- Email: [email protected]
Molecular orientation of polyimide films determined by an optical retardation method
.....
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:: :>:::..;: .,:,: ,:., ~, :j
.A> ..::~“::i:ii$:~:.iii:~::.~:.~,:.:: i:>:_>> :.::.:.:.:i:_,::, j :. : i:_,~~~:~~~,~:~i.i:::‘:,.:.: ...........i.... .‘. i.. .I
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. . ,.‘...‘.,,;,,,;,,,~,
,:.:_>
applied surface science ELSEVIER
”
Applied Surface Science lOO/lOl (1996) 124-138
Molecular orientation of polyimide films determined by an optical retardation method K. Sakamoto a,*, R. Arafune a, S. Ushioda ‘, Y. Suzuki ‘, S. Morokawa b a Research Institute of
Electrical
h Technical
Cotnrmmication.
Luborato?.
Tohoku Unicersit~.
2-1-l
Kutuhiru,
Citbetz Watch Co. Ltd., 840 Shimototni,
Aoba-ku.
Sendai 980-77. Japnn
Tokoroz,awa 359, Japan
Received 15 August 1995; accepted 29 September 1995
Abstract We have determined the molecular orientation of very thin (several hundred A) polyimide films on quartz glass substrates by measuring their optical retardation as a function of the incident angle. The molecular orientation was determined by fitting the experimental results with the theoretical calculation. Since both the multiple reflection in and the anisotropy of the polyimide film cause retardation, we calculated the optical retardation by a transfer matrix method. Then we obtained the molecular orientation using the Vuks’ relation. We also determined the molecular orientation of the polyimide films on Si substrates by IR absorption. Close agreement was obtained between the molecular orientations determined by the two different methods.
1. Introduction Rubbed polyimide films coated on substrates are widely used as alignment layers for liquid crystal (LC) devices. The bulk LC on a rubbed film aligns on average along the rubbing direction with a certain tilt angle [I]. This angle is called the ‘pretilt angle’. From previous studies [2,3] it is known that bulk LC alignment is caused mainly by the molecular orientation of the polyimide film induced by rubbing. However, the details of the alignment mechanism are not yet understood adequately. Thus. characterization of the molecular orientation of the polyimide film is important both for the understanding of the bulk LC alignment and for the realization of high quality LC devices.
* Corresponding author. Tel.: + 8 l-22-2 175498; fax: + 8 I-22. 2175500;
e-mail: [email protected].
Recently, by using polarized IR absorption we have determined the orientational distribution of poly[4,4’-oxydiphenylenepyromellitimide] (PMDAODA) molecules in the surface region oriented by rubbing [4]. However, the IR absorption technique cannot be applied to polyimide/glass system that is most important for LC device applications, because a glass substrate is not transparent in the IR region of interest. Thus to examine practical devices one needs to find a method that works in the visible region. Ellipsometry is a powerful tool to detect the dielectric anisotropy of thin films and can be applied to the polyimide/glass system. Indeed, the average tilt angle of polymer chains in rubbed polyimide films on glass substrates was determined by measuring the incident angle dependence of the optical retardation of the films [5,6]. If the polarizability of the constituent molecule is known, one can determine not only the average tilt angle but also the
0169-4332/96/$15.00 Copyright 0 1996 Elsevier Science B.V. All rights reserved PII SO I69-4332(96)002711
K. Sakantoto et al/Applied
135
Surface Science lOO/ 101 (19%) 124-128 Laboratory
molecular orientation of the film using the Vuks’ relation [7]. It relates the dielectric constant to the molecular polarizability for anisotropic media. In this study we have determined the molecular orientation of rubbed and unrubbed PMDA-ODA films on quartz glass substrates for the first time by measuring their optical retardation. The molecular orientation was determined by fitting the experimental results with a theoretical calculation. This procedure is outlined in the next section. Then we compare the molecular orientations determined by the optical retardation and IR absorption measurements. We conclude that the optical retardation measurement is applicable in studying practical LC devices that use glass substrates.
frame
Quartz substrate \ Transmitted
light
Fig. I. Planar stack of three dielectric layers.
