a solution to the q p0 issue in hicum parameter extraction · 2019. 12. 13. · 32 th bipak...

32th BipAK Workshop at STMictorelectronics, Crolles,

France, November 14&15 2019

A Solution to the Qp0 Issue in

Hicum Parameter Extraction

Zoltan Huszka

31. October 2019

Letter Session

A Solution to the Qp0 Issue in Hicum Parameter Extraction

Outline

Confidential © ams AG

• overview of the transfer current formulations

• the qp0 problem in Hicum/L2

• linking the Hicum revisions to the SGP model

• the master function M(Vbiei,Vbici)

• The c10 normalized alternative

• extraction strategy

• extraction of is and nf in SGP

• determination of the normalized low-medium bias parameters of Hicum

• return to the full Hicum model by de-normalization

• extracting qp0,hfe,hfc

• summary

• references


HBT/BJT models

The SPICE saturation current parameter occurs both in junction diodes and bipolar transistors. It is a fundamental quantity with a clear physical meaning. It is well

understandable because it can be directly related to measurements.

The transfer current of the classical (SPICE)Gummel-Poon or (S)GP bipolar transistor

model reads

+++

−−

−=

−

⋅⋅=

−

⋅⋅=

ikr

I

ikf

I

vaf

V

var

V

III

Vnr

VisI

Vnf

VisI

RF

bicibiei

RFT

T

biciR

T

bieiF

412

1

2

1

1

)(

1exp;1exp

(1)



The highly advanced Hicum/L2 model defines the transfer current as

TrBfCffcfEfeffjCijCijEijEip

T

biei

T

biei

TQQQhQhQhQhQhQ

V

V

Vmcf

Vc

I,000

10 expexp

+∆++++++

−

⋅= (2)

The familiar is parameter is lost. This created a remarkable confusion in the modeling

community which has not settled even today. Moreover the exact meaning and significance of the c10 and Qp0 parameters is not so clear as that of is. Foundries claim

that parameter extraction is a nightmare [1]. In response (partly) to these complaints the simplified model Hicum/L0 has been offered

QfE

Tf

CK

Tf

Qfh

Tf

CKr

Tr

CKf

Tf

Ef

jCid

Er

jEid

T

biei

T

biei

T

I

i

I

i

I

iw

I

i

I

i

V

v

V

v

Vmcr

V

Vmcf

Vis

I

++++++

⋅−

⋅=

21

expexp

(3)

HBT/BJT models cont’dA Solution to the Qp0 Issue in Hicum Parameter Extraction

Linking the Hicum models to SGP

The main objective of this document is to work around the over-determined nature of

Hicum/L2 in the low-medium bias region during extraction, illuminate the significance of the zero-bias hole charge, and to propose a direct extraction method for this parameter.

For Vbiei<<VT along the Vbici=0 branch (1) keeps to

T

biei

T

bieiT

V

V

nf

is

Vnf

VisI →

−

⋅= 1exp

Similarly, (2) is approximating

T

biei

pp

T

biei

TV

V

Qmcf

c

Q

Vmcf

Vc

I0

10

0

10 1exp

⋅→

−

⋅=

The two models describe IT of the same transistor around the origin if and only if

nf

mcfis

Q

cis

p

H ==0

102

Likewise for Hicum/L0

nf

mcfisisH =0



The Manual specifies mcf as the „non-ideality factor (for III-V HBTs)”. Restricting to the case of Si HBT/BJTs, mcf=1 can be assumed resulting in isH2=isH0=isH with

nf

isisH =

With the normalizationnomp

xy

xyQ

hh

0

=

the original temperature dependences of the weight functions are inherited by their

normalized counterparts. Introducing the master function

1

expexp

),( −

−

=T

T

bici

T

bieiH

bicibieiI

V

V

V

Vis

VVM

),()1(1

00000

0

000

bicibiei

qp

fhchc

nompqp

fhchc

fc

qp

fE

fe

qp

f

f

qp

jCi

jCi

qp

jEi

jEi VVMQf

Q

Qfh

Qh

Qh

Qh

Qh =

Θ

∆−+

Θ

∆+

Θ+

Θ+

Θ+

Θ

ττ

the normalized HL2 charge reads (last but one term may be modified by IT spreading)

(6)

(4)

(5)


Linking the Hicum models to SGP, cont’d




The uncertainity of the Qp0 parameter

In expression (6) the zero-bias hole charge has been split into its nominal value and

temperature dependence

In the forward active mode ITf=IT and QrT could be omitted.

Qp0 is acting only on the last - highest bias - term. Observe that selecting fthc=1 the additional base charge vanishes and Qp0 becomes

undefined. The same situation occurred if the GICCR master equation (4.84, 4.87 of [2]) had been strictly adopted and ∆QBf had also been given a weight factor. Such cases the reconstruction of the original Hicum parameters by arbitrary Qp0 gave the same

modeling results. (Q0=(1+fdqr0)Qp0 used in Rbi is a different model parameter.)

