Measuring Absorptance (k) and Refractive Index (n) of Thin Films with the PerkinElmer Lambda 950/1050 High Performance UV

Measuring Absorptance (k) and Refractive Index (n) of Thin Films with the PerkinElmer Lambda 950/1050 High Performance UV
A P P L I C AT I O N N O T E
UV/Vis Spectroscopy
Authors
Frank Padera
PerkinElmer, Inc.
Shelton, CT USA
Measuring Absorptance (k)
and Refractive Index (n)
of Thin Films with the
PerkinElmer Lambda 950/1050
High Performance
UV-Vis/NIR Spectrometers
Introduction
An optical coating consists of a
combination of thin film layers
that create interference effects
used to enhance transmission
or reflection properties for an
optical system. How well an
optical coating performs is
dependent upon the number of
factors, including the number
of layers, the thickness of each
layer and the differences in
refractive index at the layer
interfaces. The transmission properties of light are predicted by wave theory. One
outcome of the wave properties of light is that waves exhibit interference effects.
Light waves that are in phase with each other undergo constructive interference,
and their amplitudes are additive. Light waves exactly out of phase with each other
(by 180°) undergo destructive interference, and their amplitudes cancel. It is through
the principle of optical interference that thin film coatings control the reflection and
transmission of light.
When designing a thin film, though the wavelength of
light and angle of incidence are usually specified, the
index of refraction and thickness of layers can be varied
to optimize performance. As refraction and thickness are
adjusted these will have an effect on the path length of
the light rays within the coating which, in turn, will alter
the phase values of the propagated light. As light travels
through an optical component, reflections will occur at the
two interfaces of index change on either side of the coating.
In order to minimize reflection, ideally there should be a
180° phase shift between these two reflected portions when
they recombine at the first interface. This phase difference
correlates to a λ/2 shift of the sinusoid wave, which is best
achieved by adjusting the optical thickness of the layer to
λ/4. Figure 1 shows an illustration of this concept.
R1
Incident Beam (1)
R2
R1 R2
R2
l/
2
R1
at each interface which will cause different optical
performances at the two polarizations.
Determining the refractive index, n, and the absorptance
(absorption coefficient), k, of a coating are two important
parameters in thin film research. In real materials, the
polarization does not respond instantaneously to an applied
field. This causes dielectric loss, which can be expressed by
the complex index of refraction that can be defined (ref. 2):
n = n + ik
where:
n= the complex refractive index
i = the square root of -1
n= the refractive index
k= the absorption index
Here, k indicates the amount of absorption loss when the
electromagnetic wave propagates through the material. The
term k is often called the extinction coefficient in physics.
Both n and k are dependent on the wavelength. In most
circumstances k > 0 (light is absorbed).
In this paper we will show how the absorptance, refractive
index, and film thickness of thin films can be calculated
from the spectral data.
n0
l/
4
Experimental
Figure 1. For an air (n0) / film (nf) interface, illustrated is the 180° phase shift
between the two reflected beams (R1, R2), resulting in destructive interference
of the reflected beams.
Index of refraction influences both optical path length
(and phase), but also the reflection properties at each
interface. The reflection is defined through Fresnel’s
Equation (ref. 2), which provides the amount of reflection
that will occur from the refractive index change at an
interface at normal incidence:
( )
R=
np – nm
np + nm
2
2
The intensity of reflected light is not only a function of
the ratio of the refractive index of the two materials,
but also the angle of incidence and polarization of the
incident light. If the incident angle of the light is altered,
the internal angles and optical path lengths within each
layer will be affected, which also will influence the amount
of phase change in the reflected beams. It is convenient
to describe incident radiation as the superposition of two
plane-polarized beams, one with its electric field parallel
to the plane of incidence (p-polarized) and the other with
its electric field perpendicular to the plane of incidence
(s-polarized). When a non-normal incidence is used,
s-polarized and p-polarized light will reflect differently
2
To determine n and k a number of optical measurements
are needed which require accessories to be added to the
UV/Vis spectrometer. To calculate the absorption coefficient
(re: absorptance, extinction) of a thin film the transmission
and absolute reflectance spectra of the material needs to
be acquired (it follows that the material cannot be opaque).
