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f noise of the Rox™ sensor
Sensors and Actuators A 137 (2007) 51–56
1/f noise of the RoxTM sensor Piotr Ptak ∗ , Andrzej Kolek, Zbigniew Zawislak, Adam W. Stadler, Krzysztof Mleczko Department of Electronics Fundamentals, Rzesz´ow University of Technology, W. Pola 2, 35-959 Rzesz´ow, Poland Received 6 October 2006; received in revised form 28 December 2006; accepted 25 February 2007 Available online 6 March 2007
Abstract 1/f noise was measured for LakeShore RX-202A resistance temperature sensor. Its intensity increases significantly when the temperature is lowered below a few kelvin. It is shown that this rise in the noise intensity leads to the decrease in the temperature measurement resolution. For the lowest temperatures it is limited to 0.01 % only. A source of such large noise is the resistive layer of the sensor. To prove it, multi-terminal lab-made RuO2 + glass thick film samples were prepared and measurements, that allow discrimination between contact and bulk components of the sensor noise, were made. © 2007 Elsevier B.V. All rights reserved. Keywords: 1/f Noise; Temperature sensor; Temperature measurement resolution; Thick film resistor
1. Introduction The LakeShore Rox RX-202A sensor is a typical, commercially available temperature sensor, produced in Ru-based thick film technology. From our recent studies on RuO2 + glass thick film resistors (TFR) it follows, that low frequency 1/f noise increases significantly when the temperature is lowered below a few kelvin and thus it may limit the resolution of a temperature measurement [1,2]. It is then interesting to study 1/f noise of a real temperature sensor and quantitatively describe the decrease of its resolution. RX-202A sensor has been chosen for its wide applicability and very good performance in the considered temperature range. The RX-202A sensor is useful to below 50 mK. It is designed to have a monotonic sensitivity response from 0.05 up to 300 K [3]. Each LakeShore Rox sensor model adheres to a single resistance versus temperature curve. This is achieved by the trimming cut, which can be a source of the noise [4,5]. Rox-type sensors are made of thick ruthenium dioxide and bismuth ruthenate films, binders and other components, which allow obtaining the required temperature characteristics and resistance. The sensor’s bare chip has palladium silver (PdAg) contacts and is printed on aluminium oxide substrate. It can be placed in a copper canister with epoxy seal [3]. Fig. 1 shows the
∗
Corresponding author. Tel.: +48 178651113. E-mail address: [email protected] (P. Ptak).
0924-4247/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.sna.2007.02.034
bare chip of a Rox sensor, without a canister. Note that although the sensor is a 4-wire device its current and voltage leads are mounted to the same conducting pad. From the noise point of view this is another bad solution since contacts are known to produce significant 1/f noise [6,7]. For thick film devices the contact noise arises in the interfacial region between conducting and resistive layers and can even be greater than the noise generated in a bulk of resistive, thermosensitive layer. Hence, another aspect of our paper is to find out whether 1/f noise increases at lowest temperatures due to phenomena that take place in the interfacial region or in thermosensing layer. With RX-202A devices it is not possible, since its current and voltage contacts are not separated. For this reason lab-made samples with special topology have been prepared. In Section 4, such multi-terminal samples as well as the method for discrimination between bulk and contact components of their noise are described. Section 2 contains details of the noise measurement technique and results for RX-202A sensor. Section 3 includes considerations relevant to the sensor’s resolution. 2. Noise measurements Noise measurements were performed with the AC technique [8]. The main advantage of this technique is that very small voltages biasing the samples can be used. This is important at low temperature measurements as in this way self-heating of the sample can be avoided. Experimental circuit for AC technique is shown in Fig. 2. Two RX-202A specimens of total resistance
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Fig. 1. Bare chip of the LakeShore’s Rox sensor.
R were placed in the bottom arms of the Wheatstone bridge and biased by a sine wave through ballast resistors of much larger resistance RB . The bridge was balanced and the signal from its diagonal was amplified, demodulated in lock-in amplifier and Fourier transformed to obtain the power spectral density SV (f). The latter was measured in the frequency range 0.5–10 Hz at constant temperature T for various rms values of voltage V biasing the sensors. Also the background noise, i.e. the function SV (f) for V = 0 was measured. Measurements of the background noise serve as the test of the proper calibration of the measurement setup. The main components of this noise are the sensor’s thermal noise, of 4kTR, where k is Boltzmann constant, and the preamplifier’s noise, Samp (f). In Fig. 3 power spectral density of the background noise averaged ( ) over the frequency band 0.5–4 Hz is plotted versus temperature T. As only the sensors were placed in the cryostat whereas the rest of the measurement setup was kept in the room temperature, the background noise reads: 2 R SV =0 = 4kTR + 4k300KRB + Samp . (1) R + RB As can be seen in Fig. 3 experimental data follow the theoretical line of Eq. (1) quite well. The first component in this equation is the Nyquist formula. It is greater than others only at high temperatures. At low temperatures the second component becomes more important. It is because the ballast resistors
Fig. 3. Background noise SV=0 (f) as a function of temperature T. Solid line is the plot of Eq. (1). Dashed lines are plots of the first and the second components of this equation. Dotted line shows preamplifier’s noise, Samp (f) = 1.32 × 10−17 V2 /Hz (EG&G model 5186).
