B508

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B508 – Ellipsometry

Content 1 Introduction ..................................................................................................................................... 2

1.1 What is ellipsometry? .............................................................................................................. 2

1.2 Basics in optical theories ......................................................................................................... 2

1.3 Principle of ellipsometric measurements ................................................................................ 4

2 Experimental Details ....................................................................................................................... 4

2.1 The instrument ........................................................................................................................ 4

2.2 Steps for a good measurement ............................................................................................... 4

3 Experimental Results ....................................................................................................................... 5

4 Evaluation ........................................................................................................................................ 6

4.1 Plots ......................................................................................................................................... 6

4.1.1 Silicon dioxide .................................................................................................................. 6

4.1.2 Porous silicon with 90% porosity .................................................................................... 8

4.1.3 Porous silicon with 40% porosity .................................................................................... 9

4.2 Comparison to expected results............................................................................................ 10

4.2.1 Refractive indices .......................................................................................................... 10

4.2.2 Layer thicknesses ........................................................................................................... 11

5 Conclusions .................................................................................................................................... 11

6 Sources .......................................................................................................................................... 11

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1 Introduction

1.1 What is ellipsometry?

Ellipsometry is a technique used on a thin film sticking on a substrate. With ellipsometry it is possible

to measure the thickness of the thin film and to determine the index of refraction of it. It is a

common method used in labs to measure thin films. Due to its low costs and quickness it is very

popular. Other advantages are the uncomplicated sample preparation and the precision of the

measurement in view of the quickness.

1.2 Basics in optical theories

Light with the wave-particle duality in mind can be described as an electromagnetic wave.

Conveniently only the electrical part is considered. The electrical part can be split into two

compounds. They are termed E S (perpendicular to plane of incidence) and E P (parallel to plane of

incidence) and described by the formulas:

= ( 1)

= (−Δ) ( 2)

Ê S = Amplitude of the perpendicular compound

Ê P = Amplitude of the parallel compound

t = Time

ω = angular frequency

Δ = phase difference

Three possible arrangements of the electrical fields yield three different states of polarizations.

Figure 1 shows that Ê P equals Ê S and Δ = 0. Thereby wave1 is the E S and wave2 is the E P compound.

The result is a linear polarization of the lightwave.

Figure 1: Linear polarization [2]

The second case is shown in figure 2. Ê P equals Ê S and =2

. This leads to zirkularly polarization of

the light wave.

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Figure 2: Zirkularly polarization [2]

The most common case is the third one. If Ê P doesn't equals Ê S and Δ ≠ 90° or 0° the light wave will be

elliptically polarized. Figure 3 shows an example.

Figure 3: Elliptically polarization [2]

The polarization state of light changes when it passes a material. A reason for this is the electrical

field of the atoms that influence the light wave. A change of the wavelength and the phase velocity

of the light wave is the consequence. Information on this gives the so called refraction index. It is a

material property and can be described by the complex equation [3]:

= + ( 3 )

N = complex refraction number

n = real compound

k = imaginary compound (extinction)

It defines the factor how much smaller the wavelength and the phase velocity of the light become,

when it passes a specific material related to the wavelength and phase velocity in vacuum. Metals for

example show a very high extinction because of the free delocalized electrons, so the imaginary

compound k shows a high value. Amorphous materials like glass have usually a very small value for

the extinction k. Due to the change of the wavelength and the phase velocity of the light it changes

its state of polarization. If now a thin film is layered on a substrate, it will have a different refraction

index than the one of the substrate, because the thin film contains other atoms or another structure

than the substrate. A state of polarization results other than the state of polarization would appear

without t thin film. This phenomenon is applied in the ellipsometry.

Another for the ellipsometry important phenomenon of the optic that should be mentioned is the

Brewster Angle. At this angle only the perpendicular (to the plane of incidence) polarized part of the

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impinging light wave is reflected. Thus the reflected part becomes linearly polarized. The refracted

part is partially polarized.

1.3 Principle of ellipsometric measurements

If a light wave impinges on a surface it will either be transmitted and/or reflected. The ellipsometry

technique determines the change of the polarization state of light. The incoming light wave is either

linearly or circularly polarized when it impinges on the surface. While passing the thin film layer and

being reflected on the thin film-substrate boundary the dielectric properties of the thin film cause a

change of the light's polarization state. After passing the thin film the light will usually be elliptical

polarized. The index of reflection (real and complex part) and finally the thickness of the thin film are

the reason for the elliptical polarization of the light wave.