Using a high performance Lambda spectrometer (Lambda
650/750/850/950/1050) an integrating sphere accessory,
ideally the PE-Labsphere 150 mm Spectralon coated sphere,
or the Universal Reflectance Accessory (URA) are ideal
accessories for this determination. Though a smaller sphere
may be used for these measurements, the accuracy level
will decrease as the size of the sphere gets smaller. When
the absorption gets low, smaller spheres may not have the
inherent accuracy to be used. A number of other accessories
can be used where absolute specular reflectance can be
measured, accompanied by the transmission, such as the VN
8 degree absolute specular reflectance accessory.
Discussed in the next section are the procedures and some
example results for calculating absorptance using a Lambda
1050 UV/Vis/NIR spectrometer fitted with a Labsphere
Spectralon 150 mm InGaAs integrating sphere. Absorptance
is light that is not transmitted or reflected by a material,
but is absorbed. The equation T + R + A = 1 describes the
theory, where T=transmittance, R=reflectance,
and A=absorptance.
Measuring the Absorptance (k) of Materials
The procedure presented here will describe the accurate
measurement of absorptance using the 150 mm Integrating
Sphere accessory. A picture of the 150 mm integrating
sphere (L6020204) installed in a Lambda 950 is shown in
Figure 2, with a top down view of the schematic of the
sphere beneath the picture. This accessory occupies the
second sample compartment area (right side in picture) of
the instrument, leaving the primary sample compartment
free to accept liquid samples and other accessories.
In addition to the integrating sphere accessory, this
procedure requires a calibrated standard, either a calibrated
Spectralon white reference plate, or a calibrated mirror.
When measuring absorptance using the integrating sphere it
needs to be noted that samples need to be clear (haze will
cause problems with the calculation) and the coatings need
to be applied to fairly thin substrates (i.e., glass slides are
ideal). Coatings applied to thick substrates run the risk of
some of the reflected light being clipped on the port on the
return of the reflected light into the sphere.
A. Measuring Transmission using the Integrating Sphere
The %T measurements have little considerations as long as the
sample is large enough to cover the transmittance port of the
sphere, and sample and reference beams are aligned properly.
The sphere should be set for Total %R (Specular Exclusion
Port plug in place). For sample sizes that are smaller than the
instrument beam the Small Spot Kit Accessory (L6020211)
might be necessary. In transmission the Correction settings in
the method should be the same as shown in Figure 3, making
sure the 0%T baseline option is checked.
Specular Exclusion Port
Reference
Beam
Caution Label
Center-mount
Port
Cover
Transmittance Port
Sample
Beam
Reference Port
Sample
Reflectance Port
Caution Label
Figure 2. Picture of the 150 mm integrating sphere installed in a Lambda 950
with a top down view of the diagram of the sphere below. The red marked area
is where transmission of the material is done, and the green area the
reflectance of the material.
B. Measuring Reflectance with the Integrating Sphere
Reflectance measurements have a number of considerations.
The reflectance needs to be measured in Absolute %R, which
means the spectra are corrected for the reflectance of the
reference material (Light Spectral Reference), as well as the
dark level (0%R) of the sphere (Dark Spectral Reference).
Though correction of spectra with calibration reference data
can be done off-line in Excel, UVWinLab V6 has the capability
to define the calibration file in the method so that the
reflectance spectral correction is performed automatically as
data is being acquired in real-time (note: no calibration file is
required for transmission data collection).
There are two common approaches for generating Absolute
%R with an integrating sphere.
1.Use a calibrated mirror, either a primary (i.e., NIST,
OMT) or secondary standard (PE # N1010504).The latter
Figure 3. Corrections settings for a transmission scan with the sphere accessory.
3
is calibrated against a primary NIST traceable mirror,
however the error tolerances are larger than with a
primary mirror.
2.Use a Labsphere Calibrated Spectralon Standard
(i.e., PELA 9058) having a specific calibration sheet for
that standard.
Either which standard is used, the reflectance calibration
data that comes with the standard needs to be converted
to an UVWinlab V6 compatible file so it can be used in
the method to automatically correct the spectral data.
The procedure to do this is outlined in the application
note “Procedure for Creating %RC Correction Files in
UVWinlab V6.docx” (to obtain this paper contact your
local PE UV/Vis Product Specialist). Once the calibration data
has been entered into an ASC file, this file can be copied to
any location on the hard drive on to the computer operating
the Lambda spectrometer, or alternatively it can be placed
into the folder “C:\Program Files\PerkinElmer\UVWinlab\6.0\
Data\Corrections Data” where the file will be registered
automatically for method access.
