2. BJT Static Characteristics
Chapter 11
BJT Static Characteristics

3. Chapter 11
BJT Static Characteristics
Ebers-Moll Model
The Ebers-Moll model is a large-signal equivalent circuit which describes both the active and saturation regions of BJT operation.
This model is to be used to calculate IC, IE for given VBE, VBC.
IRO
IFO
If only VEB is applied (VCB = 0):
If only VCB is applied (VEB = 0):

4. Ebers-Moll Model Reciprocity relationship:
Chapter 11
BJT Static Characteristics
Ebers-Moll Model
Reciprocity relationship:
aR : reverse common base gain
aF : forward common base gain
In the general case, when VEB and VCB are non-zero:

5. Deviations from the Ideal
Chapter 11
BJT Static Characteristics
Deviations from the Ideal
Common base
Deviations, due to model limitations
Common emitter

6. Base-Width Modulation
Chapter 11
BJT Static Characteristics
Base-Width Modulation
Common-Emitter Configuration Active Mode Operation
Recalling two formulas, W P+ N P + 
VEB IE IC
DpB(x)
If –VCB increases
W decreases
bdc increases
IC increases
(VCB=0)
Increasing –VCB x W

7. Chapter 11
BJT Static Characteristics
Punch-Through
Punch-Through: E-B and C-B depletion regions in the base touch each other, so that W = 0.
As –VCB increases beyond the punch-through point, the E-B potential hill decreases and therefore increases the carrier injections and IC.
WB = xnEB + xnCB

8. Increasing reverse bias of C-B junction
Chapter 11
BJT Static Characteristics
Breakdown Mechanisms
In the common-emitter configuration, for high output voltage VCE, the output current IC will increase rapidly due to the two mechanisms: punch-through and avalanche.
Punch-through
Avalanche
Increasing reverse bias of C-B junction

9. Avalanche Multiplication
Chapter 11
BJT Static Characteristics
Avalanche Multiplication
Holes [0] are injected into the base [1], then collected by the C-B junction.
Some holes in the C-B depletion region have enough energy do impact ionization [2].
The generated electrons are swept into the base [3], then injected into the emitter [4].
Each injected electron results in the injection of IEp/IEn holes from the emitter into the base [5].
pnp BJT
For each pair created in the C-B depletion region by impact ionization, (IEp/IEn) + 1 > bdc additional holes flow into the collector.
This means that carrier multiplication in C-B depletion region is internally amplified.
M : multiplication factor

10. Geometrical Effects Emitter area is not equal to collector area.
Chapter 11
BJT Static Characteristics
Geometrical Effects
Emitter area is not equal to collector area.
Current does not flow in one direction only.
Series resistance.
Voltage drop occurs not only across the junction.
Current crowding.
Due to lateral flow, current is larger around emitter periphery than the collector periphery.

11. Graded Base Dopants are injected through diffusion.
Chapter 11
BJT Static Characteristics
Graded Base
Dopants are injected through diffusion.
More or less falling exponential distribution with distance into beneath of the semiconductor.
The doping within the base is not constant as assumed in ideal analysis.
A function of position, having maximum at E-B junction and minimum at C-B junction.
Creating a built-in electric field.
The electric field enhances the transport of minority carrier across the quasineutral width of the base.
Increase of IE and IC.
xdiff : exponential decay constant

12. Due to recombination in emitter depletion region
Chapter 11
BJT Static Characteristics
Figures of Merit
Due to recombination in emitter depletion region
Gummel Plot
Due to high level injection in base, base series resistance, and current crowding

13. Polysilicon Emitter BJT
Chapter 11
BJT Static Characteristics
Polysilicon Emitter BJT
bdc is larger for a poly-Si emitter BJT as compared with an all-crystalline emitter BJT.
This is due to reduced dpE(x)/dx at the edge of the emitter depletion region.
Lower mp
Continuity of hole current in emitter
Shallower slope  less JP
 higher g, b

14. Summary on BJT Performance
Chapter 11
BJT Static Characteristics
Summary on BJT Performance
High gain (bdc >> 1)
One-sided emitter junction, so that 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 or VCB)
One-sided collector junction, so that quasineutral base width W does not change drastically with changes in VCE or VCB.
Base doped more heavily than collector (NB > NC), W = WB – xnEB – xnCB for pnp BJT.