Download In this lab you will use the phenomenon of interference... thickness of thin films. Two interference techniques, Michelson and... Thin Film Measurement 1 Introduction

Thin Film Measurement
1 Introduction
In this lab you will use the phenomenon of interference and reflection to measure the
thickness of thin films. Two interference techniques, Michelson and Fizeau, will be studied and
compared for accuracy, resolution and ease of use. The Michelson technique uses a Michelson
interferometer with one of the mirrors replaced with the sample under test. The Fizeau technique
uses a Fizeau interferometer to measure the shift in the interference pattern created between a Fizeau
flat and the sample when they are held together with a minute air wedge between them.
Both experiments require a step height in the film and the film and sample must be reflective.
Another technique, which is used to measure thin film thickness without a step height in the film,
is ellipsometry. This technique uses the change in polarization of the reflected light from the thin
film and substrate interface to measure the film thickness. This process is more complicated and will
also be demonstrated in this lab. The student should familiarize him/herself with the process before
attempting this procedure.
2 Experimental
Michelson Technique
Two measuring techniques are used and compared with this set-up. The first involves
using the micrometer on the mirror to measure the difference in zero path length between the thin
film and no film. The second technique uses the step height change in the interference pattern much
like the Fizeau technique. Set up the experiment as shown in Figure 1. The alignment of the set up
is critical. All surfaces must be as close to perpendicular as possible. That is, the mirrors, cube
beam splitter, and microscope objective faces must be perpendicular to each other’s normal. Place
the DCX lens so that the image of the cube at the screen is focused and its largest, this is about 3.5
to 4 cm from the surface of the cube. Adjust the sample micrometer and microscope objective
spacing so a bright focused spot of about 3 cm is seen on the screen through the beam splitter. Now
adjust the mirror’s thumb screws to centre the image from the objective inside the image of the cube
beam splitter. An interference pattern should be seen within the image of the cube beam splitter.
Adjust the sample stage position to come as close to zero path length as possible (you may
have to adjust the position of the mirror so as not to change the size of the objective lens image too
much), this will be apparent as the interference pattern becomes very large then becomes small again.
Continue to adjust the mirror so the interference pattern is horizontally straight across the cube
image. This is done by off-setting the interference pattern between two patterns, one at the top and
one at the bottom of the cube image. See Figure 2 for a picture of the interference image required.
Using the X and Y positioners on the sample stage, scan the wafer across the objective and stop
when a resistor channel is found. Measure the width of this channel on the screen, compare this to
the 20 u actual width and determine the magnification factor at the screen. Now without moving the
Z position (you will change the magnification), move the sample using the X and Y micrometers
until an image of a diode, capacitor, or resistor contact well is found. Position the vertical edge in
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the middle of the interference pattern so it cuts the horizontal lines vertically in half. The
interference image now is that of one through the oxide and one off the silicon substrate where the
resistor contact pads were etched in the oxide.
Figure 1: Michelson interferometer to measure thin film thickness.
Figure 2: Interference pattern example.
Measurement
Now you have an interference pattern with a path length at the bottom of the well without
an oxide layer and one with a path length through the oxide layer. Carefully adjust the mirror
alignment so the lines are as parallel and horizontal as possible. Now move the mirror until zero
path length for one side is achieved (this is when the lines are completely horizontal and maximumly
spaced). Read the micrometer position. Now adjust the mirror position so the other side is at zero
path length and read the new micrometer position. Calculate the oxide thickness using the following
formula:
(1)
thickness =
change in micrometer position (meters)
magnification X n oxide
where noxide = 1.46
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Repeat this procedure a few times to ensure an accurate measurement. The measurement
accuracy is based on the ability to find the zero path length for each side of the well. This zero path
length point can be hard to determine so several measurements and then an average is needed. Can
you suggest another way to optically detect zero path length difference?
The second measuring technique for this set-up is the same as the Fizeau. By magnify the
interference you should be able to see the fringes bend up or down and then run horizontal again (see
fig 3). By physically measuring the step height and comparing it to the measured spacing between
the fringes you can calculate the film thickness.
