Dispersion mechanism

As with our previous work on MSQ/polystyrene-b-polybutadiene-b-polystyrene (SBS) porogen, the steric barrier effect on the PS porogens is affected by the microstructure of the cross-linkable MSQ matrix at three significant temperatures in the cure step; namely, (1) the glass transition temperature, Tg (~100^oC), (2) the onset temperature, 160°C for transformation from cage to network structure, and (3) the immobilization temperature, 175°C, which have been described in Figure 5.4(a)-(c).

Noticeable porogen aggregation occurred at T> Tg, but the aggregation occurred at a different rate during these 3 stages, depending on the diffusivity of PS particles, which is a function of viscosity and temperature as described by the Einstein-Stokes equation (Equation 5.2):

D k_BT

6



r (5.2) where kB is the Boltzmann constant, T is the absolute temperature, η is the viscosity of

the system and r is the particle radius. In this study, η, is a measure of the steric and electrostatic barrier to movement of the PS particles within the cross-linkable MSQ matrix. Thus, at T > Tg, the relaxation of the PS and MSQ molecular chains leads to reduced viscosity and higher diffusivity of the PS particles. Such high diffusivity increases PS collisions and leads to the aggregation of PS porogens from 10.0 to 13.4 nm. At T >160°C, the viscosity drops drastically to ~1.8x10⁵ poises, because of the plasticization by the large amount of H2O by-products when extensive transformation of cage to network Si–O occurs in the MSQ. This results in greater aggregation of the PS porogens, resulting in a faster change in the porogen size, from 13.4 to 15.6 nm, between 150 and 175°C. In the final stage, ~175 to 200°C, most H2O is believed to have dried off at less than 175°C. In addition, the cross-linking of the MSQ matrix with a 3D and highly cross-linked Si–O network structure at T >175°C makes the MSQ/PS hybrid behave like a solid, with a very high viscosity of ~2.2x10⁵ poises. As a result, the PS porogens are trapped or “frozen” within the highly cross-linked MSQ matrix, leading to an approximately constant porogen size of 15.6 to 16.5 nm, beyond T >175°C.

When the surfactant, either anionic or cationic, is added to PS in THF solution, negative or positive charges build up on the PS particle surface. As a result, the charged PS porogens repel each other and do not aggregate. This electrostatic repulsion also plays the dominant role in hindering the aggregation of PS porogens in the NaDBS- and

DB-modified PS/MSQ hybrid films during the slow cure process from 30 to 200^oC.

Since the surfactant is physically adsorbed only on the PS particle surface, the surface charge on the PS particles may change over time and temperature, if the surfactant desorbs from the surface, during the cure process. However, NaDBS and DB have been reported or tested to possess excellent thermal stability up to at least 200^oC [145].

Therefore, the surface density of NaDBS- or DB-modified PS particles would not be expected to degrade as the cure temperature rises to 200^oC [146,147].Compared to a weakly electrostatic dispersed PS/MSQ system without modification (zeta potential: -18 mV), the NaDBS-modified PS/MSQ system (zeta potential: -58 mV) and DB-modified PS/MSQ system (zeta potential: +66 mV) exhibits strong electrostatic repulsion, resulting in little or limited aggregation of PS porogens during a slow cure process, which produces a small porogen size with a tight distribution.

The charge on the particles has an effect on the increased viscosity, depending on the surface charge density, because the electrical double layer around each particle is distorted under shearing, i.e. the electroviscous effect [148,149]. This increased viscosity can be quantified and taken into account by introducing a correction factor, i.e.

the primary electroviscous coeffiicent, p, to the modified Einstein-Stokes equation [150]

(Equation 5.3):

_r 1k(1p) (5.3)

where ηr is the relative viscosity, φ is the volume fraction of the solid and k=2.5 for spherical and rigid particles. The “p” coefficient [145] can be represented by Equation (5.4)

p(2_o_r)²

_o_oa² (5.4) where εo is the permittivity of free space, εr is the relative permittivity, ζ is the zeta potential, λo is the specific conductivity of the continuous phase, ηo is its viscosity and a is the diameter.

