THIN FILM OPTICS EXERCISE

gds · 发表于 2010-4-2 12:53:01

                           Instruction

LABORATORY EXERCISE

THIN FILM OPTICS
Uppsala University COURSE
Optical Materials (Optiska material) COURSE CODE
Solid State Physics ROOM
Ångström 4312
(Solid State Physics’ coffee room)
CONTENTS

Part 1: Preparatory Exercises
Interference effects in thin films on semi-infinite substrates are studied for a number of different cases. Calculations of amplitude reflectance and transmittance at normal incidence are performed. The calculations account for multiple reflections using Fresnel’s formlae, which are implemented in Matlab code.

Part 2: Analysis of a low-emissivity solar control multi-layer
Reflectance and transmittance spectra for a triple layer of an oxide/metal/oxide layer on glass are studied. Using a computer program the layer stack is modelled and reflectance and transmittance spectra of the stack are simulated. The objective is to determine the thicknesses of the different films, given that the optical constants of all layers are known.

Supervisor:
Annica.Nilsson@Angstrom.uu.se, room 4241
Arne.Roos@Angstrom.uu.se, room 4244, phone 3130

The report should be completed, handed in, and (hopefully) approved in connection with the exercise.

This instruction was revised January 2009
NAME

SUPERVISOR’S COMMENTS
YEAR AND PROGRAMME

DATE                                  GROUP

APPROVED (DATE)                         BY

NOTE THAT…

…it is essential that all group members have done some of the preparatory assignments in advance. This makes it easier to do the assigned work. Ask for help if you should get stuck on a problem!

If you are used to Matlab or any other software tool you can easily write a program which can calculate and plot the reflectance and transmittance spectra according to exercises 1-7. You can also use the enclosed Matlab code. To change the input parameter values you have to write them in the code and save. The program is not interactive. If you are not used to Matlab, Annica or Arne will help you to get going. Your key cards should now give you access to the corridor where Annica and Arne have their offices and where you will perform the assignmants.

Arne Roos, Annica Nilsson

This exercise treats interference effects in thin films according to the Fresnel formalism, see chapter 5 in the optics compendium by Ribbing. For a single thin film on a substrate we get the amplitude reflectance, r, and the amplitude transmittance, t, according to equations (58) and (59) in the compendium.

At normal incidence the following applies:

   ;    ,

   ;    ,

were the phase shift, ∂, is given by



and r1 and t1 are the fresnel coefficients for the boundary between air and film and r2 and t2 are the corresponding coefficients for the boundary between film and substrate. These coefficients are given by equations 30–33 in the compendium. (Note that s- and p-polarized light are not defined for normal incidence.) With the equations above we can calculate the intensity reflectance, R, and the intensity transmittance, T, according to

         and

In our case, the medium through which the light is incident is air, i.e. N1=1.0.

Using this method it is quite simple to calculate R and T for a single film on a non-absorbing substrate. But for an absorbing film on an absorbing substrate it gets more complicated, and we would rather let a computer (or a programmable pocket calculator) make the calculations for us. In this exercise we use Matlab to study how variations in the optical constants n and k of thin films and substrates influence R and T spectra. In order to study interference effects only, we look at dispersion free materials for which n and k are not wavelength dependent. This is (approximately) valid for many oxides in the visible wavelength region, but NOT for metals.

In the second part of the exercise we will study a real case: A stack of thin films of on glass. The coating is a so called solar control coating with low emissivity, and includes a thin silver layer embedded between two dielectric layers.

Using a Matlab program for optical multilayer calculations you will try to reproduce the experimental R- and T-spectra for a multi-layer. In this case, with three films on a glass substrate, the simple formulae for a single layer on a substrate are no longer sufficient. Instead, the calculations make use of the matrix formalism, which is briefly described in the compendium.

Part 1: Preparatory exercises

I. Non-absorbing, dielectric films and substrates
Figure 1 shows a single film on a substrate. We regard the substrate as “semi-infinite” and thus disregard transmission through the substrate as well as reflectance from the back surface of the substrate and study the transmission into the substrate and reflection at the boundaries air/film and film/substrate only. Use the Fresnel formulae and Matlab and try to complete assignments 1-7 before the scheduled exercise. If you prefer some other computational tool, such as Excel, you may use that.

Fig. 1 Illustration of multiple reflections in a thin film.

We will start by examining a simple case, namely a single dielectric film on a dielectric substrate. The indices of refraction are real for both film and substrate. Put the film thickness, d, equal to 500 nm in assignments 1–4. Plot the results for the wavelength interval 300–2000 nm.

Exercise 1: Calculate R- and T-spectra for an Al2O3 film (N2=1.77) on a glass substrate with N3=1.5. Repeat the calculations for a MgF2 film (N2=1.38) and a diamond film (N2=2.43) on a glass substrate. Plot all spectra in the same graph.
a) The separation between interference maxima and minima changes with the index of refraction. Show this with an equation that includes the optical path length.
b) Which of the materials mentioned above can be used for antireflection coatings? Why?

