Chapter
7
METALSEMICONDUCTOR
JUNCTIONS
Metal-semiconductor junctions are a critical component of microelectronics. The following gures
provide an overview of Schottky barrier diodes, ohmic contacts, and interconnect delay issues.
BAND PROFILE OF A METAL AND SEMICONDUCTOR JUNCTION
Work functions of some metals
Metal
Work function, φm (volt)
Element
n-type
semiconductor
Ag, silver
Al, aluminum
Au, gold
Cr, chromium
Mo, molybdenum
Ni, nickel
Pd, palladium
Pt, platinum
Ti, titanium
W, tungsten
Contact
(a)
4.26
4.28
5.1
4.5
4.6
5.15
5.12
5.65
4.33
4.55
Electron affinity of some semiconductors
Electron affinity, χ (volt)
Element
Ge, germanium
Si, silicon
GaAs, gallium arsenide
AlAs, aluminum arsenide
φm > φs
Band profiles of disconnected
metal and semiconductor
4.13
4.01
4.07
3.5
n-type
≈ eφ
s
≈
Vacuum energy
eχs
Ec
EFs
eφm
EFm
Ev
(b)
n-semiconductor
Metal
Vacuum
Formation of a Schottky
junction
eχs
eφm
eφb
EFm
++
–
–
En
erg
y
+ + eφm – eφs = eVbi
+
Ec
EFs
Ev
(c)
W
METAL-SEMICONDUCTOR JUNCTION AT EQUILIBRIUM
© Prof. Jasprit Singh
www.eecs.umich.edu/~singh
SCHOTTKY JUNCTION ON A P-TYPE SEMICONDUCTOR
p-type
Metal and semiconductor band
profiles
Evac
≈
≈ eφ
s
eχs
eφm
Ecs
EFm
EFs
Evs
Metal
Semiconductor
(a)
Ec
Formation of a Schottky junction
for p-type materials
p-semiconductor
+
+
+
AAAAA
AAAAAAAAAA
AAAAA
Metal
EFs
Ev
eφs – eφm = eVbi
eφb
W
(b)
© Prof. Jasprit Singh
www.eecs.umich.edu/~singh
SCHOTTKY JUNCTION IN REAL SYSTEMS
Semiconductor surfaces
have a large number of
defect states (from broken
bands, impurities, etc.)
Defect levels in the bandgap at the
metal-semiconductor interface
eφb = Eg – eφο
Ec
eφο
EFm
EFs
Ev
SCHOTTKY METAL
n Si
p Si
Aluminum, Al
0.7
0.8
Titanium, Ti
0.5
0.61
Tungsten, W
0.67
Gold, Au
0.79
0.25
n GaAs
0.9
Silver, Ag
0.88
Platinum, Pt
0.86
PtSi
0.85
0.2
NiSi2
0.7
0.45
Schottky barrier heights are determined by the semiconductor and have
a rather weak dependence on the metal.
© Prof. Jasprit Singh
www.eecs.umich.edu/~singh
CURRENT FLOW IN A SCHOTTKY DIODE
• Metal-to-semiconductor barrier is unchanged by external bias
• Semiconductor-to-metal barrier is increased (reverse bias) or decreased (forward bias) by an
external bias.
+
–
V
–
V
+
Electron flow
e(Vbi – V)
eφb = e(φm – χ)
e(φm – χ)
EFs
eV
EFm
Ec
EFm
e(Vbi + V)
Ev
Ec
EFs
Forward bias
(a)
Ev
Reverse bias
(b)
I
Current dominated by electron
flow from the semiconductor
to the metal
V
Current dominated by electron
flow from the metal to the
semiconductor
(c)
Diode with area A:
I = Is exp
Is = A
(
( keVT ) –1
B
m*ekB2
2π2h3
= A R* T2 exp
)T
2 exp
–eφb
(k T )
B
–eφb
(k T )
B
m*
Richardson constant: R* = 120 mo Acm–2K–2
© Prof. Jasprit Singh
www.eecs.umich.edu/~singh
SMALL SIGNAL MODEL OF A SCHOTTKY DIODE
The Schottky diode is a majority carrier device. Unlike a p-n diode, in
forward bias no minority carrier injection occurs. Thus there is no
diffusion capacitance and the device response can be very fast.
Equivalent circuit of a diode in
series with a resistor and inductor
Cgeom
Cd
Rs
Ls
Rd
Depletion capacitance:
eN ε
Cd = A 2(V d–V)
bi
1/2
Diode resistance:
Rd = dV = keIT
dI
B
© Prof. Jasprit Singh
www.eecs.umich.edu/~singh
A COMPARISON BETWEEN THE PROPERTIES OF A P-N AND A
SCHOTTKY DIODE
p-n DIODE
SCHOTTKY DIODE
Reverse current due to minority
carriers diffusing to the depletion
layer
strong temperature
dependence
Reverse current due to majority
carriers that overcome the barrier
less temperature dependence
Forward current due to minority
carrier injection from n- and p-sides
Forward current due to majority
injection from the semiconductor
Forward bias needed to make the
device conducting (the cut-in
voltage) is large
The cut-in voltage is quite small
Switching speed controlled by
recombination (elimination) of
minority injected carriers
Switching speed controlled by
thermalization of "hot" injected
electrons across the barrier ~ few
picoseconds
Ideality factor in I-V characteristics
~ 1.2-2.0 due to recombination in
depletion region
Essentially no recombination in
depletion region
ideality factor
~ 1.0
© Prof. Jasprit Singh
www.eecs.umich.edu/~singh
METAL-SEMICONDUCTOR JUNCTIONS: OHMIC CONTACT AND
SCHOTTKY JUNCTION
OHMIC CONTACT
CURRENT
Current is linear in an
ohmic contact
resistance is very small
Schottky
barrier
VOLTAGE
OHMIC CONTACT
OHMIC CONTACT
e
METAL
Heavy doping in the
semiconductor causes a
very thin depletion width
and electrons can tunnel
across this barrier leading
to ohmic behavior
Electrons tunnel
through narrow
depletion region
e
Ec
EF
n+
REGION
n-type
SEMICONDUCTOR
Ev
© Prof. Jasprit Singh
www.eecs.umich.edu/~singh
INTERCONNECT DELAY: GOING FROM AL TO CU
As device dimensions shrink interconnect cross-sections also must shrink. This
increases the interconnect resistance and the associated time delay for signal
propagation.
TRANSISTOR GATE LENGTHS:
1999: 0.2 µm
2003: 0.1 µm
40
35
Interconnect delay for
Al-based interconnects
TIME DELAY (ps)
30
25
20
Transistor delay
15
10
Interconnect delay for
Cu-based interconnects
5
0.1
0.2
0.3
0.4
0.5
0.6
0.7
GATE LENGTH (µm)
Based on Semiconductor Industry Associates Roadmap.
© Prof. Jasprit Singh
www.eecs.umich.edu/~singh