234
M. Hiramoto
(5.58 eV). Thus, the SCL is formed up to 15 nm into the p
+ -type region. Since the
values toward which F converge and the values of E F in the 100 nm films agree
well, we conclude that, in thermal equilibrium, full alignment of the Fermi level
between the p
+ - and n
+ -type films is realized. Thus, we can say that the depletion
layer widths (W n ) for the n
+ -type region and (W p ) for the p
+ -type region are 3 and
15 nm, respectively, i.e., the total depletion layer width (W) is 18 nm, and the built-in
potential (V bi ), which is the difference between the bulk E F of n
+ -6 T:C 60 and that
of p
+ -6 T:C 60 , is 1.22 eV. Using these parameters, the ionized dopant concentrations
for the n
+ - and p
+ -type regions, N D
+ N
+
D and N A
– N
−
A , respectively, can be estimated.
According to the standard theory for uniformly doped inorganic semiconductors, the
total depletion layer width (W) of a pn-junction is given by Eqs. (9.3) and (9.4) [60].
W =
2ε r ε 0 V bi (N
−
A + N
+
D
q N
−
A N
+
D
(9.3)
q N
−
A x p = q N
+
D x n
(9.4)
Here, ε r , ε 0 , q, x p , and x n denote the relative dielectric constant of the semiconductor, the dielectric permittivity in a vacuum, the elementary charge, and the
depletion layer width in the p- and n-type regions, respectively. Furthermore, from
Eq. (9.4), since x n = W n = 3 nm and x p = W p = 15 nm, we obtain the relationship
N D
+
= 5 N A
– . Together with V bi = 1.22 eV, we find from Eq. (9.3) that N D
+
= 1.1
× 10
19 cm
−3 and N A
–
= 2.2 × 10
18 cm
−3 .
The electric potential distribution in the p
+ n
+ -junction can be described by integrating Poisson’s equation twice (5) and (6) with the values of W n , W p , N D
+ , and
N A
– , as shown in Fig. 9.9 (solid curve).
V (x) = −
q N
+
D
2ε r ε 0
(x + x n )
2
+ V bi (−x n ≤ x ≤ 0)
(9.5)
V (x) =
q N
−
A
2ε r ε 0
(x − x p )
2
(0 ≤ x ≤ x p )
(9.6)
Here, the red and green parts of the curve are the electric potentials in the n
+ - and
p
+ -type regions, respectively.
Based on this distribution, we attempted to reproduce the observed work function
change (Fig. 9.8, black squares). When an n
+ -type layer is deposited step-wise on
the p
+ -type layer, an energy band is bent not only in the n
+ -type layer but also
simultaneously in the underlying p
+ -type layer. Taking account of the fact that the
total amounts of charge due to ionized dopant in the n
+ -region (N D
+ x n ) and p
+ -region
(N A
– x p ) are identical, by depositing x n -thick n
+ -layer on the p
+ -layer, band-bending
up to a depth of x n in the n
+ -layer and that up to a depth of x p in the underlying p
+ -layer
develop simultaneously. So, in order to calculate the work function change, potential
change occurred in n
+ -layer (red solid double-headed arrow) and that occurred in
M. Hiramoto
(5.58 eV). Thus, the SCL is formed up to 15 nm into the p
+ -type region. Since the
values toward which F converge and the values of E F in the 100 nm films agree
well, we conclude that, in thermal equilibrium, full alignment of the Fermi level
between the p
+ - and n
+ -type films is realized. Thus, we can say that the depletion
layer widths (W n ) for the n
+ -type region and (W p ) for the p
+ -type region are 3 and
15 nm, respectively, i.e., the total depletion layer width (W) is 18 nm, and the built-in
potential (V bi ), which is the difference between the bulk E F of n
+ -6 T:C 60 and that
of p
+ -6 T:C 60 , is 1.22 eV. Using these parameters, the ionized dopant concentrations
for the n
+ - and p
+ -type regions, N D
+ N
+
D and N A
– N
−
A , respectively, can be estimated.
According to the standard theory for uniformly doped inorganic semiconductors, the
total depletion layer width (W) of a pn-junction is given by Eqs. (9.3) and (9.4) [60].
W =
2ε r ε 0 V bi (N
−
A + N
+
D
q N
−
A N
+
D
(9.3)
q N
−
A x p = q N
+
D x n
(9.4)
Here, ε r , ε 0 , q, x p , and x n denote the relative dielectric constant of the semiconductor, the dielectric permittivity in a vacuum, the elementary charge, and the
depletion layer width in the p- and n-type regions, respectively. Furthermore, from
Eq. (9.4), since x n = W n = 3 nm and x p = W p = 15 nm, we obtain the relationship
N D
+
= 5 N A
– . Together with V bi = 1.22 eV, we find from Eq. (9.3) that N D
+
= 1.1
× 10
19 cm
−3 and N A
–
= 2.2 × 10
18 cm
−3 .
The electric potential distribution in the p
+ n
+ -junction can be described by integrating Poisson’s equation twice (5) and (6) with the values of W n , W p , N D
+ , and
N A
– , as shown in Fig. 9.9 (solid curve).
V (x) = −
q N
+
D
2ε r ε 0
(x + x n )
2
+ V bi (−x n ≤ x ≤ 0)
(9.5)
V (x) =
q N
−
A
2ε r ε 0
(x − x p )
2
(0 ≤ x ≤ x p )
(9.6)
Here, the red and green parts of the curve are the electric potentials in the n
+ - and
p
+ -type regions, respectively.
Based on this distribution, we attempted to reproduce the observed work function
change (Fig. 9.8, black squares). When an n
+ -type layer is deposited step-wise on
the p
+ -type layer, an energy band is bent not only in the n
+ -type layer but also
simultaneously in the underlying p
+ -type layer. Taking account of the fact that the
total amounts of charge due to ionized dopant in the n
+ -region (N D
+ x n ) and p
+ -region
(N A
– x p ) are identical, by depositing x n -thick n
+ -layer on the p
+ -layer, band-bending
up to a depth of x n in the n
+ -layer and that up to a depth of x p in the underlying p
+ -layer
develop simultaneously. So, in order to calculate the work function change, potential
change occurred in n
+ -layer (red solid double-headed arrow) and that occurred in