These two extremities suggest that the parameter has a large latitude. The non-uniqueness or „instability” was already verified for a large range of Qp0 values in [3].

000 qpnompp QQ Θ⋅= (7)



The c10 normalized alternative

Normalizing (2) by c10 and denoting

one gets, as an alternative to (6)10

~;

expexp

),(~

c

hh

I

V

V

V

V

VVMxy

xy

T

T

bici

T

biei

bicibiei =

−

=

)0,(~~~1

00 bieiffjEijEi

H

VMQhQhis

=++

The saturation current can be obtained by regression. However parameter vgb which

can be directly extracted from (4) is not available for the 2nd term. Several isH(T)=>vgb=>isH(T) iterations are needed to stabilize its value. Other parameters

of Qjei also vary during AC (FT) refinements implying further cycles. Anyway this proposal is self consistent in that it does not need the import of Qp0 as opposed to

practically all previous papers e.g. [4, 5, 6, 7]. W.r.t. to the above inconveniences and to the observations on slide#13 however, isH for (5) will be computed from (4) in this work.

),(~)1(~~~~~1

1000 bicibiei

fhchc

fhchcfcfEfeffjCijCijEijEiH

VVMc

QfQfhQhQhQhQh

is=

∆−+∆+++++

ττ

On the Vbici=0 branch at low-medium biases (8)



Extraction strategy

1. determination of is(T),nf and hence, isH(T),vgb

2. extraction of hjCi

3. extraction of hjEi,ahjEi and hf0

4. define temperature coefficients

5. de-normalize parameters and return to the full Hicum

6. optimize qp0,hfe,hfc; tempcos for the two weight factors

7. verify extractions and return to the AC cycle if needed

−

∆⋅= 1exp_0

zetavgbe

nomT

gBEjEitjEi

T

T

V

Vhh

hjei

nom

hjEithjEiT

Taa

ζ

⋅=_

−

∆⋅= 1exp0_0

nomT

gBE

ftfT

T

V

Vhh

−

−⋅= 1

,exp,_,

nomT

cfetcfeT

T

V

cvgevgbhh

−

=

T

T

V

vgb

T

Tcc nom

Tnom

zetact

nom

nom 1exp1010

Temperature coefficients:

−⋅=

zei

ptpvdei

tvdeiqq

_20_0

Prerequisite: AC and resistance parameters are known with reasonable accuracy



Extraction of the SGP saturation current

Conventionally the high current term in the denominator of (1) is taken unity, providing

vbevar

isis

Vnf

vbe

i

T

C −=

−

⋅1exp

Both is and var are affected in the first order by the approximation above. A more

refined regression formula is proposed below for the Hicum application. Reformulations

show that the first order high current distortion has been shifted to the last term allowing to use the more robust extraction formula in the forward direction at vbc=0

(9)

)(var

1412

1

2

1)11( RF

RFT ii

vaf

vbcvbe

ikr

i

ikf

ii −⋅

−−=

++++−⋅

+++

+

⋅−−⋅

−−=

ikr

i

ikf

i

ikr

i

ikf

i

iiivaf

vbcvbei

RF

RF

TRFT

412

1

2

1)(

var1

C

T

C iikf

isvbe

var

isis

Vnf

vbe

i−−=

+

⋅1exp

Only is is retained from the result, var and ikf will be discarded.



equation

3varRegressionb1=w*a1b2=w*a2b3=w*a3b=w*ac011=sum(b1*b1)c012=sum(b1*b2)c013=sum(b1*b3)d01=sum(b1*b)c021=c012c022=sum(b2*b2)c023=sum(b2*b3)d02=sum(b2*b)c031=c013c032=c023c033=sum(b3*b3)d03=sum(b3*b)m21=c021/c011c122=c022-m21*c012c123=c023-m21*c013d12=d02-m21*d01m31=c031/c011c132=c032-m31*c012c133=c033-m31*c013d13=d03-m31*d01m32=if((sum(abs(a2))>0),c132/c122,0)c233=c133-m32*c123d23=d13-m32*d12x3=(if((sum(abs(a3))>0),d23/c233,0))x2=(if((sum(abs(a2))>0),(d12-x3*c123)/c122,0))x1=((d01-x2*c012-x3*c013)/c011)asim=x1*a1+x2*a2+x3*a3bsim=x1*b1+x2*b2+x3*b3delt=abs(bsim-b)err_regr=sum(delt*delt)

equation

SGPRegression_outis=x1var=x1/x2Ikf=x1/x3icnsim=asim/is

R=1 k

I=1 mA

dc simulation

DC1

Parametersweep

SW1Sim=DC1Param=VbevType=list

equation

ConditioningU=1+Vbev-Vbevvbesel=range(Vbev,vbe_lo,vbe_hi)ic=Ic_p27ic_Vbe=U*icicsel=range(ic_Vbe,vbe_lo,vbe_hi)iicn=(exp(Vbev/Vt/nf)-exp(Vbc[1]/Vt))/ic_Vbeiicnsel=range(iicn,vbe_lo,vbe_hi)

