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6.1 Introduction
The Junction-Field-Effect Transistor (JFET) and the depletion mode Metal-Oxide Semi(MOSFET) are semiconductor devices whose operation is achieved by depleting an already
existing channel via a voltage controlled p-n junction (JFET) or a gate controlled surface
depletion (MOSFET). These devices are often used as a load in high voltage MOS devices.
This long channel JFET/MOSFET model is special developed to describe the drift region of
LDMOS, EPMOS and VDMOS devices. When the n-channel MOS transistor equations are
used for p-channel MOS transistors, the sign of the terminal potentials, terminal currents and
terminal charges must be changed.
6.1.1 Survey of modelled effects
•
Accumulation at the surface (MOSFET)
•
Depletion from the surface
•
Depletion from the bulk
•
Pinch off mode
•
Velocity saturation in the channel
•
Gate charge model
•
Substrate charge model
•
Self-heating
•
Different temperature scaling for RON and VSAT
•
Include temperature scaling for RSAT
Not included in the model
Short channel effects
•
Subthreshold currents
•
Inversion at the surface at high negative gate voltages.
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Noise model
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6.2 Symbols, parameters and constants
6.2.1 Parameter list
The parameters are listed below .
Parameter
Units
Description
LEVEL
-
Model level, must be set to 3100
PARAMCHK
-
Level of clip warning info *)
RON
Ω
Ohmic resistance at zero bias
RSAT
Ω
Space charge resistance at zero bias
VSAT
V
Critical drain-source voltage for hot carriers
PSAT
−
Velocity saturation coefficient
VP
V
Pinch off voltage at zero gate and substrate voltages
VP ≤ 0: no depletion and/or accumulation in the channel
TOX
m
Gate oxide thickness
TOX > 0: MOSFET device
TOX ≤ 0: No accumulation and/or depletion at the surface
DCH
m-3
Doping level channel
DSUB
m-3
Doping level substrate
DSUB ≤ 0 : No depletion from the substrate
VSUB
V
Substrate diffusion voltage
VGAP
V
Bandgap voltage channel
CGATE
F
Gate capacitance at zero bias
CSUB
F
Substrate capacitance at zero bias
TAUSC
s
Space charge transit time of the channel
ACH
−
Temperature coefficient restivity of the channel
ACHMOD
−
Parameter to switch to extended temperature scaling
ACHRON
−
Temperature coefficient of ohmic resistance at zero bias
ACHVSAT
−
Temperature coefficient of critical drain-source voltage
for hot carriers
ACHRSAT
−
Temperature coefficient of space charge resistance at
zero bias
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Parameter
Units
Description
TREF
°C
Reference temperature
DTA
°C
Temperature offset to the ambient temperature
*) See Appendix B for the definition of PARAMCHK.
The parameters for the model including self-heating are listed in the table below.
Parameter
Units
Description
RTH
oC/W
Thermal resistance
CTH
J/oC
Thermal capacitance
ATH
−
Temperature coefficient of the thermal resistance.
The MULT and PRINTSCALED parameter arelisted in the table below.
Parameter
Units
Description
MULT
−
Multiplication factor
PRINTSCALED
−
Flag to add scaled parameters to the OP output
Parameter MULT
This parameter may be used to put several devices in parallel. The following parameters are
multiplied by MULT :
CGATE
CSUB
CTH
Divided by MULT are:
RSAT
RTH
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Default and clipping values
The default values and clipping values as usedfor the MOS level 3100 model are listed below.
Parameter
name
Units
Default
Clip low
Clip high
LEVEL
-
3100
-
-
0
-
-
PARAMCHK Ω
1.00
1e-2
-
RSAT
Ω
1.00
1e-2
-
VSAT
V
10.00
1.00 ×10-6
-
PSAT
−
1.00
0.1
-
VP
V
-1.00
-1.0
-
TOX
m
-1.00
-1.0
0.0001
DCH
m-3
1.00 ×1021
1.00 ×1011
1.00 ×1029
DSUB
m-3
1.00 ×1021
-1.0
1.00 ×1029
VSUB
V
0.60
0.05
-
VGAP
V
1.20
0.1
-
CGATE
F
0.00
0.0
-
CSUB
F
0.00
0.0
-
TAUSC
s
0.00
0.0
-
ACH
−
0.00
-
-
ACHMOD
−
0.00
0
1
ACHRON
−
0.00
-
-
ACHVSAT
−
0.00
-
-
ACHRSAT
−
0.00
-
-
TREF
°C
25
-273.0
-
DTA
°C
0.00
-
-
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The default values and clipping values of the additional parameters for the model including
self-heating (see section 6.4) is listed in the table below.
Parameter
Name
Units
Default
Clip low
Clip high
RTH
oC/W
300.0
0.000
-
CTH
J/oC
3.0¥10-9
0.000
-
ATH
-
0.0
-
-
The MULT and PRINTSCALED parameter aree listed in the table below.
Parameter
Name
Units
Default
Clip low
Clip high
MULT
-
1.000
0.000
-
PRINTSCALED
-
0
-
-
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6.3 Model equations
A full description of the long channel JFET/MOSFET model is given below.
Gate
Qgs
Q gd
Ids
Source
Drain
Qds
Qbs
Qbd
Substrate
Figure 15: Equivalent Circuit of an JFET/MOSFET
6.3.1 Model constants
q = 1.6021918 ⋅ 10
– 10
ε ox = 3.453 ⋅ 10
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C⁄V⋅m
– 11
(6.1)
C⁄V⋅m
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ε si = 1.036 ⋅ 10
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 --k- = 0.86171 × 10 –4 V ⁄ K
 q
δ v = 10
–8
V 0 = 10
ε = 10
(6.3)
(6.4)
–3
(6.5)
–2
(6.6)
The default reference temperature TREF for parameter determination is 25 °C.
6.3.2 Temperature effects
The actual simulation temperature is denoted by TEMP (in oC). The temperature at which the
parameters are determined is TREF (in oC).
• Conversions to Kelvins
3 Note
Note the addition of the voltage VdT of the thermal node in order to include self-heating, see
section 6.7.
T K = TEMP + DTA + 273.15 + V dT
(6.7)
T amb = TEMP + DTA + 273.15
(6.8)
T RK = TREF + 273.15
(6.9)
TK
T N = --------T RK
(6.10)
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Thermal Voltage
k
V T =  --- ⋅ T K
 q
•
On resistance and saturation voltage
RON T = RON ⋅ T
ACHRON
VSAT T = VSAT ⋅ T
ACHVSAT
RSAT T = RSAT ⋅ T
ACHRSAT
•
(6.12)
(6.13)
(6.14)
Substrate depletion capacitance.
k
VSUB T = – 3 ⋅  --- ⋅ T K ⋅ ln ( T N ) + VSUB ⋅ T N + ( 1 – T N ) ⋅ VGAP
 q
(6.15)
VSUB
CSUB T = CSUB ⋅ -----------------VSUB T
(6.16)
Thermal resistance
RTH T
T amb
= RTH ⋅  ------------
 T RK 
(6.17)
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6.3.3 Model preprocessing
•
Parameter dependent constants DC part
If TOX ≤ 0 CGATE = 0
If DSUB ≤ 0 DSUB = 0
If TOX < 0 & DSUB < 0 VP = 0
For both DSUB and TOX less than or equal to zero the pinch off voltage VP = 0. When
VP ≤ 0 only equations 6.29, 6.47, 6.49, 6.50, 6.62, 6.63, 6.104 and 6.105 are used. In this
case the charges Qb and Qg are equal zero.
DSUB > 0:k b =
2 ⋅ ε si ⋅ q ⋅ DSUB ⋅ DCH
-----------------------------------------------------------DSUB + DCH
(6.18)
DSUB ≤ 0:k b = 0
(6.19)
k b ⋅ VP
Q bp = ----------------------------------------------------------------VP + VSUB T + VSUB T
(6.20)
ε si ⋅ q ⋅ DCH TOX 2
V ox = -------------------------------- ⋅  ------------
 ε ox 
2
(6.21)
TOX > 0:k ox =
2 ⋅ ε si ⋅ q ⋅ DCH
(6.22)
TOX ≤ 0:k ox = 0
(6.23)
k ox ⋅ VP
Q sp = ---------------------------------------------VP + V ox + V ox
(6.24)
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Q i = Q bp + Q sp
(6.25)
Q m = k b ⋅ VP + VSUB T + k ox ⋅ VP + V ox
(6.26)
Qi
T s = -------------------q ⋅ DCH
(6.27)
ε ox
TOX > 0:C ox = -----------TOX
(6.28)
TOX ≤ 0:C ox = 0
(6.29)
kb
C b = ----------------------------2 ⋅ VSUB T
(6.30)
VSAT T
J sat = -------------------------T s ⋅ RON T
(6.31)
RSAT
VR sat = VSAT T ⋅ ---------------RON T
(6.32)
–2
2
⋅ Qi
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6.3.4 Model evaluation
Drain and source voltage
Vd ≥ Vs
sign = 1
V d1 = V d
V s1 = V s
Vd < Vs
sign = – 1
V d1 = V s
V s1 = V d
Substrate - source voltage <
VSUB T
2
DSUB > 0:
V bm = VSUB T + V s1 – V b – ε ⁄ VSUB T
(6.34)
V b1 = VSUB T + V s1 – 0.5 ⋅ ( V bm +
2
V bm
2
+4⋅ε )
DSUB ≤ 0 :V b1 = V b
Gate voltage
V g > V b1 – V g sw
DSUB > 0 & TOX > 0 :
V g sw = VSUB T – V ox + ( Q m ⁄ k ox )
2
(6.35)
2
V gm = V g – V b1 + V g sw – ε ⋅ V g sw
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2
2
2
V g 1 = V b1 – V g sw + 0.5 ⋅  V gm + V gm + 4 ⋅ ε ⋅ V g sw


