metal semi-conductor contact [1]
TRANSCRIPT
ansunMansunMHong Kong University of Science & Technology, Department of Electronic & Computer Engineering
Metal Semi-Conductor Contact [1]Band Diagram• The electron energy of reference is the vacuum level, which
is the energy to completely remove a electron from the influence of the core ion
qFM
metal
qFSqc E0
EFsEi
EV
EC
EFm
semi-conductor (Si) put together
E0
EFsEi
EV
EC
c - electron affinityFS - work-function of siliconFM - work-function of metal
E0 – vacuum energy
qFBn
qFBp
FBn- barrier height for e- to move from metal to the semiconductor
FBp- barrier height for h+ to move from metal to the semiconductor
ansunMansunMHong Kong University of Science & Technology, Department of Electronic & Computer Engineering
Schottky Barrier Contact [1]Putting metal and semiconductor together• use Al and n-silicon as an example (most often used)• Following the mechanism of PN junction
EC
EV
EF
Carrier motion
++
++
Depletion region
EC
EV
EF
qFBn qVbi
FB=FM -c Vbi=FM- FS
kTqV
DM
bi
eNn-
=
• considered as one-sided PN junction• electrons from metal cannot go to the semi-conductor due to
barrier height FB• Electron at the n-Si is blocked from entering the metal by Vbi
ansunMansunMHong Kong University of Science & Technology, Department of Electronic & Computer Engineering
Schottky Barrier Contact [2]Electro-static analysis• Solving 1-D Poisson equation as in PN junction
21
2úû
ùêë
é=
D
biSin qN
Vx
e
ND
+xnQ=qNDxn
r
xn
Si
nDxqNe
xn
V
Si
nDbi
xqNV
e2
2
=
E!
- solving for xn
n-type
++
++
- can be regard as PN junction by treating the metal as extremely heavily doped region
ansunMansunMHong Kong University of Science & Technology, Department of Electronic & Computer Engineering
Schottky Barrier Contact [3]Majority carrier device• Consider resistance value at different
regions of a metal semiconductor contact
• Hole conduction is small at the N-type semiconductor
• Metal can conduct with either holes or electrons
• As a result, conduction mainly take place by electron at the conduction band of the N-semiconductor and only limited by the number of carriers at the interface
• It is referred as a majority carrier device or unipolar device (conduction mainly take place by only one carrier)
EC
EV
EF
qVbi
ansunMansunMHong Kong University of Science & Technology, Department of Electronic & Computer Engineering
Schottky Barrier Contact [4]Current at equilibrium• Assume it is a 1-D device and
carriers are moving at thermal velocity (vth) in random direction EC
EV
EF
qVbi
nM nS
IM = q(0.5nM )vth
• Similarly, half of the carriers at the semiconductor side (nS) move to the metal contributing to a current of IS = q(0.5nS )vth
• Assume half of the electrons at the metal (nM) are moving from the metal to the semiconductor contributing a current with magnitude of
• The net current from the metal to the semiconductor is then
I = IS − IM = 0.5qvth (nS − nM )
ansunMansunMHong Kong University of Science & Technology, Department of Electronic & Computer Engineering
Schottky Barrier Contact [5]Reverse bias• In most cases, only the majority carriers are considered (lets
assume electrons)
EC
EV
EF
qFB q(Vbi - VA)
I = 0.5qvth nS − nM( )
= 0.5qvthNDe−qVbikT e
qVAkT −1
⎛
⎝⎜
⎞
⎠⎟
( ) 21
2úû
ùêë
é -=
D
AbiSin qN
VVx e
xn
( )kTVVq
DS
Abi
eNn-
-=kT
qV
DM
bi
eNn-
=
possible Zener breakdown
• Current depends on barrier height and doping concentration• Lower breakdown voltage due to Zener breakdown with
thinner barrier width
ansunMansunMHong Kong University of Science & Technology, Department of Electronic & Computer Engineering
Schottky Barrier Contact [6]Forward bias• Due to diffusion in the depletion region
• The current coefficient is grouped to I0 where
EC
EV
EFqFB
nM( )kTVVq
DS
Abi
eNn-
-=
nn0
carrier conc.
• an ideality factor n is often introduced and typically 1.0 < n <1.1 (better than a PN junction)
ID = I0 eqVAnkT −1
⎛
⎝⎜
⎞
⎠⎟
• Properties of Schottky diode are similar to regular PN diode
I = 0.5qvth nS − nM( )
= 0.5qvthNDe−qVbikT e
qVAkT −1
⎛
⎝⎜
⎞
⎠⎟
I0 = 0.5qvthNDe−qVbikT
• It can be shown that I0 can also be expressed by I0 = 0.5qvthNCe−qΦBkT
ansunMansunMHong Kong University of Science & Technology, Department of Electronic & Computer Engineering
Schottky Barrier Contact [7]
Comparison with PN junction• faster in charging/discharging during transient because no
accumulation of minority carrier necessary (smaller Cdiff)
• no high-level injection problem• low series resistance due to the use of metal
• ideality factor close to 1 (ideal case)• smaller Vbi leading to smaller turn on voltage and
exponential region
• lower breakdown voltage
ansunMansunMHong Kong University of Science & Technology, Department of Electronic & Computer Engineering
Schottky Barrier Contact [8]Applications• use as rectifiers and other diode circuits that require fast
switching• high speed demodulator in RF circuits• use as clamping device in BJT to prevent the entering into
saturation operation (to be covered in BJT notes)
More realistic MS contact and barrier structure
n
metal
cross-section
EC
EV
EF
< qFBqVbi
xM
• There is an alloy region between the metal and the semiconductor that cause a lowering of the barrier height
ansunMansunMHong Kong University of Science & Technology, Department of Electronic & Computer Engineering
Ohmic Contact [1]Problem with only Schottky contact• metal forming Schottky contacts cannot be used to
interconnect transistors due the existence of diodes• non-rectifying or resistance like contacts that gives large
reverse current
• 2 mechanisms can give this kind of contact
II I
VV V
rectifying contact
linear resistive contact
non-linear breakdown contact
ansunMansunMHong Kong University of Science & Technology, Department of Electronic & Computer Engineering
Ohmic Contact [2]Linear ohmic contact• formed between metals and silicon with metal work function
of metal close to the energy of conducting carriers in Si• FM >FS for p-Si or FM <FS for n-Si • For example, aluminum and p-silicon
• The barrier for one of the carriers is very small that the carriers can move freely across the two material
I
V
EC
EVEFEi
EC
EVEFEi
ansunMansunMHong Kong University of Science & Technology, Department of Electronic & Computer Engineering
Ohmic Contact [3]Tunneling contact• Non-rectifying contact can also be formed by using Schottky
junction with very low breakdown voltage
• Commonly formed between aluminium and n+ silicon• Very heavy n+ doping can also reduce the series resistance
I
V
EC
EV
EFEi EC
EV
EFEi
ansunMansunMHong Kong University of Science & Technology, Department of Electronic & Computer Engineering
Ohmic Contact [4]Implication of ohmic contact structures• For most devices, n+ or p+ should be added before
connecting to metal to avoid unwanted junctions• For example, more realistic structure of N+/P junction
• The heavily doped region can also reduce the series resistance of the diode
p
metal
n+ orp+p
metal
n+ p+
p+