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Measurement of local parameters in polymer films
Polymer Science U.S.S.R. Vol. 30, No. 7, pp. 1645-1647, 1988 Printed in Poland
0032-3950/88 $10.00+ .00 "~ 1989 Pergamon Press plc
METHODS OF INVESTIGATION MEASUREMENT OF LOCAL PARAMETERS IN POLYMER FILMS* S. SH. GEVORKYAN, A . S. PETROSYAN a n d M . A . ZABUNYAN K. Marx Erevan Polytechnical Institute
(Received 12 March 1987) The prism-coupler used in integral optics to measure parameters of optical waveguides can be employed for an accurate determination of parameters of polymeric films. The procedure developed in this paper ensures a high accuracy of measured values of the refractive index along directions lying either in parallel with, or perpendicularly to, the film surface.
OWING tO the technology used in their preparation, thin polymeric films often contain local inhomogeneities. These defects are decisive for the quality and practical applicability of the film, in particular when it is used as a n electrically insulating layer. Several methods including capacitance measurements can be employed to determine the parameters of polymeric films along the direction perpendicular to the film surface, but not do ensure the required accuracy n o r do they operate o n a sufficiently small scale. Information on the measurement of local characteristics in parallel with the film surface is very scare. One method measures parameters of an ellipse formed when a small area of the film covered by thermally sensitive layer is heated by means of a needle [2]. The method is simple enough but not very accurate and the involved area is still quite large.
",l/J
_--3
,7
,
7
:J FIG. 1. The experimental setup for prismqoading a film (a) and two methods for measuring the optical characteristics (b, c); 1 - t h e measured film (planar waveguide), 2 - p r i s m , 3 - s u b s t r a t e , 4 - polarizer, 5 - objective, 6 - immersion Iiquid. The method of prism-loading is widely used [3] in integral optics to measure parameters of thin-layer waveguides in intimate contact with a n inelastic substrate. Light enters the prism and undergoes total reflection at its base (Fig. la). An evanescent field is formed below the prism base where the intensity falls exponentially with the distance, similarly as in an optical waveguide. Pro* Vysokomol. soyed. A30: No. 7, 1556-1558, 1988. 1645
S. SH. GI~VORKYANet al.
1646
pagation modes can be thus excited in a thin polymeric film pressed firmly onto the prism base, provided the refractive index of the film is smaller than that of the prism. Propagation modes are excited only for some discrete values of the angle of incidence of light on the face of the prism; these so-called synchronization angles 9= depend on both the film thickness and the refractive index, and satisfy the condition that the phase velocities along the Y-axis are identical in the film and in the prism, n2 sin 0= n, sin 0, where 0 is the angle of total reflection at the prism base, 0t is the angle of internal reflection at the boundary wavegulde-substrate, nl and n2 are the respective refractive indices of the waveguide and the prism. Both the thickness and refractive index of the film can be calculated from the measured angles 9m, provided the parameters of the prism and the refractive index of the substrate are known. The method is very simple both experimentally and from the viewpoint of data evaluation. In this paper we demonstrate that this approach can be used to measure accurately and on a local scale parameters of polymeric films. One problem consists in that polymeric films are usually not rigid enough and special measures are therefore necessary: optical contact between the prism and the polymer can be achieved by introducing an immersion liquid (Fig. lb), or by using a supporting plate to press the film firmly to the prism base (Fig. lc). The first method is deficient in that the quality of contact cannot be controlled and the processing of data becomes quite complex. In the second case one cannot avoid the formation of clearances between the film and the prism and, on the other hand, between the film and the substrate; their thickness depends on the applied force which must be selected experimentally. At a high compression the clearance between the film and the substrate practically disappears; if the refractive indices satisfy the inequality n2 > nt > n3 and light enters the prism at the synchronous angle, propagation modes are excited in the polymer and light propagates owing to multiple reflections on the boundary iilm-substrate, similarly as in an integral optical waveguide [3]. From the measured values of ~0,n (Fig. 10 one can then calculate the refractive index of the film by means of the method described in [3]. To improve the accuracy and simplify the calculations it is advisable to employ the weakest possible compressive force F, selected on the basis of preliminary experiments. In this instance, if the size of the substrate 3 exceeds the dimensions of the prism base, the clearance between the substrate and the film is the larger of the two and modes in the film do not leak into the substrate even if n2 > nl. Under these conditions the film can be treated as a planar dielectric waveguide. When the electric vector E of the incident polarized wave lies in parallel with the film surface (TE polarization mode), the relationship between the refractive index n ~ and the propagation constant Bin, derived from the condition of multiple total internal reflection at the film face [3], reads 2 2 ~ 2 (N2=-l)=(n~-N~,)tan (tk 4n,-N~,),
(l)
where the quantity N~=pm/k is the effective refractive index, k=2ttl2 is the wave number, ). is the light wavelength, and t is the film thickness. When the vector E is oriented perpendicularly to the film surface (TM polarization mode), nt is related to N= through 2 1) tan2 ( t k 4 ~ ) n,(Nm-
(2)
For prism-loaded films the effective refractive indices can be determined experimentally. For those discrete values of the incidence angle 9= which excite propagation modes in the film, the value of N= can be calculated from the formula •
.
