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96/6032-50 BJT_Model (Bipolar Transistor Model)
Devices and Models, BJT
Netlist Format
Model sta tement s for t he ADS circuit simula tor ma y be stored in a n externa l le.Th is is t y pica l ly d on e w i t h fou nd ry m od el kit s. For m or e in for m a t ion on h ow t o set u pa nd use foundr y model kits, refer to the D esi gn K i t D evel opm ent manual .
model modelname BJT [parm=value]*
The model sta tement st a rts w ith t he required keyw ord m odel . It is follow ed by t hemodelname t ha t w ill be used by t ra nsistor components to refer t o the model. Theth ird pa ra meter indicat es the t ype of model; for t his model it is BJ T . U se eitherpara meter NP N= yes or P NP = yes to set th e tra nsistor t ype. The rest of the modelcont a ins pa irs of model pa ra meters a nd va lues, sepa ra ted by a n equa l sign. Thena me of the model para meter must a ppear exactly as show n in the pa ra meterst ab le-t hese names a re case sensit i ve. Some model pa ra meter s have a l ia ses, wh ich a relisted in parentheses a fter the main para meter nam e; these a re pa ra meter nam estha t can be used instead of the prima ry para meter na me. Model para meters maya ppea r in a n y or der in t h e m od el st a t em en t . Mod el pa r a m et er s t h a t a r e n ot speci e dt a k e t h e d efa u lt v a lu e in dica t e d in t h e pa r a m et er s t a b le. For m or e in for m a t ion a b ou tth e ADS circuit simula tor net list forma t, including sca le factors, subcircuits,va riables a nd equa tions, refer t o ADS Simula tor Input S ynt a x in th e U sin g Cir cui t Simulators manua l.
Example:
model Npn1 BJT \NPN=yes Is=1.5e-15 Cjc=2.0e-13
Notes/Equations
For RFDE Users I n for ma t i on a b ou t t h is m od el m us t be pr ov id ed in a m odel le; refert o Netlist Forma t on page 2-50 .
1. B J T_Model supplies va lues for B J T devices (B J T4 devices include a subst ra t e
term ina l). Ada pted from t he integra l cha rge cont rol model of G umm el andP oon, it includes severa l effect s a t h igh bia s levels. It reduces to t he simplerE bers-Moll model wh en certa in pa ra meters r equired for G umm el-P oon a re notspecied.
The DC cha ra cteristics of a m odi ed G umm el-P oon B J T a re de ned by:
Is , Bf, Ikf, Nf, Ise, a nd Ne, w hich determine forwa rd-current ga incharacteristics.
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BJT_Model (Bipolar Transistor Model) 2-51
Is, B r, Ikr, Nr, Isc, a nd Nc, w hich determine reverse-current ga incharacteristics
Va f a nd Va r, wh ich determine output conducta nces for forwa rd a nd reverseregions.
I s (sa t u r a t ion cu rr en t ). E g a n d Xt i pa r t ly d et er m in e t em per a t u re d epen den ceof Is.
Xtb determines base current tempera ture dependence.
Rb, Rc, a nd Re a re ohmic resista nces. Rb is current dependent.
The nonlinea r d epletion lay er ca pacita nces a re determined by:
Cje, Vje, a nd Mje for t he ba se-emitt er junction.
C jc, Vjc, a nd Mjc for th e ba se-collect or junction.
C js, Vjs, an d Mjs for t he collect or-subst ra t e junct ion (if vertica l B J T), or fort he base-substr a te junction (if la tera l B J T)
The collect or or ba se to subst ra t e junct ion is modeled a s a P N junct ion.
2. Substra te Termina l
Five model para meters cont rol the substr a te junction modeling: Cjs, Vjs a ndMjs model the nonlinea r substr a te junction capa cita nce; Iss a nd Ns model th enonlinea r subst ra te P -N junction current.
When B J T4_NP N or B J T4_P NP devices a re used, explicitly conn ect t hesubstr a te term ina l as requ ired. When 3-term ina l BJ T_NP N or B J T_P NPdev ices a r e used , t he subs t r a t e t ermina l is implicit l y g rounded . Th is shou ld nota ffect the simulat ion if the substra te model pa ra meters Cjs a nd Iss a re notspeci ed, as t hey default to 0.
The model La t e ra l pa ra meter changes the connect i on of the subs t r a t e junct i on .At it s defau lt sett ing of no, the subst ra te junction m odels a vert ica l bipolart ra nsist or wit h t he subst ra t e junct ion conn ect ed to the collect or. WhenLa tera l= yes, a lat eral bipolar tra nsistor is modeled with the substra te junctionconn ect ed to th e base.
3. Imax and Imel t Para mete rs
I m a x a n d I m elt s pecify t h e P -N ju nct ion explos ion cu rr en t . I m a x a n d I m elt ca nbe speci ed in t he device model or in t he Options component ; t he device modelva lue ta kes precedence over t he Options va lue.
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98/6032-52 BJT_Model (Bipolar Transistor Model)
Devices and Models, BJT
I f t he I melt va lue is less t ha n t he I ma x va lue, t he I melt va lue is in cr ea sed t o t heIma x va lue.
If I melt is speci ed (in t he m odel or in Opt ions) junct ion explosion curr ent =Im elt; otherw ise, if Ima x is speci ed (in t he model or in Opt ions) junct ion
explosion current = Im a x; ot herw ise, junction explosion current = model Im eltdefault va lue (w hich is the sa me a s th e model Ima x defa ult va lue).
DC Equations
There a re tw o components of ba se current a ssociat ed w ith th e bia s on each junction.For t he emitt er junction, a n idea l exponent ia l volta ge term I bei a rises due torecombina t ion in t he ina ctive ba se region a nd ca rrier injected int o the emitt er. Anon-ideal exponential voltage term I ben predomina tes a t low bia s due torecombina t ion in th e emitt er junction spa ced char ge region.
Simila rly, emission a nd recombina tion nea r th e collector junction result in simila rterms.
Collector Leakage Current
If Vbo is speci ed, w hen Vbc < 0 th e collect or leaka ge current Icbo is modeled by
Base Terminal Current (without substrate current)
I b ei I s V be N f V T ----------------------- exp 1 =
I b en I se V be N e V T ----------------------- exp 1
=
I b ci I s V bc
N r V T ----------------------- exp 1 =
I b cn I sc V bc N c V T ----------------------- exp 1
=
I cbo C bo G bo V b c +( ) 1 V bc
V bo ----------- exp=
I b I bei B f
----------- I b en I bci B r
----------- I b cn + + +=
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BJT_Model (Bipolar Transistor Model) 2-53
Collector Terminal Current (without substrate current)
Collector-Emitter Current
w here the norma lized ba se cha rge is Qb.
If Approxqb = yes
where
if neither K e nor Kc is speci ed
otherwise
where f ( ) is de ned a s:
If Approxqb = no
I c I bei I bci Q b
----------------------------- I bci B r
----------- I b cn =
I ce I bei I bci Q b
-----------------------------=
Q b Q 12
--------= 1 1 4 I bei I k f ----------- I b ci
I k r -----------+
+ N k +
Q 1 1
1 V bc V a f ----------- V be
V a r -----------
-------------------------------------=
Q 1 1 f K e V j e M j e ,,( ) v f K c V j c M j c ,,( ) v d 0
V bc
+d 0V be
+=
f K V M , ,( )
K 1 v V ----
M if v F c V f ----------------------- 2 q I B E K f
I B E A f
f F f e
----------- K b I B E A b
1 f F b ( )2+--------------------------------+ +=
i < ce 2 >
f ---------------------- 2 q I C E =
i < cs 2 >
f ---------------------- 2 q I
C S =
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BJT_Model (Bipolar Transistor Model) 2-65
Re = Re/ARE ARc = Rc/ARE A
The default va lue for t he ARE A par a meter is 1.
DC Operating Point Device Information
Denitions
Ic (col lector current)
I b (ba s e cu rr en t )
I e (emit t e r cu r ren t )
I s (subs t ra t e cu r ren t )
Ice (collection-emitt er current)
power (d issipa t ed power)
B et a D c Ic/Ib
where
I b = sign(ib) x Ma x (Abs(Ib), ie-20)
Rx = R B b
Cpi = C beCm u = C bcCbx = C B xCcs = Ccs i f ver t ica l BJ T
= Cbs i f la te ra l BJ T
G m d I ce d V b e -------------- d I ce
d V b c --------------+=
R p i 1
d I b d V b c -------------- --------------------=
R m u 1d I b
d V b c --------------
--------------------=
R o 1
d I ce d V b c -------------- --------------------=
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112/6032-66 BJT_Model (Bipolar Transistor Model)
Devices and Models, BJT
BetAc = Gm x Rpi
where
References
[1]P. Ant ognett i an d G. Ma ssobrio, Sem i cond uctor devi ce m odel i ng w i th SPI CE ,New York: McG ra w -H ill, Second E dit ion 1993.
F t 12 t a u R c R e +( ) C m u C b x +( )+( )( )------------------------------------------------------------------------------------------------=
t a u M a x C p i C n m C b x i e 20,+ +( )M ax G m i e 20,( )--------------------------------------------------------------------------------------=
V be B ( ) E ( )=V bc B ( ) C ( )=V ce B C ( ) E ( )=
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BJT_NPN, BJT_PNP (Bipolar Junction Transistors NPN, PNP) 2-67
BJT_NPN, BJT_PNP (Bipolar Junction Transistors NPN, PNP)
Symbol
Available in ADS and RFDE
Parameters
Notes/Equations
1. The Temp pa ra meter speci es th e physica l (opera t ing) tempera t ure of thedevice; if different t ha n t he tempera ture a t w hich t he model para meters a re
va lid or extr a ct ed (speci ed by Tnom of the a ssocia t ed model) cert a in modelpara meters ar e sca led such t ha t the device is simula ted a t i ts opera tingtempera tu re. Refer t o th e model to see w hich pa ra meter va lues a re sca led.
