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Thickness dependent dielectric breakdown of PECVD low-k carbon doped silicon dioxide dielectric thin films: modeling and experiments
Microelectronics Journal 34 (2003) 259–264 www.elsevier.com/locate/mejo
Thickness dependent dielectric breakdown of PECVD low-k carbon doped silicon dioxide dielectric thin films: modeling and experiments H. Zhoua, F.G. Shia,*, B. Zhaob a
Microelectronics Processing, Mat and Mod Lab, Department of Chemical Engineering and Materials Science, School of Engineering, University of California, 916 Engineering Tower, Irvine, CA 92697-2575, USA b Skyworks Solutions, Inc., 4311 Jamboree Road, Newport Beach, CA 92660, USA Received 16 October 2002; revised 3 December 2002; accepted 20 December 2002
Abstract The experimental results obtained on the dielectric strength EB of carbon doped silicon dioxide thin films for various film thicknesses using I – V measurements with metal – insulator – semiconductor structures suggest a new relationship between the film thickness d and the dielectric strength EB ; i.e. EB / ðd 2 dc Þ2n : This inverse power law relationship indicates the existence of a critical thickness dc which may correspond to an ultimate thickness limit below which the rate of detrapping of electron charges exceeds the rate of trapping and no dielectric breakdown can be observed. The newly obtained inverse power law relationship appears to be general since it is also supported by other published dielectric strength data for both amorphous and polycrystalline polymer thin films. q 2003 Elsevier Science Ltd. All rights reserved. Keywords: Thickness dependent; Dielectric strength; Critical thickness; Plasma-enhanced chemical vapor deposition; Low-k dielectric
1. Introduction On-chip interconnect has become a critical barrier to a continuing scaling down of IC devices. Copper is expected to alleviate the resistance problem for next few generations, the capacitance problem is expected to be alleviated by reducing the dielectric constant of intermetal dielectric that isolated conducting lines from each other. However, this later task cannot be fulfilled by simply finding a material with a low dielectric constant (low-k). The low-k materials should meet strict requirements in terms of its dielectric constant loss, moisture resistance, thermal stability and mechanical properties. Carbon doped silicon dioxide seems to meet the requirements and is expected to find wide applications as intermetal dielectric [1]. It is evident as the feature size decreases, thinner dielectric films must be employed. As expected, the film properties can deviate from that of their bulk counterparts due to the constraints imposed by confined geometry. It is found from our recent studies that that most of the structural, optical, mechanical, electrical, dielectric and thermal * Corresponding author. Tel.: þ 1-949-824-5362; fax: þ1-949-824-2541. E-mail address: [email protected] (F.G. Shi).
properties of the films are thickness dependent [2 – 11]. Thus, the thickness dependent dielectric thin film properties become an important IC design and manufacturing concern. Dielectric strength EB ; which is defined as the ratio of the breakdown voltage and the dielectric thickness [12], is considered to be one of the key properties reflecting the ability to withstand high electric fields. Thus the thickness dependence of dielectric breakdown strength of thin films has to be understood. In this work, we present the experimental results on thickness dependent dielectric strength for carbon doped silicon dioxide thin films. The experimental data obtained on the dielectric strength EB of carbon doped silicon dioxide films for various film thicknesses using I – V measurements with metal – insulator – semiconductor (MIS) structures suggest a new relationship between the film thickness d and the dielectric strength EB ; i.e. EB / ðd 2 dc Þ2n : This inverse power law relationship indicates the existence of a critical thickness dc which may correspond to an ultimate thickness limit below which the rate of detrapping of electron charges exceeds the rate of trapping and no dielectric breakdown can be observed. The newly obtained inverse power law relationship appears to be general since it
0026-2692/03/$ - see front matter q 2003 Elsevier Science Ltd. All rights reserved. doi:10.1016/S0026-2692(03)00006-5
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is also supported by other published dielectric strength data for both amorphous and polycrystalline polymer thin films.
