We present empirical models for measured frequency-dependent insertion loss (|S21|) in a prototypical through silicon via (TSV) enabled 3D-IC from Sematech for characterization of defects formation due to thermal treatment. We measure |S-21| on TSV-interconnects, as a function of the extent of thermal annealing. The model parameters are determined with a stochastic optimization implementation of the Levenberg-Marquardt method. Experimental results indicate that loss mechanisms vary with frequency. Hence, we fit our models to a low-frequency (below 3.2 GHz), and to a high-frequency (above 3.2 GHz) subset, respectively. At low frequencies, we attribute variations in frequency-dependent insertion loss to variations in the silicon oxide that isolates the coaxial TSV metal core from the silicon substrate. At frequencies above 3.2 GHz, we attribute variations in insertion loss to other mechanisms including, but not limited to, thermo-mechanical damage concentrated at the surface of the core metal fill and skin effects in the barriers in the TSV. Together with previously published work, we expect this paper to lay the foundation for assessment and improvement of process stability, product reliability, diagnostics, and lifetime predictability. Specifically, we expect the empirical models described in this work to facilitate materials selection and workflow optimization of 3D- interconnect in the semiconductor industry. (c) 2024 The Author(s). Published on behalf of The Electrochemical Society by IOP Publishing Limited. This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 License (CC BY,https://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse of the work in any medium, provided the original work is properly cited.

Ghost Imaging enables 2D reconstruction of an object even though particles transmitted or emitted by the object of interest are detected with a single pixel detector without spatial resolution. This is possible because for the particular implementation of ghost imaging presented here, the incident beam is spatially modulated with a non-configurable attenuating mask whose orientation is varied (e.g. via transverse displacement or rotation) in the course of the ghost imaging experiment. Each orientation yields a distinct spatial pattern in the attenuated beam. In many cases, ghost imaging reconstructions can be dramatically improved by factoring the measurement matrix which consists of measured attenuated incident radiation for each of many orientations of the mask at each pixel to be reconstructed as the product of an orthonormal matrix Qand an upper triangular matrix R provided that the number of orientations of the mask (N) is greater than or equal to the number of pixels (P) reconstructed. For the N<P case, we present a data augmentation method that enables QR factorization of the measurement matrix. To suppress noise in the reconstruction, we determine the Moore-Penrose pseudoinverse of the measurement matrix with a truncated singular value decomposition approach. Since the resulting reconstruction is still noisy, we denoise it with the Adaptive Weights Smoothing method. In simulation experiments, our method outperforms a modification of an existing alternative orthogonalization method where rows of the measurement matrix are orthogonalized by the Gram-Schmidt method. We apply our ghost imaging methods to experimental X-ray fluorescence data acquired at Brookhaven National Laboratory.

Johnson noise thermometry (JNT) is a purely electronic method of thermodynamic thermometry. In primary JNT, the temperature is inferred from a comparison of the Johnson noise voltage of a resistor at the unknown temperature with a pseudo-random noise synthesized by a quantum-based voltage-noise source (QVNS). The advantages of the method are that it relies entirely on electronic measurements, and it can be used over a wide range of temperatures due to the ability of the QVNS to generate programmable, scalable, and accurate reference signals. The disadvantages are the requirement of cryogenic operation of the QVNS, the need to match the frequency responses of the leads of the sense resistor and the QVNS, and long measurement times. This review collates advice on current best practice for a primary JNT based on the switched correlator and QVNS. The method achieves an uncertainty of about 1 mK near 300 K and is suited to operation between 4 K and 1000 K.

The reliability of through silicon via (TSV)-interconnects depends on various factors including integration schemes, manufacturing process (construction materials, wafer-scale homogeneity, thermal budget) and operating conditions. The magnitude of the frequency-dependent $S_{21}$ microwave scattering parameter quantifies insertion losses in TSV-interconnects. The insertion loss depends on the instantaneous electrical characteristics of the device under test. We attribute insertion loss (which affects device reliability) to reorientation of electrically active defects, cracks, voids, dielectric constant variation, and water molecules affected by heat. We model insertion losses with equivalent circuit models of varying complexity. We compare results determined with global and local models fit to low-frequency and high-frequency subsets of the full spectrum. We estimate model parameters with a stochastic optimization implementation of the Levenberg-Marquadt method. To illustrate the relevance of this methodology, for TSV-interconnects from two different providers, we quantify how estimated model parameters vary with thermal cycles for TSV-interconnects fabricated at particular wafer locations.

