SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

6.3. STATIC CHARACTERISTICS: CURRENT - VOLTAGE RELATION 257

diffusion coefficientsDbandDein the base and emitter, respectively,

IEn=InEB = eADb

dδnb(x)

dxb

∣

∣∣

∣

xb=0

(6.3.6)

IEp=IpBE = −eADe

dδp(x)

dxe

∣∣

∣∣

xe=0

(6.3.7)

These are the current components shown in figure 6.6 and represent the emitter current compo-
nents II, III, and IV. Assuming an exponentially decaying hole density into the emitter, we have,
as in the case of ap-ndiode ,

IEp=−A

(

eDepeo

Le

)[

exp

(

eVBE

kBT

)

− 1

]

(6.3.8)

Using the electron distribution derived in the base, we have for the electron part of the emitter
current

IEn = −

eADbnbo

Lbsinh

(

Wbn

Lb

)

{

cosh

(

Wbn−xb

Lb

)[

exp

(

eVBE

kBT

)

− 1

]

−cosh

(

xb

Lb

)[

exp

(

−

eVCB

kBT

)

− 1

]}∣∣

∣

∣

at xb=0

= −

eADbnbo

Lbsinh

(

Wbn

Lb

)

{

cosh

(

Wbn

Lb

)[

exp

(

eVBE

kBT

)

− 1

]

−

[

exp

(

−

eVCB

kBT

)

− 1

]}

(6.3.9)

For high emitter efficiency we wantIEnto be much larger thanIEp. This occurs if the emitter
doping is much larger than the base doping. The total emitter current becomes

IE = IEn+IEp=−

{

eADbnbo

Lb

coth

(

Wbn

Lb

)

+

eADepeo

Le

}

[

exp

(

eVBE

kBT

)

− 1

]

+

eADbnbo

Lbsinh

(

Wbn

Lb

)

[

exp

(

−

eVCB

kBT

)

− 1

]

(6.3.10)

The collector current components can be obtained by using the same approach. Thus we have

IBCn = eADb

dδnb(xb)

dxb

∣∣

∣∣

xb=Wbn

(6.3.11)

IBCp = eADp

dδp(xc)

dxc

∣∣

∣

∣

xc=0

(6.3.12)