Simulation of sputter-induced roughness for depth profiling of thin film structures

Sputtering induced surface roughening is the dominant factor that degrades depth resolution in sputter profiling of polycrystalline film samples. Due to the dependence of the sputtering yield on the crystallographic orientation, ion beam incidence angle and composition, the local sputtering rate differs from grain to grain. A simple computer program based on a model of Marton and Fine can simulate such a roughness development within one layer, an improved version can even be applied for interfaces. A further extension of the program using a model of Hauffe includes effects like shadowing and enhanced peak erosion leading to surface smoothing.     

Simulation of sputter-induced roughness for depth profiling of thin film structures

Sputtering induced surface roughening is the dominant factor that degrades depth resolution in sputter profiling of polycrystalline film samples. Due to the dependence of the sputtering yield on the crystallographic orientation, ion beam incidence angle and composition, the local sputtering rate differs from grain to grain. A simple computer program based on a model of Marton and Fine can simulate such a roughness development within one layer, an improved version can even be applied for interfaces. A further extension of the program using a model of Hauffe includes effects like shadowing and enhanced peak erosion leading to surface smoothing.     

SIMS depth profiling of semiconductor interfaces: Experimental study of depth resolution function

Reconstruction of original element distribution at semiconductor interfaces using experimental SIMS profiles encounters considerable difficulties because of the matrix effect, sputtering rate change at the interface, and also a sputtering‐induced broadening of original distributions. We performed a detailed depth profiling analysis of the Al step‐function distribution in GaAs/Al_xGa_1?xAs heterostructures by using Cs⁺ primary ion beam sputtering and CsM⁺ cluster ion monitoring (where M is the element of interest) to suppress the matrix effect. The experimental Depth Resolution Function (DRF) was obtained by differentiation of the Al step‐function profile and compared with the ‘reference’ DRF found from depth profiling of an Al delta layer. The difference between two experimental DRFs was explained by the sputtering rate change during the interface profiling. We experimentally studied the sputtering rate dependence on the Al_xGa_1?xAs layer composition and applied it for a reconstruction of the DRF found by differentiating the Al step‐function distribution: the ‘reconstructed’ and ‘reference’ DRFs were found to be in good agreement. This confirmed the correctness of the treatment elaborated. Copyright © 2010 John Wiley & Sons, Ltd.     

New horizons in sputter depth profiling inorganics with giant gas cluster sources: Niobium oxide thin films

X‐ray photoelectron spectroscopy is used to study a wide variety of material systems as a function of depth (“depth profiling”). Historically, Ar⁺ has been the primary ion of choice, but even at low kinetic energies, Ar⁺ ion beams can damage materials by creating, for example, nonstoichiometric oxides. Here, we show that the depth profiles of inorganic oxides can be greatly improved using Ar giant gas cluster beams. For NbO_x thin films, we demonstrate that using Ar_x⁺ (x = 1000‐2500) gas cluster beams with kinetic energies per projectile atom from 5 to 20 eV, there is significantly less preferential oxygen sputtering than 500 eV Ar⁺ sputtering leading to improvements in the measured steady state O/Nb ratio. However, there is significant sputter‐induced sample roughness. Depending on the experimental conditions, the surface roughness is up to 20× that of the initial NbO_x surface. In general, higher kinetic energies per rojectile atom (E/n) lead to higher sputter yields (Y/n) and less sputter‐induced roughness and consequently better quality depth profiles. We demonstrate that the best‐quality depth profiles are obtained by increasing the sample temperature; the chemical damage and the crater rms roughness is reduced. The best experimental conditions for depth profiling were found to be using a 20 keV Ar₂₅₀₀⁺ primary ion beam at a sample temperature of 44°C. At this temperature, there is no, or very little, reduction of the niobium oxide layer and the crater rms roughness is close to that of the original surface.     

Analytic function to describe interfaces and resolution consistency in sputter depth profiling

A simple analytical function is derived to describe the interface shapes measured in sputter depth profiling by using X‐ray photoelectron spectroscopy or secondary ion mass spectrometry. This function involves the convolution of a central Gaussian function, often taken to describe the roughness, together with an exponential tail to describe mixing and an exponential approach often taken to describe an information depth. This model is consistent with Hofmann's mixing‐roughness‐information model that does the same by numerical analysis, but we present a direct analytical function that is more transparent to the user. The differential of the function gives Dowsett's function for delta layers. Depending on which of the 3 base parameters are identified as sample related, the analyst can obtain the centroid of the underlying composition. These functions are used to show the extent that the common measure of depth resolution for step edges and delta functions diverge as the profile becomes less Gaussian.     