We develop an empirical model for measured frequency-dependent insertion loss ( $\vert {S}_{{21}}\vert $ ). The model parameters are determined with a stochastic optimization implementation of the Levenberg–Marquard method. We compare measured $\vert {S}_{{21}}\vert $ on through silicon via (TSV)-interconnects, from two different providers, as a function of the extent of thermal annealing. The frequency-dependent changes in the electrical characteristics of the interconnect are attributed to silanol (Si-OH) and other dangling bond polarizations at the Si–SiO interface between the silicon substrate and the lateral silicon oxide that isolates the coaxial metal core from the silicon substrate. The changes in the polarizations are traceable to changes in the chemistry of the isolation dielectric during thermal annealing. The data also suggest that the evolution of the chemical defects inherent in the “as-manufactured” products may be responsible for some of the signal integrity degradation issues and other early reliability failures observed in TSV-enabled 3-D devices.

To calibrate an optical transition edge sensor (TES), for each pulse of the light source (e.g. pulsed laser), one must determine the ratio of the expected number of photons that deposit energy and the expected number of photons created by the laser. Based on the estimated pulse height generated by each energy deposit, we form a pulse height spectrum with features corresponding to different numbers of deposited photons. We model the number of photons that deposit energy per laser pulse as a realization of a Poisson process, and the observed pulse height spectrum with a mixture model method. For each candidate feature set, we determine the expected number of photons that deposit energy per pulse and its associated uncertainty based on the mixture model weights corresponding to that candidate feature set. From training data, we select the optimal feature set according to an uncertainty minimization criterion. We then determine the expected number of photons that deposit energy per pulse and its associated uncertainty for test data that is independent of the training data. Our uncertainty budget accounts for random measurement errors, systematic effects due to mismodeling feature shapes in our mixture model, and possible imperfections in our feature set selection method.

In laser-assisted atom probe tomography, an important goal is to reconstruct the mass-to-charge ratio, (m/z), spectrum due to various ion species. In general, the probability mass function (pmf) associated with the time-of-flight (TOF) spectrum produced by each ion species is unknown and varies from species-to-species. Moreover, measuring pmfs for distinct ion species in calibration experiments is not practical. Here, we present a mixture model method to determine TOF pmfs that can vary from peak-to-peak. In this approach, we determine weights of candidate pmfs with a maximum likelihood method. In a proof-of-principle study, we apply our method to a TOF spectrum acquired from a silicon sample and determine intensity estimates of singly charged isotopes of silicon.

In experiments in a range of fields including fast neutron spectroscopy and astroparticle physics, one can discriminate events of interest from background events based on the shapes of electronic pulses produced by energy deposits in a detector. Here, I focus on a well-known pulse shape discrimination method based on the ratio of the temporal integral of the pulse over an early interval X-p and the temporal integral over the entire pulse X-t. For both event classes, for both a Gaussian noise model and a Poisson noise model, I present analytic expressions for the conditional distribution of X-p given knowledge of the observed value of X-t and a scaled energy deposit corresponding to the product of the full energy deposit and a relative yield factor. I assume that the energy-dependent theoretical prompt fraction for both classes are known exactly. With a Bayesian approach that accounts for imperfect knowledge of the scaled energy deposit, I determine the posterior mean background acceptance probability given the target signal acceptance probability as a function of the observed value of X-t. My method enables one to determine receiver-operating-characteristic curves by numerical integration rather than by Monte Carlo simulation for these two noise models.

An aerosol particle mass analyzer (APM) which classifies aerosol particles according to their mass has been developed. Mass distributions of aerosol particles can be measured by the APM combined with a particle counting device. Particle mass that can be measured in this way ranges from 3×10-18 g to 2×10-12 g, which partially fills the mass range that is not covered by existing mass measuring instruments (e.g., mass spectrometers and conventional balances). The introduction of the APM has led to various new techniques for evaluating aerosol particle properties such as effective and true densities, porosities, fractal dimensions, and mass concentrations of suspended particulates. This article describes the principle of the APM and how it differs from other instruments for classifying aerosol particles. The article also describes the significance of measuring aerosol particle mass and the course of events that led to commercialization of the APM from the viewpoint of “synthesiology.”

