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Thickness-dependent thermal reliability of low-dielectric constant polycrystalline PTFE submicron dielectric thin films
Microelectronics Journal Microelectronics Journal 32 (2001) 215–219 www.elsevier.com/locate/mejo
Thickness-dependent thermal reliability of low-dielectric constant polycrystalline PTFE submicron dielectric thin films H.K. Kim, F.G. Shi* Optoelectronic Packaging Laboratory, The Henry Samueli School of Engineering, University of California, Irvine, CA 92697-2575, USA Received 9 September 2000; revised 2 October 2000; accepted 12 October 2000
Abstract According to the SIA National Technology Roadmap for Semiconductors, interlevel dielectrics (ILDs) with a relative dielectric constant less than two will be needed for future integrated circuit devices beyond 0.1 mm generation. For possible low-dielectric constant (low-k) candidates with a relative dielectric constant less than two, polytetrafluoroethylene (PTFE) has the lowest dielectric constant among nonporous low-k materials, and thus is a strong future ILD candidate. As the feature size decreases, the ILD thickness is also expected to decrease. Thus needs exist for characterizing and understanding the possible thickness-induced thermal reliability of PTFE thin films for deep-submicron multilevel interconnection applications. The majority of low-dielectric constant candidates for ULSI ILD applications are amorphous polymers; techniques exist for characterizing the glass transition temperatures of amorphous polymers, which is the critical measure of their thermal stability. However, a simple but reliable method remained to be introduced for characterizing the thermal stability of submicron crystalline thin films such as PTFE. It is determined in the present work that the directly measured ellipsometric angles D and c can be used for detecting the solid $ liquid transition temperatures of on-wafer polycrystalline thin films. The novel approach is applied for investigating the solid $ liquid transitions of on-wafer PTFE thin films. The results show that the solid–liquid transitions depend on the film thickness as a result of film/surface, film/substrate interactions and the thickness-dependent crystal size. The results can be well described by modifying a previous model for size dependent solid–liquid transitions of nanocrystals. 䉷 2001 Elsevier Science Ltd. All rights reserved. Keywords: Solid–liquid transitions; Thickness dependence; Low-k dielectrics; Ellipsometric angles
1. Introduction According to the Semiconductor Industry Association (SIA) National Technology Roadmap for Semiconductors [1], interlevel dielectrics (ILDs) with a relative dielectric constant less than two will be needed for future integrated circuit (IC) devices beyond 0.1 mm generation. For possible low-dielectric constant (low-k) candidates with a relative dielectric constant less than two, polytetrafluoroethylene (PTFE) has the lowest dielectric constant among nonporous low-k materials, and thus is a strong future ILD candidate [2–8]. As feature sizes decrease, the ILD thickness is also expected to decrease. Thus, the thickness of ILD and other relevant conducting and dielectric thin films for IC manufacture is an important design parameter. Hence, needs exist for characterizing and understanding the possible thicknessinduced thermal reliability of PTFE thin films for deepsubmicron multilevel interconnection applications. * Corresponding author. Tel.: ⫹1-949-824-5362; fax: ⫹1-949-824-2541. E-mail address: [email protected] (F.G. Shi).
The majority of low-dielectric constant candidates for ULSI ILD applications are amorphous polymers [2], techniques exist for characterizing the glass transition temperatures of amorphous polymers, which is a critical role of their thermal stability [9,10]. However, for crystalline ILD candidates, their solid $ liquid transitions determine their thermal stability. However, simple but reliable methods remained to be introduced for characterizing the thermal stability of submicron crystalline thin films such as PTFE. The purposes of this work are to introduce a novel method for detecting solid $ liquid transitions of on-wafer crystalline submicron thin films and to apply the new method for investigating the thickness-dependent solid–liquid transitions of polycrystalline PTFE thin films. Ellipsometers measure the change in the polarization state of the light by detecting and quantifying the change in phase (D ) and amplitude (c ). The ratio of two values, D and c is highly accurate and reproducible, and highly sensitive to the presence of ultra thin films, i.e. ⬍10 nm. The expected abrupt changes in the ellipsometric angles D and c at the first-order phase transition temperatures are the basis of this
0026-2692/01/$ - see front matter 䉷 2001 Elsevier Science Ltd. All rights reserved. PII: S0026-269 2(00)00125-7
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H.K. Kim, F.G. Shi / Microelectronics Journal 32 (2001) 215–219
Fig. 1. XRD pattern of polycrystalline PTFE thin films at room temperature.