Fizeau Technique
The set up for this experiment is not much different from the Michelson set up. Block the
mirror of the previous set up with a piece of paper. Remove the X40 microscope objective and
replace with the X4 objective. Add the Fizeau flat between the objective and the sample and secure
in place such that the sample can be brought into contact with its optically flat surface. See Figure
3 for set up configuration. Remove the silicon wafer from the sample stage and replace it with the
aluminum coated glass slide with the graded step height. Now, using the Z micrometer, carefully
move the glass slide against the Fizeau flat. Position the objective lens such that the image of the
graded line on the sample is sharply focused, leave the objective in this position. By using the
thumbscrews on the sample mount, you can adjust the air wedge such that an interference pattern
of evenly spaced horizontal lines is achieved.
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Figure 3: Fizeau interferometer set-up.
Measurement
The interference pattern should look like that of Figure 4. The graded step height in the thin
film has produced a displacement of fringe lines, the amount of displacement represents the step
height (i.e. film thickness). It is known that the distance between the interference lines is exactly half
the wavelength of light used. In this case 6328 A/2 = 3164 A. Therefore, the film thickness is given
by the formula:
(2)
$
film thickness ( Α) = 3164 ×
step height
fringe spacing
The fringe spacing is the measured spacing on the screen between the interference lines and
the step height is the measured space from one step of the step to bottom of the step following one
of the fringe lines. Both these measurements would be made on the screen and would be given in
millimeters.
Figure 4: Fizeau interference pattern
Ellipsometry
Refer to the operating procedures posted in the lab to set up the ellipsometer. Allow the mercury
light to warm up for at least 10 minutes before proceeding with measurements (alignment can be
performed during this time).
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Theory
In order to electrically isolate various parts of an integrated circuit from one another, it is
necessary to grow or deposit an insulating material between the active areas. This material could
be an oxide of a few 100 to a few 1000 Angstroms in thickness. Determination of how much
oxide has been formed requires a method which is nondestructive, since you don=t want to
interfere with the integrated circuit structure, and yet be sensitive enough to give a close
approximation of the film’s thickness. These specifications are met by the ellipsometer.
Ellipsometry is the measure of reflections and their effect on the polarization of light.
Such information gained from the measurements may be interpreted to yield the optical constants
of the reflected material or, when the reflecting material is a film covered substrate, the thickness
and optical constants of the film. What happens when light is reflected off a material? A planepolarized beam of light reflected off a surface can become elliptically polarized (see Figure 5).
Figure 5: Plane polarized reflection
Ellipticity is a result of a phase change (small delta), between the Ap@ and the As@ components
of the reflected light and a change in the ratio of their amplitudes, denoted as psi (see Figure 6),
where
(2)
Ψ = arctan{R p / Rs ⋅ Es / E p }
Figure 6: Relative
phase shift between
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incident and reflected waves.
This phase change varies for the various values of the incident angle phi and for different
metals (see Figure 7). This phase angle change is referred to in ellipsometry as (capital) delta,
defined as:
(δ
(3)
p
⋅ δ s ) reflec ⋅ (δ p ⋅ δ s )incident
Figure 7: Phase change vs. Incident angle for three different metals.
The azimuth angle psi between the components R p and Rs , is a measure of the relative
absorption of these two reflected components by the material.
Rp
= tanψ
Rs
Figure 8: Rp and Rs relation.
The complete expression from a three dimensional point of view must take into consideration
not only the value of psi, but also the phase change as well. Therefore, the complete formula
becomes,
Rp
= (tanψ )(exp i∆ )
Rs
{absorbtion change} & {phase change}
The operating principle of an ellipsometer is just the reverse of that phenomena described above.
(4)
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See Figure 9 for the basic components of an ellipsometer.
Figure 9: Ellipsometer set-up
Collimated monochromatic light, normally of the mercury green line, (5460.73 A) is used.
The polarizer, (a Glan-Thompson or a Nicol prism) is mounted in a graduated circle, serving to
polarize the light emitted by the source. The compensator, is a birefringent plate usually of quarterwave thickness. It is used to convert the linearly polarized light into elliptically polarized light.
Hence, the light incident upon the sample has an azimuthal angle psi and an ellipticity predictable
from the polarizer and compensator settings. The azimuthal angle is determined by the analyzer
located in the path of the reflected beam. Therefore, any change in the light=s ellipticity and
azimuthal angle due to the reflectance from the sample is controllable.
