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Formation and dynamics of polymer surface relief gratings
Applied Surface Science 182 (2001) 272±279
Formation and dynamics of polymer surface relief gratings O. Henneberga,*, Th. Geuea, M. Saphiannikovaa, U. Pietscha, P. Rochonb, A. Natansohnc a
Institute of Physics, University of Potsdam, P.O.B. 601553, D-14415 Potsdam, Germany b Department of Physics, Royal Military College, Kingston, Ont., Canada K7K 5L0 c Department of Chemistry, Queen's University, Kingston, Ont., Canada K7L 3N6
Abstract Time resolved VIS and X-ray scattering experiments have been performed during the formation of a surface relief grating on a polymer ®lm containing an azobenzene side-chain homopolymer (poly{(4-nitrophenyl)[4-[[2-(methacryloyloxy)ethyl]ethylamino]phenyl]diazene} (pDR1M), T G 1298C) upon holographic exposure with circularly polarised laser light of 488 nm. Using ®xed geometric conditions for both experiments, the time evolution of the ®rst order grating peak was observed. Short time illumination with a light pattern of about 50 mW/cm2 shows that the evolution of the VIS and the X-ray signal depends on the pulse length of exposure. Several elastic as well as plastic processes appear. The shortest pulse length of 5 s applied at the X-ray experiment did not create a permanent grating. This is con®rmed by ex situ AFM inspections recorded after holographic treatment. VIS inspection with better time resolution reveals an elastic process during the ®rst seconds but plasti®cation of the material for longer exposure times. Partial relaxation takes place when the light is switched off. Cyclic light treatments create two periodic density gratings below the surface and a surface relief grating as well. Both scattering experiments can be explained qualitatively by ®nite element calculations assuming a viscoelastic (VE) ¯ow model. # 2001 Elsevier Science B.V. All rights reserved. PACS: 61.10.Kw; 61.44.e; 68.35.Rh; 68.65.g; 42.25.Fx Keywords: Polymer surface; Relief gratings; Viscoelastic ¯ow model
1. Introduction It is widely known that a surface relief pattern can be inscribed on the surface of an amorphous polymer ®lm containing azobenzene moieties [1±5]. This is done by exposing the sample with a periodic holographic pattern of circularly polarised light of 488 nm. This wavelength is close to the absorption maximum associated with the trans±cis isomerisation of the * Corresponding author. Tel.: 49-331-977-1278. E-mail address: [email protected] (O. Henneberg).
azobenzene moieties. Because these moieties require different free volume the periodic light pattern initiates a periodic pressure gradient along the surface. It induces material ¯ow already at temperatures 100 K below the glass transition temperature, TG, of the polymers and produces a periodic surface grating with approximately sinusoidal shape. Depending on the power of illumination and on the state of light polarisation, the grating depth may approach several hundreds of nanometers. A number of mechanisms had been proposed to explain the massive displacement that occurs even at low laser power [6±8]. Nevertheless, it is of particular interest to learn more about
0169-4332/01/$ ± see front matter # 2001 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 9 - 4 3 3 2 ( 0 1 ) 0 0 4 4 4 - 5
O. Henneberg et al. / Applied Surface Science 182 (2001) 272±279
the nature of this induced material transport in polymers. As a ®rst step, we have studied the thermal erasure of the surface relief grating [9]. During those experiments, we investigated poly{(4-nitrophenyl)[4-[[2(methacryloyloxy)ethyl]ethylamino]phenyl]diazene} (pDR1M), an amorphous polymer with no liquid crystalline properties. VIS and X-ray scattering were used simultaneously in order to reach two different length scales. Close to TG, we found a different behaviour of the X-ray and VIS grating peaks. Whereas the VIS peak intensity vanished 10±158 below TG, the X-ray peak had increased further before it also disappeared at TG [9]. This evidence initiated the assumption that the surface relief patterning is accompanied by a density modulation below the surface with a different temperature dependence. In the present study, we report on time resolved measurements of the grating formation process. To do this, we installed the apparatus for holographic exposure of the ®lm with circularly polarised light at a beamline of a Synchrotron Radiation facility (CHESS, Wilson Laboratory, Ithaka) and both the X-ray and VIS light scattering from the grating were detected after/during short time exposure and during continuous illumination. VIS probes mainly the development of the surface relief via phase contrast whereas X-rays are sensitive for charge density differences, i.e. to the induced material ¯ow below the sample surface. The periodically varying ratio of the light induced trans±cis isomerisation of the azobenzene moieties creates a lateral force acting in the polymer. The material response is elastic and plastic as well depending on the pulse length of exposure. The experimental results are interpreted in terms of ®nite element calculations using a viscoelastic (VE) ¯ow model implying the assumption that the light induced decrease of the elastic modulus is the key process for the understanding of the induced material ¯ow. 2. Experimental The samples consist of 400 nm thick ¯at polymer ®lms of pDR1M (T G 1298C) that has been spun onto a clean glass substrate. Surface relief gratings were inscribed onto the polymer ®lms using the holographic interference pattern of two plane waves
273
Fig. 1. Experimental setup used for simultaneous detection of VIS and X-ray diffraction.
