Mextram 504 parameter extraction
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Transcript Mextram 504 parameter extraction
Mextram 504 parameter extraction
F. Yuan
Advisor: Prof. C. W. Liu
Graduate Institute of Electronics Engineering
and Department of Electrical Engineering,
National Taiwan University, Taipei, Taiwan
Extraction strategy
SiGe parameters
Low current parameters
Temperature parameters
S-parameter measurement (only for fT)
High current parameters
1/f noise parameters
Lay-out structure
In S-parameter measurement, E-S are
connected and grounded to increase S/N ratio
Early-measurement can be done on two
layout structures and used as a double check
normal DC
High frequency (S-parameters)
Initial guess
We use the process parameters to set the
initial parameters
All this guess is physically based
SiGe parameters
Must be extracted first
Linear graded Ge-profile
Extract dEg
Extract Xrec by IB-VCB plot at low VCB
dI
g
(No avalanche)
dV
C
out , f
VBE VF
CB
VtC
I B1 I B 0 1 X rec 1 XI B1 I avl
Vef
g out ,r
dIE
dVEB
VBC VF
g
I
C
dEg kT ln out ,r 2 ln E ,r ln BE ,r
g
IC, f
C BC , f
out , f
Low current parameters
Depletion, overlap capacitances
Early effect
BC avalanche
Transfer current
BE base current
series resistances
PNP parasitic transistor
BE depletion capacitance
LCR-meter or S-parameter
VC=VE=VS=0, change VB but in low bias
In low bias, we can assume the voltage drop
on all parasitic resistors are zero
Smoothing factor ajE can not be extracted
C BE
C jE
vBE
1
VdE
pE
C BEO
BC, SC depletion capacitance
VB=VE=VS=0, change VC but in low bias
Xp is reach-through parameter
Cp,CS is the parasitic SC capacitance (not
modeled in Mextram 504)
CBC
1 X C
CSC
p
vBC
1
VdC
C jS
vSC
1
VdS
jC
pC
pS
X p C jC CBCO
C p ,CS
BC avalanche
Iavl related to IC, VCB
Measured at low VBE and high VCB
I B I B 0 I avl
Wavl ,Vavl
Early effect
Low bias, no BE tunneling breakdown
Calculate Ver, then Vef, and repeat again
Use the previous parameters in extraction
Early voltage may be not normal if dEg is not
zero
V
1
V
1 tC
Vef
I E IE0
V
V
1 tE tC
Ver Vef
tE
IC IC 0
Ver
I avl
VtE VtC
1
Ver Vef
VtE VdE , pE ,VBE , a jE
VtC VdC , pC ,VBC , a jC , X p
Saturation current IS
Measured in forward-Gummel (IC-VBE,
VBC=0V) at low VBE
IC
VBE
VT
ISe
V
V
1 tE tC
Ver Vef
Base current
Measured in forward-Gummel (hfe-VBE,
VBC=0V) at low VBE
I B1
IS
f
B2E1
(e
VT
1)
B2E1
I B 2 I Bf (e
h fe
mLf VT
IC
I B1 I B 2
1)
series resistance
For RE, measured VCE-IE at IC=0 and high VBE
For RB, measured VBE-IB at IC=0 and high VBE
Voff,Rb is only for optimization
VB2E1 can be obtained by IB1
VCE I E RE vB2 E1 vB2C1
RE
VCE
I E
VBE vB2 E1 vB1B2 I B RBc I C I B RE Voff , Rb
vB1B2
RBv I C 1 XI B1
VT ln1
f VT
Substrate saturation current ISS
Measured in reverse-Gummel (hfc,sub-VBC,
VBE=0V) at low VBC
Iks is the point that hfc,sub becomes large
I sub I Ss e
IE
VBC
VT
VBC
VT
ISe
V
V
1 tE tC
Ver Vef
h fc, sub
IE
I sub
IS
V
V
I Ss 1 tE tC
V
Vef
er
series resistance
Measured IX-VBE at VBC=0.6V
From IC, IB, Isub, and RBc, the RCc is given
B1C1
I sub
2 I ss (e
VT
1 1 4
1)
IS
e
I kS
B1C1
VT
B C VBC RCc I C RBc I B
1 1
Parasitic PNP
Measured in reverse-Gummel (hfc-VBC,
VBE=0V) at low VBC V V ln I 1 V
E
B1C1
I ex
BC
IS
ri
T
IS
B1C1
e
VT
B1C1
I B 3 I Br
e
VT
B1C1
1
VLr
e 2VT e 2VT
IE
IE
h fc
I B I sub
I ex I B 3
VtC
Ver Vef
tE
Temperature parameters
We don’t extract AE, AB, Aepi, Aex, AC, AS
