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Heat load problems in deep X-ray lithography
Nuclear Instruments and Methods in Physics Research A 467–468 (2001) 1265–1268
Heat load problems in deep X-ray lithography I. Cudinb, F. De Bonab, A. Gambittaa, F. P!erenn"esa,*, A. Turcheta a
Sincrotrone Trieste, Societa Consoirtile P. Azioni, Micro Fabrication Group, in Area Science Park, S.S. 14, km 163, 5, 34012 Trieste, Italy b Universita" di Udine, Via delle Scienze 208, 33100 Udine, Italy
Abstract A 3D mathematical model of a complete Deep X-Ray Lithography scanning unit based on the Finite Element Method (FEM) was developed to analyse the replication errors induced by the thermoelastic deformations occurring under irradiation. Different thermal and mechanical constraint conditions were considered in order to evaluate the maximum displacements of the irradiated mask area. The obtained results show that, to evaluate the replication errors, the support ring and its mechanical fittings have to be carefully considered in the model. It is observed that the absolute position error and the blur error and the error induced by the thermal expansion of the mask are both position dependent. # 2001 Elsevier Science B.V. All rights reserved. Keywords: Deep X-Ray lithography; X-ray mask; Thermoelasticity; FEM; Transient analysis
1. Introduction Deep X-Ray Lithography (DXRL) is the most important step of the LIGA (Lithographie, Galvanoformung, Abformung) microfabrication process [1]. In DXRL, a synchrotron radiation is used to irradiate a photosensitive resist layer through a mask to reproduce a given pattern; in the case of high power density X-ray sources, during the exposition relevant mask and resist thermoelastic deformations can occur, thus affecting the accuracy of the final structure.
*Corresponding author. Tel.: +39-040-3758018; fax: +39040-3758565. E-mail address: [email protected] (F. Pe´renne`s).
The thermoelastic analysis of the DXRL process has been developed only recently; in Ref. [2] a three dimensional time dependent FEM model of the thermoelastic mask deformation is proposed; a similar approach has followed in Ref. [3], where a thorough analysis of the temperature distribution on the mask and resist has been carried out. The temperature distribution obtained numerically was verified experimentally in Ref. [2] using ceramic temperature sensors and in Ref. [3] using a special mask. In these two works, to reduce the complexity of the FEM model, the nodal constraint conditions have been strongly simplified. In Ref. [4], due to the particularly high power density of SR source, face cooling of the mask is considered, therefore the results obtained cannot be applied to the case where a standard DXRL scanner is used.
0168-9002/01/$ - see front matter # 2001 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 9 0 0 2 ( 0 1 ) 0 0 6 5 5 - 6
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I. Cudin et al. / Nuclear Instruments and Methods in Physics Research A 467–468 (2001) 1265–1268
The aim of this work is to provide a 3D FEM model of an existing standard DXRL scanning unit that permits an effective simulation of the temperature distribution on the mask ring and membrane and the resulting displacement field, taking into account the actual boundary conditions. Three different analyses, at increasing level of complexity, will be carried out: the steady-state case, a transient analysis with heat load in fixed position, a transient analysis simulating scanning movement.
2. Steady-state analysis Fig. 1 shows the FEM model of the DXRL unit (Scanner type Jenoptik DEXO2, Germany) and the temperature distribution obtained using the bending magnet synchrotron radiation beam of Elettra (lc ¼ 0:385 nm). Not only the mask membrane/absorber and the resist layer are considered, but also the helium film filling the gap (50 mm) between the mask and the resist, and the heat exchanger ring and fitting. One important new feature of the model compare to Refs. [2,3] is to account for the temperature distribution of the mask support ring whose thermoelastic behaviour could contribute to the overall deformation of the mask membrane. 2340 shell (5nodes) isoparametric elements and 5400 brick (4 nodes) isoparametric elements were
Fig. 1. FEM model and temperature distribution (case 2).
