Publications

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In order to predict material failure accurately, it is critical to have knowledge of deformation physics. Uniquely challenging is determination of the conversion coefficient of plastic work into thermal energy. Here, we examine the heat transfer problem associated with the experimental determination of β in copper and stainless steel. A numerical model of the tensile test sample is used to estimate temperature rises across the mechanical test sample at a variety of convection coefficients, as well as to estimate heat losses to the chamber by conduction and convection. This analysis is performed for stainless steel and copper at multiple environmental conditions. These results are used to examine the relative importance of convection and conduction as heat transfer pathways. The model is additionally used to perform sensitivity analysis on the parameters that will ultimately determine b. These results underscore the importance of accurate determination of convection coefficients and will be used to inform future design of samples and experiments. Finally, an estimation of convection coefficient for an example mechanical test chamber is detailed as a point of reference for the modeling results.

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Physical property measurements including viscosity, density, thermal conductivity, and heat capacity of low-molecular weight polydimethylsiloxane (PDMS) fluids were measured over a wide temperature range (-50°C to 150°C when possible). Properties of blends of 1 cSt and 20 cSt PDMS fluids were also investigated. Uncertainties in the measurements are cited. These measurements will provide greater fidelity predictions of environmental sensing device behavior in hot and cold environments.

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This report summarizes a project in which the authors sought to develop and deploy: (i) experimental techniques to elucidate the complex, multiscale nature of thermal transport in particle-based materials; and (ii) modeling approaches to address current challenges in predicting performance variability of materials (e.g., identifying and characterizing physical- chemical processes and their couplings across multiple length and time scales, modeling information transfer between scales, and statically and dynamically resolving material structure and its evolution during manufacturing and device performance). Experimentally, several capabilities were successfully advanced. As discussed in Chapter 2 a flash diffusivity capability for measuring homogeneous thermal conductivity of pyrotechnic powders (and beyond) was advanced; leading to enhanced characterization of pyrotechnic materials and properties impacting component development. Chapter 4 describes success for the first time, although preliminary, in resolving thermal fields at speeds and spatial scales relevant to energetic components. Chapter 7 summarizes the first ever (as far as the authors know) application of TDTR to actual pyrotechnic materials. This is the first attempt to actually characterize these materials at the interfacial scale. On the modeling side, new capabilities in image processing of experimental microstructures and direct numerical simulation on complicated structures were advanced (see Chapters 3 and 5). In addition, modeling work described in Chapter 8 led to improved prediction of interface thermal conductance from first principles calculations. Toward the second point, for a model system of packed particles, significant headway was made in implementing numerical algorithms and collecting data to justify the approach in terms of highlighting the phenomena at play and pointing the way forward in developing and informing the kind of modeling approach originally envisioned (see Chapter 6). In both cases much more remains to be accomplished.

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Thermal analysts address a wide variety of applications requiring the simulation of radiation heat transfer phenomena. The re are gaps in the currently available modeling capabilities. Addressing these gaps w ould allow for the consideration of additional physics and increase confidence in simulation predictions. This document outlines a five year plan to address the current and future needs of the analyst community with regards to modeling radiation heat tran sfer processes. This plan represents a significant multi - year effort that must be supported on an ongoing basis.

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This paper reports on experimental and numerical investigations of electrically powered MEMS structures operated under different gas pressure and electrical power conditions. The structures studied are boron-doped single crystal silicon-on-insulator (SOI) microbridges that are heated by an electrical current. The microbridges are 85 μm wide, 125 μm tall and 5.5 mm long and lie 2 μm above the substrate. The impact of the narrow gap in the gas phase thermal transport is evaluated by operating the devices under various nitrogen gas pressure conditions, ranging from 625 Torr to ∼1 mTorr - spanning the continuum to noncontinuum gas heat transfer regimes. Raman thermometry is used to obtain spatially-resolved temperature measurements along the length of the device under the various operating conditions. The large dopant concentration (∼4 × 1019 cm-3) within the active silicon layer is found to affect the Raman spectrum used for thermometry via Fano-type interactions, resulting in an asymmetric Raman line shape. With large Raman peak asymmetries, use of the Raman line width as the temperature metric is less reliable as it shows decreased sensitivity to temperature. However, the asymmetry itself, when considered as a fitting parameter, was found to be a reliable indicator of sample temperature. The measured device temperatures are compared to finite element simulations of the structures. Noncontinuum gas phase heat transfer effects are incorporated into the continuum simulations via temperature discontinuities at the solid-gas interface, provided by a model developed from noncontinuum simulation results. Additionally, the impact of the large dopant concentrations is incorporated into the thermal models via a modified thermal conductivity model which considers impurity scattering effects on thermal transport. The simulation and experimental results show reasonable agreement. Copyright © 2012 by ASME.