Any ellipticity existing in the light reaching the analyzer cannot be removed by adjusting the
analyzer only. Both the polarizer and the compensator must be readjusted alternatively to remove
this ellipticity. When this has been accomplished, the light reflected from the sample is plane
polarized and can be readily extinguished by the adjustment of the analyzer. The use of a phototube
and photometer increase the accuracy for determining the final settings of the compensator and
analyzer for the points of extinction.
The determination of capital delta and psi from the ellipsometer scale readings AP@ and AA@
are related (assuming a perfect quarter-wave plate for the compensator) by the equations:
(5) and (6)
∆ = 1 2π − 2 P
Ψ = - Ap = As
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There are, however, for any given surface a multiplicity of polarizer, analyzer and compensator scale
settings that produce extinction making the determination of psi rather tedious. It is however
possible to subdivide the determinants into four areas, (or what is commonly referred to in the
literature as zones). Though the meaning of these zones will not be elaborated here, it is sufficient
to remember that they are related to the values of AP@ and AA@ as follows:
AP@ - the angle between the polarizer plane of transmission can be related to the surface
of the material as being in either the plane of incidence, or the plane of the
surface.
AA@ - can be subdivided down into A As @ and Ap@according to whether AP@ is the
angle between the polarizer plane of transmission and the plane of incidence or
the materials surface plane.
These relationships can be summarized as follows:
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The relationship between capital delta and psi and the optical parameters n, k and d of
some film are expressed by the Fresnel reflection coefficients. This reflection coefficient is a
ratio of the electric field vector Er of the reflected wave to that of the incident wave Ei , in terms
of the amplitudes of both waves and the associated phase change due to the reflection,
r = (Er Ei )eiδ
(7)
The reflection of a wave of any polarization is given by the two coefficients Rp and Rs of
the component waves. The ratio of these are,
rp rs = (Erp Ers )⋅ (Eis Eip )ei (δp −δs )
(8)
From the definition of capital delta and psi, given earlier, it follows that,
rp rs = tan Ψei∆
(9)
The Fresnel reflection coefficients for a film-covered substrate are,
i∆
tan Ψe =
(10)
rp 01 + rp12e −2 iδ
1 + rp 01rp12 e − 2iδ
×
1 + rs 01rs12e −2 iδ
rs 01 + rs12 e − 2iδ
Therefore the complete equation for ellipsometry is,
r01′ + r12′ e −2iδ
r′ =
, where ′ is p or s
1 + r01′ r12′ e − 2iδ
(11)
The Fresnel reflection coefficients for a clean substrate are,
rpab = (na cos φ2 − nb cos φ1 ) (na cos φ2 + nb cos φ1 )
(12)
and
(13)
rsab = (na cos φ1 − nb cos φ2 ) (na cos φ1 + nb cos φ2 )
where a and b represent the ambient medium and the substrate respectively.
The phase change small delta can be determined from the equation,
(14)
δ = (360 λ )d (n12 − sin 2 φ )
12
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By substituting equations (12), (13), and (14) into equation (11), d can be determined as a
function of capital delta, psi, angle of incidence, indices of refraction of the film and substrate and
the wavelength of the light used. In doing this one must remember that n1 and n2 and the angle of
reflection and refraction for an absorbing film and substrate will be complex, to say nothing of the
calculation involved. In this lab we will use a table of values of small delta given for measured
values of n1, capital delta, and psi for transparent films on silicon. The value of small delta can then
be substituted into equation (14) along with n1 to calculate d.
Report
Your report should include, along with your results and analysis of the accuracy, resolution
and practicality of all techniques, a brief discussion of ellipsometry and other optical techniques for
measuring thin film thickness. Be sure to include their advantages and disadvantages. Your report
should also include a derivation of the magnification within one arm of the Michelson interferometer
as it relates to the amplified displacement in the mirror arm (i.e., derive the formula used in the
Michelson experiment).
References
[1] Lumdmila Eckertova, author, APhysics of Thin Films@, Plenum Press, 1986.
[2] Theo Tschudi, chair, AThin Film Optics@, SPIE, 1989.
[3] Leslie L. Ward, author, AThe Optical Constants of Bulk Material and Films@, A.
Hilger, 1988.
[4] Zden Knittel, author, AOptics of Thin Films@, Wiley, 1976.
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