produced by counter-circularly polarised beams obtained from an argon ion laser operating at the wavelength of 488 nm and at a power density of 50 mW/cm2. The X-ray experiments were performed at CHESS (Cornell University Ithaca, NY; l 0:1238 nm) using an X-ray CCD camera (ADSC Quantum CCD, 1152 1152 pixels) as 2-dimensional detector, additional laser scattering (l 633 nm) at RMC Kingston using the same setup (Fig. 1). We inscribed the gratings near to the absorption maximum of pDR1M with an Ar-ion laser at 488 nm by means of a double beam interference (holographic inscription). From the raw X-ray CCD data, a substantial background was removed and the intensity was integrated over the respective grating peak. Ex situ AFM inspection of several sample surfaces after short time exposure have been performed using a Nanoscope IIIa (Digital Instruments) in tapping mode. 3. Experimental results The ef®ciency of surface pattern formation is usually probed by the scattering intensity of the ®rst grating peak using a probing laser. A similar experiment can be performed using X-rays at grazing angles. In reciprocal space the angles of incidence and exit ai and af, respectively, de®ne the out-of-plane and inplane momentum transfer qz and qx: qz
2p sin ai sin af ; l
qx
2p cos ai cos af l (1)
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O. Henneberg et al. / Applied Surface Science 182 (2001) 272±279
Fig. 2. Development of ®rst-order X-ray grating peak intensity, after exposure with shots of an interference pattern of polarised light at 488 nm for 5, 10, 15 and 60 s duration.
Fig. 3. Time development of the ®rst-order VIS grating peak intensity during short pulse exposure.
where qx 0, i.e. ai af , de®nes the specular scattering condition. Beside the specular one additional peaks appear whenever Dqx 2p= D cos f, where D is the lateral spacing of the surface relief grating and f is the angle between the incidence beam and the grating normal [9]. Using ®xed ai, the CCD registers several af simultaneously probing a particular cut across the reciprocal space. In the following, we will focus our interest on the time evolution of the ®rstorder grating peak (see inset of Fig. 2). In order to analyse the initial process of grating formation, we probed its increasing intensity after several short term illuminations of the polymer surface. The ®lm was exposed to a series of pulses with 5, 10, 15 and 60 s duration each followed by a 10 s readout time for the CCD camera in dark (Fig. 2). It was found that the maximum attainable X-ray grating intensity IX-max depends on the pulse length of the blue light. After a total exposure time of 60 s, the 10, 15 and 60 s pulses approach almost equal IX-max whereas the 5 s pulses gave much lower ef®ciency of the grating formation. Obviously, 5 s marks a critical time of the formation process for the chosen laser power. Unfortunately, the minimal time resolution of the X-ray experiment was limited by the readout time of the CCD. Therefore, similar experiments were performed outside the X-ray beamline inspecting the VIS-scattering only. Here the time resolution was in the order of 1 s. The samples were exposed to pulses of 5, 10, 15 and
60 s again separated by 60 s in dark. In contrast to the X-ray experiment, the intensity of the ®rst-order grating peak was detected continuously (Fig. 3). A multiple step development mechanism consisting of at least three different processes could be observed. A very fast increase of intensity (t < 1 s) at the beginning is followed by a further increase with a slope up to 20 times smaller than the ®rst one. Immediately after shadowing the inscribing light, the grating intensity decays exponentially indicating partial relaxation of the polymer after release of the light induced force. The remaining grating intensity depends on the pulse duration again. The ®rst steep slope is equal for all pulse lengths and can be associated with an elastic process. Pulses shorter than about 1 s would not result in a grating formation. Only the second inelastic process results in the creation of a permanent grating. Its diffraction ef®ciency depends on the process duration. This explains qualitatively the ®ndings of the Xray experiment that has probed the development of the grating after relaxation. If the grating formation is accompanied by a periodic densi®cation of the polymer near the surface, a density grating and a surface relief grating have to appear simultaneously. Although the X-ray and the VIS experiment show different sensitivity we could not distinguish between the density and the surface relief grating as the main origin of the respective scattering process. Thus, we probed the created surface relief gratings ex situ by AFM after a respective
O. Henneberg et al. / Applied Surface Science 182 (2001) 272±279
275
Fig. 4. Several AFM surface pro®les recorded from samples after holographic exposure times of 2, 5, 10 and 180 s.
