Environmental Engineering Reference
In-Depth Information
Figure 3.16 Sketches (a) intrinsic (pure) Si (b)
N-type doped Si, and (c) PN junction. Electron
energy vertically as in Figure 3.15, but wave
vector k ¼p/
electrons in P-region and p
n
holes in N-region,
which set the reverse current density. The
minority electrons in diffusion length L
n
(c,
upper left) fall down by eV
B
(across the junction)
in minority carrier lifetime t, creating reverse
current density J
rev
2e (L
n
n
p
/t) (assuming
holes behave similar to electrons). Positive
applied bias voltage V (not shown) raises bands
on the right, as indicated by increasing
probability P for electron on the right to increase
kinetic energy toward 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.
(Courtesy of M. Medikonda).
, is now assumed to be fixed at the
k location of the most important carriers
(usually k ¼0, but displaced for electrons in Si),
and x-axis denotes location in sample. It is seen
(b) that Fermi energy moves fromnear center of
gap in intrinsic material up toward conduction
band edge E
c
, with addition of donor impurities
at concentration N
D
. The concentration N
e
of
free electrons is given by Equation 3.54, but the
zero-order estimate is N
e
N
D
. (The band
density of states N
C
is given by Equation 3.53,
similarly for N
V
.) (c) shows junction formation
with energy shift eV
B
, with minority carriers: n
p
h
where we have introduced a possible forward external bias
V
, seen to reduce the band
shift. Note that permittivity is expressed as
k
and also as
e
. In practice, one side, let us
assume the N-side, may be highly doped, even to produce a metallic situation as
discussed before (3.59). In this case of a one-sided junction, the width formula
simpli
es (for
N
D
large) to