2. Theory The ellipsometric angles A and + in a transmission geometry are defined by tan*e’-\
T, = --,
(I)
P
where T, and Tp are the complex transmittance coefficients of the field amplitude for s- and p-polarized light, respectively. A is called the ‘optical retardation’ To calculate the incident angle dependence of A, we consider a planer stack of dielectric layers composed of vacuum, a PMDA-ODA film, and a quartz substrate as illustrated in Fig. 1. For a rubbed PMDA-ODA film that is not oriented uniformly across the entire film thickness, we consider it to be composed of two layers: a rubbed layer and an unrubbed layer. The XYZ-coordinates are the laboratory frame where the Z-axis is normal to the surface, and the XZ-plane is the incident plane of light. The rubbing direction is fixed in the positive X-direction. The x-, v-, and z-axes are the dielectric principal axes of the PMDA-ODA film. Since the PMDA-ODA film has a mirror symmetry with respect to the XZ-plane, the two principal dielectric axes (x- and z-axes) lie in the XZ-plane. Thus, the vz-coordinates are related to the XYZ-coordinates by only the tilt angle Stilt of the .u-axis from the XY-plane. Since the incident angle dependence of A arises from both the anisotropy of and the multiple reflec-
tion in the PMDA-ODA film, we calculate it by a transfer matrix method [8]. The explicit form of the transfer matrices for our experimental geometry will be described in Ref. [9]. Next, we express the dielectric constant of the PMDA-ODA film in terms of the molecular polarizability and the orientational distribution function of the molecules. The principal dielectric constant ei of an anisotropic medium is related to the corresponding polarizability oli by the Vuks’ relation: E;-
-= Ef2
1 $Nol,,
i=x,
v,and
:,
where N and c are the molecular number density and the average dielectric constant of the medium, respectively. The relation between the principal and the molecular polarizability tensors denoted by -(Yand -am. respectively is given by
xomCT(e, --
+, x)sinOded+dX,
where f(e, 4, X) is the molecular orientational distribution function; the angles 8, $, and X are the Eulerian angles that specify the orientation of the molecular axes with respect to the principal dielectric axes [lo]; Cc@, +J, X) is the direction cosine matrix, and C’
K. Sakamoto et al/Applied
126
Surface Science 100/101
late the principal dielectric constant of the medium with an arbitrary molecular orientation. Assuming that the polarizability of the PMDAODA molecule is uniaxial with respect to the polymer chain direction ‘, the molecular polarizability multiplied by the molecular number density (No”) can be obtained from the literature [ 121. This% sumption is reasonable for our films, because the rotational orientation of the PMDA-ODA molecules about the polymer chain direction is expected to be random for spin-coated films. NCX~ and Nor”, referred to the polymer chain direction are 0.13 and 0.073 at 6328 A, respectively. Following our previous work [4], we assume the orientational distribution function of the polymer chain with the following form:
.@A +, X) = Fexp -
(
x 1+
2a2
cc
&7,cosn$ n= 1
)
(4)
I
where F is a normalization constant and u is the standard deviation for variable 8. This distribution function can represent films in which the polymer chains are on average oriented parallel to and anisotropically oriented in the .ry-plane. The average tilt angle of the polymer chains from the film surface is represented by etilt as shown in Fig. 1. After the integration of Eq. (3) is carried out, the principal polarizability (Y contains only u and u2. The a2 coefficient des??bes the orientational anisotropy of the polymer chains between the X- and y-directions. Thus we can determine o, u2, and Oci,,by fitting the experimental results with the theoretical calculation.
3. Experiment The PMDA-ODA films were spin-coated on clean quartz glasses (1.1 mm thick). The film thickness
’ The polymer chain direction is defined by the c-axis of the unit cell of the crystalline PMDA-ODA [l Il.
(1996) 124-128
was measured by an atomic force microscope (AFM: SEIKO SPA-300) after etching away half of the film. The film thicknesse: of two sample: used in this study are 170 f 12 A and 300 k 20 A. At the same time we prepared PMDA-ODA/Si samples for IR absorption measurements. The rubbing treatment was done by a rubbing machine [4] under the following conditions: the rotating speed of the rubbing cylinder (diameter 70 mm> covered with a rayon cloth (Yoshikawa Chemical Co., YA-18-R) was 400 rpm; the sample was passed once under the cylinder at a speed of IO mm/s; the bending depth of the cloth fibers due to contact pressure [ 131 was 0.1 mm. The incident angle dependence of the optical retardation was measured by Senarmont ellipsometry (Shimazu AEP-100) [5,14]. The light source is a He-Ne laser. The incident plane of the light contains the rubbing direction. The sign of the incident angle 8,” is defined in Fig. 1. To prevent the scatter of the experimental data points due to the interference of light in the glass substrate, we inserted two lenses (focal length 60 mm) before and after the sample. This modification in the experimental geometry significantly reduced the experimental error due to the interference effect. The residual retardation of the naked quartz glass substrate is less than IfIO.05 nm between the incident angles of +40”. The residual retardation can be neglected compared with the experimental uncertainty for the PMDA-ODA/quartz samples.
