Mextram 54 Jeroen Paasschens Willy Kloosterman Laboratories, Eindhoven c Electronics N.V. 1999 Mextram 54
Introduction (1) Previous CMC: Mextram 53 gives generally good results. Why Mextram 54 Modelling of SiGe processes Easier and hence better parameter extraction Better monotony in (higher) derivatives. We have tested Mextram 54 on five CMC data sets New parameter extraction only for process A
Process A: Cap Temp=25, 125 Mextram 53.2 (2) 12 Cbe 12 Cbc 5 Ccs 1 1 4 Cbe [ff] 8 6 Cbc [ff] 8 6 Ccs [ff] 3 2 4 4 1 2 4 3 2 1 1 2 13 11 9 7 5 3 1 1 Vbc[V] 13 11 9 7 5 3 1 1 Vcs[V] 1 Cbe_ 1 Cbc_ 4 Ccs_ 9 9 38 Cbe_[fF] 8 7 Cbc_[fF] 8 7 Ccs_[fF] 36 34 6 6 32 5 25 5 75 1 125 15 Temp[C] 5 25 5 75 1 125 15 Temp[C] 3 25 5 75 1 125 15 Temp[C]
Process A: fgummel Vbc= Temp=25, 5, 75, 125, 15 Mextram 53.2 (3) 1 1 Ic Ib Is 1 2 1 3 1 3 1 3 1 4 1 4 1 4 1 5 1 5 Ic [A] 1 5 1 6 Ib [A] 1 6 1 7 Is [A] 1 6 1 7 1 7 1 8 1 8 1 8 1 9.2.4.6.8 1. 1.2 1 9 1 1.2.4.6.8 1. 1.2 1 9 1 1.2.4.6.8 1. 1.2 Ic/Ib[ ] 2 175 15 125 1 75 5 Ie/Ib 25.2.4.6.8 1. 1.2 dic/dvbe/ic [1/V] 5 4 3 2 1 (dic/dvbe)/ic.2.4.6.8 1. 1.2 (dib/dvbe)/ib [1/V] 5 4 3 2 1 (dib/dvbe)/ib.2.4.6.8 1. 1.2
Process A: rgummel Vbe= Temp=25, 5, 75, 125, 15 Mextram 53.2 (4) 1 1 Ie Ib Is 1 2 1 3 1 3 1 3 1 4 1 4 1 4 1 5 1 5 Ie [A] 1 5 1 6 Ib [A] 1 6 1 7 Is [A] 1 6 1 7 1 7 1 8 1 8 1 8 1 9.2.4.6.8 1. 1.2 Vbc[V] 1 9 1 1.2.4.6.8 1. 1.2 Vbc[V] 1 9 1 1.2.4.6.8 1. 1.2 Vbc[V] Ie/Ib[ ] Ie/Ib 1..9.8.7.6.5.4.3.2.1..2.4.6.8 1. 1.2 Vbc[V] Ie/(Ib+Is) [ ] Ie/(Ib+Is) 1 9 8 7 6 5 4 3 2 1.2.4.6.8 1. 1.2 Vbc[V] (die/dvbc)/ie [1/V] 5 4 3 2 1 (die/dvbc)/ie.2.4.6.8 1. 1.2 Vbc[V]
Process A: foutput-ib Temp=25 Ib=1, 2, 3, 4 ua Mextram 53.2 (5) 3 Ic Is 1.1 Vbe 25 1 4 1.5 Ic [ma] 2 15 1 Is [A] 1 5 1 6 1 7 1 8 Vbe [V] 1..95.9 5 1 9.85 1 2 3 4 5 6 7 8 Vce[V] 1 1..5 1. 1.5 2. Vce[V].8 1 2 3 4 5 6 7 8 Vce[V] 15 Ic/Ib 1 1 dic/dvce 5 Ic/(dIc/dVce) 125 4 Ic/Ib[ ] 1 75 5 g_out [mho] 1 2 1 3 Vef [V] 3 2 25 1 1 2 3 4 5 6 7 8 Vce[V] 1 4 1 2 3 4 5 6 7 8 Vce[V] 1 2 3 4 5 6 7 8 Vce [V]
Process A: Temp=25 f=1 GHz, Vce =.2,.5,.8, 2, 5 V Mextram 53.2 (6) 25 Hfe=Ic/Ib 1 R_bb 2 8 15 6 Ic/Ib 1 Rb 4 5 2 1 5 1 4 1 3 1 2 1 1 Ic[A] 1 5 1 4 1 3 1 2 1 1 Ic[A] 1 1 1 ft 1 11 F_uni 8 1 9 ft[hz] 6 1 9 4 1 9 F_uni[Hz] 1 1 1 9 2 1 9 1 1 5 1 4 1 3 1 2 1 1 Ic[A] 1 8 1 5 1 4 1 3 1 2 1 1 Ic[A]