used; the overall model has 9375 thermal degree of freedom and 5038 mechanical degrees of freedom. The FEM pre- and post-processor code Patran [5] and the Abaqus [6] FEM solver code were used. Three different thermal load conditions were considered: (1) Uniform heat flux on the overall exposed area of the mask (simulating an infinite scanning speed). (2) Heat flux fixed on the central position of the mask (zero scanning speed, centred beam). (3) Heat flux on the upper vertical position (zero scanning speed with the scanner in the lower position). It must be noticed that condition (1) permits the evaluation of the lowest maximum temperature occurring under direct irradiation to be obtained. The thermal conditions (2) and (3) provide the upper values of the maximum temperature in points located into the irradiated area. In case (1) a maximum temperature of 288C was obtained; the highest temperature value (328C) was obtained in case (2). Mask deformation is not only affected by the temperature distribution, but also by the constraint conditions; in the considered case the mask fitting is obtained by using two pins that do not permit radial expansion of the mask outer ring. As this constraint condition is difficult to be modelled correctly, two simplified FEM analyses were performed, in order to provide the upper and lower displacement bounds: in the first case only a single node of the outer mask ring surface was constrained, thus permitting the mask and ring free expansion; in this case a maximum displacement of 6.7 mm was obtained. In a second model the in-plane degrees of freedom of two nodes of the ring outer surface were set equal to zero, thus simulating an ideal fitting with no backlash and infinite stiffness; in this case, that obviously fits better the actual conditions, a maximum displacement of 1.65 mm was evaluated. The obtained results in term of displacements show also that mask deformations are not only due to the thermal expansion of the mask itself, but also to the thermal expansion of the ring, which can give a contribution up to 30% of the
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overall displacement. This effect cannot be emphasised with the model presented in Ref. [2] where a fully constrained support ring with a uniform temperature distribution was considered.
3. Transient analysis: Heat load in fixed position The transient analysis is solved by a fully implicit algorithm, thus avoiding oscillations of the solution due to numerical errors. The obtained results show, in agreement with [2] and [3] that the temperature distribution is mainly affected by the mask substrate conductivity. For this reason a mask membrane material with high conductivity (i.e. beryllium) has to be preferred. The temperature rise in the case of a 600 mm beryllium mask is of 128C with a time constant of 25 s (case 2). A 5 mm titanium mask shows a higher temperature rise (458C) and a smaller time constant (7 s) due to its lower thickness and conductivity. Similar results are obtained considering the displacements versus time.
Fig. 2. Temperature versus time in a beryllium mask at two different positions on the mask (scanning speed=10 mm/s).
4. Transient analysis: non-zero scanning speed In this case, the thermal loads are position and time dependent. The beam is simulated with a uniform heat distribution (0.04 W/mm2) of rectangular shape (5 60 mm2) moving stepwise. The solution shows (Fig. 2) that after few seconds the steady-state condition is reached and the temperatures in the mask follows a periodic fluctuation around a constant value at the scanning frequency. The temperature variations are dependent on the position on the mask as shown in Fig. 2. At increasing scanning speeds, a reduction both in the temperature rise and in the oscillation amplitude is observed; this effect is less evident at speed higher than 20 mm/s. It must be noted that, as pointed out in Ref. [2], only the displacements occurring in mask locations that are under exposition have to be considered. Fig. 3 shows the vertical displacements of three different points of the mask located, respectively, on the upper, lower and central position of the scanner. The results show that the mask central
Fig. 3. Vertical displacements of the mask centre, lower and upper edge (replication time is underlined).
points irradiated in the ascending scan are in different positions when they are irradiated in the descending scan; consequently, the beam transfers the mask pattern in different positions producing an error in the final structure, generally referred to as blur error. This effect is less evident in locations far away from the centre of the mask, where a static displacement prevails, producing a position error in the replicated structure. The relative contribution of these two kinds of error is also affected by the constraint conditions of the ring: the position errors are larger if the mask is free to
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expand, on the contrary blur effects prevail if the ring is overconstrained.
5. Conclusions A correct prediction of the mask displacement field requires the support ring and its mechanical fitting to be included in the model. Thermal expansion of the mask induces an absolute position error and a blur error. Both types of errors are position dependent and can be reduced increasing the scanning speed, but their relative contribution to the overall replication process accuracy is also strongly affected by the mask holder constrain conditions. It must also be noted that the proposed analysis mainly address to errors induced by mask distortions, as the hypothesis of a mask membrane 100% coated by a gold absorber (20 mm thick) has been considered. Future work should include the analysis of real mask pattern followed by an experimental verification.
Acknowledgements This work is partly supported by the Commission of the European Community (EC-TMR project FMRX-CT97-0140).
References [1] F. De Bona, M. Matteucci, J. Mohr, F.J. Pantenburg, S. Zelenika, in: E. Kulianic 0 (Ed.), Advanced Manufacturing Systems and Technology, Springer, Wien New York, 1996, pp. 487–493. [2] G. Feiertag, M. Schmidt, A. Schmidt, Microelectron. Eng. 27 (1995) 513. [3] M. Neumann, F.J. Pantenburg, M. Rohde, M. Sesterhen, Microelectron. 28 (1997) 349. [4] Khounsary, D Chojnowski, D.C. Mancini, B. Lai, R. Dejus, SPIE 3151 (1997) 92. [5] MSC/Patran, the MacNeal Schwendler Corporation, Rel.8.0, Los Angeles, 1998. [6] Abaqus Theory Manual, Hibbit, Karlsson & Sorensen, Inc., Version 5.8, Pawtucket, 1998.
