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Low temperature NbSi thin film thermometers on Silicon Nitride membranes for bolometer applications
Nuclear Instruments and Methods in Physics Research A 444 (2000) 419}422
Low temperature NbSi thin "lm thermometers on Silicon Nitride membranes for bolometer applications Ph. Camus *, L. BergeH , L. Dumoulin, S. Marnieros, J.P. Torre Institut d'Astrophysique Spatiale, Bat 121, 91405 Orsay Cedex, France CNRS/IN2P3-Centre de Spectrome& trie Nucle& aire et de Spectrome& trie Mole& culaire, Bat 108, 91405 Orsay Cedex, France CNRS-Service d'Ae& ronomie, BP3, 91371 Verrie% res-le-Buisson Cedex, France
Abstract We report the design of amorphous NbSi thin "lm bolometer thermometers on Silicon Nitride membranes. Due to the low-thermal conductivity of Si N , this material has several applications in millimeter wavelength bolometers and microcalorimetry. Compared to NTD-Ge thermometers, similar sensitivities are obtained with a 50 times lesser volume. The smallest realized "lms have a rectangular surface (100;400 lm) and are 100 nm thick. Optimization of the thermometer shape, NbSi composition and electrical material contact is discussed. The goal of this development is to manufacture a complete array of bolometers by photolithography techniques. 2000 Elsevier Science B.V. All rights reserved.
1. NbSi thermometric layer Nb Si alloys exhibit a metal}insulator V \V transition (MIT) at a composition which depends on the manufacturing process. The "lms are deposited by co-evaporation of pure Nb and Si under ultra high vacuum ((10\ mbar) conditions and the MIT is obtained for a composition of around x"9% [1}3]. The thermometers are designed to have an impedance of 10 M), optimized to a J-FET ampli"er. The alloy resistivity is primarily dependent on the composition, but also on the annealing temperature (100}1503C) [2]. This property can be used to reduce the composition scattering e!ect on resist-
* Corresponding author. Tel.: #33-1691-545-90; fax: #33169-155-268. E-mail address: [email protected] (Ph. Camus).
ance. Compositions below 9% Nb were used where the alloy behaves like an Anderson insulator [1}3]. At low bias power, the electrical behaviour can be adequately analysed within the framework of MIT theories. Over a limited temperature and composition range, the resistivity is well described by a law o"o exp(¹ /¹)L, where o and n are slowly vary ing with alloy composition. The sensitivity de"ned by A "!d ln o/d ln ¹"n ln(o/o ) depends only on the resistivity. The correlation between A and the resistivity obtained from several samples composition between 7}8.5% and at 100}500 mK is in full agreement with previous measurements [3] made on sapphire substrates (Fig. 1). To optimize the thermometer shape, non-ohmic e!ects must be considered. Numerous analyses of previous experiments showed that the resistivity of NbSi alloys can be described by an electron} phonon decoupling model P"
0168-9002/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 9 0 0 2 ( 9 9 ) 0 1 4 1 4 - X
SECTION VIII.
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Ph. Camus et al. / Nuclear Instruments and Methods in Physics Research A 444 (2000) 419}422
where P ( , P" 5gX¹
Fig. 1. Correlation between the sensitivity under low bias power and the resistivity (the "lm geometry is 100 lm;400 mm and 100 nm thick).