2. Thickness dependent dielectric strength and the critical thickness limit 2.1. Dielectric breakdown Under electric field stressing, a distortion of the chemical bond in a dielectric occurs which will induce a polarization and dipoles will be formed. A further increase in electric stressing induces the interaction of the dipole with the surrounding polarized atoms. Electrons move freely after polarization and have the possibility of being trapped between the cathode and the anode to form a conductive path. The trapped electrons also have a possibility to detrap under the perturbation produced by the electron field [13 – 15]. Thus, a dynamic tapping – detrapping process of electron charges is involved for a dielectric layer under an electric field. When the trapping rate exceeds the detrapping rate and when a critical electron trap density is reached, a conductive path will be formed as shown in Fig. 1(a) and (b). On the other hand, when the detrapping rate exceeds the trapping rate, the trapped electrons can be easily detrapped and the electron path cannot be formed as showed in Fig. 1(c). 2.2. Dielectric breakdown mechanism The exact mechanism for dielectric breakdown for dielectric films is of great interest and has been the subject of debate. Electromechanical breakdown mechanism was proposed for various dielectric films [6,16 –20] because of the similarity between mechanical property and dielectric strength. A mechanical stress will be produced when a dielectric is under electric stress. Mechanical crack propagation will be initiated if the strain energy released due to electric stress is higher than that required for the materials deformation. Since mechanical stress can also affect the dielectric strength of materials, factors affecting mechanical properties can also affect dielectric strength. A thickness dependent Young’s modulus and a thickness dependent dielectric strength was found for PTFE dielectric thin films [6]. The Young’s modulus and dielectric strength was correlated thereafter. It is found that dielectric strength is proportional to the square root of the Young’s modulus for thicker films which supported the electromechanical breakdown mechanism. Other breakdown mechanism includes thermal breakdown, electronic breakdown, partial discharge and free volume breakdown [17]. In thermal breakdown, electrical power dissipation causes heating of at least part of the insulation to above a critical temperature which results directly or indirectly in catastrophic failure. In electronic breakdown the field causes either the number or the energy of the electrons to reach unstable magnitudes such that they
Fig. 1. Schematic illustration of thickness dependent trapping–detrapping process. (a) d . dc and with a larger thickness, trapped electrons are less easier to be detrapped and conductive path is easily formed; (b) d . dc and with a smaller thickness, trapped electrons are easily detrapped and conductive path is difficult to be formed; (c) d , dc ; detrapping rate exceeds trapping rate, conductive path cannot be formed.
rise catastrophically. Ultimately this causes destruction of the lattice at least locally. In partial discharge breakdown sparks occur within voids in the insulation causing degradation of the void walls and progressive deterioration of the dielectric. In free volume breakdown carriers are accelerated through spaces within low-density amorphous regions, the energy thereby gained is lost through collisions. The exact mechanism for the carbon doped silicon dioxide will be discussed in detail in our future work. 2.3. Thickness dependent dielectric strength Studies on thickness dependent dielectric strength dates back to early 1970s. Agarwal and Srivastava studied the thickness dependent dielectric breakdown of Langmuir films of barium palmitate in the thickness range of 2.3–30 nm
H. Zhou et al. / Microelectronics Journal 34 (2003) 259–264
[21,22]. They found that the thickness dependent dielectric strength follows an inverse power law relationship of EB / d 2n
thickness, when d , dc ; the detrapping rate exceeds the rate of trapping and no dielectric breakdown can be observed.
ð1Þ
The increasing breakdown strength with decreasing film thickness was interpreted as the increased boundary scattering of electrons. Subsequent studies of Cygan and Laghari on the thickness dependent dielectric strength of polypropylene found that Eq. (1) gave a good prediction of the thickness dependent dielectric strength [23]. In 1991, the work by Helgee and Bjellheim on dielectric breakdown strength of aromatic polymers found that dielectric strength vs. sample thickness follows Eq. (1) and the exponential parameter of the power law was shown to correlate with the electron accepting properties of the polymer [24]. In mid1990s, Le Gressus and G. Blaise, etc. explained this thickness dependent dielectric strength as an electron charge trapping– detrapping process. As shown in Fig. 1(a) and (b), when the trapping rate exceeds the detrapping rate, the conductive path will be formed and the dielectric breakdown will occur. For thinner films trapped charges can flow easily because detrapping field is easily formed due to its smaller thickness, as shown in Fig. 1(b). Thus the conductive path can be formed relatively easier for thicker samples as shown in Fig. 1(a). The thickness dependent dielectric strength was theoretically explained to be related with trapping and detrapping of flowing charges [15]. Most recent work of thickness dependent dielectric strength of polycrystalline polymer thin films also demonstrated that the power law relationship was followed but with different exponential parameters in different thickness ranges [6]. For films with a larger thickness, the dielectric strength was found to be the square root of the Young’s modulus thus correlated with electromechanical breakdown mechanism. 