1. Introduction

2. Materials and Methods

3. Results and Discussions

3.2. Spectroscopic Ellipsometry (SE) and Ellipsometric Porometry (EP) Data

Table 2 presents the properties of the studied OSG low-k films, as measured by SE and EP. The film thickness decreases from 324 nm to 170 nm after annealing, due to the shrinkage, while the refractive index increases simultaneously. The highest refractive index, n = 1.392, corresponds to the film annealed at 900 °C.

Figures 4 illustrate the adsorption/desorption isotherms and pore radius distribution in the films. Within the temperature range of 350–500 °С, the median pore size increases from 1.15 to 1.51 nm. The isotherm obtained in the films annealed at 350 °C shows the presence of micropores (slope at P/P₀ < 0.05) with a small relative volume of about 5–10%. Then, the micropores volume decreases after annealing at 400 °C and becomes undetectable after 500 °C. Therefore, the increase of median size of pores and the small reduction of measured porosity are related to the collapse of micropores and the short-ranged structural rearrangement of the OSG matrix [25]. Further annealing at T_a = 600 °C shows an opposite effect of reduction of the median pore size to 1.09 nm and appearance of the micropores. This effect can be correlated with reduction of CH₃ groups’ concentration and collapse of some part of large pores. At 600 and 700 °С, the bimodal nature of the pore distribution is clearly evident, with appearance of the left peak corresponding to the presence of micropores. The micropores are becoming dominant in the films annealed at 700 °C.

Figure 4. Adsorption/desorption isotherms (top) and pore radius distribution (bottom) for the organosilicate films studied, which were heat-treated at different temperatures: 350 °С (a), 400 °С (b), 450 °С (c), 500 °С (d), 600 °С (e), and 700 °С (f).

Figure 4. Adsorption/desorption isotherms (top) and pore radius distribution (bottom) for the organosilicate films studied, which were heat-treated at different temperatures: 350 °С (a), 400 °С (b), 450 °С (c), 500 °С (d), 600 °С (e), and 700 °С (f).

The films annealed at 900 °C no longer show the presence of open pores, suggesting a complete collapse of all pores because of sintering silica matrix [26]. According to FTIR data, this film no longer contains CH₃ groups, and the position of the Si–O–Si peak corresponds to pure SiO₂. However, the refractive index of the film is 1.392, which is lower than the typical value measured in SiO₂ films (1.46). This indicates a difference between full and open porosity and suggests that some micropores (free volume) still remain in the films (Figure 5). The fact that they are not detectable by EP suggests that their size is smaller than the probe used in our EP measurements (the kinetic diameter of IPA molecules is 0.47 nm [27].

3.4. Discussion of the Leakage Mechanism

The physical mechanism of electrical conduction in OSG low-k dielectrics has been the focus of extensive research and discussion for many years. The most extensively studied models are based on field-enhanced thermal excitation of electrons entering the conduction band from the low-k interface and the trap states (SE and PF emission). Tunneling of electrons from the metal Fermi energy or trapping sites into the low-k dielectric conduction band is termed the Fowler–Nordheim (FN) mechanism. It has been concluded [21] that PF emission is more likely the dominant conduction mechanism in low-k dielectrics especially at low fields [16,32,33]. FN tunneling conduction can occur at high field ranges [34,35]. The effectiveness of these conduction mechanisms often depends on the presence of porogen (surfactant) residues. These residues are primarily formed due to suboptimal UV-assisted thermal curing and moisture trapped in internal defects caused by the integration process, such as plasma damage, which tends to remove carbon-containing groups.

