- Email: [email protected]
Exposure optimization in high-resolution e-beam lithography
Microelectronic Engineering 83 (2006) 780–783 www.elsevier.com/locate/mee
Exposure optimization in high-resolution e-beam lithography Peter Hudek a
a,*
, Dirk Beyer
b
Vorarlberg University of Applied Sciences, Dornbirn A-6850, Austria Leica Microsystems Lithography GmbH, Jena D-07745, Germany
b
Available online 21 February 2006
Abstract In this paper a new method will be described, illustrating how to determine the optimized control point spread function (PSF) for proximity effect corrections (PEC) in e-beam lithography (EBL). A software tool called ‘‘PROX-In’’ was developed in order to help lithographers to determine the numerical inputs for an arbitrary PEC system to satisfy the high critical dimension (CD) control requirements as well as to compensate the shape bias in EBL in connection with the technology steps performed. PROX-In applies new methods allowing highly customized optimum numerical proximity parameter determinations by using a set of extracted experimental data. Compared with other presented methods, this approach is fast and effective. It does not require any additional technology steps and uses only standard measuring techniques. The reviewed method was successfully implemented into mask production for achieving the 90 nm technology node and below at different absorber stacks. It is also used for high-resolution e-beam direct write and SFIL template manufacturing with sub-50 nm resolution. Ó 2006 Elsevier B.V. All rights reserved. Keywords: Electron-beam lithography; Proximity effect, Maskmaking; Direct writing
1. Introduction From the very first moment when submicron feature sizes became the crucial factor for any patterning task, ebeam writing has been confronted with parasite appearances known as proximity effect [1]. An efficient correction, however, requires an adequate knowledge and experience base to predict this proximity effect, because only then the latter is amenable to correction. Existing correction techniques rely on (i) shot-by-shot modulations of the exposure dose, (ii) modifications of the pattern geometry (shape bias), or on (iii) combining of both methods. There are available some commercial software packages, which deal with exposure dose optimization issues. They are based on schemes using a linear combination of double or multiple Gaussian functions and approximating the electron scattering phenomena (‘‘proximity function’’ or PSF) as described in [1]. In spite of the fact that there exists a well working exposure *
Corresponding author. Tel.: +43 5572 792 7202; fax: +43 5572 792 9500. E-mail address: [email protected] (P. Hudek). 0167-9317/$ - see front matter Ó 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.mee.2006.01.184
corrector, only properly selected proximity parameters are the precondition to bring as numerical inputs this system to work. Many methods have been proposed for the determination of the proximity parameters. They are all reflecting various levels of effectiveness [2–9]. Our approach, which has been materialized in the ‘‘PROX-In’’ software package, is based on a totally new method, which shall help lithographers to extract the PSF parameters required for an arbitrary exposure optimization software. In this context we used the Leica SB3XX 50 keV variable-shaped beam exposure tools together with the latest version of PROXECCOTM from PDF Solutions. Not unmentioned should be left that this software version benefits from the close cooperation between its developers and the authors of this article [10]. 2. General description of the method The main idea behind the method are model-based analyses and interpretations of generic pattern distortions of non-corrected representative patterns as well as successive back-simulations in order to achieve the best possible
P. Hudek, D. Beyer / Microelectronic Engineering 83 (2006) 780–783
3. About proximity parameters The dominant distortion in EBL originates from the scattering of electrons convoluted with additional effects, which are not exactly detachable and separately treatable. The PSF is usually described as a linear combination of two or more Gaussian functions [1]. Following this convention, the normalized PSF contains at least 3 main numerical parameters a, b and g, where a characterizes the shortrange scatter, b the backscattering and g the relative contribution of both. The PSF parameters determined from the absorbed energy density distribution (AEDD) do not contain any information about additional process- and/or tool-dependent impacts affecting also the resulting pattern distortion [9,11]. 