Thermal Excursions Research Articles

Inelastic Stress Relaxation in Single Crystal SiC Substrates

Abstract. Optical methods were used to measure thermal deformations in commercial 4H- and 6H-SiC wafers. In general, during thermal excursions to 500 o C, the radii of curvature of the wafers increased (i.e., the wafers became less bowed). Upon cooling to room temperature, nearly all the wafers retained the high temperature radius of curvature values, a characteristic of thermoplastic deformation. Further cyclic excursions to 500 o C did not yield any significant changes in the radii of curvature, thus signifying the irreversibility of the thermal deformation. The magnitude of the relieved stress following thermal deformation at 500 o C was estimated to be up to 2.14 MPa. Also observed was a significant difference in the thermoplastic deformation between the off- and on-axis wafers of both polytypes, with the former having more deformation (∆R > 3 m) than the latter (∆R < 2 m). An on-axis n-type 6H-SiC that was subjected to thermal cycling to 900 o C in vacuum also exhibited thermoplastic deformation, with an activation energy of 3.14± 0.8 eV and a relieved stress magnitude of 5.67 MPa.

Cycling copper flip chip interconnects

Use of flip chip assembly on compound semiconductor circuits is relatively new. Although solder bumping has been around for a while, use of copper bumps is also new. This discussion is intended to provide some initial data on the melding of copper flip chip bumps and compound semiconductor technologies, with respect to thermal excursion testing––cycling. For comparison, it is known that attempts to accelerate degradation caused by thermal excursions on solder bumps can result in irregular failure mechanisms. This work shows that on-chip power cycling can be used to cause identical failure mechanisms to those caused by normal temperature cycling.

Thermoplastic Deformation and Residual Stress Topography of 4H-SiC Wafers

AbstractWe have measured thermoplastic deformation in as-received, single-side polished, 4H-SiC wafers and also residual stresses in homoepitaxially grown epilayers on wafers by radius curvature measurements. The wafers studied had n-type resistivities of 0.010-0.011 ω-cm and p-type resistivities of 4.42, 4.72, 9.57 ω-cm. In a first thermal excursion to 900 °C in vacuum, the bow height of the bare substrates in all cases decreased with temperature. Upon cooling down, however, the bow heights remained largely unchanged from their values at 900 °C. A second cyclic excursion to 900 °C did not yield any significant change in the curvature, thus indicating that the substrates had thermoplastically deformed in the first heating cycle. Epilayers having nitrogen doping between 5 × 1017 and 2 × 1019 cm−3 grown on the n- and p-type substrates resulted in compressive stresses ranging between 190 and 400 MPa in the epilayers. Transmission electron microscopy (TEM) examination of the n-type epilayer (with doping levels of 5 × 1017 cm−3 and 5 × 1018 cm−3) on the n-type substrate, revealed bands of stacking faults (SFs) confined within the epilayers after the bicrystals were further annealed at 1150°C in nitrogen for thirty minutes. These doping levels are approximately one and two orders of magnitude below the reported threshold value of 3 × 1019 cm−3 previously suggested for the onset generation of SFs in annealed n-type 4H-SiC epilayers. The calculated residual stresses in all the epilayers were above the critical stress for the motion of dislocations above 1000 °C in 4H-SiC. Thus the SFs that form by glide of pre-existing partial dislocations may actually be stress induced and occur across a much wider range of doping levels. Therefore, it is possible that a significant mechanism for formation of the stacking faults and 3C bands observed in thermally treated 4H-SiC wafer is stress relief via the generation and motion of new and pre-existing partial dislocations on the basal planes of 4H-SiC.

