Page 311 - Semiconductor For Micro- and Nanotechnology An Introduction For Engineers
P. 311
Interacting Subsystems
fusion current, to give a net current of zero. Thus the following current
relations hold in thermal equilibrium
j = j + j = j ( + j ) + j ( + j ) = 0 (7.166a)
,
,
,
,
n p n Drift n Diff p Drift p Diff
j = j n Drift + j n Diff = 0 j = j p Drift + j p Diff = 0 (7.166b)
,
,
,
,
p
n
n
j = qµ nE + qD ∇ = 0 j = qµ pE qD ∇ p = 0 (7.166c)
–
n
p
n
p
n
p
Biased When the thermally equilibrated junction is biased, i.e., a voltage is
Junction applied across the junction, it either adds to or subtracts from the built-in
voltage. This has the effect of either raising or lowering the band edges
on one side of the junction w.r.t. the other:
• When the band edges on the N side of the junction are lowered w.r.t
the P side, we say that the junction is reverse biased; calculations sug-
gest that a small limiting leakage current, due mainly to drift, flows
through the diode for all reverse bias voltages. In this mode the diode
appears to have a very high series resistance.
• When the band edges on the N side of the junction are raised w.r.t the
P side, we say that the junction is forward biased; calculations sug-
gest that the current through the diode, now mainly due to diffusion,
grows as an exponential function of the forward bias voltage. In this
mode the diode appears to have a very low series resistance.
It is the above asymmetry makes the PN-junction diode so very useful
technologically, because, used alone and even better in pairs, these
diodes can be used to rectify the current flow through a particular circuit
branch, as illustrated in Figure 7.20. To simplify the bookkeeping, we
now introduce further notation. Since the diode has a P and an N doped
side, and in the vicinity of the junction we expect to find both holes and
electrons on both sides, we will term the P side holes p p and the N side
electrons n n the majority carriers, and the P side electrons n p and the N
side holes p n the minority carriers. The derivation is straightforward
[7.16] if we remember the following:
308 Semiconductors for Micro and Nanosystem Technology