new approach. Solid–liquid transitions of polycrystalline PTFE thin films ranging in thicknesses from 40 to 1200 nm were examined by the use of this new approach employing an ellipsometer coupled with a hot stage unit. The results show that the solid–liquid transitions depend on the film thickness as a result of film/surface, film/substrate interactions and the thickness-dependent crystal grain size. The results can be well described by modifying a previous model for size dependent solid–liquid transitions of nanocrystals [11,12].
2. Preparation and characterization of PTFE thin films
Fig. 2. (a) The variation of FWHM as a function of film thickness, and (b) the variation of the crystallite size as a function of film thickness.
The PTFE thin film of seven thicknesses, i.e. 48, 94, 142, 208, 528, 800, and 1141 nm, were employed to investigate the thickness-dependent solid–liquid transition temperatures. Samples were prepared on the Si wafer with spincoating method, then baked and sintered on a computer controlled hot plate for 3 min with a curing temperature of 390⬚C [7,13]. X-ray diffraction (XRD) (SIEMENS D5000 Diffractometer with Cu Ka irradiation) was used to evaluate the crystallinity of the films. The measurements were performed at low incident angles to maximize the signal from the thin layers. The intensities were collected at room temperature with 2u scanning mode. Fig. 1 shows the respective XRD scans of PTFE thin films of 142, 208, 528, and 1141 nm. The typical peak at 18⬚ [14,15] is observed. However, it was found that the (100) peak becomes more intense with increasing film thickness, which indicates that thicker films have a higher crystalline order. Fig.2(a) shows the full width at half maximum (FWHM) as a function of the film thickness obtained from Lorentzian shape fit. A rapid increase with decreasing thickness in FWHM is observed for the film thickness below 208 nm. The observation indicates that the crystalline order of films increases with increasing thickness suggesting an increase
H.K. Kim, F.G. Shi / Microelectronics Journal 32 (2001) 215–219
217
3. A new approach for detecting solid $ liquid transitions of on-wafer crystalline thin films
Fig. 3. The variation of D and c as a function of temperature for film thickness of 528 nm.
in the average crystallite size. The crystallite size in Fig. 2(b) was calculated from Scherrer’s fomula, D l=B cos u (D is the crystallite size, l is the wavelength of the incident X-rays, B is FWHM, and u is the angle of the peak) by using Lorentz shape fit. It is clearly shown that the crystallite size increases drastically from 34 to 45 nm with film thickness range of 48–208 nm, and then gradually increases from 45 to 50 nm with film thickness range of 208–1141 nm. All data can be described by the power law D ⬃ h m (h being film thickness) with log–log plot as shown in the inserted graph in Fig. 2(b), but not with a single value of m. In the present case, for the thickness between 48 and 142 nm, m 9:33 × 10 ⫺2 and m 5:20 × 10⫺2 for the thickness between 208 and 1141 nm. The presence of the intense (100) peak in the XRD pattern also indicates that the molecular chains are parallel to their substrate surface structure [16,17].
