modeling of heat transfer in an aluminum x-ray...
TRANSCRIPT
Modeling of Heat Transfer in an
Aluminum X-Ray Anode Employing
a Chemical Vapor Deposited
Diamond Heat Spreader
David J. Stupple1
Torr Scientific Ltd.,
Unit 11, Pebsham Rural Business Center,
Pebsham Lane,
Bexhill-on-Sea,
East Sussex TN40 2RZ, UK
e-mail: [email protected]
Victor KempMecway Ltd.,
1 Goring Street,
Thorndon,
Wellington 6011, New Zealand
e-mail: [email protected]
Matthew J. OldfieldDepartment of Mechanical Engineering Sciences,
University of Surrey,
Guildford GU2 7XH, UK
e-mail: [email protected]
John F. WattsProfessor
Department of Mechanical Engineering Sciences,
University of Surrey,
Guildford GU2 7XH, UK
e-mail: [email protected]
Mark A. BakerDepartment of Mechanical Engineering Sciences,
University of Surrey,
Guildford GU2 7XH, UK
e-mail: [email protected]
X-ray sources are used for both scientific instrumentation andinspection applications. In X-ray photoelectron spectroscopy(XPS), aluminum Ka X-rays are generated through electron beamirradiation of a copper-based X-ray anode incorporating a thinsurface layer of aluminum. The maximum power operation of theX-ray anode is limited by the relatively low melting point ofthe aluminum. Hence, optimization of the materials and design ofthe X-ray anode to transfer heat away from the aluminum thin filmis key to maximizing performance. Finite element analysis (FEA)has been employed to model the heat transfer of a water-cooledcopper-based X-ray anode with and without the use of a chemicalvapor deposited (CVD) diamond heat spreader. The modelingapproach was to construct a representative baseline model, andthen to vary different parameters systematically, solving for asteady-state thermal condition, and observing the effect on themaximum temperature attained. The model indicates that a CVDdiamond heat spreader (with isotropic thermal properties) brazed
into the copper body reduces the maximum temperature in the 4lm aluminum layer from 613 �C to 301 �C. Introducing realisticanisotropy and inhomogeneity in the thermal conductivity (TC) ofthe CVD diamond has no significant effect on heat transfer if thealuminum film is on the CVD diamond growth face (with the high-est TC). However, if the aluminum layer is on the CVD diamondnucleation face (with the lowest TC), the maximum temperature is575 �C. Implications for anode design are discussed.[DOI: 10.1115/1.4040953]
Introduction
X-rays are used as an excitation source in analytical techniquessuch as X-ray photoelectron spectroscopy (XPS) and X-ray dif-fraction, and in X-ray inspection and imaging. X-rays are pro-duced by accelerating high-energy electrons to strike a metallicanode where the electrons cause the emission of X-ray photonsthrough anode atomic core-level excitation. This conversion isinefficient, with 99% of the electron energy converted into heatwithin the anode assembly. It is advantageous to maximize X-rayflux to increase signal-to-noise ratio and minimize analysis time,but preventing damage to the anode from excessive heating isusually the limiting factor. In XPS, a common anode material isaluminum, producing characteristic aluminum Ka X-rays. A thincoating of aluminum is applied to the tip of a hollow copper anodebody with the internal surfaces cooled by pumped water. Often, asmaller beam spot on the anode is desirable, providing a smallerfocused X-ray spot on the sample and hence finer spatial resolu-tion of the analysis. If high X-ray flux is demanded from a smallspot, the power density at the anode can be very high. Some ano-des employ a chemical vapor deposited (CVD) diamond heatspreader, brazed flush into the copper body beneath the aluminumfilm (Fig. 1). This technical brief reports the findings of finite ele-ment analysis (FEA) of the thermal performance of a water-cooled anode both with and without a diamond heat spreader, andthe effects of material and geometry variations.
Generating a high X-ray flux may be desirable, so efficientremoval of heat from the anode film to the cooling system isimportant. CVD diamond has excellent thermal conductivity(TC), a typical quoted value being 1800 W m�1 K�1 at room tem-perature.2 Single crystal gemstone diamonds have a TC of approx-imately 2200 W m�1 K�1 at room temperature [1]. In reality,polycrystalline CVD diamond can have substantially anisotropicand inhomogeneous TC, varying from one face to another by afactor of 4 [1,2].