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Periodic porous structures offer unique material solutions to thermoelectric applications. With recent interest in phonon band gap engineering, these periodic structures can result in reduction of the phonon thermal conductivity due to coherent destruction of phonon modes characteristic in phononic crystals. In this paper, we numerically study phonon transport in periodic porous silicon phononic crystal structures. We develop a model for the thermal conductivity of phononic crystal that accounts for both coherent and incoherent phonon effects, and show that the phonon thermal conductivity is reduced to less than 4% of the bulk value for Si at room temperature. This has substantial impact on thermoelectric applications, where the efficiency of thermoelectric materials is inversely proportional to the thermal conductivity. © 2010 Springer-Verlag.

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This paper compares measurements made by Raman and infrared thermometry on a SOI (silicon on insulator) bent-beam thermal microactuator. Both techniques are noncontact and used to experimentally measure temperatures along the legs and on the shuttle of the thermal microactuators. Raman thermometry offers micron spatial resolution and measurement uncertainties of {+-}10 K; however, typical data collection times are a minute per location leading to measurement times on the order of hours for a complete temperature profile. Infrared thermometry obtains a full-field measurement so the data collection time is much shorter; however, the spatial resolution is lower and calibrating the system for quantitative measurements is challenging. By obtaining thermal profiles on the same SOI thermal microactuator, the relative strengths and weaknesses of the two techniques are assessed.

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This paper compares measurements made by Raman and infrared thermometry on a SOI (silicon on insulator) bent-beam thermal microactuator. Both techniques are noncontact and used to experimentally measure temperatures along the legs and on the shuttle of the thermal microactuators. Raman thermometry offers micron spatial resolution and measurement uncertainties of {+-}10 K; however, typical data collection times are a minute per location leading to measurement times on the order of hours for a complete temperature profile. Infrared thermometry obtains a full-field measurement so the data collection time is much shorter; however, the spatial resolution is lower and calibrating the system for quantitative measurements is challenging. By obtaining thermal profiles on the same SOI thermal microactuator, the relative strengths and weaknesses of the two techniques are assessed.

Thermoreflectance techniques are powerful tools for measuring thermophysical properties of thin film systems, such as thermal conductivity, Λ, of individual layers, or thermal boundary conductance across thin film interfaces (G). Thermoreflectance pump-probe experiments monitor the thermoreflectance change on the surface of a sample, which is related to the thermal properties in the sample of interest. Thermoreflectance setups have been designed with both continuous wave (cw) and pulsed laser systems. In cw systems, the phase of the heating event is monitored, and its response to the heating modulation frequency is related to the thermophysical properties; this technique is commonly termed a phase sensitive thermoreflectance (PSTR) technique. In pulsed laser systems, pump and probe pulses are temporally delayed relative to each other, and the decay in the thermoreflectance signal in response to the heating event is related to the thermophysical properties; this technique is commonly termed a transient thermoreflectance (TTR) technique. In this work, mathematical models are presented to be used with PSTR and TTR techniques to determine the Λ and G of thin films on substrate structures. The sensitivities of the models to various thermal and sample parameters are discussed, and the advantages and disadvantages of each technique are elucidated from the results of the model analyses. © 2010 Springer Science+Business Media, LLC.