A higher zeta potential leads to a higher viscosity, which accounts for the difference in viscosity among the three different MSQ/PS hybrid films as illustrated in Figure 5.4(a) at T > Tg. As a result, the diffusivity of the highly-charged PS porogens is hindered by the increased viscosity. Therefore, the high zeta potential of charged PS porogens further impedes the segregation and aggregation of PS within a successively cross-linked MSQ matrix through electrostatic repulsive forces and the electroviscous effect. In addition, the columbic attraction between the electron lone pair of the oxygen atoms of the Si−OHgroup and the positively charged PS particles, restrains the PS porogen and its mobility during the cure step, resulting in a further reduction in porogen aggregation. Overall, the NaDBS modified-PS/MSQ hybrid film yielded a small porogen size and tight distribution (8.7 ± 2 nm) when cured at a slow rate up to 200^oC with MSQ fully cross-linked, and a similarly small pore size (8.8 nm) after burning out

of porogen at 400^oC. In comparison, our previous work on low-k MSQ/SBS hybrid film used a rapid curing method to trap the porogen within a rapidly formed, well-cross-linked MSQ matrix, leaving its size unchanged (from as-prepared, 25^oC) with tight distribution. Thus, surface modification of PS porogens by cationic surfactant offers an alternative and simple method to control the porogen and pore size and distribution even at a slow cure rate (2^oC/min), which offers great process latitude. This simple method based on polystyrene porogen with surface potential modification, can be further improved by reducing the pore size and extended to other relevant materials as the porogen. In principle, the porogen particle size in the solvent can be reduced by using a porogen of a lower molecular weight [151] and with treatment leading to a higher surface potential [152,153]. As a result, a smaller pore size can be expected after the removal of porogen from the corresponding low-k/porogen hybrid film. In addition to polystyrene, the porogen materials can be selected from linear polymers such as polyethylene, polypropylene, poly(methyl methacrylate) [154], poly(alkylene ether)s (e.g., poly(ethylene oxide) (PEO) and poly(propylene oxide) (PPO)) [155] of lower molecular weight and good miscibility with low-k matrix precursors, such as MSQ.

5.7 Summary

An anionic surfactant, NaDBS, and a cationic surfactant, DB, were used to modify

the surface potential of PS porogen in THF solution from an initial value of -18 mV (unmodified) to -58mV and +66mV, respectively. Upon curing at a slow rate (2^oC/min), the porogen without modification aggregates and its size increases from 10.0 to 16.5 nm.

In contrast, for the NaDBS-modified and DB-modified PS systems, the high zeta potential of charged PS porogens impede the aggregation of PS within a successively cross-linked MSQ matrix through electrostatic repulsion forces and the electroviscous effect. This results in little or limited PS porogen aggregation and yields a small porogen size with tight distribution, 11.1 ± 2.4 and 8.7 ± 2.0 nm, respectively. More importantly, the columbic attractionbetween the Si−OHgroups of MSQ matrix and the DB-modified, positively charged PS particles, restrains the PS porogen and its mobility during the cure step, resulting in a further reduction in porogen aggregation. Overall, the NaDBS modified-PS/MSQ hybrid film yields a small porogen size and tight distribution (8.7 ± 2 nm) when cured at a slow rate up to 200^oC with MSQ fully cross-linked, and a similarly small pore size (8.8 nm) after burning out of porogen at 400^oC.

Treatment on PS Zeta potential (mV) PS particle size (nm)

No modification -18 49.3 ± 4.1

pH = 3 +28 12.3 ± 2.5

pH = 11 -40 11.2 ± 2.4

Anionic surfactant NaDBS

-58 9.0 ± 2.0

Cationic surfactant DB

+66 8.0 ± 1.8

Table 5.1 The zeta potential and the corresponding particle size of PS porogen in the solution as a function of surface modification.

Figure 5.1 2-D GISAXS scattering patterns of the low-k MSQ/PS hybrid films as a function of cure temperature: (a) PS without modification, (b) NaDBS-modified PS, and (c) DB-modified PS.

Figure 5.2 Porogen sizes and distribution in the low-k MSQ/PS hybrid films as a function of cure temperature: (a) PS without modification, (b) NaDBS-modified PS, and (c) DB-modified PS.

