Das, N B

Hassan, Aseel K

Panigrahi, S

IACS Institutional Repository

idian J. Phys. 76A ( I). 19-21 (2002)U P  A— an international journalDielectric constants and thickness of metallic film using attenuatedtotal reflection techniqueS Panigrahi'*, N B Das', Ascel K Hassan- and Asim K Ray^Department of Physics, R, E College. Rourkela, Onssa“76y 008, India - School of Engineering, Sheffield Hallnin University, England, UKE-mail . simanchul._rkl(^hotmail.comAbstract Gold films of thickness 40 nm to 50 nin arc deposited on ultrasonically cleaned glass slides by thcmial evaporation under vacuum of 10'' Torr and at the evaporation rule I nm/sec The gold-coated slides are brought into optical contact with the prism using an index matching fluid. T or excitation of surface plasmons a He-Ne laser source of P polarized mono-chromatic beam ( A = 633 nm) is employed The prism and the sample are placed on a 9 -2 9  rotation stage The retketanee minima in gold as a lunction of the thickness is plotted. It shows that R  ^ becomes nearly equal Id zero at d -  45 75 nm The gold film of approximately 45 nm thick is taken and subjected to further surface plasmon resonance (SPR) study The resulting SPR curve was well fitted by Fresnels theory and the value of refraclivc index (it), extinction co-efficient {k) and thickness id) are found to be 0 2 ± 0 03, 3.2 ± 0.05 and 45 ± 2 nm respectively The other observations from this experiment includes : the variations of real and imaginary parts nl metal dielectric constants with film thickness and SPR curve at different thickness eic Our results show good agreements with similar results of silver lilms and agree with the data obtained by cllipsometric measurementskeyw ords Dielectiic constants and thickness, metallic film, attenuated total refleclion PACS Nos, . 7H.20.-C, 77 55 +f1. IntroductioiiOptical dielectric constants and thickness of thin films arc two irnportunt physical parameters for optical uses of metallic films, fhese two parameters depend on both the chemistry and the structure of the film, Ellipsometry is a well-established method lor ihe characterization of both nonabsorbing and moderately absorbing dielectric films [IJ. However, for highly absorbing lilms, such as metal films, simple ellipsometry is not normally the appropriate method for a complete film characterization (w, k, r/), because the light reflected at the back surface of the metal ifim and returning to the front surface is very weak compared wiih the light reflected directly at the metal surface. Surface plasmon Resonance (SPR) with attenuated total reflection (ATR) is a well known technique for optical characterisation of metallic as well as organic overlayers. Their determination involves optical excitations of surface plasmons followed by appropriate curve fitting procedure with the Fresnel's reflection theory. Surface Plasmons (SP) arc very elementary excitations of metal- diclectric interfaces. The dispersion relation of the SP is obtained by solving Maxwell's equations with special boundary conditions, such as the finite thickness of the metal and theCorresponding Authordielectric constant. To allow the excitation of the surface plasmon oscillations the real part £, {(o) of the dielectric function e(co) has to be negative i.e. (co) < -  I and the imaginary psirt e, (co) should be very small i.e. €, (co) < | (co) | , a condition which is fulfilled in metal. Gold, silver, copper, and aluminum are some of the metals which meet these conditions for visible light at least for larger wavelengths. In the neighborhood of so called 'plasma angle' the conditions can be matched and thus the SP can be excited. Surface excitations (surface plasmons) do not couple directly to the external photons because energy and momentum can not be conserved in this transition. SPR technique with attenuated total reflection (ATR) has been widely used to excite the surface plasmons ever since it was introduced in 1968 by Otto [2] and later developed by Krctschmann f3|. The dielectric prism with refractive index n, lowers the photon dispersion curve io co= K d  n , but does not effect appreciably the surface mode. At total reflection angle 6 , l//i< sin 0 <  I , the evanescent photon waves from the prism, with parallel momenta =n ((Of c) sin0, couples to the surface plasmons in the region of  K \ o) /c< K <(o) fc)n.  