single shot of de®nite duration (Fig. 4). Up to an exposure time of 2 s there is no surface relief formation at all. The material response to the blue light is entirely elastic. After 5 s, a speckled surface modi®cation starts rising with an average height of 13 nm. After longer exposure the relief height was not grown as much but the surface relief becomes rather uniform. The ®nal height does not exceed 22 nm for short time illumination. Finally, we probed the grating formation during continuous inscription using X-ray and VIS scattering. In agreement with previous results [1,5], the continuous inscription of pattern into the polymer ®lm results in a permanent increase of the diffracted VIS light intensity. At the same time, the X-ray scattered grating peak intensity shows different behaviour (Fig. 5). After an initial increase within about 60 s up to a maximum, IX-max, it starts decreasing and saturates at a certain intensity level (here 0:8 I X-max). 4. Modelling In order to interpret the dynamics of grating formation, we carried out preliminary modelling in terms
of ®nite element (FE) calculations. Due to the twodimensional problem in question the axis x was chosen to be parallel and the z-axis to be perpendicular to the polymer surface. The model utilised a sinusoidal force varying in the x-direction [5,10,11]. Considering absorption effects of the blue light, it was assumed that the force fx decays exponentially with the distance from the ®lm surface z: z h0 2px f A exp (2) sin D m where A is a force density, h0 an initial ®lm thickness, m the light penetration depth and D is the grating period. To simulate a transient behaviour, we applied a cyclic external force: f f f 0
0 t t1 t1 t T
(3)
where T is the oscillation period of actinic light, and t1 is the pulse length. Results from numerous inscriptions of gratings indicate that under illumination, the polymer behaves like an isotropic VE material. Using hereditary integral approach a simple linear VE approach with two
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Fig. 5. Development of the VIS and X-ray ®rst-order grating peak intensity, respectively, during continuous exposure with a hologram of polarised light at 488 nm. The inset shows a measured CCD spectrum as example.
relaxation times, ti, i 1, 2, was found to be suf®cient to mimic the multiple inscriptions of gratings: Z t deij t0 0 sij t G t t0 dt (4) dt0 0 where sij are the components of the stress tensor and eij are those of the strain tensor, G is a time-dependent shear modulus: 2 X t E : G t Gn exp and G 0 tn 2 1 n n1 (5) Here E is Young's modulus, n the Poisson's ratio and tn are particular relaxation times of the system. The following material parameters were used in our study: initial densityr0 103 kg/m3, E 1 MPa, n 0:35, 0.40, 0.45, G1 0:32, G2 0:04, t1 1 s, t2 50 s. As the key point of our model, we assume that due to the light induced trans±cis isomerisations of azobenzene chromophores the polymer ®lm undergoes a considerable plasti®cation which reduces its original Young's modulus by at least three orders of magnitude. Thus, the chosen value of Young's modulus is similar to that of many other polymers at temperatures around the glass transition temperature. The FE analysis was implemented using the commercial software Mentat 3.1. A polymer block of 1 mm2 was chosen (h0 D 1 mm) as a ``sample''.
It was divided into 2500 square ®nite elements. Periodic boundary conditions were applied along x-direction. As a constraint no displacement of sample was allowed at the polymer substrate interface. The time evolution of the relief height and the density below the surface are shown in Fig. 6. As expected the application of a constant load, A 100 N/cm3, has resulted in an instantaneous elastic deformation followed by a continuous deformation with time (delayed elastic and viscous effects). A surface relief grating as well as a lateral density variation appeared from the very beginning of force application (instantaneous effect). During the ®rst seconds of illumination both pro®les can be described by sinusoidal functions of equal period D. No phase shift between the relief and density gratings appears: the polymer material is slightly compressed at the region of surface peaks and slightly expanded in between. With increasing time the polymer material becomes also compressed in the region of trenches (see Fig. 6b). With increase of sample compressibility the amplitude of the surface relief decreases and the density grating becomes more pronounced resulting in comparable density changes at the peaks and valleys of the surface relief. These results were obtained for m 1:0 mm, which means that the light penetrates down to the substrate. Decreasing the penetration depth, the amplitude of the surface relief decreases as well and for a suf®ciently small m (m 0:1 mm) the
O. Henneberg et al. / Applied Surface Science 182 (2001) 272±279
277
Fig. 7. FE calculation of the VIS experiment using pulse exposure (compare Fig. 3).
Fig. 6. Time development of the surface relief grating, h(x) (a) and the density modulation, r(x)/r0 (b) obtained by FE modelling just in the beginning and after 30, 60 and 90 s of light exposure.
relief amplitude saturates right after 2±3 min of illumination. Using the VE model, we are able to explain the ®ndings of the VIS experiment as shown in Fig. 7. We used the same pulse lengths separated by 60 s as in the experiment. Here we assumed that the scattered light intensity is proportional to the ®lm deformation considering that the Bessel function, describing the VIS intensity, grows linear if the relief amplitude and the density difference is small. The simulation does match right functional behaviour as found by the VIS experiment (Fig. 3) and in the sense of the accumulated grating formation the X-ray experiment (Fig. 2) as well. However, the model does not consider the kinetics of hardening the polymer material in the absence of illumination. This has to be ®nd out with a more elaborated model.
