Page 261 - Semiconductor Manufacturing Handbook

Geng(SMH)_CH18.qxd 04/04/2005 19:58 Page 18.2

WET CLEANING

18.2 WAFER PROCESSING

Hamaker constant (defined as a function of the Hamaker constants of the particle, the wafer surface,
and the interlaying medium), (b) the geometries of the interacting bodies, and (c) the distance
between the particle and the wafer surface.
There are two major theories for the calculation of the Hamaker constant, known as the London
and the Lifshitz theories. Both are based on the molecular properties of matter. The London theory
takes into account the pairwise addition of interactions between neighboring matter and the Lifshitz
theory is based on quantum electrodynamics. Most often, both theories yield equivalent values for
the Hamaker constant. The Hamaker constant (A ) between different matter is expressed as the geo-
12
metric mean of the individual Hamaker constants (A ) for matter “1” and “2” is expressed as
XX
A = A A
⋅
12 11 22
When two materials are separated by a third medium “3” then the Hamaker constant for the sys-
tem (A ) is calculated by
123
A 123 = A + A − A − A 23
12
13
33
Using A , it is possible to calculate the force of adhesion (F ) for a system. The calculation of
123 Ad
F varies depending on the geometry of the matter involved. A typical example used in wet clean-
Ad
ing as a theoretical model is that of a flat plane (wafer surface) and a sphere (particle). The equation
for the van der Waals force of adhesion is described as
F = Ad p
123
As
12 Z 0 2
where d is the diameter of the particle and Z is the distance between the edge of the particle and
p 0
the surface of the wafer. This is consistent for a smooth particle on a smooth surface. If either the
surface, the particle, or both are rough, this equation becomes more complex to account for a dis-
tributed adhesion rather than a single point. 2
Therefore, by the aforementioned equation, the force of adhesion for any system is directly pro-
portional to the media to which the wafer is exposed. The Hamaker constant for a system in water is
calculated to be an order of magnitude smaller than that for the same particle and wafer combination
in air. Due to this difference in the Hamaker constant, the van der Waals force of adhesion is an order
of magnitude smaller in a system containing a liquid as the interlaying medium, thus implying that
a wet cleaning technique will require less force to remove particles on a wafer surface than a dry
cleaning technique. It is important to note that the force of adhesion for a real system is highly
dependent on particle shape, wafer topography, film on wafer, and purity of interlaying media. 3

Charged Particle Interaction. Charged particle interaction is another important method of particle
adhesion. The forces are due to coulombic attractions, electrostatic contact potentials, and ionic dou-
ble layer interactions.
For coulombic attractions, the particle and/or the surface must be charged. They are best described
as the force between a particle and its “image” within the planar surface, also known as an electron-
ic double layer force. The magnitude of the force is inversely proportional to the dielectric constant
of the media between the particle and the surface and therefore this force is very weak when the sys-
tem includes an aqueous solution. 4
Greater forces are developed by electrostatic contact potentials than coulombic interactions. For
very small particles, electrostatic contact potentials induce electronic double layer forces that result
from the differences in local energy states and electronic work functions of the particle and the sur-
face. This force develops from the transfer of electrons between the particle and the surface in order
to achieve a common charge. It is directly proportional to the diameter of the particle and can achieve
magnitudes equal to the van der Waals force. 5
Still greater forces are developed when the particle and wafer are present in a liquid solution, due
to the presence of ions that create an ionic double layer interaction. This interaction results from the

Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com)
Copyright © 2004 The McGraw-Hill Companies. All rights reserved.
Any use is subject to the Terms of Use as given at the website.