3.1. Conception of b and g determination The b-value significantly determines the final dose assignment over a large area of interacting and also noninteracting patterns. b is extremely sensitive to the substrate material composition (in many cases there is not possible an exact substrate definition for the e-scattering calculation). A quick method has been developed to determine the first numerical b and g values for definite process and exposure conditions. The method is based on the analysis of widths vs. dose variations. The strong over-exposure directly visualizes the backscattering effect together with all additional impacts caused by the processes. As shown in Fig. 1, the shape of the curve is highly process-sensitive. It is the main task of this part of work to search for reasonable b and g values required for the simulation, which shall be closest to a measurement value. In other words, for the whole dose range the simulation should reconstruct the real situation of the measured line geometry variation. Often happens that some regions cannot be satisfactorily fitted using a 2 Gaussian parameter set [2,4]. This could lead to a local failure of the dose assignment for some combinations of patterns in the correction procedure. Our method allows to easily use more than 2 Gaussian functions in order to improve the quality of the proximity correction. A simulation result achieved with PROX-In is
25
180s Linewidth [µm]
reconstruction of these effects. The observed geometry variations of concrete representative pattern details are then simulated as a function of (i) exposure intensity or (ii) location of a neighborhood pattern variation. Consequently, after inserting the extracted parameters into the model, the appropriate simulation should show the same tendency of pattern geometry variations as obtained from measurements. Accordingly, if the correction algorithms are working under the same model concept as used in the proximity corrector (i.e. the same Kernels), we will receive a good recovery of the parasitic pattern distortion effects by using such a process-tailored PSF in the proximity effect correction.
781
120s
60s
20
15
20 keV 10µm Exposed Line
10
5 0
50
100
150 200 250 300 Dose [µC/cm²]
350
400
450
Fig. 1. Width variation of 10 lm lines exposed with increasing doses at 50 keV (3 various development processes of 60 s, 120 s, 180 s) and at 20 keV (250 nm ZEP7000 on Si).
Fig. 2. Back-simulation of a 15 lm exposed and etched linewidth variation on a photomask using 3-Gaussian PSF. In this case an intermediate 3rd Gaussian function helps to achieve a better fit than using a simple 2-Gaussian-based PSF.
Fig. 3. The back-simulation method is highly sensitive to changes of both (a) b and (b) g values against the extracted optimum (Fig. 2).
illustrated in Fig. 2. It shows an etched 15 lm linewidth variation on a photomask using 3-Gauss PSF. The high sensitivity of this technique to changes of the b and g values is depicted in Fig. 3. 3.2. a – the short-range scattering parameter Generally it is not recommended to directly use the a value estimated from the Monte Carlo method, because this calculation only approaches the value. A real a-value is regularly a bit larger, because apart from the scattering of electrons other additional process- and tool-dependent effects influence this highly sensitive parameter [9].
782
P. Hudek, D. Beyer / Microelectronic Engineering 83 (2006) 780–783
Dose Factor [a.u.]
2.2
Measured
2
2 Gauss PSF: α = 0.072, b = 12, h = 0.23
1.8
under-exposure of the 150nm iso-line
1.6 1.4 1.2
Simulated ≡ predicted dose-assignment from the corrector
1 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Linewidth [µm]
Dose Factor [a.u.]
2.2 2
3 Gauss PSF: α = 0.072, b = 0.3, h = 0.26 γ = 12, ν = 0.3
1.8 1.6 1.4 1.2 1 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Fig. 5. 600 nm linewidth vs. pitch variation written in Duty-Ratio from 1:20 to 1:1 L/S. The exposure dose was adjusted to provide the correct linewidth for the Iso-Line in this test.
Linewidth [µm]
should be large enough depending on the exposure energy (4x always the largest range value from PSF). Then the Base Dose equals to a value, at which the measured L/S in the middle of the grating are equal, i.e. to an optimum (1:1) L/S exposure of the given process.
Dose Factor [a.u.]
2.2
4 Gauss PSF: α = 0.072, b = 0.170, h = 0.26 γ = 0.5, ν = 0.2, γ ’ = 12, ν ’= 0.3
2 1.8 1.6 1.4 1.2 1
0.05
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Linewidth [µm]
Fig. 4. An example of a-parameter tuning with back-simulation of the measured ‘‘dose-to-line’’ dependence. As a direct output from PROX-In, the 2, 3, and 4 Gauss PSFs are used for a maskmaking process with FEP171-resist.