Under the optimum coupling, the total incident energy is dissipated through©20021ACS2 0 S Panigrahi, N B Das. Aseel K Hassan andAsim K Raydiffusion of plasmon wave in mctah the reflection coefficient falls to zero, and the surface plasmon resonance (SPR) appears as a dip in the reflected intensity as a function of the angle of incidence. Rellcctiviiy of glass- metal- air system can display a sharp minimum owing to strong absorption. The reflectivity can even vanish at the plasmon angle for optimum thickness of the film. This decrease in reflectivity is called ATR. The resulting SPR curve of three layered system (prism-melal-air) may be well fitted by Fresnel's theory so as to determine the metal layer parameters -thickness and dielectric constants. In addition to this, SPR effect is often used to construct highly sensitive optical sensors-chemical |4,5] gas |61, bio and temperature [7] sensors. Examples are the monitoring of protein adsorption and immune reactions at a silver surface. Optical methods offer the advantage of being noncontact, nondestructive, fast, precise, .sensitive and reproducible2. Optical constants of metal Him (three layered system)Let us consider an incident TM light of frequency lo in a prism- metal -vacuum (an) configuration as shown m Figure I.1 Prism k,2 Metalv3 Air i ,,(--------------/i  •)'2iCxp(i2/fo^/) (2)ff(e ) = i -[Af, -Rc(A')]" +lm(Af)’with K = + K'^ . The value of K° and K'^  are defined in theRef. [8] Here, K is the complex wave vector of the surface plasmor wave (SPW) in the Kretschmann configuration, and K9 is the complex wave vector of the SPW and is the perturbation u in the presence of the prism.The reflectance has a Lorentz dip at 6 with a half widtfWjj and minimum reflectance given byWg =  2 Im ( / r )  cos(O^j^ff )  c l  n o ) .^m,n = l - 4 r ) / ( l + 7 ] ) ^(4;(5;whereFigure 1. A Schcinalic dia^iam sliowing tiu- Kiclchiiiann conrigurahon of pnsiii-goid HIT .systemWhen the light is incident al an angle 6^  , it can couple directly with the surface plasmon wave (SPW) of the metal- vacuum interface, here 0^  = sm '(1 / /;), and n is the index of refraction of the prism. The coupling takes place when (o and K^(0) of the incident light match with the Ircqucncy co and the complex wave vector K of the SPW. Here K^(0) is the component of the incident wave vector parallel to the interface. Since is real and K is complex, only an approximate match can be reached foi (0) = Rc (AT) al6 = = sin“‘ \Rc(K)cln) = sin”' [Kxclno) \ . (1)At , the total rellection of the incident light is attenuated. The coupling can be analyzed by calculating the rcncelance R of the light given hyT7 = Im(K’‘’)/Im(Ar"). (6;With above equations, one can proceed to determine thi dielectric constant £ 2  and thickness J^of a metal film from thi measured R versus 0 curve.3. Experiment (deposition technique and characterisation)Gold films of thickness 40 nm lo 50 nm are deposited 01 ullrasonically cleaned glass slides by thermal evapcWaiion unde vacuum of 10~^  Torr and al the evaporation rale 1 nm/scc. Thi vacuum system used is a standard combination of a rotar mechanical pump and an oil diffusion pump. A crystal filii thickness monitor is used lo ensure the controlled rate 0 evaporation. This instrument measures the change in oscillato Ireqiicncy of a crystal (due lo the change in mass) placed nex lo the sample. The amount of metal deposited on the crystal i proportional lo the change in oscillating frequency. Thi instrument can be calibrated to read accurate values for the rat of deposition and the thickness.The gold coaled slides are brought into optical contact will the prism using an index matching fluid. For excitation ofsiiifac plasmons, a He-Nc laser source of P polarised mono-chromati beam ( A = 633 nm) is employed. The prism and the sample ar placed on a 0 - 2 0  rotation stage which is driven by microprocessor controlled stepping motor. The details of th experimental set up is given in Figure 2.The parameters are wcll-dclincd in Rcl. [3|. With 0 close to ^MR ’ leneclanec R can be approximately expressed as a function of 0 as(3)Figure  2. Opticul scl-up for SPR measureinent [I-H e-N c Lase 2-Aperiure, 3-Ncutral density filler. 