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We will present experimental and computational investigations of the thermal performance of microelectromechanical systems (MEMS) as a function of the surrounding gas pressure. Lowering the pressure in MEMS packages reduces gas damping, providing increased sensitivity for certain MEMS sensors; however, such packaging also dramatically affects their thermal performance since energy transfer to the environment is substantially reduced. High-spatial-resolution Raman thermometry was used to measure the temperature profiles on electrically heated, polycrystalline silicon bridges that are nominally 10 microns wide, 2.25 microns thick, 12 microns above the substrate, and either 200 or 400 microns long in nitrogen atmospheres with pressures ranging from 0.05 to 625 Torr. Finite element modeling of the thermal behavior of the MEMS bridges is performed and compared to the experimental results. Noncontinuum gas effects are incorporated into the continuum finite element model by imposing temperature discontinuities at gas-solid interfaces that are determined from noncontinuum simulations. The experimental and simulation results indicate that at pressures below 0.5 Torr the gas-phase heat transfer is negligible compared to heat conduction through the thermal actuator legs. As the pressure increases above 0.5 Torr, the gas-phase heat transfer becomes more significant. At ambient pressures, gas-phase heat transfer drastically impacts the thermal performance. The measured and simulated temperature profiles are in qualitative agreement in the present study. Quantitative agreement between experimental and simulated temperature profiles requires accurate knowledge of temperature-dependent thermophysical properties, the device geometry, and the thermal accommodation coefficient.

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This paper reports on experimental and computational investigations into the thermal performance of microelectromechanical systems (MEMS) as a function of the pressure of the surrounding gas. High spatial resolution Raman thermometry was used to measure the temperature profiles on electrically heated, polycrystalline silicon bridges that are nominally 10 μm wide, 2.25 μm thick, and either 200 or 400 μm long in nitrogen atmospheres with pressures ranging from 0.05 to 625 Torr. Finite element modeling of the thermal behavior of the MEMS bridges is performed and compared to the experimental results. Noncontinuum gas effects are incorporated into the continuum finite element model by imposing temperature discontinuities at gas-solid interfaces that are determined from noncontinuum simulations. The results indicate that gas-phase heat transfer is significant for devices of this size at ambient pressures but becomes minimal as the pressure is reduced below 5 Torr. The model and experimental results are in qualitative agreement, and better quantitative agreement requires increased accuracy in the geometrical and material property values. Copyright © 2009 by ASME.

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Due to the coupling of thermal and mechanical behaviors at small scales, a Campaign 6 project was created to investigate thermomechanical phenomena in microsystems. This report documents experimental measurements conducted under the auspices of this project. Since thermal and mechanical measurements for thermal microactuators were not available for a single microactuator design, a comprehensive suite of thermal and mechanical experimental data was taken and compiled for model validation purposes. Three thermal microactuator designs were selected and fabricated using the SUMMiT V{sup TM} process at Sandia National Laboratories. Thermal and mechanical measurements for the bent-beam polycrystalline silicon thermal microactuators are reported, including displacement, overall actuator electrical resistance, force, temperature profiles along microactuator legs in standard laboratory air pressures and reduced pressures down to 50 mTorr, resonant frequency, out-of-plane displacement, and dynamic displacement response to applied voltages.

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This report documents technical work performed to complete the ASC Level 2 Milestone 2841: validation of thermal models for a prototypical MEMS thermal actuator. This effort requires completion of the following task: the comparison between calculated and measured temperature profiles of a heated stationary microbeam in air. Such heated microbeams are prototypical structures in virtually all electrically driven microscale thermal actuators. This task is divided into four major subtasks. (1) Perform validation experiments on prototypical heated stationary microbeams in which material properties such as thermal conductivity and electrical resistivity are measured if not known and temperature profiles along the beams are measured as a function of electrical power and gas pressure. (2) Develop a noncontinuum gas-phase heat-transfer model for typical MEMS situations including effects such as temperature discontinuities at gas-solid interfaces across which heat is flowing, and incorporate this model into the ASC FEM heat-conduction code Calore to enable it to simulate these effects with good accuracy. (3) Develop a noncontinuum solid-phase heat transfer model for typical MEMS situations including an effective thermal conductivity that depends on device geometry and grain size, and incorporate this model into the FEM heat-conduction code Calore to enable it to simulate these effects with good accuracy. (4) Perform combined gas-solid heat-transfer simulations using Calore with these models for the experimentally investigated devices, and compare simulation and experimental temperature profiles to assess model accuracy. These subtasks have been completed successfully, thereby completing the milestone task. Model and experimental temperature profiles are found to be in reasonable agreement for all cases examined. Modest systematic differences appear to be related to uncertainties in the geometric dimensions of the test structures and in the thermal conductivity of the polycrystalline silicon test structures, as well as uncontrolled nonuniform changes in this quantity over time and during operation.