Dynamics of GDOES-induced surface roughening in metal interfaces

The roughness induced during glow-discharge optical-emission spectroscopy (GDOES) measurements has been reported to cause a loss of resolution during GDOES depth-profiling analysis. In this paper, we undertake for the first time a study of the dynamics of the surface morphology of chromium and titanium thin films (designed in mono and multilayer structures) under the impinging of GDOES incoming ions. We performed this study under the theoretical framework of the dynamic scaling theory, by analysing surface morphology changes, as measured ex-situ by AFM, with irradiation time. For single metal layers it was found that, after an initial surface smoothening, the surface undergoes a rapid steep roughening for both systems, with quite similar quantitative dynamics. Once this roughening ends a second temporal scaling regime arises, operating for long length scales with dynamics depending on the sputtering rate of the material. For the chromium layer, with a very high sputtering rate of 5.5 μm min^?1, this regime is consistent with the KPZ model, whereas for the titanium layer an EW scaling regime is indicated. These different scaling regimes are consistent with the development of larger surface slopes for the Cr system. In the multilayer systems, the initial roughness induced on the top Cr layer by GDOES has similar dynamics to that for single-layer Cr. However, a clear decrease in the roughness was observed once the underlying Ti layer, with a lower sputtering rate, was reached. This decrease in the induced roughness is maintained while the Ti layer is eroded. Therefore, choice of appropriate material (i.e. sputtering yield values) combinations and of their depth of location can enable tuning of GDOES-induced roughness and achieve substantial control over the depth profiling process.     

Evaluation of the van Deemter equation in terms of open‐ended flow to chromatography

Plate theory and adsorption theory are the main tools available for understanding chromatographic experiments. Both theories predict a Gaussian distribution of solute molecules within the tubular system. However, Gaussian concentration distributions are observed predominantly at slow linear flow rates, while asymmetric concentration distributions are observed at the linear flow rates most used in chromatography. Allegedly, this asymmetry originates from an inhomogeneous distribution of grain sizes in the column and column overload. However, it is an experimental fact that the distribution of chemicals within an injected volume of solute changes as a function of time, while the response is measured simultaneously. Accordingly, the obtained signal cannot be compared to the theory before some type of time‐based deconvolution of the data has been performed. Adjustments to high‐performance liquid chromatography data were thus proposed through empirical equations that describe the relevant time values, peak height, peak area, and parameters of the van Deemter equation. It was proposed that the transfer of solute from the front to the rear part of the pulse during laminar open‐ended flow occurs at rate that depends on the linear flow rate, and to a lesser extent, on properties of the response function.     

Estimation of Flat‐topped Gaussian distribution with application in system identification

Uniformly distributed uncertainty exists in industrial process; additive error introduced by quantization is an example. To be able to handle additive uniform and Gaussian measurement uncertainty simultaneously in system identification, the Flat‐topped Gaussian distribution is considered in this paper as an alternative to the Gaussian distribution. To incorporate this type of uncertainty in the maximum likelihood estimation framework, the explicit form of its density function is of necessity. This work proposes an approach for obtaining both the functional structure and corresponding parameter estimation of Flat‐topped Gaussian distribution by a moment fitting strategy. The performance of the proposed approximation function is verified by comparison to the Flat‐topped Gaussian distributed random variable with different Gaussian and uniform components. Results of numerical simulations and industrial applications in system identification are presented to verify the effectiveness of the Flat‐topped Gaussian distribution for noise distribution in handling additional uniform uncertainty.     

Double‐step block division plant‐wide fault detection and diagnosis based on variable distributions and relevant features

Large‐scale process data in plant‐wide process monitoring are characterized by two features: complex distributions and complex relevance. This study proposes a double‐step block division plant‐wide process monitoring method based on variable distributions and relevant features to overcome this limitation. First, the data distribution is considered, and the normality test method called the D‐test is applied to classify the variables with the same distribution (i.e., Gaussian distribution or non‐Gaussian distribution) in a block. Thus, the second block division is implemented on both blocks obtained in the previous step. The mutual information shared between two variables is used to generate relevant matrixes of the Gaussian and non‐Gaussian blocks. The K‐means method clusters the vectors of the relevant matrix. Principal component analysis is conducted to monitor each Gaussian subblock, whereas independent component analysis is conducted to monitor each non‐Gaussian subblock. A composite statistic is eventually derived through Bayesian inference. The proposed method is applied to a numerical system and the Tennessee Eastman process data set. The monitoring performance shows the superiority of the proposed method. Copyright © 2015 John Wiley & Sons, Ltd.     