An alternative mechanism based on phonon-assisted tunneling was proposed by Gritsenko and his colleagues for several low-k dielectrics, primarily those based on carbon-bridged PMO (see ref. [5] and the references cited therein). From a materials science perspective, the Gritsenko models primarily rely on the concept of the formation and active role of oxygen-deficient centers (ODC). The ODC’s are diamagnetic and therefore invisible to electron paramagnetic resonance (EPR) techniques, making the reliable identification of these defects quite difficult. The role of oxygen-deficient centers (ODCs) in influencing the electrical properties of silica-based materials has been widely studied using UV-induced luminescence [36,37,38,39]. However, similar luminescence studies of OSG low-k dielectrics remain limited [40,41], and the conclusions are somewhat controversial [7]. Pustovarov et al. [40] reported the presence of oxygen-deficient centers (ODC) in ethylene-bridged PMO films. However, they used an excitation wavelength of 10.6 eV, which significantly exceeds the energy required to break Si–CH₃ bonds. As a result, ODC precursors (Si dangling bonds, E’ centers [8]) can be generated during the measurements. In contrast, Rasadujjaman et al. [41] investigated the luminescence of several OSG films with varying compositions, using an excitation wavelength near 200 nm. They concluded that ODC centers do not form in OSG low-k films within the temperature range used for interconnect technology (<500 °C).

Typically, phonon-assisted tunneling and Poole–Frenkel emission are two competing mechanisms that enhance carrier emission, with their relative contributions determined by the type and charge state of the defect. In the case of OSG low-k dielectrics, the presence and active role of carbon residue and adsorbed water have been more extensively studied, and their correlation with electrical properties is well documented. A more difficult situation is with oxygen deficient centers although conclusions about their formation in OSG films were reported by Pomorski et al. [11] and in the ref. [40]. Although the luminescence is the most efficient technique some signs can also be obtained by different techniques. In stoichiometrically clean and dense dielectrics, FTIR and XPS data can be used to show the formation of oxygen-deficient suboxide-like structures. However, OSG films initially exhibit similar shifts due to the replacement of some oxygen atoms with methyl terminal groups. Another reported doubt about the possibility of formation of oxygen-deficient centers is that the low thermal budget of these films does not allow for the formation of oxygen-deficient centers. The annealing temperatures are much lower than those typically required for matrix relaxation (≥1000 °C), which is essential for ODC formation [8].

3.4.1. Verification of NG Model

The current density through the dielectric materials containing electronic traps is described by Equation (3):

$$j=e{N}^{{\displaystyle \raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}}P,$$

(3)

where N = a^–3 is the traps concentration, a is a mean distance between the traps. P is probability of the traps ionization. In NG model of phonon assisted tunneling

$$P={\displaystyle \frac{2\sqrt{\pi }\mathrm{ħ}{W}_T}{m^{\mathrm{*}}{a}^2\sqrt{2kT(W_{opt}-W_T)}}}exp\left(-{\displaystyle \frac{W_{opt}-W_T}{kT}}\right)\exp \left(-{\displaystyle \frac{2a\sqrt{2m^{\mathrm{*}}{W}_T}}{\mathrm{ħ}}}\right)\sinh \left({\displaystyle \frac{eFa}{2kT}}\right),$$

(4)

where ħ is Planck constant, W_T is thermal energy of ionization, m* is effective mass, k is Boltzmann constant, W_opt is optical energy of ionization, F is electric field.

Figure 8 shows JV curves obtained with studied samples (experimental data are replotted from the data presented in Figure 6).

Figure 8. Current–voltage curves for low-k films annealed at different temperatures. The large dots represent the results obtained from simulations using the Nasyrov–Gritsenko (NG) model.

Figure 8. Current–voltage curves for low-k films annealed at different temperatures. The large dots represent the results obtained from simulations using the Nasyrov–Gritsenko (NG) model.

JV characteristics are satisfactorily described by the model of phonon-assisted tunneling between the traps (NG model). The simulation was based on the assumption of two different trap models: the trap based on the oxygen vacancy center with thermal energy W_T = 1.6 eV (≡Si–Si≡) and the trap based on oxygen divacancy with W_T = 1.2 eV (≡Si–Si–Si≡). The agreement between modeling and experimental data was achieved in assumption that the traps are oxygen vacancies with optical energy of ionization 3.2 eV and oxygen di-vacancies with optical energy 2.4 eV (Table 3).