are outside the cryostat, in the temperature of ∼ =300 K. It follows from Eq. (1) that the contribution of this component can be suppressed by the large value of resistance RB . To obtain the spectrum of excess noise SVex (f) the background noise spectrum was subtracted from a spectrum at a given voltage V. Power spectral densities SVex (f) calculated this way are shown in Fig. 4(a). They have 1/f shape and so the product fSVex (f), shown in Fig. 4(b), is a frequency independent function. In this figure the frequency corner above 4 Hz is due to the lock-in’s output filter round-off. After averaging, the product fSVex (f) is plotted versus voltage V in Fig. 4(c) in log–log coordinates. The data follow the line of the slope of 2, which means that relation SVex ∼ V2 is fulfilled. Eventually, the relative noise intensity S can be determined, according to the definition: S≡
SV ex (f )f . V2
(2)
This dimensionless quantity is frequency and voltage independent, but it does depend on the temperature. It can be clearly seen in Fig. 5, where the results of noise measurements are presented for RX-202A sensors. Below 4 K the relative noise intensity S increases by almost two orders of magnitude when temperature decreases down to 0.3 K. Data in Fig. 5 in low temperature range can be approximated by a power law function: S∼ = aT −2.25 ,
(3)
where a is a constant. In the next section the influence of the observed phenomenon on sensor’s resolution is discussed [1,2]. 3. Sensor’s resolution The relative resolution of temperature measurement, εT ≡ T/T, for the resistance-type sensors, is related to the relative resolution of resistance measurement, εR = R/R, according to the expression [9]: Fig. 2. Experimental circuit for AC noise measurements.
εT =
εR , A
(4)
P. Ptak et al. / Sensors and Actuators A 137 (2007) 51–56
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Fig. 4. Results of noise measurements for RX-202A sensor at T = 0.4 K. (a) Power spectral densities of excess noise SVex (f) for V = 2.1; 2.9; 3.2; 3.6; 3.9; 4.6; 5.3; 5.7 mVrms (from the bottom to the top), and background noise SV=0 (f). Dashed line shows pure 1/f noise. (b) Products of the spectra SVex (f) from (a) and frequency f. (c) Products from (b) averaged ( ) over the frequency band 0.5–4 Hz versus voltage V. Solid line is the function plot: fSVex (f) = SV2 , S = 3.2 × 10−11 .
where T and R are temperature and resistance absolute measurement resolutions. They are defined as the smallest change of the parameter, which can be detected. The quantity in the denominator on the r.h.s. of Eq. (4) is the specific sensitivity, which for the resistance-type sensors is defined as A ≡ d ln R/d ln T. It can be calculated from the calibration curve R(T) of the sensor. It follows from Eq. (4) that εT can be easily calculated as soon as εR is specified. LakeShore defines R as rms value of the noise measured on a room temperature resistor after low-pass filtering with τ = 3 s time constant. For the sensor operating at low temperatures with significant 1/f noise this definition gives the quantity which has little to do with a real measurement resolution. Its usefulness is restored as soon as “room temperature” conditions are replaced with a “real temperature”. With this substitution and for the instruments operating at constant current mode we have ΔV ∼ ΔR εR ≡ = (5) = ε2th + ε20 + ε2S , R V where εth is the relative resolution related to sensor’s thermal noise, ε0 is the measurement instrument relative resolution and εS is the sensor’s relative resolution related to its 1/f noise. Modern R-meters that cooperate with temperature sensors use the AC phase sensitive detection technique described in Section 2. For a simple one-pole low-pass filter working at the lock-in’s
Fig. 5. Relative noise intensity S versus temperature T measured for RX-202A (squares) and for lab-made (triangles and circles) sensors. Solid line is the function plot: S = aT−2.25 , a = 4.4 × 10−12 .
output the required time constant of τ = 3 s is equivalent to noise bandwidth of fg = 1/4τ = 1/12 Hz. The relative resolutions in Eq. (5) can now be determined. For εth the relation is: 4kTfg εth ∼ , (6) = 2 R Irms where Irms is the rms value of the excitation current. By increasing this current it is possible to improve this resolution (see Fig. 6). The use of AC setup, phase sensitive detection technique, proper grounding and shielding makes possible to achieve the instrument’s relative resolution of 0 = 106 [10]. Relative resolution εS connected to sensor’s excess noise can be determined from the noise intensity S according to relation: fg S εS ∼ (7) df = S ln(tfg ), = 1/t f where t is the measurement time. Unlike εth the resolution εS does not depend on the biasing current. Thus, it cannot be improved by increasing Irms . As shown in the previous section, for Rox-type sensor, εS depends on temperature as the noise intensity S does.
Fig. 6. Relative resolution of resistance measurement, εR , as a function of the biasing current Irms , for RX-202A sensor coupled to the instrument with relative resolution of ε0 = 5 × 10−6 .
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Fig. 7. Shapes and dimensions of lab-made samples. Dimensions of the resistive layers are: w = 1 mm, b = 2 mm, d = 2.5 mm, c = 0.4 mm.