2. The Mode pa ra meter is used only during ha rmonic ba la nce, oscilla tor, orla rge-signa l S-pa ra meter, or C ircuit E nvelope an a lysis. B y ident ifying d evicest h a t a r e oper a t in g in t h eir lin ea r r eg ion , t h e sim ula t i on t im e m a y be d ecr ea s ed .Devices w ith Mode= linea r a re linear ized a bout t heir DC opera t ing point. In
Name Description Units Default
Model name of BJT_Model, EE_BJT2_Model, STBJT_Model, orMEXTRAM_Model
Area factor that scales certain parameter values of the model 1
Region dc operating region: 0 = off, 1 = on, 2 = rev, 3 = sat on
Temp device operating temperature C 25Trise temperature rise above ambient
C 0
Mode simulation mode: Nonlinear, Linear, Standard (refer to note 2 ) Nonlinear
Noise noise generation option: yes=1, no=0 yes
_M number of devices in parallel 1
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114/6032-68 BJT_NPN, BJT_PNP (Bipolar Junction Transistors NPN, PNP)
Devices and Models, BJT
st a nda r d en tr y m ode, t he in teger va lue 1 is used for a n on lin ea r device a n d 0 isused for a linea r device.
3. The subs t r a t e t ermina l is connect ed to g round. The subst r a t e cu r ren t is a f fect edby th e ISS a nd C J S m odel par a meters. There should be no problems w ith t his
except per ha ps in a P N P t r a nsist or w h er e t h e I S S m od el pa r a m et er is speci e d.Th is cou ld ca u se exces s cu rr en t ow a s t h e s ubs t ra t e P N ju nct ion m ig ht en d u pbeing forw a rd bia sed. If the connection of the substr a te t ermina l to ground isnot a ccepta ble, use th e BJ T4 component a nd connect its substra te t ermina l toth e a ppropria te place.
4. For informa tion on a rea dependence, refer t o the section Area D ependence ofthe B J T Model Pa ra meters on page 2-64 .
5. DC opera t ing point para meters tha t ca n be sent to the dat a set a re li sted in thefollow ing t a bles a ccordin g t o model.
Ta ble 2-2. DC Opera ting P oint I nforma tionModel = B J T_Model or E E _B J T2_Model
Name Description Units
Ic Collector current amperes
Ib Base current amperes
Ie Emitter current amperes
Is Substrate current amperes
Power DC power dissipation watts
BetaDc DC current gain
Gm Forward transconductance (dIce/dVbe) siemens
Rpi Input resistance 1/(dIbe/dVbe) ohms
Rmu Feedback resistance 1/(dIbe/dVbc) ohms
Rx Base resistance ohms
Ro Output resistance 1/(dIbe/dVbc - dIce/dVbc) ohmsCpi Base-emitter capacitance farads
Cmu Base-internal collector capacitance farads
Cbx Base-external collector capacitance farads
Ccs Substrate capacitance farads
BetaAc AC current gain
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BJT_NPN, BJT_PNP (Bipolar Junction Transistors NPN, PNP) 2-69
Ft Unity current gain frequency hertz
Vbe Base-emitter voltage voltsVbc Base-collector voltage volts
Vce Collector-emitter voltage volts
Ta ble 2-3. DC Opera ting P oint I nforma tionModel = S TB J T_Model
Name Description Units
Ic Collector current amperesIs Substrate current amperes
Ib Base current amperes
Ie Emitter current amperes
Power DC power dissipation watts
BetaDc DC current gain
BetaAc AC current gain
fTreal Unity current gain frequency, full formula hertzfTappr Unity current gain frequency, approximate
formula gm/(2*PI*C)hertz
Gm Forward transconductance (dIce/dVbe) siemens
Rpi Input resistance 1/(dIbe/dVbe) ohms
Rmu Reedback resistance 1/(dIbe/dVbc) ohms
Rx Base resistance ohms
Ro Output resistance 1/(dIbe/dVbc - dIce/dVbc) ohms
Rcv Collector resistance ohmsCpi Base-emitter capacitance farads
Cmu Base-internal collector capacitance farads
Cbx Base-external collector capacitance farads
Ccs Internal collector-substrate capacitance farads
Cbs Internal base-substrate capacitance farads
Ta ble 2-2. DC Opera ting P oint I nforma tionModel = B J T_Model or E E _B J T2_Model
Name Description Units
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116/6032-70 BJT_NPN, BJT_PNP (Bipolar Junction Transistors NPN, PNP)
Devices and Models, BJT
Cxs External base-substrate capacitance farads
Vbe Base-emitter voltage voltsVbc Base-collector voltage volts
Vce Collector-emitter voltage volts
Ta ble 2-4. DC Opera ting P oint I nforma tionModel = ME XTRAM_Model (503)
Name Description Units
Ic Collector current amperesIb Base current amperes
Ie Emitter current amperes
Is Substrate current amperes
Power DC power dissipated watts
dIc2e1_dVb2e1 (dIc2e1/dVb2e1) siemens
Gb2e1 (dIb2e1/dVb2e1) siemens
Gb1b2 (dIb1b2/dVb1b2) siemensGb1c1 (dIb1c1/dVb1c1) siemens
Gbc1 (dIbc1/dVbc1) siemens
Gb2c2 (dIb2c2/dVb2c2) siemens
Cb2e1 (dIb2e1/dVb2e1) siemens
Cb2c2 (dIb2c2/dVb2c2) siemens
Gb1e1 (dIb1e1/dVb1e1) siemens
Gc1s (dIc1s/dVc1s) siemens
dIc2e1_dVb2c2 (dIc2e1/dVb2c2) siemens
dIc2e1_dVb2c1 (dIc2e1/dVb2c1) siemens
dIc1c2_dVb2e1 (dIc1c2/dVb2e1) siemens
dIc1c2_dVb2c2 (dIc1c2/dVb2c2) siemens
dIc1c2_dVb2c1 (dIc1c2/dVb2c1) siemens
dIb2c2_dVb2e1 (dIb2c2/dVb2e1) siemens
Ta ble 2-3. DC Opera ting P oint I nforma tionModel = S TB J T_Model
Name Description Units
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BJT_NPN, BJT_PNP (Bipolar Junction Transistors NPN, PNP) 2-71
6. This device ha s no default a rtw ork a ssociat ed with i t .
References
[1]I . E. G etreu, CA D of El ectr oni c Ci r cui ts, 1; M odel i ng th e Bi pol ar T r ansistor ,
Elsevier Scientic Publishing Company, 1978.[2]P. Ant ognett i a nd G. Ma ssobrio. Sem i cond uctor D evi ce M odel i ng wi th SPI CE ,
S econd E dit ion, McG ra w -H ill, Inc., 1993.
dIb2c2_dVb2c1 (dIb2c2/dVb2c1) siemens
dIb1b2_dVb2e1 (dIb1b2/dVb2e1) siemensdIb1b2_dVb2c2 (dIb1b2/dVb2c2) siemens
dIb1b2_dVb2c1 (dIb1b2/dVb2c1) siemens
dIc1s_dVb1c1 (dIc1s/dVb1c1) siemens
dIc1s_dVbc1 (dIc1s/dVbc1) siemens
Cb1b2 (dQb1b2/dVb1b2) farads
Cc1s (dQc1s/dVc1s) farads
Cb1c1 (dQb1c1/dVb1c1) faradsCbc1 (dQbc1/dVbc1) farads
dQb2e1_dVb2c2 (dQb2e1/dVb2c2) farads
dQb2e1_dVb2c1 (dQb2e1/dVb2c1) farads
dQc2b2_dVb2e1 (dQc2b2/dVb2e1) farads
dQb2c2_dVb2c1 (dQb2c2/dVb2c1) farads
dQb1b2_dVb2e1 (dQb1b2/dVb2e1) farads
dQb1e1_dVb2e1 (dQb1e1/dVb2e1) farads
Vbe Base-emitter voltage volts
Vbc Base-collector voltage volts
Vce Collector-emitter voltage volts
Ta ble 2-4. DC Opera ting P oint Informa tion (cont inued)Model = ME XTRAM_Model (503)
Name Description Units
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118/6032-72 BJT4_NPN, BJT4_PNP (Bipolar Junction Transistors w/Substrate Terminal, NPN, PNP)
Devices and Models, BJT
BJT4_NPN, BJT4_PNP (Bipolar Junction Transistors w/SubstrateTerminal, NPN, PNP)
Symbol
Available in ADS and RFDE
Parameters
Notes/Equations
1. The Temp pa ra meter speci es th e physica l (opera t ing) tempera t ure of thedevice; if different t ha n t he tempera ture a t w hich t he model para meters a reva lid or extr a ct ed (speci ed by Tnom of the a ssocia t ed model) cert a in modelpara meters ar e sca led such t ha t the device is simula ted a t i ts opera tingtempera tu re. Refer t o th e model to see w hich pa ra meter va lues a re sca led.
2. The Mode pa ra meter is used only during ha rmonic ba la nce, oscilla tor, orla rge-signa l S-pa ra meter, or C ircuit E nvelope an a lysis. B y ident ifying d evicest h a t a r e oper a t in g in t h eir lin ea r r eg ion , t h e sim ula t i on t im e m a y be d ecr ea s ed .Devices w ith Mode= linea r a re linear ized a bout t heir DC opera t ing point. In
Name Description Units Default
Model name of BJT_Model or MEXTRAM_Model
Area factor that scales certain parameter values of the model 1
Region dc operating region: off=0, on=1, rev=2, sat=3 on
Temp device operating temperature C 25
Trise temperature rise above ambient C 0Mode simulation mode: Nonlinear, Linear, Standard (refer to note 2 ) Nonlinear
Noise noise generation option: yes=1, no=0 yes
_M number of devices in parallel 1
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st a nda r d en tr y m ode, t he in teger va lue 1 is used for a n on lin ea r device a n d 0 isused for a linea r device.
3. The fourt h t ermina l (substra te) is ava ilable for connection to a n externa lcircuit.
4. Ta ble 2-5 , Ta ble 2-6 , and Ta ble 2-7 l ist t he DC operat ing point par a meters tha tca n be sent to the da ta set .
