Metal Semiconductor Contacts

woundcallousΗμιαγωγοί

1 Νοε 2013 (πριν από 4 χρόνια και 11 μέρες)

105 εμφανίσεις

ECE 663

Metal
-
Semiconductor Interfaces


Metal
-
Semiconductor contact


Schottky Barrier/Diode


Ohmic Contacts


MESFET

ECE 663

Device Building Blocks

Schottky (MS)

p
-
n junction

HBT

MOS

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Energy band diagram of an isolated metal adjacent
to an isolated n
-
type semiconductor

q(
f
s
-
c
) = E
C



E
F

= kTln(N
C
/N
D
) for n
-
type


= E
G



kTln(N
v
/N
A
) for p
-
type


ECE 663

Energy band diagram of a metal
-
n semiconductor contact
in thermal equilibrium.

q
f
Bn

= q
f
ms

+ kTln(N
C
/N
D
)

ECE 663


Measured barrier height
f
ms

for metal
-
Si and metal
-
GaAs contacts

Theory still evolving (see review article by Tung)

ECE 663

Energy band diagrams of metal n
-
type and p
-
type semiconductors

under thermal equilibrium

ECE 663

Energy band diagrams of metal n
-
type and p
-
type semiconductors

under forward bias

Energy band diagrams of metal n
-
type and p
-
type semiconductors

under reverse bias

ECE 663

ECE 663

Charge distribution

electric
-
field
distribution

E
m

= qN
D
W/K
s
e
0

E
(x) = qN
D
(x
-
W)/K
s
e
0

(V
bi
-
V) =
-


E
(x)dx = qN
D
W
2
/K
s
e
0

0

W

V
bi
=
f
ms

(Doping does not matter!)

f
Bn

=
f
ms

+ kTln(N
C
/N
D
)

ECE 663

Depletion width

Charge per unit area

Depletion

q

ECE 663

Capacitance

Per unit area:

Rearranging:

Or:

ECE 663

1/C
2

versus applied voltage for W
-
Si and W
-
GaAs diodes

ECE 663

1/C
2

vs V


If straight line


constant doping profile




slope = doping concentration


If not straight line, can be used to find profile


Intercept = V
bi
can be used to find
f
Bn

ECE 663

Current transport by the thermionic emission process

Thermal equilibrium

forward bias

reverse bias

J = J
s

m
(V)


J
m

s
(V)

J
m

s
(V) = J
m

s
(0) = J
s

m
(0)



Barrier from metal side is pinned




Els from metal must
jump

over barrier




Current is limited by speed of jumping


electrons (that the ones jumping from


the right cancel at equilibrium)




Unipolar
majority carrier
device, since


valence band is entirely inside metal band


Note the difference with p
-
n junctions!!



Barrier is not pinned




Els with zero kinetic energy can slide


down negative barrier to initiate current




Current is limited by how fast
minority


carriers

can be removed (diffusion rate)




Both el and hole currents important


(charges X
-
over and become min. carriers)

In both cases, we’re modulating the population
of backflowing electrons, hence the Shockley
form, but…

V > 0

V < 0

V > 0

V < 0

ECE 663

Let’s roll up our sleeves and do the algebra !!

J
s

m

= 2q

f(E
k
-
E
F
)v
x

v
x
> v
min
,v
y
,v
z

dk
x
dk
y
dk
z
v
x
e
-
(E
k
-
E
F
)/kT





(2
p
)
3
/
W

= 2q

E
k
-
E
F

= (E
k
-
E
C
) + (E
C
-
E
F
)

E
C
-

E
F

= q(
f
Bn
-
V
bi
)

E
k
-

E
C

= m(v
x
2

+ v
y
2
+ v
z
2

)/2

m*v
min
2
/2 = q(V
bi


V)

k
x,y,z

= m*v
x,y,z


V > 0

V
bi

-

V

ECE 663

This means…

J
s

m

=


q(m*)
3
W
/4
p
3
ħ
3


dv
y
e
-
m*v
y
2
/2kT







-


dv
z
e
-
m*v
z
2
/2kT







-


dv
x
v
x
e
-
m*v
x
2
/2kT







v
min

x e
-
q(
f
Bn
-
V
bi
)/kT



(2
p
kT/m*)



p
kT/m*)

(kT/m*)e
-
m*v
min
2
/2kT

= (kT/m*)e
-
q(V
bi
-
V)kT

= qm*k
2
T
2
/2
p
2
ħ
3
e
-
q(
f
Bn
-
V)kT



= A*T
2
e
-
q(
f
Bn
-
V)kT



A* = 4
p
m*qk
2
/h
3



= 120 A/cm
2
/K
2



dxe
-
x
2
/2
s
2

=
s

2
p



-






dx xe
-
x
2
/2
s
2

=
s
2
e
-
A
2
/2
s
2




A





J = A*T
2
e
-
q
f
BN
/
kT
(e
qV/kT
-
1)

In regular pn junctions, charge needs to move through

drift
-
diffusion, and get whisked away by RG processes


MS junctions are majority carrier devices, and RG is not

as critical. Charges that go over a barrier already have

high velocity, and these continue with those velocities to

give the current

ECE 663


Forward current density vs applied voltage of W
-
Si and W
-
GaAs diodes

ECE 663

Thermionic Emission over the barrier


low doping

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Tunneling through the barrier


high doping

Schottky barrier becomes Ohmic !!

ECE 663