-
.
where A is the prism angle.
°(
Nm= kn2 si
A + arcsinSin---~'~ , n2 /
(3)
Measurement of local parameters in polymer films
1647
The experimental determination of the refractive index of a polymer film then involves the following steps. The required mode of polarization is set by means of the polarizer 4 (Fig. lc); for the TE mode the electric vector E must lie in the plane XOY(Fig. Ic). The angle of incidence ¢ is varied until a mode is excited in the film. Nm is calculated from the corresponding value of tpr, according to formula (3) and the refractive index nl~ (for a diree'ion parallel to the plane XO Y) is calculated from equation (1); the quantity n l , refers to the orientation of vector E. In the TE mode the vector E is perpendicular to the direction of wave propagation in the film. It is obvious that for the given mode of polarization (for the given orientation of the polarizer 4) one can determine the refractive index along all directions in parallel with the film surface by rotating the holder with the specimen by an angle ~ (Fig. 2). The values of nx, determined in this manner fall on an ellipse in the plane XOY
//'t FIG. 2. Refractive index ellipsoid of polypropylenc. (Fig. 2). When the polarizer is turned by 90 °, the light waves excited in the film have the electric vector oriented perpendicularly to the film surface (TM mode). F r o m the angles q,,~ determined experimentally for this case one again calculates Nm from equation (3); the refractive index n~: for the direction perpendicular to the film surface is then found from formula (2). Industrial films of thickness 5 to 50 f~m (polypropylene and other polymers) were studied experimentally. The prism was made of the glass TF-2 (n2= 1.6725) and the prism angle was A = 61 °29'45". The prism, the film, and the substrate were clamped together and mounted on a rotary table from the theodolite 2T2A. Light of laser LG-105 (2= 0.6328 #m) passed through the polarizer 4, was focussed by means of the objective, entered the prism and illuminated a small spot o f l 0 / z m diameter on the film surface. Figure 2 shows the results obtained for a polypropylene film of 12/tin thickness as the refractive index ellipsoid; the coordinate system is such that the axis Ycorresponds to the machine direction. As shown above, the accuracy of the refractive index determination is given by the reliability of measured values ~m. With the theodolite 2T2A angles can be measured within 1"; accordingly, for the relevant values of n2, t, and A, the refractive indices are accurate to
0.005 %. Translated by M. KUBIN REFERENCES 1. V. I. GRITSENKO, I. A. MATVEYEVA and V. P. P O R E N I N , Rost i legirovaniye poluprovodnikovykh kristallov i plenok (Growth and Doping of Semiconductor Crystals and Films). p. 310, Novosibirsk, 1977 2. F. MULLER, Odnoosnoye rastyazheniye i anizotropia. Fizika polimerov (Uniaxial Extension and Anisotropy. Polymer Physics). Translation from English, Z. A. Rogovin and A. Ya. Malkin, Eds., p. 254, Moscow, 1969 3. R. U L R I C H and R. TORGE, Appl. Opt., 12, 2901, 1973
0032-3950/88 $10.00+ .00 "~ 1989 Pergamon Press plc
METHODS OF INVESTIGATION MEASUREMENT OF LOCAL PARAMETERS IN POLYMER FILMS* S. SH. GEVORKYAN, A . S. PETROSYAN a n d M . A . ZABUNYAN K. Marx Erevan Polytechnical Institute
(Received 12 March 1987) The prism-coupler used in integral optics to measure parameters of optical waveguides can be employed for an accurate determination of parameters of polymeric films. The procedure developed in this paper ensures a high accuracy of measured values of the refractive index along directions lying either in parallel with, or perpendicularly to, the film surface.
