SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

7.5. HIGH-FREQUENCY BEHAVIOR OF A BJT 325

B

VBE(sat)

E

C

VCE(sat)

B C

E

+

–

+

–

Figure 7.9: The BJT and a simple model for a device in the saturation mode.

Note that
ICO
IEO

=

ICS

IES

=

αF

αR

(7.4.32)

The equation forVCE(sat), after some simple manipulation, can be written as

VCE(sat)=

kBT

e

ln

[ 1

αR+

IC

IB

1 −αR

αR

1 −IICB^1 −ααFF

]

(7.4.33)

We finally substitute for the current gainsβR=αR/(1−αR),βF=αF/(1−αF)to get

VCE(sat)=

kBT

e

ln

[ 1

αR+

IC

IB

1

βR

1 −IICBβ^1 F

]

(7.4.34)

Typical values ofVCE(sat)from the expression derived here are∼ 50 mV. If one adds to this
value the voltage drop across the neutral regions of the emitter and the collector, we find that
VCE(sat)is∼0.1 V. For silicon devices typical values for the various junction voltages, are

VBE(sat) ∼ 0 .8V

VCE(sat) ∼ 0 .1V (7.4.35)

7.5 HIGH-FREQUENCYBEHAVIOROFABJT...................

An important application of bipolar transistors is in the amplification of high-frequency small
signals. For this application, the device is biased as shown in figure 7.7a, and a signalvinis