We acquire ferromagnetic resonance (FMR) spectra for an out-of-plane magnetized yttrium iron garnet sample with a vector network analyzer at microwave frequencies ranging from 4.2 to 5.2 GHz. The applied static magnetic field varies from approximately 253.6 to 260.1 kA/m. Based on an empirical model for resonant features in the S-21 spectrum produced by the excitation of multiple modes and instrumental effects, we predict measured values of S-21-parameters. For each of many microwave frequencies, for each of multiple modes, we determine the resonant field value of the applied magnetic field, an amplitude, and an FMR linewidth. Based on the frequency-dependent resonant field values produced by excitation of the main mode, we determine the effective magnetization and the gyromagnetic ratio of the sample.

We directly quantify the effect of infrequent calibration on the stability of microwave radiometer temperature measurements (where a power measurement for the unknown source is acquired at a fixed time, but calibration data are acquired at variable earlier times) with robust and nonrobust implementations of a new metric. Based on our new metric, we also determine a component of uncertainty in a single measurement due to infrequent calibration effects. We apply our metric to experimental data acquired from experimental ground-based calibration data acquired from a NASA millimeter-wave imaging radiometer and a NIST radiometer (Noise Figure Radiometer-NFRad). Based on a stochastic model for the NFRad, we determine the random uncertainty of an empirical prediction model of our stability metric by a Monte Carlo method. For comparison purposes, we also present a secondary metric that quantifies stability for the case where calibration data are acquired at a fixed time, but power measurements for the unknown source are acquired at variable later times.

Given a composite null hypothesis H0, test supermartingales are non-negative supermartingales with respect to H0 with an initial value of 1. Large values of test supermartingales provide evidence against H0. As a result, test supermartingales are an effective tool for rejecting H0, particularly when the p-values obtained are very small and serve as certificates against the null hypothesis. Examples include the rejection of local realism as an explanation of Bell test experiments in the foundations of physics and the certification of entanglement in quantum information science. Test supermartingales have the advantage of being adaptable during an experiment and allowing for arbitrary stopping rules. By inversion of acceptance regions, they can also be used to determine confidence sets. We used an example to compare the performance of test supermartingales for computing p-values and confidence intervals to Chernoff-Hoeffding bounds and the “exact” p-value. The example is the problem of inferring the probability of success in a sequence of Bernoulli trials. There is a cost in using a technique that has no restriction on stopping rules, and, for a particular test supermartingale, our study quantifies this cost.

We develop empirical models to predict the contribution of topographic variations in a sample to near-field scanning probe microwave microscopy (NSMM) images. In particular, we focus on |S11| images of a thin Perovskite photovoltaic material and a GaN nanowire. The difference between the measured NSMM image and this prediction is our estimate of the contribution of material property variations to the measured image. Prediction model parameters are determined from either a reference sample that is nearly free of material property variations or directly from the sample of interest. The parameters of the prediction model are determined by robust linear regression so as to minimize the effect of material property variations on results. For the case where the parameters are determined from the reference sample, the prediction is adjusted to account for instrument drift effects. Our statistical approach black is fully empirical black and thus complementary to current approaches based on physical models that are often overly simplistic.

In preparation for the redefinition of the International System of Units (SI), five different electronic measurements of the Boltzmann constant have been performed using different Johnson noise thermometry (JNT) systems over the past seven years. In this paper, we describe in detail the JNT system and uncertainty components associated with the most recent National Institute of Standards and Technology (NIST) determination of the Boltzmann constant: k = 1.380642 9(69) × 10−23 J/K, with a relative standard uncertainty of 5.0 × 10−6 and relative offset of −4.05 × 10−6 from the Committee on Data for Science and Technology (CODATA) 2014 recommended value. We discuss the input circuits and the approach we used to match the frequency response of two noise sources. We present new measurements of the correlated noise of the 4 K on-chip resistors in the quantum-accurate, pseudorandom, voltage-noise source, which we used to estimate the correlated, frequency-dependent, nonthermal noise in our system. Finally, we contrast our system with those used in other measurements and speculate on future improvements.