Assume that increase of the sensor’s noise intensity S follows the relation of Eq. (3) also for temperatures lower than those used in the experiment. Then the sensor’s resolution εR can be calculated in the entire temperature range the sensor is designed for. Fig. 6 shows the plots of the resolution εR as a function of the measurement current Irms for various temperatures. Plots are calculated according to Eqs. (5)–(7) and (3). The product tfg in Eq. (7) was assumed to be of ∼ =10. Such a value is necessary to keep the measurement time t at least an order of magnitude larger than the output filter time constant. The instrument relative resolution was assumed as ε0 = 5 × 10−6 . It is clear from Fig. 6 that at the temperature of 50 mK the resolution εR decreases to about 10−4 (0.01%) due to the large 1/f noise. Thus, the calibration of the sensor with the 0.0001% precision does not mean that temperature can be measured with such large precision. As the sensor’s specific sensitivity A is of the order of unity in considered temperature range, we conclude that at the lowest temperatures the relative resolution εT of temperature measurement done with RX-202A sensors is limited to 0.01% only. 4. Lab-made samples PdAg contacts used in RX-202A sensors are in general commonly used in thick film technology. In the case of RuO2 thick film resistors it was shown that PdAg contacts strongly modify the interfacial region due to Ag migration from the contacts to the resistive layer. This migration leads to the changes in electrical properties of the interface, namely increase of its resistivity and 1/f noise intensity [11–13]. No such effects have been observed for Ag-free contacts. Due to this fact our lab-made sensors were prepared as thick film RuO2 resistors with Au or PtAu contacts. Lab-made sensors of two different shapes were prepared. Fig. 7 shows their shapes and dimensions. Small (Fig. 7(a)) and large (Fig. 7(b)) samples have voltage contacts separated from the current ones. Such a topology allows discrimination between the contact noise and the bulk noise of the resistor.
Fig. 8. Temperature sensitivity |dR/dT| versus temperature T for RX-202A sensors (line) and lab-made RuO2 resistors with Au contacts (circles).
The resistive paste was prepared from the mixture of RuO2 powder, glass and organic solvent with no other ingredients. It did not contain any modifiers, which could strongly affect its electrical properties. The glass, used in the mixture, contained 65% PbO, 10% B2 O3 , 25% SiO2 by weight. As the organic solvent terpineol was used. Its role was to give the paste the rheological properties suitable for printing the paste in the desired shape onto a substrate. The paste contained υ = 0.12 fraction of RuO2 by volume. It was then screen printed onto the alumina substrate (96% Al2 O3 ) through a 200 mesh screen. Prior to printing, conductive pads were prepared. As stated before, the main components of pastes used to prepare the contacts were either Au or Pt and Au. After printing, the resistors were dried and annealed. During this process all the organic components should evaporate. Afterwards the resistors were fired in a flow tunnel furnace with the given temperature profile – the maximum temperature was 850 ◦ C and the samples were kept for 10 min at this temperature. The thickness of the resistive layer, measured after firing, was about 12 m. To install the samples in the cryostat gold leads were bonded to the contact layers. Indium was used as the solder. In Fig. 8 the sensitivity |dR/dT| is plotted versus temperature T for ROX sensors and small lab-made RuO2 /Au resistors. Both graphs are similar in shape and magnitude and so the lab-made samples could be consider as devices similar to RX-202A sensors. In Fig. 5, together with noise intensity S measured for the RX-202A sensors, also results of measurements for lab-made resistors, both small and large, are shown. For small samples the noise signal was taken from the upper voltage contacts. For large samples noise was measured for the whole resistors – signal was taken from the upper current taps. In the low temperature range both type of samples are subjected to the same property: a dramatic increase of noise as temperature is lowered. 5. Contact versus bulk noise In Fig. 5 data for small samples are very close to those for RX-202A sensors and are well fitted to Eq. (3). Data for large samples can also be fitted to Eq. (3), however the exponent is slightly smaller and noise intensity is considerably lower. It is not
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voltage contacts arrange along the lines: x (8) SLx = SB + SC , L where SB (slope of the line) is the “measure” of the bulk noise of the resistive film and SC (intersection with y axis) is the “measure” of the noise of the bottom current contact [6,7,15]. It follows from the results shown in Fig. 10 that, independently of materials used to produce the contacts, the major part of the total resistors’ noise is generated in their resistive layers. 6. Summary Fig. 9. Volume independent noise index C as a function of temperature T. Data are for small (triangles) and large (squares) resistors.
surprising since 1/f noise intensity is known to scale with sample volume Ω as S ∼ 1/Ω [14]. It is then possible to calculate volume independent noise index C ≡ S Ω. This quantity is plotted in Fig. 9 for both types of lab-made resistors. Unfortunately, data for RX-202A sensors cannot be included as its volume remains unknown. As can be seen the data for large and small samples overlap. This means that relation S ∼ 1/Ω holds. As this relation is valid for a bulk phenomenon it can be concluded that the contact noise has rather little influence on the total noise of the resistors. With decreasing resistors’ length the relative size of the interfacial region increases and the influence of the contact noise on noise intensity should increase. The value of C should be larger for smaller resistors. As it is not, we conclude that increase of noise intensity, observed at low temperatures, is a bulk property of resistive film. Further arguments come from the next experiment. For large resistors bulk and contact components of the noise were measured directly. The measurements were performed with an AC cross-correlation technique described in ref. [15]. The cross power spectra SLx (f) of the noise signals on the upper current tap and successive voltage contacts were measured. Then values of SLx (f) at frequency f = 1 Hz were plotted versus position, x/L, of the voltage contacts; x is the distance of the voltage contact from the bottom current tap, L is the length of the resistor. As shown in Fig. 10, values of SLx (1 Hz) measured at central
Fig. 10. Cross power spectral density SLx (1 Hz) versus relative length x/L measured for large resistors.
