SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

260 CHAPTER 6. BIPOLAR JUNCTION TRANSISTORS

Minority charge density

Holes

Electrons

Holes

peo

nbo n

co

IE

IB

IC

Minority charge density

Holes

Electrons

Holes

IB~ 0

Minority charge density

Holes

Electrons

Holes

SATURATION FORWARD ACTIVE CUTOFF

Forward Forward Forward Reverse

Reverse Reverse

Figure 6.8: The band profile and minority charge distribution in a BJT under saturation, forward
active, and cutoff modes.

the Ebers-Moll model. We can write the currents given in equation 6.3.10 and equation 6.3.17
as

IE=−IES

[

exp

(

eVBE

kBT

)

− 1

]

+αRICS

[

exp

(

−

eVCB

kBT

)

− 1

]

(6.3.20)

IC=αFIES

[

exp

(

eVBE

kBT

)

− 1

]

−ICS

[

exp

(

−

eVCB

kBT

)

− 1

]

(6.3.21)

where

IES=

eADbnbo

Lb

coth

(

Wbn

Lb

)

+

eADepeo

Le

(6.3.22)

ICS=

eADcpco

Lc

+

eADbnbo

Lb

coth

(

Wbn

Lb

)

(6.3.23)

αFIES=αRICS=

eADbnbo

Lbsinh

(

Wbn

Lb

) (6.3.24)

Notice the symmetry underlying these equations. This symmetry allows us to develop a simple
model described in figure 6.10. The parameterαFrepresents the common-base current gain in
the forward active mode,ICSgives the reverse-bias BCJ current,αRis the common-base current
gain for the inverse active mode (i.e., EBJ is reverse biased and CBJ is forward biased) andIES