We perform scanning microwave microscopy (SMM) to study the spatially varying electronic properties and related morphology of pristine and degraded methylammonium lead-halide (MAPI) perovskite films fabricated under different ambient humidity. We find that higher processing humidity leads to the emergence of increased conductivity at the grain boundaries but also correlates with the appearance of resistive grains that contain PbI2. Deteriorated films show larger and increasingly insulating grain boundaries as well as spatially localized regions of reduced conductivity within grains. These results suggest that while humidity during film fabrication primarily benefits device properties due to the passivation of traps at the grain boundaries and self-doping, it also results in the emergence of PbI2-containing grains. We further establish that MAPI film deterioration under ambient conditions proceeds via the spatially localized breakdown of film conductivity, both at grain boundaries and within grains, due to local variations in susceptibility to deterioration. These results confirm that PbI2 has both beneficial and adverse effects on device performance and provide new means for device optimization by revealing spatial variations in sample conductivity as well as morphological differences in resistance to sample deterioration.

The unit of thermodynamic temperature, the kelvin, will be redefined in 2018 by fixing the value of the Boltzmann constant, k. The present CODATA recommended value of k is determined predominantly by acoustic gas-thermometry results. To provide a value of k based on different physical principles, purely electronic measurements of k were performed by using a Johnson noise thermometer to compare the thermal noise power of a 200 Ohm sensing resistor immersed in a triple-point-of-water cell to the noise power of a quantum-accurate pseudo-random noise waveform of nominally equal noise power. Measurements integrated over a bandwidth of 550 kHz and a total integration time of 33 days gave a measured value of k = 1.3806514(48)x10^-23 J/K, for which the relative standard uncertainty is 3.5x10^-6 and the relative offset from the CODATA 2010 value is +1.9x10^-6.

In the electronic measurement of the Boltzmann constant based on Johnson noise thermometry, the ratio of the power spectral densities of thermal noise across a resistor at the triple point of water, and pseudo-random noise synthetically generated by a quantum-accurate voltage-noise source is constant to within 1 part in a billion for frequencies up to 1 GHz. Given knowledge of this ratio, and the values of other parameters that are known or measured, one can determine the Boltzmann constant. Due, in part, to mismatch between transmission lines, the experimental ratio spectrum varies with frequency. We model this spectrum as an even polynomial function of frequency where the constant term in the polynomial determines the Boltzmann constant. When determining this constant (offset) from experimental data, the assumed complexity of the ratio spectrum model and the maximum frequency analyzed (fitting bandwidth) dramatically affects results. Here, we select the complexity of the model by cross-validation—a data-driven statistical learning method. For each of many fitting bandwidths, we determine the component of uncertainty of the offset term that accounts for random and systematic effects associated with imperfect knowledge of model complexity. We select the fitting bandwidth that minimizes this uncertainty. In the most recent measurement of the Boltzmann constant, results were determined, in part, by application of an earlier version of the method described here. Here, we extend the earlier analysis by considering a broader range of fitting bandwidths and quantify an additional component of uncertainty that accounts for imperfect performance of our fitting bandwidth selection method. For idealized simulated data with additive noise similar to experimental data, our method correctly selects the true complexity of the ratio spectrum model for all cases considered. A new analysis of data from the recent experiment yields evidence for a temporal trend in the offset parameters.

In experiments that measure the lifetime of trapped particles, in addition to loss mechanisms with exponential survival probability functions, particles can be lost by mechanisms with non-exponential survival probability functions. Failure to account for such loss mechanisms produces systematic measurement error and associated systematic uncertainties in these measurements. In this work, we develop a general competing risks survival analysis method to account for the joint effect of loss mechanisms with either exponential or non-exponential survival probability functions, and a method to quantify the size of systematic effects and associated uncertainties for lifetime estimates. As a case study, we apply our survival analysis formalism and method to the Ultra Cold Neutron lifetime experiment at NIST. In this experiment, neutrons can escape a magnetic trap before they decay due to a wall loss mechanism with an associated non-exponential survival probability function. Published by Elsevier B.V.