Numerical methods have previously been used to model thespread of surface heat through a cylindrical diamond heat
Fig. 1 (a) The beveled tip of a typical X-ray anode as used in acommercial XPS system, with (b) a cutaway view showing therecessed diamond heat spreader, one of several cooling finsand internal water cooling
1Corresponding author.Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL
OF HEAT TRANSFER. Manuscript received June 7, 2018; final manuscript received June26, 2018; published online August 28, 2018. Assoc. Editor: Milind A. Jog. 2http://www.hediamond.cn/en/product/24.html
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spreader, with isotropic and temperature-independent TC, on acopper substrate, demonstrating that performance was sensitive tothe radius of the heat spreader [3]. Finite element analysis hasbeen used to analyze stress in a revolving X-ray anode duringheating and cooling, again with heat applied at the surface [4].Monte Carlo analysis was used to simulate subsurface heatdelivery by electron emission in field effect devices, informingsubsequent numerical analysis of the heat flow [5]. FEA of heatsinks on laser diodes has shown the superior performance of CVDdiamond over aluminum nitride heat spreaders [6], again with theTC of the diamond assumed isotropic and temperature-independent. Here, we use FEA in conjunction with Monte Carloanalysis to model the use of a CVD diamond heat spreader in ageneric XPS X-ray anode. The effects of different thermal con-ductivities and of anode design variations are examined. Identifi-cation of those parameters which have the greatest effect on thethermal performance will allow design choices to be made thatcost-effectively optimize anode cooling. No previous analysisincludes subsurface heat delivery and temperature-dependent, ani-sotropic, and inhomogeneous TC of diamond.
Finite Element Analysis Modeling Approach
The commercial FEA package Mecway3 was used for pre andpostprocessing. Mecway’s internal solver was used for thesensitivity analysis of thermal properties and dimension changes.Calculix Crunchix (CCX) is a free structural FEA solver [7]. CCXwas used where both temperature dependence and anisotropy ofTC was needed.
A baseline model was created, and then parameters were variedsystematically, solving for a steady-state thermal condition, andcomparing the maximum temperature attained. Rather than a cir-cular body with a beveled tip (Fig. 1), the anode was modeled as asquare tube with a flat tip, with the mesh representing one quarterof the whole. The model comprises a copper tube, an inset CVDdiamond, a braze layer between diamond and copper, an alumi-num anode layer, and a chromium adhesion layer between alumi-num and diamond (Fig. 2).
The 20 W electron beam was modeled with a Gaussian profile[8]. Most previous studies have assumed surface heating, whilehere a software package for Monte Carlo simulation, CASINO
V2.42 [9], was used to model the vertical delivery of heat by10 keV electrons into the aluminum film.
The thermal conductivities of the materials in the baselinemodel are listed in Table 1.
The density of the sputtered aluminum film was assumed to be80% of bulk aluminum and the TC adjusted accordingly. This is areasonable assumption for a sputtered film [10]. The temperature-dependent TC values of the CVD diamond material wereextracted from published measurements [11,12], with extrapola-tion to higher temperatures (Fig. 3).
To model the effect of direct cooling on the underside of thediamond, the cooling fins and a region of the copper and brazewere removed to expose the diamond. The convection conditionwas applied to all newly exposed surfaces (Fig. 4).
Results and Discussion
Heat Spreader. The model without the heat spreader reporteda maximum aluminum temperature of 613 �C, greater by 312 �Cthan the model with a diamond heat spreader (Fig. 5).
Thermal Properties. The TC of both the diamond heatspreader and the aluminum anode material has a large effect onthe aluminum temperature (Fig. 6). The aluminum temperature is
Fig. 2 An overview of the mesh used as the basis of the analy-sis. (Color variations within components (e.g., within alumi-num) are visual aids to facilitate the modeling process.
Table 1 Thermal conductivity values for the baseline modelmaterials
MaterialThermal
conductivity/W m�1 K�1Temperaturedependence
Aluminum 189.6 NoneChromium 93.7 NoneCVD diamond 2082.4 at 20.9 �C YesBraze 100.0 NoneCopper 404.0 None
Fig. 3 A previously published temperature-dependent TC pro-file of CVD diamond used in the baseline FEA model [11,12].The curve has been extrapolated to higher temperatures (above270 �C).
Fig. 4 Baseline model modified to have direct cooling of thediamond underside
3https://mecway.com/
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relatively insensitive to the thermal conductivities of most othercomponents. This suggests that while the quality of diamond is ofgreat importance, the material choice for the anode body is moreflexible. A material with more suitable engineering propertiesthan copper might be feasible with minimal effect on the alumi-num temperature.
Dimensions. The aluminum temperature of the model is highlysensitive to the thickness of the aluminum (Fig. 7). The tempera-ture is moderately increased by reduction of the diamond thick-ness, but with little improvement from a thicker diamond. Unlikeearlier numerical modeling [3], the width of the diamond here hadlittle effect. Changes to other dimensions also had little effect,though making the copper tip thinner caused a slightly increasedtemperature.