Measurements of 1/f noise show that in RX-202A sensors the noise increases with temperature decreasing as T−2.25 in temperature range below 4 K. Such dependence was also observed in RuO2 + glass thick film resistors. This phenomenon limits the sensors’ resolution to 0.01% at the lowest temperatures. The increase of the noise intensity is the inherent feature of the thermo-sensitive (resistive) material of the sensor. Acknowledgment The work was supported by the Polish Ministry of Science and Higher Education through the research project no. 3 T11B 071 29. References [1] P. Ptak, A. Kolek, Z. Zawi´slak, A.W. Stadler, K. Mleczko, Noise resolution of RuO2 based resistance thermometers, Rev. Sci. Instrum. 76 (2005) 014901–014906. [2] A. Kolek, P. Ptak, Z. Zawi´slak, A.W. Stadler, K. Mleczko, Low frequency noise resolution of Ru-based low-temperature thick film sensors, in: Proceedings of the International AIP Conference on Noise and Fluctuations, Salamanca, Spain, 2005, pp. 163–166. [3] http://www.lakeshore.com/temp/sen/rrtd.html. [4] A. Raab, C. Jung, P. Dullenkopf, Current noise of trimmed thick-film resistors: measurement and simulation, Microelectron. Int. 15 (1998) 15–22. [5] A. Peled, Y. Zloof, S.O. Kasap, Comparison of excess 1/f noise spectra in trimmed and untrimmed thick film resistors, Int. J. Electron. 87 (2000) 1–9. [6] J.G. Rhee, T.M. Chen, Contact noise in thick film resistors, Solid State Technol. 21 (1978) 59–62. [7] A. Masoero, B. Morten, M. Prudenziati, A. Stepanescu, Proceedings of the 10th International Conference on Noise in Physical Systems, Budapest, Hungary, 1990, pp. 561–564. [8] J.H. Scofield, ac method for measuring low-frequency resistance fluctuation spectra, Rev. Sci. Instrum. 58 (1987) 985–993. [9] D.S. Holmes, S.S. Courts, Resolution and accuracy of cryogenic temperature measurements, Temperature: its Measurement and Control in Science and Industry, vol. 6, J.F. Schooley A/P, New York, 1992, pp. 1225–1230. [10] LakeShore Model 370 AC Resistance Bridge, User’s manual, ver. 1.1, 2001. [11] A. Cattaneo, M. Cocito, F. Forlani, M. Prudenziati, Influence of the metal migration from screen-and-fired terminations on electrical characteristics of thick-film resistors, Electrocomp. Sci. Technol. 4 (1977) 205–211. [12] T. Yamaguchi, Y. Nakamura, Sol-gel processing and conduction mechanism of RuO2 -glass thick-film resistors, J. Am. Ceram. Soc. 78 (1995) 1372–1374. [13] K. Bobran, A. Kusy, J. Phys. Condens. Matter 3 (1991) 7015. [14] F.N. Hooge, 1/f noise is no surface effect, Phys. Lett. A 29 (1969) 139–140. [15] A. Kolek, P. Ptak, K. Mleczko, A. Wrona, A further improvement of the measuring technique of bulk and contact components of resistance noise,
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Biographies Piotr Ptak received BS and MS degree in technical physics from AGH University of Science and Technology in Krak´ow in 1998 and 1999, respectively. He is an assistant researcher (PhD candidate) in Department of Electronics Fundamentals in Faculty of Electrical and Computer Engineering, Rzesz´ow University of Technology. Andrzej Kolek graduated from Department of Electrical Engineering, Electronics and Automatics, AGH University of Science and Technology in Krak´ow. He received his PhD degree from the Department of Electronics, Warsaw University of Technology in 1990 and Dsc degree from Department of Electronics, Wrocław University of Technology in 1998. Specializes in electronics of inho-
mogeneous materials (thick films) and phenomenon of low frequency noise. He is the author of over 30 journal papers. Currently the head of the Department of Electronics Fundamentals, and vice dean of the Faculty of Electrical and Computer Engineering, Rzesz´ow University of Technology. Zbigniew Zawi´slak graduated from Rzesz´ow University of Technology in 1997. Currently he works as R&D engineer in Department of Electronics Fundamentals, Rzesz´ow University of Technology. Adam W. Stadler is academic teacher in Department of Electronics Fundamentals, Rzeszow University of Technology. He received his PhD from Warsaw Institute of Electron Technology in 1996. His research interest is electrical transport mechanisms in disordered materials. Krzysztof Mleczko received PhD degree from Rzesz´ow University of Technology in 2003. He is an academic teacher in Department of Electronics Fundamentals, Rzesz´ow University of Technology. His research interest is electrical transport mechanisms in disordered materials.