Optimization

Nelder-Mead|2000|1e-5|0.1|1nf=0.9...1...1.2 linearerr_regr=1 MIN

RegressionSim=SW1

equation

SGPRegression_ina1=1+vbesel-vbesela2=-vbesela3=-icsela=1/iicnselw=1

equation

fgstemp_st1008Temp=[-40,-20,0,27,50,75,100,125]

equation

results_st1008is_GP=[7.847e-017]

equation

Limitsvbe_lo=0.5vbe_hi=0.75

equation

Misctemp=Temp[4]Tk=temp-T0KVt=kB*Tk/qelectronTK=Temp-T0KTnom=TK[4]Vtnom=kB*Tnom/qelectron

0.4 0.5 0.6 0.7 0.8 0.9 10

0.2

0.4

0.6

0.8

1

Vbe [V]

1/iicn/is

1/iicn/isregression

1/iicn/isregression

number

1

temp

27

is

7.847e-17

nf.opt

1.0007

vbe_lo

0.5

vbe_hi

0.75

err_regr

1.02e-37

REGRESSION

dummy

DATA

The QucsStudio is extraction worksheet

The regression engine is

started by assigning a1,a2,a3 to the RHS coefficients of (8) and a

to the LHS. Due to the small variation of the

LHS function, unit weights (w=1) have

been set. The unknowns

are read from the output variables x1,x2,x3.

is is recorded in the is_GP vector for further

use.



The is extraction worksheet, cont’d

The data is contained in the equation component fgstemp_st1008. Presently the current

Ic_p27 (p27:+27C=tnom) is invoked from the block. Range selection in QucsStudio requires a dependence from the sweep variable Vbev. It is achieved by multiplying it by

the unit vector U=1+Vbev-Vbev. The regression block is explained in [8].

Hicum model parameters zetact and vgb

can be directly extracted from the obtained

temperature results multiplied by the

temperature dependence function (7) referred to also as tc_qp0.

)(0 TqpΘ

-0.3 -0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 0.253e-221e-21

1e-20

1e-19

1e-18

1e-17

1e-16

1e-15

1e-14

1e-13

1e-12

1-Tnom/T

isH

*tc-q

p0

[A

]

erro

r

number

1

isHtcnom

7.985e-17

zetact

0.5371

vgb

1.057



Verification and comparision of the isH identifications

For testing the accuracy of isH extraction D. Celi (STM) prepared and ELDO synthetic

data using a Hicum/L2 model with c10/qp0=30.78aA. The SGP extraction range of 0.25V wide was glided along the Vbe axis to see the effect on the robustness of the result.

number

1

temp

25

is

3.058e-17

nf.opt

1.0173

vbe_lo

0.2

vbe_hi

0.45

err_regr

7.61e-39

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.3

0.6

0.9

1.2

Vbe [V]

1/iic

n/is

1/iicn/isregression

1/iicn/isregression

number

1

temp

25

is

3.003e-17

nf.opt

1.0077

vbe_lo

0.4

vbe_hi

0.65

err_regr

8.33e-41

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.3

0.6

0.9

1.2

Vbe [V]

1/iic

n/is

1/iicn/isregression

1/iicn/isregression

30.03 (2.44%)30.28 (1.62%)30.46 (1.04%)30.49 (0.94%)30.58 (0.65%)is [aA}

0.400.350.300.250.2vbe_lo [V]

SGP: isH=7.847e-17

isH identification in SGP is quite robust. isH from (8) differs by 27.9% over the range on slide#19 and the result is sensitive to interval selection. ahjei values are also different. (4) shall be retained.

number

1

temp

27

isH

1.039e-16

hjei

2.078e+30

ahjei.opt

5.379

hf0

2.726e+31

vbe_lo

0.52

vbe_hi

0.84

err_regr

0.000169

0.35 0.45 0.55 0.65 0.75 0.85 0.95

0

1e-3

0.002

0.003

0.004

0.005

3e15

1e16

1e17

1e18

Vbe [V]

M0

M0 (c10 normalization)M0-regressederror

M0 (c10 normalization)M0-regressederror



Extraction of hjCi

hjCi yields from a single variable regression in the low bias range.

In the low-medium bias the first three terms are dominating in (6). Making the difference of the smallest Vbici<0 and the Vbici=0 branches

All extraction examples will be presented on QucsStudio [9] optimization worksheets.

When needed these contain a 3-variable linear regression routine as well. The data are stored in vectors placed in Eqn (Equation) components. Visualization is performed on the

same sheets using the built-in plotting capability of the tool. The results are shown in tabular form also provided by QucsStudio. The details can be found in a parallel paper

[8].

