528
21 Diodes
(a)
(b)
Fig. 21.10 a Capacitance C (dashed line) and 1/C 2 (solid line) versus bias voltage dependence for an Au/GaAs Schottky
diode (2- µm MOVPE-grown GaAs:Si on a n-GaAs substrate) at room temperature. From the extrapolation to 1/C 2 = 0
and (21.30) we obtain V bi = 804 ±3 mV. b Donor concentration (N D = 4.8 × 10 16 cm −3 ) determined via (21.31) from
the 1/C 2 plot versus the depletion layer width (calculated using (21.29))
the bias dependence C(V ). Following we discuss the frequency and temperature dependence of the
capacitance
7 C(ω, T ), in particular when the measurement frequency is in the range of the (temperature
dependent) electron capture or emission rate (10.42, 10.43).
Bias Dependence
From (21.28) the capacitance C = |dQ/dV | (per unit area) of the space charge region is given by
C =
e N D s
2
V bi − V − β −1
=
s
w
.
(21.29)
Equation (21.29) can also be written as
1
C 2 =
2
V bi − V − β
−1
e N D s
.
(21.30)
If 1/C
2 is measured as a function of the bias voltage (C–V spectroscopy), it should be linearly
dependent on the bias voltage if the doping concentration is homogeneous (Fig. 21.10a). The doping
concentration can be determined from the slope via
N D = −
2
e s
d
dV
1
C 2
−1
,
(21.31)
(see Fig. 21.10b) and the built-in voltage V bi from the extrapolation to V = V
such that 1/C
2
= 0,
V bi = V
+ kT /e. Using (21.5) the Schottky barrier height can be determined from this [1702] via
F B n = e V
− e V n + kT −
if
B ,
(21.32)
where
if
B is the barrier lowering (21.27) due to the image force effect between the flat-band and the
zero-bias cases.
We note that for inhomogeneous doping the depth profile of the doping can be determined by C–V
spectroscopy. The 1/C
2 versus bias curve is then no longer a straight line and exhibits a varying slope.
7 Probing the capacitance as a function of the ac frequency is called admittance spectroscopy.
21 Diodes
(a)
(b)
Fig. 21.10 a Capacitance C (dashed line) and 1/C 2 (solid line) versus bias voltage dependence for an Au/GaAs Schottky
diode (2- µm MOVPE-grown GaAs:Si on a n-GaAs substrate) at room temperature. From the extrapolation to 1/C 2 = 0
and (21.30) we obtain V bi = 804 ±3 mV. b Donor concentration (N D = 4.8 × 10 16 cm −3 ) determined via (21.31) from
the 1/C 2 plot versus the depletion layer width (calculated using (21.29))
the bias dependence C(V ). Following we discuss the frequency and temperature dependence of the
capacitance
7 C(ω, T ), in particular when the measurement frequency is in the range of the (temperature
dependent) electron capture or emission rate (10.42, 10.43).
Bias Dependence
From (21.28) the capacitance C = |dQ/dV | (per unit area) of the space charge region is given by
C =
e N D s
2
V bi − V − β −1
=
s
w
.
(21.29)
Equation (21.29) can also be written as
1
C 2 =
2
V bi − V − β
−1
e N D s
.
(21.30)
If 1/C
2 is measured as a function of the bias voltage (C–V spectroscopy), it should be linearly
dependent on the bias voltage if the doping concentration is homogeneous (Fig. 21.10a). The doping
concentration can be determined from the slope via
N D = −
2
e s
d
dV
1
C 2
−1
,
(21.31)
(see Fig. 21.10b) and the built-in voltage V bi from the extrapolation to V = V
such that 1/C
2
= 0,
V bi = V
+ kT /e. Using (21.5) the Schottky barrier height can be determined from this [1702] via
F B n = e V
− e V n + kT −
if
B ,
(21.32)
where
if
B is the barrier lowering (21.27) due to the image force effect between the flat-band and the
zero-bias cases.
We note that for inhomogeneous doping the depth profile of the doping can be determined by C–V
spectroscopy. The 1/C
2 versus bias curve is then no longer a straight line and exhibits a varying slope.
7 Probing the capacitance as a function of the ac frequency is called admittance spectroscopy.