When measuring reflectance for absorption determination,
because the samples on the reflectance port also transmit
light, it is important to correct for the dark level of the sphere.
Without a sample in place on the reflectance port, due to
minute scatter of the light beam traversing the length of the
sphere and the inherent back scatter of light off the sphere
cover, it is normal to see a sphere dark level in the range of a
few tenths of a percent to nearly a percent above zero.
There are two ways of correcting for the sphere dark level
for reflection of transmitting samples:
1.Acquire a new dark deference correction every time the
method is run (the correction settings for this option are
shown in Figure 4).
The setup for the option (1) requires that in the Corrections
menu of the method, the options for both the 100%T/0A
Baseline and the 0%T/Blocked Beam Baseline are checked,
but the option Use internal attenuator is left unchecked,
as shown in Figure 4. Using this setup, when the correction
prompt is given “Block the beam and press OK to perform
a 0%T/Blocked Beam correction” the user will not actually
block the beam, but rather will remove the Spectralon white
plate from the reflectance port and replace the sphere cover.
Though it is fine to acquire the dark reference of the
sphere in this manner each time 100% and 0% corrections
are taken, it may be more convenient to acquire the dark
current scan only once and then save this file so it can
be assigned as the Dark Spectral Reference file in the
Corrections menu. To acquire this file, make sure the white
sample reflectance reference plate is removed, there is no
sample in the beam, and replace the sphere cover. Start a
scan over the widest wavelength range that will be used
(i.e., 2500 to 250 nm is typical). When completed, rightclick on the filename and select Save as ASC to any location
on the computer, or save to "C:\Program Files\PerkinElmer\
UVWinlab\6.0\Data\Corrections Data”, to add this correction
file to the list of files in the method view.
To assign the calibrated mirror or calibrated Spectralon ASC
files, and the dark current sphere file, to the UVWinlab
method, select an ordinate mode of %R, click on the
Corrections menu, under the Reflection Corrections section,
select the Correction Type “Reflectance corrected for
reference (%RC)”. Under the “Light Spectral Reference”
setting, click the down arrow and then “Select – Import”.
Browse to the location of the calibrated mirror or calibrated
Spectralon ASC file, and assign this file to the field. Repeat
this for the “Dark Spectral Reference” field. Note that when
using a Dark Reference File correction, the option for Use
internal attenuator is checked. Saving the method will store
these correction file assignments.
2.Perform dark reference correction from a stored file. The
dark reference is measured and saved as a file so it can
be assigned as the Dark Spectral Reference under the
Correction menu (the correction settings for this option
are shown in Figure 5).
Figure 5. Reflectance correction settings where the dark reference correction is
being applied from a stored spectral file.
Figure 4. Reflectance corrections settings with the integrating sphere, where a
dark reference correction is acquired before sample analysis. In this example,
the “Light Spectral Reference” has been defined with an OMT primary
4
Note that if using a calibrated Spectralon white reference,
this plate is used in place of the sample regular Spectralon
plate that is included with the sphere, and the regular
reference plate is used on the reference port of the sphere.
C. E
xample of Determining the Absorptance (k) of
a Sample
Under the Processing section of the method a single
equation can be entered to calculate the extinction as
shown Figure 7. The result is shown in Figure 8.
When both the %T and the %R files have been acquired, the
Processing section of the method can be used to calculate the
absorptance of the sample. A single equation is required.
Measuring the Refractive Index (n) of Materials
Numerous mathematical approaches exist to calculate the
refractive index and film thickness from transmittance and
reflectance spectra of thin films. Three approaches will
be discussed here, all within the capabilities of the high
performance Lambda spectrometers and UVWinlab software.
(100-Transmittance-Reflectance)/100
Shown in Figure 6 are the %T and %R scans of a sample
transmission and reflectance spectra of thin film crystalline
silicon deposited on a glass slide, for characterization of its
semiconductor properties, acquired with a Lambda 1050
with 150 mm InGaAs Integrating sphere accessory.
1.Using the Ri and Tcalc equation functions under the
Processing editor of UVWinlab V6
2.Calculating refractive index from transmission or
reflectance spectra acquired at two different angles
of incidence
3.Calculating refractive index and thin film thickness
using formulas from either the reflectance or
transmittance spectra where no interference fringe
pattern is available
Each of these approaches will be discussed in detail below.