Ta ble 2-5. DC Opera ting P oint I nforma tionModel = B J T_Model or E E _B J T2_Model
Name Description Units
Ic Collector current amperes
Ib Base current amperes
Ie Emitter current amperes
Is Substrate current amperes
Power DC power dissipation watts
BetaDc DC current gain
Gm Forward transconductance (dIce/dVbe) siemens
Rpi Input resistance 1/(dIbe/dVbe) ohms
Rmu Feedback resistance 1/(dIbe/dVbc) ohms
Rx Base resistance ohmsRo Output resistance 1/(dIbe/dVbc - dIce/dVbc) ohms
Cpi Base-emitter capacitance farads
Cmu Base-internal collector capacitance farads
Cbx Base-external collector capacitance farads
Ccs Substrate capacitance farads
BetaAc AC current gain
Ft Unity current gain frequency hertzVbe Base-emitter voltage volts
Vbc Base-collector voltage volts
Vce Collector-emitter voltage volts
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Devices and Models, BJT
Ta ble 2-6. DC Opera ting P oint I nforma tionModel = S TB J T_Model
Name Description Units
Ic Collector current amperes
Is Substrate current amperes
Ib Base current amperes
Ie Emitter current amperes
Power DC power dissipation watts
BetaDc DC current gain
BetaAc AC current gain
fTreal Unity current gain frequency, full formula hertz
fTappr Unity current gain frequency, approximateformula gm/(2*PI*C)
hertz
Gm Forward transconductance (dIce/dVbe) siemens
Rpi Input resistance 1/(dIbe/dVbe) ohms
Rmu Reedback resistance 1/(dIbe/dVbc) ohms
Rx Base resistance ohms
Ro Output resistance 1/(dIbe/dVbc - dIce/dVbc) ohms
Rcv Collector resistance ohmsCpi Base-emitter capacitance farads
Cmu Base-internal collector capacitance farads
Cbx Base-external collector capacitance farads
Ccs Internal collector-substrate capacitance farads
Cbs Internal base-substrate capacitance farads
Cxs External base-substrate capacitance farads
Vbe Base-emitter voltage volts
Vbc Base-collector voltage volts
Vce Collector-emitter voltage volts
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Ta ble 2-7. DC Opera ting P oint I nforma tionModel = ME XTRAM_Model (503)
Name Description Units
Ic Collector current amperes
Ib Base current amperes
Ie Emitter current amperes
Is Substrate current amperes
Power DC power dissipated watts
dIc2e1_dVb2e1 (dIc2e1/dVb2e1) siemens
Gb2e1 (dIb2e1/dVb2e1) siemens
Gb1b2 (dIb1b2/dVb1b2) siemens
Gb1c1 (dIb1c1/dVb1c1) siemens
Gbc1 (dIbc1/dVbc1) siemens
Gb2c2 (dIb2c2/dVb2c2) siemens
Cb2e1 (dIb2e1/dVb2e1) siemens
Cb2c2 (dIb2c2/dVb2c2) siemens
Gb1e1 (dIb1e1/dVb1e1) siemens
Gc1s (dIc1s/dVc1s) siemens
dIc2e1_dVb2c2 (dIc2e1/dVb2c2) siemensdIc2e1_dVb2c1 (dIc2e1/dVb2c1) siemens
dIc1c2_dVb2e1 (dIc1c2/dVb2e1) siemens
dIc1c2_dVb2c2 (dIc1c2/dVb2c2) siemens
dIc1c2_dVb2c1 (dIc1c2/dVb2c1) siemens
dIb2c2_dVb2e1 (dIb2c2/dVb2e1) siemens
dIb2c2_dVb2c1 (dIb2c2/dVb2c1) siemens
dIb1b2_dVb2e1 (dIb1b2/dVb2e1) siemensdIb1b2_dVb2c2 (dIb1b2/dVb2c2) siemens
dIb1b2_dVb2c1 (dIb1b2/dVb2c1) siemens
dIc1s_dVb1c1 (dIc1s/dVb1c1) siemens
dIc1s_dVbc1 (dIc1s/dVbc1) siemens
Cb1b2 (dQb1b2/dVb1b2) farads
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Devices and Models, BJT
5. This device ha s no default a rtw ork a ssociat ed with i t .
References
[1]I . E. G etreu, CA D of El ectr oni c Ci r cui ts, 1; M odel i ng th e Bi pol ar T r ansistor,Elsevier Scientic Publishing Company, 1978.
[2]P. Ant ognett i a nd G. Ma ssobrio. Sem i cond uctor D evi ce M odel i ng wi th SPI CE,S econd E dit ion, McG ra w -H ill, Inc., 1993.
Cc1s (dQc1s/dVc1s) farads
Cb1c1 (dQb1c1/dVb1c1) faradsCbc1 (dQbc1/dVbc1) farads
dQb2e1_dVb2c2 (dQb2e1/dVb2c2) farads
dQb2e1_dVb2c1 (dQb2e1/dVb2c1) farads
dQc2b2_dVb2e1 (dQc2b2/dVb2e1) farads
dQb2c2_dVb2c1 (dQb2c2/dVb2c1) farads
dQb1b2_dVb2e1 (dQb1b2/dVb2e1) farads
dQb1e1_dVb2e1 (dQb1e1/dVb2e1) faradsVbe Base-emitter voltage volts
Vbc Base-collector voltage volts
Vce Collector-emitter voltage volts
Ta ble 2-7. DC Opera ting P oint Informa tion (cont inued)Model = ME XTRAM_Model (503)
Name Description Units
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EE_BJT2_Model (EEsof Bipolar Transistor Model) 2-77
EE_BJT2_Model (EEsof Bipolar Transistor Model)
Symbol
Available in ADS and RFDE
Su pport ed via m odel include le in RF DE
Parameters
Model par a meters must be speci ed in S I unit s.
Name Description Units Default
Type NPN or PNP NPN
Nf forward-current emission coefcient 1.0
Ne base-emitter leakage emission coefcient 1.5
Nbf forward base emission coefcient 1.06
Vaf forward Early voltage V innity
Ise base-emitter leakage saturation current A 0.0Tf ideal forward transit time (Tr and Tf, along with the depletion-layer
capacitances, model base charge storage effects; Tf may bebias-dependent)
sec 0.0
Ikf corner for forward-beta high current roll-off A innity
Xtf coefcient of bias-dependence for Tf 0.0
Vtf voltage dependence of Tf on base-collector voltage V innity
Itf parameter for high-current effect on Tf A 0.0
Nbr reverse base emission coefcient 1.04Nr reverse-current emission coefcient 1.0
Nc base-collector leakage emission coefcient 2.0
Isc base-collector leakage saturation current A 0.0
Ikr corner for reverse-beta high-current roll-off A innity
A value of 0.0 is interpreted as innity
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Var reverse Early voltage V innity
Tr ideal reverse transit time (Tr and Tf, along with the depletion-layercapacitances, model base charge storage effects)
sec 0.0
Isf forward saturation current A 9.53 10 -15Ibif forward base saturation current A 1.48 10 -16Isr reverse saturation current A 1.01 10 -14Ibir reverse base saturation current A 6.71 10 -16Tamb ambient temperature of measurement and model parameter
extractionC 25
Cje base-emitter zero-bias depletion capacitance (Cje, Vje, and Mjedetermine nonlinear depletion-layer capacitance for base-emitter
junction)
F 0.0
Vje base-emitter junction built-in potential (Cje, Vje, and Mje determinenonlinear depletion-layer capacitance for base-emitter junction)
V 0.75
Mje base-emitter junction exponential factor (Cje, Vje, and Mje determinenonlinear depletion-layer capacitance for base-emitter junction)
0.33
Cjc base-collector zero-bias depletion capacitance (Cjc, Vjc, and Mjcdetermine nonlinear depletion-layer capacitance for base-collector
junction)
F 0.0
Vjc base-collector junction built-in potential (Cjc, Vjc, and Mjc determinenonlinear depletion-layer capacitance for base-collector junction)
V 0.75
Mjc base-collector junction exponential factor (Cjc, Vjc, and Mjc determinenonlinear depletion-layer capacitance for base-collector junction)
0.33
Rb base resistance ohms 10 -4
Re emitter resistance ohms 10 -4
Rc collector resistance ohms 10 -4
Fc forward-bias depletion capacitance coefcient 0.5wVsubfwd substrate junction forward bias (warning) V
wBvsub substrate junction reverse breakdown voltage (warning) V
wBvbe base-emitter reverse breakdown voltage (warning) V
wBvbc base-collector reverse breakdown voltage (warning) V
Name Description Units Default
A value of 0.0 is interpreted as innity
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EE_BJT2_Model (EEsof Bipolar Transistor Model) 2-79
Notes/Equations
1. This model speci es va lues for B J T_NP N or B J T_P NP devices.
2. E E B J T2 is t he second genera tion B J T model designed by Agilent E E sof. Themodel ha s been crea ted speci ca lly for a ut oma tic pa ra meter extra ction frommeasured da ta including D C a nd S -para meter measurements. The goa l of thismodel is to overcome some of th e problems a ssocia t ed w ith E E B J T1 orG ummel-Poon models limi ted accuracy and para mete r ex t ract ion d ifcu lty wi threga rd to silicon r f/microwa ve tra nsistors. EE B J T2 is not generally equiva lentor compa tible with th e G umm el-P oon or EE B J T1 models. EE B J T2 ca n providea rea sona bly accura te reproduction of tr a nsistor beha vior, including DC biassolution, bias-dependent S-parameters including the effects of package
pa ra sitics, a nd tr ue nonlinea r h a rmonic out put pow er. The model isqua si-sta t ic, a na lytical, a nd isoth erma l. The model does not sca le w ith a reabeca use pa ra meters a re intended t o be extra cted directly from measured da taa nd not from lay out considera tions. Defa ult va lues of some pa ra meters a rechosen from a n a vera ge of the rst E EB J T2 libra ry model pa ra meters.
3. To prevent numerical problems, the set ting of some model par a meters istr a pped by the simulat or. The pa ra meter va lues a re cha nged interna lly:
Mjc and Mje must be 0.99 F c m ust be 0.9999 Rb, Rc, a nd Re must be 10 -4
4. The Temp pa ra met er is only us ed to ca lcula t e th e noise perform a nce of th isdevice. Tempera t ure scaling of model pa ra met ers is not perform ed for t hisdevice.
wVbcfwd base-collector forward bias (warning) V
wIbmax maximum base current (warning) A
wIcmax maximum collector current (warning) A
wPmax maximum power dissipation (warning) W
AllParams name of DataAccessComponent for le-based model parametervalues
Name Description Units Default
A value of 0.0 is interpreted as innity
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5. U se AllPa ra ms w ith a Da ta AccessComponent t o specify le-based pa ra meters(refer t o Da ta AccessComponent in C ha pter 5 of t he I ntr oducti on to Cir cui t Components ma nua l). Note t ha t model para meters tha t a re explici t ly speci edta ke precedence over th ose via AllPa ra ms.