Linearly polarized light reflected from a thin film can be transformed into an elliptically polarized beam. Its physical properties, optical characteristics, composition, wavelength, polarization direction, and incident angle of the light are determined, which makes ellipsometry an useful tool in characterizing thin films. Ellipsometers measure the change in the polarization state of the light by detecting and quantifying the change in phase (D ) and amplitude (c ), which are related to the complex ratio of reflection coefficient r p =rs tan c e iD : The ratio of two values, D and c is highly accurate and reproducible, much less sensitive to fluctuations, and highly sensitive to the presence of ultra thin films, i.e. ⬍10 nm. Ellipsometry analysis yields many material parameters, such as the film thickness, surface roughness, and optical constants. Since the ellipsometer cannot measure the physical properties directly, a model of thin film systems under investigation is required. The predictions of the model and adjusting parameters provide the best fit of the generated data to the experimentally obtained data by comparing the measured D and c , which can help us determine both the film thickness and optical constants as well as other parameters of the system. Although, the temperature-dependent thickness measurement using ellipsometer can be used to detect the solid $ liquid transitions, the calculated values of film thickness often suffer from the accuracy of various assumptions adopted. Since both D and c are dependent on density and they are expected to exhibit changes at first-order phase transition temperatures, the directly measured D and/or c as a function of temperature using an ellipsometer presents a simple and more accurate method for detecting solid–liquid transitions of on-wafer crystalline thin films which has never been reported before. The ellipsometric measurements were accomplished by a Rudolph Research-IV AutoEL with a programmable hot stage. The ellipsometer was operated at l 632:8 nm under a fixed angle of incidence f 70⬚: All of the samples were heated from 25 to 360⬚C with a heating rate of 3⬚C/min. During this measurement, the D and c angles were recorded.
4. Thickness-dependent solid $ liquid transitions
Fig. 4. The variation of thickness during heating/cooling process with film thickness of 528 nm.
Fig. 3 shows the respective variation of ellipsometric angles, D and c , as a function of the temperature for onwafer polycrystalline PTFE thin film with an initial thickness of 528 nm. It is clearly observed that the D angle drops from 267 to 261, and the c angle drops from 37 to 29 at 325⬚C. Additionally, the D angle jumps from 262 to 269, and the c angle jumps from 29 to 40 at 316.5⬚C. It is seen that there is a drastic jump in D and c at 325⬚C, and a drastic drop in D and c at 316.5⬚C. However, these two transition
218
H.K. Kim, F.G. Shi / Microelectronics Journal 32 (2001) 215–219
Fig. 5. The comparison of melting temperatures obtained from observations of ellipsometric angle changes and thickness changes.
temperatures corresponding to the two jumps are not identical exhibiting the typical hysteresis of first-order phase transitions. Thus, the two jump points can be identical as the melting and solidification of the on-wafer PTFE films, respectively. The identification of melting and solidification temperatures based on the observation of temperature-dependent D and c is supported by the thickness variation as a function of temperature during heating and cooling for the PTFE film with an initial thickness of 528 nm as shown in Fig. 4. For the selected film with an initial thickness of 528 nm as shown in Fig. 4, the film thickness increases from 528 to 580 nm gradually, and then suddenly increases from 580 to 649 nm at the melting temperature. It was observed that the
film thickness increases by 10% at the melting temperature. In the cooling process, the film thickness suddenly drops from 639 to 542 nm at the solidification temperature, and then gradually decreases from 542 to 498 nm. Fig. 5 shows a comparison between observed melting temperature (Tm) based on the observation of D and c and the Tm obtained from the measurement of temperaturedependent thickness. The values of Tm obtained from the two methods are fully consistent. Thus the new method based on the temperature dependence of ellipsometric angles D and c provides a simple approach for detecting solid $ liquid transitions without resorting to the calculation of film thickness of on-wafer crystalline thin films. Fig. 6 shows the variation of Tm as a function of film
Fig. 6. Thickness dependence behavior of the melting temperature for polycrystalline PTFE thin films.
