88
V. L. Borblik
where the following boundary conditions are used:
V
r p
= 0, V (r n ) = V bi ,
(23)
V bi is the built-in potential of the junction. Matching of the potentials at r = r 1
and r = r 2 allows us to exclude const and obtain the equation
q N A
2ε S
r
2
p ln
r p
r 1
+
q N D
2ε S
r
2
n ln
r n
r 2
− A ln
r 2
r 1
= V bi .
(24)
Equations (21) and (24) have to be solved jointly in order to obtain r p and r n . All
the rest quantities are expressed through them.
The barrier capacitance C =
d Q p
dU
, where Q p is given by
Q p = q N A π
r
2
1 − r
2
p
L .
(25)
10
20
30
40
50
60
70
0.0
2.0x10
5
4.0x10
5
6.0x10
5
8.0x10
5
30,40 nm
r, nm
E, V/cm
30,50 nm
N A = N D = 5x10
18 cm
-3
30,60 nm
30,30 nm
20
30
40
50
60
70
80
1x10
5
2x10
5
3x10
5
4x10
5
5x10
5
30,30 nm
N A = 5x10
18 cm
-3 , N D = 5x10
17 cm
-3
30,60 nm
30,50 nm
E, V/cm
r, nm
30,40 nm
10
20
30
40
50
60
70
80
90
100
0
1x10
5
2x10
5
3x10
5
N A = 5x10
17 cm
-3 , N D = 5x10 18 cm -3
80,95 nm
80,85 nm
80,90 nm
r, nm
E, V/cm
80,80 nm
(a)
(b)
(c)
Fig. 7 Electric field distribution in the nanowire p-i-n diode at a N A = N D , b N A >> N D and
c N A << N D ; numbers near the curves are radial coordinates of the i-layer showing its extent,
dashed lines correspond to the i-layer of zero extent (p-n diode)