o exp+¹ /¹(1!q ¸ E/2k .¹),L [3], where X *-! is the "lm volume, q the electron charge, E the electric "eld, k Boltzmann's constant and ¸ a characteristic localization length. The elec*-! trical "eld e!ect is classically described by o(E, ¹)"o(0, ¹) exp(!q ¸ E/k ¹) [2,4], where ¸ is a characteristic length for the hopping pro cess. At low electrical "eld (E;k ¹/q ), the two lengths are related by ¸ "¸ ) n/2 ) (¹ /¹)L. *-! 2. Optimization Due to the combined e!ect of the electron} phonon coupling and the electrical "eld, there is an optimal bias power value. Considering only the Johnson noise contribution, the equivalent substrate temperature noise is given by
4k ¹ (K/(Hz). AP ( Where A is the sensitivity of the resistivity relative to the substrate temperature and P the bias ( power. A simple calculation gives a model for the sensitivity A for a given bias power in the case of constant bias current: NET"
¹ *o A C A"! " , o *¹ 1#(5#A )P C
2k ¹E e" , q ¸ *-! 1!2e A "A . C eA #(1!e)\L There is a strong in#uence of the electrical "eld on sensitivity. The main parameter available to optimize the "lm is the ratio of the electrodes length (a) to the interelectrode distance (l). The thickness (e) has the same in#uence as the electrodes length. To avoid a 2D hopping process, the thickness must be maintained well above the hopping length (e<¸ , i.e. 10}20 nm). Table 1 lists the ideal performances of di!erent geometries and temperatures. As con"rmed by parametric studies for a 10 M) "lm, there is a #at optimum for a/l between 1 and 10 if e"100 nm. An increase of a/l, or thickness, is favourable at low temperature (100 mK). The optimal bias power increases from P /g ) ¹"0.08 at ( 100 mK to 0.20 at 300 mK and the e!ective sensitivity under polarization is 2.5}3.0. Heat capacity is an important parameter in millimeter wavelength bolometer applications where NTD-Ge thermometers yield the best results. Compared to NbSi layers, their performance is limited by the same variable-range hopping conduction process and non-ohmic e!ects [4]. A common value for the electron}phonon coupling in NTDGe at 100 mK is 10}20 W/Kcm, while around 100 W/Kcm in NbSi. The volume required for the same optimal bias power with a NbSi layer is 100 times less at 100 mK. NbSi has a rather constant speci"c heat (20;10\J/K/cm) between 100}300 mK, attributed to Nb nuclear moments and NbSi localized magnetic moments [2]. A common estimation for NTD-Ge heat capacity is 10\ T J/K/cm [4], leading to approximately the same heat capacity for a given power. The main di!erence is the volume required, which is precisely why NbSi is well adapted to thin "lm thermometric layers. 3. Thermometers construction and results Rotation of the supporting system during coevaporation assured a spatial homogeneity. Gold
Ph. Camus et al. / Nuclear Instruments and Methods in Physics Research A 444 (2000) 419}422
421
Table 1 Ideal performance of thermometric layer under optimal bias power
M-Type M-Type F-Type F-Type
1 (l)
e (nm)
a/l
¹ (mK)
A
NET (nK/Hz )
P (pW)
P/P (%)
100 100 400 400
300 100 300 100
4 4 4.25 4.25
100 300 100 300
3.08 2.41 3.08 2.39
92 44 22 11
0.69 130 11.7 2200
7.2 17 7.2 17
Note: e"100 nm, g"80 W/K/cm, ¸
*-!
"10 nm, R"10 M), P "g ) T
electrodes of 100}150 nm thickness have been used to "t the thermal link to the speci"c need in bolometers applications. Nb superconducting electrodes were also used to achieve the highest thermal insulation. Two thermometers were simultaneously evaporated, one 100;400 lm (M-Type) at the center of a 4 or 5 mm square Si N mem brane (100 nm thick), and one 400;1700 lm (F-Type) on the supporting Si frame. Gold wires were used for electrical contacts and thermalization of the frame with the cryostat. A DC method was used to determine the thermal response under low bias power (P(0.1 pW) in the required temperature range. Due to the high thermal coupling, the <(I) response of thermometers deposited on the frame were used to "t the g and ¸ parameters. The results, ranging between *-! 80}200 W/K/cm and 3}15 nm, are in good agreement with previous measurements made with sapphire substrates [3]. From <(I) responses of thermometers deposited on the membrane, an estimation of the local phonon temperature is obtained. Except for the lowest temperatures (100}150 mK), non-ohmic effects are dominated by the thermal link between the centre of the membrane and the frame. The latter is supposed to be at the cryostat temperature. The in#uence of the electrode material was investigated with 4 mm square membranes. The thermal conductance de"ned by dP/d¹ (P is the bias power and ¹ the phonon temperature at the centre of the membrane) is given in Fig. 2 for various samples. With gold electrodes, the thermal conductance is dominated by a metallic conduction-type (d ln P/d ln ¹+2). The gold contribution behaviour is roughly proportionnal to the electrode
Fig. 2. Thermal conductance between the thermometer and the outer frame (open symbols for 4;4 mm membrane; "lled symbols for 5;5 mm).