4. Results Fig. 2(a) and (b) show the incident angle dependence of the optical retardationOfor the PMODA-ODA films with thicknesses of 170 A and 300 A, respectively. The filled squares and circles are the data points for the unrubbed and rubbed films, respectively. For the unrubbed films the optical retardation at normal incidence is equal to zero within the experimental uncertainty and the incident angle dependence is symmetric with respect to normal incidence. This result indicates that the unrubbed films are isotropic in the film plane, i.e. a2 = 0 and Stilt = 0”. In contrast to the unrubbed films, for the rubbed films the optical retardation is negative at normal
K. Sakamoto et al./Applied 3
,
Surface Science lOO/lOl
I (a) d=l70A
(19961 124-128
principal axis with the largest dielectric constant is oriented along the rubbing direction and tilted up from the film plane by a certain angle, i.e. a2 > 0 and otilt > 0”.
5. Determination
1 0
-1 -21 -60
.
’ -40
’
’
’
-20
’ 0
Incident Angle
.
’
’
’
20
’
40
1 60
( Degrees )
Fig. 2. Incident angle dependence of the optical retardation of PMDA-ODA films on quartz substrates: (a) for the 170 A thick film, and (b) for the 300 A thick film. The filled squares and circles with the error bars are the data points for the unrubbed and rubbed films, respectively. The solid curves are the best fit calculated results.
incidence and the incident angle dependence is asymmetric with respect to normal incidence. The minimum retardation for both films is at the incident angle around +6”. This result indicates that the
Table 1 Fitting parameters 0for the optical retardation and the IR absorption thick and the 505 A thick films by interpolation
127
of the molecular
orientation
We determine the molecular orientation of the PMDA-ODA films by a fitting procedure. The fitting parameters are u2, o, and etilt (Eq. (4) and Fig. 1). For the unrubbed films the fitting parameter is only cr, because of a, = 0 and l!Itllt= 0”. For rubbed films we first need to know the depth of the region oriented by rubbing. By measuring the thickness dependence of the IR dichroic difference of the phenyl C-Costretching vibration [4], we estimated it to be 150 A for the rubbing condition used in this study. Thus we c?nsider the rubbed films to be composed of a 150 A thick rubbed layer and a (d - 150) A thick unmbbed layer, where d is the total thickness of the PMDA-ODA film. The solid curves in Fig. 2 are the best fit calculated results. They reproduced the experimental data extremely well. The fitting parameters are summarized in Table 1. From the fitting results one can see that the polymer chains in the spin-coated films are oriented parallel to the film surface, and that by a rubbing treatment the polymer chains are oriented along the rubbing direction and tilted up from the film surface.