Exercise 2: Let N2=1.50 be constant and let N3 vary, being the refractive index of Al2O3, MgF2, and diamond, respectively. This corresponds to using a glass (SiO2) film on different substrates. Use the results to formulate a general rule for the reflectance of non-absorbing films on non-absorbing substrates according to
nfilm > nsub    Rfilm    Rsub
nfilm < nsub    Rfilm    Rsub

II. Weakly absorbing films and substrates
We will now add absorption to the films and the substrates. We start by letting n2=2.0, n3=1.52, and k > 0, but still much smaller than n, which is the case for non-metallic substrates.

Exercise 3: Calculate and plot R- and T-spectra for a film with n2=2.0 on a substrate with n3=1.52. Vary the k value for the film in a few steps between k2=0 and k2=0.2. Also plot the reflectance for the uncoated substrate without any film.
a) How can the stronger reduction in T at shorter wavelengths be explained qualitatively?
b) How does R change with increasing k? Explain!

Exercise 4: Do the same calculations as in exercise 3, but vary the imaginary part of the refractive index for the substrate, i.e. let k3 vary in a couple of steps between k3=0 and k3=0.2. (Put k2=0.) Is it surprising that T does not decrease with an increasing k?

III. Non-absorbing and absorbing, dielectric films onto metallic substrates.
We will now switch to metallic substrates, and look at the reflectance spectra only, since the transmittance (in the visible wavelength region) is zero for metals. We also distinguish between high-reflective metals (e.g. Ag and Al where n < 1 and k >> n), and low-reflective metals (e.g. Fe and Ni where n > 1 and k > n). We will study the effects of coating these metals with an interference layer. The film thickness, d, will be 70 or 110 nm.

Exercise 5: For both film thicknesses, calculate and plot R-spectra for a film with n2=2.0 and k2=0 on a high-reflective metal substrate with n3=0.15 and k3=3.5. In addition, you should plot the reflectance for the uncoated substrate.

a) What is the largest change in R obtained in the visible wavelength range? Will this be enough to give an appearance of a specific colour? In that case, which colour?
b) Will we obtain an efficient AR-(AntiReflecitve) treatment of a highly reflective metal by coating it with a non-absorbing film?

Exercise 6: Similar to assignment 5, but use a low-reflective metal with n3=1.8 and k3=3.5 as substrate. Plot the reflectance for the uncoated substrate too.

a) What is the largest change in R in the visible wavelength range? Could this change give a colour impression? If so, which colour?
b) Do we obtain an efficient AR-treatment by putting a non-absorbing film on a low-reflective metal?

Exercise 7: Now let the interference layer be somewhat absorbing. Repeat assignment 6 and 7 with a film thickness of 110 nm only, and vary k for the film in a couple of steps between k2=0 and k2=0.2. n2 should still be equal to 2.0.

a) What is the largest change in R in the visible wavelength range?
b) Do we get an efficient AR-treatment by putting an absorbing film on a low- or high-reflective metal, respectively?
c) How does k influence the colour of the deposited film?
d) By examining the results from assignments 5, 6, and 7, can you tell if it is, to any significant extent, possible to increase the reflectance of a metal with a non-metallic coating?

Part 2: Analysis of a multilayer stack

IV. Dispersion in non-absorbing, dielectric films and substrates
If the optical constants experience dispersion, which almost always is the case in reality, this affects the R- and T-spectra.

Exercise 8: Remove absorption from the film and the substrate, but add dispersion in the refractive index of the film. Let n decrease linearly from 2.4 at 300 nm to 1.4 at 800 nm. Use a constant, real, refractive index for the substrate, N3=1.50. Plot the result for a couple of film thicknesses in the interval 300–1000 nm.

a) Looking at these results, suggest a qualitative method to obtain the dispersion for a film, using a reflectance spectrum containing interference effects.
b) What do you think would be the effect of dispersion in the refractive index of the substrate? Try your theory by letting the refractive index of the substrate vary from 1.4 at 800 nm to 1.8 at 300 nm. The dispersion of the film should be the same as in 8 a).

This part of the exercise treats low-emitting (low-e) window coatings. These are transparent for solar radiation and are used to reduce the energy use in buildings. This type of coating has gained an increasing interest lately due to the increasing awareness of their potential for energy (and cost) savings. An ordinary double glazed window has a U-value of approximately 3.0 W/m2K and a well insulated wall has a U-value of approximately 0.2 W/m2K. With low emitting coatings, U-values below 1.0 can be achieved for triple glazed windows. This is a considerable improvement, which leads not only to a decrease in energy use, but also to increased comfort since the cooling effect from the window surface decreases. In addition, the heating system of a building can be simplified as radiators under the windows (to compensate for the cooled convective air flow caused by the cold glass surface) are no longer necessary. In Sweden, and other countries with cold winters, there is a great potential for energy savings by replacing the existing double glazed standard windows by energy-efficient windows with low-e coatings.