Reply to a comment on “A case for a comet impact trigger for the Paleocene/Eocene thermal maximum and carbon isotope excursion” by G.R. Dickens and J.M. Francis

Contrary to Dickens and Francis’s claim [1] that we ‘challenge the idea of a massive CH4 release during the PETM (Paleocene/Eocene thermal maximum)’, our consideration of an extraterrestrial carbon contribution to the carbon isotope excursion (CIE) is speci¢cally limited to the initial and most rapid decrease in N13C, which accounts for less than half of the full magnitude of the CIE [2]. Thermal dissociation in response to the warming at the PETM is explicitly allowed in our hypothesis, as reiterated in our conclusions that the impact ‘may have triggered a more gradual thermal dissociation of sea£oor methane hydrates’ [2]. We directly challenge only that portion of the hydrate dissociation hypothesis that relies on gradual warming intrinsic to Earth’s climate system as the triggering mechanism [3]. Such a mechanism is not consistent with the documented essentially synchronous and instantaneous warming and decrease in N13C values at the onset of the event [3,4] and is also at odds with the occurrence of the CIE during an interval of low amplitude orbital forcing of climate [5]. Instead, we postulate a comet impact as an explanation for the rapid onset of the event. Dickens and Francis state that the ‘primary di⁄culty with invoking a comet T is that there is no supporting evidence’ and then list four points from our paper that, taken out of context, are construed as damaging to our hypothesis : (1) ‘There is no crater’. If this were to be taken as a fatal problem with hypothesizing an impact then the idea of a K/T (Cretaceous/Tertiary) impact would never have gained any traction ^ it took 10 years to identify the smoking gun at Chicxulub crater [6^8]. In addition, it is hardly ‘contrived’ to acknowledge that the P/E (Paleocene/ Eocene) impact may have occurred on oceanic crust, which constitutes more than half of Earth’s surface area and where impact craters of any age have been very di⁄cult to ¢nd. (2) ‘The remarkable fossil turnovers T strongly contrast to those across the Cretaceous/Tertiary Boundary T.’ In fact, although we noted that the two events are ‘clearly diierent’ [2] and that an a priori assumption that big impacts should be

Diagnostic development for ST plasmas on NSTX**Work supported by US DOE Contract DE-AC02-76CH03073.

Spherical tori (ST) have much lower aspect ratio (a/R) and lower toroidal magnetic field than conventional tokamaks and stellarators. This paper will highlight some of the challenges and opportunities these features pose in the diagnosis of ST plasmas in the National Spherical Torus Experiment (NSTX), and discuss some of the corresponding diagnostic development that is underway. The low aspect ratio necessitates a small centre stack, with tight space constraints and large thermal excursions, complicating the design of magnetic sensors in this region. The toroidal magnetic field on the NSTX is ⩽0.6 T, making it impossible to use ECE as a good monitor of electron temperature. A promising new development for diagnosing electron temperature is electron Bernstein wave radiometry, which is currently being pursued on the NSTX. A high-resolution charge exchange recombination spectroscopy system is being installed. Since non-inductive current initiation and sustainment are top-level NSTX research goals, measurements of the current profile J(R) are essential to many planned experiments. On the NSTX several modifications are planned to adapt the motional Stark effect (MSE) technique to lower field, and two novel MSE systems are being prototyped. Several high-speed two-dimensional imaging techniques are being developed for viewing both visible and x-ray emission. The toroidal field is equivalent to the poloidal field at the outside plasma edge, producing a large field pitch (>50°) at the outer midplane. The large shear in pitch angle makes some fluctuation diagnostics like beam emission spectroscopy very difficult, while providing a means of achieving spatial localization for microwave scattering investigations of high-k turbulence, which are predicted to be virulent for NSTX plasmas. A brief description of several of these techniques will be given in the context of the current NSTX diagnostic set.This article was due to appear in issue 7 of Plasma Physics and Controlled Fusion. To access this special issue please follow this link: http://www.iop.org/EJ/toc/0741-3335/45/7.

