EE 434 Lecture 22 Bipolar Device Models. Quiz 14 The collector current of a BJT was measured to be...
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Transcript of EE 434 Lecture 22 Bipolar Device Models. Quiz 14 The collector current of a BJT was measured to be...
Quiz 14
The collector current of a BJT was measured to be 20mA and the base current measured to be 0.1mA. What is the efficiency of injection of electrons coming from the emitter to the collector?
IC
IB
Quiz 14
The collector current of a BJT was measured to be 20mA and the base current measured to be 0.1mA. What is the efficiency of injection of electrons coming from the emitter to the collector?
IC
IBSolution:
2001.
20
mA
mA
B
C
I
Iβ
α1
αβ
Efficiency = α
β1
βα
.9952001
200α
– Bipolar device operation dependent upon how minority carriers in base contribute to collector current
– Bipolar model (in high gain region)• Diode model for BE junction, injection efficiency for IC α
– Bipolar transistor is inherently a current amplifier with exponential relationship between collector current and VBE
• This property makes BJT very useful
Review from Last Time
t
BE
V
V
C eI SI~
t
BE
V
V
B eI SI~
t
BE
V
V
C eI SI~
CB IIβ
1
Bipolar Models
Simple dc Model
Small SignalModel
Frequency-Dependent Small Signal Model
Better Analytical dc Models
Sophisticated Model for Computer Simulations
Better Models for Predicting
Device Operation
Bipolar Models
Simple dc Model
Small SignalModel
Frequency-Dependent Small Signal Model
Better Analytical dc Models
Sophisticated Model for Computer Simulations
Better Models for Predicting
Device Operation
Bipolar ModelsSimple dc Model
IC C
E
BIB
VBE
VCE
following convention, pick IC and IB as dependent variables and VBE and VCE as independent variables
Simple dc modelIC C
E
BIB
VBE
VCE
t
BE
V
V
B eI SI~
t
BE
V
V
C eI SI~
qkT
Vt
From last time :
This has the properties we are looking for but the variables we usedin introducing these relationships are not standard
SI~
It can be shown that is proportional to the emitter area AE
Define and substitute this into the above equations ESAJ1~ SI
Simple dc model
t
BE
V
V
B eI SI~
t
BE
V
V
C eI SI~
qkT
Vt
t
BE
V
V
ESB e
βAJ
I
t
BE
V
V
ESC eAJI
qkT
Vt
JS is termed the saturation current density
Process Parameters : JS,β
Design Parameters: AE
Environmental parameters and physical constants: k,T,q
At room temperature, Vt is around 26mV
JS very small – around .25fA/u2
Transfer CharacteristicsJS=.25fA/u2
AE=400u2
VBE close to 0.6V for a two decade change in IC around 1mA
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.1 1 10
IC (mA)
VB
E
Transfer CharacteristicsJS=.25fA/u2
AE=400u2
VBE close to 0.6V for a four decade change in IC around 1mA
0.45
0.50
0.55
0.60
0.65
0.70
0.75
0.001 0.01 0.1 1 10 100 1000
IC (mA)
VB
E
Simple dc model
0
50
100
150
200
250
300
0 1 2 3 4 5
Vds
IdIC
VCE
VBE or IB
t
BE
V
V
ESC eAJI
Output Characteristics
Simple dc model
0
50
100
150
200
250
300
0 1 2 3 4 5
Vds
IdIC
VCE
VBE or IB
Better Model of Output Characteristics
Simple dc model
VBE or IB
Typical Output Characteristics
0
50
100
150
200
250
300
0 1 2 3 4 5
Vds
Id
IC
VCE
Forward ActiveSaturation
Cutoff
Forward Active region of BJT is analogous to Saturation region of MOSFET
Saturation region of BJT is analogous to Triode region of MOSFET
Simple dc model
VBE or IB
Typical Output Characteristics
0
50
100
150
200
250
300
0 1 2 3 4 5
Vds
Id
IC
VCE
Projections of these tangential lines all intercept the –VCE axis at the same place and this is termed the Early voltage, VAF (actually –VAF is intercept)
Typical values of VAF are in the 100V range
Simple dc model
VBE or IB
Improved Model
0
50
100
150
200
250
300
0 1 2 3 4 5
Vds
Id
IC
VCE
AF
CEV
V
SC VV
1eJI t
BE
t
BE
V
V
ESB e
βAJ
I Valid only in Forward Active Region
Simple dc model
VBE or IB
Improved Model
0
50
100
150
200
250
300
0 1 2 3 4 5
Vds
Id
IC
VCE
Valid in All regions of operation
11 t
BC
t
BE
V
V
SV
V
F
SE eJe
JI E
E AA
11 t
BC
t
BE
V
V
SV
V
SC eJ
eJIR
EE
AA
qkT
Vt
Not mathematically easy to work withNote dependent variables changes
Termed Ebers-Moll model
VAF effects can be added
Reduces to previous model in FA region
Simple dc model
11 t
BC
t
BE
V
V
SV
V
F
SE eJe
JI E
E AA
11 t
BC
t
BE
V
V
SV
V
SC eJ
eJIR
EE
AA
qkT
Vt
Ebers-Moll model
Process Parameters: {JS, αF, αR}
Design Parameters: {AE}
αF is the parameter α discussed earlierαR is termed the “reverse α”
F
F
F
αβ =
1-αR
R
R
αβ =
1-α
JS ~10-16A/μ2 βF~100, βR~0.4
Typical values for process parameters:
Completely dominant!