(6.37)
DSUB ≤ 0 or TOX ≤ 0 :
V g1 = V g
•
Pinch-off voltage
DSUB ≤ 0:V p = VP + V g 1
(6.38)
TOX ≤ 0:V p = VP + V b1
(6.39)
TOX > 0 & DSUB > 0 :
V b sw = V g 1 – 2 ⋅ ( Q i ⁄ k b ) ⋅ VSUB T – ( Q i ⁄ k b )
2
(6.40)
V b1 > V b sw :
k b ⋅ Q m DSUB + DCH
- ⋅ -----------------------------------b p = ---------------2
DCH
k ox
(6.41)
Qm 2
DSUB + DCH
c p =  ------- + ( V g 1 – V b1 + VSUB T – V ox ) ⋅ ----------------------------------- k ox
DCH
(6.42)
2
Vp
cp
= V b1 – VSUB T + ----------------------------------------------------------------------2
2
2 ⋅ bp + cp + 2 ⋅ bp ⋅ bp + cp
V b1 ≤ V bSW :
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•
MOS Model, level 3100
kb 2
b ac = V g 1 + ( Q i + k b ⋅ VSUB T ) ⁄ C ox +  ----------------
 2 ⋅ C ox
(6.44)
kb 2 kb
V p = b ac +  ---------------- – -------- ⋅ b ac + VSUB T – V b1
 2 ⋅ C ox
C ox
(6.45)
Source and drain voltage including pinch-off and velocity saturation
2
VP > 0:V sp
= 1 ⁄ 2 ⋅ V s1 + V p – ( V s1 – V p ) + δ v
(6.46)
VP ≤ 0:V sp
= V s1
(6.47)
VP > 0:V c
2 ⋅ VSAT T ⋅ ( V p – V sp )
= --------------------------------------------------------------------------------------------------------------2
2
VSAT T + V p – V sp + VSAT T + ( V p – V sp )
(6.48)
VP ≤ 0:V c
= VSAT T
(6.49)
( V d 1 – V s1 ) ⋅ V c
V dp = V sp + --------------------------------------------------------------------------PSAT
PSAT
PSAT ( V – V )
+ Vc
d1
s1
Integration boundary voltage
V sp < V g 1 :
V ad
V dp < V g 1 V ad = V dp
V dp ≥ V g 1 V ad = V g 1
V sp ≥ V g 1 :
V ad = V sp
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Transformation of voltages
V sp – V b1 + VSUB T
V sp – V b
S spb
S spb = -----------------------1 ,Y spb = -------------------------------VSUB T
1 + 1 + S spb
(6.51)
V dp – V b1 + VSUB T
V dp – V b
S dpb
S dpb = -----------------------1 , Y dpb = -------------------------------VSUB T
1 + 1 + S dpb
(6.52)
V ad – V b1 + VSUB T
S adb
V ad – V b1
S adb
= ------------------------ , Y adb = -------------------------------VSUB T
1 + 1 + S adb
(6.53)
V sp – V g 1 + V ox
V sp – V g
S spg = -----------------------1 ,
V ox
S spg
V sp ≥ V g 1 : Y spg = -------------------------------1 + 1 + S spg
(6.54)
V dp – V g 1 + V ox
S dpg
V dp – V g 1
= ------------------------ ,
V ox
S dpg
V dp ≥ V g 1 :Y dpg = --------------------------------1 + 1 + S dpg
(6.55)
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V ad – V g 1 + V ox
S adg
V ad – V g 1
= ------------------------ ,
V ox
S adg
V ad ≥ V g 1 : Y adg = --------------------------------1 + 1 + S adg
(6.56)
•
Current reduction due to substrate effect
2
I bd
•
•
2
2
3
3
– 4 ⋅ C b ⋅ VSUB T  Y dpb – Y spb Y dpb – Y spb
= ---------------------------------------- ⋅  --------------------------- + ----------------------------
Q i ⋅ RON T
2
3