Figure 5.3 2-D GISAXS scattering patterns of the low-k porous MSQ films after removal of PS porogens at 400^oC: (a) PS without modification, (b) NaDBS-modified PS, and (c) DB-modified PS.

Figure 5.4 (a) The viscosity, (b) porogen size, and (c) the ratio of network-/cage- Si−O in the low-k MSQ/PS hybrid films as a function of cure temperature for NaDBS-modified PS (●), DB-modified PS (), and PS without modification (▲).

Figure 5.5 FTIR spectra (880 to 1170 cm^-1) of low-k MSQ/PS hybrid films at 25^oC for PS without modification, NaDBS-modified, and DB-modified PS.

Figure 5.6 (a) Peak position and (b) peak intensity of Si−OH infrared absorption band as a function of cure temperature for NaDBS-modified PS (●), DB-modified PS (), and PS without modification (▲).

Chapter 6

Well-dispersed Ultra-Low-k Porous Methylsilsesquioxane using a Cationic Surfactant-modified Polystyrene Porogen

Chapter 5 indicates the surface modification method to modify and disperse the porogen in the solution and the hybrid low-k film. The electrostatic dispersion controls of porogen at 10wt% in the solvent and in the hybrid film were investigated. The modified porogen can limit the size in the precursor and hybrid film. And the size did not change in the thermal removal process. This chapter focuses on increasing porogen loading (or porosity) in the low-k matrix under modification of the porogen. In addition, the critical porosity with small pores and tight distribution is discussed. The cationic surfactant Domiphen bromide (DB), was used to modify the PS surface in the MSQ/PS hybrid film. And we adjust the different the porogen loading to increase the the porosity.

The porosity of porous low-k film will be described and elucidated by X-ray reflectivity (XRR). The pore size of the porous low-k film under different porosity were characterized by 2D GISAXS and focused ion beam scanning electron microscopy (FIB-SEM). And, the dielectric constant of porous film will be described and elucidated.

The mechanical strength was measured using a nanoindenter.

6.1 Porogen size in the precursor

Zeta potential has been recognized as a measure of the magnitude of the repulsion or attraction between PS particles in colloids. Figure 6.1 showed the initial PS is the 49.3 nm in the THF solution at pH value equal 7, and that appear the negatively surface charge -18 mV. When pH value is reduced from 7 to 5 and 3, the surface potential increased from -18 to -5.7 and +28 mV. The porogen size showed 12.3 nm at pH value of 3 and that smaller than in the pH= 7. On the other hand, the pH value from 7 to 9 and 11, the surface potential decreased from -18 to -36 and -66 mV. The porogen size at pH=

11 is also smaller than initial PS at pH= 7. Our finding on the effect of the larger absolute value of potential (>25 mV) results in better colloidal stability and a smaller particle size, due to electrostatic dispersion [135].In addition, the initial PS (pH= 7) modified by the cationic surfactant DB shows the size of 8.0 nm at surface potential +66 mV. Based on the particle size data, we will focus on the modification of PS by cationic surfactant for producing the low-k MSQ/PS hybrid film and the corresponding porous low-k film in this study. In order to define the property of high porosity porous low-k film and further reduce the dielectric constant, the porogen loading were increased at 10, 20, 30, 40 and 50 wt%. And two kinds of porogen including unmodified and modified PS were used and discussed.

6.2 Porosity and pore size, shape

All hybrid low-k films form the porous films after thermal process to remove porogen at 400^oC. The porosity of porous film was calculated by comparing the density

of porous film with a dense MSQ film (1.96 g/cm³) [156,157] by using Equation (6.1).

 

1-p

o

  (6.1)

where ρ was experimental value of film density (g/cm³), ρo was silica density (1.96 g/cm³), and p referred to porosity. All of the densities were obtained from XRR experiments. Generally if the density of porous films decreased, the porosity increased.

Table 6.1 summarizes the correlation between the porogen loading and porosity of the unmodified and modified condition. As the results, the porosity of porous film under the unmodified PS condition show the vol.% from 16.4, 25.6, 37.5, 46.9 to 55.8% by increasing the porogen loading (10 to 50 wt%). On the other hand, the porosity under the unmodified PS condition show the vol.% from 15.6, 27.8, 33.4, 45.3 to 53.8% by loading raised.