2.4. Critical thickness limit dc The expression, i.e. Eq. (1), for the thickness dependent dielectric strength was physically understood in terms of an electron charge trapping – detrapping process. One would argue that with further scaling down of the film thickness, the detrapping field would be formed so easily that the detrapping rate could exceed the trapping rate. Therefore, for dielectric films, there must exist a critical thickness limit dc : when d , dc ; detrapping rate of electron charges exceeds trapping rate and no dielectric breakdown will be observed as shown in Fig. 1(c). Thus, Eq. (1) of thickness dependent dielectric strength should contain this critical limit and be written as, EB / ðd 2 dc Þ2n
261
ð2Þ
where dc is the critical thickness limit. Eq. (2) is for the first time able to present the thickness dependent dielectric breakdown as a critical phenomena: when d . dc ; the trapping rate exceeds the rate of detrapping and the dielectric strength increases with the decreasing of film
3. Experiments The low-k dielectric thin carbon-doped silicon dioxide films were deposited at 400 8C on the Si wafers by PlasmaEnhanced Chemical Vapor Deposition (PECVD). The low-k PECVD precursor used in this process is cyclic 1,3,5,7-tetramethylcyclotetrasiloxane (TMCTS). TMCTS is prepared through hydrolysis of methyldichlorosilane to first form a linear siloxane polymer that is endcapped with trimethylsilyl groups (derived from trimethylchlorosilane) according to [25]: ðCH3 ÞSiðHÞðCl2 Þ þ ðCH3 Þ3 SiCl ! ðCH3 Þ3 Si – O – ½SiHCH3 – On – SiðCH3 Þ3 ðCH3 Þ3 Si – O – ½SiHCH3 – On – SiðCH3 Þ3 ! TMCTS þ other cyclic compounds Samples of low-k dielectric thin films with thickness of 32, 50, 76, 105 and 153 nm were studied. Metal electrodes of aluminum with area of 4 mm2 and thickness of 10 nm was deposited by thermal evaporator at vacuum pressure of 1.5 £ 1026 Pa on the top surface of the films. The dielectric breakdown was investigated using the MIS structures and were measured by an HP 4156A Precision Semiconductor Parameter Analyzer. The experimental setup is schematically shown in Fig. 2. The dielectric breakdown was also measured by a second experimental setup: a copper strip was applied as the metal electrode on top of the thin film on wafer sample and two probes were connected from a high voltage power supply and the schematic setup is shown in Fig. 3. The voltage at which a current jump occurs was recorded as the breakdown voltage. I – V measurements were performed with the voltage swept up for carbon doped silicon dioxide thin films with different thickness. Fig. 4 shows the data of breakdown voltage gathered from the two experimental setups. It is seen that the same decrease of breakdown voltage with the decrease of film thickness is observed but with a slightly higher value for the second experimental setup. The existing copper oxide on the electrode for the second setup may explain the slight difference.
4. Results and discussions 4.1. Thickness dependent dielectric breakdown strength Fig. 5 shows the I – V characteristics of carbon doped silicon dioxide with thickness of 153, 105, 76, 50 and
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Fig. 2. Schematic experimental setup for the dielectric strength measurement using MIS structure by HP semiconductor analyzer. (a) top view; (b) side view.
Fig. 3. Schematic experimental setup for the dielectric strength measurement by high voltage power supply.
32 nm. It is seen that in the ramping voltage range at room temperature no dielectric breakdown was observed for film with thickness of 153 nm and the breakdown voltage decreases with the decrease of film thickness. The experimental data on the thickness dependence of carbon doped silicon dioxide thin films is presented in Fig. 6. It is evident that the dielectric strength increases with the decrease of thickness. The film thickness dependence has been related to charge trapping and detrapping [13], material structure and morphology. For thinner films, trapped charges can flow easily because trapped charges do not accumulate within the insulator due to its smaller thickness. Hence, a higher electric field is needed to induce electron avalanches [6]. This thickness dependence dielectric strength can be fitted well by Eq. (2) where n is the fitting parameter. The n factor can be varied with different films, and is related to microscopic structure and charge transfer [13,14]. For polymers, it has been discussed in terms of the electron
Fig. 4. Comparison of breakdown voltage measurement from HP semiconductor analyzer and the second experimental setup.
