1. Thermal & Mechanical Support for Diamond Pixel Modules Justin Albert Univ. of Victoria Nov. 6, 2008 ATLAS Tracker Upgrade Workshop

2. DIAMOND IS A RAD-HARD DETECTOR OPTION, WHAT ELSE CAN IT DO FOR US? Diamond has the highest thermal conductivity of any non- superconducting material (2000 W/(m ∙ K) ≈ 5x copper). Diamond has the highest Young’s modulus of any material (carbon nanotubes excepted). ⇒ A “perfect” structural material (or at least as good as you can possibly get). Diamond sensors don’t need to be kept cold, could work even with an extremely large ΔT (even -35 to 40 °C! – as long as temperatures are constant) ATLAS Tracker Upgrade Wkshp. Thermal & Mechanical Support for Diamond Pixels Thermal & Mechanical Support for Diamond Pixels 6 Nov 08 J. Albert 2

3. How Much Cooling do we Need? Readout chips produce ~0.26 W/cm 2. No heat from sensors. We have all been using a factor of two as a safety margin: 0.5 W/cm 2. Critical issue for diamond is not ΔT – diamond leakage current is negligible up to 50 °C. The main issue instead becomes δ(ΔT), how much the temperature changes in response to, e.g., varying beam and background conditions. Even very small changes in dark current/pedestal would be a large calibration hassle (as is true in all types of sensors). ATLAS Tracker Upgrade Wkshp. Thermal & Mechanical Support for Diamond Pixels Thermal & Mechanical Support for Diamond Pixels 6 Nov 08 J. Albert 3

4. Don’t Reinvent the Wheel ATLAS Tracker Upgrade Wkshp. Thermal & Mechanical Support for Diamond Pixels Thermal & Mechanical Support for Diamond Pixels 6 Nov 08 J. Albert 4 etc...!

5. Some Basic Diamond Pixel Stave Concepts ATLAS Tracker Upgrade Wkshp. Thermal & Mechanical Support for Diamond Pixels Thermal & Mechanical Support for Diamond Pixels 6 Nov 08 J. Albert 5 35 um thick BN-loaded epoxy mounts ~200 um wall thickness Al tube (6 mm square), CO 2 cooling (1/2 full liquid), thermal grease coat (35 um thick) Conductive carbon fiber foam (2 x 6 mm square) 200 um thick diamond active pixels RVC foam 1) 1.77% X 0 /(2 layers) 4 cm 35 um thick BN-loaded epoxy mounts ~200 um wall thickness Al tube (6 mm square), CO 2 cooling (1/2 full liquid), thermal grease coat (35 um thick) Conductive carbon fiber foam (2 x 6 mm square) 200 um thick silicon active pixels 100 um thick CVD support diamond RVC foam 2) 1.87% X 0 /(2 layers) CVD bonded, NO epoxy mounts ~200 um wall thickness Be tube (6 mm square), CO 2 cooling (1/2 full liquid), CVD bonded -- NO thermal grease coat Conductive carbon fiber foam (2 x 6 mm square) 200 um thick diamond active pixels 100 um thick CVD support diamond RVC foam 3) 1.54% X 0 /(2 layers) 200 um thick silicon readout chips 100 um thick CVD support diamond 200 um thick silicon readout chips Very basic stave concepts, similar to some of the Si sensor concepts 1) and 3) have been serving as our defaults for now. 2) is a thermal/structural comparison with the analogous Si pixel design. 3) uses direct deposition of diamond on silicon chips (no glue) & bonding of cooling tube to foam (no thermal grease)

6. Might “End-Only” Cooling be Conceivable with Diamond? ATLAS Tracker Upgrade Wkshp. Thermal & Mechanical Support for Diamond Pixels Thermal & Mechanical Support for Diamond Pixels 6 Nov 08 J. Albert 6 Crazy idea – but not so crazy with diamond. (CLEO is an existence proof – much less power, & radiative cooling, though.) It is instructive to see how far away from possible it is for the B- layer… Heat equation: With end-only cooling of an (ultra-simplified) diamond sensor on diamond support, this becomes a simple ordinary diff. eq.: Answer: a 1 mm thick diamond stave cooled to -30 °C at the ends would reach +30 °C in the middle with 0.26 W/cm 2 heating.

