21.2 Metal-Semiconductor Contacts
541
At low doping, the transport is dominated by thermionic emission (21.48). In this case R c is given by
R c =
k
e A ∗ T
exp
F Bn
kT
.
(21.71)
A small barrier height (Fig. 21.23a) will lead to small contact resistance. A negative Schottky barrier
height, i.e. W m < E vac − E F for a n-type semiconductor, leads to an accumulation layer without a
barrier for carrier transport (Fig. 21.23b).
For high doping R c is determined by the tunneling current (Fig. 21.23c) and is proportional to
R c ∝ exp
F Bn
E 00
.
(21.72)
The contact resistance decreases exponentially with the doping. A theoretical calculation and experimental data are compared in Fig. 21.24 for contacts on Si.
The three mechanisms, low barrier height, accumulation layer and high doping, for the formation
of Ohmic contacts are summarized schematically in Fig. 21.23. Ohmic contacts on wide band gap
semiconductors are difficult, since metals with sufficiently small (large) work function for contacting
n-type (p-type) material are mostly not available.
Although Schottky contact devices have their place in semiconductor technology, Ohmic contacts
are indispensable for almost all devices.
12 Ohmic contacts are typically prepared by evaporating a
contact metal containing the doping material for the semiconductor, e.g. Au/Zn for a contact on p-type
GaAs [1737] and Au/Ge for a contact [1738] on n-type GaAs. The contact is alloyed around 400–500
◦ C
(see Fig. 21.25) above the eutectic temperature of T eu = 360
◦ C (for Au/Ge) to form a eutectic liquid
in which the dopant can quickly diffuse. When the eutectic liquid cools it forms a solid, a highly doped
semiconductor layer underneath the metal. The liquid-phase reactions can lead to inhomogeneous
contacts. On n-type GaAs Pd/Ge/Au contacts have been reported to have superior structural quality
[1739]. Ohmic contacts for a number of different semiconductors are reviewed in [1740, 1741].
The current-voltage characteristics of an intrinsic (low carrier density, trap-free) semiconductor with
ohmic contacts is dominated by so-called space-charge limited current (SCLC) as proposed by Mott
and Gurney [1743, 1744]. In a one-dimensional model, the semiconductor of length L is considered
with ohmic contacts and applied voltage V 0 (applied electrical field E 0 = V 0 /L). The thermal carriers
shall be negligible compared to the injected ones. The space charge density ρ in the current density
j = ρ v = ρ μ E is then in the space-charge limited regime due to the dependence of the electric field
dE/dx = ρ// within the semiconductor (also E = −dV /dx). Therefore the current density can be
written as
Fig. 21.23 Schematic conditions for the formation of an Ohmic contact, a low barrier height, b accumulation layer c
high doping (thin depletion layer)
12 Also a Schottky diode has an Ohmic back contact.
541
At low doping, the transport is dominated by thermionic emission (21.48). In this case R c is given by
R c =
k
e A ∗ T
exp
F Bn
kT
.
(21.71)
A small barrier height (Fig. 21.23a) will lead to small contact resistance. A negative Schottky barrier
height, i.e. W m < E vac − E F for a n-type semiconductor, leads to an accumulation layer without a
barrier for carrier transport (Fig. 21.23b).
For high doping R c is determined by the tunneling current (Fig. 21.23c) and is proportional to
R c ∝ exp
F Bn
E 00
.
(21.72)
The contact resistance decreases exponentially with the doping. A theoretical calculation and experimental data are compared in Fig. 21.24 for contacts on Si.
The three mechanisms, low barrier height, accumulation layer and high doping, for the formation
of Ohmic contacts are summarized schematically in Fig. 21.23. Ohmic contacts on wide band gap
semiconductors are difficult, since metals with sufficiently small (large) work function for contacting
n-type (p-type) material are mostly not available.
Although Schottky contact devices have their place in semiconductor technology, Ohmic contacts
are indispensable for almost all devices.
12 Ohmic contacts are typically prepared by evaporating a
contact metal containing the doping material for the semiconductor, e.g. Au/Zn for a contact on p-type
GaAs [1737] and Au/Ge for a contact [1738] on n-type GaAs. The contact is alloyed around 400–500
◦ C
(see Fig. 21.25) above the eutectic temperature of T eu = 360
◦ C (for Au/Ge) to form a eutectic liquid
in which the dopant can quickly diffuse. When the eutectic liquid cools it forms a solid, a highly doped
semiconductor layer underneath the metal. The liquid-phase reactions can lead to inhomogeneous
contacts. On n-type GaAs Pd/Ge/Au contacts have been reported to have superior structural quality
[1739]. Ohmic contacts for a number of different semiconductors are reviewed in [1740, 1741].
The current-voltage characteristics of an intrinsic (low carrier density, trap-free) semiconductor with
ohmic contacts is dominated by so-called space-charge limited current (SCLC) as proposed by Mott
and Gurney [1743, 1744]. In a one-dimensional model, the semiconductor of length L is considered
with ohmic contacts and applied voltage V 0 (applied electrical field E 0 = V 0 /L). The thermal carriers
shall be negligible compared to the injected ones. The space charge density ρ in the current density
j = ρ v = ρ μ E is then in the space-charge limited regime due to the dependence of the electric field
dE/dx = ρ// within the semiconductor (also E = −dV /dx). Therefore the current density can be
written as
Fig. 21.23 Schematic conditions for the formation of an Ohmic contact, a low barrier height, b accumulation layer c
high doping (thin depletion layer)
12 Also a Schottky diode has an Ohmic back contact.