Cyclotron Radiation Transport in Burning Plasmas

The transport and net loss of cyclotron radiation for burning plasmas represented by the ITER, FIRE and IGNITOR designs are assessed using the CYTRAN radiation transport code. Although cyclotron radiation might be expected to be a bigger issue in the higher field devices (FIRE and IGNITOR), the reference operating conditions in those devices are at lower temperatures so that the relative importance is nearly constant for all three. At the reference operating conditions for each of these devices, the net energy loss from cyclotron radiation is about 10% of the alpha power, and the axial loss is typically about 15% of the local alpha power density. If the same fusion power is generated at higher temperature and lower density than the reference operating points (as may be the case in advanced confinement modes), both the net and axial loss fractions strongly increase and are more competitive with other energy transport processes. The increase is much stronger for the high field devices where the axial loss can approach the local alpha energy production rate for T(0) ~ 30 keV. However, if the temperature increases at constant density (as in a thermal excursion), cyclotron radiation loss remains an almost constant fraction of the alpha production rate. This implies that it will not make a significant contribution to thermal stabilization. However, these and other calculations of cyclotron radiation transport are sensitive to assumptions of reflection, plasma geometry and profile shapes. Therefore, the effect of cyclotron radiation on operating conditions and burn dynamics will undoubtedly be a generic issue that any burning plasma will have to address.

Shock-wave production of nanoparticles during high-energy ion sputtering

Several previous studies have shown that the size distributions of smaller nanoparticles ( n⩽40 where n is the number of atoms in a given cluster) generated by ion sputtering obey an inverse power law, with an exponent varying between −8 and −4, dependent upon the total sputtering yield. Such large negative exponents have not been explained by any simple physical mechanism. We reported electron microscopy studies of the size distributions of the larger nanoparticles ( n>500) that are sputtered from the surface by high-energy ion impacts. These measurements also yielded an inverse power law, but one with an exponent of −2, and one that is independent of total sputtering yield. This inverse-square dependence indicates that the clusters are produced when shock waves, generated by sub-surface displacement cascades, impact and ablate the surface. Many smaller clusters can result from fragmentation of these larger ones, which helps explain the large negative exponents that have been reported previously. In this paper, we briefly review the previous results. In addition, we present new results demonstrating that the same inverse-square size distribution is generated in both transmission and reflection sputtering geometries. An important corollary from these results is that the sputtered nanoparticles consist of simple fragments of the original surface, that is particles which have not experienced any large thermal excursions. Hence high-energy ion sputtering should provide a convenient method for synthesizing a broad distribution of nanoparticles of a wide variety of alloy phases.

Characterizing surface discoloration

A stamped coin exhibited visible discolored areas, seen as a tan haze on the surface (Fig. 1). In this case, the discoloration was considered merely cosmetic. The nonstained and stained regions were studied using a scanning electron microscope equipped with an energy-dispersive X-ray spectrometer (SEM/EDS). The SEM allows for high-magnification study of surfaces by utilizing electrons instead of visible light. This instrument is equipped with magnetic lenses and Tinting on these copper parts is evident in this photograph Introduction This paper describes several instances where discoloration was a key element in component failure. Discoloration of the surface of a component can be the result of many different factors, and its effect on function can range from simple visual anomalies to complete failure. Discoloration is generally caused either by the presence of adherent contaminants or by chemical changes on the surface. Sometimes discoloration is merely cosmetic, but even cosmetic changes may lead to part rejection in instances where appearance is of great importance. Additionally, discoloration can be an indicator of more serious problems, including adherent contaminants, thermal excursions, and/or corrosion, which could lead to eventual malfunction or complete failure. In any case, it is important to understand the analysis techniques that can be used to characterize surface discoloration and how these techniques can be used to determine the nature, cause, and relevance of the discoloration to the function of the component.

Afm Studies of Deformation and Interfacial Sliding in Interconnect Structures in Microelectronic Devices

AbstractBack-end interconnect structures (BEIS) of micro-electronic devices are susceptible to several deformation phenomena during thermal excursions, because of large differences in thermal expansion coefficients (CTE) between Si, interlayer dielectric (ILD) and metal lines. Here we use atomic force microscopy (AFM) to study plastic deformation and interfacial sliding of Cu interconnect lines on embedded in a low K dielectric (LKD). Following thermal cycling, changes were observed in both inplane Cu line dimensions, as well as out-of plane step height between Cu and LKD in single layer structures. The results of AFM measurements following both ex-situ and in-situ thermal cycling presented. A shear-lag based model is utilized to simulate the thermal cycling response, and rationalize the observed interfacial sliding behavior. Results of in-situ AFM experiments to observe the deformation of Cu-low K interconnect structures under far-field (i.e., package-level) stresses are also presented.