data. The values in parentheses
are obtained
from those of the 153 A
Method
Thickness
Unrubbed
Rubbed
Retardation
17oA
20 + 5”
0.44 f 0.02
17+5”
9 + 2”
0.49 + 0.04
10 f 7”
14f4”
3chJA IR
10+7”
121 A
0.33 + 0.02
12*2”
7.0 * 1”
149 A
0.32 + 0.02
11 f2”
7.5 * 1”
153A
6.5 f 1”
0.21 + 0.02
11+2”
5.0 + 1”
201 A
(7.0”)
0.33 * 0.02
10*3”
8.5 k 1”
359 A
(8.5”)
0.27 + 0.02
20 f 3”
10.0 * lo
455 A
(9.5”)
0.32 + 0.02
15*5”
10.0 + 1”
505 A
lo*
0.31 f 0.02
15f5”
15.0 + 1”
5”
128
K. Sakamoto et al./Applied
Suface Scierm lOO/ 101
6. Discussion To check the validity of the molecular orientation determined by the optical retardation measurement, we compare it with the molecular orientation of the PMDA-ODA films on Si substrates determined by IR absorption [4]. The fitting parameters for the IR absorption data are also shown in Table 1. One can see from Table 1 that the molecular orientations determined by the two different methods almost agree. There is slight disagreement in the a, coefficients. We believe that this disagreement is due to the difference in the surface roughness between the quartz and Si substrates. This is because the work done on the polyimide film during a rubbing treatment is expected to increase as its surface roughness increases. Indeed, the root-mean-squared amplitudes of the roughness of the 170 A thick POMDA-ODOA films on Si and quartz substrates are 5 A and 20 A, respectively. These values were obtained from the AFM images over a 2 p,rn X 2 pm area. Thus the molecular orientation determined by the optical retardation is seen to be reliable. Here, it is worth noting that the incident angle 0 m,n for the minimum retardation is not coincident with the average tilt angle fltilt of the polymer chains in the rubbed layer. The angle 0,,, depends not only on the average tilt angle eti,, but also on the dielectric constant and the thickness of the polyimide film, the depth of the region oriented by rubbing, the molecular orientation of the layer unaffected by rubbing, and the dielectric constant of the substrate. Thus, the angle em,” is not simply related to the average tilt angle tItilt. Therefore, we emphasize that the calculation described in Section 2 must be carried out to determine the average tilt angle oli,, as well as the molecular orientation.
7. Conclusion We have demonstrated that the molecular orientation of the PMDA-ODA film on a quartz glass substrate can be determined by optical retardation measurements. We obtained a close agreement be-
f 19961124-128
tween the molecular orientations determined by the optical retardation and IR absorption measurements. We pointed out that the calculation described in Section 2 must be carried out to determine the average tilt angle of the polymer chains as well as the molecular orientation.
Acknowledgements We would like to thank Mr. S. Murata of Chisso Co. Ltd. for providing us with PMDA-ODA polyimide. We also thank Mr. S. Tanuma of TOK Co. Ltd. for providing us with a resist material (OFPR800) for etching polyimide films. This work was supported in part by a Grant-in-Aid for Scientific Research from Ministry of Education, Science and Culture. We also thank Takahashi Foundation for financial assistance.
References [II M.E. Becker, R.A. Kilian, B.B. Kosmowski and D.A. Mlynski, Mol. Cryst. Liq. Cryst. 132 (1986) 167. El E.S. Lee, P. Vetter. T. Miyashita and T. Uchida. Jpn. J. Appl. Phys. 32 (1993) L1339. [31 M.B. Feller. W. Chen and Y.R. Shen. Phys. Rev. A 43 (1991) 6778. [Jl K. Sakamoto. R. Arafune. N. Ito, S. Ushioda. Y. Suzuki and S. Morokawa, Jpn. J. Appl. Phys. 33 (1994) L1323. [51 K.-Y. Han, P. Vetter and T. Uchida. Jpn. J. Appl. Phys. 32 (19931 Ll242. lb1 D.-S. Seo. K. Araya, N. Yoshida, M. Nishikawa, Y. Yabe and S. Kobayashi, Jpn. J. Appl. Phys. 34 (1995) L503. [71 M.F. Vuks, Optics Spectrosc. 20 (1966) 361. l81 P. Yeh. J. Opt. Sot. Am. 69 (1979) 742. [91 K. Sakamoto, R. Arafune, N. Ito. S. Ushioda. Y. Suzuki and S. Morokawa, to be published. [lOI E.B. Wilson, Jr., J.C. Decius and P.C. Cross, in: Molecular Vibrations (Dover, New York, 1980) p. 285. D.Ya. Tsvankin, B.M. Ginsburg, Sh. [III L.G. Kazaryan. Tuichiev, L.N. Korzhavin and S.Ya. Frenkel, Vysokomol. Soed. A I4 (1972) 1199; Polym. Sci. USSR 14 (1972) 1344. [I21 T.P. Russell, H. Gugger and J.D. Swalen, J. Polym. Sci. Polym. Phys. Ed. 21 (1983) 1745. [I31 D.-S. Seo, K. Muroi and S. Kobayashi, Mol. Cryst. Liq. Cryst. 213 (1992) 223. I141 H. de Senarmont. Ann. Chem. Phys. 73 (1840) 337.
i’:.::+
:: :>:::..;: .,:,: ,:., ~, :j
.A> ..::~“::i:ii$:~:.iii:~::.~:.~,:.:: i:>:_>> :.::.:.:.:i:_,::, j :. : i:_,~~~:~~~,~:~i.i:::‘:,.:.: ...........i.... .‘. i.. .I
..
