Surface analysis insight note: Differentiation methods applicable to noisy data for determination of sp2-versus sp3-hybridization of carbon allotropes and AES signal strengths

The derivatives of the spectra are commonly used for quantification in Auger Electron Spectroscopy (AES) spectra, while the derivative of the KLL C Auger line has proven to be valuable in obtaining a measure of the relative proportions of sp(2)- and sp(3)-hybridization using the D-parameter in both AES and X-ray Photoelectron Spectroscopy (XPS). Differentiation of X-ray Photoelectron Spectroscopy (XPS) and Auger Electron Spectroscopy (AES) spectra by numerical means is presented and illustrated for polymeric, such as PEEK and Nylon, as well as for graphitic materials including highly ordered pyrolytic graphite and graphene oxide. The most commonly available Savitzky-Golay method is explained mathematically and developed through the case of constructing a 5-point quadratic polynomial convolution kernel suitable for differentiating spectra of adequate signal to noise. The concept of differentiation of spectra where signal to noise is less than adequate is also developed. Two alternative strategies to Savitzky-Golay differentiation are presented, which fit curves to data that allow derivatives to be obtained where Savitzky-Golay would otherwise fail. These alternative methods involve constructing a parametric curve that fits data over the entire energy interval of interest. Derivatives of spectra are then obtained by differentiating these parametric curves directly. A comparison of results for different materials for which specific sp(2)- vs sp(3)-hybridized carbon proportions are of interest is used to emphasize the importance of characterizing methods used to differentiate spectra and understanding the characteristics of instrumentation used to measure spectra. The case for using Principal Component Analysis noise reduction with C KLL spectra is made for spectra collected from a heterogeneous graphene oxide sample.