Transcript Doping and Crystal Growth Techniques

Doping and Crystal
Growth Techniques
Types of Impurities

Substitutional Impurities
– Donors and acceptors
– Isoelectronic Defects

Vacancies
– Charged Vacancies
 Color centers in solids (alkali halides)

Interstitial Atoms
– Mid Gap Trap

Antisite Defects
Back to the Periodic Table
Column V Atoms
Have 5 outer shell electrons
The extra electron on the phosphorous atom is easily removed and becomes a
free electron without generating a hole.
The phosphorous atom becomes positively charged (ionized).
Back to the Periodic Table (again)
Column III Atoms
Have 3 outer shell electrons
The boron atom ‘steals’ an electron from a neighboring Si atom to complete the
four bonds with the surrounding Si atoms, generating a hole at the neighboring
Si atom.
The boron atom becomes negatively charged (ionized).
n-type Semiconductors

Are doped with donor atoms, which have an
extra electron that they donate to the crystal
– When the concentration of donor atoms is much
greater than the intrinsic carrier concentration, the
electron concentration is composed of these donated
electrons.
n  Nd
p-type Semiconductors

Are doped with acceptor atoms, which generate
holes in the crystal
– When the concentration of acceptor atoms is much
greater than the intrinsic carrier concentration, the
hole concentration is composed of the holes
generated by the acceptors.
p  Na
Carrier Concentrations
n-type semiconductor
p-type semiconductor
ni  n  p
ni  n  p
n  Nd
p  Na
2
2
ni
p
Nd
2
2
ni
n
Na
Bohr model for Hydrogen atom
4
mo q
13.6eV
En  Evac 
 Evac 
2 2 2
2
2(4o )  n
n
4o  n
2
rn 

0
.
053
n
nm
4
mo q
2
2
Translation to Donor Atom
Include relative dielectric constant
 Extra electron has a effective mass equal to
the conduction band electrons

mn* mo q 4
13.6 mn*
En  EC 
 EC  2
2 2 2
2(4o r )  n
n r2
4o r  n
r 2
rn 
 0.053 * n nm
*
4
mn mo q
mn
2
2
Translation to Acceptor Atom
Include relative dielectric constant
 Missing electron has a effective mass equal to
the valence band electrons

En  EV 
m*p mo q 4
2(4o r )  n
2
2
2
 EV 
*
m
13.6 p
4o r  2 n 2
r 2
rn 
 0.053 * n nm
*
4
m p mo q
mp
n
2
r
2
Heisenberg’s Uncertainty Principle
In quantum mechanics, we talk about
the probability of finding a particle in
a certain place.
DxDp ≥ħ/2
DtDn ≥1/4
DtDE ≥ħ/2
Impurity Level
DeBroglie’s relation
p  k
1
DxDk 
2
The deeper the impurity level from either Ec or Ev, the
smaller rn is – i.e, the electron or hole is more tightly
bound to the impurity.
http://kottan-labs.bgsu.edu/teaching/workshop2001/chapter6.htm
GaP LEDs have a low concentration of N impurities in them. The impurity energy
level has a large k that extends from the X minima to the G minima, allowing the
trapped electrons to radiative recombine with holes.
Types of Impurities

Substitutional Impurities
– Donors and acceptors
– Isoelectronic Defects

Vacancies
– Charged Vacancies
 Color centers in solids (alkali halides)

Interstitial Atoms
– Mid Gap Trap

Antisite Defects
Types of Crystal Growth

Product is a boule from which wafers are
then cut
– Czochralski (CZ)
– Float Zone (FZ)
– Bridgeman
Czochralski
www.qahill.com/tz/sil
icon/silicon.html
http://www.tf.unikiel.de/matwis/amat/elmat_
en/kap_6/illustr/i6_1_1.html
http://www.tf.uni-kiel.de/matwis/amat/elmat_en/kap_6/backbone/r6_1_2.html#_dum_1
Impurity Segregation
CS
ko 
CL
CS  Co ko (1  f )
k o 1
Where Co is the initial concentration of th impurity in the melt
Impurity Segregation
Atom
ko
Atom
ko
Cu
Ag
Au
C
Ge
Sn
As
4 · 10–4
10–6
2.5 · 10–5
7 · 10–2
3.3 · 10–2
1.6 · 10–2
0.3
O
B
Ga
Fe
Co
Ni
Sb
0.5
0.8
8 · 10–3
8 · 10–6
8 · 10–6
4 · 10–4
2.3 · 10–2
Float Zone
www.mrsemicon.com
/crystalgrowth.htm
www.tms.org/pubs/journals/JOM/9802/Li/
Impurity Segregation