Outline (7) Introduction and previous Mextram 53 results Reformulation of the epilayer model Results Conclusions
f T -example (8) Process A Single Poly BiCMOS process V CE =.2,.5,.8, 2., 5. 1 1 1 Emitter size: :6 5:4 m Double base contact: r p = 1 k Maximum cut off f frequency T T : 1 GHz @ V CE = 5 V f f T : 6 GHz @ V CE = :5 V ft [Hz] 8 1 9 6 1 9 4 1 9 2 1 9 1 1 4 1 3 1 2 Ic[A]
sb 2 s C 2 s E 1 Internal base-collector bias (9) The internal base-collector bias increases strongly due to the (variable) epilayer resistance. When V B2 C 2 > V dc the junction is open. The bias increases only slightly. This happens quite abrupt. dpoly1, Vcb = 1, 3, 5 s C 1 1 R Cv V_b2c2-1 -2 A A A -3-4 A AA -5.5.1.15.2 Ic
Basics of the epilayer model (1) i When there is no injection into the epilayer: ( Wepi x = ) V epi V = B2 C, V 2 B2 C 1 and I = V epi SCR Cv V epi + I hc SCR Cv V epi + I hc R Cv Iepi.1.8.6.4 Current in the epilayer I_epi Limits Ihc.2 2 4 6 8 Vepi
Basics of the epilayer model (11) Vce = 5V;,Vbe =.87,.88,.9V; Ic =.32,.44,.74 ma 21 i In case of injection ( Wepi x > ) 2 V epi ' V dc, V B2 C 1 log(concentration (cm^-3)) 19 18 17 16 Injection thickness is given by (Kull model) 15 x i Wepi B 2 C ) f (, V 2 B2 ) C 1 R f ( V = C 2 C 1 Cv I 14..1.2.3.4.5.6.7 Distance (Microns) I C 1 C 2 = V epi SCR Cv (1, x i Wepi )2 V epi I + hc SCR Cv, x i (1 Wepi )2 V epi I + hc R Cv, x i (1 Wepi )
Mextram 53 (12) Voltages V B2 C 2 and V B2 C 1 are given. Combine the equations to find a third order equation for I C 1 C 2..1 Current in the epilayer From V B2 C 2 calculate.8.6 Reverse current I r Iepi.4 Reverse base charge Q BC.2 I_(xi=) Limits Ihc Iepi -3-2 -1 Vb2c2 1 2 3 Epilayer charge Q epi (from charge control relation) Uses also V B2 C 1 and I C 1 C 2 )
Mextram 54 concept (13) Injection starts when V B2 C 2 ' V dc :.4.35 Ic Iqs Cbimos3, Ib = 25u, 5u, 1u, 2u V qs V dc, V B2 C 1.3.25 I qs qs SCR V V qs + I hc SCR Cv Cv V qs + I hc R Cv Ic, Iqs.2.15.1.5 5 1 15 Vce Example without velocity saturation
