SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

4.3. CURRENT FLOW: P-N DIODE UNDER BIAS 159

forx>Wn

δnp(x)=Δnpoexp ((x+Wp)/Ln)

= npo[ exp (eV /kBT)−1] exp [(x+Wp)/Ln] (4.3.10)

⎧

⎨

⎩

x<−Wp

xis negative

Wpis positive

⎫

⎬

⎭

.

Holes are injected into then-side and the value of this diffusion current is

Ip(x)=−eADp

d(δp(x))

dx

=eA

Dp

Lp

(δp(x)) x>Wn (4.3.11)

The hole current injected into then-side is given by the hole current atx=Wn(after using the
value ofδp(x=Wn)from equation 4.3.9)

Ip(Wn)=e

ADp

Lp

pn( exp (eV /kBT)−1) (4.3.12)

Using similar arguments, the total electron current injected across the depletion region into the
p-side region is given by

In(−Wp)=

eADn

Ln

npo( exp (eV /kBT)−1) (4.3.13)

In this section we will assume that the diode is ideal which essentially means there is noe-h
recombination within the depletion region. In the next section we will discuss the case where
recombination occurs for a real diode. For the ideal diode the total current can be simply obtained
by adding the hole current injected acrossWnand electron current injected across−Wp,which
is clear from figure 4.7c. The sum of the electron and hole currents in the depletion region,
I=Ip+Inis given byIp(Wn)+In(−Wp)as the currents do not change in the depletion
region due to the assumption of no generation - recombination. The diode current is therefore

I(V)=Ip(Wn)+In(−Wp)

= eA

[

Dp

Lp

pn 0 +

Dn

Ln

npo

]

( exp (eV /kBT)−1)

I(V)=Io( exp (eV /kBT)−1) (4.3.14)

This is the diode equation. Under reverse bias, the current simply goes toward the value−Io,
whereIois the prefactor of the diode equation.

Io=eA

(

Dppn 0

Lp

+

Dnnpo

Ln

)

(4.3.15)

Notice that the diode current increases rapidly when a forward bias is applied and has a small
value at negative bias. This gives the diode its rectification properties.