H.K. Kim, F.G. Shi / Microelectronics Journal 32 (2001) 215–219
thickness for PTFE thin films. It is evident that Tm increases with increasing film thickness in the range of 48–1141 nm, and Tm for the films are lower than Tm for bulk PTFE, 327⬚C. Hence phase behavior such as the solid–liquid transitions should be different from bulk materials, if the system is confined with finite scale. All data can be described by the power law Tm ⬃ h n with log–log plot as shown in the inserted graph in Fig. 6, but not with a single value of n. In the present case, for the thickness between 48 and 142 nm, n 1:29 × 10 ⫺3 and n 5:53 × 10⫺3 for the thickness between 208 and 1141 nm. The observations can be well explained in view of the fact that the thickness dependence of the melting temperature results from the dependence of Tm on both the crystallite size and the film thickness, 2Tm 2Tm dD ⫹ dh; dTm 2D h 2h D or
d ln Tm 2 ln Tm 2 ln D 2 ln Tm ⫹ d ln h 2 ln D h 2 ln h 2 ln h D
where D is the average size of crystallites, and h is the film thickness. In the above equation, 2 ln D=2 ln h are given in Fig. 2(b), and the values for 2 ln Tm =2 ln D and 2 ln Tm =2 ln h are determined by our previous models [10,11] for the size dependent melting temperature and the thickness-dependent melting temperature, respectively. Based on our previous models, and the experimentally obtained values for d ln Tm =d ln h and 2 ln D=2 ln h as presented in Figs. 6 and 2(b), values for d ln Tm =d ln h and 2 ln Tm 2 ln D 2 ln Tm ⫹ 2 ln D h 2 ln h 2 ln h D in the above equation are 1.29 × 10 ⫺3 and 1.26 × 10 ⫺3 for the thickness between 48 and 142 nm, and 4.53 × 10 ⫺3 and 4.30 × 10 ⫺3 for the thickness between 208 and 1141 nm.
Tm from the two methods are fully consistent. Thus the new method based on the temperature dependence of ellipsometric angles D and c provides a simple approach for detecting solid $ liquid transitions without resorting to the calculation of film thickness of on-wafer crystalline thin films. The results have shown that the solid–liquid transitions depend on the film thickness as a result of film/ surface, film/substrate interactions and the thickness-dependent crystal size. The XRD observations have shown that the crystallite size of PTFE thin films increases from 34 to 50 nm with increasing film thickness in the range of 48–1141 nm. The observations can be well explained in view of the fact that the thickness dependence of the melting temperature results from the dependence of Tm on both the crystallite size and the film thickness by modifying a previous model for size dependent solid–liquid transitions of nanocrystals.
Acknowledgements This work is supported by the State of California Microelectronics Innovation and Computer Research Opportunities (MICRO) program.
References [1] [2] [3] [4] [5]
[6] [7] [8]
5. Conclusions [9]
A novel method has been introduced for detecting solid $ liquid transitions of on-wafer crystalline submicron thin films based on the temperature dependence of the experimentally measured ellipsometric angles D and c . This method has been applied for investigating the thickness-dependent solid–liquid transitions of low-k polycrystalline PTFE thin films. It has been observed that an abrupt change in the ellipsometric angles D and c at the first-order phase transition can be identical as melting and solidification, respectively, of the on-wafer PTFE thin films, and the melting temperature of PTFE thin films increases with increasing film thickness in the range of 48–1141 nm. A comparison between observed Tm based on the observation of D and c and the Tm obtained from the measurement of temperature-dependent thickness shows that the values of
219
[10]
[11] [12] [13] [14] [15] [16] [17]