Basics of the epilayer model (recap) (14) Vce = 5V;,Vbe =.87,.88,.9V; Ic =.32,.44,.74 ma 21 i In case of injection ( Wepi x > ) 2 V epi ' V dc, V B2 C 1 log(concentration (cm^-3)) 19 18 17 16 Injection thickness is given by (Kull model) 15 x i Wepi B 2 C ) f (, V 2 B2 ) C 1 R f ( V = C 2 C 1 Cv I 14..1.2.3.4.5.6.7 Distance (Microns) I C 1 C 2 = V epi SCR Cv (1, x i Wepi )2 V epi I + hc SCR Cv, x i (1 Wepi )2 V epi I + hc R Cv, x i (1 Wepi )
Mextram 54 (15) calculate from and i x Wepi 2 B V C1 2 C 1 (third order C I equation) x i Wepi =, I qs 1 C 1 C 2 I no velocity saturation x_i / Wepi Injection thickness.7 53 54.6 No velocity saturation.5.4.3.2 Velocity saturation 1, I qs C 1 C 2 I velocity saturation.1 1 Iepi / Iqs 2 3
Mextram 54 (16) Calculate V B 2 C 2 from the equation for x i Wepi (Kull model approximated): x i Wepi ( B f ), V f ( V 2 C 2 B2 C ) 1 R 2 C C 1 Cv I = From V B 2 C 2 calculate Reverse current I r Reverse base charge Q BC Epilayer charge Q epi This describes also charge in Ic, Ib, x_i / Wepi 1.1.1 1e-6 1e-8 1e-1 axi=.1 axi=.3 53 Gummelplot, cbimos3 hard saturation (I C 1 C 2 ' ) 1e-12.4.6.8 1 1.2 Vbe
Current definition (17) Question: How do we find I C 1 C 2? Use the epilayer resistance as a current sensor. Node voltage V B2 C 2 is only used to define the current: C s 1 R Cv s C 2 B 2 C 2 f V ), f ( V 2 B2 C ) + V 1 C1 C 2 I ( 1 C R Cv (Kull model; also = C used in reverse) sb 2 A A A A AA =) V B2 C 2 is always reasonably physical. s E 1
Process A: h fe (18) 2 15 Vce =.2,.6,.9, 1.5, 3. 53 54 hfe 1 5 1 4 1 3 1 2 Ic[A]
Current and derivatives (19).3.25 Cbimos3, Vce=.8 53 54 1.9.8 Cbimos3, Vce=.8 53 54 Ic.2.15.1 d^2ic/dvbe^2.7.6.5.4.3.2.5.1.7.8.9 1 1.1 Cbimos3, Vbe Vce=.8.14 53 54.12 -.1.7.8.9 1 1.1 Cbimos3, Vbe Vce=.8 15 53 1 54 5.1 dic/dvbe.8.6.4 d^2ic/dvbe^2-5 -1-15 -2-25.2-3 -35.7.8.9 1 1.1 Vbe -4.7.8.9 1 1.1 Vbe
Process A: fgummel Vbc= Temp=25,5,75 Mextram 54 (2).2 dic/dvbe 1. d2ic/dvbe 15 d3ic/dvbe dic/dvbe [A/V].15.1.5 d2ic/dvbe [A/V^2].5..5 d3ic/dvbe[a/v^3] 1 5 5 1..3.5.7.9 1.1 1.3 1..3.5.7.9 1.1 1.3 15.3.5.7.9 1.1 1.3 2 dib/dvbe 1 d2ib/dvbe.5 d3ib/dvbe dib/dvbe[ma/v] 15 1 5 d2ib/dvbe [ma/v^2] 8 6 4 2 d3ib/dvbe [A/V^3].3.1.1.3.3.5.7.9 1.1 1.3.3.5.7.9 1.1 1.3.5.3.5.7.9 1.1 1.3
