DVCED UDERGRDUTE LORTORY EXPERIMET 3, FILM Thi Film Iterferece Refereces updated by arbara Chu, ugust 6 Revisio: March 6 by Yi Chai Origial y: Jaso Harlow, 6
1. Itroductio The iterferece of reflected waves of light from trasparet layers of material is resposible for may beautiful pheomea i ature, such as butterfly wigs, peacock feathers ad soap bubbles. Multiple layers of thi trasparet films with various idices of refractio ca be deposited o glass or metal substrates i a variety of ways to cotrol light. This has may applicatios i sciece ad idustry, icludig ati-reflectio coatigs, mirrors ad optical filters. Sice the discovery of the pheomeo of iterferece colors associated with thi solid films, immese studies of the sciece ad techology of thi film have bee coducted for early two ceturies. Majority iterest i this field has bee domiated by the uforesee behaviors of solid films ad the usefuless of cosequetial optical properties with potetial applicatios i mirrors ad iterferometers. I particular, exploitatio of the optical iterferece pheomeo has led to developmet of istrumets with tuable reflectace ad trasmittace. Whe thi film based mirrors are used for the purposes of reflectio ad trasmissio, the most ideal system bears a miimized absorptio of icidet light. Such systems are made possible by formatio of o-metallic, or dielectric, coated thi films, sometimes referred to as dielectric mirrors. The process ivolves depositio of multilayer dielectric material oto glass substrate. The choices of the type ad thickess of the dielectric layers allow for adjustable reflectace targetig at specific rage of wavelegths. This experimet carries out the fabricatio of multilayer high reflectace arrowbad thi films by the photometric method.. Theory To ivestigate the optics of thi film iterferece, we will follow the derivatio of Fowles Chapter, ad Hecht Chapter 9. The geeral solutio ecompassig oblique icidet light ca be deduced followig the derivatio of Chopra [] page 7. Sigle Layer Dielectric Thi Film First cosider the case of a sigle layer of dielectric material, with thickess d ad idex of refractio, deposited oto a substrate with idex of refractio S. This sample is exposed to a medium with idex of refractio, typically air. s show i Figure 1, whe light of vacuum wavelegth λ is ormally icidet o the sample, trasmissio ad reflectio from both iterfaces occur.
E k k 1 E 1 k E k 1 E 1 d T E T S k T Figure 1. Electric ad Magetic fields across a sigle dielectric layer The boudary coditios require that the electric ad magetic fields be cotiuous at both iterfaces. They yield the followig equatios: First iterface E + E E + (1) 1 E1 E E E1 E1 () Secod iterface ikd ikd E 1 e + E1e ET (3) ikd ikd E 1 e E1e S ET () To get equatios () ad () the relatio c E was used. The phase factors e ikd ad e -ikd i equatios (3) ad () result from the fact that the wave has traveled a distace of d iside the dielectric layer; thus it is advaced or delayed by a phase of kd, where k is the wave umber. y elimiatig the amplitudes withi the layer, E 1 ad E 1, equatios (1) through () ca be combied to yield: E is ET 1 + cos kd si kd (5) E E E E T i si kd + S cos kd ) (6) E E Equatios (5) ad (6) ca be represeted by a matrix equatio of the form: 1 1 1 r M t + (7) S I equatios (7), r is called the reflectio coefficiet with 3
ad t is called the trasmissio coefficiet with fially, M is the trasfer matrix ad Solvig for r ad t gives m M m 11 1 m m E r E t 1 E T E cos kd i si kd i si kd cos kd m + m m m r m11 + m1s + m1 + ms t m + m + m + m (1) 11 11 1 S 1 S (9) 1 S 1 S s the result, the measuremet of the reflectace R ad the trasmittace T are give by R r ad T t, respectively. Physically, R ad T idicate the proportio of light itesity reflected by ad trasmitted through the dielectric system. Questio.1. With kd, evaluate R ad T for sigle layer dielectric films of ZS (.3) ad MgF ( 1.35). How do these values compare with those of a bare glass substrate (for glass, 1.5)? Questio.. I geeral, for kd, what happes to R ad T if a sigle layer of thi film o glass substrate exposed to air for: i) of dielectric greater tha S? ii) of dielectric larger tha S? Substitute some values of differet dielectric materials ad verify. Cosult Chopra page 75 Table III for refractive idices of some commo materials used i thi film. 3 Questio.3. Repeat questio. for kd ad kd Multilayer