L. Peters, Semicond. Int. 23 (6) (2000) 108–124. R.D. Miller, Science 286 (5439) (1999) 421–423. L. Peters, Semicond. Int. 22 (13) (1999) 56–64. L. Peters, Semicond. Int. 21 (10) (1998) 64–74. H.K. Kim, F.G. Shi, B. Zhao, M. Brongo, Conference Record of the 2000 IEEE International Symposium on Electrical Insulation, 2000, pp. 62–65. J. Wang, H.K. Kim, F.G. Shi, B. Zhao, T.G. Nieh, Thin Solid Films (2000) (in press). J. Wang, F.G. Shi, T.G. Nieh, B. Zhao, M.R. Brongo, S. Qu, T. Rosenmayer, Scripta Mater. 42 (7) (2000) 687–694. D.T. Hsu, H.K. Kim, F.G. Shi, B. Zhao, M. Brongo, Mater. Sci., Process. Reliabil. Issues 99-7 (2000) 62–68 (Proceedings of the Fourth International Symposium of Low and High Dielectric Constant Materials). D.T. Hsu, H.K. Kim, F.G. Shi, B. Zhao, M. Brongo, P. Schilling, S.-Q. Wang, SPIE Proc. 3883 (1999) 60–67 (Conference on Multilevel Interconnect Technology III). D.T. Hsu, F.G. Shi, B. Zhao, M. Brongo, Mater. Sci., Process. Reliabil. Issues 99-7 (2000) 53–61 (Proceedings of the Fourth International Symposium of Low and High Dielectric Constant Materials). F.G. Shi, J. Mater. Res. 9 (5) (1994) 1307–1313. Q. Jiang, H.Y. Tong, D.T. Hsu, K. Okuyama, F.G. Shi, Thin Solid Films 312 (1/2) (1998) 357–361. C.T. Rosenmayer, J.W. Bartz, J. Hammes, Symposium on LowDielectric Constant Materials III, 1997, pp. 231–236. Y. Ueno, T. Fujii, F. Kannari, Appl. Phys. Lett. 65 (11) (1994) 1370–1372. S.T. Li, E. Arenholz, J. Heitz, D. Bauerle, Appl. Surf. Sci. 125 (1) (1998) 17–22. W.B. Jiang, M.G. Norton, L. Tsung, J.T. Dickinson, J. Mater. Res. 10 (4) (1995) 1038–1043. H. Usui, H. Koshikawa, K. Tanaka, J. Vac. Sci. Technol., A 13 (5) (1995) 2318–2324.
Thickness-dependent thermal reliability of low-dielectric constant polycrystalline PTFE submicron dielectric thin films H.K. Kim, F.G. Shi* Optoelectronic Packaging Laboratory, The Henry Samueli School of Engineering, University of California, Irvine, CA 92697-2575, USA Received 9 September 2000; revised 2 October 2000; accepted 12 October 2000
Abstract According to the SIA National Technology Roadmap for Semiconductors, interlevel dielectrics (ILDs) with a relative dielectric constant less than two will be needed for future integrated circuit devices beyond 0.1 mm generation. For possible low-dielectric constant (low-k) candidates with a relative dielectric constant less than two, polytetrafluoroethylene (PTFE) has the lowest dielectric constant among nonporous low-k materials, and thus is a strong future ILD candidate. As the feature size decreases, the ILD thickness is also expected to decrease. Thus needs exist for characterizing and understanding the possible thickness-induced thermal reliability of PTFE thin films for deep-submicron multilevel interconnection applications. The majority of low-dielectric constant candidates for ULSI ILD applications are amorphous polymers; techniques exist for characterizing the glass transition temperatures of amorphous polymers, which is the critical measure of their thermal stability. However, a simple but reliable method remained to be introduced for characterizing the thermal stability of submicron crystalline thin films such as PTFE. It is determined in the present work that the directly measured ellipsometric angles D and c can be used for detecting the solid $ liquid transition temperatures of on-wafer polycrystalline thin films. The novel approach is applied for investigating the solid $ liquid transitions of on-wafer PTFE thin films. The results show that the solid–liquid transitions depend on the film thickness as a result of film/surface, film/substrate interactions and the thickness-dependent crystal size. The results can be well described by modifying a previous model for size dependent solid–liquid transitions of nanocrystals. 䉷 2001 Elsevier Science Ltd. All rights reserved. Keywords: Solid–liquid transitions; Thickness dependence; Low-k dielectrics; Ellipsometric angles
1. Introduction According to the Semiconductor Industry Association (SIA) National Technology Roadmap for Semiconductors [1], interlevel dielectrics (ILDs) with a relative dielectric constant less than two will be needed for future integrated circuit (IC) devices beyond 0.1 mm generation. For possible low-dielectric constant (low-k) candidates with a relative dielectric constant less than two, polytetrafluoroethylene (PTFE) has the lowest dielectric constant among nonporous low-k materials, and thus is a strong future ILD candidate [2–8]. As feature sizes decrease, the ILD thickness is also expected to decrease. Thus, the thickness of ILD and other relevant conducting and dielectric thin films for IC manufacture is an important design parameter. Hence, needs exist for characterizing and understanding the possible thicknessinduced thermal reliability of PTFE thin films for deepsubmicron multilevel interconnection applications. * Corresponding author. Tel.: ⫹1-949-824-5362; fax: ⫹1-949-824-2541. E-mail address: [email protected] (F.G. Shi).