The thermal properties of microelectromechanical systems (MEMS) devices are governed by the structure and composition of the constituent materials as well as the geometrical design. With the continued reduction of the characteristic sizes of these devices, experimental determination of the thermal properties becomes more difficult. In this study, the thermal conductivity of polycrystalline silicon (polysilicon) microbridges are measured with the transient 3ω technique and compared to measurements on the same structures using a steady state joule heating technique. The microbridges with lengths from 200 microns to 500 microns were designed and fabricated using the Sandia National Laboratories SUMMiT™ V surface micromachining process. The differences between the two measurements, which arise from the geometry of the test structures, are explained by bond pad heating and thermal boundary resistance effects. Copyright © 2008 by ASME.

This study examines the effects of bond pads on the measurement of thermal conductivity for micromachined polycrystalline silicon using suspended test structures and a steady state resistance method. Bond pad heating can invalidate the assumption of constant temperature boundary conditions used for data analysis. Bond pad temperatures above the heat sink temperature arise from conduction out of the bridge test element and Joule heating in the bond pad. Simulations results determined correction factors for the electrical resistance offset, Joule heating effects in the beam, and Joule heating in the bond pads. Fillets at the base of the beam reduce the effect of bond pad heating until they become too large. Copyright © 2007 by ASME.

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Analysis of the Raman Stokes peak position and its shift has been frequently used to estimate either temperature or stress in microelectronics and microelectromechanical system devices. However, if both fields are evolving simultaneously, the Stokes shift represents a convolution of these effects, making it difficult to measure either quantity accurately. By using the relative independence of the Stokes linewidth to applied stress, it is possible to deconvolve the signal into an estimation of both temperature and stress. Using this property, a method is presented whereby the temperature and stress were simultaneously measured in doped polysilicon microheaters. A data collection and analysis method was developed to reduce the uncertainty in the measured stresses resulting in an accuracy of ±40 MPa for an average applied stress of -325 MPa and temperature of 520 °C. Measurement results were compared to three-dimensional finite-element analysis of the microheaters and were shown to be in excellent agreement. This analysis shows that Raman spectroscopy has the potential to measure both evolving temperature and stress fields in devices using a single optical measurement. © 2007 American Institute of Physics.

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Capillary condensation of water can have a significant effect on rough surface adhesion. To explore this phenomenon between micromachined surfaces, the authors perform microcantilever experiments as a function of surface roughness and relative humidity (RH). Below a threshold RH, the adhesion is mainly due to van der Waals forces across extensive noncontacting areas. Above the threshold RH, the adhesion jumps due to capillary condensation and increases towards the upper limit of Γ = 144 mJ/m2. A detailed model based on the measured surface topography qualitatively agrees with the experimental data only when the topographic correlations between the upper and lower surfaces are considered. © 2007 American Institute of Physics.

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A capability for measuring the thermal conductivity of microelectromechanical systems (MEMS) materials using a steady state resistance technique was developed and used to measure the thermal conductivities of SUMMiT{trademark} V layers. Thermal conductivities were measured over two temperature ranges: 100K to 350K and 293K to 575K in order to generate two data sets. The steady state resistance technique uses surface micromachined bridge structures fabricated using the standard SUMMiT fabrication process. Electrical resistance and resistivity data are reported for poly1-poly2 laminate, poly2, poly3, and poly4 polysilicon structural layers in the SUMMiT process from 83K to 575K. Thermal conductivity measurements for these polysilicon layers demonstrate for the first time that the thermal conductivity is a function of the particular SUMMiT layer. Also, the poly2 layer has a different variation in thermal conductivity as the temperature is decreased than the poly1-poly2 laminate, poly3, and poly4 layers. As the temperature increases above room temperature, the difference in thermal conductivity between the layers decreases.

