1. Reading: Pierret 11.1-11.2; Hu 8.2-8.6
Lecture 26
OUTLINE
The BJT (cont’d)
Ideal transistor analysis
Narrow base and narrow emitter
Ebers-Moll model
Base-width modulation
Reading: Pierret ; Hu

2. Notation (PNP BJT) NE  NAE DE  DN tE  tn LE  LN nE0  np0 = ni2/NE
NB  NDB
DB  DP
tB  tp
LB  LP
pB0  pn0  ni2/NB
NC  NAC
DC  DN
tC  tn
LC  LN
nC0  np0  ni2/NC
EE130/230A Fall 2013
Lecture 26, Slide 2
R. F. Pierret, Semiconductor Device Fundamentals, Fig. 11.1

3. “Game Plan” for I-V Derivation
Solve the minority-carrier diffusion equation in each quasi-neutral region to obtain excess minority-carrier profiles
different set of boundary conditions for each region
Find minority-carrier diffusion currents at depletion region edges
Add hole & electron components together  terminal currents
EE130/230A Fall 2013
Lecture 26, Slide 3

4. Emitter Region Analysis
Diffusion equation:
General solution:
Boundary conditions:
Solution:
EE130/230A Fall 2013
Lecture 26, Slide 4

5. Collector Region Analysis
Diffusion equation:
General solution:
Boundary conditions:
Solution:
EE130/230A Fall 2013
Lecture 26, Slide 5

6. Base Region Analysis Diffusion equation: General solution:
Boundary conditions:
Solution:
EE130/230A Fall 2013
Lecture 26, Slide 6

7. Since
we can write as
EE130/230A Fall 2013
Lecture 26, Slide 7

8. EE130/230A Fall 2013
Lecture 26, Slide 8

9. BJT Terminal Currents We know: Therefore: EE130/230A Fall 2013
Lecture 26, Slide 9

10. BJT with Narrow Base
In practice, we make W << LB to achieve high current gain. Then, since
we have:
EE130/230A Fall 2013
Lecture 26, Slide 10
R. F. Pierret, Semiconductor Device Fundamentals, Fig. 11.2

11. BJT Performance Parameters
Assumptions:
emitter junction forward biased, collector junction reverse biased
W << LB
Replace LE with WE’ if WE’ << LE
EE130/230A Fall 2013
Lecture 26, Slide 11

12. Ebers-Moll Model
increasing
(npn) or VEC (pnp)
C. C. Hu, Modern Semiconductor Devices for Integrated Circuits, Figure 8-2
The Ebers-Moll model is a large-signal equivalent circuit which describes both the active and saturation regions of BJT operation.
Use this model to calculate IB and IC given VBE and VBC
EE130/230A Fall 2013
Lecture 26, Slide 12

13. If only VEB is applied (VCB = 0):
aR : reverse common base gain
aF : forward common base gain
If only VCB is applied (VEB = 0): :
Reciprocity relationship:
EE130/230A Fall 2013
Lecture 26, Slide 13

14. In the general case, both VEB and VCB are non-zero:
IC: C-B diode current + fraction of E-B diode current that makes it to the C-B junction
IE: E-B diode current + fraction of C-B diode current that makes it to the E-B junction
Large-signal equivalent circuit for a pnp BJT
R. F. Pierret, Semiconductor Device Fundamentals, Fig. 11.3
EE130/230A Fall 2013
Lecture 26, Slide 14

15. Base-Width Modulation
Common Emitter Configuration, Active Mode Operation W IE IC P+ N P + 
VEB
DpB(x) IC
(VCB=0) x
VEC
W(VBC)
EE130/230A Fall 2013
Lecture 26, Slide 15

16. Ways to Reduce Base-Width Modulation
Increase the base width, W
Increase the base dopant concentration NB
Decrease the collector dopant concentration NC
Which of the above is the most acceptable action?
EE130/230A Fall 2013
Lecture 26, Slide 16

17. Early Voltage, VA Output resistance:
A large VA (i.e. a large ro ) is desirable IC
IB3
IB2
IB1
VEC VA
EE130/230A Fall 2013
Lecture 26, Slide 17

18. Derivation of Formula for VA
Output conductance:
for fixed VEB
where xnC is the width of the
collector-junction depletion region
on the base side
xnC P+ N P
EE130/230A Fall 2013
Lecture 26, Slide 18

19. EE130/230A Fall 2013
Lecture 26, Slide 19

20. Summary: BJT Performance Requirements
High gain (bdc >> 1)
One-sided emitter junction, so emitter efficiency g  1
Emitter doped much more heavily than base (NE >> NB)
Narrow base, so base transport factor aT  1
Quasi-neutral base width << minority-carrier diffusion length (W << LB)
IC determined only by IB (IC  function of VCE,VCB)
One-sided collector junction, so quasi-neutral base width W does not change drastically with changes in VCE (VCB)
Based doped more heavily than collector (NB > NC)
(W = WB – xnEB – xnCB for PNP BJT)
EE130/230A Fall 2013
Lecture 26, Slide 20