The other 8 parameters should be extracted
T A
AQB 0
Ver ,Vef
Vg B
IS
Vg C
I Br , C jC
Vg j
I Bf
Vg S
I SS
dVg f
f
dVg
ri
dVg
r
E
E
Temperature parameters
Extract all low current parameters at
reference temperature
Extract temperature parameters at elevated
temperature (temperature independence
parameters will set the same as ref temp)
Extract high current parameters
High current parameters
Self-heating
Output-characteristics
Cutoff frequency
Quasi-saturation
Self-heating
IB fixed, increase VCE to self-heating
Then IS will increase with temperature
VBE will now decrease by fixed IB
No avalanche (Iavl << IB)
T Rth I BVBE I CVCE
No hard saturation
v
I S (T ) V
IB
e
(Iex, Isub << IB)
f (T )
B2E1
T
VBE vB2 E1 I C RE (T )
Output characteristics
I B I B1 (vB2 E1 ) I B 2 (vB2 E1 )
vB2C1 vB2 E1 I C RCcT I B I C RET
v*B2C2
v B2E1
I C1C2 I N I ST
e
VT
e
qB
vB2 E1 , vB2C1 , I C1C2 , vB* 2C2
VT
IB fixed,
VCE=0…VCB,max+1
Solve the voltage of all
V internal nodes
No hard saturation
(Iex, Isub << IB)
CE
Cutoff frequency
S-parameters are measured
fT measurement is very easy
The fT value from extracted parameters
should be compared to the measured value
h fe h21
Y21
Y11
Cutoff frequency
VB2E1, VB2C1, IC1C2
Small signal variable (VCE constant)
v
v
dv
dv
dv
Solve two equation
v
v
Calculate dQ and fT dI I dv I dv
CE
CE
CE
B2 E1
B2 E1
B2C1
N
N
dQ
vB2 E1
Q
Q
Q
dvB2 E1
dvB2C1
dIC1C2
vB2 E1
vB2C1
I C1C2
1
dQ
T
2fT
dIC
VCE
B2C1
N
B2 E1
vB2C1
dvB2 E1 dvB2C1
,
dIC1C2 dIC1C2
Q dvB2 E1
Q dvB2C1
Q
vB2 E1 dIC1C2 vB2C1 dIC1C2 I C1C2
B2C1
vCE
dIC1C2 0
I C1C2
I N
dIC1C2 dIC1C2
I C1C2
Cutoff frequency
For some parameters in Q , we use the initial
guess only
Only E left for extraction
Ver 1 XC jE C jE
No avalanche (Iavl << IB) B
Ik
V
2
No hard saturation
I I R
epi B S k 2Cv e V
4VT
(Iex, Isub << IB)
dC
T
1 XC jC
R B epi
XC jC
Quasi-saturation
External VCB > 0, but Internal VCB < 0
VCB,in VCB,out IC RC
Quasi-saturation
Extract Ik (hfe-VBE at high VCE)
Extract Rcv (forward-Gummel)
Repeat first two procedures
Extract E at maximum fT and high VCB
Extract epi , I hc , SCRcv at fT roll-off
axi , m ,VdC can be used as fitting parameters
Repeat the whole loop again (and again)
Avalanche at high current
Extract SFh
I B I B1 (vB2 E1 ) I B 2 (vB2 E1 ) Gem vB2 E1 , I C1C2 I C1C2
I N I C1C2 1 Gem vB2 E1 , I C1C2
Xext
vB2 E1 VBE I N RET I ex I B 3 I sub RBCT
v B2C2
I N I ST
e
VT
qB vB2 E1 , vB2C2
I C1C2 vB2C1 , vB2C2 I N
vB2C1 vB1C1
VBC vB1C1 I ex I B 3 I sub RBCT
I ex I B 3 I N XIex RCCT
IE IN
I B I ex XIex I sub XIsub I B 3
I sub ,ext I sub XIsub
We can take IB,IE-VBC
(reverse-Gummel)
VB2E1, VB2C2, VB2C1,
VB1C1, Xext
Check IE, IB, Isub,ext
Y-parameters
Y21
Y11
Only for fT measuring
We can also use it to double check the
extracted parameters (at small current)
h fe h21
g m rB
1
Y11
gm
j Cex Cin C BE
Y21 g m j Cex Cin 1 g m rB C BE g m rB
Y12 2 rB Cin Cin C BE j Cex Cin
Y22 g out j Cex Cin 1 g m rB CSC
1/f noise parameters
SIB is base current noise spectral density
S IB ,1Hz S IB f
S IB
Af
2
i
I
K f b , b 1
f
f
S IB ,1Hz K f I B f
A
logS IB ,1Hz logK f A f logI B
Thermal capacitance
Can be measured in time-domain
RthCth will be the order of 1us
Geometric scaling
There is a primitive scaling rules in Mextram
504 parameter extraction
If the devices have different B, E fingers or
different contacts, the model may inaccurate
High current parameters can be more easily to
extract