Anisotropy and Inhomogeneity. Introducing anisotropic andinhomogeneous thermal properties of CVD diamond [1,2] showsthat the orientation of the diamond is important. In the CVD pro-cess, the nucleation face of the diamond is next to the substrate,and the growth face is furthest from the substrate. With thealuminum anode on the growth face, temperatures are similar tothe isotropic model; with the anode on the nucleation face—where the TC is lower [2]—the maximum temperature is 273 �Chigher at 575 �C.
The primary role of the diamond is to facilitate the vertical flowof heat away from the hot spot at the center. The high TC of the
diamond heat spreader allows it to maintain a comparable temper-ature gradient to that of the copper model despite the considerablylower maximum temperature (Fig. 8). This gradient drives theheat flux. With the anode film on the nucleation face, where TC
Fig. 5 The copper-bodied model (right) has a maximum steady-state temperature 613 �C, whereas the baseline model withthe diamond heat spreader (left, same temperature scale) has maximum 301 �C
Fig. 6 Effect of varying TCs of components, and the convection coefficient ofthe cooling water. The steep curves indicate those thermal properties that havethe greatest effect on the aluminum temperature.
Fig. 7 The peak temperature of the aluminum for differentdimensions in the model. The aluminum temperature of thebaseline model is highly sensitive to the thickness of the alumi-num layer (steep curve).
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may be lower by a factor of 4 [2], the removal of heat from thehot spot is impaired.
Away from the center, both the diamond and the copper bodyserve to channel the heat mainly horizontally to the side walls(Fig. 9). In both models, approximately 65% of the heat isremoved via the side walls, so that most of the heat flux in the tipis horizontal, rather than vertically toward the nearest cooled sur-face, as might be expected. Any restriction of the heat flow to thewalls will raise the maximum temperature reached in the alumi-num. This is why making the copper wall of the anode tip thinnercaused a slight increase in temperature.
Likewise, removing a part of the metal body so that the diamondis directly cooled by the water (Fig. 4) had no beneficial effect.With the diamond cooled directly, the aluminum reached 310 �C. Amodel with no through-hole in the copper reached 307 �C. Remov-ing copper material restricts the heat flow to the side walls.
Design Implications
This model suggests that the TC of the diamond heat spreadershould be as high as possible and that the aluminum coatingshould be applied to the growth surface of the diamond to mini-mize the effect of anisotropic microstructure in the CVD diamondmaterial. The diamond should not be made too thin, in this modelno thinner than 100 lm. The TC of the aluminum thin film shouldbe enhanced by ensuring that the film is as dense and pure as pos-sible. The film should be as thin as the application will allow.
There is no benefit to be gained from having a hole in the metalbody such that the diamond is directly cooled by water. The lat-eral flow of heat should not be impaired by having the metal bodytoo thin or in poor thermal contact with the side walls.
The contribution of the side walls to heat removal is impor-tant. The return route of the cooling water should be fullyexploited by passing the water over as much internal surface aspossible.
The TC of the anode body does not seem to be a critical factor.It might be beneficial to choose a metal with more suitablemechanical properties than copper, without necessarily affectingthe anode cooling, especially if the material is one that resistsfouling by the cooling fluid.
Conclusions
The analysis confirms that a high-quality CVD diamond heatspreader can drastically reduce the steady-state temperature of theanode, here by 312 �C, but the diamond must have its growth faceoutermost because of the effects of anisotropic microstructure.Fitting the diamond with the nucleation face outermost increasesthe model temperature by 273 �C.
Even with a greatly reduced maximum temperature, heat flowboth within the aluminum film and in adjacent components ismaintained when the heat spreader is present. The high TC of dia-mond allows it to efficiently remove heat at the base of the anodefilm. This maintains a temperature gradient within the aluminumthat is similar in magnitude to the copper-bodied anode and thatdrives the heat flow.
Around 65% of the heat is removed by the coolant via the sidewalls. Measures that might be expected to assist cooling, such asthinning the wall at the tip, or having direct cooling of the dia-mond, actually throttle heat flow to the walls, giving highertemperatures.
The main implications for anode design are as follows:
(i) reduce the aluminum layer thickness as much as practi-cally allowable;
(ii) fabricate the aluminum layer to be dense and thermallyconductive;
(iii) fit the CVD diamond heat spreader with the growth faceoutermost;
(iv) do not impede the flow of heat to the side walls by thin-ning the anode walls.
More broadly, anode designs might incorporate a metal that iseasier to braze to and less prone to fouling than copper. The routeof the coolant must be optimized to fully exploit the coolingopportunities both at and away from the anode tip; anode designswhere the return path from the tip is via a narrow channel may befar from optimum.
