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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
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
and as a result the fraction increases.
Since the reverse injection of carriers from the base increases, the emitter-
EP EN
EP I I
γ =. By
increasing the base doping, I (^) EN increases and this reduces the fraction. As a result,
No direct effect (to a first order).
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.
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.
Increases since increasing the reverse bias of the C-B junction effectively reduce
I EP, show that the base transport factor is given by (see equation 11.42 in the textbook)
2 B
2 B
T
2
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 )
(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
α =
with
B
B B
B 2
τ
α =
We also know that, L B = D BτB
So,
2 B
2 B
T
α =
Straightforward manipulation of the equations for I C and I EP results in the above
B E E
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
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.