1/f noise of the RoxTM sensor Piotr Ptak ∗ , Andrzej Kolek, Zbigniew Zawislak, Adam W. Stadler, Krzysztof Mleczko Department of Electronics Fundamentals, Rzesz´ow University of Technology, W. Pola 2, 35-959 Rzesz´ow, Poland Received 6 October 2006; received in revised form 28 December 2006; accepted 25 February 2007 Available online 6 March 2007
Abstract 1/f noise was measured for LakeShore RX-202A resistance temperature sensor. Its intensity increases significantly when the temperature is lowered below a few kelvin. It is shown that this rise in the noise intensity leads to the decrease in the temperature measurement resolution. For the lowest temperatures it is limited to 0.01 % only. A source of such large noise is the resistive layer of the sensor. To prove it, multi-terminal lab-made RuO2 + glass thick film samples were prepared and measurements, that allow discrimination between contact and bulk components of the sensor noise, were made. © 2007 Elsevier B.V. All rights reserved. Keywords: 1/f Noise; Temperature sensor; Temperature measurement resolution; Thick film resistor
1. Introduction The LakeShore Rox RX-202A sensor is a typical, commercially available temperature sensor, produced in Ru-based thick film technology. From our recent studies on RuO2 + glass thick film resistors (TFR) it follows, that low frequency 1/f noise increases significantly when the temperature is lowered below a few kelvin and thus it may limit the resolution of a temperature measurement [1,2]. It is then interesting to study 1/f noise of a real temperature sensor and quantitatively describe the decrease of its resolution. RX-202A sensor has been chosen for its wide applicability and very good performance in the considered temperature range. The RX-202A sensor is useful to below 50 mK. It is designed to have a monotonic sensitivity response from 0.05 up to 300 K [3]. Each LakeShore Rox sensor model adheres to a single resistance versus temperature curve. This is achieved by the trimming cut, which can be a source of the noise [4,5]. Rox-type sensors are made of thick ruthenium dioxide and bismuth ruthenate films, binders and other components, which allow obtaining the required temperature characteristics and resistance. The sensor’s bare chip has palladium silver (PdAg) contacts and is printed on aluminium oxide substrate. It can be placed in a copper canister with epoxy seal [3]. Fig. 1 shows the
∗
Corresponding author. Tel.: +48 178651113. E-mail address: [email protected] (P. Ptak).
0924-4247/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.sna.2007.02.034
bare chip of a Rox sensor, without a canister. Note that although the sensor is a 4-wire device its current and voltage leads are mounted to the same conducting pad. From the noise point of view this is another bad solution since contacts are known to produce significant 1/f noise [6,7]. For thick film devices the contact noise arises in the interfacial region between conducting and resistive layers and can even be greater than the noise generated in a bulk of resistive, thermosensitive layer. Hence, another aspect of our paper is to find out whether 1/f noise increases at lowest temperatures due to phenomena that take place in the interfacial region or in thermosensing layer. With RX-202A devices it is not possible, since its current and voltage contacts are not separated. For this reason lab-made samples with special topology have been prepared. In Section 4, such multi-terminal samples as well as the method for discrimination between bulk and contact components of their noise are described. Section 2 contains details of the noise measurement technique and results for RX-202A sensor. Section 3 includes considerations relevant to the sensor’s resolution. 2. Noise measurements Noise measurements were performed with the AC technique [8]. The main advantage of this technique is that very small voltages biasing the samples can be used. This is important at low temperature measurements as in this way self-heating of the sample can be avoided. Experimental circuit for AC technique is shown in Fig. 2. Two RX-202A specimens of total resistance
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Fig. 1. Bare chip of the LakeShore’s Rox sensor.
R were placed in the bottom arms of the Wheatstone bridge and biased by a sine wave through ballast resistors of much larger resistance RB . The bridge was balanced and the signal from its diagonal was amplified, demodulated in lock-in amplifier and Fourier transformed to obtain the power spectral density SV (f). The latter was measured in the frequency range 0.5–10 Hz at constant temperature T for various rms values of voltage V biasing the sensors. Also the background noise, i.e. the function SV (f) for V = 0 was measured. Measurements of the background noise serve as the test of the proper calibration of the measurement setup. The main components of this noise are the sensor’s thermal noise, of 4kTR, where k is Boltzmann constant, and the preamplifier’s noise, Samp (f). In Fig. 3 power spectral density of the background noise averaged ( ) over the frequency band 0.5–4 Hz is plotted versus temperature T. As only the sensors were placed in the cryostat whereas the rest of the measurement setup was kept in the room temperature, the background noise reads: 2 R SV =0 = 4kTR + 4k300KRB + Samp . (1) R + RB As can be seen in Fig. 3 experimental data follow the theoretical line of Eq. (1) quite well. The first component in this equation is the Nyquist formula. It is greater than others only at high temperatures. At low temperatures the second component becomes more important. It is because the ballast resistors
Fig. 3. Background noise SV=0 (f) as a function of temperature T. Solid line is the plot of Eq. (1). Dashed lines are plots of the first and the second components of this equation. Dotted line shows preamplifier’s noise, Samp (f) = 1.32 × 10−17 V2 /Hz (EG&G model 5186).
