vertical stylus displacement as a function of position. A typical profilometer can measure small vertical features ranging in height from 10 nm to
50 µm. In fact, most of the world’s surface finish standards are written for
contact profilometers. Unfortunately, the technique is “invasive” in that
the stylus makes contact with the surface and may well damage the film.
Furthermore, profilometry requires a region of exposed substrate with an
abrupt edge, such as a scratch in the film, to provide a reference height for
calculating the thickness. There are noncontact profilometers that use
light as a way of measuring the height of surface features. However,
noncontact profilometry cannot measure the thickness of films on the
order of 10
–10 m (angstroms).
A technique known as ellipsometry has been used extensively to measure
film thicknesses as low as a few angstroms. Ellipsometry is a noncontact
and nondestructive technique used for measuring both the thickness and
the refractive index of thin films on solid surfaces. Thin films ranging in
thickness from a few angstroms to ~1 µm can be measured accurately and
quickly using this method. Ellipsometry analyzes the state of polarization
of light reflecting from a surface and uses the laws of electromagnetism
(specifically, Maxwell’s equations) to resolve the thickness and refractive
index of the nanofilm.
8.3.1 Basic principles of electromagnetic theory
and polarized light
In Chapters 5 and 6, we frequently discussed light in its classical representation as an electromagnetic wave. Ellipsometry measures the change
in the polarization (direction of the electric field, not to be confused with
polarization of electrons) of a light beam after its reflection from the solid
surface of the sample being characterized. Although detailed coverage of
the theory of ellipsometry is beyond the scope of this book, we include a
brief overview of electromagnetic theory in order to better understand the
basis of ellipsometry.
As previously discussed, light can be viewed as an oscillating electromagnetic field propagating through space. The oscillating field of light has
two mutually perpendicular components; an electric field and a magnetic
field. These are both perpendicular to the direction of light propagation, which we will arbitrarily define as the z-axis. Only the electric field
component is considered here since the magnetic component does not
interact appreciably with most molecules. The electric field can be represented mathematically as a complex exponential function
CHAPTER 8: Surface Characterization and Imaging Methods
266
50 µm. In fact, most of the world’s surface finish standards are written for
contact profilometers. Unfortunately, the technique is “invasive” in that
the stylus makes contact with the surface and may well damage the film.
Furthermore, profilometry requires a region of exposed substrate with an
abrupt edge, such as a scratch in the film, to provide a reference height for
calculating the thickness. There are noncontact profilometers that use
light as a way of measuring the height of surface features. However,
noncontact profilometry cannot measure the thickness of films on the
order of 10
–10 m (angstroms).
A technique known as ellipsometry has been used extensively to measure
film thicknesses as low as a few angstroms. Ellipsometry is a noncontact
and nondestructive technique used for measuring both the thickness and
the refractive index of thin films on solid surfaces. Thin films ranging in
thickness from a few angstroms to ~1 µm can be measured accurately and
quickly using this method. Ellipsometry analyzes the state of polarization
of light reflecting from a surface and uses the laws of electromagnetism
(specifically, Maxwell’s equations) to resolve the thickness and refractive
index of the nanofilm.
8.3.1 Basic principles of electromagnetic theory
and polarized light
In Chapters 5 and 6, we frequently discussed light in its classical representation as an electromagnetic wave. Ellipsometry measures the change
in the polarization (direction of the electric field, not to be confused with
polarization of electrons) of a light beam after its reflection from the solid
surface of the sample being characterized. Although detailed coverage of
the theory of ellipsometry is beyond the scope of this book, we include a
brief overview of electromagnetic theory in order to better understand the
basis of ellipsometry.
As previously discussed, light can be viewed as an oscillating electromagnetic field propagating through space. The oscillating field of light has
two mutually perpendicular components; an electric field and a magnetic
field. These are both perpendicular to the direction of light propagation, which we will arbitrarily define as the z-axis. Only the electric field
component is considered here since the magnetic component does not
interact appreciably with most molecules. The electric field can be represented mathematically as a complex exponential function
CHAPTER 8: Surface Characterization and Imaging Methods
266