ll-dielectric Thi Film ow cosider the situatio where there are dielectric layers coated above the substrate. The layers are labeled {1,, 3 }. They have idices of refractio { 1,, 3 } ad thickesses {d 1, d, d 3 d }, respectively. Similarly, the reflectio ad trasmissio coefficiets of this system are related by a matrix equatio: 1 1 1 1 r M effective t M M M M t + 1 3 K S (11) S where M i deotes the trasfer matrix of the i th layer ad the trasfer matrix M effective is the product of the trasfer matrix of the various layers. ll other properties remai idetical to the case of a sigle dielectric layer but makig use of M effective. High-Reflectace Films First cosider a double layer thi film composed of two dielectric materials, ad. These two adjacet layers have idex of refractio ad. Furthermore, both layers are cotrolled such that their thickess, d ad d, equals a quarter-wavelegth of correspodig light withi the layers. The (8)
5 wavelegth of propagatig light i dielectric layer, λ, is related to the vacuum wavelegth by the followig [3]: λ λ So the thickess of each layer ca be calculated to be: d ad d λ λ λ λ (1) I this case, usig equatio (8) ad (11), the trasfer matrix is foud to be: effective i i i i M cos si si cos cos si si cos ow cosider a stack of alteratig layers of dielectric ad dielectric. If there are pairs of such double layer dielectrics, the trasfer matrix becomes: pairs for effective M Substitutig this result ito equatio (9) oe ca fid the reflectio coefficiet to be: 1 1 + S S r It is easy to verify that, with the icrease of, R approaches uity if ad are differet. Cosequetially, a stack of quarter-wavelegth alteratig dielectric layers forms a high-reflectace thi film at a particular wavelegth, λ. Questio.. How is the wave umber k related to λ? Questio.5. Verify that kd for quarter wavelegth thickess. Questio.6. For a 8-layer high reflectace thi film composed of alteratig ZS ad MgF o glass substrate, sketch a plot of the reflectace versus umber of depositio layers, quatitatively idicatig the local miimums ad maximums. How would the plot chage if MgF is deposited first rather tha ZS? I either case, what is the et chage of reflectace? s you ca see, eve for small value of, theory predicts a reflectace close to uity. Questio.7. beam of white light falls at ormal icidece o a plate of glass of idex ad thickess d. Show that miimum reflectace occur at those wavelegths such that d λ, where λ is the vacuum wavelegth ad is a iteger. This meas that reflectio ad trasmissio fuctios are periodic with respect to wavelegth ad this is called a chaeled spectrum.
Fabry-Perot Filter? Descriptio eeded. 3. Depositio Techique Operatio uder Vacuum The multilayer thi film is to be fabricated uder vacuum i this experimet. efore begiig, read the write-up for the secod-year laboratory Evaporatio of Silver Films for a thorough uderstadig of the compoets of a vacuum system ad the evaporatio process. Do ot worry about the thickess estimatio methods sice a differet oe will be used. ecome familiar with the operatio of the Edwards High Vacuum System used i this experimet. The Photometric Method For dielectric films deposited o a trasparet substrate of a differet refractive idex (glass is used i this experimet), the optical reflectace ad trasmittace behavior of the film-substrate combiatio, at fixed wavelegth of icidet light, shows a oscillatory behavior as a fuctio of film thickess because of iterferece effects. Recall from questio., reflectace is reduced or ehaced depedig o the relative values of refractive idices of the film ad the glass substrate. The setup of photometric moitorig is summarized i the diagram below, cosult Chopra page 99 ad explai the fuctioality of the method. Thi Mirror Detecto Filte Mirror eam Light Figure. The photometric moitorig setup. 6