)0,(),()(

min,

0

min,

bieibicibiei

qp

bicijCi

jCi VMVVMVQ

h −≈Θ

(10)



The hjCi extraction sheet

dc simulation

DC1

Parametersweep


R=Rmin

I=Vbc_Vbe/Rmin

R=1 G

R=Rmin

I=Vbcm_Vbe/Rmin

R=1 G

equation

Solvec11=Qjcim.V-Qjci.Vc1=Mmt-M0tvbeavg=range(Vbev,vbe_loavg,vbe_hiavg)hjciall=c1/c11hjciplot=range(hjciall,vbe_lo,vbe_hi)hjciavg=range(hjciall,vbe_loavg,vbe_hiavg)hjci=average(hjciavg)hjciv=range(U*hjci,vbe_lo,vbe_hi)Export=yes

equation

Results_NFtc_qp0=[0.9832,0.9880,0.9929,1,1.006,1.014,1.021,1.029]nf=1.0007hjci_t=[8.643e12,1.082e12,4.229e12,6.715e12,5.355e12,2.372e12,8.122e12,1.018e13]Tf0v=[1.993e-13,2.057e-13,2.138e-13,2.277e-13,2.2422e-13,2.606e-13,2.819e-13,3.06e-13]Vcompl=[0.64,0.61,0.59,0.52,0.47,0.43,0.39,0.33]

equation

fgstempm05_st1009

equation

fgstempp05_st1009

equation

fgstemp_st1009Temp=[-40,-20,0,27,50,75,100,125]

C++

vin cout

qout tf0

File=hicjq.vatnom=27.0temp=temp

C++

vin cout

qout tf0

File=hicjq.vatnom=27.0temp=temp

equation

Misctemp=Tempv[7]tcqp0=tc_qp0[7]isH=is_regr[7]/nfTk=temp-T0KVt=kB*Tk/qelectronTnom=Temp[4]-T0KVtnom=kB*Tnom/qelectronRmin=1e-4

equation

Limitsvbe_lo=0.35vbe_hi=0.85vbe_loavg=Vcompl[7]vbe_hiavg=0.64Export=yes

equation

Conditioning_VbcminVbcm=Vbcm05Vbcm_Vbe=U*Vbcmvbcmsel=range(Vbcm_Vbe,vbe_lo,vbe_hi)Icm=Icm05_p100Icm_Vbe=U*Icmicmsel=range(Icm_Vbe,vbe_lo,vbe_hi)dexpm=exp(Vbev/Vt)-exp(Vbcm_Vbe/Vt)Mmt=tcqp0*(isH*dexpm/Icm_Vbe-1)Mmtsel=range(Mmt,vbe_lo,vbe_hi)Qjcimsel=range(Qjcim.V,vbe_lo,vbe_hi)Export=yes

equation

Conditioning_VbczeroU=1+Vbev-Vbevvbesel=range(Vbev,vbe_lo,vbe_hi)Vbc_Vbe=U*Vbcvbcsel=range(Vbc_Vbe,vbe_lo,vbe_hi)Ic=Ic_p100Ic_Vbe=U*Icicsel=range(Ic_Vbe,vbe_lo,vbe_hi)dexp=exp(Vbev/Vt)-exp(Vbc_Vbe/Vt)M0t=tcqp0*(isH*dexp/Ic_Vbe-1)M0tsel=range(M0t,vbe_lo,vbe_hi)Qjcisel=range(Qjci.V,vbe_lo,vbe_hi)Export=yes

Qjci

Qjcim Tf0m

Tf0

0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.850

5e12

1e13

1.5e13

2e13

Vbe [V]

hjc

i

number

1

temp

100

hjci

8.382e+12

Tf0.V[1]

2.819e-13

Tf0m.V[1]

3.038e-13

vbe_loavg

0.39

vbe_hiavg

0.64



The temperature independence of hjCi

The forward Early parameter needs the knowledge of QjCi. This is computed in the two Verilog-A program blocks hicjq.va. The related program segments are copy-and-

pasted from the original Hicum codes. A system simulation (voltage signal flow) scheme proved to be a perfect solution. Besides the Qjci output, the Tf0 transit time is also exported for computing Qf0 in the next step. A Norton lossy voltage source equivalent

supplies the input voltage for bypassing a QucsStudio bug.

The extracted values are averaged since no regular temperature dependence is apparent. This is in

compliance to the model as well which neither

assumes temperature dependence. The relatively large spread is typical with forward Early extraction at

high speed transistors

number

1

average(hjciv2)

6.058e+12

-40 -20 0 20 40 60 80 100 1201e12

3e12

5e12

7e12

9e12

1.1e13

temp [degC]

hjc

i

hjci extractedhjci averaged

hjci extractedhjci averaged


Extraction of hjEi,ahjEi and hf0

At Vbici=0 and assuming low-medium bias

00

0

00

)0,( MVMQ

hQ

h bieiqp

f

fqp

jEi

jEi ==Θ

+Θ

zvjahjeizzvjQzzvj

zzvjearly jEi __;

_

1)_exp(⋅=

−=Defining

the regression equation yields as 0000)( qpffjei MQhahjeiearlyh Θ⋅=+

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.01

0.1

1

10

100

Vbe [V]

M0

t

M0tM0tsel

M0tM0tsel

number

1

temp

0

hjei

1.5e+14

ahjei.opt

5.97

hf0

6.969e+15

vbe_lo

0.59

vbe_hi

0.899

err_regr

0.008286

This is a typical regression plot with ahjei optimized until the 2-variable linear regression in hjei and hf0 gets

minimized. M0t denotes the RHS of (11), the line represents the regressed curve.