OWING tO the technology used in their preparation, thin polymeric films often contain local inhomogeneities. These defects are decisive for the quality and practical applicability of the film, in particular when it is used as a n electrically insulating layer. Several methods including capacitance measurements can be employed to determine the parameters of polymeric films along the direction perpendicular to the film surface, but not do ensure the required accuracy n o r do they operate o n a sufficiently small scale. Information on the measurement of local characteristics in parallel with the film surface is very scare. One method measures parameters of an ellipse formed when a small area of the film covered by thermally sensitive layer is heated by means of a needle [2]. The method is simple enough but not very accurate and the involved area is still quite large.
",l/J
_--3
,7
,
7
:J FIG. 1. The experimental setup for prismqoading a film (a) and two methods for measuring the optical characteristics (b, c); 1 - t h e measured film (planar waveguide), 2 - p r i s m , 3 - s u b s t r a t e , 4 - polarizer, 5 - objective, 6 - immersion Iiquid. The method of prism-loading is widely used [3] in integral optics to measure parameters of thin-layer waveguides in intimate contact with a n inelastic substrate. Light enters the prism and undergoes total reflection at its base (Fig. la). An evanescent field is formed below the prism base where the intensity falls exponentially with the distance, similarly as in an optical waveguide. Pro* Vysokomol. soyed. A30: No. 7, 1556-1558, 1988. 1645
S. SH. GI~VORKYANet al.
1646
pagation modes can be thus excited in a thin polymeric film pressed firmly onto the prism base, provided the refractive index of the film is smaller than that of the prism. Propagation modes are excited only for some discrete values of the angle of incidence of light on the face of the prism; these so-called synchronization angles 9= depend on both the film thickness and the refractive index, and satisfy the condition that the phase velocities along the Y-axis are identical in the film and in the prism, n2 sin 0= n, sin 0, where 0 is the angle of total reflection at the prism base, 0t is the angle of internal reflection at the boundary wavegulde-substrate, nl and n2 are the respective refractive indices of the waveguide and the prism. Both the thickness and refractive index of the film can be calculated from the measured angles 9m, provided the parameters of the prism and the refractive index of the substrate are known. The method is very simple both experimentally and from the viewpoint of data evaluation. In this paper we demonstrate that this approach can be used to measure accurately and on a local scale parameters of polymeric films. One problem consists in that polymeric films are usually not rigid enough and special measures are therefore necessary: optical contact between the prism and the polymer can be achieved by introducing an immersion liquid (Fig. lb), or by using a supporting plate to press the film firmly to the prism base (Fig. lc). The first method is deficient in that the quality of contact cannot be controlled and the processing of data becomes quite complex. In the second case one cannot avoid the formation of clearances between the film and the prism and, on the other hand, between the film and the substrate; their thickness depends on the applied force which must be selected experimentally. At a high compression the clearance between the film and the substrate practically disappears; if the refractive indices satisfy the inequality n2 > nt > n3 and light enters the prism at the synchronous angle, propagation modes are excited in the polymer and light propagates owing to multiple reflections on the boundary iilm-substrate, similarly as in an integral optical waveguide [3]. From the measured values of ~0,n (Fig. 10 one can then calculate the refractive index of the film by means of the method described in [3]. To improve the accuracy and simplify the calculations it is advisable to employ the weakest possible compressive force F, selected on the basis of preliminary experiments. In this instance, if the size of the substrate 3 exceeds the dimensions of the prism base, the clearance between the substrate and the film is the larger of the two and modes in the film do not leak into the substrate even if n2 > nl. Under these conditions the film can be treated as a planar dielectric waveguide. When the electric vector E of the incident polarized wave lies in parallel with the film surface (TE polarization mode), the relationship between the refractive index n ~ and the propagation constant Bin, derived from the condition of multiple total internal reflection at the film face [3], reads 2 2 ~ 2 (N2=-l)=(n~-N~,)tan (tk 4n,-N~,),
(l)
where the quantity N~=pm/k is the effective refractive index, k=2ttl2 is the wave number, ). is the light wavelength, and t is the film thickness. When the vector E is oriented perpendicularly to the film surface (TM polarization mode), nt is related to N= through 2 1) tan2 ( t k 4 ~ ) n,(Nm-
(2)
For prism-loaded films the effective refractive indices can be determined experimentally. For those discrete values of the incidence angle 9= which excite propagation modes in the film, the value of N= can be calculated from the formula •
.
