21.3 Metal-Insulator-Semiconductor Diodes
551
(a)
(b)
Fig. 21.35 Properties of the ideal MIS diode as a function of bias voltage V ; same semiconductor parameters as in
Fig. 21.33 with an amorphous SiO 2 ( r = 3.9, d = 5 nm) insulator (and W ms = 0). a Voltage drops V i (blue) across
the insulator and s (black) across the semiconductor. b Total charge (absolute values) in the semiconductor in linear
(black) and logarithmic (blue) scale
V = V i + s ,
(21.89)
with V i = Q s /C i being the voltage drop across the insulator. For the insulator capacitance (per area)
C i see (21.93). Both partial voltages are shown in Fig. 21.35a as a function of the bias. The voltage
drop in the insulator becomes significant for V > 2 B .
In the case of inversion, the charge (per unit area) in the space-charge region
Q s = Q d + Q n
(21.90)
is composed of the depletion charge (ionized acceptors)
Q d = −e w N A ,
(21.91)
with w being the width of the depletion region, and the inversion charge Q n , which is present only close
to the interface. The charge as a function of bias is depicted in Fig. 21.35b where in the semi-logarithmic
plot, the depletion and inversion charges can be distinguished. The charge becomes significant for
V > 2 B .
The metal surface carries the opposite charge
Q m = −Q s
(21.92)
due to global charge neutrality. The insulator itself does not contribute charges in the case of an ideal
MIS diode.
21.3.3 Capacitance
The insulator represents a capacitor with the dielectric constant i and a thickness d. Therefore, the
capacitance is
C i =
i
d
.
(21.93)
551
(a)
(b)
Fig. 21.35 Properties of the ideal MIS diode as a function of bias voltage V ; same semiconductor parameters as in
Fig. 21.33 with an amorphous SiO 2 ( r = 3.9, d = 5 nm) insulator (and W ms = 0). a Voltage drops V i (blue) across
the insulator and s (black) across the semiconductor. b Total charge (absolute values) in the semiconductor in linear
(black) and logarithmic (blue) scale
V = V i + s ,
(21.89)
with V i = Q s /C i being the voltage drop across the insulator. For the insulator capacitance (per area)
C i see (21.93). Both partial voltages are shown in Fig. 21.35a as a function of the bias. The voltage
drop in the insulator becomes significant for V > 2 B .
In the case of inversion, the charge (per unit area) in the space-charge region
Q s = Q d + Q n
(21.90)
is composed of the depletion charge (ionized acceptors)
Q d = −e w N A ,
(21.91)
with w being the width of the depletion region, and the inversion charge Q n , which is present only close
to the interface. The charge as a function of bias is depicted in Fig. 21.35b where in the semi-logarithmic
plot, the depletion and inversion charges can be distinguished. The charge becomes significant for
V > 2 B .
The metal surface carries the opposite charge
Q m = −Q s
(21.92)
due to global charge neutrality. The insulator itself does not contribute charges in the case of an ideal
MIS diode.
21.3.3 Capacitance
The insulator represents a capacitor with the dielectric constant i and a thickness d. Therefore, the
capacitance is
C i =
i
d
.
(21.93)