21.4 Bipolar Diodes
553
10
1
10
10
10
0
-1
-2
w (µm)
m
10
14
10
15
10
16
10
17
10
18
N (cm )
B
-3
GaAs
Ge
Si
Fig. 21.37 Maximum width of the depletion layer w m (21.97) at room temperature for deep depletion for GaAs, Si and
Ge diodes as a function of bulk doping level
inversion regime is given by
C ∼ =
i
d + w m i // s
.
(21.98)
21.3.4 Nonideal MIS Diode
In a real, i.e. nonideal, MIS diode, the difference φ ms in the work functions of the metal and semiconductor (cf. (21.77)) is no longer zero. Therefore, the capacitance versus voltage relation is shifted with
respect to the ideal MIS diode characteristic by the flat-band voltage shift V FB
V FB = φ ms −
Q ox
C i
.
(21.99)
Additionally, the flat-band voltage can be shifted by charges Q ox in the oxide that have been neglected
so far. Such charges can be trapped, i.e. fixed with regard to their spatial position, or mobile, e.g. ionic
charges such as sodium.
For Al as metal (φ m = 4.1 eV) and n-type Si (φ s = 4.35 eV), the flat-band voltage shift is φ ms =
−0.25 V, as shown schematically in Fig. 21.38a for zero bias. V FB is split into 0.2 eV and 0.05 eV for the
oxide and the silicon, respectively. In Fig. 21.38b, the dependence of φ ms on the doping, conductivity
type and metal is shown for various SiO 2 /Si MIS diodes. An Au-SiO 2 /Si diode with p-type Si and
N A ≈ 10
15 cm
−3 fulfills the condition of an ideal MIS diode with regard to φ ms = 0.
21.4 Bipolar Diodes
A large class of diodes is based on pn junctions. In a homo pn junction an n-doped region is next
to a p-doped region of the same semiconductor. Such a device is called bipolar. At the junction a
depletion region forms. The transport properties are determined by the minority carriers. An important
variation is the pin-diode in which an intrinsic (or lowly doped) region is between the doped region
553
10
1
10
10
10
0
-1
-2
w (µm)
m
10
14
10
15
10
16
10
17
10
18
N (cm )
B
-3
GaAs
Ge
Si
Fig. 21.37 Maximum width of the depletion layer w m (21.97) at room temperature for deep depletion for GaAs, Si and
Ge diodes as a function of bulk doping level
inversion regime is given by
C ∼ =
i
d + w m i // s
.
(21.98)
21.3.4 Nonideal MIS Diode
In a real, i.e. nonideal, MIS diode, the difference φ ms in the work functions of the metal and semiconductor (cf. (21.77)) is no longer zero. Therefore, the capacitance versus voltage relation is shifted with
respect to the ideal MIS diode characteristic by the flat-band voltage shift V FB
V FB = φ ms −
Q ox
C i
.
(21.99)
Additionally, the flat-band voltage can be shifted by charges Q ox in the oxide that have been neglected
so far. Such charges can be trapped, i.e. fixed with regard to their spatial position, or mobile, e.g. ionic
charges such as sodium.
For Al as metal (φ m = 4.1 eV) and n-type Si (φ s = 4.35 eV), the flat-band voltage shift is φ ms =
−0.25 V, as shown schematically in Fig. 21.38a for zero bias. V FB is split into 0.2 eV and 0.05 eV for the
oxide and the silicon, respectively. In Fig. 21.38b, the dependence of φ ms on the doping, conductivity
type and metal is shown for various SiO 2 /Si MIS diodes. An Au-SiO 2 /Si diode with p-type Si and
N A ≈ 10
15 cm
−3 fulfills the condition of an ideal MIS diode with regard to φ ms = 0.
21.4 Bipolar Diodes
A large class of diodes is based on pn junctions. In a homo pn junction an n-doped region is next
to a p-doped region of the same semiconductor. Such a device is called bipolar. At the junction a
depletion region forms. The transport properties are determined by the minority carriers. An important
variation is the pin-diode in which an intrinsic (or lowly doped) region is between the doped region