The results presented in Table 3 indicate that, according to the ODC-based model, single oxygen vacancies can be considered traps at temperatures of 350, 400, 450, 500, and 900 °C, while divacancies are present at 600 and 700 °C. These conclusions seem unusual, as the formation of oxygen vacancies at these temperatures is generally considered improbable. If, for some unknown reason, oxygen vacancies and even divacancies are forming at 600 and 700 °C, their formation at 900 °C should be even more favorable. Additionally, the calculated trap concentrations are unusual. According to the traditional view, the presence of a suboxide-like band in FTIR spectra suggests the formation of ODCs, but the data presented in Figure 3 show an opposite trend: increasing temperature gradually shifts the Si–O–Si band to its matrix position. Therefore, if ODCs were formed as defects originating from precursors, their concentration should decrease with increasing annealing temperature. Consequently, we can conclude that the model based on phonon-assisted tunneling between ODC centers does not apply in this case.

3.4.2. Verification of SE and PF Models

The experimental current–voltage characteristics obtained through two models (Schottky Emission (SE) and Poole–Frenkel (PF)) of charge transfer are illustrated in Figure 9 and Figure 10. Utilizing a regression method, we determined the coefficients of the equations corresponding to the linear sections of the data [42]. The slope of these approximating lines allows us to identify the predominant mechanism of charge carrier transport. To achieve this, we calculated the values of the high-frequency (optical) dielectric permittivity of the film based on the slope angle coefficients for the lines plotted in Schottky and Poole–Frenkel coordinates, employing the formulas derived from Equations (5) and (6).

$${\epsilon }_i={\displaystyle \frac{1}{{\left(k_B·T\right)}^2}}·{\displaystyle \frac{q^3}{4·\pi ·{\epsilon }_0}}·{\displaystyle \frac{1}{{\left(K_{Sh}\right)}^2}}$$

(5)

$${\epsilon }_i={\displaystyle \frac{1}{{\left(k_B·T\right)}^2}}·{\displaystyle \frac{q^3}{\pi ·{\epsilon }_0}}·{\displaystyle \frac{1}{{\left(K_{P-F}\right)}^2}}$$

(6)

where K_Sh and K_P-F – the slope angle coefficients of the approximating straight lines in Schottky and Poole–Frenkel coordinates, respectively.

To elucidate the mechanisms underlying current flow attributed to Schottky (Figure 9) and Poole–Frenkel (Figure 10) emissions, graphical representations were constructed. These representations depict the relationship of ($\mathrm{l}\mathrm{n}\left(I\right)$ versus$\sqrt{E}$) for Schottky emissions and ($\mathrm{l}\mathrm{n}(I/E)$ versus$\sqrt{E}$) for Poole–Frenkel emissions, utilizing experimental data as the foundation for analysis.

The values of ε_i for organosilicate films at various annealing temperatures, as determined through linear approximation in Poole–Frenkel and Schottky coordinates, are presented in Table 4. The mechanism yielding a calculated ε_i value closest to n². As indicated by the calculated ε_i values in Table 3, it is evident that the predominant mechanism of charge carrier transfer is Poole–Frenkel emission in all instances.

At annealing temperatures of 350, 400, and 900 °C, the calculated values of ε_i as determined by the Poole–Frenkel model, align most closely with the experimental data. At an annealing temperature of T_a = 450 °C it is evident that both Poole–Frenkel and Schottky mechanisms are active. Between T_a = 500–700 °C the films demonstrate complex mechanisms, predominantly characterized by Poole–Frenkel emission, which warrants further investigation. Nonetheless, the findings from the study of leakage current models in OSG films subjected to various annealing temperatures lead to the conclusion that, in the presence of high electric field strengths (>120 kV/cm) the most likely mechanism for charge carrier transfer is Poole–Frenkel emission.