Due to the mentioned facts the electric fields E s and E p change the phase between each other and in

addition the amplitudes of the E s and E p fields are changed. These facts lead to a elliptical polarization

of the light wave after it passed through the thin film. A rotation analyzer measures the phases of the

incoming light wave while a detector measures the light intensity of it. The received data is

transferred into a computer where a program processes the data in a complicated way to finally

show the results of the measurement on the monitor. The measurements can then be processed into

a chart to analyze the values like in this lab report.

2 Experimental Details

2.1 The instrument

The instrument of choice is the PLASMOS SD2300 ellipsometer. Its laser as well as its detector are

independent adjustable in angle to the sample holder. The sample holder can be moved in three

directions and tilt to align the optical axis. An optical microscope with two crosses is used to calibrate

the settings. It is also possible to adjust the detected intensity by moving the sample holder in its

height. The measurements are managed at the computer. Here it is necessary to transfer some

theoretical parameters about the specimen like number of layers, refractive indices and/or

thicknesses. Therefore a special interface is used. In addition to that the manually adjusted angles of

laser and detector have to be entered. A schematic illustration can be taken from the script [4].

2.2 Steps for a good measurement

The measurement contains various steps to achieve precise data.

At first the specimen is putted on the sample holder. Now the angles of laser and detector are

adjusted to the same value. After every adjustment of the instrument the correct setting of the

optical axis must be checked by matching the two crosses in the optical microscope.

Further settings are now entered in the software program. Basic settings as the number of layers and

the type of calculation are chosen at the beginning of the experimental series. There are two types of

calculation methods named n-fix and n-float . The n-fix method is used for samples with known

refractive indices, so just the layer thickness is calculated. In this experiment the n-float method is

chosen, where the refractive index as well as the thickness is calculated.

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In the next step for each single measurement specific parameters are given to the computer such as

the angle ρ of the laser/detector and the estimated refractive indices and layer thicknesses. Also a

certain gain can be aligned; here it is set to 4 for the whole series.

Before starting the measurement now, one has to check the intensity shown at the display on top of

the instrument. The angle of the polarizer has to be checked too, because it must be set to 45°degrees. If these checks are okay, the measurement is ready to be started.

3 Experimental ResultsThe first sample has a thin layer of silicon dioxide on a silicon substrate. It was made in an

electrochemical way. Its thickness d is supposed to be around 15 nm, what is about to be measured

in this first experiment. Furthermore a refractive index of 2= 1,455 (2

= 0) is expected for

the thin film. Silicon has a complex refractive index of = 3,875 and = 0,018. These are the

parameters given to the computer as well as the angle ρ, which is now changed in ten degree steps

from ρ = 40° to ρ = 70°.

Table 1: refractive indices and layer thicknesses of SiO2 from ellipsometric measurement

ρ 40° 50° 60° 70°

number n d /nm n d /nm n d /nm n d /nm

1. 1,5554 14,19 1,4695 14,46 1,5507 12,61 1,6723 12,88

2. 1,5053 14,72 1,4863 13,83 1,5514 13,53 1,4844 13,56

3. 1,4939 14,50 1,4563 13,97 1,5856 13,21 1,4673 13,48

4. 1,5204 13,69 1,4902 14,24 1,5720 13,04 1,6155 12,63

5. 1,5098 14,60 1,4603 14,25 1,5900 12,89 1,5398 12,59

average 1,5170 14,34 1,4725 14,15 1,5699 13,06 1,5559 13,03

σ 0,0235 0,41 0,0152 0,25 0,0185 0,34 0,0871 0,46

The second specimen is again a silicon substrate, but the thin layer on top is now from porous silicon.

For the thin layer a porosity of 90% is estimated. Its Thickness d should be almost 1000 nm, while its

refractive index is estimated to 90% ≈ 1,2, which was told by the supervisor. This estimation can

also be done with the Brüggemann theory, which is explained later on in the text.

Table 2: refractive indices and thicknesses of thin layered porous Silicon 90%

ρ 40° 50° 60° 70°


1. 1,1291 1152,15 1,1706 830,30 1,1582 948,97 1,2300 901,90

2. 1,1424 1127,00 1,1631 847,74 1,1261 1029,32 1,1029 727,37

3. 1,1914 1049,27 1,1722 821,85 1,1309 1007,69 1,2300 913,64

4. 1,1439 1125,91 1,1693 838,14 1,1574 947,74 1,2300 920,76

5. 1,1902 1050,25 1,1459 877,78 1,1332 1002,16 1,2300 898,23

average 1,1594 1100,92 1,1642 843,16 1,1412 987,18 1,2046 872,38

σ 0,0292 47,87 0,0108 21,59 0,0154 36,87 0,0568 81,56

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The thin layer of the third specimen is again from porous silicon, but this time with 40% porosity. Its

thickness may be 1000 nm like at the second one and the refractive index should be 40% ≈ 2,3.