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263
shows the thickness dependence dielectric strength for polycrystalline and amorphous polymer thin films [6,23]. It is evident that Eq. (2) is well supported by the experimental data on dielectric strength of amorphous and polycrystalline polymer thin films. 5. Conclusions
Fig. 5. Thickness dependent I – V characteristics of carbon doped silicon dioxide thin films.
affinity [6,21]. This power law relationship has also found to be thickness dependent: different n values in different thickness region [6]. In the present case, n is fitted to be 0.57, which is in the range of 0.5– 1.0 of the reported values [14,22,24].
The experimental results obtained on the dielectric strength EB of carbon doped silicon dioxide films for various film thicknesses using I – V measurements with MIS structures support the relationship between the thickness d and EB ; EB / ðd 2 dc Þ2n : This inverse power law relationship indicates the existence of a critical thickness dc which may correspond to an ultimate thickness limit below which the rate of detrapping of electron charges exceeds the rate of trapping and no dielectric breakdown can be observed. The newly obtained inverse power law relationship appears to be general since it is also supported by other published dielectric strength data for both amorphous and polycrystalline polymer thin films. Acknowledgements
4.2. The critical thickness limit The modified inverse power law relationship of Eq. (2) not only presents the thickness dependence of dielectric strength as the inverse power law relationship [6,24], but it also indicates the existence of a critical thickness limit dc : When d , dc ; detrapping of electron charge is dominant and no dielectric breakdown will be observed. For the present case of carbon doped silicon dioxide thin film, dc ¼ 3:04 nm as shown in Fig. 6. The figure also
Fig. 6. Thickness dependent dielectric strength for carbon doped silicon dioxide thin films, polycrystalline and amorphous polymer films. The solid line represents Eq. (2).
The authors would like to express their thanks to Toby Lee for his help on the experimental measurement, H.K. Kim for the helpful discussions and J. Yota for preparing the thin films. Support of this study by the MICRO program (01-080) of the State of California is also greatly acknowledged. References [1] P. Sermon, K. Beekmann, S. McClatchie, Low-k dielectrics for future IC fabrication. Semiconductor Fabtech, 11th ed 2002. [2] D.T. Hsu, H.K. Kim, F.G. Shi, B. Zhao, M. Brongo, P. Schilling, S.Q. Wang, ILD thermal stability in deep-submicron technologies: from thin to ultrathin dielectric films, Proc. SPIE Conf. Multilevel Interconnect Technol. III 3883 (1999) 60 –67. [3] D.T. Hsu, H.K. Kim, F.G. Shi, B. Zhao, M. Brongo, Thickness dependent dielectric properties of low-k materials: a theoretical model, Proceedings of the Fourth International Symposium Low and High Dielectric Constant Materials: Materials Science, Processing, and Reliability Issues, Seattle, WA, May 2000, 99-7, pp. 62 –68. [4] D.T. Hsu, F.G. Shi, B. Zhao, M. Brongo, Theory for the thickness dependent glass transition temperature of amorphous polymer thin films, Proceedings of the Fourth International Symposium of Low and High Dielectric Constant Materials: Materials Science, Processing, and Reliability Issues, Seattle, WA, May 2000, 99-7, pp. 53 –61. [5] H.K. Kim, F.G. Shi, B. Zhao, M. Brongo, Low-k dielectrics for ULSI multilevel interconnections: thickness dependent electrical and dielectric properties, Conference Record of the 2000 IEEE International Symposium on Electrical Insulation, Piscataway, NJ, USA, 2000, pp. 269–271. [6] H.K. Kim, F.G. Shi, Thickness dependent dielectric strength of a lowpermittivity dielectric film, IEEE Trans. Dielectr. Electr. Insulat. 8 (2) (2001) 248–252.
