Thermal & Mechanical Support for Diamond Pixel Modules Justin Albert Univ. of Victoria Nov. 6, 2008...

Thermal & Mechanical Thermal & Mechanical

Support for Diamond Pixel Support for Diamond Pixel

ModulesModules

Justin

Albert

Univ. of Victoria

Nov. 6, 2008

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http://www.uvic.ca/

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)

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Thermal & Mechanical Support for Diamond PixelsThermal & Mechanical Support for Diamond Pixels 6 Nov 08 J.

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http://www.uvic.ca/

How Much Cooling do we Need?

• Readout chips produce ~0.26 W/cm2. No heat from sensors.

• We have all been using a factor of two as a safety margin: 0.5 W/cm2.

• 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).



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http://www.uvic.ca/

Don’t Reinvent the Wheel



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etc...!

Some Basic Diamond Pixel Stave Concepts



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35 um thick BN-loaded epoxy mounts

~200 um wall thickness Al tube (6 mm square), CO2 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% X0/(2 layers)

4 cm




200 um thick silicon active pixels

100 um thick CVD support diamond

RVC foam

2) 1.87% X0/(2 layers)

CVD bonded, NO epoxy mounts

~200 um wall thickness Be tube (6 mm square), CO2 cooling (1/2 full liquid), CVD bonded -- NO thermal grease coat




RVC foam

3) 1.54% X0/(2 layers)

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)

Might “End-Only” Cooling be Conceivable with Diamond?



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• 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/cm2 heating.

€

∂∂x

k∂T

∂x

⎛

⎝ ⎜

⎞

⎠ ⎟+

∂

∂yk

∂T

∂y

⎛

⎝ ⎜

⎞

⎠ ⎟+

∂

∂zk

∂T

∂z

⎛

⎝ ⎜

⎞

⎠ ⎟= q

€

d2T

dz2=

q

k⇒ T(z) =

q

2ktL

2( )2

− z2 ⎛ ⎝ ⎜ ⎞

⎠ ⎟+ T0

Simple Uncooled Stave



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• 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 = (thickness3 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.

€

∂2

∂x 2YI

∂ 2u

∂x 2

⎛

⎝ ⎜

⎞

⎠ ⎟= w(x)

€

ucenter =ρgL4

32Yt 2,

Simple Material Budgets



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MaterialAvg. Thickness (mm) (1)

X0 (%) (1)

Avg. Thickness (mm) (2)

X0 (%) (2)

Avg. Thickness (mm) (3)

X0 (%) (3)

Silicon 0.4 0.427 0.8 0.854 0.4 0.427

Diamond 0.6 0.494 0.2 0.165 0.6 0.494

RVC foam 3.3 0.039 3.3 0.039 3.3 0.039Conductive carbon fibre foam 1.8 0.229 1.8 0.229 1.8 0.229

Aluminum 0.12 0.135 0.12 0.135

Beryllium 0.12 0.034

CO2 liquid 0.45 0.174 0.45 0.174 0.45 0.174

BN-loaded epoxy glue 0.14 0.115 0.14 0.115

Thermal grease 0.21 0.017 0.21 0.017

Copper traces 0.02 0.139 0.02 0.139 0.02 0.139

Fluorinert liquid

Total 1.769 1.867 1.536





RVC foam

1)

4 cm





RVC foam

2)200 um thick silicon readout chips


3) Same as 1), but with no glue & thermal grease, and Be tube.

1) 2) 3)

• 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!



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Stave Temperatures



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• Situation 1):

°C

ΔT

mm

Thinner Staves



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Different Concepts



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RVC foam

1) 1.37% X0/(2 layers)

4 cm






RVC foam

2) 1.47% X0/(2 layers)

CVD bonded, NO epoxy mounts

~200 um wall thickness Be tube (6 mm square), CO2 cooling (1/2 full liquid), CVD bonded -- NO thermal grease coat




RVC foam

3) 1.14% X0/(2 layers)





To-do List – Diamond Stave Modelling



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• 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.

Prototype Making



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• 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.

Thermal Conductivity Measurement



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• 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.

Conclusions



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• 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.

Backup Slide: Cooling Mist….



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• 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?



0.61% X0/layer

4 cm

~ Fluorinert FC-87 mist ~


• 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..

Thermal & Mechanical Support for Diamond Pixel Modules Justin Albert Univ. of Victoria Nov. 6, 2008...

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