Graham Beck, QMUL. Oxford Tracker Forum, June Thermal Design of the ATLAS Upgrade Strip Staves 2007 (start of my involvement in thermal study): Q. What are the thermal limitations on upgrade performance? A. Probably Thermal Runaway and Shot Noise (both T-dependent)... Not sure which is the more critical! I will concentrate on thermal runaway: - Brief look at existing ATLAS Barrel module design (late 1990s). - How understanding evolved during Upgrade design (2007-)  Thermal structure and performance of the proposed Staves.

Graham Beck, QMUL. Oxford Tracker Forum, June After radiation damage, leakage current I is dominated by bulk generation. Shot Noise (strip) ~ √I Sensor heat, Q ~ I × V bias Assuming mid-gap carrier generation, expect: (non-linear behaviour responsible for runaway …) The silicon band gap (~ 1.11 eV at 300K) falls with T (independently of radiation damage) contributing appreciably to T dependence of intrinsic carrier concentration. Fit to T range of interest: E g [eV] ≈ 1.21– m.T [K] => - close to measured T dependence for ATLAS irradiated sensors. - explained + investigated to greater accuracy by Alex Chilingarov (RD ) [ “np ~ exp(-1.21/kT)”, Morin&Maita, Bell Labs, 1954 !!]. (backup:Biard) Temperature Dependence

Graham Beck, QMUL. Oxford Tracker Forum, June Double-sided module, bridged readout hybrid. Evaporative C3F8 cooling at nominal -25C. 4 Si wafers glued to TPG baseboard (dashed outline). High thermal conductivity, but prone to delamination => laser perforated + encapsulated in epoxy. Baseboard design (FEA) aimed to: - minimise sensor Tmax (was thought to dominate runaway) - minimise mass (%X 0 ) => relatively small  T (~1.5C) across sensor Existing SCT Barrel Module - thermal features However: ~75% of thermal resistance (sensor heat => fluid) contributed by cooling path outside the sensor area: small area (narrow, ½ sensor length) resistive layers (grease, glue, kapton, fluid film). Common path for heat from both sides of module. TPG Epoxy BeO Thermal Grease Cu/Kapton shunt shield Epoxy+BN Al block Cooling pipe C 3 F 8 evap.film. 64 mm

Graham Beck, QMUL. Oxford Tracker Forum, June Existing SCT Barrel Module - thermal FEA features (1) Concerns about uncertainty in radiation damage motivated plots of Sensor maximum Temperature vs. Sensor Power (at 0C). Generally: difficult to find end point of these curves accurately Note: a rise in coolant temperature of about 7C is enough to lose “headroom” wrt expected power. Above plot is from an FEA model built after assembly, so input fairly well known …

Graham Beck, QMUL. Oxford Tracker Forum, June Existing SCT Barrel Module - thermal FEA features (2) Some “Quirks” mainly during design phase ~ 1. Off-module cooling structure not well known / not rigorously included in FEA. Eventually: FEA consistent with study of an irradiated module => power headroom factor slightly > 2. Deemed Adequate, but (hindsight) => only a 7C headroom in coolant temperature – a bit tight??... We did not have a very sound understanding of runaway dynamics. 3. Some strange-looking plots - ending in mysterious vertical lines – defensible? 2. There was a perception that thermal runaway happens “at” the location of maximum T

Graham Beck, QMUL. Oxford Tracker Forum, June UPGRADE for sLHC: increased instantaneous & integrated Luminosity. l Improve Track Resolution => Shorter strips at low radius (120 mm => ~25 mm: 4 rows on a 100mm square sensor) Bigger strip detector (replace straw tubes) => multi-module STAVES (end insertion) l ~5-fold increase in ultimate Sensor power density (at same T) => CO2 evaporative cooling => Lower temperature (easily gains a factor > 2). Improve cooling geometry: ~ whole length of wafer, improved cooling pipe contact. Variety of design concepts: d/s module (development of existing) – asymmetric cooling (hybrid L, sensor R) – etc. Baseline (since 2008) is the Integrated Stave: modules (sensor+hybrids) mounted on a CFRP “plank” Plank incorporates a U-shaped cooling pipe (evenly distributed across width). (S.Diez Cornell, 2011)

Graham Beck, QMUL. Oxford Tracker Forum, June Runaway Performance – crude comparison of the various designs FEA not practical for the many, evolving designs! Approximate as 2-d thermal R network (~30 nodes). Iterate for sensor max.T vs Q(0C) Wrapping up this study resulted in a compelling plot - Runaway Power is inversely proportional to Initial Slope ?? WHY? - and is it easy to predict runaway? (max sensor T was used here: expect a better fit for mean T).

Graham Beck, QMUL. Oxford Tracker Forum, June “Analytic model of thermal runaway in silicon detectors” G.Beck, G.Viehhauser NIMA 618 (2010) 131. “Minimal Model” approximation, assumes: - T variation across the sensor can be neglected (sensor effectively point-like) - Negligible T dependence of all thermal conductivities (and fluid htc). Q(T S ) R TSTS T0T0 Remainder of thermal circuit is equivalent (Thevenin’s theorem) to a single thermal resistor R connected to a sink at T 0. T 0 = Sensor temperature at zero Q (but with readout electronics powered). Temperature variation of power dissipated by sensor: where T A = 1.2eV/2k ≈ 7000K (carrier activation temperature) The two parameters R and T 0 are found from FEA. Sensor mean temperature rise and critical values for runaway are then given by a set of ~simple formulae.