4. Conclusion

References

1. Bohr, M.T. Interconnect scaling—the real limiter to high performance ULSI. Solid State Technol. 1996, 39, 105–111. [Google Scholar] [CrossRef]
2. Havemann, R.H.; Hutchby, J.A. High-performance interconnects: An integration overview. Proc. IEEE 2001, 89, 586–601. [Google Scholar] [CrossRef]
3. Moon, J.H.; Jeong, E.; Kim, S.; Kim, T.; Oh, E.; Lee, K.; Han, H.; Kim, Y.K. Materials quest for advanced interconnect metallization in integrated circuits. Adv. Sci. 2023, 10, 2207321. [Google Scholar] [CrossRef]
4. Volksen, W.; Miller, R.D.; Dubois, G. Low dielectric constant materials. Chem. Rev. 2010, 110, 56–110. [Google Scholar] [CrossRef] [PubMed]
5. Grill, A.; Gates, S.M.; Ryan, T.E.; Nguyen, S.V.; Priyadarshini, D. Progress in the development and understanding of advanced low k and ultralow k dielectrics for very large-scale integrated interconnects—State of the art. Appl. Phys. Rev. 2014, 1, 011306. [Google Scholar] [CrossRef]
6. Michalak, D.J.; Blackwell, J.M.; Torres, J.M.; Sengupta, A.; Kreno, L.E.; Clarke, J.S.; Pantuso, D. Porosity scaling strategies for low-k films. J. Mater. Res. 2015, 30, 3363–3385. [Google Scholar] [CrossRef]
7. Baklanov, M.R.; Gismatulin, A.A.; Naumov, S.; Perevalov, T.V.; Gritsenko, V.A.; Vishnevskiy, A.S.; Rakhimova, T.V.; Vorotilov, K.A. Comprehensive Review on the Impact of Chemical Composition, Plasma Treatment, and Vacuum Ultraviolet (VUV) Irradiation on the Electrical Properties of Organosilicate Films. Polymers 2024, 16, 2230. [Google Scholar] [CrossRef]
8. Baklanov, M.R.; Jousseaume, V.; Rakhimova, T.V.; Lopaev, D.V.; Mankelevich, Y.A.; Afanas’ev, V.V.; Shohet, J.L.; King, S.W.; Ryan, E.T. Impact of VUV photons on SiO2 and organosilicate low-k dielectrics: General behavior, practical applications, and atomic models. Appl. Phys. Rev. 2019, 6, 011301. [Google Scholar] [CrossRef]
9. Grill, A.; Neumayer, D.A. Structure of low dielectric constant to extreme low dielectric constant SiCOH films: Fourier transform infrared spectroscopy characterization. J. Appl. Phys. 2003, 94, 6697–6707. [Google Scholar] [CrossRef]
10. Afanas’ev, V.V.; Keunen, K.; Stesmans, A.; Jivanescu, M.; Tőkei, Z.; Baklanov, M.R.; Beyer, G.P. Electron spin resonance study of defects in low-κ oxide insulators (κ = 2.5–2.0). Microelectron. Eng. 2011, 88, 1503–1506. [Google Scholar] [CrossRef]
11. Pomorski, T.A.; Bittel, B.C.; Lenahan, P.M.; Mays, E.; Ege, C.; Bielefeld, J.; Michalak, D.; King, S.W. Defect structure and electronic properties of SiOC: H films used for back end of line dielectrics. J. Appl. Phys. 2014, 115, 234508. [Google Scholar] [CrossRef]
12. King, S.W.; French, B.; Mays, E. Detection of defect states in low-k dielectrics using reflection electron energy loss spectroscopy. J. Appl. Phys. 2013, 113, 044109. [Google Scholar] [CrossRef]
13. Lauer, J.L.; Sinha, H.; Nichols, M.T.; Antonelli, G.A.; Nishi, Y.; Shohet, J.L. Charge trapping within UV and vacuum UV irradiated low-k porous organosilicate dielectrics. JES 2010, 157, G177. [Google Scholar] [CrossRef]
14. Liniger, E.G.; Shaw, T.M.; Cohen, S.A.; Leung, P.K.; Gates, S.M.; Bonilla, G.; Canaperi, D.F.; Rao, S.P. Processing and moisture effects on TDDB for Cu/ULK BEOL structures. Microelectron. Eng. 2012, 92, 130–133. [Google Scholar] [CrossRef]
