Peter J. Sherman

Pad Surface Roughness and Slurry Particle Size Distribution Effects on Material Removal Rate in Chemical Mechanical Planarization

The ability to predict material removal rates in chemical mechanical planarization (CMP) is an essential ingredient for low cost, high quality IC chips. Recently, models that address the slurry particles have been proposed. We address three such models. The first two differ only in how the number of active particles is computed. Both assume that pad asperities are identical and nonrandom. The third is dynamic in accommodating changing pad properties. For larger mean particle size (diameter), the role of the standard deviation of particle size distribution is uncertain. The dynamic behavior of the third model is compared with experimental observations.

A geometric approach to the maximum likelihood spectral estimator for sinusoids in noise

The problem of estimating sinusoids that have been corrupted by additive stationary noise is addressed. It is shown how the Naimark dilation for the data correlation sequence can be used to provide additional insight into some fundamental results on orthogonal polynomials and to give a new interpretation of the maximum-likelihood (ML) spectral estimator. >

A stochastic model for the effects of pad surface topography evolution on material removal rate decay in chemical-mechanical planarization

The role of stochastic variations in pad surface topography evolution during a chemical-mechanical planarization or polishing (CMP) process is investigated. The roughness of the pad surface is considered, while the blanket film wafer is smooth and flat. The material removal rate (MRR) for CMP is modeled utilizing elastic as well as inelastic contact between the wafer and pad. Evolution of the pad surface topography is observed to have a significant influence on the MRR variations. A distinguishing feature of this paper is the MRR evolution equation for a single asperity. It is observed that an elastic contact model significantly underestimates the experimental trend. The selection of the initial probability density function (pdf) used in an MRR time-evolution model is shown to be a key issue. It is observed that reasonably small changes in numerical estimates of pdf parameters can have a significant effect on the accuracy of material removal model predictions. By extending the model to the case of inelastic contact between the wafer and pad asperities, it is found that model performance can be notably improved. Finally, it should be mentioned that the emphasis here on statistical elements, combined with the approach of developing mean MRR models based on models for individual asperities, allows one to easily incorporate more realistic model assumptions, an example being that pad asperities have tip curvatures and spacing that are random.

Improved periodic spectral analysis with application to diesel vibration data

The purpose of this work is to begin the development of a comprehensive time/frequency spectral analysis approach that can be applied to complex signals associated with real world systems, such as rotating machinery. Rotating machinery operating at nominally constant speed comprise a large class of important real world systems that have received relatively little attention in terms of stochastic characterizations of any greater sophistication than those associated with wide sense stationary processes. In this work, a periodic‐time/frequency characterization procedure is introduced in the context of vibration analysis associated with a diesel engine operating at nominally constant speed. This application highlights a number of difficulties, such as the need for accurate period estimation, accommodation of noninteger periods in relation to digital processing, and identification and separation of tonal components from the signature in order to arrive at a more parsimonious characterization. A theorem relating to the limiting influence of these difficulties is presented. These difficulties are addressed using advanced signal processing tools, such as a recently developed tone identification procedure and extended Kalman filtering, which to the authors’ knowledge have not been considered to date in such a setting. Results include a simple correction algorithm for noninteger periods, excellent separation of tonal components whose frequencies are slowly varying, and subsequently a modest improvement in the spectral characterization of the remainder of the process. These results have some significance in relation to diesel engine vibration, since they unambiguously identify tonal vibration components, in addition to a random structure which appears to include random excitation of resonances.

Diffusion-Limited Agglomeration and Defect Generation during Chemical Mechanical Planarization

Chemical mechanical planarization (CMP) of copper involves removal of surface asperities with abrasive particles and polishing processes. This leads to copper-containing nanoparticles extruded into the solution. We model the diffusion-limited agglomeration (DLA) of such nanoparticles which can rapidly grow to large sizes. These large particles are detrimental because they can participate in polishing, causing scratches and surface defects during CMP. The agglomeration is much slower in the reaction-limited agglomeration process. Under realistic conditions the defect generation probability can increase significantly over time scales of {approx}10 to 20 min from DLA, unless prevented by slurry rejuvenation or process modification measures.

On the convergence of the minimum variance spectral estimator in nonstationary noise

A simple proof is presented of the convergence of the minimum variance spectral estimator to the point spectrum, as the order of the covariance matrix goes to infinity. This is done in the multichannel setting where the corrupting unknown noise process is allowed to be nonstationary. Explicit bounds are also obtained on the rate of convergence. >

Asymptotic statistical properties of AR spectral estimators for processes with mixed spectra

The influence of a point spectrum on large sample statistics of the autoregressive (AR) spectral estimator is addressed. In particular, the asymptotic distributions of the AR coefficients, the innovations variance, and the spectral density estimator of a finite-order AR(p) model to a mixed spectrum process are presented. Various asymptotic results regarding AR modeling of a regular process with a continuous spectrum are arrived at as special cases of the results for the mixed spectrum setting. Finally, numerical simulations are performed to verify the analytical results.

Identifying Periodic Components in Atmospheric Data Using a Family of Minimum Variance Spectral Estimators

Abstract This work describes the application of a recently developed signal processing technique for identifying periodic components in the presence of unknown colored noise. Specifically, the application of this technique to the identification of strongly periodic components in meteorological time series is examined. The technique is based on the unique convergence properties of the family of minimum variance (MV) spectral estimators. The MV convergence methodology and computational procedures are described and are illustrated with a theoretical example. The utility of this method to atmospheric signals is demonstrated with a 26-year (1964–1989) time series of 70-mb wind components at Truk Island in the equatorial Pacific. The MV method clearly shows that although equatorial disturbances with periods of 3–5 days have a strong signal, they do not show a strong periodic component. As expected, MV convergence illustrates that the 70-mb zonal wind series at this location has a significant periodic component ...

System identification and coherence analysis in the presence of a harmonic signal

Abstract This work is concerned with estimation of transfer function and coherence information associated with periodic systems, such as rotating machinery, which involve random processes having infinite as well as finite energy. We propose new complementary spectral-based approaches for system identification and coherence estimation which anticipate this mixture of processes. Their value is demonstrated in a comparative setting, wherein the limitations of FFT and AR methods are highlighted.

Practical issues concerning the family of multichannel MV spectra for recovery of point spectrum

The paper addresses some of the practical issues associated with the multichannel point spectrum identification scheme of Foias et al. (1990). These include a convergence test for detecting signal frequencies and identifying the associated spectral matrices. An in-depth example is presented. >