7. Simple Uncooled Stave ATLAS Tracker Upgrade Wkshp. Thermal & Mechanical Support for Diamond Pixels Thermal & Mechanical Support for Diamond Pixels 6 Nov 08 J. Albert 7 More lovely physics that we should all know, or be reminded of: the deflection of a rigid beam under a (gravitational) load is given by the Euler-Bernoulli equation: where Y is the Young’s modulus, I = (thickness 3 x width)/12 is the area moment of inertia, u is the deflection, and w is the load force. Thus the maximum deflection (at the center of a bar) is which is, for a 1 mm thick, 60 cm long diamond stave, ~130 um. Clearly real life is more complicated than this, but it is always instructive to start with the relevant equations, which still hold.

8. Simple Material Budgets ATLAS Tracker Upgrade Wkshp. Thermal & Mechanical Support for Diamond Pixels Thermal & Mechanical Support for Diamond Pixels 6 Nov 08 J. Albert 8 Material Avg. Thickness (mm) (1) X0 (%) (1) Avg. Thickness (mm) (2) X0 (%) (2) Avg. Thickness (mm) (3) X0 (%) (3) Silicon0.40.4270.80.8540.40.427 Diamond0.60.4940.20.1650.60.494 RVC foam3.30.0393.30.0393.30.039 Conductive carbon fibre foam1.80.2291.80.2291.80.229 Aluminum0.120.1350.120.135 Beryllium0.120.034 CO2 liquid0.450.1740.450.1740.450.174 BN-loaded epoxy glue0.140.1150.140.115 Thermal grease0.210.0170.210.017 Copper traces0.020.1390.020.1390.020.139 Fluorinert liquid Total1.7691.8671.536 35 um thick BN- loaded epoxy mounts ~200 um wall thickness Al tube (6 mm square), CO 2 cooling (1/2 full liquid), thermal grease coat (35 um thick) Conductive carbon fiber foam (2 x 6 mm square) 200 um thick diamond active pixels RVC foam 1) 4 cm 200 um thick silicon readout chips 100 um thick CVD support diamond ~200 um wall thickness Al tube (6 mm square), CO 2 cooling (1/2 full liquid), thermal grease coat (35 um thick) 200 um thick silicon active pixels RVC foam 2) 200 um thick silicon readout chips 100 um thick CVD support diamond 3) Same as 1), but with no glue & thermal grease, and Be tube. 1)2)3)

9. No need to learn ANSYS (or pay for a license)! ☺ We now have a very simple (& freely available, if you’re interested) Fortran program (run as a PAW macro) to quickly find the steady-state temperatures in a 2-D or 3-D stave. Anyone can run and modify it – even a physicist! All dimensions, materials, etc., are adjustable. Works on a finite difference grid, using successive overrelaxation. Produces a nice color plot of the temperature distribution: Quick Stave Temperature Calculation Program! ATLAS Tracker Upgrade Wkshp. Thermal & Mechanical Support for Diamond Pixels Thermal & Mechanical Support for Diamond Pixels 6 Nov 08 J. Albert 9

10. Stave Temperatures ATLAS Tracker Upgrade Wkshp. Thermal & Mechanical Support for Diamond Pixels Thermal & Mechanical Support for Diamond Pixels 6 Nov 08 J. Albert 10 Situation 1): °C ΔT mm

11. Thinner Staves ATLAS Tracker Upgrade Wkshp. Thermal & Mechanical Support for Diamond Pixels Thermal & Mechanical Support for Diamond Pixels 6 Nov 08 J. Albert 11