. . ,.‘...‘.,,;,,,;,,,~,
,:.:_>
applied surface science ELSEVIER
”
Applied Surface Science lOO/lOl (1996) 124-138
Molecular orientation of polyimide films determined by an optical retardation method K. Sakamoto a,*, R. Arafune a, S. Ushioda ‘, Y. Suzuki ‘, S. Morokawa b a Research Institute of
Electrical
h Technical
Cotnrmmication.
Luborato?.
Tohoku Unicersit~.
2-1-l
Kutuhiru,
Citbetz Watch Co. Ltd., 840 Shimototni,
Aoba-ku.
Sendai 980-77. Japnn
Tokoroz,awa 359, Japan
Received 15 August 1995; accepted 29 September 1995
Abstract We have determined the molecular orientation of very thin (several hundred A) polyimide films on quartz glass substrates by measuring their optical retardation as a function of the incident angle. The molecular orientation was determined by fitting the experimental results with the theoretical calculation. Since both the multiple reflection in and the anisotropy of the polyimide film cause retardation, we calculated the optical retardation by a transfer matrix method. Then we obtained the molecular orientation using the Vuks’ relation. We also determined the molecular orientation of the polyimide films on Si substrates by IR absorption. Close agreement was obtained between the molecular orientations determined by the two different methods.
1. Introduction Rubbed polyimide films coated on substrates are widely used as alignment layers for liquid crystal (LC) devices. The bulk LC on a rubbed film aligns on average along the rubbing direction with a certain tilt angle [I]. This angle is called the ‘pretilt angle’. From previous studies [2,3] it is known that bulk LC alignment is caused mainly by the molecular orientation of the polyimide film induced by rubbing. However, the details of the alignment mechanism are not yet understood adequately. Thus. characterization of the molecular orientation of the polyimide film is important both for the understanding of the bulk LC alignment and for the realization of high quality LC devices.
* Corresponding author. Tel.: + 8 l-22-2 175498; fax: + 8 I-22. 2175500;
e-mail: [email protected].
Recently, by using polarized IR absorption we have determined the orientational distribution of poly[4,4’-oxydiphenylenepyromellitimide] (PMDAODA) molecules in the surface region oriented by rubbing [4]. However, the IR absorption technique cannot be applied to polyimide/glass system that is most important for LC device applications, because a glass substrate is not transparent in the IR region of interest. Thus to examine practical devices one needs to find a method that works in the visible region. Ellipsometry is a powerful tool to detect the dielectric anisotropy of thin films and can be applied to the polyimide/glass system. Indeed, the average tilt angle of polymer chains in rubbed polyimide films on glass substrates was determined by measuring the incident angle dependence of the optical retardation of the films [5,6]. If the polarizability of the constituent molecule is known, one can determine not only the average tilt angle but also the
0169-4332/96/$15.00 Copyright 0 1996 Elsevier Science B.V. All rights reserved PII SO I69-4332(96)002711
K. Sakantoto et al/Applied
135
Surface Science lOO/ 101 (19%) 124-128 Laboratory
molecular orientation of the film using the Vuks’ relation [7]. It relates the dielectric constant to the molecular polarizability for anisotropic media. In this study we have determined the molecular orientation of rubbed and unrubbed PMDA-ODA films on quartz glass substrates for the first time by measuring their optical retardation. The molecular orientation was determined by fitting the experimental results with a theoretical calculation. This procedure is outlined in the next section. Then we compare the molecular orientations determined by the optical retardation and IR absorption measurements. We conclude that the optical retardation measurement is applicable in studying practical LC devices that use glass substrates.
frame
Quartz substrate \ Transmitted
light
Fig. I. Planar stack of three dielectric layers.