Graham Beck, QMUL. Oxford Tracker Forum, June Steady State Continuity – balance of generated and conducted sensor heat. The heat generated by the sensor at T S is given by: Two solutions for T S : stable (e.g. operating point O above) and unstable, at higher temperature. where Q ref is its value at some reference temperature Tref (usually 0C). This must be balanced by conduction: So that: FEA normally explores the stable region, remember -

Graham Beck, QMUL. Oxford Tracker Forum, June Comparison with “First Observation of Thermal Runaway in the Radiation Damaged Silicon Detector” Kohriki et al, IEEE Trans.Nucl.Sci, (1996). The above continuity curve, expressed in terms of current and voltage has the same (double valued) form. A rough fit of R to the Kohriki data shows how the higher T solution is stabilised by a current limiting power supply. CDF Sensor, p/cm 2

Graham Beck, QMUL. Oxford Tracker Forum, June Thermal FEA of Upgrade Stave Module Each stave (half barrel length) will be 13 modules long. Thermal FEA model is of a single module (now with proposed 256 channel r/o chips cf 128 in photo!) Sensor FEA elements are thermoelectric, with T-dependent resistivity (as Andreas/CMS). We (usually) neglect convection & radiation – so conduction only – and assume coolant T C = -30C with htc 8000W/m 2 K. Graphitised foam + Epoxy/BN joints CFRP facings Hybrids placed asymmetrically (bcs!) - expect eventually symmetric. Hybrid heat ~ 5.6W/ face.

Graham Beck, QMUL. Oxford Tracker Forum, June T distributions (Serial Powering – zero sensor power) Sensor max-min = 3.5C Mean Sensor T = -25.2C = T 0 in the analytic model Next: run with a small amount of sensor heat defined at 0C, and find the resultant mean temperature. The slope gives the other parameter for the analytic model, here: R = 0.90 C/W

Graham Beck, QMUL. Oxford Tracker Forum, June RESULTS from FULL FEA and ANALYTIC MODEL Red dots: full FEA results. Blue line: analytic continuity curve (T 0 = -25.2C, R = 0.9 C/W). After 3000 fb -1 expect max. fluence (r = 38cm, z=1.2m) of 1.2 x neq/cm 2 (includes a safety factor x2) => sensor power = 0.65mW/mm 2 (at 0C, 500V bias). => Runaway headroom of ~ factor ×9.4 in terms of sensor power OR 21 degrees in coolant temperature. Sensor mean T vs q (at 0C) (at T C -30C) Sensor (T – T C ) vs T C at q=0.65mW/mm 2

Graham Beck, QMUL. Oxford Tracker Forum, June So: we appear to have a lot of headroom against thermal runaway. Quick FEA runs + the analytic model allow us to explore sensitivity to reducing component thicknesses or conductivities. And there are a few uncertainties of course…

Graham Beck, QMUL. Oxford Tracker Forum, June Update to hybrid power (V ddd =1.2V) and more realistic (75% ) power conversion efficiency: 5.6W => 6.7W => 1C reduction in headroom (short arrow) IFF double ASIC power (track trigger) => Direct 5C reduction in headroom (long arrow) Headroom for some changes wrt the Baseline

Graham Beck, QMUL. Oxford Tracker Forum, June We should be careful that performance isn’t degraded at the ends of the stave: End of Stave electronics – GBT + optolink + power conversion: will reduce temperature headroom by only ~ 1.5 degrees. But the main problem here is to cool the GBT etc effectively – to be investigated … C Z=0 Sensor surface We have already extended thermal coupling around the pipe U-bend to avoid this potential 6 degree loss of headroom.

Graham Beck, QMUL. Oxford Tracker Forum, June And what about that shot noise question? Is it more important than runaway? The analytic model tells us that that at the critical Q ref for runaway the actual sensor power is given by: Q crit = T 0 2 / R.T A ≈ 9W Taking rms enc = √ ( 6 * I[nA] * 25 [ns] ) (ABCN shaper), 5120 strips and 500V bias gives: 3.8  A/strip, rms shot noise: 760 e. - slightly worse (830 e) if the coolant temperature rises instead. Maybe not much to choose between them, after all !

Graham Beck, QMUL. Oxford Tracker Forum, June BACKUP

Graham Beck, QMUL. Oxford Tracker Forum, June BACKUP SLIDES

Graham Beck, QMUL. Oxford Tracker Forum, June FEA Input Data

Graham Beck, QMUL. Oxford Tracker Forum, June Plot from “Band Gap Regulator Analysis” - J. R. Biard, Honeywell, 9/10/2002 presentation Note that when the linear fit is substituted in the Boltzmann factor exp(-E g /2kT) it is the intercept that gives E ef ! Y.P.Varshni form (1967) (Shift of CB wrt VB)

Graham Beck, QMUL. Oxford Tracker Forum, June Time-dependent FEA. Thermal Capacitance?

Graham Beck, QMUL. Oxford Tracker Forum, June (Existing Barrel Module) T-distribution is well behaved even during runaway

Graham Beck, QMUL. Oxford Tracker Forum, June C (fluid) QMUL Abaqus (2007, 2009). FLUID -25C. Leakage Power 120  W/mm 2 at 0C (target value) Temperature Contours at 1C intervals from -21C to +3C. (1C agreement with ATLAS thermistor data) T rise across sensor is rather small (below runaway). Mean T S ~ 9.8 C. At Zero Leakage Power: ~11.9 C (2.1C lower). Deduce 70% of thermal resistance is “off-sensor” (~ as end-cap, upgrade stave designs…).