(6.57)
Current increase due to accumulation
2
2
2
C ox ⋅ V ox  S spg – S adg
= -------------------------- ⋅  ---------------------------
Q i ⋅ RON T 
2

V sp < V g 1
I sa
V sp ≥ V g 1
I sa = 0
(6.58)
(6.59)
Current reduction due to depletion at the surface
V dp ≥ V g 1 : I
sd
2
2
2
3
3
– 4 ⋅ C ox ⋅ V ox  Y dpg – Y adg Y dpg – Y adg
= --------------------------------- ⋅  ---------------------------- + -----------------------------
Q i ⋅ RON T 
2
3

(6.60)
V dp < V g 1 : I sd = 0
Total ohmic current
VP > 0 :
V dp – V sp
I ohm = ----------------------- + I bd + I sa + I sd
RON T
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VP ≤ 0 :
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V dp – V sp
I ohm = ----------------------RON T
(6.62)
Total current including velocity saturation
V d 1 – V dp
I ds = sign ⋅ I ohm ⋅  1 + -----------------------

VR sat 
(6.63)
6.3.5 Substrate charge model
4
( V p – V sp )
V dp – V sp
-----------------------------------F c = --------------------------------------------------------------⋅
4
4 V +V
–
V
0
dp
sp
( V p – V sp ) + ( VP ⁄ 100 )
2
2
2
3
(6.64)
3
4 ⋅ VSUB T  Y dpb – Y spb Y dpb – Y spb
Vb 1 = -------------------------------- ⋅  --------------------------- + ----------------------------
RON T ⋅ I ohm 
2
3

3
3
3
4
(6.65)
4
– 8 ⋅ C b ⋅ VSUB T  Y dpb – Y spb Y dpb – Y spb
Vb 2 = ------------------------------------------ ⋅  --------------------------- + ----------------------------
Q i ⋅ RON T ⋅ I ohm 
3
4

3
3
3
4
4
– 8 ⋅ C b ⋅ VSUB T  Y dpb – Y spb Y dpb – Y spb
Vb 2 = ------------------------------------------ ⋅  --------------------------- + ----------------------------
Q i ⋅ RON T ⋅ I ohm 
3
4

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For TOX ≤ 0:V b 3 = V b 4 = 0
(6.68)
V sp < V g 1
3
V b3
4 ⋅ C ox ⋅ VSUB T
= ------------------------------------------ ⋅
Q i ⋅ RON T ⋅ I ohm
V g 1 – V b1  Y 2adb – Y 2spb Y 3adb – Y 3spb
----------------------- ⋅  ---------------------------- + ---------------------------- –
VSUB T 
2
3

3
3
4
4
5
5
Y adb – Y spb Y adb – Y spb
 Y adb – Y spb
 2 ⋅ ---------------------------- + 3 ⋅ ---------------------------- + ----------------------------
3
4
5


(6.69)
V sp ≥ V g 1 :V b3 = 0
V dp ≥ V g 1 :z 0 = ( V g 1 – V b1 – V ox + VSUB T ) ⁄ 2
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– k ox ⋅ k b
------------------------------------------------------ ⋅
Q i ⋅ RON T ⋅ C b ⋅ I ohm
exact
Vb 4
 ( V ox – VSUB T ) ⋅ [ ( Y dpb – Y dpg ) – ( Y adb – Y adg ) ]



