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Micronic-size cryogenic thermometer for turbulence measurements O. Chanal, B. Baguenard,a) O. Be´thoux, and B. Chabaudb) CNRS-Centre de Recherches sur les Tre`s Basses Tempe´ratures, associated with Universite´ Joseph-FourierGrenoble I, BP 166, 38042 Grenoble Cedex 9, France ~Received 27 December 1996; accepted for publication 14 February 1997! Micronic-size thermometers (1.531.530.5 m m3) designed for local measurements in turbulent gaseous helium in the range of 4–80 K, have been developed and tested. Their very short time response (<1 m s) and micronic spatial resolution allow to perform measurements down to the Kolmogorov dissipative length scale, for high Reynolds or Rayleigh numbers flows. These thermometers, designed to be nonperturbative in the flow, are based on Au–Ge thin films deposited by sputtering process on drawn glass fibers. Their relative sensitivities s 5 u (T/R)(dR/dT) u are ranging from 0.15 to 0.9, and are nearly constant on the whole temperature range. © 1997 American Institute of Physics. @S0034-6748~97!01706-1# I. INTRODUCTION 4 For more than 20 years, gaseous helium ( He) has been widely used as a working fluid for developed turbulence experiments.1–5 Such nonlinear experiments have to be very sensitive and well controlled, and this can be obtained within cryogenic environment. Close to its critical point ~at 5.2 K and under 0.22 MPa!, gaseous helium has the smallest known kinematic viscosity: n 5231028 m2/s, giving access to the largest Reynolds ~Re! or Rayleigh ~Ra! numbers in given size experiments. Furthermore, this kinematic viscosity can be easily adjusted at low temperature by varying the pressure ( n 3 P'cste.). This allows to continuously explore a large range of Reynolds or Rayleigh control parameters,6,7 within laboratory-size experiments and with constant geometry flows. On the other hand, such a small kinematic viscosity is a challenging problem, since the smallest ~dissipative! lengthscale in the flow is very small: it can be as small as a few microns for a Re5106 flow, and the corresponding shortest temperature ~or velocity! fluctuation timescale is about 1 ms. To perform temperature measurements down to these smallest time and length scales, micronic glass fiber sensors have been developed,8,9 taking advantage of both of thin films techniques and of the very small heat capacity of materials at low temperature. Thin metallic wires ~for instance Pt wire! working as thermometers appeared to be inefficient, since these wires do not have high relative sensitivities in our temperature working range. Furthermore, Pt wires have a large thermal conductivity, leading to a mediocre spatial resolution. In Sec. II, we present the thermometer fabrication, and we shall discuss the Au–Ge thin films behavior in Sec. III. Both static and dynamic characterizations will then be presented in Sec. IV. II. THE THERMOMETER The detector is made of a stainless steel rigid frame ('1 cm31.5 cm) on which three copper 150-mm-diam a! Present address: Laboratoire de Spectrome´trie Ionique et Mole´culaire, Universite´ Claude Bernard ~Lyon I!, 69622 Villeurbanne cedex, France. b! Electronic mail: chabaud@labs. polycnrs-gre.fr 2442 Rev. Sci. Instrum. 68 (6), June 1997 wires are epoxy glued ~Fig. 1!. These wires are both a mechanical support for the sensor, and electrical leads for the signal. Two 50-mm-diam Ag arms are indium soldered to a couple of adjacent copper wires, and bent in front of each other in order to support the glass fiber. A reference resistor ~75 V! is connected just outside the stainless steel frame, between the third Cu wire and the middle one. Such a compact bridge design is intended to minimize the inductive wire loops. When performing local measurements in a turbulent flow, one has to use sensors as nonperturbative as possible, i.e., transparent for the flow. The sensor was designed according to the ‘‘one order of magnitude’’ rule: any object has