Burn Control in Fusion Reactors via Nonlinear Stabilization Techniques

Control of plasma density and temperature magnitudes, as well as their profiles, are among the most fundamental problems in fusion reactors. Existing efforts on model-based control use control techniques for linear models. In this work, a zero-dimensional nonlinear model involving approximate conservation equations for the energy and the densities of the species was used to synthesize a nonlinear feedback controller for stabilizing the burn condition of a fusion reactor. The subignition case, where the modulation of auxiliary power and fueling rate are considered as control forces, and the ignition case, where the controlled injection of impurities is considered as an additional actuator, are treated separately.The model addresses the issue of the lag due to the finite time for the fresh fuel to diffuse into the plasma center. In this way we make our control system independent of the fueling system and the reactor can be fed either by pellet injection or by puffing. This imposed lag is treated using nonlinear backstepping.The nonlinear controller proposed guarantees a much larger region of attraction than the previous linear controllers. In addition, it is capable of rejecting perturbations in initial conditions leading to both thermal excursion and quenching, and its effectiveness does not depend on whether the operating point is an ignition or a subignition point.The controller designed ensures setpoint regulation for the energy and plasma parameter β with robustness against uncertainties in the confinement times for different species. Hence, the controller can increase or decrease β, modify the power, the temperature or the density, and go from a subignition to an ignition point and vice versa.

Damage and Failure Mechanisms in High Pressure Silicon-Glass-Metal Microfluidic Connections

ABSTRACTThe characteristics and mechanisms of damage and failure in microfluidic joints consisting of Kovar metal tubes attached to silicon using borosilicate glass seals have been investigated. These joints are representative of seals for the MIT microrocket which is a silicon-based MEMS device. A key concern in such joints is the occurrence of cracks in silicon and glass due to residual stresses caused by a large thermal excursion during processing and the dissimilar coefficients of thermal expansion of the constituent materials. Joints with two types of glass compositions and joint configurations were fabricated, tested, and inspected. Axial tension tests were performed to investigate load carrying capability and the effect of thermally-induced cracks. Finite element models were used to obtain residual stresses due to the fabrication, and the location of the cracks from the experiments were found to coincide with the locations of the maximum principal stresses. The current work shows that the certain types of thermally-induced cracks are more detrimental to joint strength than others and a good bond between the Kovar tube and the silicon sidewall can help increase joint strength via shear load transfer.

A Review of the Variable Frequency Microwave Technology in Material Processing

The Variable Frequency Microwave (VFM) processing technology is an emerging technique that foregoes many of the inherent problems obtained in fixed-frequency microwave processing. By sweeping through a bandwidth of frequencies, a time-averaged uniformity is obtained which can eliminate heating non-uniformities as well as catastrophic thermal excursions sometimes experienced in conventional microwave technology Primarily aimed at processing advanced materials, advantages include uniform heating, arc-free processing, a higher degree of controllability, higher coupling efficiency and the ability to choose “specific” frequency or frequency bands suitable for particular applications. The review within provides an overview of the theory behind the technique as well as an outline of the advances regarding this method in both the academic and industrial stage. Current and future applications using this emerging technology as well as numerical modeling are also discussed.