Using Fig. 6, we can distinguish at least three gratings: a surface relief grating with an amplitude hmax hmin , a ®rst density grating with r1,max at the position hmax, and a second density grating with r2,max at the position hmin. Assuming different time evolutions of the three gratings, we are able to explain the different time dependence of the VIS and X-ray scattering at continuous exposure. The VIS scattering intensity has to be described by Bessel functions: 2 X IVIS I0 Jm f t (6) i using fi t
2p DA1 t DA2 t DA3 t lVIS
(7)
and assuming a general time dependence of the coef®cients t DAi Ai;max 1 exp : (8) ti It can be shown that IVIS will grow and saturate after several minutes similar to predictions of FE analysis. This result does not depend on the absolute values of the time constants, ti, but we assume that A1;max t hmax t hmin t > A2;3;max r2;3;max t hri and t1 t2 ! t3 .
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Fig. 8. Semi-empirical modelling of the evolution of the VIS, j(t), and X-ray, F(t)2, grating peak intensities during continuous exposure using t1 t2 2 s and t3 200 s.
Such a behaviour is not obtained in the X-ray case. Here the scattering intensity is proportional to the square of the X-ray structure factor F IX-ray I0 F t2
(9)
given by the Fourier transform of the grating pro®les X Z 2p 2p F t exp i x DAi sin x di : lX-ray lX-ray i (10) Using A1;max t hmax t hmin t and A2;3;max r2;3;max t hri, with d1 d2 0 but d3 p and the same time constants as used at the VIS simulation, the X-ray intensity is found to grow as long as t1 dominates the evolution process but decreases later on as found in experiment. One possible scenario is shown in Fig. 8. The decrease of X-ray intensity becomes pronounced even if the layer thickness is small because r1,max and r2,max may achieve a similar value. The model has to be checked with a more precise measurement. 5. Conclusions Both time resolved experiments can be explained by the simultaneous formation of a density grating below the ®lm surface and the surface relief grating on top of the ®lm. Using the viscoelastic ¯ow model, we can understand that the response of the polymer
material to the light induced lateral force is entirely elastic during the 1±2 s but plasti®cation takes place later on. The key assumption of our model is the light induced reduction of the Young's modulus during exposure down to values which are typical for polymers close to the glass transition temperature. Surface relief grating and density grating behave differently with time. We can distinguish between two density gratings: the ®rst grating develops from the beginning below the peaks of the surface grating and the second one develops later below the valleys of the surface grating. This may explain the different time evolution of VIS and X-ray grating peaks measured at continuous exposure. Our experiments have been performed at very low laser power. To understand how high laser powers affect the formation of gratings further experiments have to be performed and the modelling has to be adjusted as well. Several experiments are also under way to clarify the origin of the lateral force causing the material transport, which is still an unsolved question. Acknowledgements This work was supported by the DFG under grant Pi217/17-1 and 436 RUS 17/18/01. M.G. Saphiannikova acknowledges support from Russian Foundation for Fundamental Research (grant 99-03-33314). The authors thank for allocating beam time and Dr. Ken Finkelstein for supporting the X-ray experiment. Additional thanks is addressed to Dr. LiFeng Chi (University of MuÈnster) for giving opportunity and assistance in the AFM measurements. References [1] P. Rochon, E. Batalla, A. Natansohn, Appl. Phys. Lett. 66 (1995) 136. [2] D.Y. Kim, S.K. Tripathy, L. Li, J. Kumar, Appl. Phys. Lett. 66 (1995) 1166. [3] C.J. Barrett, A.L. Natansohn, P.L. Rochon, J. Phys. Chem. 100 (1996) 8836. [4] D.Y. Kim, T.S. Lee, X. Wang, X.L. Jiang, L. Li, J. Kumar, S.K. Tripathy, SPIE 2298 (1995) .195. [5] C.L. Barrett, P.L. Rochon, A.L. Natansohn, J. Chem. Phys. 109 (1998) 1505. [6] T.G. Pedersen, P.M. Johansen, N.C.R. Holme, P.S. Ramanujam, S. Hvilsted, Phys. Rev. Lett. 80 (1998) 89.
O. Henneberg et al. / Applied Surface Science 182 (2001) 272±279 [7] N.K. Viswanathan, S. Balasubramanian, L. Li, J. Kumar, S.K. Tripathy, J. Phys. Chem. B102 (1998) 6064. [8] P. Le®n, C. Fiorini, J.-M. Nunzi, Pure Appl. Opt. 7 (1998) 71. [9] Th. Geue, M. Schultz, J. Grenzer, U. Pietsch, A. Natansohn, P. Rochon, J. Appl. Phys. 87 (11) (2000) 7712.