The a determination is carried out on the basis of further simulations to reconstruct the geometry variation of highresolution single Iso Lines under real process conditions (see Fig. 4). The procedure uses the extracted b and g values (from Section 3.1) as well as data from a precise Doseto-Line (Gap) measurement for optimum patterning of each particular Iso Line (Gap) characterized by a linewidth down to the resolution limit of the process. The dose to be indicated in the y-axis in Fig. 4 must be provided in a normalized form relative to the Base Dose (dimensionless dose factor, please refer to Section 3.3). As a cross-check and for final fine-tuning of the process parameters it is recommended to use at least one test-pattern, the geometry variation of which should be influenced by the neighboring patterns. PROX-In analyses the width variation of a line in a pyramid-like pattern and/or in arrays with various line-to-space (L/S) rates (Fig. 5). The goal is to determine the best PSF-parameter set with respect to the model, which will be able to reconstruct the deformation of the measured lines.
4. Conclusion We presented a new method allowing the determination of PSF parameters. Compared with other frequently used techniques, the main advantages of our approach are the following: (i) only a small amount of test patterns is required, which allows to vary the global pattern loading to determine this effect and to adopt it to the process; (ii) test patterns are written without any correction; (iii) direct determination of the pattern CD-changes by varying the PSF parameters; (iv) interactive fine-tuning of the parameters to achieve the best possible CD-requirements; (v) using 2 or more Gaussian parameter sets with a check that is the reason why an additional Gaussian set is necessary and (vi) fast and cost effective method. The presented method was successfully implemented into mask production for achieving the 90 nm technology node and below [12]. Furthermore, it is broadly used for direct write and SFIL template manufacturing with sub50 nm resolution [13]. Acknowledgement The authors acknowledge the active cooperation with Hans Eisenmann and Nikola Belic from PDF Solutions during this work. References
3.3. Base dose determination The base dose can be determined on the basis of measurements taken on gratings with L/S (1:1), which were patterned with finely varying doses. The grating area
[1] T.H.P. Chang, J. Vac. Sci. Technol. 12 (1975) 1271. [2] E. Kratschmer, J. Vac. Sci. Technol. 19 (4) (1981) 1264. [3] L. Stevens, R. Jonckheere, E. Froyen, S. Decoutere, D. Lanneer, Microelectron. Eng. 5 (1986) 141. [4] S.A. Rishton, D.P. Kern, J. Vac. Sci. Technol. B 5 (1) (1987) 135.
P. Hudek, D. Beyer / Microelectronic Engineering 83 (2006) 780–783 [5] H. Schmoranzer, J. Vac. Sci. Technol. B 6 (6) (1988) 2053. [6] A. Misaka, K. Harafuji, N. Nomura, J. Appl. Phys. 68 (12) (1990) 6472. [7] V. Boegli, L. Johnson, H. Kao, L. Veneklasen, U. Hoffmann, I. Finkelstein, S. Stovall, S. Rishton, J. Vac. Sci. Technol. B 18 (6) (2000) 3138. [8] E.S. Park, J.H. Lee, D.I. Park, W.G. Jeong, S.K. Seo, J.M. Kim, Sang-Soo Choi, Soo-Hong Jeong, Proc. SPIE 4889 (2002) 792. [9] M. Rooks, N. Belic, E. Kratschmer, R. Viswanathan, J. Vac. Sci. Technol. B 23 (6) (2005) 2769.
783
[10] N. Belic, R. Jaritz, P. Hudek, H. Eisenmann, in: Proc. Mask Patterning for 100 nm Technology Node, SEMICON Europa 2002, SEMIÒ Presents, April 16, 2002, Munich, Germany. [11] S.H. Kim, S.-W. Choi, J.-M. Sohn, J.R. Park, J. Vac. Sci. Technol. B 21 (6) (2003) 3041. [12] S.D. Tzu, C.H. Chang, W.Ch. Chen, K.-H. Kliem, P. Hudek, D. Beyer, Proc. SPIE 5645 (2004) 100–108. [13] W.J. Dauksher, D. Mancini, K. Nordquist, D.J. Resnick, P. Hudek, D. Beyer, T. Groves, O. Fortagne, Microelectron. Eng. 75 (2004) 345–351.
