Krypton Gas Adsorption for Thin Film Pore Size Analysis

Mesoporous silica thin films have important applications in many fields, including sensors and low-k dielectrics. Lowering the bulk dielectric constant can occur by introducing pores into the material, where the pore size of interest is below 10 nm. Detailed knowledge of the pore size and pore volume is therefore crucial in optimizing the development and fabrication of such thin film materials for micro- and nano-electronic applications.

Many experimental methods are available for characterizing porous materials, including SAXS, SANS, XRD, mercury porosimetry, electron microscopy, solid state NMR methods, and gas sorption. Each method is pore size range-limited. Gas sorption is the most popular because it allows a wide range of pore sizes to be assessed – from 0.35 nm up to over 100 nm. Gas adsorption experiments are also more cost effective, easy to prepare, and non-destructive compared to other techniques.

Gas Sorption for Pore Size Determination

Multiple adsorptives (N2, Ar, Kr, CO2) allow one to obtain information about the specific surface area, pore diameter and size distribution (PSD), and pore volume of porous solids without affecting the material. N2 and Ar adsorption, while well-suited for conventional surface area and micro- and mesopore size analysis, cannot be applied for the pore size analysis of thin films, which are typically only a few hundred nanometers thick. Since the total absolute pore volume and surface area in a thin film measurement is extremely small, the pressure changes due to adsorption cannot be assessed with sufficient precision and accuracy under conventional adsorption conditions (N2 at 77 K or Ar at 87 K). This is because a large number of non-adsorbed gas molecules exist in the sample cell void volume due to the high saturation pressure (~760 torr) of N2 and Ar at their boiling points. Success is achieved by reducing the number of non-adsorbed molecules in the void volume, which is accomplished using krypton adsorption at 77 or 87 K.

Krypton Adsorption Solutions

At 77 K and 87 K, krypton sublimes with a pressure (P0 solid) of approximately 1.6 torr and 13 torr, respectively. Under both conditions, the number of non-adsorbed molecules is significantly reduced compared to similar conditions using N2 and Ar adsorption. Hence, Kr adsorption at cryogenic temperatures is considerably more sensitive and useful for thin film materials. Krypton adsorption at 77 K is already routinely employed for the analysis of very low surface area materials possessing areas less than 1 m2/g. Micro- and mesoporous thin film analyses using krypton at 87 K are routinely performed on the Autosorb iQ-MP and Quadrasorb evo Kr/MP.

Krypton adsorption was not traditionally employed for pore size analysis because classical methods for pore size determination, such as the BJH method, do not apply. BJH requires assumptions about the thermophysical properties of the pore fluid (surface tension, liquid and solid density, contact angle, etc.). These properties are undefined below the triple point temperature (Kr triple point = 115.77 K) and they also depend strongly on pore size due to confinement effects. Microscopic methods, such as NLDFT or GCMC, have not yet been developed for pore size analysis based on Kr adsorption below its triple point temperatures.

Anton Paar has developed the following procedure (standard with the Autosorb iQ and Quadrasorb instruments and VersaWin software) for the pore size analysis of thin films.

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This information has been sourced, reviewed and adapted from materials provided by Quantachrome Instruments.

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