We present an analytic form for the response function measured in a SIMS depth profile of an impurity layer less than 1 nm wide (a delta layer). Although the process used to evolve the function can be justified on physical grounds, we make no claim that the justification is rigorous or that the function is universal. At present we examine its use in making a consistent and utilitarian definition of frequently employed resolution parameters. The function is found to give an accurate fit (lying everywhere within the statistical noise on the profile over several orders of magnitude in signal intensity) to responses from boron, antimony, germanium and isotopically pure silicon deltas in a silicon matrix, and to silicon, aluminium and beryllium deltas in gallium arsenide. The fit is also good over the full primary ion energy range examined (1-11 keV). There are four fitting parameters for a normalized data set, one related to the depth of the delta below the surface and three independently related to depth resolution. The function has an analytic Fourier transform, and may be used as a smooth, noise-free substitute for the measured data in profile synthesis (convolution) and in deconvolution whenever convolution is a valid model for the SIMS measurement process.

The subject of this review is the secondary ion mass spectrometry (SIMS) analysis of ultrathin or delta layers of impurity in a semiconductor matrix and their use in establishing the limitations of SIMS depth profiling, exploring the fundamental processes occurring during analysis, and enhancing the quantification of SIMS data. Methods for extracting accurate information for the grower (concerning the material) and the analyst (concerning the SIMS instrument) are described. It is demonstrated that sets of SIMS profiles obtained over a range of analytical conditions are desirable if accurate information is required. In this context, the observation of dopant interaction occurring in codoped samples during SIMS analysis is reported for the first time. It is shown that quite large discrepancies exist between different measurements of decay length and associated parameters for the same impurity/matrix combination. These need to be explained before attempting to relate delta profile shape to primary ion beam induced mass transport mechanisms. The concept of the delta profile as a response function and the use of deconvolution as a complete quantification method are discussed. The use of delta profiles in setting up models of the ion–solid interaction such as IMPETUS is illustrated.

The action of the probe ions in SIMS depth profiling causes a number of mass transport phenomena. Consequently the data obtained are both broadened and shifted in a manner dependent on the species of the matrix, impurity and probe, and the experimental conditions. Quantification methods based on implanted standards and crater depth measurement are hampered by inaccuracies in the depth measurement, and take no account of the blurring processes. This paper reports the development of an alternative method. The blurring processes are not yet well enough understood for complete modelling. An empirical model, valid in the dilute limit, is that the true depth distribution is convoluted with an instrumental response to give the SIMS signal. If the response function is carefdly defined, inversion of the convolution equation should give a fully quantified depth profile, correcting for blurring effects and any differential shift, mapping primary ion dose density (or time) back to depth and mapping signal intensity back to concentration in one mathematical operation. The sample from which the response fuoction is measured becomes a complete concentration and depth standard. Deconvolution is non-trivial as there is no unique solution in the real case, where the profile data and measured response consist of a finite number of data points. The method used here is based on the use of maximum entropy and returns the least biased (least structured) of the possible solutions. The use of this method to fully quantify two samples will be demonstrated and the results compared with ordinary quantification. QUANTIFICATION PROBLEMSDynamic SIMS data require two processes for complete quantification. For a single matrix sample the dose-todepth mapping is approximately linear and is commonly determined by a measurement of the final crater. For a multilayer structure more complex techniques may be appropriate.' Concentrations are obtained by comparison with data from a known (typically an implanted) standard, measured under the same conditions. This method of quantification is simple, well tried and with care can give extremely good results. However, accurate measurement of the crater depth is difficult (an accuracy of 4% is currently the best available using surface profilometry or interference microscopy). Moreover, where the crater bottom contains a significant number of retained probe atoms, the measured depth will differ from that of the matrix-eroded depth : reactive species at around normal incidence can change the average spacing of matrix atoms' and even inert probes may, in extreme cases, cause bli~tering.~ For reasons to be discussed later, the linear mapping is also unlikely to be a good approximation except for deep craters. The calibration of concentration should be reliable provided an accurate standard, in the appropriate concentration region, is available. Unfortunately, errors due to inaccu-* Author to whom correspondence should be addressed. rate depth measurement and unnoticed variations in erosion rate propagate into thi...

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.