Heat load problems in deep X-ray lithography I. Cudinb, F. De Bonab, A. Gambittaa, F. P!erenn"esa,*, A. Turcheta a
Sincrotrone Trieste, Societa Consoirtile P. Azioni, Micro Fabrication Group, in Area Science Park, S.S. 14, km 163, 5, 34012 Trieste, Italy b Universita" di Udine, Via delle Scienze 208, 33100 Udine, Italy
Abstract A 3D mathematical model of a complete Deep X-Ray Lithography scanning unit based on the Finite Element Method (FEM) was developed to analyse the replication errors induced by the thermoelastic deformations occurring under irradiation. Different thermal and mechanical constraint conditions were considered in order to evaluate the maximum displacements of the irradiated mask area. The obtained results show that, to evaluate the replication errors, the support ring and its mechanical fittings have to be carefully considered in the model. It is observed that the absolute position error and the blur error and the error induced by the thermal expansion of the mask are both position dependent. # 2001 Elsevier Science B.V. All rights reserved. Keywords: Deep X-Ray lithography; X-ray mask; Thermoelasticity; FEM; Transient analysis
1. Introduction Deep X-Ray Lithography (DXRL) is the most important step of the LIGA (Lithographie, Galvanoformung, Abformung) microfabrication process [1]. In DXRL, a synchrotron radiation is used to irradiate a photosensitive resist layer through a mask to reproduce a given pattern; in the case of high power density X-ray sources, during the exposition relevant mask and resist thermoelastic deformations can occur, thus affecting the accuracy of the final structure.
*Corresponding author. Tel.: +39-040-3758018; fax: +39040-3758565. E-mail address: [email protected] (F. Pe´renne`s).
The thermoelastic analysis of the DXRL process has been developed only recently; in Ref. [2] a three dimensional time dependent FEM model of the thermoelastic mask deformation is proposed; a similar approach has followed in Ref. [3], where a thorough analysis of the temperature distribution on the mask and resist has been carried out. The temperature distribution obtained numerically was verified experimentally in Ref. [2] using ceramic temperature sensors and in Ref. [3] using a special mask. In these two works, to reduce the complexity of the FEM model, the nodal constraint conditions have been strongly simplified. In Ref. [4], due to the particularly high power density of SR source, face cooling of the mask is considered, therefore the results obtained cannot be applied to the case where a standard DXRL scanner is used.
0168-9002/01/$ - see front matter # 2001 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 9 0 0 2 ( 0 1 ) 0 0 6 5 5 - 6
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I. Cudin et al. / Nuclear Instruments and Methods in Physics Research A 467–468 (2001) 1265–1268
The aim of this work is to provide a 3D FEM model of an existing standard DXRL scanning unit that permits an effective simulation of the temperature distribution on the mask ring and membrane and the resulting displacement field, taking into account the actual boundary conditions. Three different analyses, at increasing level of complexity, will be carried out: the steady-state case, a transient analysis with heat load in fixed position, a transient analysis simulating scanning movement.
2. Steady-state analysis Fig. 1 shows the FEM model of the DXRL unit (Scanner type Jenoptik DEXO2, Germany) and the temperature distribution obtained using the bending magnet synchrotron radiation beam of Elettra (lc ¼ 0:385 nm). Not only the mask membrane/absorber and the resist layer are considered, but also the helium film filling the gap (50 mm) between the mask and the resist, and the heat exchanger ring and fitting. One important new feature of the model compare to Refs. [2,3] is to account for the temperature distribution of the mask support ring whose thermoelastic behaviour could contribute to the overall deformation of the mask membrane. 2340 shell (5nodes) isoparametric elements and 5400 brick (4 nodes) isoparametric elements were
Fig. 1. FEM model and temperature distribution (case 2).