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[7] H.K. Kim, F.G. Shi, Thickness-dependent thermal reliability of lowdielectric constant polycrystalline PTFE submicron dielectric thin films, Microelectron. J. 32 (3) (2001) 215 –219. [8] J. Wang, F.G. Shi, T.G. Nieh, B. Zhao, M. Brongo, S. Qu, T. Rosenmayer, Thickness dependence of elastic modulus and hardness of on-wafer low-k ultrathin poly-tetrafluoroethylene films, Scripta Mater. 42 (2000) 687 –694. [9] H. Zhou, H.K. Kim, F.G. Shi, B. Zhao, J. Yota, Thickness dependent glass transition temperature of PECVD low-k dielectric thin films: effect of deposition methods, Microelectron. J. 33 (3) (2002) 221–227. [10] H. Zhou, H.K. Kim, F.G. Shi, B. Zhao, J. Yota, Optical properties of PECVD dielectric thin films: thickness and deposition method dependence, Microelectron. J. (2003) 33(11) 999 –1004. [11] J. Wang, H.K. Kim, F.G. Shi, B. Zhao, T.G. Nieh, Thickness dependence of morphology and mechanical properties of on-wafer low-k PTFE dielectric films, Thin Solid Films 377–378 (2000) 413–417. [12] M.M. Ueki, M. Zanin, Influence of additives on the dielectric strength of high-density polyethylene, IEEE Trans. Dielectr. Electr. Insulat. 6 (6) (1999) 876–881. [13] K.H. Oh, C.K. Ong, B.T.G. Tan, C. Le Gressus, G. Blaise, Variation of trapping–detrapping properties as a function of the insulator size, J. Appl. Phys. Lett. 74 (1993) 1960–1967. [14] G. Damamme, C. Le Gressus, Effect of insulator size on the breakdown strength, IEEE 1997 Annual Report Conference On Electrical Insulation and Dielectric Phenomena, 1997, pp. 92–95. [15] G. Blaise, Space-charge physics and the breakdown process, J. Appl. Phys. 77 (7) (1995) 2916–2927.
[16] J.C. Fothergill, Filamentary electromechanical breakdown, IEEE Trans. Electr. Insulat. 26 (6) (1991) 1124–1129. [17] J.C. Fothergill, Filamentary electromechanical breakdown in polymers, Proceedings of the Fourth International Conference on Conduction and Breakdown in Solid Dielectrics, Sestri Levante, Italy, June 1992, pp. 323– 327. [18] G.R. Greenway, A.S. Vaughan, S.M. Moody, Morphology and electro-mechanical breakdown model in polyethylene, Conf. Electr. Insulat. Dielectr. Phenom. 2 (1999) 666 –669. [19] S. Jeffery, C.J. Sofield, J.B. Pethica, The influence of mechanical stress on the dielectric breakdown field strength of thin SiO2 films, Appl. Phys. Lett. 73 (2) (1998) 172–174. [20] T.J. Lewis, New electro-mechanical concepts of the primary mechanisms of electrical breakdown in liquids. Roma, Italy, July 1996, pp. 273 –278. [21] V.K. Agarwal, V.K. Srivastava, Thickness dependent studies of dielectric breakdown in Langmuir thin molecular films, Solid State Commun. 12 (1973) 829–834. [22] V.K. Agarwal, V.K. Srivastava, Thickness dependence of breakdown field in thin films, Thin solid films 8 (1971) 377 –381. [23] S. Cygan, J.R. Laghari, Dependence of the electric strength on thickness area and volume of polypropylene, IEEE Trans. Electr. Insulat. 22 (6) (1987) 835– 837. [24] B. Helgee, P. Bjellheim, Electric breakdown strength of aromatic polymers: dependence on film thickness and chemical structure, IEEE Trans. Electr. Insulat. 26 (6) (1991) 1147–1152. [25] R.K. Laxman, N.H. Hendricks, B. Arkles, T.A. Tabler, Synthesizing low-k CVD materials for fab use, Semicond. Int. 23 (2000) 95– 102.
Thickness dependent dielectric breakdown of PECVD low-k carbon doped silicon dioxide dielectric thin films: modeling and experiments H. Zhoua, F.G. Shia,*, B. Zhaob a
Microelectronics Processing, Mat and Mod Lab, Department of Chemical Engineering and Materials Science, School of Engineering, University of California, 916 Engineering Tower, Irvine, CA 92697-2575, USA b Skyworks Solutions, Inc., 4311 Jamboree Road, Newport Beach, CA 92660, USA Received 16 October 2002; revised 3 December 2002; accepted 20 December 2002
Abstract The experimental results obtained on the dielectric strength EB of carbon doped silicon dioxide thin films for various film thicknesses using I – V measurements with metal – insulator – semiconductor structures suggest a new relationship between the film thickness d and the dielectric strength EB ; i.e. EB / ðd 2 dc Þ2n : This inverse power law relationship indicates the existence of a critical thickness dc which may correspond to an ultimate thickness limit below which the rate of detrapping of electron charges exceeds the rate of trapping and no dielectric breakdown can be observed. The newly obtained inverse power law relationship appears to be general since it is also supported by other published dielectric strength data for both amorphous and polycrystalline polymer thin films. q 2003 Elsevier Science Ltd. All rights reserved. Keywords: Thickness dependent; Dielectric strength; Critical thickness; Plasma-enhanced chemical vapor deposition; Low-k dielectric
1. Introduction On-chip interconnect has become a critical barrier to a continuing scaling down of IC devices. Copper is expected to alleviate the resistance problem for next few generations, the capacitance problem is expected to be alleviated by reducing the dielectric constant of intermetal dielectric that isolated conducting lines from each other. However, this later task cannot be fulfilled by simply finding a material with a low dielectric constant (low-k). The low-k materials should meet strict requirements in terms of its dielectric constant loss, moisture resistance, thermal stability and mechanical properties. Carbon doped silicon dioxide seems to meet the requirements and is expected to find wide applications as intermetal dielectric [1]. It is evident as the feature size decreases, thinner dielectric films must be employed. As expected, the film properties can deviate from that of their bulk counterparts due to the constraints imposed by confined geometry. It is found from our recent studies that that most of the structural, optical, mechanical, electrical, dielectric and thermal * Corresponding author. Tel.: þ 1-949-824-5362; fax: þ1-949-824-2541. E-mail address: [email protected] (F.G. Shi).