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[10] S. Bian, L. Li, J. Kumar, D.Y. Kim, J. Williams, S.K. Tripathy, Appl. Phys. Lett. 73 (1998) 1817. [11] K. Sumaru, T. Yamanaka, T. Fukuda, H. Matsuda, Appl. Phys. Lett. 75 (1999) 1878.
Formation and dynamics of polymer surface relief gratings O. Henneberga,*, Th. Geuea, M. Saphiannikovaa, U. Pietscha, P. Rochonb, A. Natansohnc a
Institute of Physics, University of Potsdam, P.O.B. 601553, D-14415 Potsdam, Germany b Department of Physics, Royal Military College, Kingston, Ont., Canada K7K 5L0 c Department of Chemistry, Queen's University, Kingston, Ont., Canada K7L 3N6
Abstract Time resolved VIS and X-ray scattering experiments have been performed during the formation of a surface relief grating on a polymer ®lm containing an azobenzene side-chain homopolymer (poly{(4-nitrophenyl)[4-[[2-(methacryloyloxy)ethyl]ethylamino]phenyl]diazene} (pDR1M), T G 1298C) upon holographic exposure with circularly polarised laser light of 488 nm. Using ®xed geometric conditions for both experiments, the time evolution of the ®rst order grating peak was observed. Short time illumination with a light pattern of about 50 mW/cm2 shows that the evolution of the VIS and the X-ray signal depends on the pulse length of exposure. Several elastic as well as plastic processes appear. The shortest pulse length of 5 s applied at the X-ray experiment did not create a permanent grating. This is con®rmed by ex situ AFM inspections recorded after holographic treatment. VIS inspection with better time resolution reveals an elastic process during the ®rst seconds but plasti®cation of the material for longer exposure times. Partial relaxation takes place when the light is switched off. Cyclic light treatments create two periodic density gratings below the surface and a surface relief grating as well. Both scattering experiments can be explained qualitatively by ®nite element calculations assuming a viscoelastic (VE) ¯ow model. # 2001 Elsevier Science B.V. All rights reserved. PACS: 61.10.Kw; 61.44.e; 68.35.Rh; 68.65.g; 42.25.Fx Keywords: Polymer surface; Relief gratings; Viscoelastic ¯ow model
1. Introduction It is widely known that a surface relief pattern can be inscribed on the surface of an amorphous polymer ®lm containing azobenzene moieties [1±5]. This is done by exposing the sample with a periodic holographic pattern of circularly polarised light of 488 nm. This wavelength is close to the absorption maximum associated with the trans±cis isomerisation of the * Corresponding author. Tel.: 49-331-977-1278. E-mail address: [email protected] (O. Henneberg).
azobenzene moieties. Because these moieties require different free volume the periodic light pattern initiates a periodic pressure gradient along the surface. It induces material ¯ow already at temperatures 100 K below the glass transition temperature, TG, of the polymers and produces a periodic surface grating with approximately sinusoidal shape. Depending on the power of illumination and on the state of light polarisation, the grating depth may approach several hundreds of nanometers. A number of mechanisms had been proposed to explain the massive displacement that occurs even at low laser power [6±8]. Nevertheless, it is of particular interest to learn more about
0169-4332/01/$ ± see front matter # 2001 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 9 - 4 3 3 2 ( 0 1 ) 0 0 4 4 4 - 5
O. Henneberg et al. / Applied Surface Science 182 (2001) 272±279
the nature of this induced material transport in polymers. As a ®rst step, we have studied the thermal erasure of the surface relief grating [9]. During those experiments, we investigated poly{(4-nitrophenyl)[4-[[2(methacryloyloxy)ethyl]ethylamino]phenyl]diazene} (pDR1M), an amorphous polymer with no liquid crystalline properties. VIS and X-ray scattering were used simultaneously in order to reach two different length scales. Close to TG, we found a different behaviour of the X-ray and VIS grating peaks. Whereas the VIS peak intensity vanished 10±158 below TG, the X-ray peak had increased further before it also disappeared at TG [9]. This evidence initiated the assumption that the surface relief patterning is accompanied by a density modulation below the surface with a different temperature dependence. In the present study, we report on time resolved measurements of the grating formation process. To do this, we installed the apparatus for holographic exposure of the ®lm with circularly polarised light at a beamline of a Synchrotron Radiation facility (CHESS, Wilson Laboratory, Ithaka) and both the X-ray and VIS light scattering from the grating were detected after/during short time exposure and during continuous illumination. VIS probes mainly the development of the surface relief via phase contrast whereas X-rays are sensitive for charge density differences, i.e. to the induced material ¯ow below the sample surface. The periodically varying ratio of the light induced trans±cis isomerisation of the azobenzene moieties creates a lateral force acting in the polymer. The material response is elastic and plastic as well depending on the pulse length of exposure. The experimental results are interpreted in terms of ®nite element calculations using a viscoelastic (VE) ¯ow model implying the assumption that the light induced decrease of the elastic modulus is the key process for the understanding of the induced material ¯ow. 2. Experimental The samples consist of 400 nm thick ¯at polymer ®lms of pDR1M (T G 1298C) that has been spun onto a clean glass substrate. Surface relief gratings were inscribed onto the polymer ®lms using the holographic interference pattern of two plane waves
273
Fig. 1. Experimental setup used for simultaneous detection of VIS and X-ray diffraction.