are outside the cryostat, in the temperature of ∼ =300 K. It follows from Eq. (1) that the contribution of this component can be suppressed by the large value of resistance RB . To obtain the spectrum of excess noise SVex (f) the background noise spectrum was subtracted from a spectrum at a given voltage V. Power spectral densities SVex (f) calculated this way are shown in Fig. 4(a). They have 1/f shape and so the product fSVex (f), shown in Fig. 4(b), is a frequency independent function. In this figure the frequency corner above 4 Hz is due to the lock-in’s output filter round-off. After averaging, the product fSVex (f) is plotted versus voltage V in Fig. 4(c) in log–log coordinates. The data follow the line of the slope of 2, which means that relation SVex ∼ V2 is fulfilled. Eventually, the relative noise intensity S can be determined, according to the definition: S≡
SV ex (f )f . V2
(2)
This dimensionless quantity is frequency and voltage independent, but it does depend on the temperature. It can be clearly seen in Fig. 5, where the results of noise measurements are presented for RX-202A sensors. Below 4 K the relative noise intensity S increases by almost two orders of magnitude when temperature decreases down to 0.3 K. Data in Fig. 5 in low temperature range can be approximated by a power law function: S∼ = aT −2.25 ,
(3)
where a is a constant. In the next section the influence of the observed phenomenon on sensor’s resolution is discussed [1,2]. 3. Sensor’s resolution The relative resolution of temperature measurement, εT ≡ T/T, for the resistance-type sensors, is related to the relative resolution of resistance measurement, εR = R/R, according to the expression [9]: Fig. 2. Experimental circuit for AC noise measurements.
εT =
εR , A
(4)
P. Ptak et al. / Sensors and Actuators A 137 (2007) 51–56
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Fig. 4. Results of noise measurements for RX-202A sensor at T = 0.4 K. (a) Power spectral densities of excess noise SVex (f) for V = 2.1; 2.9; 3.2; 3.6; 3.9; 4.6; 5.3; 5.7 mVrms (from the bottom to the top), and background noise SV=0 (f). Dashed line shows pure 1/f noise. (b) Products of the spectra SVex (f) from (a) and frequency f. (c) Products from (b) averaged ( ) over the frequency band 0.5–4 Hz versus voltage V. Solid line is the function plot: fSVex (f) = SV2 , S = 3.2 × 10−11 .
where T and R are temperature and resistance absolute measurement resolutions. They are defined as the smallest change of the parameter, which can be detected. The quantity in the denominator on the r.h.s. of Eq. (4) is the specific sensitivity, which for the resistance-type sensors is defined as A ≡ d ln R/d ln T. It can be calculated from the calibration curve R(T) of the sensor. It follows from Eq. (4) that εT can be easily calculated as soon as εR is specified. LakeShore defines R as rms value of the noise measured on a room temperature resistor after low-pass filtering with τ = 3 s time constant. For the sensor operating at low temperatures with significant 1/f noise this definition gives the quantity which has little to do with a real measurement resolution. Its usefulness is restored as soon as “room temperature” conditions are replaced with a “real temperature”. With this substitution and for the instruments operating at constant current mode we have ΔV ∼ ΔR εR ≡ = (5) = ε2th + ε20 + ε2S , R V where εth is the relative resolution related to sensor’s thermal noise, ε0 is the measurement instrument relative resolution and εS is the sensor’s relative resolution related to its 1/f noise. Modern R-meters that cooperate with temperature sensors use the AC phase sensitive detection technique described in Section 2. For a simple one-pole low-pass filter working at the lock-in’s
Fig. 5. Relative noise intensity S versus temperature T measured for RX-202A (squares) and for lab-made (triangles and circles) sensors. Solid line is the function plot: S = aT−2.25 , a = 4.4 × 10−12 .
output the required time constant of τ = 3 s is equivalent to noise bandwidth of fg = 1/4τ = 1/12 Hz. The relative resolutions in Eq. (5) can now be determined. For εth the relation is: 4kTfg εth ∼ , (6) = 2 R Irms where Irms is the rms value of the excitation current. By increasing this current it is possible to improve this resolution (see Fig. 6). The use of AC setup, phase sensitive detection technique, proper grounding and shielding makes possible to achieve the instrument’s relative resolution of 0 = 106 [10]. Relative resolution εS connected to sensor’s excess noise can be determined from the noise intensity S according to relation: fg S εS ∼ (7) df = S ln(tfg ), = 1/t f where t is the measurement time. Unlike εth the resolution εS does not depend on the biasing current. Thus, it cannot be improved by increasing Irms . As shown in the previous section, for Rox-type sensor, εS depends on temperature as the noise intensity S does.
Fig. 6. Relative resolution of resistance measurement, εR , as a function of the biasing current Irms , for RX-202A sensor coupled to the instrument with relative resolution of ε0 = 5 × 10−6 .
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Fig. 7. Shapes and dimensions of lab-made samples. Dimensions of the resistive layers are: w = 1 mm, b = 2 mm, d = 2.5 mm, c = 0.4 mm.