An analytical depth resolution function for the MRI model

The mixing roughness information depth model is frequently used for the quantification of sputter depth profiles. In general, the solution of the convolution integral for any kind of in‐depth distributions is achieved by numerical methods. For a thin delta layer, an analytical depth resolution function is presented, which enables a simple and user‐friendly quantification of measured delta layer profiles in AES, XPS and SIMS. Copyright © 2013 John Wiley & Sons, Ltd.     

Depth resolution in sputter profiling revisited

Based on a brief review of the well‐established framework of definitions, measurement and evaluation principles of the depth resolution in sputter profiling for interfaces, delta layers, single layers and multilayers, an extension to additional definitions is presented, which include the full‐width‐at‐half‐maximum of layer profiles and non‐Gaussian depth resolution functions as defined by the Mixing‐Roughness‐Information depth (MRI) model. Improved evaluation methods for adequate analysis of sputter depth profiles as well as improved definitions of depth resolution are introduced in order to meet new developments in ToF‐SIMS and GDOES, and in cluster ion sputtering of so‐called delta layers in organic matrices. In conclusion, the full‐width‐at‐half‐maximum definition and measurement of depth resolution, Δz(FWHM), is found to be more appropriate than the traditional Δz(16–84%) in order to characterize depth profiles of single layers and multilayers, because it is also valid for non‐Gaussian depth resolution functions. Copyright © 2016 John Wiley & Sons, Ltd.     

Depth profiling of light elements in PAMBE‐grown GaN and helium‐implanted titanium with heavy ion time‐of‐flight elastic recoil detection

The heavy ion time‐of‐flight elastic recoil detection analysis (HI‐ERDA) technique was used to investigate the possibility of measuring near‐surface elemental depth profiles of light and mid‐Z elements in thin films of plasma‐assisted molecular beam epitaxy (PAMBE)‐grown GaN and helium‐implanted titanium. The great advantage of HI‐ERDA is the ability to measure mass‐separated elemental depth profiles simultaneously. However for some materials it is not certain whether HI‐ERDA can be used successfully because significant sputtering or other beam‐induced damage may occur. The damage to the surfaces by a 77 MeV iodine beam was assessed using RBS, AFM and profilometry. The results show that for thin PAMBE‐grown polycrystalline GaN films and for titanium that has been heavily implanted with helium a significant modification of the near‐surface region is caused by the probing heavy ion beam. For the PAMBE‐grown GaN films the most significant loss trend is observed for nitrogen. Surprisingly this was not accompanied by a change in surface topology. In contrast, an almost complete removal of the heavily helium‐implanted surface layer was measured for the titanium specimens. The investigation shows that reference measurements with additional techniques such as RBS, AFM and profilometry have to be performed to ascertain sample integrity before HI‐ERDA data can be used. Copyright © 2004 John Wiley & Sons, Ltd.     

Surface topography effects on glow discharge depth profiling analysis

Glow discharge optical emission spectroscopy (GD‐OES) has been shown to be of immense value in elemental depth profiling of thin or thick films on conductive or non‐conductive substrates. For aluminium, GD‐OES has been employed to examine locations of markers and tracers in anodic films, thereby assisting understanding of transport phenomena. In order to investigate the influence of surface topography on depth profiling analysis, anodic aluminium oxide films of various thicknesses, with incorporated electrolyte species, were produced on superpure aluminium substrates of controlled roughnesses. The distributions of incorporated species in the films were subsequently probed. Surface topography modifications and consequent depth resolution degradation were examined during depth profiling analysis performed by GD‐OES. The results reveal that the sputtering process leads to the roughening or smoothing of the surface topography of the specimen for a ratio of the film thickness to the amplitude of the substrate texture less, or greater, than 1 respectively. As a consequence of the surface topography dependence of the ion bombardment, analysis of thin films over rough surfaces suffers from depth resolution limitations due to sputtering‐induced topography changes, thereby limiting quantification of the resultant spectra. Copyright © 2010 John Wiley & Sons, Ltd.     

Choice of Spin–Orbit Correction Terms in Gaussian Model Chemistries

Spin–orbit correction terms for use in Gaussian‐2 theory and other model chemistries for third‐row atoms and molecules are calculated by several methods with the objective of finding a reliable method that can be applied in a routine and economical manner in the spirit of Gaussian model chemistries. The results are evaluated for the test set of molecules and ions used in the original extension of Gaussian‐2 theory to third‐row atoms. Further results are presented for systems where Gaussian‐2 results are reported in the literature without spin–orbit correction terms and for some larger molecules. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1552–1556, 2001     

SIMS depth profiling of ‘frozen’ samples: in search of ultimate depth resolution regime

We have performed secondary ion mass spectrometry depth profiling analysis of III–V based hetero‐structures at different target temperatures and found that both the surface segregation and surface roughness caused by ion sputtering can be radically reduced if the sample temperature is lowered to ?150 °C. The depth profiling of ‘frozen’ samples can be a good alternative to sample rotation and oxygen flooding used for ultra‐low‐energy depth profiling of compound semiconductors. Copyright © 2016 John Wiley & Sons, Ltd.     