to be at least 10 times its dimensions away from the sensitive part of the detector. The stainless steel frame is 1 mm thick, the Cu wires are 2 mm downstream the flow, and the Ag arms are about half a millimeter away from the Au–Ge sensitive spot. Such an empirical rule would not be easily fulfilled with lithography techniques. We thus have developed since a few years glass fiber based, handmade sensors. The glass fiber is prepared addition to the following procedure: a 5-mm-diam glass fiber of ‘‘E’’ borosilica without soda10 is cleaned during 5 min in an ultrasonic cleaner filled with a 5% alkaline solution11 in distillated water at 60 °C. It is then drawn down to a diameter comprised between 1 and 1.5 mm. This drawing process is necessary first because commercial glass samples thinner than 5 mm are not easily found, and second because it provides a good glass surface quality. A small paper weight ~1 mg! is hung to the fiber which is placed along the vertical axis of a resistive micro-oven coil ~Fig. 2!. The oven is made from a 150-mm-diam steel wire ~resistance: 10 V!, which is red heated with a 5.5 W power. Radiation heated, the glass fiber undergoes the glassy transition, and becomes slowly longer and thinner. Its diameter is estimated from its final length: in a 1-cm-high microcoil, a '1 cm fiber lengthening corresponds to a 1.5 mm final fiber diameter. When it reaches a diameter comprised between 1 and 1.5 mm, the glass fiber is removed from the oven, and glued onto the Ag wires with silver paint. The overall length of the fiber between the Ag wires ranges from 0.4 ~for 1.5-mm-diam 0034-6748/97/68(6)/2442/5/$10.00 © 1997 American Institute of Physics Downloaded¬16¬Feb¬2009¬to¬147.173.59.38.¬Redistribution¬subject¬to¬AIP¬license¬or¬copyright;¬see¬http://rsi.aip.org/rsi/copyright.jsp FIG. 1. The thermometer design. drawn fibers! to 1 mm ~for 5-mm-diam fibers!. The frame supporting the glass fiber is then placed into a rf magnetron sputtering unit. The glass fiber is situated 40 mm away in front of a 5-cm-diam target of cast Au–Ge alloy. The mean Au concentration in the target is 17 at. %. The glass fiber is one-side covered with a 3000-Å-thick amorphous Au–Ge thin film ~sputtering Ar pressure: 0.37 Pa, deposition rate measured by a quartz crystal oscillator: 2.360.1 Å/s!. To increase its temperature sensitivity, the Au–Ge film has to be annealed ~typically t a 51 h, T5105 °C controlled within 61 °C! under an inert Ar atmosphere. This leads to an increase of both the thin film resistivity, as well as its relative sensitivity s 5 u (T/R) 3(dR/dT) u ~see Sec. III!. To limit the sensitive ~temperature dependent! part of the fiber to a short length, the Au–Ge film is short circuited by another film of low resistivity, deposited by evaporation, except on the middle part of the fiber, where a short mask is positioned. This mask is a glass fiber ~0.5–1.5 mm diam! which is hand-placed cross to the Au–Ge coated one. Because of its good thin film adhesion, a 400-Å-thick Ag layer is first evaporated on the Au–Ge sublayer, followed by a 1600-Å-thick Au layer, providing a good resistance to oxidation. This 2000-Å-thick Ag1Au layer has a small electrical resistance ~70 V at 4.2 K for a 0.5 mm long, 1.5 mm diam, coated glass fiber!, which represents less than 6% of the final thermometer resistance at low temperature. The screening wire is then removed, leaving a short ('0.5 m m) uncovered sensitive Au–Ge spot in the middle of the fiber ~Fig. 1!. III. Au–Ge THIN FILMS BEHAVIOR FIG. 2. The resistive micro-oven coil. Rev. Sci. Instrum., Vol. 68, No. 6, June 1997 Au–Ge thin films deposited on glass fibers have the same qualitative electrical behavior as other similar films studied elsewhere.12 When deposited at room temperature and sufficiently low deposition rate, the Au–Ge alloy is amorphous, and its resistivity does not depend very much on temperature. It has to be annealed to exhibit some temperature sensitivity. On annealing, the electrical resistance— measured at any temperature—and its temperature sensitivity begin to increase with annealing temperature and duration, until crystallization occurs. Beyond this point, the resistance drops rapidly and becomes again almost temperature insensitive. Since Au and Ge are each other insoluble in equilibrium, the resistance increase before crystallization is probably due to progressive segregation of Au atoms throughout the initial Micron-size thermometer 2443 Downloaded¬16¬Feb¬2009¬to¬147.173.59.38.