6. This device ha s no default a rtw ork a ssociat ed with i t .Equations
Base-Emitter and Base-Collector Current
The base-emitt er current in the B J T ha s been cha nged signi ca nt ly from t heG umm el-P oon a nd other ea rlier m odels. These models assum e tha t t he non-lea ka geba se-emitt er current is relat ed to t he collector-emitt er current by a simple const a nt ,known a s beta . Observa tion of ba se-emitt er current in both silicon a nd AlG a Asdevices ha s show n t ha t t his a ssumption is incorrect. D if culties wit h t his method of
modeling ba se current ha ve been observed for ma ny yea rs. A la rge, verybias-dependent ba se resista nce in t he modi ed G umm el-P oon m odel in B erkeleyS P I C E h a s been u sed t o a t t e mpt t o cor rect t h e pr oblem w it h t h e ba s e-em it t er cu rr en texpressions. This ba se resista nce va lue an d its va ria tion is often extra ct ed from D Cda ta only, w ith t he result t ha t th e beha vior of the device over frequency is oftenpoorly modeled. This pr oblem is t hen sol ved by a ssigning some fra ction of th eba se-collector capa cita nce to either side of the ba se in a distribut ed ma nner.
Agilent E E sof s experience wit h E E B J T2 ha s shown t ha t properly modeledba se-emitt er current a nd conducta nce renders bot h t he lar ge bia s-dependent ba seresista nce a nd dist ributed ba se-collector ca pa cita nce unnecessa ry a nd grea tlyimproves both th e DC a nd AC a ccura cy of the resulting model.
E E _B J T2 models the ba se-emitt er current w ith tw o non-ideal exponentia lexpressions, one for th e bulk recombina t ion current (usua lly domina nt in silicondevices), a nd one for other recombina t ion current s (usua lly a tt ributed t o surfa celeakage).
where
where
k is B oltzma nns const a nt , an d q is devicear y cha rge.
I b e I b i f ex p V be
N bf V T ( )-------------------------( ) 1.0
I se exp V be
N e V T ( )----------------------------( ) 1.0
+=
V T k T a m b
q ---------------------------=
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EE_BJT2_Model (EEsof Bipolar Transistor Model) 2-81
Note tha t Nbf is not neces sa r i ly 1.0, wh ich is effect ively the case in the Gummel-Poonmodel.
The ba se-collector curren t is sim ila rly modeled:
Virtua lly a ll silicon r f/microwa ve tr a nsistors a re vertical pla na r devices, so thesecond current term cont a ining Isc a nd Nc is usua lly negligible.
Th e t ot a l ba s e cu rr en t I b is t h e su m of I be a n d I bc. Not e t h a t t h is m et h od of m od elin gba se current obsoletes t he concept of a const a nt beta .
Collector-Emitter Current
The forwa rd and reverse components of the col lector-emit te r cur ren t a re modeled in ama nner simila r t o the G umm el-P oon m odel, but w ith more exibility. Observa tion ofcollector-emitt er current behavior ha s show n t ha t t he forw a rd a nd reversecomponents do not necessa rily sha re identical sa tu ra tion current s, a s in theG um mel-P oon model. The ba sic expressions in E E _B J T2, not including high -levelinjection effects a nd E a rly effects, a re:
w here Isf a nd Isr a re not exa ctly equa l but a re usually very close. Nf and Nr a re notnecessa rily equa l or 1.0, but a re usua lly very close. Ca reful contr ol of a mbienttempera tu re during device mea surement is required for precise extra ct ion of a ll ofth e sat ura tion current s a nd emission coef cient s in the model.
The effects of high-level inject ion a nd bia s-dependent ba se cha rge st ora ge a remodeled via a norma lized base cha rge, simila r t o the G umm el-P oon model:
where
I b c I b i r ex p V bc N br V T ( )-------------------------( ) 1.0
I sc exp V bc N c V T ( )----------------------------( ) 1.0
+=
I cf I s f ex p V be N f V T ( )
----------------------------( ) 1.0 =
I cr I sr exp V bc N r V T ( )----------------------------( ) 1.0 =
I ce I cf I cr ( )Q b
----------------------------=
Q b Q 12.0-------- 1.0 1.0 4.0 Q 2( )++( )=
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a nd
Note All ca lcu la t ions of the exponent ia l expressions used in the model a re l inear izedto prevent num erica l overow or under ow a t la rge forw a rd or reverse biascond it ions, respectively.
Base-Emitter and Base-Collector Capacitances
Diffusion and deplet ion capacit ances a re modeled for both junct ions of the t r ans is t ormodel in a ma nner very simila r t o the G umm el-P oon model.
for Vbc Fc Vjc
where
a nd
for Vbc > Fc Vjc
for Vbe Fc Vje
Q 1 1.0
1.0 V bc
V a f ----------- V be
V a r -----------
----------------------------------------------------------=
Q 2 I sf I k f --------- exp V be
N f V T ( )----------------------------( ) 1.0
I sf
I k f --------- exp V bc
N r V T ( )----------------------------( ) 1.0
+=
C bc C bc d i f f u s i o n C bc dep le t i on +=
C bc d i f f u s i o n T r I c r N r V T -----------------------=
C bc dep le t i on C j c
1.0 V bc
V j c ----------
M j c ---------------------------------------------=
C bc dep le t i on C j c
1.0 F c ( )M j c ----------------------------------- 1.0 M j c V b c F c V j c ( )
VJ j c 1.0 F c ( )-------------------------------------------------------- +
=
C be C b e d i f f u s i o n C be dep le t i on +=
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EE_BJT2_Model (EEsof Bipolar Transistor Model) 2-83
where
for Vbe > Fc Vje
Th e d iffu sion ca p a cit a n ce for C be is s om ew h a t d iffer en t ly for m ula t e d vs. t h a t of C bc.The tr a nsit t ime is not a const a nt for t he diffusion capa cita nce for C be, but is afunction of both junction volt a ges, formula ted in a ma nner simila r t o the modi edG umm el-P oon m odel. The t ota l ba se-emitt er cha rge is equa l to t he sum of t he
ba se-emit t er depletion cha rge (w hich is a function of Vbe only) an d t he so-ca lledtr a nsit cha rge (w hich is a function of both Vbe a nd Vbc).
where
a nd
a nd
Noise Model
Therma l noise genera t ed by res is t or s Rb, Rc, and Re is cha ract er ized by the followingspectr a l density :
C be dep le t i on C j e
1.0 V be
V j e ----------
M j e ---------------------------------------------=
C be dep le t i on C j e
1.0 F c ( )M j e ----------------------------------- 1.0 M j e V b e F c V j e ( )( )
V j e 1.0 F c ( )------------------------------------------------------------- +
=
Q t r a n si t T f f I cf
Q b -------- =
T ff T f 1.0 X t f I cf I cf I t f +----------------------- 2.0 exp V bc
1.44 V t f --------------------------( )+ =
C be d i f f u s i o n V be ( ) V be Q t r a n si t =
C be d i f f u s i o n V bc ( ) V bc Q t r a n si t =
i < 2 >f --------------------
4 k T R
-----------=
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Devices and Models, BJT
S h ot n oise gen er a t ed by ea ch of t h e D C cu rr en t s ow in g fr om ba s e t o em it t er, ba s e t ocollect or, a nd collect or t o emit t er is cha ra cterized by th e follow ing spect ra l density :
In t he previous expressions, k is B oltzma nns consta nt , T is the opera tingtempera ture in K elvin, q is t he electr on cha rge, an d f is the noise ba ndw idth.F licker a n d bu rs t n ois e for t h is d evice is n ot m od eled in t h is ver sion of t h e sim ula t or.H ow ever, th e bias -dependent noise sources I_NoiseB D a nd V_NoiseB D ca n beconn ect ed externa l to th e device to model icker or bur st noise.
References
[1]J . J. E bers a nd J . L. Moll. La rge Signa l B eha viour of J unction Tra nsistors,
P roc. I.R.E . 42, 1761 (1954).[2]H . K . Gummel and H. C . Poon . An In t eg ra l Cha rge-Con t rol Rela t i on for B ipola r
Transistors, Bell Syst. Techn. J. 49, 115 (1970).
[3]S P IC E 2: A Computer P rogra m to Simula te Semiconductor Circuits, Un iversityof Ca liforn ia , B erkeley.
[4]P. C. G rossma n a nd A. Oki. A La rge S igna l D C Model for G a As/G a xAl1-xAsH eterojunction B ipola r Tra nsistors, P roceedings of t he 1989 IE E E B ipola rC ircuit s a nd Techn ology Meet ing, pp. 258-262, Sept ember 1989.
