Deconvolution of narrow boron SIMS depth profiles in Si and SiGe

Abstract

We present results on deconvolution of molecular beam epitaxy (MBEkgrown boron profiles in Si and SiGe that are of crucial importance for Si/SiGe heterojunction bipolar transistors (HBTs). They are based on the assump tions of linearity and homogeneity of the measurement. We determine experimentally the physical limits of these assumptions by investigating sequences of boron spikes in Si and SiGe. The deconvolution is performed by Fourier transformation into the k-domain, preceded by a physically motivated least-squares fitting of the measurement data. In this way, the high-frequency noise contributions are eliminated to a great extent without producing a systematic broadening. The numerical evaluation of the SIMS profiles is extremely fast in comparison to forward techniques and the numerical error is shown to be small. We discuss the deconvoluted SIMS profiles of MBEgrown boron spikes in Si and SiGe after annealing. Our method is suited to give information about the dopant outdiffusion from th SiGe layer in the case of HBTs.

High-resolution depth profiling of InxGa1−xAs/GaAs multiple quantum well structures by combination of secondary ion mass spectrometry and x-ray diffraction techniques

“…As is well known, the profile of a dopant distribution, extending for a few monolayers (␦-doped layers͒, coincides in the dilute limit assumption [18][19][20] with the resolution function. Therefore, the response function can be experimentally determined by profiling ␦-doped distributions incorporated in a given matrix.…”

“…Therefore, the response function can be experimentally determined by profiling ␦-doped distributions incorporated in a given matrix. 1,3,[16][17][18][19]21,22 Once the resolution function has been determined a deconvolution method allows one to determine the true element profile. 1,3,[16][17][18][19]21,22 Once the resolution function has been determined a deconvolution method allows one to determine the true element profile.…”

“…3,18,19 Some authors found that ␦-doped layers grown by molecular beam epitaxy ͑MBE͒ are useful candidates for response function determination. 19,23 Several deconvolution methods were reported in literature based on Fourier transform or equivalent methods. 19,23 Several deconvolution methods were reported in literature based on Fourier transform or equivalent methods.…”

Multi-Scale Deconvolution of Mass Spectrometry Signals

“…Thus, the results must be regularized (Tikhonov, 1963;Barakat et al, 1997;Prost et al, 1984;Burdeau et al, 2000;Herzel et al, 1995;Iqbal, 2003;Varah, 1983;Essah, 1988;Brianzi, 1994;Stone, 1974;Connolly et al, 1998;Berger et al, 1999;Fischer et al, 1998). To this end, the solution is superimposed with certain limitations by introducing some additional limitative operators, whose shape is chosen depending on the formalism used for the solution of the ill-posed problem, into a goal function; usually the goal function is the mismatch between the convoluted solution and the initial data (Makarov, 1999).…”

“…These methods, which constrain the data to be positive everywhere, are sensitive to noise, i.e., a little perturbation in the data can lead to a great difference in the deconvoluted solution. A truncation of the negative data is an arbitrary operation and it is not acceptable, since it results in an artificially steep slope and can lead to the adoption of subjective criteria for profile assessment (Herzel et al, 1995). Moreover, noise in the data increases the distance between the real signal and its estimate, therefore a priori constraint is not enough, and a free-oscillation deconvolution is necessary.…”