Impact of Doping and Geometry on BJT Parameters in Microelectronics - Prof. E. Fred Schube, Assignments of Electrical and Electronics Engineering

Solutions to class activity 20 questions related to microelectronics technology, focusing on the impact of doping and geometry on the base transport factor (αt), emitter injection efficiency (γ), common base current gain (αdc), and common emitter current gain (βdc) in a pnp bjt. The derivation of equations and the calculation of material parameters.

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ECSE-2210 Microelectronics Technology
Class Activity 20 – Solution
1. In a BJT, indicate what happens (increase, decrease or no-effect: choose one and
understand “why”):
a. to
γ
if we increase the emitter doping?
Increases. It is the fraction of emitter current carried by the emitter majority
carriers. If we increase the majority carriers in the emitters, this fraction increases.
In a pnp transistor,
ENEP
EP
II
I
+
=
γ
. By increasing the emitter doping, IEP increases
and as a result the fraction increases.
b. to
γ
if we increase the base doping?
Since the reverse injection of carriers from the base increases, the emitter-
injection efficiency (
γ
) decreases. In a pnp transistor,
ENEP
EP
II
I
+
=γ . By
increasing the base doping, IEN increases and this reduces the fraction. As a result,
the emitter-injection efficiency (
γ
) decreases.
c. to
γ
if we increase the collector doping?
No direct effect (to a first order).
d. to
α
T if we increase the base width?
Decreases since the distance the minority carriers have to travel increases. With
the increase in the base width more carriers recombine and the base transport
factor reduces.
e. to
α
T if we increase the lifetime in the base?
Increases since the minority carriers can be collected by the collector with
negligible recombination. The carriers spend more time in the base before they
recombine, increasing the probability of being collected by the base.
f. to
α
T if we increase the C-B reverse voltage?
Increases since increasing the reverse bias of the C-B junction effectively reduce
the base width. With a reduction of the base width the
α
T increases.
2. The base transport factor,
α
T, is IC/IEP. Using the equations derived in class for IC and
IEP, show that the base transport factor is given by (see equation 11.42 in the
textbook)
2
B
2
B
T
2
1
1
L
W
+
=α
pf3

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ECSE-2210 Microelectronics Technology Class Activity 20 – Solution

  1. In a BJT, indicate what happens ( increase, decrease or no-effect : choose one and understand “why” ):

a. to γ if we increase the emitter doping?

Increases. It is the fraction of emitter current carried by the emitter majority carriers. If we increase the majority carriers in the emitters, this fraction increases.

In a pnp transistor, EP EN

EP I I

I

γ =. By increasing the emitter doping, IEP increases

and as a result the fraction increases.

b. to γ if we increase the base doping?

Since the reverse injection of carriers from the base increases, the emitter-

injection efficiency ( γ ) decreases. In a pnp transistor,

EP EN

EP I I

I

γ =. By

increasing the base doping, I (^) EN increases and this reduces the fraction. As a result,

the emitter-injection efficiency ( γ ) decreases.

c. to γ if we increase the collector doping?

No direct effect (to a first order).

d. to αT if we increase the base width?

Decreases since the distance the minority carriers have to travel increases. With the increase in the base width more carriers recombine and the base transport factor reduces.

e. to αT if we increase the lifetime in the base?

Increases since the minority carriers can be collected by the collector with negligible recombination. The carriers spend more time in the base before they recombine, increasing the probability of being collected by the base.

f. to αT if we increase the C-B reverse voltage?

Increases since increasing the reverse bias of the C-B junction effectively reduce

the base width. With a reduction of the base width the αT increases.

2. The base transport factor, αT, is I C / I EP. Using the equations derived in class for I C and

I EP, show that the base transport factor is given by (see equation 11.42 in the textbook)

2 B

2 B

T

2

L

W

α =

I EP = q A ( D B / W B ) p B0 [exp ( q V (^) EB / kT )] + q A [ W B /(2 τB )] p B0 [exp ( q V EB / kT )] I c = q A ( D B / W B ) p B0. exp ( q V EB / kT )

We know that, αT = I C / I EP

(D /W ) [exp( / )] [ /(2 )] p [exp( / )]

qA( / )p .exp( / ) B B B0 EB B B B0 EB

B B B0 EB T (^) qA p qV kT qAW qV kT

D W qV kT

  • τ

α =

with

B

B B

B 2

D

T W W

τ

α =

We also know that, L B = D BτB

So,

2 B

2 B

T

L

W

α =

Straightforward manipulation of the equations for I C and I EP results in the above

equation. Note that D B τB = L B^2.

  1. (Derivation of equation 11.41 in the textbook): Show that the emitter injection efficiency is given by:

B E E

1 E B B

DN L

DNW

Use: γ = I EP / ( I EP + I EN) γ = 1 / (1 + I EN/ I EP )

γ = 1 / [1+ (C) / (B)] γ =

0

B B B

E E EO

D W p

D L n

γ =

0

B E B

E B E D L p

DWn

B E E

1 E B B

D N L

D N W

γ=

In the equation for IEP, you can neglect the recombination part of the emitter hole current since it is small in comparison to the emitter current. This will simplify the equation.