i < 2 >f -------------------- 2 q I D C =
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EE_BJT2_Model (EEsof Bipolar Transistor Model) 2-85
Equivalent Circuit
Intrinsic Model(NPN or PNP)
+
-Vbe
+
-Vbc
Cbc
Cbe
Ibc
Ibe
Ice
IcfIcr
Ib
Ic
Ie
Intrinsic Model
+
-
Vbc
+
-
Vbe
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Devices and Models, BJT
HICUM_Model (Bipolar Transistor Model)
Symbol
Available in ADS and RFDE
Su pport ed via m odel include le in RF DE
Parameters
Name Description Units Default
NPN NPN model type: yes, no yes
PNP PNP model type: yes, no no
C10 ICCR constant (=I SQp0 ) A2s 2e-30
Qp0 zero-bias hole charge As 2.0e-14
Ich high-current correction for 2D/3D-ICCR amperes 1e20
Hfe GICCR weighing factor for Q E f in HBTs 1
Hfc GICCR weighing factor for Q fc (mainly for HBTs) 1
Hjei GICCR weighing factor for Q jei in HBTs 1
Hjci GICCR weighing factor for Q jci in HBTs 1
Mcf GICCR weighing factor for Q jci in HBTs 1
Alit factor for additional delay time of iT 0.0
Cjei0 zero-bias value farads 0.0
Vdei built-in voltage volts 0.9
Zei exponent coefcient 0.5
Aljei factor for adjusting maximum value of Cjei0 2.5
Cjci0 zero-bias value farads 0.0
Vdci built-in voltage volts 0.7
Zci exponent coefcient 0.4
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Vptci punch-through voltage (=qN C iw 2
C i /(2) volts 1e20
T0 low-current transit time at V BC=0 seconds 0
Dt0h time constant for base and BC SCR width modulation seconds 0.0Tbvl voltage for modeling carrier jam at low Vces seconds 0.0
Tef0 neutral emitter storage time seconds 0.0
Gtfe exponent factor for current dependent emitter storage time 1
Thcs saturation time constant at high current densities seconds 0.0
Alhc smoothing factor for current dependent C and B transit time seconds 0.1
Fthc partitioning factor for base and collector portion 0.0
Alqf factor for additional delay time of Qf 0.0
Rci0 low-eld resistance of internal collector region (including scaling) ohms 150
Vlim limitation voltage separating ohmic and SCR regime volts 0.5
Vpt punch-through voltage of BC SCR through (epi) collector volts 3
Vces internal CE saturation voltage volts 0.1
Tr time constant for inverse operation seconds 0 sec
Ibeis BE saturation current amperes 1e-18
Mbei BE non-ideality factor 1.0
Ireis BE recombination saturation current amperes 0.0
Mrei BE recombination non-ideality factor 2.0
Ibcis BC saturation current amperes 1e-16
Mbci BC non-ideality factor 1.0
Favl pre-factor for CB avalanche effect 1/V 0
Qavl exponent factor for CB avalanche effect 0
Rbi0 value at zero-bias ohms 0
Fdqr0 correction factor for modulation by BE and BC SCR 0.0Fgeo geometry factor (default value corresponds to long emitter stripe) 0.6557
Fqi ratio of internal to total minority charge 1.0
Fcrbi ration of h.f. shunt to total internal capacitance 0.0
Latb scaling factor for Q fC in b E direction 0
Latl scaling factor for Q fC in lE direction 0
Name Description Units Default
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Cjep0 zero-bias value farads 0
Vdep built-in voltage volts 0.9
Zep depletion coefcient 0.5
Aljep factor for adjusting maximum value of Cjep0 2.5
Ibeps saturation current amperes 0.0
Mbep non-ideality factor 1.0
Ireps recombination saturation current amperes 0.0
Mrep recombination non-ideality factor 2.0
Ibets saturation current amperes 0
Abet exponent coefcient 40
Cjcx0 zero-bias depletion value farads 0
Vdcx built-in voltage volts 0.7
Zcx exponent coefcient 0.4
Vptcx punch-through voltage volts 1.0e20
Ccox collector-oxide capacitance farads 0
Fbc partitioning factor for Ccbx=Cjcx0+Ccox 0.0
Ibcxs saturation current amperes 0.0
Mbcx non-ideality factor 1.0Ceox emitter oxide (overlap) capacitance farads 0
Rbx external base series resistance ohms 0
Re emitter series resistance ohms 0
Rcx external collector series resistance ohms 0
Itss transfer saturation current amperes 0.0
Msf non-ideality factor for forward transfer current 1.0
Msr non-ideality factor for inverse transfer current component 1.0
Iscs saturation current of CS diode (latch-up modeling) amperes 0.0
Msc non-ideality factor of CS diode 1
Tsf storage time (constant) for minority charge seconds 0.0
Cjs0 zero-bias value of CS depletion capacitance farads 0
Vds built-in voltage volts 0.6
Zs exponent coefcient 0.5
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HICUM_Model (Bipolar Transistor Model) 2-89
Vpts punch-through voltage volts 1.0e20
Rsu substrate series resistance ohms 0
Csu substrate capacitance given by permittivity of bulk material farads 0
Kf icker noise factor (no unit only for a F =2!) 0
Af icker noise exponent factor 2.0
Krbi factor for internal base resistance 1
Vgb bandgap voltage volts 1.17
Alb relative temperature coefcient of forward current gain 1/K 5e-3
Zetaci temperature coefcient (mobility) for epi collector 0.0
Alvs relative temperature coefcient of saturation drift velocity 1/K 0.0
Alt0 temperature coefcient for low-current transmit time t0 (linear term) 1/K 8.25e-4
Kt0 temperature coefcient for low-current transmit time t0 (quad. term) 1/K 0.0
Alces relative temperature coefcient of Vces 1/K 0.0
Zetarbi temperature coefcient (mobility) for internal base resistance 0.0
Zetarbx temperature coefcient (mobility) for external base resistance 0.0
Zetarcx temperature coefcient (mobility) external collector resistance 0.0
Zetare temperature coefcient (mobility) emitter resistance 0.0
Alfav relative temperature coefcient for avalanche breakdown 1/K 0.0Alqav relative temperature coefcient for avalanche breakdown 1/K 0.0
Tnom temperature for which parameters are valid oC 25
Trise temperature rise above ambient C 0Rth thermal resistance ohms 0
Cth thermal capacitance farads 0
Imax explosion current A 1e4
Imelt (similar to Imax; refer to note 4) A ImaxAcModel selects which small signal models to use for ac and S-parameter
analyses (1 or 2); refer to note 51
SelfheatingModel
selects which power dissipation equations to use for modelingself-heating effect (1 or 2); refer to note 6
1
wVsubfwd substrate junction forward bias (warning) V
wBvsub substrate junction reverse breakdown voltage (warning) V
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Netlist Format
Model sta tement s for t he ADS circuit simula tor ma y be stored in a n externa l le.Th is is t y pica l ly d on e w i t h fou nd ry m od el kit s. For m or e in for m a t ion on h ow t o set u pa nd use foundr y model kits, refer to the D esi gn K i t D evel opm ent manual .
model modelname HICUM [parm=value]*
The model sta tement st a rts w ith t he required keyw ord m odel . It is follow ed by t hemodelname t ha t w ill be used by t ra nsistor components to refer t o the model. Theth ird pa ra meter indicat es the t ype of model; for t his model it is H I CU M . U se eitherpara meter NP N= yes or P NP = yes to set th e tra nsistor t ype. The rest of the modelcont a ins pa irs of model pa ra meters a nd va lues, sepa ra ted by a n equa l sign. Thena me of the model para meter must a ppear exactly as show n in the pa ra meterst ab le-t hese names a re case sensit ive. Some model pa ra meter s have a l ia ses, wh ich a relisted in parentheses a fter the main para meter nam e; these a re pa ra meter nam estha t can be used instead of the prima ry para meter na me. Model para meters maya ppea r in a n y or der in t h e m od el st a t em en t . Mod el pa r a m et er s t h a t a r e n ot speci e dt a k e t h e d efa u lt v a lu e in dica t e d in t h e pa r a m et er s t a b le. For m or e in for m a t ion a b ou tth e ADS circuit simula tor net list forma t, including sca le factors, subcircuits,va riables and equa tions, refer to ADS S imulat or Input Synt a x in the U sin g Cir cui t Simulators manua l.
Example:
model Npn3 HICUM \NPN=yes Alfav=8e-5 T0=5e-12
wBvbe base-emitter reverse breakdown voltage (warning) V
wBvbc base-collector reverse breakdown voltage (warning) V
wVbcfwd base-collector forward bias (warning) V
wIbmax maximum base current (warning) A
wIcmax maximum collector current (warning) A
wPmax maximum power dissipation (warning) W
AllParams name of DataAccessComponent for le-based model parametervalues
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Notes/Equations
For RFDE Users I n for ma t i on a b ou t t h is m od el m us t be pr ov id ed in a m odel le; refert o Netlist Forma t on page 2-90 .
1. This m odel (version 2.1) supplies va lues for a H IC U M device.
2. Th e im por t a n t ph ys ica l a n d elect r ica l effect s t a k en in t o a ccou nt by H I C U M a r esummarized:
high-current effects (including qua si-sa tura tion)
distr ibuted high-frequency m odel for t he externa l ba se-collect or r egion
emitt er periphery injection a nd a ssociat ed cha rge storage
emitt er current crow ding (thr ough a bia s-dependent int ernal ba se resista nce
2- a nd 3-dimensiona l collector current spreading
para si t ic (bia s independent) ca pacita nces betw een ba se-emitt er an dba se-collect or t ermin a l
vertica l non-qua si-sta tic (NQS) effects for tr a nsfer current a nd minoritycharge
tempera ture dependence a nd self-heat ing w eak a vala nche brea kdow n a t t he base-collector junction
tunn eling in the base-emitt er junction
paras i t ic subs t ra te t rans is tor
ban dga p differences (occurring in H B Ts)
la t e r a l sca l ab ilit y
For det a iled physica l a nd electr ica l effects, a s w ell a s model equa tions, refer t oMicha el S chr ot er s H I C U M , A Sca lable Ph ysics-ba sed Compa ct B ipolarTra nsistor Model , D escr i pt i on of m odel ver sion 2.1 , D ecem ber, 2000; a pd f le isava i la ble a t http://www.iee.et.tu-dresden.de/iee/eb/comp_mod.html .
3. C on st a n t t r a nsit t im e Tf (a t d c bia s ) is u sed in h a rm on ic ba la n ce a n a ly sis for I tcurrent delay.
4. Imax and Imel t Para mete rs
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I m a x a n d I m elt s pecify t h e P -N ju nct ion explos ion cu rr en t . I m a x a n d I m elt ca nbe speci ed in t he device model or in t he Options component ; t he device modelva lue ta kes precedence over t he Options va lue.
I f t he I melt va lue is less t ha n t he I ma x va lue, t he I melt va lue is in cr ea sed t o t he
Ima x va lue.If I melt is speci ed (in t he m odel or in Opt ions) junct ion explosion curr ent =Im elt; otherw ise, if Ima x is speci ed (in t he model or in Opt ions) junct ionexplosion current = Im a x; ot herw ise, junction explosion current = model Im eltdefault va lue (w hich is the sa me a s th e model Ima x defa ult va lue).
5. Sma l l-s igna l ac model g iven in the ref er ence cit ed in n ot e 1 is a d er iva t ion of t h ela rge-signa l cha rge model. However, it is not fully compa tible wit h t he cha rgemodel wit h t he sma ll input. The AcModel pa ra meter can be set to eit her t hesma ll-signa l model (AcModel= 1) or t he cha rge m odel compa t ible model(AcModel= 2) for sm a ll-signa l a c an d S -par a meter a na lyses.