(11)

(Hicum notations)




Extraction of hjEi, ahjEi and hf0 cont’d

The master function should go zero exactly at Vbiei=0 which is not the case with

practical measurements. Leakages shift the zero point to the right. The data can be utilized only above this intercept. The derivative of M0t exhibits either a post-zero

minimum or a flat section. This helps to select the low limit (compliance point) of the regressions. The high limit will be determined by the start up of self-heating, shown later.

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.003

0.01

0.1

1

10

100

1e3

1e4

Vbev [V]

diff(

M0

t)

measurementmeasurement

indep: 0.59measurement: 7.89indep: 0.59measurement: 7.89

number

1

temp

0

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.003

0.01

0.1

1

10

100

Vbe [V]

M0

t

M0t M0t

indep: 0.59M0t: 1.59indep: 0.59M0t: 1.59

number

1

temp

0



Extraction of hjEi, ahjEi and hf0 cont’d

dc simulation

DC1

Parametersweep


R=Rmin

I=Vbev/Rmin

equation

3varRegressionb1=w*a1b2=w*a2b3=w*a3b=w*ac011=sum(b1*b1)c012=sum(b1*b2)c013=sum(b1*b3)d01=sum(b1*b)c021=c012c022=sum(b2*b2)c023=sum(b2*b3)d02=sum(b2*b)c031=c013c032=c023c033=sum(b3*b3)d03=sum(b3*b)m21=c021/c011c122=c022-m21*c012c123=c023-m21*c013d12=d02-m21*d01m31=c031/c011c132=c032-m31*c012c133=c033-m31*c013d13=d03-m31*d01m32=if((sum(abs(a2))>0),c132/c122,0)c233=c133-m32*c123d23=d13-m32*d12x3=(if((sum(abs(a3))>0),d23/c233,0))x2=(if((sum(abs(a2))>0),(d12-x3*c123)/c122,0))x1=((d01-x2*c012-x3*c013)/c011)asim=x1*a1+x2*a2+x3*a3bsim=x1*b1+x2*b2+x3*b3delt=abs(bsim-b)err_regr=sum(delt*delt)

equation

Regression_outhjei=x1hf0=x2

equation

fgstempm05_st1008

equation

fgstempp05_st1008

equation

fgstemp_st1008Temp=[-40,-20,0,27,50,75,100,125]

equation

results_st1008

Optimization

Nelder-Mead|2000|1e-5|0.1|1ahjei=1...5...20 linearerr_regr=1 MIN

RegressionSim=SW1

equation

ConditioningU=1+Vbev-Vbevvbesel=range(Vbev,vbe_lo,vbe_hi)ic=Ic_p27ic_Vbe=U*iciicn=(exp(Vbev/Vt)-exp(Vbc[1]/Vt))/ic_Vbeiicnsel=range(iicn,vbe_lo,vbe_hi)earlysel=range(early.V,vbe_lo,vbe_hi)tc_qp0sel=range(tc_qp0.V,vbe_lo,vbe_hi)icsel=range(ic_Vbe,vbe_lo,vbe_hi)Qf0=Tf0v[4]*ic_VbeQf0sel=range(Qf0,vbe_lo,vbe_hi)M0=isH*iicn-1M0sel=range(M0,vbe_lo,vbe_hi)M0t=M0*tc_qp0.VM0tsel=range(M0t,vbe_lo,vbe_hi)M0e=M0*tc_qp0.V/early.VM0esel=range(M0e,vbe_lo,vbe_hi)Qf0e=Qf0/early.VQf0esel=range(Qf0e,vbe_lo,vbe_hi)vjsel=range(vj.V,vbe_lo,vbe_hi)

equation

Miscnf=1.0007isH=is_regr[4]/nftemp=Tempv[4]Tk=temp-T0KVt=kB*Tk/qelectronTK=Tempv-T0KTnom=TK[4]Vtnom=kB*Tnom/qelectronRmin=1e-4

equation

vbe_lo=Vcompl[4]vbe_hi=Vhlim[4]

C++

vin eaout

tcout misc

File=ahjei.vaahjei=ahjeivgb=1.057E+00temp=temp

equation

Regression_ina1=earlysela2=Qf0sela3=0a=abs(M0tsel)w=1

early

tc_qp0 vj

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0

0.01

0.02

0.03

0.04

0.05

0.03

0.1

1

10

100

Vbe [V]

M0t e

rror

M0tM0t-opterror

M0tM0t-opterror

number

1

temp

27

hjei

1.321e+14

ahjei.opt

6.178

hf0

9.77e+14

vbe_lo

0.52

vbe_hi

0.84

err_regr

0.0132

REGRESSION

SIMULATOR

MEAS. DATA

The vector is_regr used

for computing isH has not

been discussed so far. It is the regressed (smothed) line over isH=is_GP/nf similar

to slide#12 but w/o adopting

the temperature coefficient tc_qp0.