properties of the films are thickness dependent [2 – 11]. Thus, the thickness dependent dielectric thin film properties become an important IC design and manufacturing concern. Dielectric strength EB ; which is defined as the ratio of the breakdown voltage and the dielectric thickness [12], is considered to be one of the key properties reflecting the ability to withstand high electric fields. Thus the thickness dependence of dielectric breakdown strength of thin films has to be understood. In this work, we present the experimental results on thickness dependent dielectric strength for carbon doped silicon dioxide thin films. The experimental data obtained on the dielectric strength EB of carbon doped silicon dioxide films for various film thicknesses using I – V measurements with metal – insulator – semiconductor (MIS) structures suggest a new relationship between the film thickness d and the dielectric strength EB ; i.e. EB / ðd 2 dc Þ2n : This inverse power law relationship indicates the existence of a critical thickness dc which may correspond to an ultimate thickness limit below which the rate of detrapping of electron charges exceeds the rate of trapping and no dielectric breakdown can be observed. The newly obtained inverse power law relationship appears to be general since it
0026-2692/03/$ - see front matter q 2003 Elsevier Science Ltd. All rights reserved. doi:10.1016/S0026-2692(03)00006-5
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is also supported by other published dielectric strength data for both amorphous and polycrystalline polymer thin films.
2. Thickness dependent dielectric strength and the critical thickness limit 2.1. Dielectric breakdown Under electric field stressing, a distortion of the chemical bond in a dielectric occurs which will induce a polarization and dipoles will be formed. A further increase in electric stressing induces the interaction of the dipole with the surrounding polarized atoms. Electrons move freely after polarization and have the possibility of being trapped between the cathode and the anode to form a conductive path. The trapped electrons also have a possibility to detrap under the perturbation produced by the electron field [13 – 15]. Thus, a dynamic tapping – detrapping process of electron charges is involved for a dielectric layer under an electric field. When the trapping rate exceeds the detrapping rate and when a critical electron trap density is reached, a conductive path will be formed as shown in Fig. 1(a) and (b). On the other hand, when the detrapping rate exceeds the trapping rate, the trapped electrons can be easily detrapped and the electron path cannot be formed as showed in Fig. 1(c). 2.2. Dielectric breakdown mechanism The exact mechanism for dielectric breakdown for dielectric films is of great interest and has been the subject of debate. Electromechanical breakdown mechanism was proposed for various dielectric films [6,16 –20] because of the similarity between mechanical property and dielectric strength. A mechanical stress will be produced when a dielectric is under electric stress. Mechanical crack propagation will be initiated if the strain energy released due to electric stress is higher than that required for the materials deformation. Since mechanical stress can also affect the dielectric strength of materials, factors affecting mechanical properties can also affect dielectric strength. A thickness dependent Young’s modulus and a thickness dependent dielectric strength was found for PTFE dielectric thin films [6]. The Young’s modulus and dielectric strength was correlated thereafter. It is found that dielectric strength is proportional to the square root of the Young’s modulus for thicker films which supported the electromechanical breakdown mechanism. Other breakdown mechanism includes thermal breakdown, electronic breakdown, partial discharge and free volume breakdown [17]. In thermal breakdown, electrical power dissipation causes heating of at least part of the insulation to above a critical temperature which results directly or indirectly in catastrophic failure. In electronic breakdown the field causes either the number or the energy of the electrons to reach unstable magnitudes such that they
Fig. 1. Schematic illustration of thickness dependent trapping–detrapping process. (a) d . dc and with a larger thickness, trapped electrons are less easier to be detrapped and conductive path is easily formed; (b) d . dc and with a smaller thickness, trapped electrons are easily detrapped and conductive path is difficult to be formed; (c) d , dc ; detrapping rate exceeds trapping rate, conductive path cannot be formed.