Exposure optimization in high-resolution e-beam lithography Peter Hudek a
a,*
, Dirk Beyer
b
Vorarlberg University of Applied Sciences, Dornbirn A-6850, Austria Leica Microsystems Lithography GmbH, Jena D-07745, Germany
b
Available online 21 February 2006
Abstract In this paper a new method will be described, illustrating how to determine the optimized control point spread function (PSF) for proximity effect corrections (PEC) in e-beam lithography (EBL). A software tool called ‘‘PROX-In’’ was developed in order to help lithographers to determine the numerical inputs for an arbitrary PEC system to satisfy the high critical dimension (CD) control requirements as well as to compensate the shape bias in EBL in connection with the technology steps performed. PROX-In applies new methods allowing highly customized optimum numerical proximity parameter determinations by using a set of extracted experimental data. Compared with other presented methods, this approach is fast and effective. It does not require any additional technology steps and uses only standard measuring techniques. The reviewed method was successfully implemented into mask production for achieving the 90 nm technology node and below at different absorber stacks. It is also used for high-resolution e-beam direct write and SFIL template manufacturing with sub-50 nm resolution. Ó 2006 Elsevier B.V. All rights reserved. Keywords: Electron-beam lithography; Proximity effect, Maskmaking; Direct writing
1. Introduction From the very first moment when submicron feature sizes became the crucial factor for any patterning task, ebeam writing has been confronted with parasite appearances known as proximity effect [1]. An efficient correction, however, requires an adequate knowledge and experience base to predict this proximity effect, because only then the latter is amenable to correction. Existing correction techniques rely on (i) shot-by-shot modulations of the exposure dose, (ii) modifications of the pattern geometry (shape bias), or on (iii) combining of both methods. There are available some commercial software packages, which deal with exposure dose optimization issues. They are based on schemes using a linear combination of double or multiple Gaussian functions and approximating the electron scattering phenomena (‘‘proximity function’’ or PSF) as described in [1]. In spite of the fact that there exists a well working exposure *
Corresponding author. Tel.: +43 5572 792 7202; fax: +43 5572 792 9500. E-mail address: [email protected] (P. Hudek). 0167-9317/$ - see front matter Ó 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.mee.2006.01.184
corrector, only properly selected proximity parameters are the precondition to bring as numerical inputs this system to work. Many methods have been proposed for the determination of the proximity parameters. They are all reflecting various levels of effectiveness [2–9]. Our approach, which has been materialized in the ‘‘PROX-In’’ software package, is based on a totally new method, which shall help lithographers to extract the PSF parameters required for an arbitrary exposure optimization software. In this context we used the Leica SB3XX 50 keV variable-shaped beam exposure tools together with the latest version of PROXECCOTM from PDF Solutions. Not unmentioned should be left that this software version benefits from the close cooperation between its developers and the authors of this article [10]. 2. General description of the method The main idea behind the method are model-based analyses and interpretations of generic pattern distortions of non-corrected representative patterns as well as successive back-simulations in order to achieve the best possible
P. Hudek, D. Beyer / Microelectronic Engineering 83 (2006) 780–783
3. About proximity parameters The dominant distortion in EBL originates from the scattering of electrons convoluted with additional effects, which are not exactly detachable and separately treatable. The PSF is usually described as a linear combination of two or more Gaussian functions [1]. Following this convention, the normalized PSF contains at least 3 main numerical parameters a, b and g, where a characterizes the shortrange scatter, b the backscattering and g the relative contribution of both. The PSF parameters determined from the absorbed energy density distribution (AEDD) do not contain any information about additional process- and/or tool-dependent impacts affecting also the resulting pattern distortion [9,11]. 3.1. Conception of b and g determination The b-value significantly determines the final dose assignment over a large area of interacting and also noninteracting patterns. b is extremely sensitive to the substrate material composition (in many cases there is not possible an exact substrate definition for the e-scattering calculation). A quick method has been developed to determine the first numerical b and g values for definite process and exposure conditions. The method is based on the analysis of widths vs. dose variations. The strong over-exposure directly visualizes the backscattering effect together with all additional impacts caused by the processes. As shown in Fig. 1, the shape of the curve is highly process-sensitive. It is the main task of this part of work to search for reasonable b and g values required for the simulation, which shall be closest to a measurement value. In other words, for the whole dose range the simulation should reconstruct the real situation of the measured line geometry variation. Often happens that some regions cannot be satisfactorily fitted using a 2 Gaussian parameter set [2,4]. This could lead to a local failure of the dose assignment for some combinations of patterns in the correction procedure. Our method allows to easily use more than 2 Gaussian functions in order to improve the quality of the proximity correction. A simulation result achieved with PROX-In is
25
180s Linewidth [µm]
reconstruction of these effects. The observed geometry variations of concrete representative pattern details are then simulated as a function of (i) exposure intensity or (ii) location of a neighborhood pattern variation. Consequently, after inserting the extracted parameters into the model, the appropriate simulation should show the same tendency of pattern geometry variations as obtained from measurements. Accordingly, if the correction algorithms are working under the same model concept as used in the proximity corrector (i.e. the same Kernels), we will receive a good recovery of the parasitic pattern distortion effects by using such a process-tailored PSF in the proximity effect correction.