The majority of low-dielectric constant candidates for ULSI ILD applications are amorphous polymers [2], techniques exist for characterizing the glass transition temperatures of amorphous polymers, which is a critical role of their thermal stability [9,10]. However, for crystalline ILD candidates, their solid $ liquid transitions determine their thermal stability. However, simple but reliable methods remained to be introduced for characterizing the thermal stability of submicron crystalline thin films such as PTFE. The purposes of this work are to introduce a novel method for detecting solid $ liquid transitions of on-wafer crystalline submicron thin films and to apply the new method for investigating the thickness-dependent solid–liquid transitions of polycrystalline PTFE thin films. Ellipsometers measure the change in the polarization state of the light by detecting and quantifying the change in phase (D ) and amplitude (c ). The ratio of two values, D and c is highly accurate and reproducible, and highly sensitive to the presence of ultra thin films, i.e. ⬍10 nm. The expected abrupt changes in the ellipsometric angles D and c at the first-order phase transition temperatures are the basis of this
0026-2692/01/$ - see front matter 䉷 2001 Elsevier Science Ltd. All rights reserved. PII: S0026-269 2(00)00125-7
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H.K. Kim, F.G. Shi / Microelectronics Journal 32 (2001) 215–219
Fig. 1. XRD pattern of polycrystalline PTFE thin films at room temperature.
new approach. Solid–liquid transitions of polycrystalline PTFE thin films ranging in thicknesses from 40 to 1200 nm were examined by the use of this new approach employing an ellipsometer coupled with a hot stage unit. The results show that the solid–liquid transitions depend on the film thickness as a result of film/surface, film/substrate interactions and the thickness-dependent crystal grain size. The results can be well described by modifying a previous model for size dependent solid–liquid transitions of nanocrystals [11,12].
2. Preparation and characterization of PTFE thin films
Fig. 2. (a) The variation of FWHM as a function of film thickness, and (b) the variation of the crystallite size as a function of film thickness.
The PTFE thin film of seven thicknesses, i.e. 48, 94, 142, 208, 528, 800, and 1141 nm, were employed to investigate the thickness-dependent solid–liquid transition temperatures. Samples were prepared on the Si wafer with spincoating method, then baked and sintered on a computer controlled hot plate for 3 min with a curing temperature of 390⬚C [7,13]. X-ray diffraction (XRD) (SIEMENS D5000 Diffractometer with Cu Ka irradiation) was used to evaluate the crystallinity of the films. The measurements were performed at low incident angles to maximize the signal from the thin layers. The intensities were collected at room temperature with 2u scanning mode. Fig. 1 shows the respective XRD scans of PTFE thin films of 142, 208, 528, and 1141 nm. The typical peak at 18⬚ [14,15] is observed. However, it was found that the (100) peak becomes more intense with increasing film thickness, which indicates that thicker films have a higher crystalline order. Fig.2(a) shows the full width at half maximum (FWHM) as a function of the film thickness obtained from Lorentzian shape fit. A rapid increase with decreasing thickness in FWHM is observed for the film thickness below 208 nm. The observation indicates that the crystalline order of films increases with increasing thickness suggesting an increase
H.K. Kim, F.G. Shi / Microelectronics Journal 32 (2001) 215–219
217
3. A new approach for detecting solid $ liquid transitions of on-wafer crystalline thin films
Fig. 3. The variation of D and c as a function of temperature for film thickness of 528 nm.
in the average crystallite size. The crystallite size in Fig. 2(b) was calculated from Scherrer’s fomula, D l=B cos u (D is the crystallite size, l is the wavelength of the incident X-rays, B is FWHM, and u is the angle of the peak) by using Lorentz shape fit. It is clearly shown that the crystallite size increases drastically from 34 to 45 nm with film thickness range of 48–208 nm, and then gradually increases from 45 to 50 nm with film thickness range of 208–1141 nm. All data can be described by the power law D ⬃ h m (h being film thickness) with log–log plot as shown in the inserted graph in Fig. 2(b), but not with a single value of m. In the present case, for the thickness between 48 and 142 nm, m 9:33 × 10 ⫺2 and m 5:20 × 10⫺2 for the thickness between 208 and 1141 nm. The presence of the intense (100) peak in the XRD pattern also indicates that the molecular chains are parallel to their substrate surface structure [16,17].