Process C: fgummel Vbc= Temp=25, 75, 125 Mextram 54 (21) dic/dvbe [A/V].5.4.3.2.1 dic/dvbe..4.6.8 1. 1.2 d2ic/dvbe [A/V^2].4.3.2.1. d2ic/dvbe.1.4.6.8 1. 1.2 d3ic/dvbe[a/v^3] d3ic/dvbe 5 4 3 2 1 1 2 3 4 5.4.6.8 1. 1.2 2. dib/dvbe 2 d2ib/dvbe 3 25 d3ib/dvbe dib/dvbe[ma/v] 1.5 1..5..4.6.8 1. 1.2 d2ib/dvbe [ma/v^2] 15 1 5.4.6.8 1. 1.2 d3ib/dvbe [ma/v^3] 2 15 1 5 5 1.4.6.8 1. 1.2
Output characteristics (22).2.18 Cbimos3, ib = 25u, 5u, 1u, 2u 53 54.1 Cbimos3, ib = 25u, 5u, 1u, 2u 53 54.16.14.12.1 Ic.1 gout.8.6.1.4.2 2 4 6 8 1 Vce 1e-5 2 4 6 8 1 Vce
Process A: foutput-ib Temp=25 Ib=1, 2, 3, 4 ua Mextram 53.2 (23) 3 Ic Is 1.1 Vbe 25 1 4 1.5 Ic [ma] 2 15 1 Is [A] 1 5 1 6 1 7 1 8 Vbe [V] 1..95.9 5 1 9.85 1 2 3 4 5 6 7 8 Vce[V] 1 1..5 1. 1.5 2. Vce[V].8 1 2 3 4 5 6 7 8 Vce[V] 15 Ic/Ib 1 1 dic/dvce 5 Ic/(dIc/dVce) 125 4 Ic/Ib[ ] 1 75 5 g_out [mho] 1 2 1 3 Vef [V] 3 2 25 1 1 2 3 4 5 6 7 8 Vce[V] 1 4 1 2 3 4 5 6 7 8 Vce[V] 1 2 3 4 5 6 7 8 Vce [V]
Process A: foutput-ib Temp=25 Ib=1, 2, 3, 4 ua Mextram 54 (24) 3 Ic Is 1.1 Vbe Ic [ma] 25 2 15 1 5 Is [A] 1 4 1 5 1 6 1 7 1 8 1 9 Vbe [V] 1..9.8.7 1 2 3 4 5 6 7 8 Vce[V] 1 1..5 1. 1.5 2. Vce[V].6 1 2 3 4 5 6 7 8 Vce[V] 15 Ic/Ib 1 1 dic/dvce 5 Vef 125 4 Ic/Ib[ ] 1 75 5 dic/dvce [A/V] 1 2 1 3 Vef [V] 3 2 25 1 1 2 3 4 5 6 7 8 Vce[V] 1 4 1 2 3 4 5 6 7 8 Vce [V] 1 2 3 4 5 6 7 8 Vce [V]
One new parameter (25) Basically we only need one new parameter: a xi 9e+9 8e+9 Cbimos3, Vce =.8, 2. Mextram 54 axi =.3 axi =.3 axi = 1. 7e+9 6e+9 ft 5e+9 4e+9 3e+9 2e+9 1e+9.8.9 1 Vbe We also add the transit time parameters B, epi, and R. (In Mextram 53 these are calculated from DC parameters)
Process A: f T, V ce = :2,.5,.8, 2., 5. (26) Mextram 53 Mextram 54 1 1 1 1 1 1 8 1 9 8 1 9 ft [Hz] 6 1 9 4 1 9 ft [Hz] 6 1 9 4 1 9 2 1 9 2 1 9 1 1 4 1 3 1 2 Ic[A] 1 1 4 1 3 1 2 Ic[A]
Conclusions (27) Mextram 54 has much smoother characteristics Better description of measurements, improved parameter extraction features must still be demonstrated. SiGe modelling: Mextram 53 results are reasonable. Physical description and geometric scaling better with Mextram 54 Not enough experience (yet) with SiGe (e.g. not tested in production) Mextram 54 will contain self-heating network Mextram 54 model equations are ready except for details Further testing mainly within