781
120s
60s
20
15
20 keV 10µm Exposed Line
10
5 0
50
100
150 200 250 300 Dose [µC/cm²]
350
400
450
Fig. 1. Width variation of 10 lm lines exposed with increasing doses at 50 keV (3 various development processes of 60 s, 120 s, 180 s) and at 20 keV (250 nm ZEP7000 on Si).
Fig. 2. Back-simulation of a 15 lm exposed and etched linewidth variation on a photomask using 3-Gaussian PSF. In this case an intermediate 3rd Gaussian function helps to achieve a better fit than using a simple 2-Gaussian-based PSF.
Fig. 3. The back-simulation method is highly sensitive to changes of both (a) b and (b) g values against the extracted optimum (Fig. 2).
illustrated in Fig. 2. It shows an etched 15 lm linewidth variation on a photomask using 3-Gauss PSF. The high sensitivity of this technique to changes of the b and g values is depicted in Fig. 3. 3.2. a – the short-range scattering parameter Generally it is not recommended to directly use the a value estimated from the Monte Carlo method, because this calculation only approaches the value. A real a-value is regularly a bit larger, because apart from the scattering of electrons other additional process- and tool-dependent effects influence this highly sensitive parameter [9].
782
P. Hudek, D. Beyer / Microelectronic Engineering 83 (2006) 780–783
Dose Factor [a.u.]
2.2
Measured
2
2 Gauss PSF: α = 0.072, b = 12, h = 0.23
1.8
under-exposure of the 150nm iso-line
1.6 1.4 1.2
Simulated ≡ predicted dose-assignment from the corrector
1 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Linewidth [µm]
Dose Factor [a.u.]
2.2 2
3 Gauss PSF: α = 0.072, b = 0.3, h = 0.26 γ = 12, ν = 0.3
1.8 1.6 1.4 1.2 1 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Fig. 5. 600 nm linewidth vs. pitch variation written in Duty-Ratio from 1:20 to 1:1 L/S. The exposure dose was adjusted to provide the correct linewidth for the Iso-Line in this test.
Linewidth [µm]
should be large enough depending on the exposure energy (4x always the largest range value from PSF). Then the Base Dose equals to a value, at which the measured L/S in the middle of the grating are equal, i.e. to an optimum (1:1) L/S exposure of the given process.
Dose Factor [a.u.]
2.2
4 Gauss PSF: α = 0.072, b = 0.170, h = 0.26 γ = 0.5, ν = 0.2, γ ’ = 12, ν ’= 0.3
2 1.8 1.6 1.4 1.2 1
0.05
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Linewidth [µm]
Fig. 4. An example of a-parameter tuning with back-simulation of the measured ‘‘dose-to-line’’ dependence. As a direct output from PROX-In, the 2, 3, and 4 Gauss PSFs are used for a maskmaking process with FEP171-resist.