Linearly polarized light reflected from a thin film can be transformed into an elliptically polarized beam. Its physical properties, optical characteristics, composition, wavelength, polarization direction, and incident angle of the light are determined, which makes ellipsometry an useful tool in characterizing thin films. Ellipsometers measure the change in the polarization state of the light by detecting and quantifying the change in phase (D ) and amplitude (c ), which are related to the complex ratio of reflection coefficient r p =rs tan c e iD : The ratio of two values, D and c is highly accurate and reproducible, much less sensitive to fluctuations, and highly sensitive to the presence of ultra thin films, i.e. ⬍10 nm. Ellipsometry analysis yields many material parameters, such as the film thickness, surface roughness, and optical constants. Since the ellipsometer cannot measure the physical properties directly, a model of thin film systems under investigation is required. The predictions of the model and adjusting parameters provide the best fit of the generated data to the experimentally obtained data by comparing the measured D and c , which can help us determine both the film thickness and optical constants as well as other parameters of the system. Although, the temperature-dependent thickness measurement using ellipsometer can be used to detect the solid $ liquid transitions, the calculated values of film thickness often suffer from the accuracy of various assumptions adopted. Since both D and c are dependent on density and they are expected to exhibit changes at first-order phase transition temperatures, the directly measured D and/or c as a function of temperature using an ellipsometer presents a simple and more accurate method for detecting solid–liquid transitions of on-wafer crystalline thin films which has never been reported before. The ellipsometric measurements were accomplished by a Rudolph Research-IV AutoEL with a programmable hot stage. The ellipsometer was operated at l 632:8 nm under a fixed angle of incidence f 70⬚: All of the samples were heated from 25 to 360⬚C with a heating rate of 3⬚C/min. During this measurement, the D and c angles were recorded.
4. Thickness-dependent solid $ liquid transitions
Fig. 4. The variation of thickness during heating/cooling process with film thickness of 528 nm.
Fig. 3 shows the respective variation of ellipsometric angles, D and c , as a function of the temperature for onwafer polycrystalline PTFE thin film with an initial thickness of 528 nm. It is clearly observed that the D angle drops from 267 to 261, and the c angle drops from 37 to 29 at 325⬚C. Additionally, the D angle jumps from 262 to 269, and the c angle jumps from 29 to 40 at 316.5⬚C. It is seen that there is a drastic jump in D and c at 325⬚C, and a drastic drop in D and c at 316.5⬚C. However, these two transition
218
H.K. Kim, F.G. Shi / Microelectronics Journal 32 (2001) 215–219
Fig. 5. The comparison of melting temperatures obtained from observations of ellipsometric angle changes and thickness changes.
temperatures corresponding to the two jumps are not identical exhibiting the typical hysteresis of first-order phase transitions. Thus, the two jump points can be identical as the melting and solidification of the on-wafer PTFE films, respectively. The identification of melting and solidification temperatures based on the observation of temperature-dependent D and c is supported by the thickness variation as a function of temperature during heating and cooling for the PTFE film with an initial thickness of 528 nm as shown in Fig. 4. For the selected film with an initial thickness of 528 nm as shown in Fig. 4, the film thickness increases from 528 to 580 nm gradually, and then suddenly increases from 580 to 649 nm at the melting temperature. It was observed that the
film thickness increases by 10% at the melting temperature. In the cooling process, the film thickness suddenly drops from 639 to 542 nm at the solidification temperature, and then gradually decreases from 542 to 498 nm. Fig. 5 shows a comparison between observed melting temperature (Tm) based on the observation of D and c and the Tm obtained from the measurement of temperaturedependent thickness. The values of Tm obtained from the two methods are fully consistent. Thus the new method based on the temperature dependence of ellipsometric angles D and c provides a simple approach for detecting solid $ liquid transitions without resorting to the calculation of film thickness of on-wafer crystalline thin films. Fig. 6 shows the variation of Tm as a function of film
Fig. 6. Thickness dependence behavior of the melting temperature for polycrystalline PTFE thin films.