The next task is to clarify the pore variation under all conditions. The pore morphology and pore size of porous low-k film under the different porosity without and with modification were investigated by SEM as shown in Figure 6.2(a) show the cross-section of porous film from unmodified PS at 16.4, 25.6, 37.5, 46.9 and 55.8 vol.% porosity. The results show that the pore shape was spherical at 16.4 and 25.6

vol.%, and the pore size was about 15 to 16nm. When the porosity increased to 37.5 vol.%, the pore shape changed from sphere to worm-like (interconnected pores) and size (or length) of about 20 nm. At porosity 46.9 vol.%, the pore from the larger interconnect pore in this tern obviously. Finally, a lot of worm pore appeared in the porous film and the length was > 20nm at 55.8 vol.%. Figure 6.2(b) shows the pore morphology variation for the modified PS case. The pictures show that the pore shape was spherical at 15.6, 27.8, 33.4 and 45.3 vol.% porosity. When the porosity was increased, the pore size did not grow and remained at 9-10 nm. At 56.9 vol.% porosity, the pore aggregate and pore size was about 15 nm. In particular, the picture shows that the pore size increased, but worm-like pores appeared at 56.9 vol.% porosity.

Furthermore, the pore size of the porous film with different porosity was characterized by 2D GISAXS. From GISAXS scattering patterns, the pore sizes in the porous MSQ films cured under different porosity with and without surface modification can be further determined. Figure 6.3 shows the GISAXS patterns of the different porosity low-k porous films for PS porogens without and with DB surfactant modification, respectively. Figure 6.3(a) shows a weaker scattering pattern than the other one. This indicates that the pores did not disperse well in the porous low-k film under the unmodified PS condition. With increasing porosity, scattering patterns illustrated in Figure 6.3(a), were confined in the low-q region, indicating that the pores

tended to aggregate and start at porosity ≥ 37.5 vol.%. In contrast, the scattering patterns shown in Figure 6.3(b) are stronger and more uniform in the high-q region than the corresponding ones (without modification) in Figure 6.3(a) until porosity was 56.9 vol.%. The results of these successive scattering patterns indicate that the pore sizes in the modified low-k porous films were smaller than those in the unmodified film at specific porosity ≤ 45.3 vol.%. Accordingly, the scattering intensity of individual particles, I(q), can be defined by Equation (6.2).

^{I(q)np(pm)2Vp2P(q)S(q)} (6.2) where the wavevector q = 4^-1sin is defined by the wavelength  and the scattering angle 2 of X-rays; np is the number density of particles; ρ　 p and ρ　 m are the scattering density of the particle and the matrix; Vp denotes the volume of particles; P(q) is a form factor, and S(q) is a structure factor. The structure factor S(q) is close to 1 in a disordered system and thus can be ignored. Therefore, the scattering profile of I(q) is only related to the form factor P(q) of the particles. As a result, I (q) can be furthered to the Guinier’s expression, involving radius of gyration Rg for spherical pore as described by Eq. 2, and radius of cylinder for rod-like (worm-like) shape pore could be approximated by using Kratky-Porod approximation as by Equation (6.3) (6.4) [158].





In the spherical case, a linear relationship exists between ln(I) and q², with a slope of (-Rg2/3). In addition, a linear relationship exists between ln(I) and q², with a slope of (-Rc2/2) for the rod-like (worm-like) case. In order to develop more profound structural information from the scattering patterns, initial approximation was defined by using the Guinier plot (ln(I) versus qxy2) for spherical pores and the Kratky-Porod plot (ln(I).Q versus qxy2) for cylindrical pores shape. Figure 6.3 also illustrates the ln(I).Q versus qxy2

of porous low-k film for both the in plane and out of plane direction. In-plane direction refers to x-y plane direction (parallel to the substrate) and out-of-plane refers to the z-direction (perpendicular to the substrate). Thus, based on Equation (6.3), the slope was directly related to the radius(R) of the pores in either the in-plane or out-of-plane direction for rod-like pores. The porous low-k film from unmodified PS would be discussed for the rod-like pores shape at porosity ≥ 37.5 vol.%.