Figure 6. Transmission (green) and reflectance (red)spectra of thin film
cyrstalline silicon acquired for absorptance determination.
1. C
alculating Refractive Index and Film thickness using
the built-in Ri and Tcalc Equation Functions
Thin films in the thickness range of about 0.1 to 10 microns
can exhibit a constructive-destructive interference pattern
as a function of wavelength. If the film thickness if known,
the refractive index can be calculated using the built-in
Ri equation function under the Processing section of the
software. Conversely, if the refractive index is known, the
film thickness can be calculated using the Tcalc function.
The equations programmed into these functions are shown
in Figure 9 (ref 2).
Figure 7. Equation (boxed) programmed into the Processing section of
UVWinLab to calculate absorptance (k). The filenames assigned for the %T
and %R measurements are variables.
t=
n=
(λ1 x λ2) c
2((λ1 - λ2) ((n2 - sin2a)½))
N (λ1 x λ2) c
2(λ1 - λ2) t
2
½
+ sin a
2
where:
λ1 = maximum wavelegnth
λ2= minimum wavelegnth
N = number of fringes
n = refractive index
a = angle of incidence
c = conversion factor to angstroms
Figure 8. Equation calculated absorptance (k) from the %T and %R spectra
shown in Figure 6.
Figure 9. Film thickness and refractive index equations programmed into the
Tcalc and Ri equation functions of UVWinlab.
5
To calculate film thickness and refractive index the user enters the required data, including the wavelength range, the
refractive index (or film thickness), the number of fringes, and angle of incidence in the equation formats for Tcalc and Ri
shown below.
Film thickness (Tcalc) and refractive index (Ri) preprogrammed equations:
In the example shown in Figure 10, a polycarbonate
protection lens having a thin film anti-abrasion coating
with a nominal film thickness of 6 microns is shown.
Figure 10. Spectra acquired from a lens having a thin film anti-abrasion
coating, showing a characteristic constructive-destructive interference pattern.
In this example a film thickness of 6.00 microns was entered in the Ri function under the Processing section of the method,
and a refractive index of 1.467 was calculated between 675 and 548 nm (6 fringe peaks. Conversely, the film thickness
was calculated by entering a refractive index of 1.467. The results from these calculations are put into the Results table, as
shown in Figure 11.
Figure 11. Film thickness and refractive index calculated by the Ri and the Tcalc functions of UVWinlab for the lens sample in Figure 10.
2. C
alculating Refractive Index from Spectra
Measured at Two Different Angles of Incidence
For samples that exhibit an optical thin film interference
pattern it is possible to calculate the refractive index by
acquiring the transmittance or reflectance spectra at
two different angles of incidence, and entering the shift
observed in the interference pattern into an equation
(Figure 12). For this measurement a variable angle
transmission or a variable angle specular reflectance
accessory is required. This can be a relative (i.e., B0137314)
or absolute variable angle (i.e., Universal Reflectance
Accessory – URA L6020202) reflectance accessory.
Additionally, because light impinging on the sample at
oblique angles will be transmitted or reflected in two
orthogonal planes, s-polarized or p-polarized, either a
Common Beam Depolarizer (CBD) is recommended, or a
polarizer drive unit fitted with a polarizer crystal allowing
measurement at a known angle of polarization.
Procedure:
1.Using a variable angle transmittance or variable
angle specular reflectance accessory measure at two
different angles of incidence.
2. Obtain the fringe pattern at each angle.
3.For each angle of incidence, measure the spacing
between adjacent fringes.
4.Use the following formula to calculate the refractive
index (ref. 4):
n = ((sin2θ1∆v12 - sin2θ2∆v22) / (∆v12 - ∆v22))½
where θ1 and θ2 are the two different angles of
incidence, and ∆v1 and ∆v2 are the fringe spacing
for adjacent fringes measured at angles θ1 and θ2
respectively (note: if entering wavelength values
the result is multiplied by 10e7).
Figure 12. Formula to calculate refractive index from thin film spectra at two
different angles of incidence.
6
The Universal Reflectance Accessory (URA) was used to acquire the absolute reflectance data at two different angles of
incidence of a silicon nitride coated semiconductor wafer. Like the 150 mm integrating sphere accessory, the URA fits into
the second sample compartment area of the High Performance Lambda spectrometer (Figure 13). A close-up of the URA is
shown below. Samples are laid horizontal over the beam port for measurements, and the motorized accessory will drive to
the angles programmed.