4-Polariscr, 5-Beani choppe 6-Apcraturc, 7-Beain Spinier. 8-(<?-26^) prism table, 9-photo dctecto l()-Lock-in-aniplificr, 11-microprocessor, 1 2 (0 -2 0  drive)].When optical coupling is optimum, the total incident energ is dissipated through diffusion of the plasmon wave in gold TilrDielectric constants and thickness of metallic fdm etc 21I and the reflection intensity falls to zero. The reflectance minima I K in gold as a function of the angle of incidence for different thicknesses are plotted in Figure-3. It shows that becomes nearly equal to zero a id -  45.75 nm.Figure 3. Measured reflectivity of gold films of different thickness as the iiintiion of angle of incidenceThe gold films of approximately 45 nm thick is taken and subjected to further SPR study. Tlie resulting SPR curve was well ruled by Fresnel's theory and the values of n, k and d  for i!old arc found to be 0.2 ± 0.03, 3.2 ± 0.05 and 45 ± 2 nm rcspccUvcIy. The thickness dependence resonance position of the surface plasmons at the melal/air interface is shown in Figure4. A kind of inverse relation exist between them.Figure 4. Variation of SPR angle with An film thicknessMonitored thickness (nm)t*iKure 5. Variation of monitored thickness with calculated thickness.Thinner films are known to result in more radiation losses and hence shallower and broader resonance curves, where as thicker films result in increased intrinsic losses. The monitored film thickness of the gold films are plotted against the calculated film thickness in Figure 5. The relation is linear with slope approximately unity.4. ConclusionIn the work, an attempt is made to characterize the optical properties (dielectric constant and thickness) of vacuum deposited thin films of gold. Basically, it is understood that the dielctric constant of metal films is a function of the incident light frequency [9] and that film geometry can be a factor only when the film thickness is below a certain value [ 10]. It is important to note that the value of gold dielectric constant for example is at variance for the same film thickness among different reports in the literature. This is not unusual since solids exhibit different structural and morphological properties when prepared as thin films. Such variations can be a.scribed to several reasons which include the purity of the starting material, the background pressure of the vacuum chamber, the rale of evaporation. All these parameters may lead to variation in the smoothness of the layer, the size of the crystallized particles and the adhesion of the layer to the substrate. Consequently, such variations may result in differing properties of the material when its thickness or preparation conditions arc varied.The fitting method is suitable for determining optical parameters of metal films (Au) for a thickness range 100 to I (XX)A^  ^where the leakage loss and the joule loss of SPW are comparable. If the film is thinner, coupling is increased and the rellection minimum becomes broader and shallower; if the film is thicker the coupling becomes weaker and the retlcclion minimum decreases. As a consequence, there is an upper and lower thickness limit for the application. However for thickness greater than 1000 A^ the dielectric constants of metallic thin films can be derived using the expressions given under the Section 2.R eferences[1] R M A A/zam and N M Ra.shara Ellipsomeirx oml Polunsed Li^ht (New York Nonh-Holland) (1987)[2] A Otro Z Phys, 216 398 (1968)[3] E Krctschmann Z Phys 241 313 (1971)[4] B Licdbcrg. C Nylander and I Lund.strom Seti,s and An, 4 299 (1983)f.S] M T Flanagan and R H Fanlell Electron Lett 20 968 (1984)[6J P S Vukusic and J R Sainhie.s Thin Solid Films 221 311 (1992)[7] B Chadwick and M Gal Jpn J. Appi Phyx. 32 2716 (1993)'8J >V P Chen and J M Chen J Opt Soi. Am. 11 189 (1981)[91 R A Innes and J R Samblc.s J Phys. ¥11 277 (1987)[10] P B Johnson and R W Christy Phys. Rev. B6 4370 (1972)

Dielectric Constants and Thickness of Metallic Film using Attenuated Total Reflection Technique

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Dielectric Constants and Thickness of Metallic Film using Attenuated Total Reflection Technique

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