The AcModel pa ra met er ha s no effect on la rge-signa l an a lysis.
6. Tw o pow er dissipa t ion formula s for modeling th e self-hea t ing effect ha ve beenimplement ed in ADS .
When Selfhea tingModel = 1, the simpli ed formula pow er = It vce -Iave vbc will be used.
When S elfheat ingModel = 2, formula 2.1.16-1 from Schroter s document a thttp://www.iee.et.tu-dresden.de/iee/eb/comp_mod.html w ill be used; th eformu la ca n be found u nder Gener al D escr i pt i on > H ICU M -Equat ions >section 2.1.16, equation 2.1.16-1.
The simpli ed formu la is implement ed in D r. Schroter s D E VIC E progra m.
7. U se AllPa ra ms w ith a Da ta AccessComponent t o specify le-based pa ra meters(refer t o Da ta AccessComponent in C ha pter 5 of t he I ntr oducti on to Cir cui t Components ma nua l). Note t ha t model pa ra meters tha t a re explici t ly speci edta ke precedence over t hose speci ed via AllPa ra ms.
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Equivalent Circuit
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Devices and Models, BJT
HICUM_NPN, HICUM_PNP (HICUM Bipolar Transistors, NPN, PNP)
Symbol
Available in ADS and RFDE
Parameters
Notes/Equations
1. The Temp pa ra meter speci es th e physica l (opera t ing) tempera t ure of thed evice. I f t h is is d iffer en t t h a n t h e t em per a t ur e a t w h ich t h e m od el pa r a m et er sa re va lid or extra cted (speci ed by th e Tnom par a meter of the a ssocia tedH IC U M_Model) certa in model para meters a re sca led such tha t th e device issimula ted a t i ts operat ing temperat ure.
2. The Mode pa ra meter is used only during ha rmonic ba la nce, oscilla tor, orla rge-signa l S-pa ra meter, or C ircuit E nvelope an a lysis. B y ident ifying d evicest h a t a r e oper a t in g in t h eir lin ea r r eg ion , t h e sim ula t i on t im e m a y be d ecr ea s ed .Devices w ith Mode= linea r a re linear ized a bout t heir DC opera t ing point. Inst a nda r d en tr y m ode, t he in teger va lue 1 is used for a n on lin ea r device a n d 0 isused for a linea r device.
Name Description Units DefaultModel name of a HICUM_Model
Temp device operating temperature C 25Trise temperature rise above ambient C 0Mode simulation mode: Nonlinear, Linear, Standard (refer to note 2) Nonlinear
Noise noise generation option: yes=1, no=0 yes
Selfheating turn on the self-heating effect on this device: yes, no (refer to note 3 )
_M number of devices in parallel 1
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HICUM_NPN, HICUM_PNP (HICUM Bipolar Transistors, NPN, PNP) 2-95
3. The H IC U M implement s self-hea ting. As t he tr a nsistor dissipa tes pow er, itca uses its t empera tu re to rise a bove a mbient. The model par a meters Rt h a ndCth con t rol t h is : T = P d iss x R th . To en a ble t his, set t he S elfh ea t in g a g t o y esor leave it blan k, an d ensure tha t t he model para meter Rt h is > 0. Whenself-hea ting is ena bled, it ma y be necessar y t o increa se the ma ximum num berof i terat ions due t o the a ddit iona l unknow n (tempera ture r ise) th a t must besolved for. Sim ula t ion us ing self-hea t ing m a y t a ke 50 to 100% more tim e th a nth e sa me simula tion with out self-hea ting.
Self-heat ing ca n be used w ith ei ther a n int ernal or externa l therma l node.
I f t he th ( fth ) node is either conn ect ed to ground or not given in t he net list,HI CU M_NP N a nd H ICU M_P NP use a n interna l node to keep tra ck of thet empera tu re rise of the tr a nsistor.
I f t he th ( ft h) node is eith er left open (un conn ect ed) or connected t o ath ermal coupling netw ork, then HIC U M_NP N a nd H ICU M_P NP use thisnode to keep tra ck of th e tempera tu re rise of th e tr a nsistor.
4. Ta ble 2-8 l ists th e DC operat ing point para meters tha t can be sent t o theda tase t .
Ta ble 2-8. DC Opera ting P oint I nforma tion
Name Description Units
Ic Collector current amperesIb Base current amperes
Ie Emitter current amperes
Is Substrate current amperes
Power DC power dissipated watts
Gbiei (dIbiei/dVbiei) siemens
Cbiei Base-emitter capacitance farads
Gbici (dIbici/dVbici) siemens
Cbici Base-collector capacitance farads
Gbcx (dI/dV) siemens
Gbep (dI/dV) siemens
Cbep (dQ/dV) farads
Gbet (dI/dV) siemens
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5. This device ha s no default a rtw ork a ssociat ed with i t .
Gsc (dI/dV) siemens
dIt_dVbi (dIt/dVbi) siemens
dIt_dVci (dIt/dVci) siemens
dIt_dVei (dIt/dVei) siemens
Sfbav (dI/dV) siemens
Sfcav (dI/dV) siemens
Cjs Substrate-collector capacitance farads
C1bcx Base-collector capacitance farads
C2bcx Base-collector capacitance farads
Vbe Base-emitter voltage voltsVbc Base-collector voltage volts
Vce Collector-emitter voltage volts
Ta ble 2-8. DC Opera ting P oint I nforma tion
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MEXTRAM_Model (MEXTRAM Model) 2-97
MEXTRAM_Model (MEXTRAM Model)
Symbol
Available in ADS and RFDE
Su pport ed via m odel include le in RF DE
Parameters
Model par a meters must be speci ed in S I unit s.
Name Description Units Default
NPN NPN model type yes
PNP PNP model type no
Release model level 503
Exmod ag for extended modeling of reverse current gain yes
Exphi ag for distributed high-frequency effects in transient yes
Exavl ag for extended modeling of avalanche currents yes
Is collector-emitter saturation current A/m2 9.6369 10 -18Bf ideal forward current gain 138.9
Xibi fraction of ideal base current that belongs to sidewall 0.0
Ibf saturation current of non-ideal forward base current A/m2 2.7223 10 -15Vlf crossover voltage of non-ideal forward base current V 0.6181
Ik high-injection knee current A/m2 1.5 10 -2Bri ideal reverse current gain 6.243
Ibr saturation current of non-ideal reverse base current A4.6066 10
-14
Vlr crossover voltage of non-ideal reverse base current V 0.5473
Xext part of I E X, Q E X, Q TE X and I S U B that depends onbase-collector voltage V B C 1
0.5358
Qb0 base charge at zero bias 9.3424 10 -14Eta factor of built-in eld of base (= ) 4.8
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Avl weak avalanche parameter 76.43
E electric eld intercept (with Exavl=1) 0.7306
Ihc critical current for hot carriers A/m2 5.8359
10 -4
Rcc constant part of collector resistance /m 2 11.09Rcv resistance of unmodulated epilayer /m 2 981.9Scrcv space charge resistance of epilayer /m 2 1769Sfh current spreading factor epilayer 0.3556
Rbc constant part of base resistance /m 2 134.4Rbv variable part of base resistance at zero bias /m 2 307.7Re emitter series resistance /m 2 1.696Taune minimum delay time of neutral and emitter charge sec 6.6626 10 -12Mtau non-ideality factor of the neutral and emitter charge S 1
Cje zero bias base-emitter depletion capacitance F/m 2 4.9094 10 -14Vde base-emitter diffusion voltage V 0.8764
Pe base-emitter grading coefcient 0.3242
Xcje fraction of base-emitter depletion capacitance that belongs tosidewall 0.26
Cjc zero bias base-collector depletion capacitance F/m 2 8.7983 10 -14Vdc base-collector diffusion voltage V 0.6390
Pc base-collector grading coefcient variable part 0.6135
Xp constant part of Cjc 0.5
Mc collector current modulation coefcient 0.5
Xcjc fraction of base-collector depletion capacitance under emitter
area2.7018 10 -2
Tref (Tnom) reference temperature C 25Dta (Trise) difference of device temperature to ambient temperature
( TDevice=TAmbient +Dta)C 0
Vge emitter bandgap voltage V 1.129
Vgb base bandgap voltage V 1.206
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Vgc collector bandgap voltage V 1.120
Vgj emitter-base junction band-gap voltage V 1.129
Vi ionization voltage base dope V 2.1
10 -2
Na maximum base dope concentration cm -3 4.4 10 17Er temperature coefcient of Vlf and Vlr 210 -3Ab temperature coefcient resistivity base 1.0
Aepi temperature coefcient resistivity of the epilayer 1.9
Aex temperature coefcient resistivity of the extrinsic base 0.31
Ac temperature coefcient resistivity of the buried layer 0.26
Kf icker noise coefcient ideal base current 0Kfn icker noise coefcient non-ideal base current 0
Af icker noise exponent 1.0
Iss base-substrate saturation current A/m2 5.8602 10 17Iks knee current of the substrate A/m2 6.7099 10 -6Cjs zero bias collector-substrate depletion capacitance F/m 2 2.2196 10 -13Vds collector-substrate diffusion voltage V 0.5156
Ps collector-substrate grading coefcient 0.3299
Vgs substrate bandgap voltage V 1.12
As for closed buried or an open buried layer 1.9
wVsubfwd substrate junction forward bias (warning) V
wBvsub substrate junction reverse breakdown voltage (warning) V
wBvbe base-emitter reverse breakdown voltage (warning) V
wBvbc base-collector reverse breakdown voltage (warning) V
wVbcfwd base-collector forward bias (warning) VwIbmax maximum base current (warning) A
wIcmax maximum collector current (warning) A
wPmax maximum power dissipation (warning) W
AllParams name of DataAccessComponent for le-based modelparameter values
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Devices and Models, BJT
Netlist Format
Model sta tement s for t he ADS circuit simula tor ma y be stored in a n externa l le.Th is is t y pica l ly d on e w i t h fou nd ry m od el kit s. For m or e in for m a t ion on h ow t o set u pa nd use foundr y model kits, refer to the D esi gn K i t D evel opm ent manual .
model modelname MextramBJT [parm=value]*
The model sta tement st a rts w ith t he required keyw ord m odel . It is follow ed by t hemodelname t ha t w ill be used by t ra nsistor components to refer t o the model. Theth ird pa ra meter indicat es the t ype of model; for t his model it is M extramBJ T . Useeither pa ra meter NP N= yes or P NP = yes to set t he tra nsistor type. The rest of th emodel conta ins pairs of model pa ra meters a nd va lues, sepa ra ted by a n equa l sign.The na me of the model pa ra meter must a ppear exactly a s show n in th e pa ra meterst ab le-t hese names a re case sensit i ve. Some model pa ra meter s have a l ia ses, wh ich a relisted in parentheses a fter the main para meter nam e; these a re pa ra meter nam estha t can be used instead of the prima ry para meter na me. Model para meters maya ppea r in a n y or der in t h e m od el st a t em en t . Mod el pa r a m et er s t h a t a r e n ot speci e dt a k e t h e d efa u lt v a lu e in dica t e d in t h e pa r a m et er s t a b le. For m or e in for m a t ion a b ou tth e ADS circuit simula tor net list forma t, including sca le factors, subcircuits,va riables a nd equa tions, refer t o ADS Simula tor Input S ynt a x in th e U sin g Cir cui t Simulators manua l.