Thermal treatment of C–S–H gel at 1 bar H 2O pressure up to 200 °C

Homogeneous CaO–SiO 2–H 2O gels were prepared at Ca/Si molar ratios 0.83, 1.01, 1.21, 1.50, 1.83 and 2.02. These were aged for 12–24 months at 25 °C and subsequently treated in steam, 1 bar total pressure, at 130 or 200 °C; also in water at 55 and 85 °C. Gels with low Ca/Si ratios partially crystallised at 85 °C. At 130 °C in steam, crystalline products included 11 and 14 Å tobermorite, xonotlite, afwillite, portlandite and another incompletely characterised phase. At 200 °C, the gels retained much water but remained amorphous to X-ray powder diffraction (XRD). However, electron microscopy, coupled with diffraction and analysis, disclosed that the “amorphous” product obtained at 85–200 °C had undergone crystallisation with domains typically 10–1000 nm. At higher bulk Ca/Si ratios, 1.83 and 2.02, much nanoscale precipitation of Ca(OH) 2 occurs, probably by exsolution, such that the residual C–S–H product has a Ca/Si ratio in the range 1.4–1.5. The complex thermal history of the products is reflected in their pH conditioning ability, measured at 25 °C. The results are applied to predict the evolution of pH in a cement-conditioned nuclear waste repository which experiences a prolonged thermal excursion.

Approaches to modelling chemically induced transformation superplasticity

Abstract Transformation superplasticity is a Newtonian deformation mechanism observed when polymorphic materials are subjected to small external stresses during their phase transformation. Although mostly studied during thermal excursions, recent investigations have observed this mechanism during excursions in chemical composition in the Ti-H system. In this work, methodologies for modelling this so-called ‘chemically induced transformation superplasticity’ are discussed, simultaneously considering the kinetic moving-boundary diffusion problem associated with the titanium α-β transformation, as well as the internal strains due to chemical swelling and the transformation. Two existing models, including, firstly, an analytical model for thermal-cycling-induced transformation superplasticity and, secondly, a numerical model for creep under conditions of chemical cycling, are adapted to the case of chemically induced transformation superplasticity. Both modelling approaches predict the main features of transformation superplasticity and are found to agree reasonably with the existing experimental data.

Approaches to modelling chemically induced transformation superplasticity

Abstract Transformation superplasticity is a Newtonian deformation mechanism observed when polymorphic materials are subjected to small external stresses during their phase transformation. Although mostly studied during thermal excursions, recent investigations have observed this mechanism during excursions in chemical composition in the Ti-H system. In this work, methodologies for modelling this so-called ‘chemically induced transformation superplasticity’ are discussed, simultaneously considering the kinetic moving-boundary diffusion problem associated with the titanium α-β transformation, as well as the internal strains due to chemical swelling and the transformation. Two existing models, including, firstly, an analytical model for thermal-cycling-induced transformation superplasticity and, secondly, a numerical model for creep under conditions of chemical cycling, are adapted to the case of chemically induced transformation superplasticity. Both modelling approaches predict the main features of transformation superplasticity and are found to agree reasonably with the existing experimental data.

Size effects on the mechanical properties of thin polycrystalline metal films on substrates

An analysis of the effects of the thickness and grain size of polycrystalline thin films on substrates is presented with the objective of linking the film mismatch stress to the underlying characteristic size scales. The model is predicated on the notion that the relaxation of mismatch strain in the film is accommodated by the introduction of dislocation loops whose population, dimensions and interaction energies are controlled by the film thickness and microstructural dimensions. The model is capable of capturing the combined effects of these size scales by accounting for the interaction energies of the constrained dislocation structure, and provides quantitative predictions of the evolution of film stress during thermal excursions. The predictions of the analysis are compared with available experimental results for polycrystalline films of face-centered cubic materials on Si substrates. It is shown that the model correctly predicts the observed influence of film thickness and grain size on stress evolution during thermal excursions. Aspects of strain hardening in thin polycrystalline films with high dislocation densities are also discussed.

Warming the fuel for the fire: Evidence for the thermal dissociation of methane hydrate during the Paleocene-Eocene thermal maximum

Dramatic warming and upheaval of the carbon system at the end of the Paleocene Epoch have been linked to massive dissociation of sedimentary methane hydrate. However, testing the Paleocene-Eocene thermal maximum hydrate dissociation hypothesis has been hindered by the inability of available proxy records to resolve the initial sequence of events. The cause of the Paleocene-Eocene thermal maximum carbon isotope excursion remains speculative, primarily due to uncertainties in the timing and duration of the Paleocene-Eocene thermal maximum. We present new high-resolution stable isotope records based on analyses of single planktonic and benthic foraminiferal shells from Ocean Drilling Program Site 690 (Weddell Sea, Southern Ocean), demonstrating that the initial carbon isotope excursion was geologically instantaneous and was preceded by a brief period of gradual surface-water warming. Both of these findings support the thermal dissociation of methane hydrate as the cause of the Paleocene-Eocene thermal maximum carbon isotope excursion. Furthermore, the data reveal that the methane-derived carbon was mixed from the surface ocean downward, suggesting that a significant fraction of the initial dissociated hydrate methane reached the atmosphere prior to oxidation.