 + VSUB T ⋅ Y dpb ⋅ [ Y dpb ⋅ ( 1 + Y dpb ) + Y dpg ⋅ ( 3 + 3 ⋅ Y dpb + Y 2dpb ) ] 




2
1
--- ⋅ VSUB T ⋅ V ox ⋅  – VSUB T ⋅ Y adb ⋅ [ Y adb ⋅ ( 1 + Y adb ) + Y adg ⋅ ( 3 + 3 ⋅ Y adb + Y adb ) ] 
4


2
 +V ⋅Y

⋅
[
Y
⋅
(
1
+
Y
)
+
Y
⋅
(
3
+
3
⋅
Y
+
Y
)
]
ox
dpg
dpg
dpg
dpb
dpg
dpg




2
=
 – V ox ⋅ Y adg ⋅ [ Y adg ⋅ ( 1 + Y adg ) + Y adb ⋅ ( 3 + 3 ⋅ Y adg + Y adg ) ]

VSUB T ⋅ ( 1 + Y dpb ) + V ox ⋅ ( 1 + Y dpg )
2
– z 0 ⋅ ln -------------------------------------------------------------------------------------------------------VSUB T ⋅ ( 1 + Y adb ) + V ox ⋅ ( 1 + Y adg )
–2⋅
3⁄2
VSUB T
2
2
3
3
 Y dpb – Y adb Y dpb – Y adb
⋅ V ox ⋅  ----------------------------+ -----------------------------
2
3


2
2
3
3
 Y dpg – Y adg Y dpg – Y adg
3⁄2
– 2 ⋅ V ox ⋅ VSUB T ⋅  ----------------------------- + ------------------------------
2
3


(6.71)
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– k ox ⋅ k b
------------------------------------------------------ ⋅
Q i ⋅ RON T ⋅ C b ⋅ I ohm
2
2
3
3
V dp – V ad
V dp – V ad 

1
-------------------------------------------- ⋅  ( V dp – V ad ) ⋅ [ V b ⋅ V g ] – ------------------------- ⋅ [ V g + V b ] + ------------------------ +
1
1
1
1
2
3
4 ⋅ VSUB T ⋅ V ox 

appro
Vb 4
 { ( V dp – V ad ) ⋅ [ V b 1 ⋅ V g 1 ⋅ ( V g 1 ⋅ VSUB T + V b1 ⋅ V ox ) ] –

=
V 2 – V 2
2
2
dp
ad
 ------------------------ ⋅ [ V g ⋅ VSUB T + V b ⋅ V ox + 2 ⋅ V b ⋅ V g ⋅ ( VSUB T + V ox ) ] +
1
1
1
1

2

1
3
3
-------------------------------------------------------⋅
3 ⁄ 2  V dp – V ad
 ------------------------- ⋅ [ V ⋅ ( 2 ⋅ VSUB + V ) + V ⋅ ( VSUB + 2 ⋅ V ) ] –
16 ⋅ ( VSUB T ⋅ V ox )
g1
T
ox
b1
T
ox

3

V 4 – V 4
dp
ad
 ------------------------ ⋅ [ VSUB T + V ox ]

4
(6.72)
2
Y sw
2
2
2
VSUB T ⋅ ( Y dpb + Y adb ) + V ox ⋅ ( Y dpg + Y adg )
= --------------------------------------------------------------------------------------------------------------2
V 0 ⋅ ( VSUB T + V ox )
(6.73)
2
( 1 + 2 ⋅ V o ) ⋅ Y sw
Sw = ----------------------------------------- – Vo
2
1 + Y sw
(6.74)
exact
Sw ≥ 1
V b4 = Vb 4
Sw ≤ 0
V b4 = Vb 4
Sw > 0 & Sw < 1
Vb 4 = Sw ⋅ Vb 4
V dp ≤ V g 1
Vb 4 = 0
(6.75)
appr
(6.76)
exact
(6.77)
(6.78)
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











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MOS Model, level 3100
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Q b x = – C SUB T ⋅ ( Vb 1 + Vb 2 + Vb 3 + Vb 4 )
(6.79)
Q b y = – C SUB T ⋅ VSUB T ⋅ ( Y dpb + Y spb )
(6.80)
Cb fix = 0.01 ⋅ CSUB + MULT ⋅ 10
– 17
(6.81)
Qb = 0.99 ⋅ { F c ⋅ Q b x + ( 1 – F c ) ⋅ Q b y } + Cb fix ⋅ { Vb 1 – ( V d + V s ) ⁄ 2 } (6.82)
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6.3.6 Gate charge model
2
2
2
– V ox
 S spg – S adg
= -------------------------------- ⋅  ---------------------------
RON T ⋅ I ohm 
2

V sp < V g 1 :
V g1
V sp ≥ V g 1 :
V g1 = 0
(6.83)
(6.84)
2
2
2
3
3
4 ⋅ V ox
 Y dpg – Y adg Y dpg – Y adg
= -------------------------------- ⋅  ---------------------------- + -----------------------------
RON T ⋅ I ohm 
2
3

V dp ≥ V g 1 :
V g2
V dp < V g 1 :
V g2 = 0
(6.86)
DSUB ≤ 0 :
V g3 = V g4 = 0
(6.87)
DSUB > 0 :
Cb
V g 3 = -------- ⋅ V b3
C ox
(6.88)
Cb
V g 4 = -------- ⋅ V b4
C ox
(6.89)
3
3
(6.85)
3
C ox ⋅ V ox
 S spg – S adg
= ------------------------------------------ ⋅  ---------------------------
Q i ⋅ RON T ⋅ I ohm 
3

