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Plans. What does MCDE give us for the gain? How can we use the equation to improve the gain? Can we develop a compact circuit model for a BJT?. BJT Coordinate system and parameters. Forward Active minority carrier distribution. P. N. P+. p B (x). n E (x’). n E0. p B0. n C0.

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plans
Plans
  • What does MCDE give us for the gain?
  • How can we use the equation to improve the gain?
  • Can we develop a compact circuit model for a BJT?

ECE 663

slide3

Forward Active minority carrier distribution

P

N

P+

pB(x)

nE(x’)

nE0

pB0

nC0

nC(x’’)

ECE 663

emitter region
Emitter Region
  • Minority carrier diffusion equation:
  • Boundary conditions:

P

N

P+

pB(x)

nC0

pB0

nE(x’)

nC(x’’)

nE0

Wide emitter region

Law of the junction

ECE 663

base region
Base Region
  • Minority carrier diffusion equation:
  • Boundary conditions:

P

N

P+

pB(x)

nC0

pB0

nE(x’)

nC(x’’)

nE0

Law of the junction(s)

ECE 663

collector region
Collector Region
  • Minority carrier diffusion equation:
  • Boundary conditions:

P

N

P+

pB(x)

nC0

pB0

nE(x’)

nC(x’’)

nE0

Wide collector region

Law of the junction

ECE 663

currents
Currents

ECE 663

solutions in the base region
Solutions in the Base Region
  • Need to keep both positive and negative exponential terms in the general solution.
  • Apply Boundary conditions:
  • Solve for A1 and A2 and plug-in to general solution

ECE 663

collector hole current
Collector hole current

IE

IC

IEp

ICp

C

E

IEn

ICn

IB

ECE 663

simplify
Simplify
  • Active mode biasing: VEB>0 (forward bias) and VCB<0 (reverse bias)
  • Can keep only terms with emitter-base exponential

ECE 663

emitter efficiency
Emitter Efficiency
  • Want to express in terms of doping:

ECE 663

slide19

Can also calculate total emitter and collector currents by adding up electron and hole currents in the collector and emitter

Fortunately, for usable transistors (high gain) usually, the base is small

Compared to the minority carrier diffusion length and the equations

simplify

ECE 663

narrow base approximation w l b
Narrow Base Approximation: W<<LB
  • Can simplify hyperbolic functions involving W/LB
  • If <<1, then sinh()  and cosh ()1 + 2/2

Linear concentration dependence across the base

ECE 663

narrow base emitter efficiency
Narrow Base Emitter Efficiency
  •  has

If you want high emitter injection efficiency, then NB/NE << 1

 High emitter doping

ECE 663

performance factors base transport factor a t
Performance factors: Base Transport factor aT

If you want high base transport (T 1) then you want as small of a Base as possible W << LB or alternatively large LB = large p

ECE 663

performance factors common base gain a dc
Performance factors: Common Base Gain adc

Want both high emitter doping and narrow base for high gain

ECE 663

performance factors common emitter gain b dc
Performance factors: Common Emitter Gain bdc

Want both high emitter doping and narrow base for high gain

ECE 663

circuit models
Circuit models
  • If VCB=0 then the equation for the emitter current looks like the ideal diode equation:

ECE 663

slide26

Circuit models

If VEB=0, then the collector current equation also reduces to one that looks like an ideal diode equation:

ECE 663

ebers moll model
Ebers-Moll Model

The exp(VCB) term in the emitter equation and the exp(VEB) term in the collector current equation have the same prefactor:

The emitter and collector current equations can be written in terms of four parameters (three are independent):

Can show thatF= dc

ECE 663

characteristics common base
Characteristics: Common Base

Input

Output

Ebers-Moll equation

After some manipulation

ECE 663

common emitter characteristics

IC

IB

IE

Common Emitter Characteristics

Output

Input

Start with Ebers-Moll equations and some algebra to get them into the right form:

ECE 663

common base characteristics
Common Base Characteristics

Output

Input

ECE 663

common emitter characteristics1

NEW

Common Emitter Characteristics

Input

(Forward Biased

PN junction)

Output

(Reverse biased

PN junction ..

Is controlled by IB)

ECE 663