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We describe a Laboratory Directed Research and Development (LDRD) effort to develop and apply laser-based thermometry diagnostics for obtaining spatially resolved temperature maps on working microelectromechanical systems (MEMS). The goal of the effort was to cultivate diagnostic approaches that could adequately resolve the extremely fine MEMS device features, required no modifications to MEMS device design, and which did not perturb the delicate operation of these extremely small devices. Two optical diagnostics were used in this study: microscale Raman spectroscopy and microscale thermoreflectance. Both methods use a low-energy, nonperturbing probe laser beam, whose arbitrary wavelength can be selected for a diffraction-limited focus that meets the need for micron-scale spatial resolution. Raman is exploited most frequently, as this technique provides a simple and unambiguous measure of the absolute device temperature for most any MEMS semiconductor or insulator material under steady state operation. Temperatures are obtained from the spectral position and width of readily isolated peaks in the measured Raman spectra with a maximum uncertainty near {+-}10 K and a spatial resolution of about 1 micron. Application of the Raman technique is demonstrated for V-shaped and flexure-style polycrystalline silicon electrothermal actuators, and for a GaN high-electron-mobility transistor. The potential of the Raman technique for simultaneous measurement of temperature and in-plane stress in silicon MEMS is also demonstrated and future Raman-variant diagnostics for ultra spatio-temporal resolution probing are discussed. Microscale thermoreflectance has been developed as a complement for the primary Raman diagnostic. Thermoreflectance exploits the small-but-measurable temperature dependence of surface optical reflectivity for diagnostic purposes. The temperature-dependent reflectance behavior of bulk silicon, SUMMiT-V polycrystalline silicon films and metal surfaces is presented. The results for bulk silicon are applied to silicon-on-insulator (SOI) fabricated actuators, where measured temperatures with a maximum uncertainty near {+-}9 K, and 0.75-micron inplane spatial resolution, are achieved for the reflectance-based measurements. Reflectance-based temperatures are found to be in good agreement with Raman-measured temperatures from the same device.

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In this paper, we report spatially resolved temperature profiles along the legs of working V-shaped electrothermal (ET) actuators using a surface Raman scattering technique. The Raman probe provides nonperturbing optical data with a spatial resolution of 1.2 μm, which is required to observe the 3-μm-wide actuator beams. A detailed uncertainty analysis reveals that our Raman thermometry of polycrystalline silicon is performed with fidelity of ±10 to 11 K when the peak location of the Stokes-shifted optical phonon signature is used as an indicator of temperature. This level of uncertainty is sufficient for temperature mapping of many working thermal MEMS devices which exhibit characteristic temperature differences of several hundred Kelvins. To our knowledge, these are the first quantitative and spatially resolved temperature data available for thermal actuator structures. This new temperature data set can be used for validation of actuator thermal design models and these new results are compared with finite-difference simulations of actuator thermal performance. © 2006 IEEE.

The response of microsystem components to laser irradiation is relevant to the use of laser processing, optical diagnostics, and optical microelectromechanical systems (MEMS) device design and performance. The dimensions of MEMS are on the same order as infrared laser wavelengths which results in interference phenomena when the parts are partially transparent. Four distinct polycrystalline structures were designed and irradiated with 808 nm laser light to determine the effect of layers and the presence of a substrate via on the laser power threshold for damage. The presence of a substrate via resulted in lower damage thresholds, and interference phenomena resulted in a single layer structure having the highest damage threshold.

Microsystems are potentially exposed to laser irradiation during processing, diagnostic measurements, and, in some cases, device operation. The behavior of the components in an optical MEMS device that are irradiated by a laser needs to be optimized for reliable operation. Utilizing numerical simulations facilitates design and optimization. This paper reports on experimental and numerical investigations of the thermomechanical response of polycrystalline silicon microcantilevers that are 250 {micro}m wide, 500 {micro}m long, and 2.25 {micro}m thick when heated by an 808 nm laser. At laser powers above 400 mW significant deflection is observed during the laser pulse using a white light interferometer. Permanent deformation is detected at laser powers above 650 mW in the experiments. Numerical calculations using a coupled physics finite element code, Calagio, agree qualitatively with the experimental results. Both the experimental and numerical results reveal that the initial stress state is very significant. Microcantilevers deflect in the direction of their initial deformation upon irradiation with a laser.

Interfacial adhesion is an important factor in determining the performance and reliability of microelectromechanical systems (MEMS). Van der Waals dispersion forces are the dominant adhesion mechanism in the low relative humidity (RH) regime. At small roughness values, adhesion is mainly due to van der Waals dispersion forces acting across extensive non-contacting areas and is related to 1/Dave2, where Dave is the average surface separation. These contributions must be considered due to the close proximity of the surfaces, which is a result of the planar deposition technology. At large roughness values, van der Waals forces at contacting asperities become the dominating contributor to the adhesion. Capillary condensation of water has a significant effect on rough surface adhesion in the moderate to high RH regime. Above a threshold RH, which is a function of the surface roughness, the adhesion jumps due to meniscus formation at the interface and increases rapidly towards the upper limit of Γ=2γcosθ=44 mJ/m2, where γis the liquid surface energy and θis the contact angle. Copyright © 2006 by ASME.