The pore sizes/distributions were quantitatively determined by the same method described in detail in our previous study. Accordingly, the calculated pore size and distribution of the porous low-k films without and with modification, as a function of porosity are shown in Figure 6.4. For low-k porous film with porogen surface modification, the average pore size/distribution increased noticeably from 9.51, 9.56,

specific, the pore size increased slightly to 15.72 nm for a porosity of 56.9 wt%. In contrast, for the unmodified condition, the pore size was 15.8 and 16.23 nm at porosity of 16.4 and 25.6 vol.%. Because of the pore shape of 37.5, 46.9 and 55.8 vol.% porous films as shown in the SEM picture, the length of the worm-like pores will be discussed and compared to the other spherical pore condition. The pore length was 20.81 23.38 and 25.39 nm in the porosity of 37.5, 46.9 and 55.8 vol.%. Based on pore analysis of low-k MSQ porous films, the different PS conditions under the different loadings can be summarized as below. The unmodified PS step, when porogen loading was from 10 to 20 wt%, the pore size did not aggregate obviously. When the porogen loading was 30 wt%, the pores would change in size and shape as length of worm-like pores was about 20.81 nm. That indicates that porogen underwent a lot of aggregation during the porogen loading 20 to 30 wt%. In the literature suggests that 25 wt% loading is an ideal value of porogen addition in the hybrid low-k film. Above 25 wt% loading, the porogen might cause much aggregation due to the position of porogen being close to each other and forming larger mass. At 40 and 50 wt% porogen loading, the pore size (length) increased to 23.38 and 25.39 nm. In contrast, the porous film formed by modified PS, the pore size remained constant under porogen loading from 10 to 40 wt%. This indicates that the pore size did not grow obviously even when the porosity was 45.3 vol.%. The results show that the modified PS would disperse well in the hybrid low-k

film. When the temperature was increased, the porogen size and the later pore size and shape was also controlled even at a high porogen loading (> 25 wt %). Yet, the pore size still slightly increased at 50 wt% porogen loading. In particular, the pore size under high porosity (56.9 vol.%) was smaller than the for other condition.

6.3 Dielectric constant and mechanical properties

Next, the effect of porous low-k film on dielectric constant and mechanical strength of porous film were showed in the Figure 6.5. The dielectric constant of the pure MSQ film was 2.78, and the k values of porous MSQ films decreased by increasing the porosity. A positive deviation of the dielectric constant by C–V measurement from the estimated value of the ideal mixing rule [kporous = kMSQ × (1 porosity) + k^ air × porosity] aggravated with increasing porosity in the two kinds of porous films (without and with surface modification) as shown by Figure 6.5(a). The porous films from the modified PS showed the curve close to the ideal mixing rule, and the k value were 2.57, 2.36, 2.25, 2.12 and 1.93 by increasing the porosity from 15.6, 27.8, 33.4, 45.3 to 56.9 vol.%, respectively. Therefore, the porous films from the unmodified PS showed the k value were 2.58, 2.44, 2.18, 2.07 and 2.01 for the porosity at 16.4, 25.6, 37.5, 46.9 and 55.8 vol.%, respectively. Base on the pore size, morphology and porosity data, the k value dressers effectly by increasing porosity and k value is only related by porosity.

Figure 6.5(b) showed that the ratio of network/cage different porosity porous film with and without modification. When the porogen was adding in the hybrid film, the porogen would form a steric barrier to limit the cross-linking of matrix. In addition, the positively charge porogen attack the OH⁻ group would decrease the ratio of network/cage obviously. The ratio of network/cage would reduce with increasing porosity in all condition. And results indicate the ratio of network/cage in the modified

Figure 6.5(b) showed that the ratio of network/cage different porosity porous film with and without modification. When the porogen was adding in the hybrid film, the porogen would form a steric barrier to limit the cross-linking of matrix. In addition, the positively charge porogen attack the OH⁻ group would decrease the ratio of network/cage obviously. The ratio of network/cage would reduce with increasing porosity in all condition. And results indicate the ratio of network/cage in the modified

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