req 15/24

22 State of art Method Result Determination of C from Imag(Y 12 ) at high injection At low injection and V BC <.4V C dc, then: ( Y12) imag dtf I + C I j.2. π.freq dvb ' C ' ( Y12) dt dv f TF. dc TF. B ' C ' imag dtf dc 1 d C = DTH. + TBVL.. j.2. π.f req. ITF dvb ' C ' dvb ' C ' Cjci Tj dv ( ) ( jci( Tj) ) B ' C ' c = Cjci ( Tj) Cjci ( Tj) 1 = T + D.( c 1 ) + T. 1 c Tf TH BVL 2 dc c d C =. dvb ' C ' Cjci(Tj) dv ( jci( Tj) ) B ' C ' T BVL and D TH are extracted from a linear regression: ( Y12) jci( j) req ITF d Cjci( Tj) imag C T 2 f =. = TBVL c. D j.2. π.f. ( ) dvb ' C ' TH f TBVL VBC >.4V CdC DTH c 16/24

23 State of art Method Result Determination of C from Imag(Y 12 ) at high injection For the high injection region (after the Ft peak): ( Cjci( Tj) ) dc 1 d C = ITF. DTH. + TBVL.. + CdC * B ' C ' jci( j) B ' C ' dv C T dv C dc imag( Y12) dc 1 d C * = ITF. DTH. + TBVL.. j.2. π.freq dv C ( T ) dv peak Ft C C extracted Verilog A imag j.2. π.f ( Y12) req calc ( jci( Tj) ) B ' C ' jci j B ' C ' I TF I TF calc peak Ft 17/24

24 T F 2 15 State of art Method Result Real improvement T f imag ( Y11 + Y12) π j.2..f req. g m Tf extracted Verilog-A Code 2 T F 15 T f imag j.2. π.f ( Y11) req. g m C g m Tf extracted Verilog-A Code I TF I TF Without C the result is the same as the Malorny/Shröter and Huszka methods Full matrix deembedding convenient but actually not necessary Real improvement: T BVL & D TH extraction and dt F calculation (C ). 18/24

25 State of art Method Result II Extraction Results

26 State of art Method Result Application on measurement Final transit time extraction BICMOS9 W E =.3µm, L E =3.7µm 3 Extracted T F [ps] T F [ps] Smoothing Raw extraction ST-BICMOS9 technology (.13µm) : F T = 16 GHz, F max = 16 GHz 19/24

27 State of art Method Result Application on measurement Base-emitter capacitance correction BICMOS9 W E =.3µm, L E =3.7µm 4 F T F T deembedded Matrix Tuning V DE / Z E 14 C BE extracted C BE simulation E-4 1E-3 1E-2 1E-1 I TF V BE 2/24

28 State of art Method Result Application on measurement BICMOS9 W E =.3µm, L E =3.7µm 8 C extracted imag j.2. π.f ( Y12) req f 1.5 T BVL and D TH extraction 6 1. VBC >.4V CdC DTH. TBVL I TF c 21/24

29 State of art Method Result Application on measurement Base-Collector capacitance correction C BC parameters not enough accurate for V BC > BICMOS9 W E =.3µm, L E =3.7µm F T measurement F T simulation 25 Tuning V DC / Z C 14 C BC extracted C BC simulation V BC >> I TF After direct T BVL & D TH extraction V BC 22/24

30 State of art Method Result Application on measurement Final transit time extraction BICMOS9 W E =.3µm, L E =3.7µm 25 F T measurement F T simulation 3 T F measurement /24

31 State of art Method Result IV Conclusion

32 State of art Method Result Conclusion Highly accurate T F extraction method including the saturation region - Better approximation of T F (better than C de = g m.t F ) - Full matrix deembedding convenient but not necessary T BVL & D TH extraction from Y 12 - Extraction using a linear regression - Method mainly sensitive to the well known C BC capacitance only Capacitance parameters optimization in forward mode - FOM: deembeded F T after matrix deembedding - Capacitance optimization without modifying the capacitance in reverse mode New approach for r bi* extraction (Not presented): - rbi* extraction less sensitive to the avalanche phenomenon 24/24