produced by counter-circularly polarised beams obtained from an argon ion laser operating at the wavelength of 488 nm and at a power density of 50 mW/cm2. The X-ray experiments were performed at CHESS (Cornell University Ithaca, NY; l 0:1238 nm) using an X-ray CCD camera (ADSC Quantum CCD, 1152 1152 pixels) as 2-dimensional detector, additional laser scattering (l 633 nm) at RMC Kingston using the same setup (Fig. 1). We inscribed the gratings near to the absorption maximum of pDR1M with an Ar-ion laser at 488 nm by means of a double beam interference (holographic inscription). From the raw X-ray CCD data, a substantial background was removed and the intensity was integrated over the respective grating peak. Ex situ AFM inspection of several sample surfaces after short time exposure have been performed using a Nanoscope IIIa (Digital Instruments) in tapping mode. 3. Experimental results The ef®ciency of surface pattern formation is usually probed by the scattering intensity of the ®rst grating peak using a probing laser. A similar experiment can be performed using X-rays at grazing angles. In reciprocal space the angles of incidence and exit ai and af, respectively, de®ne the out-of-plane and inplane momentum transfer qz and qx: qz
2p sin ai sin af ; l
qx
2p cos ai cos af l (1)
274
O. Henneberg et al. / Applied Surface Science 182 (2001) 272±279
Fig. 2. Development of ®rst-order X-ray grating peak intensity, after exposure with shots of an interference pattern of polarised light at 488 nm for 5, 10, 15 and 60 s duration.
Fig. 3. Time development of the ®rst-order VIS grating peak intensity during short pulse exposure.
where qx 0, i.e. ai af , de®nes the specular scattering condition. Beside the specular one additional peaks appear whenever Dqx 2p= D cos f, where D is the lateral spacing of the surface relief grating and f is the angle between the incidence beam and the grating normal [9]. Using ®xed ai, the CCD registers several af simultaneously probing a particular cut across the reciprocal space. In the following, we will focus our interest on the time evolution of the ®rstorder grating peak (see inset of Fig. 2). In order to analyse the initial process of grating formation, we probed its increasing intensity after several short term illuminations of the polymer surface. The ®lm was exposed to a series of pulses with 5, 10, 15 and 60 s duration each followed by a 10 s readout time for the CCD camera in dark (Fig. 2). It was found that the maximum attainable X-ray grating intensity IX-max depends on the pulse length of the blue light. After a total exposure time of 60 s, the 10, 15 and 60 s pulses approach almost equal IX-max whereas the 5 s pulses gave much lower ef®ciency of the grating formation. Obviously, 5 s marks a critical time of the formation process for the chosen laser power. Unfortunately, the minimal time resolution of the X-ray experiment was limited by the readout time of the CCD. Therefore, similar experiments were performed outside the X-ray beamline inspecting the VIS-scattering only. Here the time resolution was in the order of 1 s. The samples were exposed to pulses of 5, 10, 15 and
60 s again separated by 60 s in dark. In contrast to the X-ray experiment, the intensity of the ®rst-order grating peak was detected continuously (Fig. 3). A multiple step development mechanism consisting of at least three different processes could be observed. A very fast increase of intensity (t < 1 s) at the beginning is followed by a further increase with a slope up to 20 times smaller than the ®rst one. Immediately after shadowing the inscribing light, the grating intensity decays exponentially indicating partial relaxation of the polymer after release of the light induced force. The remaining grating intensity depends on the pulse duration again. The ®rst steep slope is equal for all pulse lengths and can be associated with an elastic process. Pulses shorter than about 1 s would not result in a grating formation. Only the second inelastic process results in the creation of a permanent grating. Its diffraction ef®ciency depends on the process duration. This explains qualitatively the ®ndings of the Xray experiment that has probed the development of the grating after relaxation. If the grating formation is accompanied by a periodic densi®cation of the polymer near the surface, a density grating and a surface relief grating have to appear simultaneously. Although the X-ray and the VIS experiment show different sensitivity we could not distinguish between the density and the surface relief grating as the main origin of the respective scattering process. Thus, we probed the created surface relief gratings ex situ by AFM after a respective
O. Henneberg et al. / Applied Surface Science 182 (2001) 272±279
275
Fig. 4. Several AFM surface pro®les recorded from samples after holographic exposure times of 2, 5, 10 and 180 s.
