Download 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 
dI E
dVEB
VBC VF
 g
I
C
dE g  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)
C BC

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  I E0
V
V
1  tE  tC
Ver Vef
tE
IC  IC0
Ver
V
V
1  tE  tC
Ver Vef
 I avl
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 ln 1 


 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
 VtE VtC 

I Ss 1 

 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 r  ri
dVg 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 )
B2 E1
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 
dI C1C2
vB2 E1
vB2C1
I C1C2
1
dQ
 T 
2fT
dI C
VCE 
B2C1

N
B2 E1
vB2C1
dvB2 E1 dvB2C1
,
dI C1C2 dI C1C2
Q dvB2 E1
Q dvB2C1
Q


vB2 E1 dI C1C2 vB2C1 dI C1C2 I C1C2
B2C1

vCE
dI C1C2  0
I C1C2
I N
dI C1C2  dI C1C2
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  I C 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  XI ex RCCT
IE  IN
I B  I ex  XI ex  I sub  XI sub  I B 3
I sub,ext   I sub  XI sub
 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
log S IB ,1Hz   log K f   A f log I 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