Optical actuation is a necessity for the development of all-optical MEMS devices. Optically-powered actuators relying on a photothermal process are limited by overheating and structural damage resulting from the absorption of laser power. Surface micromachined polycrystalline silicon (polysilicon) optical actuators, powered using an 808 nm continuous wave laser, were evaluated for displacement performance and susceptibility to damage. The tested actuators were of a flexure-type design fabricated from either a single 2.25 μm polysilicon layer or a 4.5 μm polysilicon laminate layer, and in three different designs. Displacement of the actuators was linear with power for all tested designs for powers below those that cause damage to the irradiated surface. Maximum displacement observed was in the 7-9 μm range regardless of actuator design. After surface damage is initiated, displacement of the actuator during irradiation recedes in all actuators, with actuators with a 50 μm-wide target surface exhibiting complete recession in their displacement. The return position of the actuators after the irradiated surface has damaged also exhibits recession on the order of 4-5 μm for surfaces damaged with up to 650 mW. Exposing the actuator surfaces to longer irradiation times had no effect on the displacement if the surface had no damage, but resulted in regression of the displacement as the irradiation time increased if the surface had preexisting damage. Copyright © 2006 by ASME.

Optical microswitches are being developed for use in communication and security systems because of their small size and fast response time. However, as the intensity of the light incident on the microswitches increases, the thermal and mechanical responses of the reflective surfaces are becoming a concern. It is important to dissipate heat adequately and to minimize any deformation on the reflective surfaces. To understand the mechanical responses of these microswitches, a set of microstructures have been fabricated and tested to evaluate how the surfaces deform when irradiated with a high-intensity laser beam. To evaluate and further investigate the experimental findings, the coupled physical analysis tool, Calagio, has been applied to simulate the mechanical behavior of these test structures when they are optically heated. Code prediction of the surface displacement will be compared against measurement. Our main objective is to assess the existing material models and our code predictive capability so that it will be used to qualify the performance of microswitches being developed.

Experimentally measured temperature profiles along the micron-scale beam of a working thermal actuator are reported for the first time. Using a surface Raman scattering technique, temperature measurements are obtained in a noncontact fashion with submicron spatial resolution and to within an uncertainty of better than ± 10 K. The experimental data are used to validate computational predictions of the actuator thermal performance with reasonable agreement between the data and predicted temperatures. Copyright © 2005 by ASME.

Optical actuation of microelectromechanical systems (MEMS) is advantageous for applications for which electrical isolation is desired. Thirty-two polycrystalline silicon opto-thermal actuators, optically-powered MEMS thermal actuators, were designed, fabricated, and tested. The design of the opto-thermal actuators consists of a target for laser illumination suspended between angled legs that expand when heated, providing the displacement and force output. While the amount of displacement observed for the opto-thermal actuators was fairly uniform for the actuators, the amount of damage resulting from the laser heating ranged from essentially no damage to significant amounts of damage on the target. The likelihood of damage depended on the target design with two of the four target designs being more susceptible to damage. Failure analysis of damaged targets revealed the extent and depth of the damage.

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Optical MEMS devices are commonly interfaced with lasers for communication, switching, or imaging applications. Dissipation of the absorbed energy in such devices is often limited by dimensional constraints which may lead to overheating and damage of the component. Surface micromachined, optically powered thermal actuators fabricated from two 2.25 μm thick polycrystalline silicon layers were irradiated with 808 nm continuous wave laser light with a 100 μm diameter spot under increasing power levels to assess their resistance to laser-induced damage. Damage occurred immediately after laser irradiation at laser powers above 275 mW and 295 mW for 150 urn diameter circular and 194 urn by 150 μm oval targets, respectively. At laser powers below these thresholds, the exposure time required to damage the actuators increased linearly and steeply as the incident laser power decreased. Increasing the area of the connections between the two polycrystalline silicon layers of the actuator target decreases the extent of the laser damage. Additionally, an optical thermal actuator target with 15 μm × 15 μm posts withstood 326 mW for over 16 minutes without exhibiting damage to the surface. Copyright © 2005 by ASME.

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