A variation of the low-e coating is a so called solar control coating. This type of coating should be transparent for visible radiation, but reflect as much as possible of the invisible infrared part of the solar spectrum. The solar control coating reduces the incoming solar heat gain and thus reduces the cooling need. As a result it can reduce the cost of purchased electrical energy for air conditioning systems. For this kind of windows, a low U-value is also beneficial, as the outdoor temperature in hot climates is often 10–20 degrees Celsius above the indoor temperature. Fig. 2 shows the solar spectrum, the sensitivity curve for a human eye, and the black body spectrum at three different temperatures. These spectra govern the design of the low emitting coatings.

Fig. 2 The solar spectrum (ISO AM 1.5), the sensitivity curve for a human eye,                            and black body spectra for three different temperatures.

Many functional coatings on the market today are based on some of the noble metals copper, silver or gold. Thin films of these metals have optical properties that make them well suited for the purpose. A drawback of these films, however, is the poor long-term outdoor stability, which in practice constrain the use of them to permanently sealed insulated glass units.

Some interesting alternatives to the noble metals, that have been studied by the Solid State Physics group, are TiN, ZrN, and HfN. Thin films of ZrN are manufactured in a PVD (Physical Vapour Deposition) process, where metallic zirconium is sputtered in a nitrogen atmosphere. The process parameters must be carefully controlled in order to get a stoichiometric ZrN of good quality. It has been shown that a moderate heating of the substrate increases the quality of the film from an optical point of view. An advantage with ZrN, compared to the noble metals, is its chemical and mechanical stability. By performing accelerated aging tests, we have shown that triple layers of ZrO2/ZrN/ZrO2 are considerably more stable than noble metal based layers.

In this case the studied coating is a commercial solar control coating from one of the major European glass manufacturers.

Exercise 9: Measure the R and T spectra for the provided triple layer. How do the R and T spectra differ between different wavelength ranges, and how can this be used for functional coatings, considering the shape of the solar spectrum and the heat radiation curve at room temperature?

R and T can be calculated if the optical constants (n and k) of the constituent films are known. The calculations can be performed using the matrix formalism described in the Ribbing compendium. The Matlab program on the computer in the optics laboratory uses existing data files with the optical constants for silver and some dielectric materials. The thicknesses of the three films and the incident angle of the light can be given as input parameters.

Exercise 10: Vary the thicknesses of the three layers (or maybe four?)in the thin film program, and model the R and T spectra so that these coincide with the experimental spectra.
a) What properties of the different layers and knowledge from the preparatory assignments can be used to make the search more systematic?
b) Is it possible to get a good agreement with experimental data?
c) How thick are the different layers?
d) What can cause deviations between experiments and modelling?

****************MATLAB CODE****************

%Template for Matlab program for thin film calculations using Fresnel's formulae
%Updated February 2007 by Arne och Andreas
% "%" means "comments"
clear;
%clf                         %Removes old figure

%******************Input your data here*****************'
d = 250;                         %Give film thickness!
lambda = (300:10:2000);          %Wavelength interval (from:step:to)
N1 = 1;                         %Give index of refraction for ambient
N2 = 2.0+0.1*i;                %Give index of refraction for film
                                 %if N is complex just write it as a complex number
                                 %e.g. N2 = 2.0 + 0.02*i
N3 = 1.50;                      %Give index of refraction for substrate
%********************end input******************************
%Fresnel equations
delta = -2*pi./lambda*N2*d;       %NOTE that "." in front of "* / ^" is needed for matrices!
r1 = (N2-N1)/(N2+N1);
r2 = (N3-N2)/(N3+N2);
r =  (r1+r2.*exp(-2*i.*delta))./(1+r1*r2.*exp(-2*i.*delta));
t1 = 2/(N1+N2);
t2 = 2*N2/(N2+N3);
t = t1*t2.*exp(-i.*delta)./(1+r1*r2.*exp(-2*i.*delta));
%Calculate R and T
R = r.*conj(r);
T = t.*conj(t)*real(N3/N1);
%Plot figure
figure(1);
hold on;                      %new spectra will be plotted in samne graph as previous ones
                                 %remove this commande by typing % in the first position

plot(lambda,R,lambda,T) ;       %Plot R and T
xlabel('Lambda (nm)');
title(['d=', num2str(d),', N1=',num2str(N1)',', N2=', num2str(N2),' och N3=', num2str(N3)]);
%title('d=500 N1=1, N2=1.77 och N3=1.50');
legend('R','T');
ylabel('R och T');

grid;

% Your graph can easily be transferred to a Word-document:
%Open "Edit menu" => "Copy Figure" and then just paste into the Word
%document where you can also write some comments.

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