Example:
model Npn4 MextramBJT \NPN=yes Ibf=3e-15 Qb0=1e-13
Notes/Equations
For RFDE Users I n for ma t i on a b ou t t h is m od el m us t be pr ov id ed in a m odel le; refert o Netlist Forma t on pa ge 2-100 .
1. This model (version 503) supplies va lues for B J T_NP N, B J T_P NP, B J T4_NP N,
a nd B J T4_P NP devices.2. For t he ME XTRAM bipola r t ra nsist or model, model equ a t ions a re explicit
functions of interna l bran ch volta ges; th erefore, no interna l qua nt ities aresolved itera tively. Tra nsistor pa ra meters a re discussed w here releva nt ; mostpara meters ca n be extra cted from capa cita nce, DC, a nd f T measurements, a nda re process a nd t ra nsist or la yout (geomet ry) dependent . Init ia l/predict ivepa r a m et er s et s ca n be ca l cu la t e d fr om pr oces s a n d la y ou t d a t a . Th is m od el d oes
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MEXTRAM_Model (MEXTRAM Model) 2-101
not cont a in extensive geomet rica l or process sca ling ru les (only m ult iplica t ionfa ctors to put t ra nsist ors in pa ra llel). The ext ended modeling of reversebeh a vior, t h e in cr ea s e of t h e a v a la n ch e cu rr en t w h en t h e cu rr en t d en sit y in t h eepila yer exceeds the doping level, a nd t he dist ribut ed high-frequ ency effect a reoptiona l a nd can be switched on by sett ing a gs. B esides th e NPN t ra nsistor aP NP model description is a va ila ble, both w ith a nd w ithout substra te (discretetr a nsistors) modeling.
3. Th e P h ilips m od el u ses t h e M U LT p a r a m et er a s a s ca l in g fa ct or. I n AD S , MU LTis im plem en t ed a s AR E A, w h ich h a s t h e s a m e m a t h em a t ica l effect . B e ca u se t h eP hilips model uses MU LT a s t he mu ltiplier/scaling, t he va lues a re inmea surements su ch a s Amps. However, in ADS , units of ar ea a re m 2, so t heyare lis ted accord ing ly. This accounts for d ifferences in repor t ing of some unit s inth e P hillips document a tion.
4. U se AllPa ra ms w ith a Da ta AccessComponent t o specify le-based pa ra meters(refer t o Da ta AccessComponent in C ha pter 5 of t he I ntr oduction to Cir cui t Components ma nua l). Note t ha t model pa ra meters tha t a re explici t ly speci edta ke precedence over t hose speci ed via AllPa ra ms.
Survey of Modeled Effects
Tempera t ure effect s
Cha rge s t or age effect s
Subs t r a t e ef fect s and pa ra s it ic PNP
High-inject ion effects
B uil t -in elect r ic eld in base region
B ias -dependent Ea r ly effect
Low -level non-idea l base currents
H a r d a n d q ua s i-s a t ur a t ion
Wea k a va la n ch e Hot carrier effects in t he collector epilayer
E xplici t modeling of ina ctive regions
Split base-collector depletion capa cita nce
Current crow ding and conductivity modulat ion for base resista nce
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First -order a pproxima tion of distributed high-frequency effect s in theint rinsic bas e (high -frequ ency curr ent crow ding a nd excess pha se-shift ).
Active Transistor
Main Current
In t he ME XTRAM model t he Moll-Ross relat ion is used t o t a ke into a ccount t hedepletion a nd diffusion cha rges:
(2-1
(2-2
(2-3
The deplet ion charges are represen ted by Qt e a nd Qt c. The ca lcu la t ion of the d iffusioncha rges Qb e and Qb c is ba sed directly on t he solution of t he differentia l equa tion forthe ma jori ty carriers in the neutra l base region a nd relat es the cha rges to theinject ed minorit y ca rrier concentr a t ions a t t he emit t er (no) a nd collector edges (nb).These concent ra t ions, in tur n, depend on th e int erna l junct ion volt a ges Vb 2e1 a ndVb 2c by considering t he P -N product a t both junctions. In th is w a y h igh injection,bias-dependent current ga in, a current - dependent tr a nsit t ime, a nd t he effect of the
built-in electr ic eld a re included. The idea l forw a rd a nd reverse current a re givenby:
(2-4
w here V t is the th ermal volta ge.
The pa ra meters a re:
Is = extra cted from G ummel plot a t low V be
Qb0 = integra l of ba se cha rge extr a cted from reverse Ea rly effectXcjc = fra ction of Cjc underneat h emitt er; obta ined from forwa rd E a rly effect
Ik = from ga in fa ll-off: only one knee curr ent
E ta = built -in eld in th e base due to the doping pro le. This par a meter isnorma lly betw een 3 a nd 6. It is dif cult t o obta in from direct m easur ements, an dha s a w eak in uence on calculat ed currents a nd charges.
I n I f I r ( )
1 Q t e Q t c Q b e Q b c + + +( ) / Q b 0+----------------------------------------------------------------------------------------=
Q b e f 1 n o ( )=
Q b c
f 2 n
b ( )=
I f I r I s exp Vb 2e 1 V t ( ) exp Vb 2c 2 V t ( )( )=
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Ideal Forward Base Current
Th e id ea l for w a rd ba s e cu rr en t is d e n ed in t h e u su a l w a y. Th e t ot a l ba s e cu rr en t h a sa bot t om a n d a s id ew a l l con t ribu t ion . Th e sepa r a t i on is g iven by t h e fa ct or XI b 1. Thisfa ct or ca n be d et er min ed by a n a ly zin g t h e m a xim um cu rr en t ga in of t r a nsist or s w it h
different geometries.
(2-5
The pa ra meters a re:
B f = idea l forwa rd current ga in
Xibi = fra ct ion of idea l base current t ha t belongs t o th e sidewa ll
Non-Ideal Forward Base Current
The non-idea l bas e curr ent origina t es from t he recombina t ion in t he deplet edbase-emitter region:
(2-6
Form ula t ion of the non-idea l ba se curr ent differs from t he G um mel-P oon m odel. TheME XTRAM form ula t ion is less exible tha n t he G umm el-P oon m odel. Thefor mu la t i on is t h e s a m e w h en in t h e ME XTR AM m od el Vl
fi s smal l (
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d iffu sion volt a g e. Th e m a xim um ca p a cit a n ce is d et er m in ed by t h e v a lu e of K a n d t h egra ding coef cient P e. The va lue of K is a model const a nt a nd is t a ken equa l to 0.01.When Pe= 0.4, th e ma ximum is a pproxima tely thr ee times th e ca pacita nce a t zerobias. The para meters a re:
Cjc = zone bias ba se-emitt er depletion ca pa cita nceVde = ba se-emitt er diffusion volta ge
P e = ba se-emitt er gra ding coef cient
Base-Collector Depletion Charge
The base-collector depletion capacitance underneath the emitter Qtc, takes intoa ccount th e nite th ickness of the epilayer a nd current modula t ion:
(2-8
(2-9
The fun ction f(Vc 1c2) equa ls one when Ic 1c2 = Vc1c2 = 0, a nd becomes zero w hen th ecurrent densit y in t he epila yer exceeds th e doping level (Vc 1c2 > Ih c Rcv). The
para meters a re:Cjc = zero bia s ba se-collect or d epletion capa cit a nce
Xcjc = pa rt of Cjc undernea th emitt er
Vdc = ba se-collect or diffusion volt a ge
P c = ba se-collect or gr a ding coef cient
Xp = depletion la yer t hickness a t zero bias divided by epila yer t hickness
Mc = collector current modula t ion coef cient (0.3 < m c < 0.5)C jc , P c a nd Xp is obta ined from C V mea surements; Vdc must be extra cted from thequa si-sa tu ra t ion regime; Xcjc is obta ined from t he forw a rd E a rly-effect.
Neutral Base and Emitter Diffusion Charge
The neut ra l bas e-emit t er diffusion cha rge (Q n ) is given by:
C t c X cj c C j c 1 X p ( ) f V c
1c
2( )
1 V b 2 c 2( ) V d c ( ) ( )P c
------------------------------------------------------------------- X p +
=
f V c 1 c 2( ) 1V c 1c 2
V c 1c 2 I h c R cv +-------------------------------------------------
M c
=
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(2-10
Th e ch a rge Qn 0 is ca l cu la t e d fr om t h e t r a n sit t im e Ta u n e a n d M t a u. Th e pa r a m et er s
(extra cted from th e ma ximum va lue of th e cut -off frequency, f T) a re:Ta une = minimum dela y t ime of neutra l an d emitter cha rge
Mta u = non-idea lity factor of the neutra l a nd emitt er cha rge; in m ost ca sesM t a u = 1
Base-Charge Partitioning
Dist ributed h igh-frequency effect s a re modeled, in rst order a pproxima tion, bot h inla tera l di rect ion (current crowding) a nd in ver t ica l di rect ion (excess phase-shif t ). The
distribut ed effects a re a n optiona l fea tu re of th e MEXTRAM model, a nd ca n besw itched on a nd off by a g E xphi (on: Exphi - 1; off: Exphi = 0). In ver t ica l direct ion(excess phase-shif t ), base cha rge par t i t ioning is used; for s implici ty, i t i s implementedfor forwa rd ba se cha rge (Qb e) a nd low -level inject ion only. No ad dit iona l pa ra met ers.