15. Lloyd, J.R.; Shaw, T.M.; Liniger, E.G. Effect of moisture on the time dependent dielectric breakdown (TDDB) behavior in an ultra-low-k (ULK) dielectric. In 2005 IEEE International Integrated Reliability Workshop, South Lake Tahoe, CA, USA, 17–20 October 2005. [Google Scholar] [CrossRef]
16. Michelon, J.; Hoofman, R.J. Moisture influence on porous low-k reliability. IEEE Trans. Device Mater. Reliab. 2006, 6, 169–174. [Google Scholar] [CrossRef]
17. Li, Y.; Ciofi, I.; Carbonell, L.; Heylen, N.; Van Aelst, J.; Baklanov, M.R.; Groeseneken, G.; Maex, K.; Tőkei, Z. Influence of absorbed water components on SiOCH low-k reliability. J. Appl. Phys. 2008, 104, 034113. [Google Scholar] [CrossRef]
18. Cheng, Y.L.; Leon, K.W.; Huang, J.F.; Chang, W.Y.; Chang, Y.M.; Leu, J. Effect of moisture on electrical properties and reliability of low dielectric constant materials. Microelectron. Eng. 2014, 114, 12–16. [Google Scholar] [CrossRef]
19. Krishtab, M.; Afanas’ev, V.; Stesmans, A.; De Gendt, S. Leakage current induced by surfactant residues in self-assembly based ultralow-k dielectric materials. Appl. Phys. Lett. 2017, 111, 032908. [Google Scholar] [CrossRef]
20. Sze, S.M.; Li, Y.; Ng, K.K. Physics of Semiconductor Devices, 2nd ed.; Wiley: New York, 1981; pp. 44–60. [Google Scholar]
21. Wu, C.; Li, Y.; Baklanov, M.R.; Croes, K. Electrical reliability challenges of advanced low-k dielectrics. ECS J. Solid State Sci. Technol. 2014, 4, N3065–N3070. [Google Scholar] [CrossRef]
22. Nasyrov, K.A.; Gritsenko, V.A. Charge transport in dielectrics via tunneling between traps. J. Appl. Phys. 2011, 109, 097705. [Google Scholar] [CrossRef]
23. Vishnevskiy, A.S.; Naumov, S.; Seregin, D.S.; Wu, Y.H.; Chuang, W.T.; Rasadujjaman, M.; Zhang, J.; Leu, J.; Vorotilov, K.A.; Baklanov, M.R. Effects of Methyl Terminal and Carbon Bridging Groups Ratio on Critical Properties of Porous Organosilicate Glass Films. Materials 2020, 13, 4484. [Google Scholar] [CrossRef] [PubMed]
24. Baklanov, B.M.; Mogilnikov, K.P.; Polovinkin, V.G.; Dultsev, F.N. Determination of pore size distribution in thin films by ellipsometric porosimetry. J. Vac. Sci. Technol. 2000, 18, 1385–1391. [Google Scholar] [CrossRef]
25. Iacopi, F.; Travaly, Y.; Eyckens, B.; Waldfried, C.; Abell, T.; Guyer, E.P.; Gage, D.M.; Dauskardt, R.H.; Sajavaara, T.; Houthoofd, K.; et al. Short-ranged structural rearrangement and enhancement of mechanical properties of organosilicate glasses induced by ultraviolet radiation. J. Appl. Phys. 2006, 99, 053511. [Google Scholar] [CrossRef]
26. Woignier, T.; Prassas, M.; Duffours, L. Sintering of aerogels for glass synthesis, J. Sol. Gel Sci. Technol 2019, 90, 76–86. [Google Scholar] [CrossRef]
27. Sawamura, K.I.; Furuhata, T.; Sekine, Y.; Kikuchi, E.; Subramanian, B.; Matsukata, M. Zeolite Membrane for Dehydration of Isopropylalcohol−Water Mixture by Vapor Permeation. ACS Appl. Mater. Interfaces 2015, 7, 13728–13730. [Google Scholar] [CrossRef] [PubMed]
28. Marsik, P.; Verdonck, P.; De Roest, D.; Baklanov, M.R. Porogen residues detection in optical properties of low-k dielectrics cured by ultraviolet radiation. Thin Solid Films 2010, 518, 4266–4272. [Google Scholar] [CrossRef]