single shot of de®nite duration (Fig. 4). Up to an exposure time of 2 s there is no surface relief formation at all. The material response to the blue light is entirely elastic. After 5 s, a speckled surface modi®cation starts rising with an average height of 13 nm. After longer exposure the relief height was not grown as much but the surface relief becomes rather uniform. The ®nal height does not exceed 22 nm for short time illumination. Finally, we probed the grating formation during continuous inscription using X-ray and VIS scattering. In agreement with previous results [1,5], the continuous inscription of pattern into the polymer ®lm results in a permanent increase of the diffracted VIS light intensity. At the same time, the X-ray scattered grating peak intensity shows different behaviour (Fig. 5). After an initial increase within about 60 s up to a maximum, IX-max, it starts decreasing and saturates at a certain intensity level (here 0:8 I X-max). 4. Modelling In order to interpret the dynamics of grating formation, we carried out preliminary modelling in terms
of ®nite element (FE) calculations. Due to the twodimensional problem in question the axis x was chosen to be parallel and the z-axis to be perpendicular to the polymer surface. The model utilised a sinusoidal force varying in the x-direction [5,10,11]. Considering absorption effects of the blue light, it was assumed that the force fx decays exponentially with the distance from the ®lm surface z: z h0 2px f A exp (2) sin D m where A is a force density, h0 an initial ®lm thickness, m the light penetration depth and D is the grating period. To simulate a transient behaviour, we applied a cyclic external force: f f f 0
0 t t1 t1 t T
(3)
where T is the oscillation period of actinic light, and t1 is the pulse length. Results from numerous inscriptions of gratings indicate that under illumination, the polymer behaves like an isotropic VE material. Using hereditary integral approach a simple linear VE approach with two
276
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Fig. 5. Development of the VIS and X-ray ®rst-order grating peak intensity, respectively, during continuous exposure with a hologram of polarised light at 488 nm. The inset shows a measured CCD spectrum as example.
relaxation times, ti, i 1, 2, was found to be suf®cient to mimic the multiple inscriptions of gratings: Z t deij t0 0 sij t G t t0 dt (4) dt0 0 where sij are the components of the stress tensor and eij are those of the strain tensor, G is a time-dependent shear modulus: 2 X t E : G t Gn exp and G 0 tn 2 1 n n1 (5) Here E is Young's modulus, n the Poisson's ratio and tn are particular relaxation times of the system. The following material parameters were used in our study: initial densityr0 103 kg/m3, E 1 MPa, n 0:35, 0.40, 0.45, G1 0:32, G2 0:04, t1 1 s, t2 50 s. As the key point of our model, we assume that due to the light induced trans±cis isomerisations of azobenzene chromophores the polymer ®lm undergoes a considerable plasti®cation which reduces its original Young's modulus by at least three orders of magnitude. Thus, the chosen value of Young's modulus is similar to that of many other polymers at temperatures around the glass transition temperature. The FE analysis was implemented using the commercial software Mentat 3.1. A polymer block of 1 mm2 was chosen (h0 D 1 mm) as a ``sample''.
It was divided into 2500 square ®nite elements. Periodic boundary conditions were applied along x-direction. As a constraint no displacement of sample was allowed at the polymer substrate interface. The time evolution of the relief height and the density below the surface are shown in Fig. 6. As expected the application of a constant load, A 100 N/cm3, has resulted in an instantaneous elastic deformation followed by a continuous deformation with time (delayed elastic and viscous effects). A surface relief grating as well as a lateral density variation appeared from the very beginning of force application (instantaneous effect). During the ®rst seconds of illumination both pro®les can be described by sinusoidal functions of equal period D. No phase shift between the relief and density gratings appears: the polymer material is slightly compressed at the region of surface peaks and slightly expanded in between. With increasing time the polymer material becomes also compressed in the region of trenches (see Fig. 6b). With increase of sample compressibility the amplitude of the surface relief decreases and the density grating becomes more pronounced resulting in comparable density changes at the peaks and valleys of the surface relief. These results were obtained for m 1:0 mm, which means that the light penetrates down to the substrate. Decreasing the penetration depth, the amplitude of the surface relief decreases as well and for a suf®ciently small m (m 0:1 mm) the
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Fig. 7. FE calculation of the VIS experiment using pulse exposure (compare Fig. 3).
