lect5 diffusion

Diffusion and Ion Implantation

Processes Involved in IC Manufacturing on the Wafer:Diffusion/ion implantationPhotolithographyDepositionOxidationEtching

Lecture 4

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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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.


Comparison


Doping Profiles


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.


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.


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)


Diffusion mechanism (contd.)

4. Interstitialcy Diffusion (B and P)

5. Interchange Diffusion6. Grain Boundary Diffusion7. Combination effects


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 fluxC=concentration of solute (function of x and t only)x=coordinate axis in the direction of solute flowt=diffusion timeD=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 n1 and n2 be the no. of atoms in layers1 and 2 respectively and their respective concentration C1 and C2 so that,

11

3nC

Ad

22

3nC

Adand


We assume atoms jump at a frequency of v such that,halfof them jump right and the other half jump left. So, thenet flow of atoms across plane R in direction of x is

1 2

1 22 ( )1 2 3

n nn v Ad

C Ct

v

1 2

/ 3

C CC

x d

But

2

6

n vAd C

t x

So,

Let J= rate of change of no. of impurities per unit area, then,


2

6

n vd CJ

A t x

D, diffusivity

CJ D

x

( , )C x tJ D

x

Fick’s First Law

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.


Fick’s second law

• Consider a long bar of material with uniform cross-sectional area A. For a small volume of length dx,

• J1 is the flux entering into the volume and J2 is the flux leaving the volume. Then,

• The continuity equation gives,

2 1J J J

dx x

2 1( )C J

Adx A J J Adxt x


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 tD

t x x

2

2

( , ) ( , )C x t C x tD

t x

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Ms. Neha Singh

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 SiO2


lect5 diffusion

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diffusion process

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diffusion fluxc

slow diffusion

b diffusion bykick

interstitial diffusion