2. Theory The ellipsometric angles A and + in a transmission geometry are defined by tan*e’-\
T, = --,
(I)
P
where T, and Tp are the complex transmittance coefficients of the field amplitude for s- and p-polarized light, respectively. A is called the ‘optical retardation’ To calculate the incident angle dependence of A, we consider a planer stack of dielectric layers composed of vacuum, a PMDA-ODA film, and a quartz substrate as illustrated in Fig. 1. For a rubbed PMDA-ODA film that is not oriented uniformly across the entire film thickness, we consider it to be composed of two layers: a rubbed layer and an unrubbed layer. The XYZ-coordinates are the laboratory frame where the Z-axis is normal to the surface, and the XZ-plane is the incident plane of light. The rubbing direction is fixed in the positive X-direction. The x-, v-, and z-axes are the dielectric principal axes of the PMDA-ODA film. Since the PMDA-ODA film has a mirror symmetry with respect to the XZ-plane, the two principal dielectric axes (x- and z-axes) lie in the XZ-plane. Thus, the vz-coordinates are related to the XYZ-coordinates by only the tilt angle Stilt of the .u-axis from the XY-plane. Since the incident angle dependence of A arises from both the anisotropy of and the multiple reflec-
tion in the PMDA-ODA film, we calculate it by a transfer matrix method [8]. The explicit form of the transfer matrices for our experimental geometry will be described in Ref. [9]. Next, we express the dielectric constant of the PMDA-ODA film in terms of the molecular polarizability and the orientational distribution function of the molecules. The principal dielectric constant ei of an anisotropic medium is related to the corresponding polarizability oli by the Vuks’ relation: E;-
-= Ef2
1 $Nol,,
i=x,
v,and
:,
where N and c are the molecular number density and the average dielectric constant of the medium, respectively. The relation between the principal and the molecular polarizability tensors denoted by -(Yand -am. respectively is given by
xomCT(e, --
+, x)sinOded+dX,
where f(e, 4, X) is the molecular orientational distribution function; the angles 8, $, and X are the Eulerian angles that specify the orientation of the molecular axes with respect to the principal dielectric axes [lo]; Cc@, +J, X) is the direction cosine matrix, and C’
K. Sakamoto et al/Applied
126
Surface Science 100/101
late the principal dielectric constant of the medium with an arbitrary molecular orientation. Assuming that the polarizability of the PMDAODA molecule is uniaxial with respect to the polymer chain direction ‘, the molecular polarizability multiplied by the molecular number density (No”) can be obtained from the literature [ 121. This% sumption is reasonable for our films, because the rotational orientation of the PMDA-ODA molecules about the polymer chain direction is expected to be random for spin-coated films. NCX~ and Nor”, referred to the polymer chain direction are 0.13 and 0.073 at 6328 A, respectively. Following our previous work [4], we assume the orientational distribution function of the polymer chain with the following form:
.@A +, X) = Fexp -
(
x 1+
2a2
cc
&7,cosn$ n= 1
)
(4)
I
where F is a normalization constant and u is the standard deviation for variable 8. This distribution function can represent films in which the polymer chains are on average oriented parallel to and anisotropically oriented in the .ry-plane. The average tilt angle of the polymer chains from the film surface is represented by etilt as shown in Fig. 1. After the integration of Eq. (3) is carried out, the principal polarizability (Y contains only u and u2. The a2 coefficient des??bes the orientational anisotropy of the polymer chains between the X- and y-directions. Thus we can determine o, u2, and Oci,,by fitting the experimental results with the theoretical calculation.
3. Experiment The PMDA-ODA films were spin-coated on clean quartz glasses (1.1 mm thick). The film thickness
’ The polymer chain direction is defined by the c-axis of the unit cell of the crystalline PMDA-ODA [l Il.
(1996) 124-128
was measured by an atomic force microscope (AFM: SEIKO SPA-300) after etching away half of the film. The film thicknesse: of two sample: used in this study are 170 f 12 A and 300 k 20 A. At the same time we prepared PMDA-ODA/Si samples for IR absorption measurements. The rubbing treatment was done by a rubbing machine [4] under the following conditions: the rotating speed of the rubbing cylinder (diameter 70 mm> covered with a rayon cloth (Yoshikawa Chemical Co., YA-18-R) was 400 rpm; the sample was passed once under the cylinder at a speed of IO mm/s; the bending depth of the cloth fibers due to contact pressure [ 131 was 0.1 mm. The incident angle dependence of the optical retardation was measured by Senarmont ellipsometry (Shimazu AEP-100) [5,14]. The light source is a He-Ne laser. The incident plane of the light contains the rubbing direction. The sign of the incident angle 8,” is defined in Fig. 1. To prevent the scatter of the experimental data points due to the interference of light in the glass substrate, we inserted two lenses (focal length 60 mm) before and after the sample. This modification in the experimental geometry significantly reduced the experimental error due to the interference effect. The residual retardation of the naked quartz glass substrate is less than IfIO.05 nm between the incident angles of +40”. The residual retardation can be neglected compared with the experimental uncertainty for the PMDA-ODA/quartz samples.
