21.2 Metal-Semiconductor Contacts
535
(a)
1µm
(b)
(c)
Fig. 21.15 a I –V characteristic of ZnO Schottky diode (solid line) with fits due to regions with three different barrier
heights (dashed lines). b Thermography image at bias of 1 V. The white square marks the area where one hot spot was
investigated in detail. c SEM image of FIB prepared cross section of a defect (Al 2 O 3 particle) causing the lowest barrier
hot spots, inset: plane view of such defect before preparation. Adapted from [1723]
n =
1
1 − ρ 2 + ρ 3 /(2kT )
,
(21.59)
where ρ 2 (ρ 3 ) is the (temperature-independent) proportionality coefficient of the bias dependence of
the mean barrier height (standard deviation), i.e.
ρ 2 =
1
e
∂ ¯
F Bn
∂ V
(21.60a)
ρ 3 =
1
e
∂ σ
2
F
∂ V
.
(21.60b)
The fit of 1/n − 1 versus 1/T in Fig. 21.16c yields ρ 2 = −0.025 and ρ 3 = −0.028 eV for the ZnO
diodes under investigation.
The forward I –V characteristic of an Au/GaAs Schottky diode reported in [1726, 1727] is shown in
Fig. 21.17a at various temperatures. The current amplitude decreases with decreasing temperature due
to the temperature dependence of the saturation current (21.48). Also, the slope V
−1
0 of the characteristic
j = j s exp(V /V 0 ) varies with temperature. Looking at the temperature dependence of V 0 , it is described
as V 0 = k(T + T 0 )/e rather than with an ideality factor n in the form of V 0 = nkT /e. In other words,
the ideality factor follows a temperature dependence n = 1 + T 0 /T . In view of (21.59), such behavior
means for small T 0 that n ≈ 1/(1 − T 0 /T ) and thus ρ 2 = 0 and ρ 3 = 2kT 0 . For T 0 = 45 K, ρ 3
is 0.008 eV, which is a fairly small value. Thus, the temperature behavior of the diode is due to the
narrowing of the Gaussian distribution of barrier height with bias voltage [1720].
In a set of similar diodes with varying magnitude of barrier inhomogeneities, it is found that the effective
barrier height and the ideality factor correlate [1728]. The extrapolation to n = n if yields the limit
of the barrier height for a homogeneous barrier (Fig. 21.18). For silicon, it is found that the surface
orientation has a minor influence on the Schottky barrier height (Fig. 21.18b) for an unreconstructed
surface. The presence of a reconstruction lowers the barrier height
11 (Fig. 21.18a).
11 Reconstructions are accompanied by redistributions of the valence charge with respect to the undisturbed bulk
(Sect. 11.4). The subsequent extra interface dipoles alter the barrier heights of reconstructed interfaces [1728].
535
(a)
1µm
(b)
(c)
Fig. 21.15 a I –V characteristic of ZnO Schottky diode (solid line) with fits due to regions with three different barrier
heights (dashed lines). b Thermography image at bias of 1 V. The white square marks the area where one hot spot was
investigated in detail. c SEM image of FIB prepared cross section of a defect (Al 2 O 3 particle) causing the lowest barrier
hot spots, inset: plane view of such defect before preparation. Adapted from [1723]
n =
1
1 − ρ 2 + ρ 3 /(2kT )
,
(21.59)
where ρ 2 (ρ 3 ) is the (temperature-independent) proportionality coefficient of the bias dependence of
the mean barrier height (standard deviation), i.e.
ρ 2 =
1
e
∂ ¯
F Bn
∂ V
(21.60a)
ρ 3 =
1
e
∂ σ
2
F
∂ V
.
(21.60b)
The fit of 1/n − 1 versus 1/T in Fig. 21.16c yields ρ 2 = −0.025 and ρ 3 = −0.028 eV for the ZnO
diodes under investigation.
The forward I –V characteristic of an Au/GaAs Schottky diode reported in [1726, 1727] is shown in
Fig. 21.17a at various temperatures. The current amplitude decreases with decreasing temperature due
to the temperature dependence of the saturation current (21.48). Also, the slope V
−1
0 of the characteristic
j = j s exp(V /V 0 ) varies with temperature. Looking at the temperature dependence of V 0 , it is described
as V 0 = k(T + T 0 )/e rather than with an ideality factor n in the form of V 0 = nkT /e. In other words,
the ideality factor follows a temperature dependence n = 1 + T 0 /T . In view of (21.59), such behavior
means for small T 0 that n ≈ 1/(1 − T 0 /T ) and thus ρ 2 = 0 and ρ 3 = 2kT 0 . For T 0 = 45 K, ρ 3
is 0.008 eV, which is a fairly small value. Thus, the temperature behavior of the diode is due to the
narrowing of the Gaussian distribution of barrier height with bias voltage [1720].
In a set of similar diodes with varying magnitude of barrier inhomogeneities, it is found that the effective
barrier height and the ideality factor correlate [1728]. The extrapolation to n = n if yields the limit
of the barrier height for a homogeneous barrier (Fig. 21.18). For silicon, it is found that the surface
orientation has a minor influence on the Schottky barrier height (Fig. 21.18b) for an unreconstructed
surface. The presence of a reconstruction lowers the barrier height
11 (Fig. 21.18a).
11 Reconstructions are accompanied by redistributions of the valence charge with respect to the undisturbed bulk
(Sect. 11.4). The subsequent extra interface dipoles alter the barrier heights of reconstructed interfaces [1728].