Accurate determination of the thickness or mass per unit area of thin foils and single-crystal wafers for x-ray attenuation measurements

Abstract

The determination of the local mass per unit area m/A=∫ρdt and the thickness of a specimen is an important aspect of its characterization and is often required for material quality control in fabrication. We discuss common methods which have been used to determine the local thickness of thin specimens. We then propose an x-ray technique which is capable of determining the local thickness and the x-ray absorption profile of a foil or wafer to high accuracy. This technique provides an accurate integration of the column density which is not affected by the presence of voids and internal defects in the material. The technique is best suited to specimens with thickness substantially greater than the dimensions of the surface and void structure. We also show that the attenuation of an x-ray beam by a nonuniform specimen is significantly different from that calculated by using a simple linear average of the mass per unit area and quantify this effect. For much thinner specimens or in the presence of a very structured surface profile we propose a complementary technique capable of attaining high accuracy by the use of a secondary standard. The technique is demonstrated by absolute measurements of the x-ray mass attenuation coefficient of copper and silver.