These valuables were told by the supervisor. In chapter 0 an estimation by Brüggemann is introduced

for this refractive index.

Table 3: refractive indices and thicknesses of thin layered porous Silicon 40%

ρ 40° 50° 60° 70°


1. 2,4215 1025,25 2,3627 1070,78 2,3959 1068,73 2,3197 974,59

2. 2,3973 1035,18 2,3660 1065,84 2,4189 1059,33 2,3657 953,44

3. 2,4447 1015,52 2,4413 1030,45 2,3903 929,00 2,3316 969,32

4. 2,3980 1035,05 2,4966 1006,50 2,3942 1070,87 2,3921 941,05

5. 2,4116 1030,92 2,4367 1033,06 2,3503 946,96 2,3577 957,25

average 2,4146 1028,38 2,4207 1041,33 2,3899 1014,98 2,3534 959,13

σ 0,0196 8,25 0,0566 26,78 0,0248 70,71 0,0286 13,28

4 Evaluation

4.1 Plots

For every specimen the average refractive indices as well as the average thicknesses of the layers are

plotted against the angle ρ. The errors are built from the standard deviations.

Since angles in vicinity of the Brewster angle are best suited to yield good measurement results [2],

one could expect that angles, for which the errors of the measured film parameters minimize, are

close to the Brewster angle.

4.1.1 Silicon dioxide

Figure 4 shows the average results for refractive indices of the first measurement of the sample with

silicon dioxide layer. The smallest refractive index was measured up to n = 1,4725 ± 0,0152 at an

angle of 50°. Also one can see the smallest error here, compared to settings at other angles. The

biggest index occurs at 60° with n = 1,5699 ± 0,0185. Obviously the sensitivity got bad at higher

angles around 70° because big errors show up.

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Figure 4: average refractive indices of silicon dioxide due to ellipsometry measurement

The average thicknesses d over angle ρ of the SiO2 layer are shown in Figure 5. Here also the

parameter at 50° has a minimal error compared to the others although the differences in errors don’t

vary as much as in the measurement of refractive indices.

Figure 5: thickness of silicon dioxide layer measured with ellipsometry

1,4

1,45

1,5

1,55

1,6

1,65

1,7

35 40 45 50 55 60 65 70 75

n

ρ/°

nSiO2

n

12

12,5

13

13,5

14

14,5

15

35 40 45 50 55 60 65 70 75

d / n m

ρ/°

dSiO2

d

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4.1.2 Porous silicon with 90% porosity

The indices for 90% porous silicon are pretty much the same for the angles 40° to 60°. The result at

70° is higher but shows also the biggest error. At 50° the smallest error shows up.

Figure 6: average refractive indices of porous silicon (90%) due to ellipsometry measurement

Figure 7 shows the thickness of the porous silicon layer measured by ellipsometry. One can see the

results differ a lot. The biggest value is measured at 40° with n pSi = 1100,92 while the smallest occurs

at 50° n pSi = 843,16. There is a difference of ca. 250 nm, which is not within the range of the errors.

Figure 7: thickness of pSi layer measured with ellipsometry

1,1

1,12

1,14

1,16

1,18

1,2

1,22

1,24

1,26

1,28

35 40 45 50 55 60 65 70 75

n

ρ/°

npSi 90%

n

600,00

700,00

800,00

900,00

1000,00

1100,00

1200,00

35 40 45 50 55 60 65 70 75

d / n m

ρ/°

dpSi 90%

d

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4.1.3 Porous silicon with 40% porosity

In Figure 8 one can see the refractive indices of 40% porous silicon. The biggest error is at 50°, the

smallest at 40°.

Figure 8: average refractive indices of porous silicon (40%) due to ellipsometry measurement

The thickness measurement results of pSi 40% are shown in Figure 9. Here the size differences

between the errors are noticeable. At an angle of 40 degrees the measurement had good

reproducibility, so that the error is small compared to the one at 60 degrees.