The a determination is carried out on the basis of further simulations to reconstruct the geometry variation of highresolution single Iso Lines under real process conditions (see Fig. 4). The procedure uses the extracted b and g values (from Section 3.1) as well as data from a precise Doseto-Line (Gap) measurement for optimum patterning of each particular Iso Line (Gap) characterized by a linewidth down to the resolution limit of the process. The dose to be indicated in the y-axis in Fig. 4 must be provided in a normalized form relative to the Base Dose (dimensionless dose factor, please refer to Section 3.3). As a cross-check and for final fine-tuning of the process parameters it is recommended to use at least one test-pattern, the geometry variation of which should be influenced by the neighboring patterns. PROX-In analyses the width variation of a line in a pyramid-like pattern and/or in arrays with various line-to-space (L/S) rates (Fig. 5). The goal is to determine the best PSF-parameter set with respect to the model, which will be able to reconstruct the deformation of the measured lines.
4. Conclusion We presented a new method allowing the determination of PSF parameters. Compared with other frequently used techniques, the main advantages of our approach are the following: (i) only a small amount of test patterns is required, which allows to vary the global pattern loading to determine this effect and to adopt it to the process; (ii) test patterns are written without any correction; (iii) direct determination of the pattern CD-changes by varying the PSF parameters; (iv) interactive fine-tuning of the parameters to achieve the best possible CD-requirements; (v) using 2 or more Gaussian parameter sets with a check that is the reason why an additional Gaussian set is necessary and (vi) fast and cost effective method. The presented method was successfully implemented into mask production for achieving the 90 nm technology node and below [12]. Furthermore, it is broadly used for direct write and SFIL template manufacturing with sub50 nm resolution [13]. Acknowledgement The authors acknowledge the active cooperation with Hans Eisenmann and Nikola Belic from PDF Solutions during this work. References
3.3. Base dose determination The base dose can be determined on the basis of measurements taken on gratings with L/S (1:1), which were patterned with finely varying doses. The grating area
[1] T.H.P. Chang, J. Vac. Sci. Technol. 12 (1975) 1271. [2] E. Kratschmer, J. Vac. Sci. Technol. 19 (4) (1981) 1264. [3] L. Stevens, R. Jonckheere, E. Froyen, S. Decoutere, D. Lanneer, Microelectron. Eng. 5 (1986) 141. [4] S.A. Rishton, D.P. Kern, J. Vac. Sci. Technol. B 5 (1) (1987) 135.
P. Hudek, D. Beyer / Microelectronic Engineering 83 (2006) 780–783 [5] H. Schmoranzer, J. Vac. Sci. Technol. B 6 (6) (1988) 2053. [6] A. Misaka, K. Harafuji, N. Nomura, J. Appl. Phys. 68 (12) (1990) 6472. [7] V. Boegli, L. Johnson, H. Kao, L. Veneklasen, U. Hoffmann, I. Finkelstein, S. Stovall, S. Rishton, J. Vac. Sci. Technol. B 18 (6) (2000) 3138. [8] E.S. Park, J.H. Lee, D.I. Park, W.G. Jeong, S.K. Seo, J.M. Kim, Sang-Soo Choi, Soo-Hong Jeong, Proc. SPIE 4889 (2002) 792. [9] M. Rooks, N. Belic, E. Kratschmer, R. Viswanathan, J. Vac. Sci. Technol. B 23 (6) (2005) 2769.
783
[10] N. Belic, R. Jaritz, P. Hudek, H. Eisenmann, in: Proc. Mask Patterning for 100 nm Technology Node, SEMICON Europa 2002, SEMIÒ Presents, April 16, 2002, Munich, Germany. [11] S.H. Kim, S.-W. Choi, J.-M. Sohn, J.R. Park, J. Vac. Sci. Technol. B 21 (6) (2003) 3041. [12] S.D. Tzu, C.H. Chang, W.Ch. Chen, K.-H. Kliem, P. Hudek, D. Beyer, Proc. SPIE 5645 (2004) 100–108. [13] W.J. Dauksher, D. Mancini, K. Nordquist, D.J. Resnick, P. Hudek, D. Beyer, T. Groves, O. Fortagne, Microelectron. Eng. 75 (2004) 345–351.