The TC models of hjEi, ahjEi and hf0

The sheet contains an additional Verilog-A block for computing the function early and the temperature coefficient of Qp0. The Hicum macros QJMODF and TEMPHICJ moreover

part of the hjei_vbe code segment are copy-and-pasted here. The obtained

temperature values are used for extracting the tempcos.

-40 -20 0 20 40 60 80 100 120

9e13

1e14

1.1e14

1.2e14

1.3e14

1.4e14

1.5e14

1.6e14

temp

hje

i

syncTC regression

syncTC regression

number

1

hjeinom

1.326e+14

dvgbe

-0.003293

zetavgbe.opt

5.644

-40 -20 0 20 40 60 80 100 1200

2e15

4e15

6e15

8e15

1e16

temp

hf0

syncTC regression

syncTC regression

number

1

hf0nom

1.766e+15

dvgbe

-0.1267


The TC models of hjEi, ahjEi and hf0, cont’d

-40 -20 0 20 40 60 80 100 1203

4

5

6

7

8

9

temp

ahje

i

syncTC regression

syncTC regression

number

1

ahjeinom

5.881

zetahjei

-1.495

-40 -20 0 20 40 60 80 100 1200.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

Tempv

hje

i

hjei-extractedhjei-Tfit

hjei-extractedhjei-Tfit

number

1

hjeinom

0.03632

dvgbe

-0.04649

zetavgbe.opt

1.547

-40 -20 0 20 40 60 80 100 1200

0.2

0.4

0.6

0.8

1

Tempv

hf0

hf0-extractedhf0-Tfit

hf0-extractedhf0-Tfit

number

1

hf0nom

0.2897

dvgbe

-0.09129

The dvgbe in the hjei and hf0 parameters modelwise

agree but they are not the same in practice. No paper was

found to verify this link of the TC models. Even the introductory paper adopted different dvgbe values.

It is proposed to allow different parameters in the two TC descriptions.

Digitized and re-extracted hjei and

hf0 TC data

from [10]Confidential © ams AG


Returning to the full Hicum model

When the normalized parameters and TCs of the low-medium bias model have been

extracted we have to return to the complete Hicum model. It is necessary because at higher currents the system is subject to self heating. Its accurate consideration - not to

say the resistive voltage drops - is nearly impossible outside the full model framework.

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0

1e-3

0.002

0.003

0.004

0.005

0.006

3e-111e-10

1e-9

1e-8

1e-7

1e-6

1e-5

1e-4

1e-3

0.01

0.1

Vbe [V]

Ic [A

]

rela

tive e

rror

Ic [A]Icsim [A]

Ic [A]Icsim [A]

number

1

temp

75

trise

3.153

hjei.opt

1.06e+14

ahjei.opt

5.15

hf0.opt

1.041e+15

vbe_lo

0.43

vbe_hi

0.79

err_opt

0.0001451

Upper limit of the low-medium current

range is arbitrarily selected at an SH temperature rise of 3C0. These values are

recorded and invoked at low range extractions to reduce parameter

uncertainty.


A Solution to the Qp0 Issue in Hicum Parameter ExtractionReturning to the full Hicum model, cont’d

R=Rmin

I=Vbev/Rmin

Ic

R=Rmin

I=Vbev/Rmin

equation

Parameters_M0thf0_=1.766e15hjei_=1.326e14ahjei_=5.881hjci_=6.058e12vgb=1.057zetact=0.5371dvgbe_hjei=-0.003293dvgbe_hf0=-0.1267zetahjei=-1.495zetavgbe=5.644nf=1.0007Rmin=1e-4Export=yes

dc simulation

DC1output=dc

C++

cb

es

tnode

File=hicumL2V2p4p0.vac10=c10qp0=qp0hf0=hf0hfe=hfehfc=hfchjei=hjeiahjei=ahjei_hjci=hjcifthc=0.8000vgb=vgbzetact=zetactalb=dvgbe_hjeidvgbe=dvgbe_hf0zetahjei=zetahjeizetavgbe=zetavgbetnom=2.7000e+01temp=temp

equation

Temperature_branchVlow=Vcompl[4]temp=Tempv[4]isH=isH_regr[4]ic_Vbe=U*Ic_p27cf=exp(-vgb/Vtnom*(1-Tnom/Tk))isH_tcorr=cf*isH

equation

fgstemp_st1008Tempv=[-40,-20,0,27,50,75,100,125]

Parametersweep


equation

High_bias_parametersc10=qp0*isHhjei=qp0*hjei_hf0=qp0*hf0_hjci=qp0*hjci_

Optimization

Nelder-Mead|2000|1e-5|0.1|1qp0=1e-18...1e-16...1e-14 linearhfe=0...1...100 linearhfc=0...1...1000 linearerr_opt=1 MIN