Figure 9: thickness of pSi layer measured with ellipsometry

2,3000

2,32002,3400

2,3600

2,3800

2,4000

2,4200

2,4400

2,4600

2,4800

2,5000

35 40 45 50 55 60 65 70 75

n

ρ/°

npSi 40%

n

920,00

940,00

960,00

980,00

1000,00

1020,00

1040,00

1060,00

1080,00

1100,00

35 40 45 50 55 60 65 70 75

d / n m

ρ/°

dpSi 40%

d

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4.2 Comparison to expected results

4.2.1 Refractive indices

For every measurement on refractive indices it is helpful to give the computer parameters. The

parameters shall show within which range the results are expected. So it is necessary to calculate

theoretical refractive indices for specimen, of which these indices are unknown. The Brüggemann

theory is useful to calculate such indices for porous materials or more generally for materials with

homogeneous suspended additives. If the refractive indices of both, the matrix material nM as well as

the additive material nad , and their respective volume fractions V are known, one now can estimate

the resulting refractive index neff by formula [5]:

− + 2

= − − + 2

( 4 )

After some shifting one get for 40% porous silicon (V M = V Si = 0,6 and V ad = V air = 0,4):

+ 240% − 40% − 240%2

= − + 240% − 40% − 240%2

( 5 )

Now let’s put the volume fractions into the formula and do some more shifting:

240%2 − − 0,240% − 0,840% = 0 ( 6 )

With the refractive indices of silicon nSi = 3,875 and nair = 1 of air one gets:

240%² − 3,2540% − 3,875 = 0 ( 7 )

40%,1 = 2,42

40%,2 = −0,80

It is obvious, that neff40%,1 = 2,42 is the parameter of choice.

The same procedure can be done with silicon of 90% porosity and one gets:

90%,1 = 1,16

90%,2 = −1,67

Here one can say, that neff90%, 1 = 1,16 is the expected refractive index for 90% porous silicon.

In order to compare the measured results with the theoretical values it is meaningful to use the ones

where the smallest error occurs. This would be for 90% pSi at 50° the refractive index of

n = 1,1642 ± 0,0108. Compared to the theoretical index n = 1,16 one sees that the expected and the

measured values match. Either this speaks for the quality of the Brüggemann equation or the quality

of the method of experiment.

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In case of 40% porosity pSi the index from experiment is n = 2,4146 ± 0,0196. As the expected index

is n = 2,42 one can see again, that theory and measuring match.

The first specimen was SiO2 for which the refractive index is well known: nSiO2 = 1,455 [6]. Looking at

the experimental results and comparing with the measured index at 50° n = 1,4725 ± 0,0196, theory

fits to experiment as well.

4.2.2 Layer thicknesses

As the layer thicknesses are parameters that follow from fabrication process, the values for each

specimen were given by the supervisor.

SiO2 was supposed to have a layer thickness of d ≈ 15 nm. The experiment gives the result of

d = (14,15 ± 0,25) nm at 50° measuring angle. One sees, that the measured results do not match

perfectly the expected thickness, but due to the unknown quality and homogeneity of the specimen

and also due to possible damage and pollution on its surface, one can say the experiment is within a

good range to the plausible values. In order to do more precise statements, more detailedinformation about the specimen is needed.

Both porous silicon specimens should be a 1000 nm in diameter. For 90% porous silicon the results

differ a lot. If the value with the smallest error (d = (843,16 ± 21,59) nm) is compared to the expected

thickness, a deviation of ca. 25% occurs. Here is now again to say, that more detailed information

about the layer and its fabrication method is needed to explain these differences. A possible

explanation would be that the layer is not homogeneously, due to its high porosity. Against that

conclusion speaks that the measuring of the refractive indices was quite precise. At least the value

measured at an angle of 60° fits to the expected 1000 nm: d = (987,18 ± 36,87) nm.

The results for 40% porous silicon don’t spread that much from the expectation, but for the minimal

error value of d = (1028,38 ± 8,25) nm it is still 2%. Maybe the smaller deviation compared to the

previous results, is explained by the smaller degree of porosity.

In general one could say that at least for porous materials a larger number of measuring repetitions

is needed to get precise results.

5 ConclusionsThis experiment showed a way how to measure parameters of thin films by ellipsometry. It made

clear how the usage of polarized light make precise measurements on low length scale works. There

for a basic view into electromagnetic wave theory was given.

6 Sources[1] Script to the lab course B508

[2] http://www.jawoollam.com/tutorial_2.html

[3] Bergmann Schäfer / Lehrbuch der Experimentalphysik Band 6 Festkörper; Page 443; Walter de

Gruyter & Co 1992

[4] Script, page 5, figure 3

[5] Given by supervisor

[6] Script – Appendix A

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