542
21 Diodes
Fig. 21.24 Theoretical and
experimental values of
specific contact resistances
at T = 300 K for Al/n-Si
[1735] and PtSi/n-Si [1736]
contacts as a function of
donor concentration. Solid
lines are theoretical
dependencies for different
values of the barrier height
as labeled. Adapted
from [574]
10
10
10
10
10
10
6
4
2
0
-2
-4
10
-6
N (cm )
D
-3
0
10
19
10
18
10
17
R ( cm )
c
2
N
(10 cm )
D
5
1 0
3 0
10
20
Pt/Si
Al/Si
0.60V
B =0.85V
0.40V
Fig. 21.25 Specific
contact resistance for
Ni/Au-Ge on n-type
epitaxial GaAs for varying
alloying temperatures
(2 min). Arrow at T eu
denotes the eutectic
temperature of Au-Ge.
Adapted from [1742]
j = μ E
dE
dx
.
(21.73)
Integration (remember that j is independent of x) and the boundary condition E(x = 0) = 0 yields
E(x) =
2 j
μ μ
1/2 √
x .
(21.74)
We integrate again and find
V (x) =
2
3
2 j
μ μ
1/2
x
3/2
,
(21.75)
21 Diodes
Fig. 21.24 Theoretical and
experimental values of
specific contact resistances
at T = 300 K for Al/n-Si
[1735] and PtSi/n-Si [1736]
contacts as a function of
donor concentration. Solid
lines are theoretical
dependencies for different
values of the barrier height
as labeled. Adapted
from [574]
10
10
10
10
10
10
6
4
2
0
-2
-4
10
-6
N (cm )
D
-3
0
10
19
10
18
10
17
R ( cm )
c
2
N
(10 cm )
D
5
1 0
3 0
10
20
Pt/Si
Al/Si
0.60V
B =0.85V
0.40V
Fig. 21.25 Specific
contact resistance for
Ni/Au-Ge on n-type
epitaxial GaAs for varying
alloying temperatures
(2 min). Arrow at T eu
denotes the eutectic
temperature of Au-Ge.
Adapted from [1742]
j = μ E
dE
dx
.
(21.73)
Integration (remember that j is independent of x) and the boundary condition E(x = 0) = 0 yields
E(x) =
2 j
μ μ
1/2 √
x .
(21.74)
We integrate again and find
V (x) =
2
3
2 j
μ μ
1/2
x
3/2
,
(21.75)