H.K. Kim, F.G. Shi / Microelectronics Journal 32 (2001) 215–219
thickness for PTFE thin films. It is evident that Tm increases with increasing film thickness in the range of 48–1141 nm, and Tm for the films are lower than Tm for bulk PTFE, 327⬚C. Hence phase behavior such as the solid–liquid transitions should be different from bulk materials, if the system is confined with finite scale. All data can be described by the power law Tm ⬃ h n with log–log plot as shown in the inserted graph in Fig. 6, but not with a single value of n. In the present case, for the thickness between 48 and 142 nm, n 1:29 × 10 ⫺3 and n 5:53 × 10⫺3 for the thickness between 208 and 1141 nm. The observations can be well explained in view of the fact that the thickness dependence of the melting temperature results from the dependence of Tm on both the crystallite size and the film thickness, 2Tm 2Tm dD ⫹ dh; dTm 2D h 2h D or
d ln Tm 2 ln Tm 2 ln D 2 ln Tm ⫹ d ln h 2 ln D h 2 ln h 2 ln h D
where D is the average size of crystallites, and h is the film thickness. In the above equation, 2 ln D=2 ln h are given in Fig. 2(b), and the values for 2 ln Tm =2 ln D and 2 ln Tm =2 ln h are determined by our previous models [10,11] for the size dependent melting temperature and the thickness-dependent melting temperature, respectively. Based on our previous models, and the experimentally obtained values for d ln Tm =d ln h and 2 ln D=2 ln h as presented in Figs. 6 and 2(b), values for d ln Tm =d ln h and 2 ln Tm 2 ln D 2 ln Tm ⫹ 2 ln D h 2 ln h 2 ln h D in the above equation are 1.29 × 10 ⫺3 and 1.26 × 10 ⫺3 for the thickness between 48 and 142 nm, and 4.53 × 10 ⫺3 and 4.30 × 10 ⫺3 for the thickness between 208 and 1141 nm.
Tm from the two methods are fully consistent. Thus the new method based on the temperature dependence of ellipsometric angles D and c provides a simple approach for detecting solid $ liquid transitions without resorting to the calculation of film thickness of on-wafer crystalline thin films. The results have shown that the solid–liquid transitions depend on the film thickness as a result of film/ surface, film/substrate interactions and the thickness-dependent crystal size. The XRD observations have shown that the crystallite size of PTFE thin films increases from 34 to 50 nm with increasing film thickness in the range of 48–1141 nm. The observations can be well explained in view of the fact that the thickness dependence of the melting temperature results from the dependence of Tm on both the crystallite size and the film thickness by modifying a previous model for size dependent solid–liquid transitions of nanocrystals.
Acknowledgements This work is supported by the State of California Microelectronics Innovation and Computer Research Opportunities (MICRO) program.
References [1] [2] [3] [4] [5]
[6] [7] [8]
5. Conclusions [9]
A novel method has been introduced for detecting solid $ liquid transitions of on-wafer crystalline submicron thin films based on the temperature dependence of the experimentally measured ellipsometric angles D and c . This method has been applied for investigating the thickness-dependent solid–liquid transitions of low-k polycrystalline PTFE thin films. It has been observed that an abrupt change in the ellipsometric angles D and c at the first-order phase transition can be identical as melting and solidification, respectively, of the on-wafer PTFE thin films, and the melting temperature of PTFE thin films increases with increasing film thickness in the range of 48–1141 nm. A comparison between observed Tm based on the observation of D and c and the Tm obtained from the measurement of temperature-dependent thickness shows that the values of
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