¬Redistribution¬subject¬to¬AIP¬license¬or¬copyright;¬see¬http://rsi.aip.org/rsi/copyright.jsp FIG. 3. Influence of the annealing temperature and duration, on the resistance vs temperature dependence, for four different 1.5-mm-diam thermometers. ~a! Before annealing ~as-deposited!: in the 4–80 K range, s 5 u (T/R)(dR/dT) u 50.039. ~b! Annealed 30 mn at 100 °C: s 50.25. ~c! Annealed 110 mn at 105 °C: s 50.96. ~d! Annealed 130 mn at 105 °C: s 50.021. amorphous forced solution, leading to a Ge-rich matrix in which domains with higher Au concentration are growing. The decrease in electron carriers, together with the increase of the Au–rich domains mean distance, causes the hopping13 and/or tunneling conductivities to decrease as observed. In the annealed state, the temperature dependence of the electrical resistance is negative, and roughly linear in log-log scale ~Fig. 3!. The resistance can thus be approximated by a temperature power law over the temperature range measured: R5R 0 T 2 s . ~1! The s exponent ~mean slope of the log-log plot! is equal to the relative sensitivity of the Au–Ge thin film, used as a resistive thermometer: s 52 U U T dR d ln R 5 . d ln T R dT ~2! The s exponent being nearly constant, the temperature resolution dT/T will be nearly constant, provided the resistance is measured with a constant resolution dR/R. The effects of annealing on R(T) dependence is illustrated in Fig. 3. As sputtered, Au–Ge thin films are almost not temperature dependent @curve ~a!#. If the annealing temperature and/or annealing duration are small (T<100 °C, t a <1 h), the final relative sensitivity s is small and slightly decreases at low temperature @curve ~b!#. On the other hand, a too high annealing temperature (T>110 °C) or a too long annealing duration may induce Au–Ge crystallization, accompanied with the complete vanishing of s @curve ~d!#. Strong temperature dependencies ( s .0.9) can be obtained with t a .1 h at T5105 °C @curve ~c!#, but such high relative sensitivities correspond to quite high resistance at low temperature (>53104 V), that are not compatible with high frequencies measurements ( f '1 MHz). We rather select limited s values ( s '0.2), corresponding to low temperature resistances ranging from 1000 to 5000 V, in order 2444 Rev. Sci. Instrum., Vol. 68, No. 6, June 1997 FIG. 4. Resistance evolution during an annealing process at T510561 °C, for two 5-mm-diam Au–Ge coated glass fibers. ~a! No crystallization occurred. ~b! The resistance starts decreasing after t a 52 h, due to the beginning of thin film crystallization. not to be limited by the RC time response of the thermometer, where C is the electric capacitance of the connecting wires ~C525 pF for a twisted 20-cm-long Cu wires pair!. To real-time control the annealing process, the thermometer resistance is measured inside the oven. Resistance variations such as those presented in Fig. 4 are obtained. One can first observe an instantaneous negative resistance step, due to the rapid temperature increase ~from 20 to 105 °C! when the sensor is introduced into the hot chamber of the oven. Then a slow resistance increase follows, corresponding to the Au atoms segregation. If the annealing lasts a long time, the resistance goes through a maximum value @plot ~b! in Fig. 4# and then starts decreasing, due to the crystallization process. The final positive step corresponds to the temperature rapid decrease when the sensor is taken away from the hot chamber of the