SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

160 CHAPTER 4. JUNCTIONS IN SEMICONDUCTORS:P-NDIODES

4.3.2 Minority and Majority Currents in thep-nDiode

Thep-ndiode is a bipolar device in which electrons and holes both carry current. To obtain
the diode current we have simply added the electron current and hole current injection across
the depletion region. This current was evaluated at its peak value at the edges of the depletion
region. The diffusion current decreases rapidly in the majority region because of recombination.
As the holes recombine with electrons in then-region, an equal number of electrons are injected
into the region. These electrons provide a drift current in then-side to exactly balance the hole
current that is lost through recombination. Let us consider the hole diffusion current in then-type
region. This current is, from equation 4.3.11, using the value ofδp(x)from equation 4.3.10,

Ip(x)=eA

Dp

Lp

pn 0 exp

(

−

x−Wn

Lp

)[

exp

(

eV

kBT

)

− 1

]

x>Wn

We have also seen that the total current is

I=eA

(

Dp

Lp

pn 0 +

Dn

Ln

npo

)[

exp

(

eV

kBT

)

− 1

]

(4.3.16)

Thus the electron current in then-type region is

In(x)=I−Ip(x)(forx>Wn)

=eA

{

Dp

Lp

pn 0

[

1 −exp

(

−

x−Wn

Lp

)]

+

Dn

Ln

np 0

}[

exp

(

eV

kBT

)

− 1

]

AstheholecurrentdecreasesfromWnintothen-side,theelectroncurrentincreasescorrespondingly
tomaintainaconstantcurrent. A similar situation exists on thep-side region. As the electron
injection current decays, the hole current compensates. The electron and hole currents flowing
in the diode have a behavior shown schematically in figure 4.7.
The rectifying properties of a diode are shown in figure 4.8. The reverse current saturates
toavalueIogiven by equation 4.3.15. Since this value is quite small, the diode is essentially
nonconducting. On the other hand, when a positive bias is applied, the diode current increases
exponentially and the diode becomes strongly conducting. The forward bias voltage at which
the diode current density becomes significant (∼ 103 A·cm−^2 ) is called the cut-in voltage. This
voltage is∼0.8V for Si diodes and∼1.2 V for GaAs diodes. The cut-in voltage is approximately
80 %of the material bandgap.

4.3.3 NarrowDiodeCurrent ...........................

In the discussion for the diode current we have assumed thenandp-sides have lengths that
are much greater than the minority carrier diffusion lengths. Often this is not the case. This
is true for high speed diodes and forp-njunctions in bipolar transistors. In this such case we