(2-11)
(2-12
Modeling of Epilayer Current Charges
The epila yer resist a nce depends on t he supplied collect or volta ge a nd curr ent ,imposed prima rily by ba se-emitt er volta ge. The effective resista nce of th e epila yer isstr ongly volta ge- a nd current -dependent beca use:
In t he forwa rd mode of opera tion, the interna l ba se cha rge junction volta ge(Vb 2c2) ma y become forw a rd-bia sed a t h igh collect or current s(quas i-s a tu r a t ion ). When th is happens, t he r eg ion in the collector nea r the baseis in ject ed by ca r r ier s fr om t h e ba s e, ca u sin g t h e r eg ion t o becom e low r esis t ive.
In th e reverse mode of opera tion, both t he externa l a nd internal base cha rgejunction volta ges are forw a rd bia sed, ooding th e whole epita xial lay er wit hcar riers, wh ich cau ses it t o become low resist ive.
Th e cu rr en t ow in t h e h ig hly -r es ist ive r eg ion is oh mic if t h e ca r r ier d en sit y (n )is low ( ), a n d spa ce-ch a rge-lim it ed if t h e ca r rier den sit y exceed s t h e
doping level ( ).
Q n Q n 0V b 2e 1
M t a u V t -----------------------------
exp 1 =
Q 'b e 1 q c E t a ( )( ) Q b e =
Q 'b c Q b c q c + E t a ( ) Q b e =
n N ep i
N ep i
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Current spreading in the epila yer reduces th e resista nce a nd is of specialimport a nce if t he carr ier d ensity exceeds N epi . In t he la t t er ca se, the ca rriersmove w ith t he sa tu ra ted drift velocity, V sa t (hot-car rier current - ow ).
A compa ct m oda l form ula t ion of qu a si-sa t ura t ion is given by Kull et a l [1]. The Kull
model is va lid on ly if t he collector cu r ren t densit y is below the cr it ica l cu r ren t densit y(J hc) for h ot car riers:
(2-13
The Kull form ula t ion ha s served a s a ba sis for t he epilay er model in ME XTRAM.
Collector Resistance Model
The Kull model is based on char ge neutra lity (p + N epi n) a nd gives the current
th rough t he epilayer (Ic 1c2) a s a function of the int erna l a nd externa l b.c. junctionvolt a ge. These volta ges a re given by t he solution vect or of t he circuit s imula t or. The na l equa tions of th e Kull formula tion [1] a re:
(2-14
(2-15
(2-16
(2-17
(2-18
Voltage source (E c) ta kes int o account t he decrea se in resista nce due to ca rriers
inject ed from t he ba se into th e collect or epilay er. If both junctions a re reverse bia sed(Vb 2c1 - Vd c a nd Vb 2c2 - Vd c a re nega t ive), E c is zero a nd w e have a simple const a ntr es is t ance (Rcv). Because of th is, t h is model does not t a ke in to account the hot -ca r r ierbehavior (ca rriers m oving w ith th e sa tu ra ted drift-velocity) in t he lightly-dopedcollect or epilay er. The model is valid if t he t ra nsist or opera t es in th e reverse mode(reverse-bia sed b.e. junct ion, forwa rd-bia sed b.c. junct ion). Then the ent i re epi layer is lled w ith ca rriers a nd a space-cha rge region does not exist. The derivat ion of the
J h c q N ep i v sa t =
I c 1c 2E c V b 2c 2 V b 2c 1+
R cv -----------------------------------------------------=
E c V t K 0 K w K 0 1+
K w 1+------------------
ln=
K 0 1 4 V b 2c 2 V d c ( ) V t [ ]exp+=
K w 1 4 V b 2c 1 V d c ( ) V t [ ]exp+=
V t k T
q ----=
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MEXTRAM epilayer r es is t ance model is published in de G raa ff and Kloos t erman [2].In t he end, t he follow ing equa t ions a re found:
(2-19
(2-20
(2-21
Wher e X i/W epi is t he t hickness of t he injected region of t he epila yer.
Substitution of equations (2-19 ) and (2-20 ) into equa tion (2-21 ) gives a cubicequa t ion . The epi layer cur ren t (Ic 1c2) is ca l cu la t ed by solv ing the cubic equa t i on . Thecomplex ca lcula tion ca n be done w ith rea l va ria bles. Summ a rizing, th e epila yerresista nce model ta kes into account :
Ohmic current ow a t low current densit ies
D ecr ea s e in r esist a n ce d ue t o ca r rier s in ject ed fr om t h e ba s e if on ly t h e in t er na lbase-collector junction is forward biased (quasi-saturation), and if both theinte rna l and exte rna l base-collector junct ions are forwa rd biased (reverse modeof opera t ion)
Space cha rge l imi ted current ow a t h igh current densit ies
Cur ren t spread ing in the epilayer
The model para meters a re:
(2-22
(2-23
(2-24
X i W ep i -------------
E c I c 1c 2 R cv -------------------------------=
I l ow I hc V c 1c 2
V c 1c 2 I h c R cv 1 X i W ep i ( )+----------------------------------------------------------------------------------------------=
I c 1c 2 I l ow S f +( ) V c 1c 2 I l ow R cv 1 X i W ep i ( )
S cr cv 1 X i W ep i ( )2
------------------------------------------------------------------------------------------------=
I h c q N ep i A em v sa t 1 S f l +
cf ------------------=
R cv W ep i
q N ep i A em ---------------------------------------------------
cf 1 S f l +------------------=
S cr cv W 2ep i 2 v sa t A em -----------------------------------------------
cf 1 S f h +--------------------=
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(2-25
(2-26
where
, (2-27
, (2-28
l = the spreading a ngle at low current levels (Ic 1c2 < Ihc)h = the sprea ding an gle a t high current levels Ic 1c2 > Ihc)cf = the fra ction of Ic1c2 ow ing through the emitt er oor a reaLe = the length of the emitter str ipe.
The turnover f rom equa t ions (2-20 ) a nd (2-21 ) in t h e for w a rd m od e t o eq ua t ion (2-14in t he reverse mode does not give discont inuities in th e rst a nd second d erivat ive.The th ird der iva t ive is d is con t inuous. Pa rameter S fh depends on t r ans is t or geomet rya nd t he decrea se in ga in a nd cutoff frequency will be affected by th is pa ra meter. SF 1is included in Rcv a nd Ih c, an d not needed a s a sepa ra te par a meter. In most ca ses,Vdc is ca l cu la t ed d ir ect ly from the doping level. Rcv, Ihc, and Scrcv a re ext r act ed fromth e qua si-sa tu ra tion regime a t low va lues of Vce.
Diffusion Charge of the Epilayer
The diffusion cha rge of th e epilay er ca n be ea sily derived by a pplying t he Moll-Rossrela t ion t o t he ba se + collector region (from node e 1 t o node c 1):
(2-29
Subtracting equation (2-1 ), t he expression for Q epi becomes:
(2-30
V d c V t N ep i n i ( )2
ln=
S f h 2
3---
h ( )tan W
ep i 1
H e ------- 1
L e ------+
=
Aem H e L e =
S f l h ( )tan W ep i 1
H e ------- 1
L e ------+
=
I n I c 1c 2I s V b 2e 1 V t ( ) V b 2c 1 V t ( )expexp{ }
1Q
t e Q
t c Q
be Q
b c Q
ep i + + + +
Q b 0-----------------------------------------------------------------------------+
-------------------------------------------------------------------------------------------------------------= =
Q ep i I s Q b 0 V b 2c 1 V t ( ) V b 2c 1 V t ( )expexp
I c 1c 2------------------------------------------------------------------------------------------=
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In t he tra nsition from forw a rd t o reverse mode, Ic 1c2 passes zero a nd num erica lproblems can be expected. Substitution of equation (2-14 ) into equa tion (2-29 ) lea dsin th e ca se wh ere Vb 2c2 Vb 2c1 t o th e follow ing expression for Q epi :
(2-31
(2-32
(2-33
Avalanche Multiplication ModelDu e to th e high-elect ric eld in t he spa ce-cha rge region, a va la nche current s a regenera ted; t his genera tion str ongly depends on t he ma ximum electr ic eld. Thema ximum electr ic eld ma y reside a t t he base cha rge junction or at th e buried lay er.The genera tion of a va la nche current in Kloosterm a n a nd de G ra a ff [3] is only afunction of th e electr ic eld a t th e interna l ba se cha rge junction. Therefore, theva lidity of th is model is restr ict ed to low curr ent levels (Ic 1c2
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(2-34
B eca use only wea k ava la nche mult iplica tion is considered, th e genera ted a va lan checurrent is proport iona l wit h t he ma in current (I n ):
(2-35
Xd = th e bounda ry of the spa ce-cha rge region.
To ca lcula t e th e a va la nche current , we must eva lua te th e integra l of equa tion (2-34 )in the space-cha rge reg ion . Th is in t eg ra l is det ermined by the max imum elect r ic eld .We ma ke a suit a ble a pproxima tion a round th e ma ximum electr ic eld:
= th e point w here th e extr a pola ted electr ic- eld is zero.Then t he genera ted a va la nche current becomes:
The m a ximum electric eld (E m ), t he depletion la yer t hickness (X d), an d th eint ersect ion point ( ) a re ca lcula ted using th e cha rge model of Q t c a nd t he collect orresista nce model. The model pa ra meters a re:
Avl = obt a ined from th e decrea se of I b a t h igh Vcb a nd low Ic valuesSfh = equa t ion (2-26 )S fl = equa t ion (2-27 )E = used in extended ava lanche model only
P n n b n E
--------- exp=
I g I n n x 0=x X d=
b n E x ( )--------------- d x exp=
E x ( ) E m 1 x --- E m
1 x +-------------------=
I g I n ------
n b n ------- E m
b n
E m --------- b n
E m --------- 1
X d --------+
expexp =
A v l b n 2