Image Processing Reference
In-Depth Information
(a)
(b)
Metal
electrode
+
+
+
N
D
+
+
+
x
x
0
x
Maximum potential is
located in the center
FIGURE 2.14
Simplified model of potential profile of buried MOS structure: (a) spatial distribution; (b) potential
distribution.
ɛ
0
= vacuum permittivity
e
= elementary charge
N
D
= donor density
Thus, as a quadratic differential is a constant value, the potential distribution ϕ is
expressed as follows:
φ=
−
eN
xx c
(
)
+
2
D
−
(2.2)
0
κε
2
0
Therefore, as Figure 2.14b shows, the potential profile is expressed by a quadratic func-
tion of
x
, whose curvature is in proportion to donor density and convex downward, and
the maximum value is
c
at the coordinate point
x
=
x
0
. This means the potential maxi-
mum is located in the center. Downward is defined as potentially positive here as usual.
The boundary condition in a real device is not bilaterally symmetric, which means that
the selected part of a quadratic function curve only shifts to either side according to the
boundary condition and is really a part of the quadratic function curve that Equation 2.2
shows. The nonuniformity of the impurity density in a real device only causes partial dis-
tortion from a perfect quadratic curve.
As a result, the potential profile in the
n
-type layer, as has been considered in Figure 2.13d,
is understood to be a convex downward quadratic curve, as shown in Figure 2.15.
It is important that the maximum point of the potential is located inside the silicon, sepa-
rate both spatially and energetically from the silicon-oxide interface so that the electrons
can exist and pass without touching the interface. In practice, this enables avoidance of the
influence of the interface state existing in the interface, which will be described as a basic
structure of the buried CCD in Section 5.1.1.