Regression2Sim=SW1

equation

Limitsvbe_lo=Vcompl[4]vbe_hi=1trise=yvalue(trise.V,vbe_hi)

equation

ConditioningU=1+Vbev-Vbevvbesel=range(Vbev,vbe_lo,vbe_hi)Iclow=yvalue(ic_Vbe,Vlow)Ic_low=yvalue(ic_Vbe,vbe_lo)icmsel=range(ic_Vbe,vbe_lo,vbe_hi)icsel=range(Ic.I,vbe_lo,vbe_hi)delt=abs(1-icsel/icmsel)err_opt=sum(delt*delt)Export=yes

trise

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0

0.01

0.02

0.03

0.04

0.05

0.06

3e-11

1e-10

1e-9

1e-8

1e-7

1e-6

1e-5

1e-4

1e-3

0.01

Vbe [V]

Ic [A

]

rela

tive e

rror

Ic [A]Icsim [A]

Ic [A]Icsim [A]

number

1

c10

7.938e-31

hf0

17.54

hjei

1.317

hjci

0.06017

number

1

temp

27

trise

50.65

qp0.opt

9.933e-15

hfe.opt

20.86

hfc.opt

0

vbe_lo

0.52

vbe_hi

1

err_opt

0.055307

The rectangular symbol represents the hicumL2v2.4.0 model with its parameters

made visible and modifiable in the column shown on its right. Parameter

passing is possible through symbolic

variables providing an exceptional flexibility during extraction.The Qp0 value obtained at this nominal

temperature optimization is not modified

any more during the next temperature

extraction steps.



Returning to the Hicum model cont’d

As a first step, qp0, hfe and hfc are optimized at nominal temperature from the low compliance point (blue mark) till the highest Vbe. Equation „High_bias_parameters”

converts hjei, hf0, hjci to their de-normalized values moreover c10 is also

computed in terms of isH and the optimized qp0. The formerly extracted parameters

have been collected in the equation block „Parameters_M0t” where they are passed from

to the transistor through the „High_bias_parameters” converter.When the optimizer has delivered qp0 the de-normalized values of the Hicum

parameters c10, hjei, hf0, hjci become all known. The obtained nominal values

of these parameters are collected in the block „Return to Hicum” to be ready for use on the next temperature steps. Since hfc=0 resulted in Tnom extraction, only hfe will be

optimized at every other temperature with all other parameters kept frozen.Due to the different dvgbe parameters extracted for hjei and hf0 the unused alb

parameter was used for dvgbe_hjei with a coincidental modification of the Hicum

code:Confidential © ams AG

//hjei0_t = hjei*exp(dvgbe/VT*(exp(zetavgbe*ln(qtt0))-1));

hjei0_t = hjei*exp(alb/VT*(exp(zetavgbe*ln(qtt0))-1));


Correction cfe to compensate the internally applied TC of hfe during optimization. The net TC is shown

below.

−

−−= 1exp

nomT T

T

V

vgevgbcfe

-40 -20 0 20 40 60 80 100 1200

10

20

30

40

50

60

70

80

temp [degC]hfe

hfeTC regression

hfeTC regression

number

1

vgb

1.057

vge

1.1556

hfe_nom

20.78

High bias weighting factors

R=Rmin

I=Vbev/Rmin

Ic

R=Rmin

I=Vbev/Rmin

equation

Parameters_M0thf0_=1.766e15hjei_=1.326e14ahjei_=5.881hjci_=6.058e12vgb=1.057zetact=0.5371dvgbe_hjei=-0.003293dvgbe_hf0=-0.1267zetahjei=-1.495zetavgbe=5.644nf=1.0007Rmin=1e-4Export=yes

dc simulation

DC1output=dc

equation

fgstemp_st1008Tempv=[-40,-20,0,27,50,75,100,125]

Parametersweep


equation

ConditioningU=1+Vbev-Vbevvbesel=range(Vbev,vbe_lo,vbe_hi)Iclow=yvalue(ic_Vbe,Vlow)Ic_low=yvalue(ic_Vbe,vbe_lo)icmsel=range(ic_Vbe,vbe_lo,vbe_hi)icsel=range(Ic.I,vbe_lo,vbe_hi)delt=abs(1-icsel/icmsel)err_opt=sum(delt*delt)Export=yes

Optimization

Nelder-Mead|2000|1e-5|0.1|1hfe=0...1...100 linearerr_opt=1 MIN

Regression2Sim=SW1

equation

Return_to_Hicumc10=7.938e-31qp0=9.933e-15hf0=17.54hjei=1.317hjci=0.06017hfe=20.78hfc=0

equation

Temperature_branchTk=temp-T0KVlow=Vcompl[8]temp=Tempv[8]isH=isH_regr[8]ic_Vbe=U*Ic_p125cf=exp(-vgb/Vtnom*(1-Tnom/Tk))isH_tcorr=cf*isHcfe=exp(-(vgb-1.1556)/Vtnom*(1-Tnom/Tk))

equation

Limitsvbe_lo=Vcompl[8]vbe_hi=1trise=yvalue(trise.V,vbe_hi)