4. Results Fig. 2(a) and (b) show the incident angle dependence of the optical retardationOfor the PMODA-ODA films with thicknesses of 170 A and 300 A, respectively. The filled squares and circles are the data points for the unrubbed and rubbed films, respectively. For the unrubbed films the optical retardation at normal incidence is equal to zero within the experimental uncertainty and the incident angle dependence is symmetric with respect to normal incidence. This result indicates that the unrubbed films are isotropic in the film plane, i.e. a2 = 0 and Stilt = 0”. In contrast to the unrubbed films, for the rubbed films the optical retardation is negative at normal
K. Sakamoto et al./Applied 3
,
Surface Science lOO/lOl
I (a) d=l70A
(19961 124-128
principal axis with the largest dielectric constant is oriented along the rubbing direction and tilted up from the film plane by a certain angle, i.e. a2 > 0 and otilt > 0”.
5. Determination
1 0
-1 -21 -60
.
’ -40
’
’
’
-20
’ 0
Incident Angle
.
’
’
’
20
’
40
1 60
( Degrees )
Fig. 2. Incident angle dependence of the optical retardation of PMDA-ODA films on quartz substrates: (a) for the 170 A thick film, and (b) for the 300 A thick film. The filled squares and circles with the error bars are the data points for the unrubbed and rubbed films, respectively. The solid curves are the best fit calculated results.
incidence and the incident angle dependence is asymmetric with respect to normal incidence. The minimum retardation for both films is at the incident angle around +6”. This result indicates that the
Table 1 Fitting parameters 0for the optical retardation and the IR absorption thick and the 505 A thick films by interpolation
127
of the molecular
orientation
We determine the molecular orientation of the PMDA-ODA films by a fitting procedure. The fitting parameters are u2, o, and etilt (Eq. (4) and Fig. 1). For the unrubbed films the fitting parameter is only cr, because of a, = 0 and l!Itllt= 0”. For rubbed films we first need to know the depth of the region oriented by rubbing. By measuring the thickness dependence of the IR dichroic difference of the phenyl C-Costretching vibration [4], we estimated it to be 150 A for the rubbing condition used in this study. Thus we c?nsider the rubbed films to be composed of a 150 A thick rubbed layer and a (d - 150) A thick unmbbed layer, where d is the total thickness of the PMDA-ODA film. The solid curves in Fig. 2 are the best fit calculated results. They reproduced the experimental data extremely well. The fitting parameters are summarized in Table 1. From the fitting results one can see that the polymer chains in the spin-coated films are oriented parallel to the film surface, and that by a rubbing treatment the polymer chains are oriented along the rubbing direction and tilted up from the film surface.