V sp < V g 1 :
V g5
V sp ≥ V g 1 :
V g5 = 0
(6.90)
(6.91)
3
3
3
4
4
– 8 ⋅ C ox ⋅ V ox
 Y dpg – Y adg Y dpg – Y adg
= ------------------------------------------ ⋅  ---------------------------- + -----------------------------(6.92)

Q i ⋅ RON T ⋅ I ohm 
3
4

V dp ≥ V g 1 :
V g6
V dp < V g 1 :
V g6 = 0
(6.93)
Q g x = – CGATE ⋅ ( V g 1 + V g 2 + V g 3 + V g 4 + V g 5 + V g 6 )
(6.94)
:
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V sp + V dp
V sp + V dp
V g 1 ≥  ------------------------ : Q gy = CGATE ⋅ V g 1 –  ------------------------




2
2
2 ⋅ CGATE ⋅ [ V g 1 – ( V sp + V dp ) ⁄ 2 ]
V sp + V dp

V g 1 < ------------------------ : Q g y = ---------------------------------------------------------------------------------------

2
V g 1 – ( V sp + V dp ) ⁄ 2
1 + 1 – -------------------------------------------------V ox
Cg fix = 0.01 ⋅ CGATE + MULT ⋅ 10
– 17
(6.95)
(6.96)
(6.97)
Q g = 0.99 ⋅ { F c ⋅ Q g x + ( 1 – F c ) ⋅ Q g y } + Cg fix ⋅ { V g 1 – ( V d + V s ) ⁄ 2 }
(6.98)
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6.3.7 Drain and source charge model
VP > 0 :
V g 1 ≥ V sp :Q s = – C ox ⋅ V ox ⋅ S spg
(6.99)
V g 1 < V sp : Q s = – 2 ⋅ C ox ⋅ V ox ⋅ Y spg
(6.100)
Q spx = Q i + Q s – 2 ⋅ C b ⋅ VSUB T ⋅ Y spb
(6.101)
2
T sp
VP ≤ 0 :
Q spx + Q spx + δ q
= ------------------------------------------2 ⋅ q ⋅ DCH
(6.102)
I hc = J sat ⋅ T sp
(6.103)
I hc = VSAT T ⁄ RON T
(6.104)
1 ⁄ ( 2 ⋅ PSAT )
Q ds = sign ⋅ TAUSC ⋅ I hc
I ds  2 ⋅ PSAT 