oven. Such a real-time plot is a useful tool, indicating when to stop the annealing process, before the resistance reaches its maximum. We have observed that the final s relative sensitivity depends on the ratio between the final ~annealed! and the starting ~as deposited! resistances ~Fig. 5!. This correlation provides a good method to roughly estimate the thermometer sensitivity before testing it at a low temperature. Furthermore, it gives the possibility to stop the annealing process for a predetermined s value ~usually s '0.2!. Four glass fibers can be Au–Ge coated in one run. From run to run ~with the same coating parameters!, and for glass fibers that are placed at the same position in the sputtering unit, the reproducibility of Au–Ge thin films resistivity r, is about 15%. On the other hand, in the same run, since the 4 glass fibers are 2 to 3 cm away from each other in the sputtering apparatus, the resistivities range from 55 to 75 mV m at room temperature for 1.5-mm-diam fibers. Furthermore, thin films do not have a similar behavior when annealed: with the same annealing process (t a 51 h, T5105 °C), relative sensitivities as different as 50% can be obtained. This is probably due to differences in Au concentration, and /or temMicron-size thermometer Downloaded¬16¬Feb¬2009¬to¬147.173.59.38.¬Redistribution¬subject¬to¬AIP¬license¬or¬copyright;¬see¬http://rsi.aip.org/rsi/copyright.jsp FIG. 5. Correlation between the s relative sensitivity and the ratio between final ~annealed! and starting ~as-deposited! resistances. perature inhomogeneities within the sputtering plasma, leading to different thin films microstructures. Diagnosis for the more than 60 samples we have manufactured is not easy, first because the small fibers dimensions do not allow to perform x-rays or BEM analysis, and second because Au–Ge coatings are easily flashed by electrostatic discharges ~when soldering wires! or electric pulses ~during measurement!. Another important parameter is the Au–Ge deposition rate. Since the glass fiber is very small and has a tiny heat capacity, it thermalizes very fast within the sputtering plasma. The greater the deposition rate, the higher the fiber temperature during Au–Ge deposition. We thus have observed that for a deposition rate greater than 3 Å/s, crystallization process probably occurs in the sputtering unit, and the thin film obtained is no more sensitive to the following annealing treatment. Good amorphous thin films were obtained with 2.3 to 2.4 Å/s deposition rate. IV. CHARACTERIZATION AND DISCUSSION Both static and dynamic responses were measured. Static resistance versus temperature calibrations were performed from room temperature to 4.2 K, under the atmospheric pressure of stratified He gas above a liquid He bath. The thermometer resistance is measured by means of four-wires ac bridge14 (measurement current50.1 mA), whose resistance resolution dR/R is about 1025 . Temperature is obtained from a calibrated carbon thermistor, which is four-wires connected to a Siemensmeter.14 The calibration resolution is dT/T51023 . Calibrations are plotted in log-log scales, in order to evidence the thermometer relative sensitivity s. Systematic R(T) calibrations were performed after the annealing process, i.e., before the Ag plus Au evaporation @curve ~a! in Fig. 6#. This calibration is very useful, first to test the temperature sensitivity obtained, and second because it provides a control of the Ag plus Au over Au–Ge adherence: if the ratio between the annealed Au–Ge wire resistance over the sensitive spot one ~global resistance minus the Ag plus Au contribution!, is of the order of the ratio between the total Rev. Sci. Instrum., Vol. 68, No. 6, June 1997 FIG. 6. Calibration curves for a 1.5-mm-diam glass fiber, coated with a 3000-Å-thick Au–Ge film, annealed 40 mn at 100 °C. ~a! First characteristic: s 5 u (T/R)(dR/dT) u 5 0.238 for 4 K , T , 80 K. ~b! The same fiber after a 400-Å-thick Ag11600-Å-thick Au deposition: s 