C S ( x)  Co 1  (1  ko )e

ko x

L



Where Co is the initial concentration of the impurity in the
solid and L is the width of the melted region within RF coil
Bridgeman

Used for some compound semiconductors
– Particularly those that have a high vapor
pressure
– Produced “D” shaped boules
Crystalline Defects

Point Defects
– Vacancies
– Impurities
– Antisite Defects

Line Defects
– Dislocations
 Edge
 Loop

Volume Defects
– Voids
– Screw Dislocations
Edge Dislocation
http://courses.eas.ualberta.ca/eas421/lecturepages/mylonite.html
Screw Dislocation
http://focus.aps.org/story/v20/st3
Strain induced Dislocations

The temperature profile across the
diameter of a boule is not constant as the
boule cools
– the outer surface of the boule contracts at a
different rate than the internal region
– Thermal expansion differences produces edge
dislocations within the boule
 Typical pattern is a “W”
Strain due to Impurities

An impurity induces strain in the crystal
because of differences in
– ionic radius as compared to the atom it
replaced
 Compressive strain if the ionic radius is larger
 Tensile strain if the ionic radius is smaller
– local distortions because of Coulombic
interactions

Both cause local modifications to Eg
Dislocation Count

When you purchase a wafer, one of the
specifications is the EPD, Etch Pit Density
– Dislocations etch more rapidly in acid than
crystalline material
– Values for EPD can run from essentially zero
(FZ grown under microgravity conditions) to
106 cm-2 for some materials that are
extremely difficult to grow.
 Note that EPD of 106 cm-2 means that there is a
dislocation approximately every 10mms.
Wafer Manufacturing
Boules are polished into cylinders
 Aligned using an x-ray diffraction system
 Cut into slices using a diamond edged saw

– Slices are then polished smooth using a
colloidal grit
 Mechanical damage from sawing causes point
defects that can coalesce into edge dislocations if
not removed
http://www.tf.uni-kiel.de/matwis/amat/elmat_en/kap_6/backbone/r6_1_2.html#_dum_1
SCS Manufacturing
•
•
For wafers <200mm, the
flats are used to
determine the crystal
orientation and the
impurity type of the
wafer.
After some processing steps
such as dicing, lapping,
etching, and polishing, silicon
wafers will be ready to be used.
Carrier Mobility and Velocity

Mobility - the ease at which a carrier
(electron or hole) moves in a
semiconductor
– Symbol: mn for electrons and mp for holes

Drift velocity – the speed at which a
carrier moves in a crystal when an electric
field is present
– For electrons: vd = mn E
– For holes:
vd = mp E
L
H
W
Va
Va
Resistance
L
L
R
 
WH
A
Resistivity and Conductivity

Fundamental material properties
1
1


q m n no  m p po  q m n  m p ni

1

Current Flow
Va
Va
I

R

L 
1

A  q m n no  m p po  
Va
I
Aqm n no  m p po 
L
Va
E
L
I  Aqm n no  m p po E
Resistivity
n-type semiconductor
1

q m n no  m p po 

1

ni 

q m n N d  m p

N
d 

1

qm n N d
2
p-type semiconductor
1

qm n no  m p po 

1
 ni 2

q m n
 m p N a 
 Na

1

qm p N a
Diffusion

When there are changes in the
concentration of electrons and/or holes
along a piece of semiconductor
– the Coulombic repulsion of the carriers force
the carriers to flow towards the region with a
lower concentration.
Diffusion Currents
I diffn
A
I diff p
A
I diff
A
 J diffn
dno
 qDnno  qDn
dx
 J diffp
dpo
 qD p po   qD p
dx
 J diffn  J diffp  q Dnno  D p po 
Relationship between Diffusivity
and Mobility
Dn
kT

mn
q
Dp
kT

mp
q
Wafer Characterization

X-ray Diffraction
– Crystal Orientation

Van der Pauw or Hall Measurements
– Resistivity
– Mobility

Four Point Probe
– Resisitivity

Hot Point Probe
– n or p-type material