I this setup, the reflected light passes by a badpass filter so that a short rage of wavelegth is moitored by the detector. Questio 3.1. How ca oe achieve the same fuctioality without usig a badpass filter? Questio 3.. Use the spectroscopy described i sectio, measure the visible wavelegth rage trasmissio spectrum of the filter used i the above setup. How good is this filter? Questio 3.3. What are some limitatios to the photometric method? What happes with icreasig umber of layers deposited? Determiig the film thickess Film thickess is related to ad ca be determied from the maxima ad miima of the reflectace which occur at itervals give by (Chopra, page 99) λ m d [13] where m is the order of the maximum or miimum ad all other variables as previously defied. The illustratio below shows the observed variatio of the reflectace ad trasmittace of alteratig ZS ad MgF quarter wavelegth films. Figure 3. Reflectace ad Trasmittace of icreasig umber of multilayers Steckelmacher et al., Vacuum, 9:171 (1959) Questio 3.. Show that, after two maxima or miima are traversed (first beig the value at zero depositio), thickess for a sigle layer film is quarter wavelegth. (Hit: cosider 7
equatio (1)). Therefore by moitorig maxima ad miima while depositig, the thickess of each film is cotrolled to be quarter wavelegth. Questio 3.5. Calculate the actual thickess of quarter wavelegth layers of ZS, MgF, ad cryolite (a 3 lf 6 ) if blue light is moitored. Questio 3.6. Make predictios to the shape of the chael spectrum with respect to the filter used, idicatig quatitatively the critical poits. 3. Evaluatig Optical Properties of Your Film The spectrometer cosists of a wavelegth dispersive device ad a photomultiplier. prism is used to pick out photos of specified wavelegth ad trasmit them to the photomultiplier. mechaical system of gears ad sprigs attached to the prism is adjusted to vary the specified wavelegth. With your multilayer thi film at the slit opeig, obtai trasmissio spectra by scaig through the visible wavelegths of light. (Hit: overlay the spectra o top of a white light source spectrum for ease of compariso.) The Photomultiplier Photomultipliers are extremely sesitive detectors of light, or photos. Icidet photos strike the cathode material, ad produce electros as the result of photoelectric effect. These electros are accelerated towards the electrode, while udergoig the process of secodary emissio. Secodary emissio effectively multiplies the electro sigal. The electro multiplier cosists of umerous small electrodes called dyodes. Each dyode is held at a positive voltage with respect to the previous oe. Whe electros leave the photocathode, they have the eergy of the icomig photo. While travelig towards the first dyode, the electros gai eergy from the electric field. O arrivig at the dyode with much greater eergy, the electros ca cause emissio of low eergy electros. The origial electros from the cathode, together with the ewly geerated low eergy electros, the are accelerated toward the secod dyode. This process repeats ad a cascadig effect occurs, which result i a high accumulatio of charge arrivig at the aode. This effect iduces a sharp oticeable curret pulse i the device eve if oly a sigle photo eters the cathode. Measure the chael spectrum of your multilayer thi film i the visible wavelegth. Questio.1. Compare ad cotrast the measured chael spectrum with respect to theoretical predictios. Questio.. How does the slit width of the spectrometer affect the shape of your spectra? What is a suitable slit width to yield a represetative spectrum? Questio.3. With a arrow slit width (approximately 1 µm), take spectra of your thi film at differet positios o the thi film. Does this have a effect o the shape o the chael spectrum? If so, is it uderstadable? What part of the experimet most likely resulted i such chages i the chael spectrum? Questio.. How would icidet light at differet agles affect the chael spectrum? Some Discussio Questios 8
1. What is a Fabry-Perot Filter? Describe its fuctioality ad compositio. Why might oe wish to use MgF istead of cryolite i makig thi films with ZS? 3. How does the additio of a silver depositio layer o top of the multilayer high reflectace thi film affect its performace? You may wish to add a silver depositio layer ad cotrast the chael spectrum from before ad after.. I a oe-way mirror, the metallic/dielectric coatigs o the surface of glass substrate actually result i a so called half-layer thi film. This just meas that either of trasmittace or reflectace is very high or very low. The how does a oe-way mirror work? (Hit: thik about the slit width ad the white light source i the spectroscopy sectio) Refereces 1) Chopra, K.L. (1969). Thi film pheomea. ew York: McGraw-Hill. ) Fowles, G.R. (1975). Itroductio to moder optics. d ed. ew York: Holt, Riehart ad Wisto. 3) Hecht, E. (). Optics. th ed. Readig, Mass.: ddiso-wesley. 9