Report On

Diffusion & Measurement Of

Sheet Resistance

By:- Prateek Agrawal

ECE/67/08

Diffusion

Diffusion can be defined as the

random walk of an ensemble of

particles from regions of high

concentration to regions of lower

concentration.

In integrated circuit fabrication,

diffusion is used to introduce dopants

in controlled amounts into the

semiconductor substrate.

Laws Of Diffusion

First law Of Diffusion

According to the First Law of

Diffusion, the transfer of solute atoms

per unit area in a one-dimensional

flow can be described by the following

equation:

where J is the particle flux,

C is the concentration of the solute,

D is the diffusion coefficient,

x is the distance into the substrate, and

t is the diffusion time.

The negative sign indicates that the diffusing mass flows

in the direction of decreasing concentration.

From the Conservation of Mass, we also know that:

Second Law Of Diffusion

If we combine this relationship with the 1st

Law of Diffusion, then we have derived the

2nd Law of Diffusion (otherwise known as

Fick's Law), which states:

Two solutions to Fick's Law are generally

encountered in IC fabrication: infinte-source

and limited-source diffusion

Sheet Resistance And Its

Measurement Sheet resistance is a measure of resistance of thin

films that are nominally uniform in thickness. It is

commonly used to characterize materials made by

semiconductor doping, metal deposition, resistive

paste printing, and glass coating. Examples of these

processes are: doped semiconductor regions

(e.g., silicon or polysilicon), and the resistors that are

screen printed onto the substrates of thick-film hybrid

microelectronic.

Methods To Measure The Resistance

There are mainly two methods

a) Four Probe Method

b) Van Der Pauw Method

Four Probe Method

A four point probe is used to avoid contact resistance,

which can often be the same magnitude as the sheet

resistance.

Typically a constant current is applied to two probes and

the potential on the other two probes is measured with a

high impedance voltmeter.

The key advantage of four-terminal sensing is that

the separation of current and voltage electrodes

eliminates the impedance contribution of the wiring

and contact resistance

Operating Principle

Ckt Diagram When a Kelvin

connection is used,

current is supplied via

a pair

of force connections

(current leads). These

generate a voltage

drop across the

impedance to be

measured according

to Ohm’s Law V=RI.

Van Der Pauw Method

The van der Pauw Method is a technique

commonly used to measure the

Resistivity and the Hall Coefficient of

a sample. Its power lies in its ability to

accurately measure the properties of a

sample of any arbitrary shape, so long

as the sample is approximately two-

dimensional (ie. it is much thinner than it

is wide) and the electrodes are placed

on its perimeter.

Vander Pauw Contact

Placement

THANX FOR YOUR ATTENTION

Presented By:-

Prateek AgrawalECE/67/08