NONLINEAR BACKSTEPPING CONTROL FOR THE FUEL DIFFUSION LAG IN FUSION REACTORS

Control of plasma density and temperature magnitudes, as well as their profiles, are among the most fundamental problems in fusion reactors. Existing efforts use control techniques based on linearized models. In this work, a zero-dimensional nonlinear model involving approximate conservation equations for the energy and the densities of the species was used to synthesize a nonlinear feedback controller for stabilizing the burn condition of a fusion reactor. The model addresses the issue of the lag due to the finite time for the fresh fuel to diffuse into the plasma center. Nonlinear backstepping is used to deal with this imposed lag. In this way we make our control system independent of the fueling system and the reactor can be fed either by pellet injection or by gas puffing. The controller exhibits excellent properties of robustness and the boundness of the state variables is guaranteed for a large set of values of the lag constant. In addition the nonlinear controller proposed guarantees a much larger region of attraction than the previous linear controllers, it is capable of rejecting perturbations in initial conditions leading to both thermal excursion and quenching, and its effectiveness does not depend on whether the operating point is an ignition or a subignition point.

Precision high temperature lead-free solder interconnections by means of high-energy droplet deposition techniques

This paper presents a number of numerical models that illustrate the experimental details of the key physical phenomena affecting the operation of novel materials deposition processes for electronics assembly. These processes include both laser and electric arc based droplet deposition processes. These are being developed in the electronics industry to allow the use of new lead-free alloys as replacements for high temperature lead based alloys, such as Sn5Pb95. The paper presents models of physical processes with respect to the desired process metrics of droplet size and deposition accuracy and reviews the potential limiting product - process interactions such as excessive thermal excursions and their effects on the target materials being joined.

Magma storage prior to the 1912 eruption at Novarupta, Alaska

New analytical and experimental data constrain the storage and equilibration conditions of the magmas erupted in 1912 from Novarupta in the 20th century's largest volcanic event. Phase relations at H2O+CO2 fluid saturation were determined for an andesite (58.7 wt% SiO2) and a dacite (67.7 wt%) from the compositional extremes of intermediate magmas erupted. The phase assemblages, matrix melt composition and modes of natural andesite were reproduced experimentally under H2O-saturated conditions (i.e., PH2O=PTOT) in a negatively sloping region in T–P space from 930 °C/100 MPa to 960 °C/75 MPa with fO2~NNO+1. The H2O-saturated equilibration conditions of the dacite are constrained to a T–P region from 850 °C/50 MPa to 880 °C/25 MPa. If H2O-saturated, these magmas equilibrated at (and above) the level where co-erupted rhyolite equilibrated (~100 MPa), suggesting that the andesite-dacite magma reservoir was displaced laterally rather than vertically from the rhyolite magma body. Natural mineral and melt compositions of intermediate magmas were also reproduced experimentally under saturation conditions with a mixed (H2O + CO2) fluid for the same range in PH2O. Thus, a storage model in which vertically stratified mafic to silicic intermediate magmas underlay H2O-saturated rhyolite is consistent with experimental findings only if the intermediates have XH2O fl=0.7 and 0.9 for the extreme compositions, respectively. Disequilibrium features in natural pumice and scoria include pristine minerals existing outside their stability fields, and compositional zoning of titanomagnetite in contact with ilmenite. Variable rates of chemical equilibration which would eliminate these features constrain the apparent thermal excursion and re-distribution of minerals to the time scale of days.