data. The values in parentheses
are obtained
from those of the 153 A
Method
Thickness
Unrubbed
Rubbed
Retardation
17oA
20 + 5”
0.44 f 0.02
17+5”
9 + 2”
0.49 + 0.04
10 f 7”
14f4”
3chJA IR
10+7”
121 A
0.33 + 0.02
12*2”
7.0 * 1”
149 A
0.32 + 0.02
11 f2”
7.5 * 1”
153A
6.5 f 1”
0.21 + 0.02
11+2”
5.0 + 1”
201 A
(7.0”)
0.33 * 0.02
10*3”
8.5 k 1”
359 A
(8.5”)
0.27 + 0.02
20 f 3”
10.0 * lo
455 A
(9.5”)
0.32 + 0.02
15*5”
10.0 + 1”
505 A
lo*
0.31 f 0.02
15f5”
15.0 + 1”
5”
128
K. Sakamoto et al./Applied
Suface Scierm lOO/ 101
6. Discussion To check the validity of the molecular orientation determined by the optical retardation measurement, we compare it with the molecular orientation of the PMDA-ODA films on Si substrates determined by IR absorption [4]. The fitting parameters for the IR absorption data are also shown in Table 1. One can see from Table 1 that the molecular orientations determined by the two different methods almost agree. There is slight disagreement in the a, coefficients. We believe that this disagreement is due to the difference in the surface roughness between the quartz and Si substrates. This is because the work done on the polyimide film during a rubbing treatment is expected to increase as its surface roughness increases. Indeed, the root-mean-squared amplitudes of the roughness of the 170 A thick POMDA-ODOA films on Si and quartz substrates are 5 A and 20 A, respectively. These values were obtained from the AFM images over a 2 p,rn X 2 pm area. Thus the molecular orientation determined by the optical retardation is seen to be reliable. Here, it is worth noting that the incident angle 0 m,n for the minimum retardation is not coincident with the average tilt angle fltilt of the polymer chains in the rubbed layer. The angle 0,,, depends not only on the average tilt angle eti,, but also on the dielectric constant and the thickness of the polyimide film, the depth of the region oriented by rubbing, the molecular orientation of the layer unaffected by rubbing, and the dielectric constant of the substrate. Thus, the angle em,” is not simply related to the average tilt angle tItilt. Therefore, we emphasize that the calculation described in Section 2 must be carried out to determine the average tilt angle oli,, as well as the molecular orientation.
7. Conclusion We have demonstrated that the molecular orientation of the PMDA-ODA film on a quartz glass substrate can be determined by optical retardation measurements. We obtained a close agreement be-
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tween the molecular orientations determined by the optical retardation and IR absorption measurements. We pointed out that the calculation described in Section 2 must be carried out to determine the average tilt angle of the polymer chains as well as the molecular orientation.
Acknowledgements We would like to thank Mr. S. Murata of Chisso Co. Ltd. for providing us with PMDA-ODA polyimide. We also thank Mr. S. Tanuma of TOK Co. Ltd. for providing us with a resist material (OFPR800) for etching polyimide films. This work was supported in part by a Grant-in-Aid for Scientific Research from Ministry of Education, Science and Culture. We also thank Takahashi Foundation for financial assistance.
References [II M.E. Becker, R.A. Kilian, B.B. Kosmowski and D.A. Mlynski, Mol. Cryst. Liq. Cryst. 132 (1986) 167. El E.S. Lee, P. Vetter. T. Miyashita and T. Uchida. Jpn. J. Appl. Phys. 32 (1993) L1339. [31 M.B. Feller. W. Chen and Y.R. Shen. Phys. Rev. A 43 (1991) 6778. [Jl K. Sakamoto. R. Arafune. N. Ito, S. Ushioda. Y. Suzuki and S. Morokawa, Jpn. J. Appl. Phys. 33 (1994) L1323. [51 K.-Y. Han, P. Vetter and T. Uchida. Jpn. J. Appl. Phys. 32 (19931 Ll242. lb1 D.-S. Seo. K. Araya, N. Yoshida, M. Nishikawa, Y. Yabe and S. Kobayashi, Jpn. J. Appl. Phys. 34 (1995) L503. [71 M.F. Vuks, Optics Spectrosc. 20 (1966) 361. l81 P. Yeh. J. Opt. Sot. Am. 69 (1979) 742. [91 K. Sakamoto, R. Arafune, N. Ito. S. Ushioda. Y. Suzuki and S. Morokawa, to be published. [lOI E.B. Wilson, Jr., J.C. Decius and P.C. Cross, in: Molecular Vibrations (Dover, New York, 1980) p. 285. D.Ya. Tsvankin, B.M. Ginsburg, Sh. [III L.G. Kazaryan. Tuichiev, L.N. Korzhavin and S.Ya. Frenkel, Vysokomol. Soed. A I4 (1972) 1199; Polym. Sci. USSR 14 (1972) 1344. [I21 T.P. Russell, H. Gugger and J.D. Swalen, J. Polym. Sci. Polym. Phys. Ed. 21 (1983) 1745. [I31 D.-S. Seo, K. Muroi and S. Kobayashi, Mol. Cryst. Liq. Cryst. 213 (1992) 223. I141 H. de Senarmont. Ann. Chem. Phys. 73 (1840) 337.