Development of B‐doped Si multiple delta‐layer reference materials for SIMS profiling

B‐doped Si multiple delta‐layers (MDL) were developed as certified reference materials (CRM) for secondary ion mass spectrometry (SIMS) depth profiling analysis. Two CRMs with different delta‐layer spacing were grown by ion beam sputter deposition (IBSD). The nominal spacing of the MDL for shallow junction analysis is 10 nm and that for high energy SIMS is 50 nm. The total thickness of the film was certified by high resolution transmission electron microscopy (HR‐TEM). The B‐doped Si MDLs can be used to evaluate SIMS depth resolution and to calibrate the depth scale. A consistency check of the calibration of stylus profilometers for measurement of sputter depth is another possible application. The crater depths measured by a stylus profilometer showed a good linear relationship with the thickness measured from SIMS profiling using the calibrated film thickness for depth scale calibration. The sputtering rate of the amorphous Si thin film grown by sputter deposition was found to be the same as that of the crystalline Si substrate, which means that the sputtering rate measured with these CRMs can be applied to a real analysis of crystalline Si. Copyright © 2005 John Wiley & Sons, Ltd.     

Quantification problems in depth profiling of pwr steels using Ar+ ion sputtering and XPS analysis.

The oxide scales of AISI 304 formed in boric acid solutions at 300 degrees C and pH = 4.5 have been studied using X-ray photoelectron spectroscopy (XPS) depth profiling. The present focus is depth profile quantification both in depth and chemical composition on a molecular level. The roughness of the samples is studied by atomic force microscopy before and after sputtering, and the erosion rate is determined by measuring the crater depth with a surface profilometer and vertical scanning interferometry. The resulting roughness (20-30 nm), being an order of magnitude lower than the crater depth (0.2-0.5 microm), allows layer-by-layer profiling, although the ion-induced effects result in an uncertainty of the depth calibration of a factor of 2. The XPS spectrum deconvolution and data evaluation applying target factor analysis allows chemical speciation on a molecular level. The elemental distribution as a function of the sputtering time is obtained, and the formation of two layers is observed-one hydroxide (mainly iron-nickel based) on top and a second one deeper, mainly consisting of iron-chromium oxides.     

Surface‐Roughness Evolution During the Cementation of Silver Ions on Solid Copper in Aqueous Sulfuric Acid Solution

The evolution of the surface roughness during cementation of Ag⁺ conducted either in O₂‐free or O₂‐saturated aqueous H₂SO₄/CuSO₄ was investigated at two different initial concentrations of Ag⁺. The kinetics data of the process determined previously in the rotating cylinder were linked directly with scanning‐electron‐microscope (SEM) images and surface‐height‐distribution diagrams calculated for various cementation times. It was found that, at the beginning of the process, the surface roughness decreases due to formation of a flat Ag layer on the top of the surface, independent of the presence or absence of O₂ in the system. With increasing reaction time, an increase in the surface roughness was observed. The rate enhancement of the process is mainly responsible for the increase of the surface roughness in the O₂‐saturated solutions, especially at the higher initial Ag⁺ concentration (100 mg/dm³). The rate enhancement observed at a latter stage of the process, connected with the increase of the effective surface area of the cathodic sites, was separated from the rate enhancement induced by the competitive chemical process occurring in O₂‐free solution. The difference in the mechanisms of the processes conducted under aerobic and anaerobic conditions was reflected in the surface‐heigth distributions calculated from the SEM images.     

Application of Sputter-Assisted EPMA to Depth Profile Analysis

 A common problem in depth profile measurement is the calibration of the depth scale. The new technique of sputter assisted electron probe microanalysis offers the possibility of calculating the composition as well as the depth scale solely from the acquired X-ray intensity data without further information, e.g. sputter rates. To achieve a depth resolution that is smaller than the depth of information of the electron probe, i.e. 0.1–1 μm, special deconvolution algorithms must be applied to the acquired data. To assess the capabilities of this new technique it was applied to a Ti/Al/Ti multilayer on Si under different measurement conditions. Quantitative depth profiles were obtained by application of a deconvolution algorithm based on maximum entropy analysis. By comparison of these profiles with AES depth profiles and AFM roughness measurements, it was shown that the limiting factor to the achievable depth resolution is the occurrence of surface roughening induced by the sputtering process rather than the relatively large depth of information of the electron probe. We conclude that for certain applications sputter-assisted EPMA can be regarded as a valid depth profiling technique with a depth resolution in the nm range.