Simple dc model
11 t
BC
t
BE
V
V
SV
V
F
SE eJe
JI E
E AA
11 t
BC
t
BE
V
V
SV
V
SC eJ
eJIR
EE
AA
qkT
Vt
Ebers-Moll model
JS ~10-16A/μ2 βF~100, βR~0.4
With typical values for process parameters in forward active region (VBE~0.6V, VBC~-3V), with Vt=26mV and if AE=100μ2:
11 t
BC
t
BE
V
V
SV
V
SC eJ
eJIR
EE
AA
1410 1 128
-14
10 -51
C
10I 1.05x10 7.7x10
.
Makes no sense to keep anything other thanBE
t
V
V
C SI J e
EA
in forward active
Simple dc model
11 t
BC
t
BE
V
V
SV
V
F
SE eJe
JI E
E AA
11 t
BC
t
BE
V
V
SV
V
SC eJ
eJIR
EE
AA
qkT
Vt
Ebers-Moll model
Alternate equivalent expressions for dependent variables {IC, IB} defined earlier for Ebers-Moll equations in terms of independent variables {VBE, VCE}
1CEBE
t t
-VV
V VR
C S E
R
1+βI J A e e
β
CEBE
t t
-VV
V V
B S E
F R
1 1I J A e - e
β β
No more useful than previous equation but in form consistent with notation Introduced earlier
Simple dc modelSimplified Multi-Region Model
IC
VCE
VBE1
VBE2
VBE3
VBE4
VBE5
IC
VCE
VBE1
VBE2
VBE3
VBE4
VBE5
VCESAT
Ebers-Moll Model Simplified Multi-Region Model
1CEBE
t t
-VV
V V CER
C S E
R AF
V1+βI J A e e 1+
β V
AF
CEV
V
ESC V
V1eAJI t
BE
VBE=0.7VVCE=0.2V
IC=IB=0
CEBE
t t
-VV
V V
B S E
F R
1 1I J A e - e
β β
t
BE
V
V
ESB e
βAJ
I
Forward Active
Saturation
Cutoff
Simple dc modelSimplified Multi-Region Model
AF
CEV
V
ESC V
V1eAJI t
BE
t
BE
V
V
ESB e
βAJ
I
q
kTVt
VBE=0.7VVCE=0.2V
IC=IB=0
Forward Active
Saturation
Cutoff
Simple dc modelSimplified Multi-Region Model
AF
CEV
V
ESC V
V1eAJI t
BE
t
BE
V
V
ESB e
βAJ
I
q
kTVt
VBE=0.7VVCE=0.2V
IC=IB=0
Forward Active
Saturation
Cutoff
VBE>0.4V
VBC<0
IC<βIB
VBE<0
VBC<0
A small portion of the operating region is missed with this model but seldom operate in the missing region
Simple dc modelEquivalent Simplified Multi-Region Model
AF
CEBC V
V1βII
t
BE
V
V
ESB e
βAJ
I
q
kTVt
VBE=0.7VVCE=0.2V
IC=IB=0
Forward Active
Saturation
Cutoff
VBE>0.4V
VBC<0
IC<βIB
VBE<0
VBC<0
A small portion of the operating region is missed with this model but seldom operate in the missing region