Atoms, Molecules, and Semiconductor Devices - Nanophysics of Solar and Renewable Energy - page 82

This makes explicit the strong temperature dependence of the reverse current,
since we know from (3.58) that n i ¼N c N v exp( E G / k B T ) with strong exponential
variation with T .
Since the reverse current density J rev is an important parameter in the operation of
solar cells, it is clear that their operating temperature is an important factor. The
minority carrier diffusion length is important in solar cells. The absorbed light photons
generate electron - hole pairs, and it is desirable to have the resulting minority carrier
reach the junction field and transfer across to drive current in the external circuit,
before recombining. In solar cell design, optimization is needed between the distance
to fully absorb light (the absorption length) and theminority carrier diffusion length, to
allow all of the photons to be converted, and then all of the resulting electron - hole pairs
to diffuse to reach the junction field and cause external current ow.
The current density under applied bias V , from these considerations, can be
expressed as

J ¼ J rev ½ exp ðeV = k B TÞ 1 : ð 3 : 68 Þ

Positive applied bias voltage V (not shown in Figure 3.16c) raises bands on the
right, as indicated by probability P for electron on the right to attain kinetic energy
equal to barrier height and flow to the left: P¼ exp( e ( V B V )/ k B T ). Forward current

in this device is electrons from right to left, forward bias reduces the band bending.
Positive or forward bias for this device is de ned as the bias direction that reduces the
band shift, and shifts the electron conduction band (on the N-side, the right side) up
to allowmore ready transfer of electrons into the p-type region, from right to left, the
energy shift being e ( V b V ). So, forward bias, positive V , reduces the shift of the
bands.
At strong forward bias, with applied potential V¼V B , the electrons will flow from
right to left without any barrier at all from the n-type side to the p-type side and this
will be like a short circuit. So, the forward I - V characteristics of the PN junction are
governed by the factor exp( e ( VV b )/ k B T ). It is an exponentially rising characteristic
versus V .
In reverse bias, the only current that flows is the described diffusion current that is
independent of applied voltage. This current comes as thermally present electrons
and thermally present holes diffuse and reach the junction electric field at the center
of the junction.
If light falls on the PN junction, as sketched in Figure 3.16c, the result will be
generation of electron - hole pairs. This amounts to generating large numbers of
minority carriers, and these photogenerated minority carriers will greatly enhance
the reverse current. The resulting current density fromabsorbed light is described by
J¼J L that would flow if the junction were short-circuited.
If the junction is open circuit, so the current is zero, then J ¼ J rev (exp( eV / k B T )
1) J L ¼ 0. That is equivalent to a maximum open-circuit voltage

V oc ¼ðk B T = eÞ ln ðJ L = J rev þ 1 Þ: ð 3 : 69 Þ