SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

7.4. BIPOLAR JUNCTION TRANSISTORS: A CHARGE-CONTROL ANALYSIS 323

Forward-

biased

EBJ

Total

minority

charge Forward-

biased

BCJ Q

A

QR QS

QF

Figure 7.8: Minority charge in the base of a BJT in saturation mode. Charge is injected from
the emitter and the collector into the base. The figure on the right shows a representation of the
charge in terms of a uniform chargeQSand chargeQA.

The chargesQFandQRare shown in figure 7.8. The total base charge may be written as shown
on the right-hand side of figure 7.8:

QB = QF+QR

= QA+QS (7.4.16)

whereQArepresents the charge at the edge of saturation (EOS) andQSis the overdrive charge
that drives the device into saturation. The chargeQAcan be written as

QA = τFIC(EOS)=τBFIB(EOS)

IC(EOS)

IB(EOS)

= βF (7.4.17)

The overdrive chargeQScan be written as

QS=τSIBS (7.4.18)

whereIBSis the base current over and aboveIB(EOS)that brings the device to the edge of
saturation. The timeτSis the weighted mean ofτBFandτBR.
The static base current in saturation is

IB=IB(EOS)+IBS (7.4.19)

The instantaneous value of the base current is

iB(t)=

QA

τBF

+

QS

τS

+

dQS

dt

(7.4.20)

We can use the relation
QA
τBF

=

τFIC(EOS)

τBF

=

IC(EOS)

βF

(7.4.21)