rise catastrophically. Ultimately this causes destruction of the lattice at least locally. In partial discharge breakdown sparks occur within voids in the insulation causing degradation of the void walls and progressive deterioration of the dielectric. In free volume breakdown carriers are accelerated through spaces within low-density amorphous regions, the energy thereby gained is lost through collisions. The exact mechanism for the carbon doped silicon dioxide will be discussed in detail in our future work. 2.3. Thickness dependent dielectric strength Studies on thickness dependent dielectric strength dates back to early 1970s. Agarwal and Srivastava studied the thickness dependent dielectric breakdown of Langmuir films of barium palmitate in the thickness range of 2.3–30 nm
H. Zhou et al. / Microelectronics Journal 34 (2003) 259–264
[21,22]. They found that the thickness dependent dielectric strength follows an inverse power law relationship of EB / d 2n
thickness, when d , dc ; the detrapping rate exceeds the rate of trapping and no dielectric breakdown can be observed.
ð1Þ
The increasing breakdown strength with decreasing film thickness was interpreted as the increased boundary scattering of electrons. Subsequent studies of Cygan and Laghari on the thickness dependent dielectric strength of polypropylene found that Eq. (1) gave a good prediction of the thickness dependent dielectric strength [23]. In 1991, the work by Helgee and Bjellheim on dielectric breakdown strength of aromatic polymers found that dielectric strength vs. sample thickness follows Eq. (1) and the exponential parameter of the power law was shown to correlate with the electron accepting properties of the polymer [24]. In mid1990s, Le Gressus and G. Blaise, etc. explained this thickness dependent dielectric strength as an electron charge trapping– detrapping process. As shown in Fig. 1(a) and (b), when the trapping rate exceeds the detrapping rate, the conductive path will be formed and the dielectric breakdown will occur. For thinner films trapped charges can flow easily because detrapping field is easily formed due to its smaller thickness, as shown in Fig. 1(b). Thus the conductive path can be formed relatively easier for thicker samples as shown in Fig. 1(a). The thickness dependent dielectric strength was theoretically explained to be related with trapping and detrapping of flowing charges [15]. Most recent work of thickness dependent dielectric strength of polycrystalline polymer thin films also demonstrated that the power law relationship was followed but with different exponential parameters in different thickness ranges [6]. For films with a larger thickness, the dielectric strength was found to be the square root of the Young’s modulus thus correlated with electromechanical breakdown mechanism. 2.4. Critical thickness limit dc The expression, i.e. Eq. (1), for the thickness dependent dielectric strength was physically understood in terms of an electron charge trapping – detrapping process. One would argue that with further scaling down of the film thickness, the detrapping field would be formed so easily that the detrapping rate could exceed the trapping rate. Therefore, for dielectric films, there must exist a critical thickness limit dc : when d , dc ; detrapping rate of electron charges exceeds trapping rate and no dielectric breakdown will be observed as shown in Fig. 1(c). Thus, Eq. (1) of thickness dependent dielectric strength should contain this critical limit and be written as, EB / ðd 2 dc Þ2n
261
ð2Þ
where dc is the critical thickness limit. Eq. (2) is for the first time able to present the thickness dependent dielectric breakdown as a critical phenomena: when d . dc ; the trapping rate exceeds the rate of detrapping and the dielectric strength increases with the decreasing of film
3. Experiments The low-k dielectric thin carbon-doped silicon dioxide films were deposited at 400 8C on the Si wafers by PlasmaEnhanced Chemical Vapor Deposition (PECVD). The low-k PECVD precursor used in this process is cyclic 1,3,5,7-tetramethylcyclotetrasiloxane (TMCTS). TMCTS is prepared through hydrolysis of methyldichlorosilane to first form a linear siloxane polymer that is endcapped with trimethylsilyl groups (derived from trimethylchlorosilane) according to [25]: ðCH3 ÞSiðHÞðCl2 Þ þ ðCH3 Þ3 SiCl ! ðCH3 Þ3 Si – O – ½SiHCH3 – On – SiðCH3 Þ3 ðCH3 Þ3 Si – O – ½SiHCH3 – On – SiðCH3 Þ3 ! TMCTS þ other cyclic compounds Samples of low-k dielectric thin films with thickness of 32, 50, 76, 105 and 153 nm were studied. Metal electrodes of aluminum with area of 4 mm2 and thickness of 10 nm was deposited by thermal evaporator at vacuum pressure of 1.5 £ 1026 Pa on the top surface of the films. The dielectric breakdown was investigated using the MIS structures and were measured by an HP 4156A Precision Semiconductor Parameter Analyzer. The experimental setup is schematically shown in Fig. 2. The dielectric breakdown was also measured by a second experimental setup: a copper strip was applied as the metal electrode on top of the thin film on wafer sample and two probes were connected from a high voltage power supply and the schematic setup is shown in Fig. 3. The voltage at which a current jump occurs was recorded as the breakdown voltage. I – V measurements were performed with the voltage swept up for carbon doped silicon dioxide thin films with different thickness. Fig. 4 shows the data of breakdown voltage gathered from the two experimental setups. It is seen that the same decrease of breakdown voltage with the decrease of film thickness is observed but with a slightly higher value for the second experimental setup. The existing copper oxide on the electrode for the second setup may explain the slight difference.
