Research Highlights of Polymers Division

Pore size distributions in low-k dielectric thin films from X-ray porosimetry

The rapid and sustained advances in ultra-large scale integrated circuit performance have been driven, to a large extent, by miniaturization of the circuitry. At these nanoscopic sizes, interlayers with extremely low dielectric constants (low-k) are imperative to reduce cross-talk and to increase processor speed. While the candidate materials differ in their base chemistries, a common theme emerges in the push to develop low-k dielectric materials: nano-scale porosity must be introduced in a controlled manner to further reduce the dielectric constant. Techniques are needed to accurately and non-invasively characterize the porosity in these films while attached on a silicon substrate.

Capillary porosimetry is a prime candidate to measure the pore size distribution (PSD) of the nanoporous films. Bulk materials have been characterized in this manner by measurement of the mass gain of the material when exposed to a controlled pressure of solvent vapor. As the pressure of the probe solvent increases, pores become filled hierarchically by size as is described by the appropriate thermodynamic analysis such as the Kelvin equation:

X-ray reflectivity (XR) has been extensively used in the Polymers Division to measure the thickness and density of 1 mm nanoporous thin films. A method of x-ray porosimetry (XRP) has been developed to create a controlled solvent environment around the thin film so that an equilibrium amount of adsorption occurs. The value of P/P0 can be varied either by mixing volumes of solvent saturated and dry air at a constant temperature, or by blanketing the sample in air that has reached solvent saturation at a low temperature and increasing the temperature of the thin film. Under such conditions, a standard XR scan gives accurate values of the total density that is a combination of wall density and solvent filled pores. The mass uptake as a function of partial pressure is calculated from these results.

As an example, the reflectivity data from the porous hydrogen silsesquioxane (HSQ) and the silica xerogel films are shown in Figure 1. Each of the two samples has several data sets plotted together to show the effect of solvent adsorption. A critical edge is clearly visible at low qz values as the sharp drop in log(Reflectivity) from the initially flat reflectivity curve. In Figure 1, four curves are shown for each sample, varying from the sample exposed to dry air (left most curve) to sample in saturated toluene vapor (right most curve). There is a progression of the critical edge to higher qz as the vapor pressure increases, due to the increased electron density of the film as the smaller pores become saturated with liquid toluene.

Figure 1. XR curves of a porous organosilsesquioxane (XLKÔ) and xerogel films under controlled partial toluene vapor pressure.

At P/P0 = 1, toluene will condense in all of the accessible pores or open pores by definition, so the uptake at saturation, W0, is a measure of the porosity. It should be emphasized that this porosity only reflects those pores that the toluene can infiltrate. There may also be closed pores not accessible to toluene vapor and therefore not reflected in the XR porosity. Therefore, a matrix density that is a combination of dense wall material and inaccessible closed pores can be calculated.

Figure 2 presents the adsorption/desorption data for a porous methyl silsesquioxane (MSQ) spin-on glass (SOG) film in which P/P0 is varied through the substrate temperature. The solid lines are cubic spline fits through the data and accurately mimic the shape of the curves. The data points have considerably less scatter than the data in which the isothermal technique is employed. The hysteresis loop is very well defined with data outside of the loop coinciding accurately. If the principle of temperature-pressure equivalency is valid, the temperature control method clearly increases the accuracy of the measurement.

Figure 2. XR toluene vapor adsorption data from MSQ SOG films by varying the substrate temperature.

The pore size distribution can be calculated by use of the Kelvin equation and other thermodynamic considerations from a point-by-point differentiation, as shown in Figure 3.

Figure 3. PSD of MSQ SOG films by varying the substrate temperature (where AU = arbitrary units).

There are several advantages of XRP over other techniques to determine pore size in ultrathin films. Some methods require that the film be deposited on a special substrate, such as the piezoelectric surfaces required for both the quartz crystal microbalance and surface acoustic waves techniques. XRP can be done on any smooth substrate, including the Si wafers used in the semiconductor industry. In many ways, XRP is similar and complimentary to optical methods such as ellipsometric porosimetry (EP). However, the EP analysis requires knowledge of the optical constants, for both the matrix and the adsorbate. With EP it is also necessary to invoke the additional assumption that the polarizabilities are additive. XRP does not require these additional assumptions.

Another potential advantage of XRP is the ability to quantify not only the average film density, but also the density profile normal to the film surface. X-ray reflectivity has been used to extract non-uniform density profiles in a series of low-k films. It may be possible to use XRP to extract pore size distributions as a function of depth into film. To prevent dielectric breakdown it is desirable to have low porosity or very small pores near the surfaces with the majority of the porosity in the localized in the center of the thin film. XRP could prove to be very useful for characterizing these types of structures.

"The SANS/SXR measurements have become a key metric in our low-k dielectric materials characterization and screening process "

Dr. Jeffrey Wetzel - Manager, Low-k Materials Technology, International SEMATECH

"The NIST x-ray reflectivity program is useful, perhaps even critical, to the industry"

Dr. Abner Bello -Technical Staff Member, Defect and Thin Film Characterization Laboratory, Applied Materials Inc.

For more information on this topic:

Barry J. Bauer, Wen-li Wu (Polymers Division, NIST)

Hae-Jeong Lee, Christopher L. Soles, Da-wei Liu, Barry J. Bauer and Wen-li Wu, "Pore size distributions in low-k dielectric thin films from X-ray porosimetry", Journal of Polymer Science, Polymer Physics Edition, in press.