Fig. 8 A comparison of vertical and horizontal temperatureprofiles in models with and without a diamond heat spreader.The profiles are taken from the top/center of each model. Whilethe temperatures are higher without a heat spreader, the tem-perature gradients are quite similar.
Fig. 9 A schematic diagram of the heat flux through a central section of the anode tip, withthe anode tip center at top left. For clarity, the heat flux magnitude range of 0–1.5 MW m22 ischosen, such that the highest fluxes near the center of the tip (top left) are not shown. Thesection shown is from the heat spreader model; the model with no heat spreader shows a sim-ilar pattern. The flux magnitude is proportional to arrow length.
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Funding Data
� Engineering and Physical Sciences Research Council(EPSRC Grant No. EP/G037388/1) via the MiNMaT Centrefor Doctoral Training at the University of Surrey, in collab-oration with Torr Scientific Ltd.
References[1] Graebner, J. E., Jin, S., and Kammlott, G. W., 1992, “Large Anisotropic Thermal
Conductivity in Synthetic Diamond Films,” Nature, 359(6394), pp. 401–403.[2] Graebner, J. E., Altmann, H., and Balzaretti, N. M., 1998, “Report on a Second
Round Robin Measurement of the Thermal Conductivity of CVD Diamond,”Diamond Relat. Mater., 7(11–12), pp. 1589–1604.
[3] Hui, P., and Tan, H. S., 1994, “Temperature Distributions in a Heat DissipationSystem Using a Cylindrical Diamond Heat Spreader on a Copper Heat Sink,”J. Appl. Phys., 75(2), pp. 748–757.
[4] Plankensteiner, A., and R€odhammer, P., 2001, “Finite Element Analysis of X-Ray Targets,” 15th International Plansee Seminar 2001: Powder MetallurgicalHigh Performance Materials, Reutte, Austria, accessed Sept. 5, 2017, https://www-plansee-com.azureedge.net/fileadmin/user_upload/Finite_Element_Analysis_of_X-Ray_Targets.pdf
[5] Fisher, T. S., Walker, D. G., and Weller, R. A., 2003, “Analysis and Simulationof Anode Heating Due to Electron Field Emission,” IEEE Trans. Compon.Packag. Technol., 26(2), pp. 317–323.
[6] Labudovic, M., and Burka, M., 2003, “Heat Transfer and Residual Stress Mod-eling of a Diamond Film Heat Sink for High Power Laser Diodes,” IEEE Trans.Compon. Packag. Technol., 26(3), pp. 575–581.
[7] Dhondt, G., and Wittig, K., 2016, “CALCULIX,” R€ohrmoos, Germany,accessed Apr. 1, 2017, http://www.calculix.de/
[8] BSI, 2005, “Lasers and Laser-Related Equipment. Test Methods for Laser BeamWidths, Divergence Angles and Beam Propagation Ratios. Part 1: Stigmatic andSimple Astigmatic Beams,” BSI, London, Standard No. BS EN ISO 11146-1:2005.
[9] Drouin, D., Couture, A. R., and Joly, D., 2007, “CASINO V2.42—a Fast andEasy-to-Use Modeling Tool for Scanning Electron Microscopy and Microanal-ysis Users,” Scanning, 29(3), pp. 92–101.
[10] Mattox, D. M., and Kominiak, G. J., 1972, “Structure Modification by Ion Bom-bardment During Deposition,” J. Vac. Sci. Technol., 9(1), pp. 528–532.
[11] Diamond Materials, 2004, “The CVD Diamond Booklet,” Diamond MaterialsGmbH, Freiburg, Germany, accessed Mar. 1, 2016, http://www.diamond-materials.com/downloads/cvd_diamond_booklet.pdf
[12] W€orner, E., Wild, C., and M€uller-Sebert, W., 1996, “Thermal Conductivity ofCVD Diamond Films: High-Precision, Temperature-Resolved Measurements,”Diamond Relat. Mater., 5(6–8), pp. 688–692.
Appendix: Conversions of values in the text to U.S. customaryunits
�C �F lm Millipoints mm Points
270 518 1 2.8 1 2.8273 523 2 5.7 1.8 5.0301 574 3 8.5 2 5.7307 585 4 11.3 5.6 15.7310 590 5 14.2312 594 8 22.7 nm millipoints
575 1067 90 25520 0.06613 1135 100 283200 0.57150 425
W m�1 K�1 Btu/(h �F ft)420 1191
MW m�2 Btu/(h in2)
93.7 54.1
450 1276
1.5 3302100 57.8
980 2778
189.6 109.5 W Btu/h
404 233.420 682082.4 1203.2
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