4. Results and discussions 4.1. Thickness dependent dielectric breakdown strength Fig. 5 shows the I – V characteristics of carbon doped silicon dioxide with thickness of 153, 105, 76, 50 and
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Fig. 2. Schematic experimental setup for the dielectric strength measurement using MIS structure by HP semiconductor analyzer. (a) top view; (b) side view.
Fig. 3. Schematic experimental setup for the dielectric strength measurement by high voltage power supply.
32 nm. It is seen that in the ramping voltage range at room temperature no dielectric breakdown was observed for film with thickness of 153 nm and the breakdown voltage decreases with the decrease of film thickness. The experimental data on the thickness dependence of carbon doped silicon dioxide thin films is presented in Fig. 6. It is evident that the dielectric strength increases with the decrease of thickness. The film thickness dependence has been related to charge trapping and detrapping [13], material structure and morphology. For thinner films, trapped charges can flow easily because trapped charges do not accumulate within the insulator due to its smaller thickness. Hence, a higher electric field is needed to induce electron avalanches [6]. This thickness dependence dielectric strength can be fitted well by Eq. (2) where n is the fitting parameter. The n factor can be varied with different films, and is related to microscopic structure and charge transfer [13,14]. For polymers, it has been discussed in terms of the electron
Fig. 4. Comparison of breakdown voltage measurement from HP semiconductor analyzer and the second experimental setup.
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shows the thickness dependence dielectric strength for polycrystalline and amorphous polymer thin films [6,23]. It is evident that Eq. (2) is well supported by the experimental data on dielectric strength of amorphous and polycrystalline polymer thin films. 5. Conclusions
Fig. 5. Thickness dependent I – V characteristics of carbon doped silicon dioxide thin films.
affinity [6,21]. This power law relationship has also found to be thickness dependent: different n values in different thickness region [6]. In the present case, n is fitted to be 0.57, which is in the range of 0.5– 1.0 of the reported values [14,22,24].
The experimental results obtained on the dielectric strength EB of carbon doped silicon dioxide films for various film thicknesses using I – V measurements with MIS structures support the relationship between the thickness d and EB ; EB / ðd 2 dc Þ2n : This inverse power law relationship indicates the existence of a critical thickness dc which may correspond to an ultimate thickness limit below which the rate of detrapping of electron charges exceeds the rate of trapping and no dielectric breakdown can be observed. The newly obtained inverse power law relationship appears to be general since it is also supported by other published dielectric strength data for both amorphous and polycrystalline polymer thin films. Acknowledgements
4.2. The critical thickness limit The modified inverse power law relationship of Eq. (2) not only presents the thickness dependence of dielectric strength as the inverse power law relationship [6,24], but it also indicates the existence of a critical thickness limit dc : When d , dc ; detrapping of electron charge is dominant and no dielectric breakdown will be observed. For the present case of carbon doped silicon dioxide thin film, dc ¼ 3:04 nm as shown in Fig. 6. The figure also
Fig. 6. Thickness dependent dielectric strength for carbon doped silicon dioxide thin films, polycrystalline and amorphous polymer films. The solid line represents Eq. (2).
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