This preview shows page 1. Sign up to view the full content.
ECE 440
Homework XII
Spring 2006
Due: Friday, March 31, 2006
1.
Assume that a p
+
n diode with a uniform cross section area, A, is built with an n region
width
l
smaller than a hole diffusion length (
l
< L
p
). This is the socalled narrow
base diode. Since for this case holes are injected into a short n region under forward
bias, we cannot use the assumption
δ
p(x
n
=
∞
) = 0 in Eq. 435. Instead, we must use
as a boundary condition the fact that
δ
p =0 at x
n
=
l
.
(a) Solve the diffusion equation to obtain
δ
px
pe
e
ee
n
n
xL
x
L
LL
np
n
p
pp
( )
=
−
⎡
⎣
⎢
⎤
⎦
⎥
−
−
()
−
−
∆
ll
(b) Show that the current in the diode is
I
=
qAD p
L
ctnh
L
e
pn
qV
kT
l
⎛
⎝
⎜
⎞
⎠
⎟
−
⎛
⎝
⎜
⎞
⎠
⎟
1
(c ) If the nregion is relatively short compared to the diffusion length, the excess hole
δ
p(x
n
)
can be approximated as a straight line, i.e. it varies linearly from
∆
p
n
at x
n
=0 to zero at the
ohmic contact (x
n
=
l
). Find the steadystate
total
excess charges, Q
p
in the nregion and
determine the percentage of error comparing the
total
excess holes in the nregion obtained
This is the end of the preview. Sign up
to
access the rest of the document.
 Spring '11
 Leburton

Click to edit the document details