Fig. 6. Time development of the surface relief grating, h(x) (a) and the density modulation, r(x)/r0 (b) obtained by FE modelling just in the beginning and after 30, 60 and 90 s of light exposure.
relief amplitude saturates right after 2±3 min of illumination. Using the VE model, we are able to explain the ®ndings of the VIS experiment as shown in Fig. 7. We used the same pulse lengths separated by 60 s as in the experiment. Here we assumed that the scattered light intensity is proportional to the ®lm deformation considering that the Bessel function, describing the VIS intensity, grows linear if the relief amplitude and the density difference is small. The simulation does match right functional behaviour as found by the VIS experiment (Fig. 3) and in the sense of the accumulated grating formation the X-ray experiment (Fig. 2) as well. However, the model does not consider the kinetics of hardening the polymer material in the absence of illumination. This has to be ®nd out with a more elaborated model.
Using Fig. 6, we can distinguish at least three gratings: a surface relief grating with an amplitude hmax hmin , a ®rst density grating with r1,max at the position hmax, and a second density grating with r2,max at the position hmin. Assuming different time evolutions of the three gratings, we are able to explain the different time dependence of the VIS and X-ray scattering at continuous exposure. The VIS scattering intensity has to be described by Bessel functions: 2 X IVIS I0 Jm f t (6) i using fi t
2p DA1 t DA2 t DA3 t lVIS
(7)
and assuming a general time dependence of the coef®cients t DAi Ai;max 1 exp : (8) ti It can be shown that IVIS will grow and saturate after several minutes similar to predictions of FE analysis. This result does not depend on the absolute values of the time constants, ti, but we assume that A1;max t hmax t hmin t > A2;3;max r2;3;max t hri and t1 t2 ! t3 .
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Fig. 8. Semi-empirical modelling of the evolution of the VIS, j(t), and X-ray, F(t)2, grating peak intensities during continuous exposure using t1 t2 2 s and t3 200 s.
Such a behaviour is not obtained in the X-ray case. Here the scattering intensity is proportional to the square of the X-ray structure factor F IX-ray I0 F t2
(9)
given by the Fourier transform of the grating pro®les X Z 2p 2p F t exp i x DAi sin x di : lX-ray lX-ray i (10) Using A1;max t hmax t hmin t and A2;3;max r2;3;max t hri, with d1 d2 0 but d3 p and the same time constants as used at the VIS simulation, the X-ray intensity is found to grow as long as t1 dominates the evolution process but decreases later on as found in experiment. One possible scenario is shown in Fig. 8. The decrease of X-ray intensity becomes pronounced even if the layer thickness is small because r1,max and r2,max may achieve a similar value. The model has to be checked with a more precise measurement. 5. Conclusions Both time resolved experiments can be explained by the simultaneous formation of a density grating below the ®lm surface and the surface relief grating on top of the ®lm. Using the viscoelastic ¯ow model, we can understand that the response of the polymer
material to the light induced lateral force is entirely elastic during the 1±2 s but plasti®cation takes place later on. The key assumption of our model is the light induced reduction of the Young's modulus during exposure down to values which are typical for polymers close to the glass transition temperature. Surface relief grating and density grating behave differently with time. We can distinguish between two density gratings: the ®rst grating develops from the beginning below the peaks of the surface grating and the second one develops later below the valleys of the surface grating. This may explain the different time evolution of VIS and X-ray grating peaks measured at continuous exposure. Our experiments have been performed at very low laser power. To understand how high laser powers affect the formation of gratings further experiments have to be performed and the modelling has to be adjusted as well. Several experiments are also under way to clarify the origin of the lateral force causing the material transport, which is still an unsolved question. Acknowledgements This work was supported by the DFG under grant Pi217/17-1 and 436 RUS 17/18/01. M.G. Saphiannikova acknowledges support from Russian Foundation for Fundamental Research (grant 99-03-33314). The authors thank for allocating beam time and Dr. Ken Finkelstein for supporting the X-ray experiment. Additional thanks is addressed to Dr. LiFeng Chi (University of MuÈnster) for giving opportunity and assistance in the AFM measurements. References [1] P. Rochon, E. Batalla, A. Natansohn, Appl. Phys. Lett. 66 (1995) 136. [2] D.Y. Kim, S.K. Tripathy, L. Li, J. Kumar, Appl. Phys. Lett. 66 (1995) 1166. [3] C.J. Barrett, A.L. Natansohn, P.L. Rochon, J. Phys. Chem. 100 (1996) 8836. [4] D.Y. Kim, T.S. Lee, X. Wang, X.L. Jiang, L. Li, J. Kumar, S.K. Tripathy, SPIE 2298 (1995) .195. [5] C.L. Barrett, P.L. Rochon, A.L. Natansohn, J. Chem. Phys. 109 (1998) 1505. [6] T.G. Pedersen, P.M. Johansen, N.C.R. Holme, P.S. Ramanujam, S. Hvilsted, Phys. Rev. Lett. 80 (1998) 89.
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