Assume that increase of the sensor’s noise intensity S follows the relation of Eq. (3) also for temperatures lower than those used in the experiment. Then the sensor’s resolution εR can be calculated in the entire temperature range the sensor is designed for. Fig. 6 shows the plots of the resolution εR as a function of the measurement current Irms for various temperatures. Plots are calculated according to Eqs. (5)–(7) and (3). The product tfg in Eq. (7) was assumed to be of ∼ =10. Such a value is necessary to keep the measurement time t at least an order of magnitude larger than the output filter time constant. The instrument relative resolution was assumed as ε0 = 5 × 10−6 . It is clear from Fig. 6 that at the temperature of 50 mK the resolution εR decreases to about 10−4 (0.01%) due to the large 1/f noise. Thus, the calibration of the sensor with the 0.0001% precision does not mean that temperature can be measured with such large precision. As the sensor’s specific sensitivity A is of the order of unity in considered temperature range, we conclude that at the lowest temperatures the relative resolution εT of temperature measurement done with RX-202A sensors is limited to 0.01% only. 4. Lab-made samples PdAg contacts used in RX-202A sensors are in general commonly used in thick film technology. In the case of RuO2 thick film resistors it was shown that PdAg contacts strongly modify the interfacial region due to Ag migration from the contacts to the resistive layer. This migration leads to the changes in electrical properties of the interface, namely increase of its resistivity and 1/f noise intensity [11–13]. No such effects have been observed for Ag-free contacts. Due to this fact our lab-made sensors were prepared as thick film RuO2 resistors with Au or PtAu contacts. Lab-made sensors of two different shapes were prepared. Fig. 7 shows their shapes and dimensions. Small (Fig. 7(a)) and large (Fig. 7(b)) samples have voltage contacts separated from the current ones. Such a topology allows discrimination between the contact noise and the bulk noise of the resistor.
Fig. 8. Temperature sensitivity |dR/dT| versus temperature T for RX-202A sensors (line) and lab-made RuO2 resistors with Au contacts (circles).
The resistive paste was prepared from the mixture of RuO2 powder, glass and organic solvent with no other ingredients. It did not contain any modifiers, which could strongly affect its electrical properties. The glass, used in the mixture, contained 65% PbO, 10% B2 O3 , 25% SiO2 by weight. As the organic solvent terpineol was used. Its role was to give the paste the rheological properties suitable for printing the paste in the desired shape onto a substrate. The paste contained υ = 0.12 fraction of RuO2 by volume. It was then screen printed onto the alumina substrate (96% Al2 O3 ) through a 200 mesh screen. Prior to printing, conductive pads were prepared. As stated before, the main components of pastes used to prepare the contacts were either Au or Pt and Au. After printing, the resistors were dried and annealed. During this process all the organic components should evaporate. Afterwards the resistors were fired in a flow tunnel furnace with the given temperature profile – the maximum temperature was 850 ◦ C and the samples were kept for 10 min at this temperature. The thickness of the resistive layer, measured after firing, was about 12 m. To install the samples in the cryostat gold leads were bonded to the contact layers. Indium was used as the solder. In Fig. 8 the sensitivity |dR/dT| is plotted versus temperature T for ROX sensors and small lab-made RuO2 /Au resistors. Both graphs are similar in shape and magnitude and so the lab-made samples could be consider as devices similar to RX-202A sensors. In Fig. 5, together with noise intensity S measured for the RX-202A sensors, also results of measurements for lab-made resistors, both small and large, are shown. For small samples the noise signal was taken from the upper voltage contacts. For large samples noise was measured for the whole resistors – signal was taken from the upper current taps. In the low temperature range both type of samples are subjected to the same property: a dramatic increase of noise as temperature is lowered. 5. Contact versus bulk noise In Fig. 5 data for small samples are very close to those for RX-202A sensors and are well fitted to Eq. (3). Data for large samples can also be fitted to Eq. (3), however the exponent is slightly smaller and noise intensity is considerably lower. It is not
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voltage contacts arrange along the lines: x (8) SLx = SB + SC , L where SB (slope of the line) is the “measure” of the bulk noise of the resistive film and SC (intersection with y axis) is the “measure” of the noise of the bottom current contact [6,7,15]. It follows from the results shown in Fig. 10 that, independently of materials used to produce the contacts, the major part of the total resistors’ noise is generated in their resistive layers. 6. Summary Fig. 9. Volume independent noise index C as a function of temperature T. Data are for small (triangles) and large (squares) resistors.
surprising since 1/f noise intensity is known to scale with sample volume Ω as S ∼ 1/Ω [14]. It is then possible to calculate volume independent noise index C ≡ S Ω. This quantity is plotted in Fig. 9 for both types of lab-made resistors. Unfortunately, data for RX-202A sensors cannot be included as its volume remains unknown. As can be seen the data for large and small samples overlap. This means that relation S ∼ 1/Ω holds. As this relation is valid for a bulk phenomenon it can be concluded that the contact noise has rather little influence on the total noise of the resistors. With decreasing resistors’ length the relative size of the interfacial region increases and the influence of the contact noise on noise intensity should increase. The value of C should be larger for smaller resistors. As it is not, we conclude that increase of noise intensity, observed at low temperatures, is a bulk property of resistive film. Further arguments come from the next experiment. For large resistors bulk and contact components of the noise were measured directly. The measurements were performed with an AC cross-correlation technique described in ref. [15]. The cross power spectra SLx (f) of the noise signals on the upper current tap and successive voltage contacts were measured. Then values of SLx (f) at frequency f = 1 Hz were plotted versus position, x/L, of the voltage contacts; x is the distance of the voltage contact from the bottom current tap, L is the length of the resistor. As shown in Fig. 10, values of SLx (1 Hz) measured at central
Fig. 10. Cross power spectral density SLx (1 Hz) versus relative length x/L measured for large resistors.