-------- 1 +  I -

hc


–1
(6.105)
Q d = – 0.5 ⋅ ( Q g + Q b + Q ds )
(6.106)
Q s = – 0.5 ⋅ ( Q g + Q b – Q ds )
(6.107)
Numerical Adaptation
To implement MOS Model, level 3100 in a circuit simulator, care must be taken of the
numerical stability of the simulation program. The functions as well as their derivatives
should be continuous at any bias condition that may occur during the iteration cycle.
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6.4 Self-heating
Self-heating is part of the model. It is defined in the usual way by adding a self-heating network (see Figure 16) containing a current source describing the dissipated power and both a
thermal resistance RTH and a thermal capacitance CTH.
dT
RTHT
CTH
Pdiss
Material
ATH
Si
Ge
GaAs
AlAs
InAs
InP
GaP
SiO2
1.3
1.25
1.25
1.37
1.1
1.4
1.4
0.7
Figure 16: On the left, the self-heating network, where the node voltage VdT is used in the
temperature scaling relations. Note that for increased flexibility the node dT is
available to the user. On the right are parameter values that can be used for Ath.
The resistance and capacitance are both connected between ground and the temperature node
dT. The value of the voltage VdT at the temperature node gives the increase in local temperature, which is included in the calculation of the temperature scaling relation (6.4), see section
6.3.2 on page 177.
For the value of ATH we recommend using values from literature that describe the temperature scaling of the thermal conductivity. For the most important materials, the values are
given in Figure 16, which is largely based on Ref. [1 ], see also [ 2].
For example, if the value of VdT is 0.5V, the increase in temperature is 0.5 degrees Celsius.
The total dissipated power is a sum of the dissipated power of each branch of the equivalent
circuit and is given by:
P diss = I DS ⋅ V DS
The total dissipation applies for the geometrical model (mnt1, mpt2, mos3100t3).
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Below a Pstar example is given to illustrate how self-heating works.
q Example
Title: example self-heating 3100;
circuit;
mnt_1(Vd, Vg, Vs, 0, dt) level=3100, Rth=1e6,Cth=1e-9;
R_1 ( Vdd, Vd) 100;
R_2 ( Vgg, Vg) 1k;
R_3 ( Vs, 0) 100;
e_SRC_2 (Vgg ,net101) 5;
e_SRC_1 ( Vdd, 0) 1;
e_SRC_3 ( net101, 0) 0;
end;
dc;
print: vn(dt), op(pdiss.mnt_1);
end; run;
result:
DC
Analysis.
VN(DT)
Pdiss.MNT_1
=
=
24.764E+00
24.764E-06
The voltage on node dT is 24.764e+0 V, which means that the local temperature is increased
by 24.764e+0 oC.
1.Pstar model name.
2.Pstar model name.
3.Spectre/ADS model name.
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6.5 DC Operating point output
The DC operating point output facility gives information on the state of a device at its operation point. Besides terminal currents and voltages, the magnitudes of linearized internal elements are given. In some cases meaningful quantities can be derived which are then also
given (e.g. u). The objective of the DCOP-facility is twofold:
•
•
Calculate small-signal equivalent circuit element values.
Open a window on the internal bias conditions of the device and its basic capabilities (e.g.
u).
Below the printed items are described. Cxy indicates the derivate of the charge Q at terminal x
to the voltage at terminal y, when all other terminals remain constant.
Quantity
Equation
Description
Level
3100
Model level
Ids
Ids
Drain Source current
Vds
Drain Source voltage
Vgs
Gate Source voltage
Vbs
Bulk Source voltage
Vp
Vp
Channel pinch-off voltage
gm
dIds/dVg
Transconductance
gmb
dIds/dVb
Bulk transconductance
gds
dIds/dVd
Output conductance
Qg
Cgd
-dQg/dVd
Gate charge dependence on drain voltage
Cgg
dQg/dVg
Gate charge dependence on gate voltage
Cgs
-dQg/dVs
Gate charge dependence on source voltage
Cgb
-dQg/dVb
Gate charge dependence on bulk voltage
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Cbd
-dQb/dVd
Bulk charge dependence on drain voltage
Cbg
-dQb/dVg
Bulk charge dependence on gate voltage
Cbs
-dQb/dVs
Bulk charge dependence on source voltage
Cbb
dQb/dVb
Bulk charge dependence on bulk voltage
Qd
Drain charge
Cdd
+dQd/dVd
Drain charge dependence on drain voltage
Cdg
-dQd/dVg
Drain charge dependence on gate voltage
Cds
-dQd/dVs
Drain charge dependence on source voltage
Cdb
-dQd/dVb
Drain charge dependence on bulk voltage
Qs
Source charge
Csd
-dQs/dVd
Source charge dependence on drain voltage
Csg
-dQs/dVg
Source charge dependence on gate voltage
Css
+dQs/dVs
Source charge dependence on source voltage
Csb
-dQs/dVb
Source charge dependence on bulk voltage
u
gm/gds
Transistor gain
Rout
1/gds
Small signal output resistance
Vearly
Ids/gds
Equivalent Early voltage
Iohm
Iohm
Drain source current excluding velocity saturation
Ihc
Ihc
Critical current for velocity saturation.
The additional operating point output for the model including self-heating (see section 6.4) is
listed in the table below.
Quantity
Equation
Description
TK
TK
Actual temperature including self-heating
Pdiss
Pdiss
Power dissipation
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When the parameter PRINTSCALED is set to 1, the device parameter set after geometrical
and temperature scaling is added to the OP output:
Quantity
Description
RONT
Ohmic resistance at zero bias
RSATT
Space charge resistance at zero bias
VSATT
Critical drain-source voltage for hot carriers
PSAT
Velocity saturation coefficient