-
.
where A is the prism angle.
°(
Nm= kn2 si
A + arcsinSin---~'~ , n2 /
(3)
Measurement of local parameters in polymer films
1647
The experimental determination of the refractive index of a polymer film then involves the following steps. The required mode of polarization is set by means of the polarizer 4 (Fig. lc); for the TE mode the electric vector E must lie in the plane XOY(Fig. Ic). The angle of incidence ¢ is varied until a mode is excited in the film. Nm is calculated from the corresponding value of tpr, according to formula (3) and the refractive index nl~ (for a diree'ion parallel to the plane XO Y) is calculated from equation (1); the quantity n l , refers to the orientation of vector E. In the TE mode the vector E is perpendicular to the direction of wave propagation in the film. It is obvious that for the given mode of polarization (for the given orientation of the polarizer 4) one can determine the refractive index along all directions in parallel with the film surface by rotating the holder with the specimen by an angle ~ (Fig. 2). The values of nx, determined in this manner fall on an ellipse in the plane XOY
//'t FIG. 2. Refractive index ellipsoid of polypropylenc. (Fig. 2). When the polarizer is turned by 90 °, the light waves excited in the film have the electric vector oriented perpendicularly to the film surface (TM mode). F r o m the angles q,,~ determined experimentally for this case one again calculates Nm from equation (3); the refractive index n~: for the direction perpendicular to the film surface is then found from formula (2). Industrial films of thickness 5 to 50 f~m (polypropylene and other polymers) were studied experimentally. The prism was made of the glass TF-2 (n2= 1.6725) and the prism angle was A = 61 °29'45". The prism, the film, and the substrate were clamped together and mounted on a rotary table from the theodolite 2T2A. Light of laser LG-105 (2= 0.6328 #m) passed through the polarizer 4, was focussed by means of the objective, entered the prism and illuminated a small spot o f l 0 / z m diameter on the film surface. Figure 2 shows the results obtained for a polypropylene film of 12/tin thickness as the refractive index ellipsoid; the coordinate system is such that the axis Ycorresponds to the machine direction. As shown above, the accuracy of the refractive index determination is given by the reliability of measured values ~m. With the theodolite 2T2A angles can be measured within 1"; accordingly, for the relevant values of n2, t, and A, the refractive indices are accurate to
0.005 %. Translated by M. KUBIN REFERENCES 1. V. I. GRITSENKO, I. A. MATVEYEVA and V. P. P O R E N I N , Rost i legirovaniye poluprovodnikovykh kristallov i plenok (Growth and Doping of Semiconductor Crystals and Films). p. 310, Novosibirsk, 1977 2. F. MULLER, Odnoosnoye rastyazheniye i anizotropia. Fizika polimerov (Uniaxial Extension and Anisotropy. Polymer Physics). Translation from English, Z. A. Rogovin and A. Ya. Malkin, Eds., p. 254, Moscow, 1969 3. R. U L R I C H and R. TORGE, Appl. Opt., 12, 2901, 1973