used; the overall model has 9375 thermal degree of freedom and 5038 mechanical degrees of freedom. The FEM pre- and post-processor code Patran [5] and the Abaqus [6] FEM solver code were used. Three different thermal load conditions were considered: (1) Uniform heat flux on the overall exposed area of the mask (simulating an infinite scanning speed). (2) Heat flux fixed on the central position of the mask (zero scanning speed, centred beam). (3) Heat flux on the upper vertical position (zero scanning speed with the scanner in the lower position). It must be noticed that condition (1) permits the evaluation of the lowest maximum temperature occurring under direct irradiation to be obtained. The thermal conditions (2) and (3) provide the upper values of the maximum temperature in points located into the irradiated area. In case (1) a maximum temperature of 288C was obtained; the highest temperature value (328C) was obtained in case (2). Mask deformation is not only affected by the temperature distribution, but also by the constraint conditions; in the considered case the mask fitting is obtained by using two pins that do not permit radial expansion of the mask outer ring. As this constraint condition is difficult to be modelled correctly, two simplified FEM analyses were performed, in order to provide the upper and lower displacement bounds: in the first case only a single node of the outer mask ring surface was constrained, thus permitting the mask and ring free expansion; in this case a maximum displacement of 6.7 mm was obtained. In a second model the in-plane degrees of freedom of two nodes of the ring outer surface were set equal to zero, thus simulating an ideal fitting with no backlash and infinite stiffness; in this case, that obviously fits better the actual conditions, a maximum displacement of 1.65 mm was evaluated. The obtained results in term of displacements show also that mask deformations are not only due to the thermal expansion of the mask itself, but also to the thermal expansion of the ring, which can give a contribution up to 30% of the
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overall displacement. This effect cannot be emphasised with the model presented in Ref. [2] where a fully constrained support ring with a uniform temperature distribution was considered.
3. Transient analysis: Heat load in fixed position The transient analysis is solved by a fully implicit algorithm, thus avoiding oscillations of the solution due to numerical errors. The obtained results show, in agreement with [2] and [3] that the temperature distribution is mainly affected by the mask substrate conductivity. For this reason a mask membrane material with high conductivity (i.e. beryllium) has to be preferred. The temperature rise in the case of a 600 mm beryllium mask is of 128C with a time constant of 25 s (case 2). A 5 mm titanium mask shows a higher temperature rise (458C) and a smaller time constant (7 s) due to its lower thickness and conductivity. Similar results are obtained considering the displacements versus time.
Fig. 2. Temperature versus time in a beryllium mask at two different positions on the mask (scanning speed=10 mm/s).
4. Transient analysis: non-zero scanning speed In this case, the thermal loads are position and time dependent. The beam is simulated with a uniform heat distribution (0.04 W/mm2) of rectangular shape (5 60 mm2) moving stepwise. The solution shows (Fig. 2) that after few seconds the steady-state condition is reached and the temperatures in the mask follows a periodic fluctuation around a constant value at the scanning frequency. The temperature variations are dependent on the position on the mask as shown in Fig. 2. At increasing scanning speeds, a reduction both in the temperature rise and in the oscillation amplitude is observed; this effect is less evident at speed higher than 20 mm/s. It must be noted that, as pointed out in Ref. [2], only the displacements occurring in mask locations that are under exposition have to be considered. Fig. 3 shows the vertical displacements of three different points of the mask located, respectively, on the upper, lower and central position of the scanner. The results show that the mask central
Fig. 3. Vertical displacements of the mask centre, lower and upper edge (replication time is underlined).
points irradiated in the ascending scan are in different positions when they are irradiated in the descending scan; consequently, the beam transfers the mask pattern in different positions producing an error in the final structure, generally referred to as blur error. This effect is less evident in locations far away from the centre of the mask, where a static displacement prevails, producing a position error in the replicated structure. The relative contribution of these two kinds of error is also affected by the constraint conditions of the ring: the position errors are larger if the mask is free to
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expand, on the contrary blur effects prevail if the ring is overconstrained.
5. Conclusions A correct prediction of the mask displacement field requires the support ring and its mechanical fitting to be included in the model. Thermal expansion of the mask induces an absolute position error and a blur error. Both types of errors are position dependent and can be reduced increasing the scanning speed, but their relative contribution to the overall replication process accuracy is also strongly affected by the mask holder constrain conditions. It must also be noted that the proposed analysis mainly address to errors induced by mask distortions, as the hypothesis of a mask membrane 100% coated by a gold absorber (20 mm thick) has been considered. Future work should include the analysis of real mask pattern followed by an experimental verification.
Acknowledgements This work is partly supported by the Commission of the European Community (EC-TMR project FMRX-CT97-0140).
References [1] F. De Bona, M. Matteucci, J. Mohr, F.J. Pantenburg, S. Zelenika, in: E. Kulianic 0 (Ed.), Advanced Manufacturing Systems and Technology, Springer, Wien New York, 1996, pp. 487–493. [2] G. Feiertag, M. Schmidt, A. Schmidt, Microelectron. Eng. 27 (1995) 513. [3] M. Neumann, F.J. Pantenburg, M. Rohde, M. Sesterhen, Microelectron. 28 (1997) 349. [4] Khounsary, D Chojnowski, D.C. Mancini, B. Lai, R. Dejus, SPIE 3151 (1997) 92. [5] MSC/Patran, the MacNeal Schwendler Corporation, Rel.8.0, Los Angeles, 1998. [6] Abaqus Theory Manual, Hibbit, Karlsson & Sorensen, Inc., Version 5.8, Pawtucket, 1998.