at a detector is the electron impact cross-section. Early approximations (in cm2) of the cross-section were based on the work of Worthington and Tomlin, with b acting as a scaling factor between 0.25 and 0.35, and C a function of the primary electron beam energy, . While this value of is calculated for an isolated atom, a simple modification can be made to account for matrix effects: where α is the angle to the surface normal of the incident electron beam; rm can be established empirically and encompasses electron interactions with the matrix such as ionization due to backscattered electrons. Thus the total yield can be written as: Here Nx is the number of x atoms per volume, λ the electron escape depth, θ the analyzer angle, T the transmission of the analyzer, I(t) the electron excitation flux at depth t, dΩ the solid angle, and δt is the thickness of the layer being probed. Encompassed in these terms, especially the Auger yield, which is related to the transition probability, is the quantum mechanical overlap of the initial and final state wave functions. Precise expressions for the transition probability, based on first-order perturbation Hamiltonians, can be found in Thompson and Baker. Often, all of these terms are not known, so most analyses compare measured yields with external standards of known composition. Ratios of the acquired data to standards can eliminate common terms, especially experimental setup characteristics and material parameters, and can be used to determine element composition. Comparison techniques work best for samples of homogeneous binary materials or uniform surface layers, while elemental identification is best obtained from comparison of pure samples. Uses There are a number of electron microscopes that have been specifically designed for use in Auger spectroscopy; these are termed scanning Auger microscopes (SAMs) and can produce high resolution, spatially resolved chemical images. SAM images are obtained by stepping a focused electron beam across a sample surface and measuring the intensity of the Auger peak above the background of scattered electrons. The intensity map is correlated to a gray scale on a monitor with whiter areas corresponding to higher element concentration. In addition, sputtering is sometimes used with Auger spectroscopy to perform depth profiling experiments. Sputtering removes thin outer layers of a surface so that AES can be used to determine the underlying composition. Depth profiles are shown as either Auger peak height vs. sputter time or