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+