In the example shown in Figure 15 is a silicon nitride coated
semiconductor wafer on silicon which was scanned in
reflectance at a 15 and a 45 degree angle of incidence. The
interference patterns are clearly observed, and the adjacent
peak wavelength separation can be measured easily.
Figure 13. The Universal Reflectance Accessory (URA) fitted into a Lambda
950. The URA is a programmable motorized absolutel reflectance with an
angle range of 8-68 degrees.
The parameter setup screen and the sample table entries
for the measurements are shown in Figure 14. Once the
angles are programmed, all angle changes and corrections
proceed automatically without operator intervention.
Figure 15. Silicon nitride thin film coating on a silicon substrate semiconductor
wafer scanned in absolute reflectance at two different angles of incidence
(red = 15°, green = 45°) using the URA accessory.
Using the peaks at 800.1 and 644.3 for 15°, and 732.0
and 595.5 for 45°, deltas of 155.8 nm and 138.5 nm
were calculated respectively. After entering the equation
in Figure 12 into the Processing section of UVWinLab a
refractive index of 2.22 was calculated for this sample. The
equation output is shown below:
Figure 14. Universal Reflectance Accessory parameter page and associated
sample table to acquire absolute reflectance data at 15 and 45 degrees angle
of incidence, using a beam size of 5x5 mm (length x width). When the run is
started all angle changes and corrections are done automatically.
7
3. C
alculating Refractive Index Using Formulas From
Either the Reflectance or Transmittance Spectra
Besides providing information on the absorption of a
sample, transmission and reflectance spectra can be used to
calculate the refraction indices of a sample. If the absorption
if high with no or minimal interferences the sample
refractive index nf can be calculated using the equations
below (ref.1):
the refractive index over that part of the spectrum. Again,
the equation was entered into the Processing section
of UVWinlab.
Shown in Figure 18 are the calculated refractive indices at a
select number of wavelengths, with a mean refractive index
of 4.87 calculated from 2500 to 1800 nm.
1
If interferences are determined, from the maxima in the
transmission spectra the refractive index of the substrate can
be derived by the following equation. Note this formula only
applies to cases where absorption of the substrate is negligible:
Figure 16. Transmission (green) and reflectance (red) spectra of thin film
crystalline silicon deposited on a glass slide.
2
If the absorption is low and there are no or minimal
interferences the sample refractive index can be calculated
from the transmission minima by using the following formula:
3
Figure 17. Absorptance spectrum calculated from the spectra in Figure 16.
Figure 18. Refractive index calculated over the range of 2500-1800 nm using
the first equation (1) above from the reflectance spectrum (Figure 15) of thin
film crystalline silicon deposited on a glass slide. The equation was programmed
into the Processing section of UVWinlab and a mean refractive index of 4.87
was determined.
Conclusion
Since the absorption of thin film coatings is usually not
uniform as a function of wavelength, ranging from low to
high absorption, the formulas above can be applied to the
appropriate sections of the spectra for a valid calculation of
refractive index.
Shown in Figure 16 are the transmission and reflectance
spectra of thin film crystalline silicon deposited on a glass
slide, for characterization of its semiconductor properties.
Shown in Figure 17 is the absorptance spectrum. In the area
between 1800 and 2500 nm the absorption was significant,
so the first equation above (1) above was used to calculate
8
The reference grade high performance Lambda 1050 when
fitted with the proper accessories becomes an ideal tool for
the determination of optical thin film constants. In this paper
procedures were described for the determination of refractive
index (n), absorptance (k), and film thickness for thin films.
The 150 mm InGaAs integrating sphere and the Universal
Reflectance Accessory proved to be ideal accessories for
acquiring the data for the examples presented in this paper.
References
1. M. Born and E. Wolf, Principles of Optics, 7th Edition,
Cambridge University Press, 2005
2. M. Rand, Spectrophotometric Thickness Measurement for Very Thin SiO2 Films on Si, Journal of Applied Physics, Volume 41, Number 2, 1970
3. J. Rancourt, Optical Thin Films User’s Handbook,
McGraw-Hill Publishing Company, 1987
4. PerkinElmer Publication 0993-8288, Applications of Variable Angle Specular Reflectance, 1988
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