VP
Pinch off voltage at zero gate and substrate voltages
TOX
Gate oxide thickness
DCH
Doping level channel
DSUB
Doping level substrate
VSUBT
Substrate diffusion voltage
CGATE
Gate capacitance at zero bias
CSUBT
Substrate capacitance at zero bias
TAUSC
Space charge transit time of the channel
Remarks:
•
When Vds<0, gm and gmb are calculated with drain and source terminals interchanged (see
section on Channel Type Declarations). The terminal voltages and IDS keep their sign.
• The signs of Vp follow the conventions of the model parameter set. The parameter set is
always assumed to correspond to an n-channel device.
•
MULT is a scaling parameter that multiplies all currents and charges by the value of
MULT. This is equivalent to putting MULT (a number) MOS transistors in parallel. And as a
consequence MULT effects the operating point output.
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A non-existent conductance, Gmin, is connected between the nodes DS. This conductance
Gmin does not influence the DC-operating point.
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6.6 Simulator specific items
6.6.1 Pstar syntax
n channel
p channel
n channel self-heating
p channel self-heating
:
:
:
:
mn_n (d,g,s,b)
mp_n (d,g,s,b)
mnt_n (d,g,s,b, dt)
mpt_n (d,g,s,b, dt)
level=3100, <parameters>
level=3100, <parameters>
level=3100, <parameters>
level=3100, <parameters>
n
:
occurrence indicator
<parameters>
:
list of model parameters
d,g,s, b and dt are drain, gate, source, bulk and self-heating terminals respectively.
6.6.2 Spectre syntax
n channel
:
p channel
:
n channel self-heating:
p channel self-heating:
model modelname mos3100 type=n <modpar>
componentname d g s b modelname <inpar>
model modelname mos3100 type=p <modpar>
componentname d g s b modelname <inpar>
model modelname mos3100t type=n <modpar>
componentname d g s b dt modelname <inpar>
model modelname mos3100t type=p <modpar>
componentname d g s b dt modelname <inpar>
modelname
:
name of model, user-defined
componentname
:
occurrence indicator
<modpar>
:
list of model parameters
<inpar>
:
list of instance parameters
d,g,s, b and dt are drain, gate, source, bulk and self-heating terminals respectively.
3 Note
Warning! In Spectre, use only the parameter statements type=n or type=p. Using any other
string and/or numbers will result in unpredictable and possibly erroneous results.
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6.6.3 ADS syntax
n channel
:
p channel
:
model modelname mos3100 gender=1 <modpar>
modelname:componentname d g s b <instpar>
model modelname mos3100 gender=0 <modpar>
modelname:componentname d g s b <instpar>
model modelname mos3100t gender=1 <modpar>
modelname:componentname d g s b dt <instpar>
model modelname mos3100t gender=0 <modpar>
modelname:componentname d g s b dt <instpar>
n channel self-heating:
p channel self-heating:
modelname
:
name of model, user-defined
componentname
:
occurrence indicator
<modpar>
:
list of model parameters
<instpar>
:
list of instance parameters
d,g,s, b and dt are drain, gate, source, bulk and self-heating terminals respectively.
6.6.4 The ON/OFF condition for Pstar
The solution for a circuit involves a process of successive calculations. The calculations are
started from a set of ‘initial guesses’ for the electrical quantities of the nonlinear elements. A
simplified DCAPPROX mechanism for devices using ON/OFF keywords is mentioned in [3].
By default the devices start in the default state.
Nu
n-channel
ON
OFF
VDS
2.0
2.0
2.0
VGS
-2.0
-2.0
VSB
0.0
0.0
© NXP 1992-2011
Default
ON
OFF
VDS
-2.0
-2.0
-2.0
-4.0
VGS
2.0
2.0
4.0
2.0
VSB
0.0
0.0
-2.0
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6.6.5 The ON/OFF condition for Spectre
Nu
n-channel
OFF
Triode
Saturation
Subthreshold
Reverse
Forward Breakdown
VDS
0.0
0.75
1.25
0.0
0
0
0
VGS
0.0
2.0
1.25
0.0
0
0
0
VSB
0.0
0.0
0.0
0.0
0
0
0
N
p-channel
OFF
Triode
Saturation
Subthreshold
Reverse
Forward Breakdown
VDS
0.0
-0.75
-1.25
0.0
0
0
0
VGS
0.0
-2.0
-1.25
0.0
0
0
0
VSB
0.0
0.0
0.0
0.0
0
0
0
6.6.6 The ON/OFF condition for ADS
n-channel
p-channel
Default
Default
VDS
0
VDS
0
VGS
0
VGS
0
VSB
0
VSB
0
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6.7 References
[1] V. Palankovski R. Schultheis and S. Selberherr, Modelling of power heterojunction bipolar transistor on gallium arsenide,IEEE Trans. Elec. Dev., vol 48, pp.
1264-1269, 2001. Note: the paper uses α = 1.65 for Si, but α = 1.3 goves a better fit:
also, k300 for GaAs is closer to 40 than to the published value of 46 (Palankovski,
personal communication).
[2] Sze, S.M., Physics of semiconductor devices, 2nd edition, John Wiley & Sons,
Inc., New York, 1981
[3] Pstar User Manual.
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Hyp functions
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hyp1
ε
0
Figure 7:
X
1
2
2
hyp 1 ( x ;ε ) = --- ⋅ ( x + x + 4 ⋅ ε )
2
x0
ε
hyp2
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hyp 2 ( x ; x 0 ;ε ) = x – hyp 1 ( x – x 0 ;ε )
t
Figure 8:
x
x0
0
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Hyp functions
xo+hyp1(-xo;ε)
ε
hyp3
x0
0
Figure 9:
x
hyp 3 ( x ; x 0 ;ε ) = hyp 2 ( x ; x 0 ;ε ) – hyp 2 ( 0 ; x 0 ;ε )
for ε = ε ( x 0 )
hyp4
ε
-hyp1(-xo;ε)
xo
x
0
hyp 4 ( x ; x 0 ;ε ) = hyp 1 ( x – x 0 ;ε ) – hyp 1 ( – x 0 ;ε )
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x0
ε
hyp5
xo
0
x
2