Measurements of 1/f noise show that in RX-202A sensors the noise increases with temperature decreasing as T−2.25 in temperature range below 4 K. Such dependence was also observed in RuO2 + glass thick film resistors. This phenomenon limits the sensors’ resolution to 0.01% at the lowest temperatures. The increase of the noise intensity is the inherent feature of the thermo-sensitive (resistive) material of the sensor. Acknowledgment The work was supported by the Polish Ministry of Science and Higher Education through the research project no. 3 T11B 071 29. References [1] P. Ptak, A. Kolek, Z. Zawi´slak, A.W. Stadler, K. Mleczko, Noise resolution of RuO2 based resistance thermometers, Rev. Sci. Instrum. 76 (2005) 014901–014906. [2] A. Kolek, P. Ptak, Z. Zawi´slak, A.W. Stadler, K. Mleczko, Low frequency noise resolution of Ru-based low-temperature thick film sensors, in: Proceedings of the International AIP Conference on Noise and Fluctuations, Salamanca, Spain, 2005, pp. 163–166. [3] http://www.lakeshore.com/temp/sen/rrtd.html. [4] A. Raab, C. Jung, P. Dullenkopf, Current noise of trimmed thick-film resistors: measurement and simulation, Microelectron. Int. 15 (1998) 15–22. [5] A. Peled, Y. Zloof, S.O. Kasap, Comparison of excess 1/f noise spectra in trimmed and untrimmed thick film resistors, Int. J. Electron. 87 (2000) 1–9. [6] J.G. Rhee, T.M. Chen, Contact noise in thick film resistors, Solid State Technol. 21 (1978) 59–62. [7] A. Masoero, B. Morten, M. Prudenziati, A. Stepanescu, Proceedings of the 10th International Conference on Noise in Physical Systems, Budapest, Hungary, 1990, pp. 561–564. [8] J.H. Scofield, ac method for measuring low-frequency resistance fluctuation spectra, Rev. Sci. Instrum. 58 (1987) 985–993. [9] D.S. Holmes, S.S. Courts, Resolution and accuracy of cryogenic temperature measurements, Temperature: its Measurement and Control in Science and Industry, vol. 6, J.F. Schooley A/P, New York, 1992, pp. 1225–1230. [10] LakeShore Model 370 AC Resistance Bridge, User’s manual, ver. 1.1, 2001. [11] A. Cattaneo, M. Cocito, F. Forlani, M. Prudenziati, Influence of the metal migration from screen-and-fired terminations on electrical characteristics of thick-film resistors, Electrocomp. Sci. Technol. 4 (1977) 205–211. [12] T. Yamaguchi, Y. Nakamura, Sol-gel processing and conduction mechanism of RuO2 -glass thick-film resistors, J. Am. Ceram. Soc. 78 (1995) 1372–1374. [13] K. Bobran, A. Kusy, J. Phys. Condens. Matter 3 (1991) 7015. [14] F.N. Hooge, 1/f noise is no surface effect, Phys. Lett. A 29 (1969) 139–140. [15] A. Kolek, P. Ptak, K. Mleczko, A. Wrona, A further improvement of the measuring technique of bulk and contact components of resistance noise,
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Biographies Piotr Ptak received BS and MS degree in technical physics from AGH University of Science and Technology in Krak´ow in 1998 and 1999, respectively. He is an assistant researcher (PhD candidate) in Department of Electronics Fundamentals in Faculty of Electrical and Computer Engineering, Rzesz´ow University of Technology. Andrzej Kolek graduated from Department of Electrical Engineering, Electronics and Automatics, AGH University of Science and Technology in Krak´ow. He received his PhD degree from the Department of Electronics, Warsaw University of Technology in 1990 and Dsc degree from Department of Electronics, Wrocław University of Technology in 1998. Specializes in electronics of inho-
mogeneous materials (thick films) and phenomenon of low frequency noise. He is the author of over 30 journal papers. Currently the head of the Department of Electronics Fundamentals, and vice dean of the Faculty of Electrical and Computer Engineering, Rzesz´ow University of Technology. Zbigniew Zawi´slak graduated from Rzesz´ow University of Technology in 1997. Currently he works as R&D engineer in Department of Electronics Fundamentals, Rzesz´ow University of Technology. Adam W. Stadler is academic teacher in Department of Electronics Fundamentals, Rzeszow University of Technology. He received his PhD from Warsaw Institute of Electron Technology in 1996. His research interest is electrical transport mechanisms in disordered materials. Krzysztof Mleczko received PhD degree from Rzesz´ow University of Technology in 2003. He is an academic teacher in Department of Electronics Fundamentals, Rzesz´ow University of Technology. His research interest is electrical transport mechanisms in disordered materials.