Post on 17-Oct-2021
Lundstrom ECE 305 S15
ECE-305: Spring 2015
BJTs: Ebers-Moll Model
Professor Mark Lundstrom
Electrical and Computer Engineering Purdue University, West Lafayette, IN USA
lundstro@purdue.edu
4/27/15
Pierret, Semiconductor Device Fundamentals (SDF) pp. 403-407
1
last lecture
Lundstrom ECE 305 S15 2
1) Emitter injection efficiency 2) Base transport factor 3) Early effect 4) Speed (base transit time) 5) Effects of saturation 6) Gummel plots 7) Transconductance 8) HBTs 9) Emitter crowding
2D effects
3
n+ emitter
p base
n collector
n+
p base n-collector
n+
n+
double
diffused
BJT
emitter current crowding
4
p base
n-collector
n+
n+
IBIB
Lundstrom ECE 305 S15
emitter current crowding
5
p base
n-collector
n+
n+
IBIB
Vbase+
−
Lundstrom ECE 305 S15
emitter current crowding
6
n-collector
n+
n+
IBIB
Lundstrom ECE 305 S15
emitter and collector areas
7
p base n-collector
n+
n+
IBIB
AE
AC
AC >> AE
Lundstrom ECE 305 S15
Q1) Which is the base transport factor?
8
n+ emitter
p base
n collector
n+
FB RB IE ICIEn
IEp
ICn
IB
a) b) c) d) e)
IEn IEn + IEp( )
ICn IEp
ICn IEn IEp
ICn IEn + IEp( )
Q2) Which is beta_dc?
9
n+ emitter
p base
n collector
n+
FB RB IE ICIEn
IEp
ICn
IB
a) b) c) d) e)
IEn IEn + IEp( )
ICn IEp
ICn IEn IEp
ICn IEn + IEp( )
Q3) Which is alpha_dc?
10
n+ emitter
p base
n collector
n+
FB RB IE ICIEn
IEp
ICn
IB
a) b) c) d) e)
IEn IEn + IEp( )
ICn IEp
ICn IEn IEp
ICn IEn + IEp( )
Q4) Which is the base current?
11
n+ emitter
p base
n collector
n+
FB RB IE ICIEn
IEp
ICn
IB
a) b) c) d) e)
IEn IEn + IEp( )
ICn IEp
ICn IEn IEp
ICn IEn + IEp( )
Q5) Which is the emitter injection efficiency?
12
n+ emitter
p base
n collector
n+
FB RB IE ICIEn
IEp
ICn
IB
a) b) c) d) e)
IEn IEn + IEp( )
ICn IEp
ICn IEn IEp
ICn IEn + IEp( )
forward active region
13
n+ emitter
p base
n collector
n+
FB RB IE ICIEn
IEpIE = IEn + IEp
ICn ≈ IEn
IC ≈ IEn
IB = IEp
emitter current: forward active region
14
n+ emitter
p base
n collector
n+
FB RB IE ICIEn
IEpIE = IEn + IEp
IEn
IC ≈ IEn
IB = IEp
IEn = qAEni2
NAB
⎛⎝⎜
⎞⎠⎟Dn
WB
eqVBE /kBT
IEp = qAEni2
NDE
⎛⎝⎜
⎞⎠⎟Dp
WE
eqVBE /kBT
IE = IEn + IEp
IE = IF0 eqVBE kBT −1( )
IF0 = qAEni2
NAB
⎛⎝⎜
⎞⎠⎟Dn
WB
+ qAEni2
NDE
⎛⎝⎜
⎞⎠⎟Dp
WE
collector current: forward active region
15
n+ emitter
p base
n collector
n+
FB RB IE ICIEn
IEpIE = IEn + IEp
αT IEn
IC ≈ IEn
IB = IEp
IEn = qAEni2
NAB
⎛⎝⎜
⎞⎠⎟Dn
WB
eqVBE /kBT
IEp = qAEni2
NDE
⎛⎝⎜
⎞⎠⎟Dp
WE
eqVBE /kBT
IC =αT IEn
IC =αF IF0 eqVBE kBT −1( )
IC =αTγ F IE
αF =αTγ F
Lundstrom ECE 305 S15
base current: forward active region
16
n+ emitter
p base
n collector
n+
FB RB IE ICIEn
IEpIE = IEn + IEp
IEn
IC ≈ IEn
IB = IEp
IB = IE − IC
IC =αF IF0 eqVBE kBT −1( )
αF =αTγ F
IE = IF0 eqVBE kBT −1( )
IB = IE − IC
IB = 1−αF( ) IF0 eqVBE kBT −1( )Lundstrom ECE 305 S15
summary: forward active region
17
n+ emitter
p base
n collector
n+
FB RB IE ICIEn
IEpIE = IEn + IEp
IEn
IC ≈ IEn
IB = IEp
IC =αF IF0 eqVBE kBT −1( )
IE = IF0 eqVBE kBT −1( )
IB = 1−αF( ) IF0 eqVBE kBT −1( )IF0 = qAE
ni2
NAB
⎛⎝⎜
⎞⎠⎟Dn
WB
+ qAEni2
NDE
⎛⎝⎜
⎞⎠⎟Dp
WE
αF =αTγ F
Ebers-Moll model
18 18
Lundstrom ECE 305 S15
Question: How do we describe the BJT in any region of operation?
emitter-base junction (the forward diode)
19 19
n+ emitter
p base
n collector
n+ IE IC
IB
IEn ICn
IEp
Lundstrom ECE 305 S15
ICp
IEn = −qA Dn
WB
ni2
NAB
eqVBE kBT −1( )
IEp = −qADp
WE
ni2
NDE
eqVBE kBT −1( )
IE VBE( ) = −IEn VBE( )− IEp VBE( )
IE VBE( ) = IF0 eqVBE kBT −1( )
Base-collector junction (the reverse diode)
20 20
n+ emitter
p base
n collector
n+ IE IC
IB
IEn ICn
IEp
Lundstrom ECE 305 S15
ICp
ICn VBC( ) = qA Dn
WB
ni2
NAB
eqVBC kBT −1( )
ICp VBC( ) = qA Dp
WC
ni2
NDC
eqVBC kBT −1( )
IC VBC( ) = − ICn VBC( ) + ICp VBC( )⎡⎣ ⎤⎦
IC VBC( ) = −IR0 eqVBC kBT −1( )
Both junctions….