50.275 for 4 K , T ,80 K. The sensitive Au–Ge length is 0.5 mm. fiber length over the sensitive Au–Ge one, then the adherence is good. For the 1.5-mm-diam fiber whose calibration curves are presented in Fig. 6, we have R Au–Ge 189 kV 51167 5 R Au1Ag1Au–Ge2R Au1Ag 312 V2150 V ' L Fiber L Au–Ge spot 5 550 m m 0.5 m m 51100. ~3! A final characterization, after the Ag plus Au evaporation is then performed @curve ~b! in Fig. 6#. Within the 4–80 K range ~being the interesting one for our application!, the power law calibration curve is R51800 T 20.275. ~4! R being in V and T in Kelvin. This law fits the measured resistance dependence within 2% in the 4–80 K range. With a dR/R51025 resolution resistance bridge, the temperature resolution is less than 0.2 mK at 4 K, and about 3 mK at 80 K. This R(T) dependence is very similar to that observed on planar Au–Ge films.12 From previous measurements8,9 and calculations,8,9,15 the response time of such a thermometer is expected to be less than 1 ms. This is due to its very small dimensions, as well as the very low heat capacity of materials at low temperature. The spatial resolution of the sensor is of the order of the sensitive Au–Ge spot dimension. It is being measured, both experimentally in turbulent flows, and from numerical simulations of the sensor behavior.16 A preliminary test in a turbulent cryogenic flow was performed ~Fig. 7!. The thermometer was placed on the axis of a mixing axial jet: a full 4.2 K liquid He jet ~4.2 mm diam! is surrounded by a round 90 K gaseous He jet ~5.6 mm external diam!. Very strong temperature fluctuations (dT/dt.53105 K/s) between constant temperature regimes are the signature of liquid drops dragged by the gas. The thermometer resistance is measured by means of a 400 kHz driven bridge. Square currents with chosen amplitude ratio Micron-size thermometer 2445 Downloaded¬16¬Feb¬2009¬to¬147.173.59.38.¬Redistribution¬subject¬to¬AIP¬license¬or¬copyright;¬see¬http://rsi.aip.org/rsi/copyright.jsp worth noticing that such a thermometer as it is, can also be used as an anemometer: driven by a small current (<1 m A), its resistance fluctuations are measuring the temperature fluctuations, while larger currents ('10– 100 m A) can heat the sensitive spot, leading to hot-wire behavior.16 ACKNOWLEDGMENTS We thank Yves Ladam and Laurent Puech who recorded the time signal with their rocket experiment. We are indebted to Jean-Louis Bret and Jean-Paul Faure for the electronics they developed. D. C. Threlfall, J. Fluid Mech. 67, 17 ~1975!. B. Castaing, G. Gunaratne, F. Heslot, L. Kadanoff, A. Libchaber, S. Thomae, X. Z. Wu, S. Zaleski, and G. Zanetti, J. Fluid Mech. 204, 1 ~1989!. 3 X. Z. Wu, L. Kadanoff, A. Libchaber, and M. Sano, Phys. Rev. Lett. 64, 2140 ~1990!. 4 X. Z. Wu and A. Libchaber, Phys. Rev. A 45, 842 ~1992!. 5 C. Barenghi, C. J. Swanson, and R. J. Donnelly, J. Low Temp. Phys. 100, 385 ~1995! and references therein. 6 B. Chabaud, A. Naert, J. Peinke, F. Chilla`, B. Castaing, and B. He´bral, Phys. Rev. Lett. 73, 3227 ~1994!. 7 X. Chavanne, F. Chilla`, B. Chabaud, B. Castaing, J. Chaussy, and B. He´bral, J. Low Temp. Phys. 104, 109 ~1996!. 8 B. Castaing, B. Chabaud, and B. He´bral, Rev. Sci. Instrum. 63, 4167 ~1992!. 9 B. Chabaud, Thesis ~unpublished!. 10 Manufactured by Vetrotex-St. Gobain, 767 Quai des Allobroges, 73009 Chambe´ry, France. 11 RBS-HCW, Produced by Traitements Chimiques de Surfaces, Rue Ampe`re, 59236 Frelinghien, France. 12 O. Be´thoux, R. Brusetti, J. C. Lasjaunias, and S. Sahling, Cryogenics 35, 447 ~1995!. 13 B. W. Dodson, W. L. McMillan, J. M. Mochel, and R. C. Dynes, Phys. Rev. Lett. 46, 46 ~1981!. 14 Manufactured by A. B. B. Barras-Provence, Z. I. Saint-Joseph, 04100 Manosque, France. 15 V. Emsellem, C. R. Acad. Sci. 322, 11 ~1996!. 16 B. Castaing, J. L. Bret, and J. P. Faure ~unpublished!. 17 J. L. Bret and J. P. Faure ~unpublished!. 1 2 FIG. 7. Time record of temperature fluctuations in a turbulent mixing He flow at low temperature (4.2 K