29. Baklanov, M.R.; Zhao, L.; Van Besien, E.; Pantouvaki, M. Effect of porogen residue on electrical characteristics of ultra low-k materials. Microelectron. Eng. 2011, 88, 990–993. [Google Scholar] [CrossRef]
30. Van Besien, E.; Pantouvaki, M.; Zhao, L.; De Roest, D.; Baklanov, M.R.; Tőkei, Z.; Beyer, G. Influence of porosity on electrical properties of low-k dielectrics. Microelectron. Eng. 2012, 92, 59–61. [Google Scholar] [CrossRef]
31. Proost, J.; Baklanov, M.; Maex, K.; Delaey, L. Compensation effect during water desorption from siloxane-based spin-on dielectric thin films. J. Vac. Sci. Technol. 2000, 18, 303–306. [Google Scholar] [CrossRef]
32. Lloyd, J.R.; Liniger, E.; Shaw, T.M. Simple model for time-dependent dielectric breakdown in inter-and intralevel low-k dielectrics. J. Appl. Phys. 2005, 98, 084109. [Google Scholar] [CrossRef]
33. Wu, C.; Li, Y.; Barbarin, Y.; Ciofi, I.; Tang, B.; Kauerauf, T.; Croes, K.; Bommels, J.; De Wolf, I.; Tőkei, Z. Towards the understanding of intrinsic degradation and breakdown mechanisms of a SiOCH low-k dielectric. 2014 IEEE International Reliability Physics Symposium, Waikoloa, HI, USA, 01–05 June 2014; pp. 3A.2.1–3A.2.6. [Google Scholar] [CrossRef]
34. Gischia, G.; Croes, K.; Groeseneken, G.; Tőkei, Zs.; Afanas’ev, V.; Zhao, L. Study of leakage mechanism and trap density in porous low-k materials. IEEE International Reliability Physics Symposium (IRPS), Anaheim, CA, USA, 02–06 May 2010; pp. 549–555. [Google Scholar] [CrossRef]
35. Wu, C.; Li, Y.; Barbarin, Y.; Ciofi, I.; Croes, K.; Bömmels, J.; De Wolf, I.; Tőkei, Z. Correlation between field dependent electrical conduction and dielectric breakdown in a SiCOH based low-k (k = 2.0). Appl. Phys. Lett. 2013, 103, 032904. [Google Scholar] [CrossRef]
36. Skuja, L. Optically active oxygen-deficiency-related centers in amorphous silicon dioxide. J. Non-Cryst. Solids 1998, 239, 16–48. [Google Scholar] [CrossRef]
37. Salh, R. Defect Related Luminescence in Silicon Dioxide Network: A Review. In Crystalline Silicon - Properties and Uses; InTech, 2011; pp. 135–172. [Google Scholar] [CrossRef]
38. Trukhin, A.; Smits, K.; Chikvaidze, G.; Dyuzheva, T.; Lityagina, L. Luminescence of silicon Dioxide—silica glass, α-quartz and stishovite. Open Phys. 2011, 9, 1106–1113. [Google Scholar] [CrossRef]
39. Trukhin, A.N.; Goldberg, M.; Jansons, J.; Fitting, H.J.; Tale, I.A. Silicon dioxide thin film luminescence in comparison with bulk silica. J. Non-Cryst. Solids 1998, 223, 114–122. [Google Scholar] [CrossRef]
40. Pustovarov, V.A.; Zatsepin, A.F.; Biryukov, D.Y.; Aliev, V.S.; Iskhakzay, R.K.; Gritsenko, V.A. Synchrotron-Excited Luminescence and Converting of Defects and Quantum Dots in Modified Silica Films. J. Non-Cryst. Solids 2023, 602, 122077. [Google Scholar] [CrossRef]
41. Rasadujjaman, M.; Zhang, J.; Spassky, D.A.; Naumov, S.; Vishnevskiy, A.S.; Vorotilov, K.A.; Yan, J.; Zhang, J.; Baklanov, M.R. UV-Excited Luminescence in Porous Organosilica Films with Various Organic Components. Nanomaterials 2023, 13, 1419. [Google Scholar] [CrossRef]
42. Sze, S.M. Current Transport and Maximum Dielectric Strength of Silicon Nitride Films. J. Appl. Phys 1965, 38, 2951–2956. [Google Scholar] [CrossRef]