Maximum entropy quantification of SIMS depth profiles—behaviour as a function of primary ion energy

Abstract

Previous publications have proposed the use of reconstruction as a method of quantification of SIMS depth profiles, taking the convolution integral as an approximate model for the measurement process in the dilute limit. We present here a demonstration of the maximum entropy (MaxEnt) reconstruction method for SIMS depth profile quantification at a number of primary ion energies. Neither implanted standard nor crater depth measurement are required by the technique, although both are used here as comparisons. The erosion rate calculated directly from the delta layer is found to be equivalent to that from crater depth measurement to within experimental accuracy. It is demonstrated that the MaxEnt reconstruction method can quantify a delta layer in ideal circumstances, removing all energy-dependent effects. For another sample (a set of three alleged delta layers) the MaxEnt reconstruction method is found to yield improvements in depth resolution at all energies, removing the energy dependence of the rise and decay slopes and almost halving the measured feature widths (full width at half-maximum). This improvement in accuracy in quantification has enabled us to analyse more critically the sample, demonstrating that the layers had finite widths, a fact that was not evident from conventional quantification methods.

Carbon-13 labeling for improved tracer depth profiling of organic materials using secondary ion mass spectrometry

“…Analogous behavior has been observed for 30 Si implants in a 28 Si matrix [18]. Here we employ a simplified version of a convolution scheme that has been outlined previously [18,19]. It combines a Gaussian with a standard deviation eff that accounts for ion-induced mixing and sources of uncorrelated convolution, such as sample roughness, and an exponential for the observed tailing, which has a characteristic decay length d .…”

Carbon-13 Labeled Polymers: An Alternative Tracer for Depth Profiling of Polymer Films and Multilayers Using Secondary Ion Mass Spectrometry

“…Analogous behavior has been observed for 30 Si implants in a 28 Si matrix . A physically meaningful convolution function is required in order to compare SIMS depth profiles to various theoretical models when probing physical phenomena at polymer surfaces and heterogeneous interfaces. , Here we employ a simplified version of a convolution scheme that has been outlined previously. , It combines a Gaussian with a standard deviation σ eff that accounts for ion-induced mixing and sources of uncorrelated convolution, such as sample roughness and intrinsic interfacial width, , and an exponential for the observed tailing, which has a characteristic decay length λ d . The Gaussian convolution function is and the exponential decay is described by G ( z ) and F ( z ) are numerically convoluted, using the Fourier transform method, with a Heaviside step function θ( z ), where to approximate the experimental profiles.…”

Improvement of Depth Resolution in Secondary Ion Mass Spectrometry Analysis Using Multiresolution Deconvolution

“…In this way, different approaches of deconvolution have been proposed taking into account the different physical phenomena that limit depth resolution, such as collisional mixing, roughness, and segregation. [1][2][3][4][5][6][7][8][10][11][12][13][14] However, most problems encountered in these deconvolution methods are due to the noise content in the measured profiles. This instrumental phenomenon, which cannot be eliminated by the improvement of operating conditions, strongly influences the depth resolution and therefore the quality of the deconvoluted profiles.…”

“…3) Indeed, different forms of limitative operator have been used. For example, Collins and Dowssett 12) and Allen and Dowssett 13) have used the entropy function as a limitative operator. Based on the Tikhonov-Miller regularization, Gautier et al 4) have used a limitative operator that was defined as smoothness of the solution.…”

“…Depth profiling in SIMS analysis is mathematically described by the convolution integral which is governed by the depth resolution function (DRF), hðzÞ. If the integral over hðzÞ is normalized to unity, then the measured (convolved) signal is given by the well-known convolution integral [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15] yðzÞ ¼…”