Using these three equations, we can now present the fundamental
equation of ellipsometry:
r =
R
p
R
s = tan ye
iΔ = tan y( cos Δ + i sin Δ)
(8.19)
Δ and y are the experimental quantities measured by the ellipsometer
and fitted to a computer model to yield refractive index and film thickness
(which are embedded in the equations for R
p and R
s ).
Most ellipsometry experiments are performed on nanofilms at the solidair interface. Silicon is a convenient substrate due to its availability, wellknown optical constants, and ease of functionalization. However, many
materials may be used, although materials that are transparent at the
wavelength used for the experiment may require careful selection of
observation angle and addition of a low-reflectivity opaque backing
(which may be as simple as a piece of electrical tape) to limit reflection
from the back of the substrate. The determination of refractive index and
film thickness for these samples is often done as follows. Suppose we have
a substrate covered by a film as in Figure 8.9. Generally, Δ and y are
obtained for the bare substrate and the instrument determines the
refractive index information of silicon and the native SiO 2 layer directly
above it. This is done prior to any film deposition. A table of Δ and y
values as a function of film thickness (called a del/psi trajectory) is
determined. The del/psi trajectory is obtained using a computer program
separate from the ellipsometer, although some instruments have programs to compute del/psi trajectories integrated with the instrumentation. The film is then deposited on the substrate and Δ and y are obtained
for the substrate and film. The unknown thickness of the deposited film
may then be obtained by comparison of the Δ and y values with the
calculated del/psi trajectory for the bare substrate. The optical constants
of the thin film, such as the refractive index, must be input in order for the
program to produce the trajectory. The user makes an educated guess at
these values.
Although the ellipsometer accurately determines Δ and y, these values
are meaningless unless the program used to calculate the del/psi trajectory assumes the correct model. The model used is typically a twolayer model, such as that shown in Figure 8.9 for a silicon dioxide/silicon
wafer substrate.
CHAPTER 8: Surface Characterization and Imaging Methods
274
equation of ellipsometry:
r =
R
p
R
s = tan ye
iΔ = tan y( cos Δ + i sin Δ)
(8.19)
Δ and y are the experimental quantities measured by the ellipsometer
and fitted to a computer model to yield refractive index and film thickness
(which are embedded in the equations for R
p and R
s ).
Most ellipsometry experiments are performed on nanofilms at the solidair interface. Silicon is a convenient substrate due to its availability, wellknown optical constants, and ease of functionalization. However, many
materials may be used, although materials that are transparent at the
wavelength used for the experiment may require careful selection of
observation angle and addition of a low-reflectivity opaque backing
(which may be as simple as a piece of electrical tape) to limit reflection
from the back of the substrate. The determination of refractive index and
film thickness for these samples is often done as follows. Suppose we have
a substrate covered by a film as in Figure 8.9. Generally, Δ and y are
obtained for the bare substrate and the instrument determines the
refractive index information of silicon and the native SiO 2 layer directly
above it. This is done prior to any film deposition. A table of Δ and y
values as a function of film thickness (called a del/psi trajectory) is
determined. The del/psi trajectory is obtained using a computer program
separate from the ellipsometer, although some instruments have programs to compute del/psi trajectories integrated with the instrumentation. The film is then deposited on the substrate and Δ and y are obtained
for the substrate and film. The unknown thickness of the deposited film
may then be obtained by comparison of the Δ and y values with the
calculated del/psi trajectory for the bare substrate. The optical constants
of the thin film, such as the refractive index, must be input in order for the
program to produce the trajectory. The user makes an educated guess at
these values.
Although the ellipsometer accurately determines Δ and y, these values
are meaningless unless the program used to calculate the del/psi trajectory assumes the correct model. The model used is typically a twolayer model, such as that shown in Figure 8.9 for a silicon dioxide/silicon
wafer substrate.
CHAPTER 8: Surface Characterization and Imaging Methods
274