C++

cb

es

tnode

File=hicumL2V2p4p0.vac10=c10qp0=qp0hf0=hf0hfe=hfe*cfehfc=hfchjei=hjeiahjei=ahjei_hjci=hjcifthc=0.8000vgb=vgbvge=1.1556e+00zetact=zetactalb=dvgbe_hjeidvgbe=dvgbe_hf0zetahjei=zetahjeizetavgbe=zetavgbetnom=2.7000e+01temp=temp

trise

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0

0.01

0.02

0.03

0.04

1e-9

1e-8

1e-7

1e-6

1e-5

1e-4

1e-3

0.01

Vbe [V]

Ic [A] e

rror

Ic [A]Icsim [A]

Ic [A]Icsim [A]

number

1

temp

125

trise

63.24

hfe.opt

7.963

vbe_lo

0.33

vbe_hi

1

err_opt

0.015534




Verification of the results

A slight measurement incompliance is still present at the lowest temperature lines. This

is due to the relatively large leakage of the bias-tee of high frequency VNAs. At the high end it is proposed to go till Vbe=1.2V with the measurements for a wider (by 20 points)

range for high current parameter identification.

Correction cfe is removed,

Optimization is deactivated and

simulations are performed in Vbe=0.2V...1V at each temperature. Simulated data stored in the *.dat file

can be accessed by the QucsStudio io function loadQucsVariable and

converted to individual Ic_m40.dat,

Ic_m20.dat etc. files for plotting.0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

1e-9

1e-8

1e-7

1e-6

1e-5

1e-4

1e-3

0.01

0.1

Vbe [V]

Ic [A

]

bottom to top: tamb [degC]= -40, -20, 0, 27, 50, 75, 100, 125



Summary

• a robust solution has been proposed for fixing the so far unresolved qp0 problem in Hicum/L2

• the c10/qp0 ratio has been proved to be physically equivalent to the is/nf ratio of the SGP model

• the master function M(Vbiei,Vbici) is a common starting point for the extraction of HL2, HL0, VBIC and even Mextram

•qp0 can be optimized in the SH affected domain using the complete model

• it has been shown that qp0 is a „weak” parameter explaining that reasonable results could be formerly obtained by using q0 from tetrode structures despite that it is different from qp0

• it is proposed to adopt different dvgbe parameters for the TCs of hjei and hf0

• extractions were all performed on QucsStudio worksheets demonstrating the suitability of this open tool for solving sophisticated engineering tasks



Acknowledgment

Thanks are due to Didier Celi (STM) for providing the measurements and for preparing the HL2 synthetic data of undisclosed parameters for the verification of the theoretically

predicted link between the HICUM and SGP saturation currents

References



[1] D. Celi, „Step by step Extraction of HICUM/L2 High-Current Parameters,” 8th HICUM Workshop, Böblingen,May 2008.

[2] M. Schroter and A. Chakravorty, „Compact Hierarchical Bipolar Transistor Modeling With HICUM,” Singapore: Word Scientific, Aug. 2010.

[3] Zoltan Huszka and Ehrenfried Seebacher, „Restoring the Uniqueness of the HICUM/L2v2.3x revisions,” 16th HICUM Workshop 2016 at

Rhode & Schwarz in Munich, Germany, 12 May 2016

[4] A. Pawlak, M. Schröter, J. Krause, “A HICUM extension for medium current densities,” HICUM Workshop, Würtzburg, October 2009.

[5] A. Pawlak, M. Schröter, “Application of Hicum/L2v2.30 to advanced multi-100GHz SiGe HBTs,” Bipolar Arbeitskreis, October 2010,

STMicroelectronics, Crolles, France.

[6] A. Pawlak, M.Schröter, J. Krause, D. Celi, N. Derrier and A. Mukherjee, „HICUM/2 v2.3 Parameter Extraction for Advanced SiGe-

Heterojunction Bipolar Transistors,” BCTM 2011, Atlant, Georgia,USA, October 9-11.

[7] T. Rosenbaum, „Evaluierung von Methoden zur Parameterextraktion für moderne Heterostruktur-Bipolartransistoren,” Diplomarbeit,

Technische Universitaet Dresden, 2011

[8] Z. Huszka, “Parameter extraction with QucsStudio_v2.5.7,” 32nd BipAK Workshop 2019 at STMicroelectronics, Crolles, France November

14 & 15, 2019.

[9] http://dd6um.darc.de/QucsStudio/qucsstudio.html

[10] A. Pawlak, M. Schröter, “Application of Hicum/L2v2.30 to advanced multi-100GHz SiGe HBTs,” Bipolar Arbeitskreis, October 2010,

STMicroelectronics, Crolles, France.

Thank you!Please visit our website www.ams.com

a solution to the q p0 issue in hicum parameter extraction · 2019. 12. 13. · 32 th bipak...

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