SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

4.8. DIODE APPLICATIONS: AN OVERVIEW 187

A similar set of equations for electrons gives us the following expression fornp(x)in the neutral
p-region:

np(x)=(np 0 +τnGL)

[

1 −exp

(

x+Wp

Ln

)]

(4.8.6)

The slope of the charge profile at the edge of the depletion region is

dpn(Wn)

dx

=

pn 0 +τpGL

Lp

(4.8.7)

Therefore

Jp(x=Wn)=eDp

(

pn 0 +τpGL

Lp

)

(4.8.8)

Similarly,

Jn(x=Wp)=eDn

(

np 0 +τnGL

Ln

)

(4.8.9)

The reverse saturation currentJRis then given by

JR=e

[

Dn

np,bulk

Ln

+Dp

pn,bulk

Lp

]

(4.8.10)

wherenp,bulk(pn,bulk)is the minority carrier concentration in the bulk in non-equilibrium (steady
state). Herenp,bulk=np 0 +τnGL. By changing the slope of the minority profile at the edge
of the junction, such as by shining light on the diode, it is possible to control the reverse cur-
rent across the diode. This is shown schematically in figure 4.25c. Controlling and monitoring
the current flowing across a reverse bias diode forms the basis of a large number of devices,
including photodetectors and bipolar transistors. As the incident light intensity is enhanced, or
equivalently the electron-hole pair generation rate is increased, the reverse current increases as
is shown schematically in figure 4.24, where theI−Vplane is demarcated into four quadrants.
The photodetector operation is in the third quadrant. Notice here that the current and voltage
have the same sign (negative) and hence the device dissipates power (a positive product of cur-
rent and voltage). However, if a positive voltage is applied to the diode while light is incident on
the junction then the sign of the current is negative and the sign of the voltage across the diode
is positive. This results in a negative product of current and voltage or the diode is a source of
power and not a dissipater of power. This is the regime of operation of the solar cell and is in
the fourth quadrant of theI−Vplane. The current characteristic is best analyzed by employing
the rule that the current through the diode isalways the sum of forward and reverse currents. In
the absence of any energy source (other than thermal) carriers contributing to both forward and
reverse currents are generated thermally (either by the thermal ionization of dopants, or band-
to-band generation). At zero bias these currents balance each other. In a solar cell under optical
excitation the forward current is unchanged and continues to be provided by the thermal injection
of carriers across the junction (as has been described before) whereas the reverse current changes
dramatically and is carried dominantly by photo-generated carriers. This is the reason why the
net current is not zero at zero applied bias in an illuminated solar cell. This current is called