12. Different Concepts ATLAS Tracker Upgrade Wkshp. Thermal & Mechanical Support for Diamond Pixels Thermal & Mechanical Support for Diamond Pixels 6 Nov 08 J. Albert 12 35 um thick BN-loaded epoxy mounts ~200 um wall thickness Al tube (1 mm square), CO 2 cooling (1/2 full liquid), thermal grease coat (35 um thick) Conductive carbon fiber foam (2 x 6 mm square) 200 um thick diamond active pixels RVC foam 1) 1.37% X 0 /(2 layers) 4 cm 35 um thick BN-loaded epoxy mounts ~200 um wall thickness Al tube (6 mm square), CO 2 cooling (1/2 full liquid), thermal grease coat (35 um thick) Conductive carbon fiber foam (2 x 6 mm square) 200 um thick silicon active pixels 100 um thick CVD support diamond RVC foam 2) 1.47% X 0 /(2 layers) CVD bonded, NO epoxy mounts ~200 um wall thickness Be tube (6 mm square), CO 2 cooling (1/2 full liquid), CVD bonded -- NO thermal grease coat Conductive carbon fiber foam (2 x 6 mm square) 200 um thick diamond active pixels 100 um thick CVD support diamond RVC foam 3) 1.14% X 0 /(2 layers) 200 um thick silicon readout chips 100 um thick CVD support diamond 200 um thick silicon readout chips

13. To-do List – Diamond Stave Modelling ATLAS Tracker Upgrade Wkshp. Thermal & Mechanical Support for Diamond Pixels Thermal & Mechanical Support for Diamond Pixels 6 Nov 08 J. Albert 13 Build prototypes, and compare them with simulations… Do more comparisons with ANSYS, Cosmos, … Test other configurations, coolants, cooling pipe and other materials, 3-D modelling (with end cooling), radiation (& possibly estimates of convection). Model deflections, thermal deformation.

14. Prototype Making ATLAS Tracker Upgrade Wkshp. Thermal & Mechanical Support for Diamond Pixels Thermal & Mechanical Support for Diamond Pixels 6 Nov 08 J. Albert 14 In the next few months we will be constructing a teststand to measure the thermal and structural properties of diamond pixel stave candidates. Use 2 cm x 6 cm, 500 um thick structural pCVD diamond sheets to model sensors / diamond support. Use current through thin graphite foil glued to the back, to model heating.

15. Thermal Conductivity Measurement ATLAS Tracker Upgrade Wkshp. Thermal & Mechanical Support for Diamond Pixels Thermal & Mechanical Support for Diamond Pixels 6 Nov 08 J. Albert 15 We need to determine the thermal conductivity of the structural pCVD diamond sheets. We now have the use of a far-infrared thermography camera (sensitive to ±0.1 °C) to assist in measuring both thermal conductivity and the temperature distribution over the surface of a stave. Will use this and compare with expected thermal conductivity (~1500 W/mK), and our simulated temperature distributions, respectively.

16. Conclusions ATLAS Tracker Upgrade Wkshp. Thermal & Mechanical Support for Diamond Pixels Thermal & Mechanical Support for Diamond Pixels 6 Nov 08 J. Albert 16 The properties of diamond are highly favorable for structural and thermal stability. Has the potential to result in material reduction and simplification. We have some initial thermal models for very basic, simplified, diamond stave concepts. We have a simple, physicist-friendly thermal modelling program. We will be constructing prototype diamond staves, using available structural diamond sheets.

17. Backup Slide: Cooling Mist…. ATLAS Tracker Upgrade Wkshp. Thermal & Mechanical Support for Diamond Pixels Thermal & Mechanical Support for Diamond Pixels 6 Nov 08 J. Albert 17 As was noted earlier, simple end cooling is almost good enough for diamond pixels. We don’t need much more than that. Diamond pixels can run at any temperatures ~+30 °C or below (limited by the silicon readout chips, not the pixels). Why not do away with cooling lines completely and just use a tiny bit of cooling mist, blown through the detector? 200 um thick diamond active pixels 200 um thick CVD support diamond 0.61% X 0 /layer 4 cm ~ Fluorinert FC-87 mist ~ 200 um thick silicon readout chips There are several fluids used for electronics cooling that conveniently boil (at atm. pressure) around ~30 °C (3M Fluorinert FC-87 and Novec 7000). When misted & blown, would be an extraordinarily efficient cooling mechanism (right on chips!)… Would require a great deal of (highly nontrivial) modelling and prototyping, however, as such a technique has never been used..