nonlinear devices

8/10/2019 Nonlinear Devices

1/603


2/603


3/603


4/603


5/603


6/603


7/603


8/603


9/603


10/603


11/603


12/603


13/603


14/603


15/603


16/603


17/603


18/603


19/603


20/603


21/603


22/603


23/603


24/603


25/603


26/603


27/603


28/603


29/603


30/603


31/603


32/603


33/603


34/603


35/603


36/603


37/603


38/603


39/603


40/603


41/603


42/603


43/603


44/603


45/603


46/603


47/603


48/603


49/603


50/603


51/603


52/603


53/603


54/603


55/603


56/603


57/603


58/603


59/603


60/603


61/603


62/603


63/603


64/603


65/603


66/603


67/603


68/603


69/603


70/603


71/603


72/603


73/603


74/603


75/603


76/603


77/603


78/603


79/603


80/603


81/603


82/603


83/603


84/603


85/603


86/603


87/603


88/603


89/603


90/603


91/603


92/603


93/603


94/603


95/603


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.


97/603

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.




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 + + +=


99/603


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 =


111/603


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 -------------- --------------------=




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 ( )=


113/603

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


114/6032-68 BJT_NPN, BJT_PNP (Bipolar Junction Transistors NPN, PNP)


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


115/603


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


Ic Collector current amperesIs Substrate current amperes






fTreal Unity current gain frequency, full formula hertzfTappr Unity current gain frequency, approximate

formula gm/(2*PI*C)hertz



Rmu Reedback resistance 1/(dIbe/dVbc) ohms


Ro Output resistance 1/(dIbe/dVbc - dIce/dVbc) ohms

Rcv Collector resistance ohmsCpi Base-emitter capacitance farads



Ccs Internal collector-substrate capacitance farads

Cbs Internal base-substrate capacitance farads




116/6032-70 BJT_NPN, BJT_PNP (Bipolar Junction Transistors NPN, PNP)


Cxs External base-substrate capacitance farads



Ta ble 2-4. DC Opera ting P oint I nforma tionModel = ME XTRAM_Model (503)


Ic Collector current amperesIb Base 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


Gc1s (dIc1s/dVc1s) siemens

dIc2e1_dVb2c2 (dIc2e1/dVb2c2) siemens

dIc2e1_dVb2c1 (dIc2e1/dVb2c1) siemens

dIc1c2_dVb2e1 (dIc1c2/dVb2e1) siemens

dIc1c2_dVb2c2 (dIc1c2/dVb2c2) siemens


dIb2c2_dVb2e1 (dIb2c2/dVb2e1) siemens




117/603


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


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


Ta ble 2-4. DC Opera ting P oint Informa tion (cont inued)Model = ME XTRAM_Model (503)



118/6032-72 BJT4_NPN, BJT4_PNP (Bipolar Junction Transistors w/Substrate Terminal, NPN, PNP)


BJT4_NPN, BJT4_PNP (Bipolar Junction Transistors w/SubstrateTerminal, NPN, PNP)

Symbol


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


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




119/603

BJT4_NPN, BJT4_PNP (Bipolar Junction Transistors w/Substrate Terminal, NPN, PNP) 2-73

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 .











Rmu Feedback resistance 1/(dIbe/dVbc) ohms

Rx Base resistance ohmsRo Output resistance 1/(dIbe/dVbc - dIce/dVbc) ohms

Cpi Base-emitter capacitance farads



Ccs Substrate capacitance farads


Ft Unity current gain frequency hertzVbe Base-emitter voltage volts















fTreal Unity current gain frequency, full formula hertz

fTappr Unity current gain frequency, approximateformula gm/(2*PI*C)

hertz



Rmu Reedback resistance 1/(dIbe/dVbc) ohms


Ro Output resistance 1/(dIbe/dVbc - dIce/dVbc) ohms

Rcv Collector resistance ohmsCpi Base-emitter 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




