Lect5 Diffusion

1. Diffusion and Ion
Implantation
Processes Involved in IC
Manufacturing on the Wafer:
Diffusion/ion implantation
Photolithography
Deposition
Oxidation
Etching
Lecture 4

2. Impurity Doping
•Two methods for introducing impurities into Si
to control the majority-carrier type and
resistivity of layers
–Diffusion: dopant atoms move from the surface
into Si by thermal means via substitutional or
interstitial diffusion mechanisms.
–Ion implantation: dopant atoms are forcefully
added into Si in the form of energetic ion beam
injection.
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3. Need of doping
–Formation of pn junction and fabrication of
devices during wafer fabrication.
–alter the type and level of conductivity of
semiconductor materials.
–form bases, emitters, and resistors in bipolar
devices, as well as drains and sources in MOS
devices.
–dope polysilicon layers.
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4. Comparison
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5. Doping Profiles
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6. Diffusion
•Diffusion: movement of a chemical species from an
area of high concentration to an area of lower
concentration.
•The diffusion process begins with the deposition of a
shallow high concentration of the desired impurity in
the Si surface through windows etched in the
protective barrier layer.
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7. Diffusion mechanism (7 methods)
1. Interstitial diffusion (Na, Li)
- fast process.
- diffuses in interstitials.
- does not depend upon vacancy concentration.
2. Substitutional diffusion
-Diffuse in vacancy.
-Slow diffusion.
-Thus controlled.
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8. Diffusion mechanism (contd.)
3. Interstitial-substitutional Diffusion
3.a) Diffusion by
dissociative
mechanism
(Cu, Ni)
3.b) Diffusion by
kick-out mechanism
(Gold and Platinum)
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9. Diffusion mechanism (contd.)
4. Interstitialcy Diffusion (B and P)
5. Interchange Diffusion
6. Grain Boundary Diffusion
7. Combination effects
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10. Fick’s First Law of Diffusion
•Based on analogy between material transfer in a
solution and heat transfer by conduction.
J=rate of transfer of solute per unit area or diffusion flux
C=concentration of solute (function of x and t only)
x=coordinate axis in the direction of solute flow
t=diffusion time
D=diffusivity (Diffusion constant)
Statement: The local rate of transfer of solute per unit area per
unit time is proportional to the concentration gradient of the
solute and defines the proportionality constant as diffusivity
of the solute. The negative sign shows the flow towards lower
concentration of solute.
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Here, d is the distance between tetrahedral sites. Let n
1

and n
2
be the no. of atoms in layers1 and 2 respectively
and their respective concentration C
1
and C
2
so that,
1
1
3n
C
Ad
=
2
2
3n
C
Ad
=
and

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We assume atoms jump at a frequency of v such that,half
of them jump right and the other half jump left. So, the
net flow of atoms across plane R in direction of x is
1 2
1 2
2
( )
1 23
n n
n v Ad
C C
t
v
-
D
= = -
D
1 2
/ 3
C CC
xd
-D
=
D
But
2
6
n vAd C
t x
D D
=
D D
So,

13. Let J= rate of change of no. of impurities per unit
area, then,
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2
6
n vd C
J
A t x
D D
= =-
D D
D, diffusivity
C
J D
x
¶
=-
¶
( , )C xt
J D
x
¶
=-
¶
Fick’s First Law

14. Limitation of first law
•Though it describes diffusion process
accurately.
•But, has no convenient measure of current
density of the impurity.
•Thus, second law developed to describe the
concept with more readily measurable
quantities.
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15. Fick’s second law
•Consider a long bar of material with uniform cross-
sectional area A. For a small volume of length dx,
•J
1
is the flux entering into the volume and J
2
is the flux
leaving the volume. Then,
•The continuity equation gives,
2 1
J J J
dx x
-¶
=
¶
2 1
( )
C J
Adx A J J Adx
t x
¶ ¶
=- - =-
¶ ¶
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16. Fick’s second Law of Diffusion
•Law of conservation of matter: change in solute
concentration per unit time= local decrease in
diffusion flux in the absence of source or sink.
•Combining with Fick’s first law,
•At low concentration of solute, diffusivity at a
particular temperature can be considered a constant
( , ) ( , )C x t C x t
D
t x x
¶ ¶ ¶ é ù
=
ê ú
¶ ¶ ¶ë û
2
2
( , ) ( , )C x t C x t
D
t x
¶ ¶
=
¶ ¶
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17. End of Lecture 5
In the next lecture we shall
-solve the Fick’s second law for various conditions.
-See the effect of electric field on diffusion.
-See diffusion in SiO
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