ε 
Figure 11: hyp 5 ( x ; x 0 ;ε ) = x 0 – hyp 1  x 0 – x – ----- ,ε
x0 

for ε = ε ( x 0 )
The hypm-function:
x⋅ y
hypm [ x, y;m ] = ---------------------------------------------------2⋅m
2 ⋅ m 1 ⁄ (2 ⋅ m)
(x
+y
)
(1.289)
setlength{unitlength}{0.40900pt} begin{picture}(1500,900)(0,0) enrm hinlines drawline[-50](264,158)(1436,158) hinlines drawline[-50](264,158)(264,787) hicklines path(264,158)(264,178)
hicklines path(264,787)(264,767) put(264,113){makebox(0,0){0}} hicklines path(264,158)(1436,158)(1436,787)(264,787)(264,158) put(45,472){makebox(0,0)[l]{shortstack{hyp
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Spectre Specific Information
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Imax, Imelt, Jmelt parameters
Introduction
Imax, Imelt and Jmelt are Spectre-specific parameters used to help convergence and to prevent numerical problems. We refer in this text only to the use of Imax model parameter in
Spectre with SiMKit devices since the other two parameters, Imelt and Jmelt, are not part of
the SiMKit code. For information on Imelt and Jmelt refer to Cadence documentation.
Imax model parameter
Imax is a model parameter present in the following SiMKit models:
– juncap and juncap2
– psp and pspnqs (since they contain juncap models)
In Mextram 504 (bjt504) and Modella (bjt500) SiMKit models, Imax is an internal parameter
and its value is set through the adapter via the Spectre-specific parameter Imax.
The default value of the Imax model parameter is 1000A. Imax should be set to a value which
is large enough so it does not affect the extraction procedure.
In models that contain junctions, the junction current can be expressed as:
V
I = I s exp  ------------------ – 1
 N ⋅ φ TD 
(1.290)
The exponential formula is used until the junction current reaches a maximum (explosion)
current Imax.
V exp l
I max = I s exp  ----------------– 1
 N ⋅ φ TD- 
(1.291)
The corresponding voltage for which this happens is called Vexpl (explosion voltage). The
voltage explosion expression can be derived from (1):
I max
V exp l = N ⋅ φ TD log  ---------- + 1
 Is 
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V > V exp l the following linear expression is used for the junction current:
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(1.292)
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Spectre Specific Information
Is
V exp l
I = I max + ( V – V exp l ) ------------------ exp  ------------------
 N ⋅ φ TD
N ⋅ φ TD
(1.293)
Region parameter
Region is an Spectre-specific model parameter used as a convergence aid and gives an estimated DC operating region. The possible values of region depend on the model:
– For Bipolar models:
– subth: Cut-off or sub-threshold mode
– fwd: Forward
– rev: Reverse
– sat: Saturation.
– off1
–
– For MOS models:
– subth: Cut-off or sub-threshold mode;
– triode: Triode or linear region;
– sat:
Saturation
1
– off
For PSP and PSPNQS all regions are allowed, as the PSP(NQS) models both have a MOS
part and a juncap (diode). Not all regions are valid for each part, but when e.g. region=forward is set, the initial guesses for the MOS will be set to zero. The same holds for setting a
region that is not valid for the JUNCAP.
– For diode models:
– fwd: Forward
– rev: Reverse
– brk: Breakdown
– off1
Model parameters for device reference temperature in Spectre
This text describes the use of the tnom, tref and tr model parameters in Spectre with SiMKit
devices to set the device reference temperature.
1.Off is not an electrical region, it just states that the user does not know in what state the
device is operating
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A Simkit device in Spectre has three model parameter aliases for the model reference temperature, tnom, tref and tr. These three parameters can only be used in a model definition, not as
instance parameters.
There is no difference in setting tnom, tref or tr. All three parameters have exactly the same
effect. The following three lines are therefore completely equivalent:
model nmos11020 mos11020 type=n tnom=30
model nmos11020 mos11020 type=n tref=30
model nmos11020 mos11020 type=n tr=30
All three lines set the reference temperature for the mos11020 device to 30 C.
Specifying combinations of tnom, tref and tr in the model definition has no use, only the
value of the last parameter in the model definition will be used. E.g.:
model nmos11020 mos11020 type=n tnom=30 tref=34
will result in the reference temperature for the mos11020 device being set to 34 C, tnom=30
will be overridden by tref=34 which comes after it.
When there is no reference temperature set in the model definition (so no tnom, tref or tr is
set), the reference temperature of the model will be set to the value of tnom in the options
statement in the Spectre input file. So setting:
options1 options tnom=23 gmin=1e-15 reltol=1e-12 \
vabstol=1e-12 iabstol=1e-16
model nmos11020 mos11020 type=n
will set the reference temperature of the mos11020 device to 23 C.
When no tnom is specified in the options statement and no reference temperature is set in the
model definition, the default reference temperature is set to 27 C.
So the lines:
options1 options gmin=1e-15 reltol=1e-12 vabstol=1e-12 \
iabstol=1e-16
model nmos11020 mos11020 type=n
will set the reference temperature of the mos11020 device to 27 C.
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The default reference temperature set in the SiMKit device itself is in the Spectre simulator
never used. It will always be overwritten by either the default "options tnom", an explicitly
set option tnom or by a tnom, tref or tr parameter in the model definition.
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June 2010
OvervoltageSpecification
OvervoltageSpecification
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OvervoltageSpecification
June 2010
Overvoltage warnings in SiMKit
Introduction
Overvoltage flagging is signalling that a (terminal) voltage is outside a specified safe range.
A warning will be given when the conditions for giving a warning are fulfilled.
Simple checks for overvoltage have been added to the following models: mos903, mos1100,
mos1101, mos1102, mos2002, mos2003, mos3100, mos4000, psp102, psp103.
The checks are done on terminal voltages of the models.
There are many ways to define overvoltage. For a general overvoltage flagging solution Verilog-A should be used.
Extra parameters for overvoltage flagging
A set of extra parameters has been added to the mos models mos903, mos1100, mos1101,
mos1102, mos2002, mos2003, mos3100, mos4000, psp102, psp103.
Table 6:
Name
Unit
Default Description
VBOX
V
0.0
Oxide breakdown voltage.
Checking will be done if VBOX > 0
VBDS
V
0.0
Drain-source breakdown voltage
Checking will be done if VBDS > 0
TMIN
s
0.0
Ovcheck tmin value
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For mos models the safe region is:
V gs < VBOX and V gd < VBOX and V ds < VBDS
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OvervoltageSpecification
enter msg
VBOX
leave msg
Ovcheck: two terminal dummy model
A (dummy) two-terminal model ovcheck has been implemented that can be used to check if
the voltage between the two terminals is within or without a so called safe region.
The model parameters are:
Name
Unit
Default Description
VLOW
V
0.0
Lower bound of safe region
VHIGH
V
0.0
Upper bound of safe region
Checking will be done when VHIGH > VLOW
TMIN
s
0.0
Ovcheck tmin value
For the ovcheck model the safe region is:
VLOW ≤ V t1 – V t2 ≤ VHIGH , where t1 is the first and t2 is the second terminal.
Functionality
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In Spectre and Pstar
At the end of a DC analysis or in a transient analysis after each time step a check wil be done
if the device is inside or outside the safe region.
A warning is given whenever the device enters or leaves the safe region.
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OvervoltageSpecification
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In Spectre only
To prevent too many warnings in a Spectre transient analysis the model parameter TMIN has
been introduced. If the time between leaving and entering the safe region is less than the
TMIN value no warning is given.
Because of the TMIN parameter a warning cannot be issued when leaving the safe region. A
warning is given when the device enters the safe region again. This warning includes the time
and the voltage when the safe region was exited.At the end of the transient warnings are
given for devices that are still out of the safe range.
In Pstar TMIN may be specified as a model parameter, but it will be ignored.
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Parameter PARAMCHK
Parameter PARAMCHK
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Parameter PARAMCHK
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Parameter PARAMCHK
Introduction
All models have the parameter PARAMCHK. It is not related to the model behavior, but has
been introduced control the clip warning messages. Various situations may call for various
levels of warnings. This is made possible by setting this parameter.
PARAMCHK model parameter
This model parameter has been added to control the amount of clip warnings.
PARAMCHK <
PARAMCHK
≥
0 Clip warnings for instance parameters (default)
PARAMCHK
≥
1
PARAMCHK
≥
2 Clip warnings for electrical parameters at initialisation
PARAMCHK
≥
3 Clip warnings for electrical parameters during evaluation.
This highest level is of interest only for selfheating jobs,
where electrical parameters may change dependent on
temperature.
Clip warnings for model parameters
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0 No clip warnings
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Bibliography
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Bibliography
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