121/603

BJT4_NPN, BJT4_PNP (Bipolar Junction Transistors w/Substrate Terminal, NPN, PNP) 2-75

Ta ble 2-7. DC Opera ting P oint I nforma tionModel = ME XTRAM_Model (503)







dIc2e1_dVb2e1 (dIc2e1/dVb2e1) siemens


Gb1b2 (dIb1b2/dVb1b2) siemens


Gbc1 (dIbc1/dVbc1) siemens


Cb2e1 (dIb2e1/dVb2e1) siemens

Cb2c2 (dIb2c2/dVb2c2) siemens


Gc1s (dIc1s/dVc1s) siemens

dIc2e1_dVb2c2 (dIc2e1/dVb2c2) siemensdIc2e1_dVb2c1 (dIc2e1/dVb2c1) siemens

dIc1c2_dVb2e1 (dIc1c2/dVb2e1) 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





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



dQc2b2_dVb2e1 (dQc2b2/dVb2e1) farads

dQb2c2_dVb2c1 (dQb2c2/dVb2c1) farads

dQb1b2_dVb2e1 (dQb1b2/dVb2e1) farads

dQb1e1_dVb2e1 (dQb1e1/dVb2e1) faradsVbe Base-emitter voltage volts



Ta ble 2-7. DC Opera ting P oint Informa tion (cont inued)Model = ME XTRAM_Model (503)



123/603

EE_BJT2_Model (EEsof Bipolar Transistor Model) 2-77

EE_BJT2_Model (EEsof Bipolar Transistor Model)

Symbol


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.


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


124/6032-78 EE_BJT2_Model (EEsof Bipolar Transistor Model)


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




125/603


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






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 ---------------------------=


127/603


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( )++( )=




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 +=


129/603


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

-----------=




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 =


131/603


Equivalent Circuit

Intrinsic Model(NPN or PNP)

+

-Vbe

+

-Vbc

Cbc

Cbe

Ibc

Ibe

Ice

IcfIcr

Ib

Ic

Ie

Intrinsic Model

+

-

Vbc

+

-

Vbe


132/6032-86 HICUM_Model (Bipolar Transistor Model)


HICUM_Model (Bipolar Transistor Model)

Symbol



Parameters


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


133/603

HICUM_Model (Bipolar Transistor Model) 2-87

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





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



135/603


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






Netlist Format


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



wVbcfwd base-collector forward bias (warning) V

wIbmax maximum base current (warning) A



AllParams name of DataAccessComponent for le-based model parametervalues



137/603


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




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.


139/603


Equivalent Circuit


140/6032-94 HICUM_NPN, HICUM_PNP (HICUM Bipolar Transistors, NPN, PNP)


HICUM_NPN, HICUM_PNP (HICUM Bipolar Transistors, NPN, PNP)

Symbol


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


Selfheating turn on the self-heating effect on this device: yes, no (refer to note 3 )



141/603

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


Ic Collector current amperesIb Base current amperes




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


142/6032-96 HICUM_NPN, HICUM_PNP (HICUM Bipolar Transistors, NPN, PNP)



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



Ta ble 2-8. DC Opera ting P oint I nforma tion



143/603

MEXTRAM_Model (MEXTRAM Model) 2-97

MEXTRAM_Model (MEXTRAM Model)

Symbol



Parameters

Model par a meters must be speci ed in S I unit s.


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


144/6032-98 MEXTRAM_Model (MEXTRAM Model)


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



145/603


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




wVbcfwd base-collector forward bias (warning) VwIbmax maximum base current (warning) A



AllParams name of DataAccessComponent for le-based modelparameter values





Netlist Format


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


147/603


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




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 ( )( )=


149/603


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 (




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

=


151/603


(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




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 ----=


153/603


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 +--------------------=




(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------------------------------------------------------------------------------------------=


155/603


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




(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

nonlinear devices

Documents