A new paradigm is introduced for the investigation of errors in frequency-domain measurements. The propagation of errors from time-domain measurements to the desired complex variables in the frequency domain was analyzed for the frequency response analysis ͑FRA͒ algorithm, one of two techniques commonly used for spectroscopy measurements. Errors in the frequency domain were found to be normally distributed, even when the errors in the time-domain were not normally distributed and when the measurement technique introduced bias errors. For additive errors in time-domain signals, the errors in the real and imaginary impedance were found to be uncorrelated, and the variances of the real and imaginary parts of the complex impedance were equal. The equality of variances was realized except for cases where the time-domain signals contained proportional errors. The statistical characteristics of the results were in good agreement with experimental observations. Weighted complex nonlinear regression techniques are typically used to extract information from electrochemical impedance data. The error structure of the measurement is used implicitly in regression analysis and has a significant influence on the quality and amount of information that can be extracted from impedance data. The variance of the stochastic error can be incorporated explicitly into the weighting strategy for the regression and can provide a means for determining whether observed features lie outside the noise level of the measurement. The stochastic errors can also influence the use of the Kramers-Kronig relations for determining the internal consistency of the data.For the purposes of the discussion presented here, the errors in an impedance measurement are expressed in terms of the difference between the observed value Z ob () and a model value Z mod () aswhere res represents the residual error, fit () is the systematic error that can be attributed to inadequacies of the model, bias () represents the systematic experimental bias error that cannot be attributed to model inadequacies, and stoch () is the stochastic error with expectation E͕ stoch ()͖ ϭ 0. The experimental bias errors, as referred to here, may be caused by a nonstationary behavior or by instrumental artifacts.Typically, the impedance is a strong function of frequency and can vary over several orders of magnitude through the experimentally accessible frequency range. The stochastic errors of the impedance measurement are strongly heteroskedastic, which means that the variance of the stochastic errors is also a strong function of frequency. 1-4 Selection of an appropriate weighting strategy is, therefore, critical for interpretation of data.A distinction is drawn, in the present work, between stochastic errors that are randomly distributed about a mean value of zero, errors caused by the lack of fit of a model, and experimental bias errors. The problem of interpretation of impedance data is therefore defined as consisting of two parts, one of identification of experimental errors, which ...
A new paradigm established for the investigation of errors in frequency-domain measurements was applied to the phase sensitive detection ͑PSD͒ algorithm used in lock-in amplifiers, one of two techniques commonly used for spectroscopy measurements. For additive errors in time-domain signals, the errors in the phase angle and magnitude were found to be uncorrelated, even when time-domain errors were not normally distributed. In contrast to results obtained using the frequency response analysis algorithm, errors in the real and imaginary impedance were found to be correlated, and the variances of the real and imaginary parts of the complex impedance were not equal, except at a phase angle of Ϫ/4. A propagation of error model was established to explain and confirm the calculated statistical properties. The statistical characteristics of the results were in good agreement with experimental observations.
This past year has witnessed a sharp increase in EUV lithography progress spanning production tools, source and infrastructure to better position the technology for HVM readiness. While the exposure source remains the largest contributor to downtime and availability, significant strides in demonstrated source power have bolstered confidence in the viability of EUVL for insertion into HVM production. The ongoing development of an EUV pellicle solution alleviates industry concern about one significant source of line-yield risk. In addition to continued expected improvements in EUV source power and availability, the ability to deliver predictable yield remains an ultimate gate to HVM insertion. Ensuring predictable yield requires significant emphasis on reticles. This includes continued pellicle development to enable the readiness and supply of a robust pellicle solution in advance of 250W source power, as well as improvements in mask blank defectivity and techniques to detect and mitigate reticle blank and pattern defects.
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