21 21
n+ emitter
p base
n collector
n+ IE IC
IB
IEn ICn
IEp
Lundstrom ECE 305 S15
ICp
IC VBC( ) = −IR0 eqVBC kBT −1( )
IE VBE( ) = IF0 eqVBE kBT −1( )
But…. The two junctions are coupled!
Ebers-Moll model
22 22
n+ emitter
p base
n collector
n+ IE IC
IB
IEn ICn
IEp
Lundstrom ECE 305 S15
ICp
IC VBE ,VBC( ) =αF IF0 eqVBE kBT −1( )− IR0 eqVBC kBT −1( )
IE VBE ,VBC( ) = IF0 eqVBE kBT −1( )−α RIR0 eqVBC kBT −1( )
Ebers-Moll model
23 23
Lundstrom ECE 305 S15
IC VBE ,VBC( ) =αF IF0 eqVBE kBT −1( )− IR0 eqVBC kBT −1( )
IE VBE ,VBC( ) = IF0 eqVBE kBT −1( )−α RIR0 eqVBC kBT −1( )
IB VBE ,VBC( ) = IE VBE ,VBC( )− IC VBE ,VBC( )
See Pierret SDF, Chapter 11, sec. 11.1.4
Ebers-Moll model
24 Lundstrom ECE 305 S15
IC VBE ,VBC( ) =αF IF0 eqVBE kBT −1( )− IR0 eqVBC kBT −1( )
IE VBE ,VBC( ) = IF0 eqVBE kBT −1( )−α RIR0 eqVBC kBT −1( )
αF IF0 =α RIR0
IF0 = qAEni2
NAB
⎛⎝⎜
⎞⎠⎟Dn
WB
+ qAEni2
NDE
⎛⎝⎜
⎞⎠⎟Dp
WE
αF =αTγ F
α R =αTγ R IR0 = qAEni2
NAB
⎛⎝⎜
⎞⎠⎟Dn
WB
+ qAEni2
NDC
⎛⎝⎜
⎞⎠⎟Dp
WC
Ebers-Moll model
25 25
Lundstrom ECE 305 S15
IC VBE ,VBC( ) =αF IF0 eqVBE kBT −1( )− IR0 eqVBC kBT −1( )
IE VBE ,VBC( ) = IF0 eqVBE kBT −1( )−α RIR0 eqVBC kBT −1( )
IB VBE ,VBC( ) = IE VBE ,VBC( )− IC VBE ,VBC( )
See Pierret SDF, Chapter 11, sec. 11.1.4
αF IF0 =α RIR0
Check active region
Lundstrom ECE 305 S15 26
IC VBE ,VBC( ) =αF IF0 eqVBE kBT −1( )− IR0 eqVBC kBT −1( )→αF IF0e
qVBE kBT + IR0
IE VBE ,VBC( ) = IF0 eqVBE kBT −1( )−α RIR0 eqVBC kBT −1( )→ IF0e
qVBE kBT +α RIR0
IB VBE ,VBC( ) = IE VBE ,VBC( )− IC VBE ,VBC( )→ 1−αF( ) IF0eqVBE kBT − 1−α R( ) IR0
IC ≈αF IF0eqVBE kBT
IB ≈ 1−αF( ) IF0eqVBE kBT =1−αF( )αF
IC = 1βdc
IC✔
What is ID?
27 IE = ID
IB
VBC
VBE
IE = ID
VCE =VD VD
ID
What is ID?
28 IE = ID
IBIC =αF IF0 e
qVBE kBT −1( )− IR0 eqVBC kBT −1( )
IE = IF0 eqVBE kBT −1( )−α RIR0 e
qVBC kBT −1( )
VBC = 0
VBC
VBE
IE = ID
VCE =VD
IE = IF0 eqVBE kBT −1( )
ID = IF0 eqVD kBT −1( )
IC
What is IC?
29 IE
IB = 0
IC =αF IF0 eqVBE kBT −1( )− IR0 eqVBC kBT −1( )
IE = IF0 eqVBE kBT −1( )−α RIR0 e
qVBC kBT −1( )VBC
VBE
IC
VCE
Ebers-Moll model
30 30
Lundstrom 12.5.14
IC VBE ,VBC( ) =αF IF0 eqVBE kBT −1( )− IR0 eqVBC kBT −1( )
IE VBE ,VBC( ) = IF0 eqVBE kBT −1( )−α RIR0 eqVBC kBT −1( )
IB VBE ,VBC( ) = IE VBE ,VBC( )− IC VBE ,VBC( )
αF IF0 =α RIR0
See Pierret SDF, Chapter 11, sec. 11.1.4
Ebers-Moll model (ii)
31 31 Lundstrom 12.5.14
IR0 = qADnB
WB
ni2
NAB
+DpC
WC
ni2
NDC
⎛⎝⎜
⎞⎠⎟
IF0 = qADnB
WB
ni2
NAB
+DpE
WE
ni2
NDE
⎛⎝⎜
⎞⎠⎟
αF = γ FαT
αF IF0 =α RIR0 →α R =αFIF0IR0
α R = γ RαT