thickness (100}150 nm). Niobium electrodes were used to estimate the amorphous membrane contribution. The estimated contribution of phonon conduction in superconducting electrodes is negligible ((1%). A comparison is given for two membranes sizes (4 and 5 mm). The membrane conductance is compared to a theoretical estimate based on a thermal conductivity k"14.5;10\ T W/cm/K [5] (Fig. 2). The temperature dependence and the in#uence of the membrane size are not explained by this di!usive model. The conductance is signi"catively higher at 300 mK (800 pW/K for a 5 mm membrane). A millimeter wavelength bolometer made on such a membrane would be limited by phonon noise and adapted for medium background power (&100 pW) at 300 mK, which is adequate for selected ground-based applications.
SECTION VIII.
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Ph. Camus et al. / Nuclear Instruments and Methods in Physics Research A 444 (2000) 419}422
Acknowledgements This work has been partially funded under EEC contract TMR-ERBFMRXCT980167 and supported by an ESA doctoral fellowship.
References [1] L. Dumoulin, et al., Nucl. Instr. and Meth. 370 (1995) 211. [2] S. Marnieros, Phy. B 259}261 (1999) 826.
[3] S. Marnieros, Ph.D. Thesis, UniversiteH Paris-Sud France, 1998. [4] T.W. Kenny, et al., Phy. Rev. B. 39 (12) (1989) 8476. [5] M.M. Leivo, J.P. Pekola, Appl. Phy. Lett. 72 (11) (1998) 1305.
Low temperature NbSi thin "lm thermometers on Silicon Nitride membranes for bolometer applications Ph. Camus *, L. BergeH , L. Dumoulin, S. Marnieros, J.P. Torre Institut d'Astrophysique Spatiale, Bat 121, 91405 Orsay Cedex, France CNRS/IN2P3-Centre de Spectrome& trie Nucle& aire et de Spectrome& trie Mole& culaire, Bat 108, 91405 Orsay Cedex, France CNRS-Service d'Ae& ronomie, BP3, 91371 Verrie% res-le-Buisson Cedex, France
Abstract We report the design of amorphous NbSi thin "lm bolometer thermometers on Silicon Nitride membranes. Due to the low-thermal conductivity of Si N , this material has several applications in millimeter wavelength bolometers and microcalorimetry. Compared to NTD-Ge thermometers, similar sensitivities are obtained with a 50 times lesser volume. The smallest realized "lms have a rectangular surface (100;400 lm) and are 100 nm thick. Optimization of the thermometer shape, NbSi composition and electrical material contact is discussed. The goal of this development is to manufacture a complete array of bolometers by photolithography techniques. 2000 Elsevier Science B.V. All rights reserved.
1. NbSi thermometric layer Nb Si alloys exhibit a metal}insulator V \V transition (MIT) at a composition which depends on the manufacturing process. The "lms are deposited by co-evaporation of pure Nb and Si under ultra high vacuum ((10\ mbar) conditions and the MIT is obtained for a composition of around x"9% [1}3]. The thermometers are designed to have an impedance of 10 M), optimized to a J-FET ampli"er. The alloy resistivity is primarily dependent on the composition, but also on the annealing temperature (100}1503C) [2]. This property can be used to reduce the composition scattering e!ect on resist-
* Corresponding author. Tel.: #33-1691-545-90; fax: #33169-155-268. E-mail address: [email protected] (Ph. Camus).
ance. Compositions below 9% Nb were used where the alloy behaves like an Anderson insulator [1}3]. At low bias power, the electrical behaviour can be adequately analysed within the framework of MIT theories. Over a limited temperature and composition range, the resistivity is well described by a law o"o exp(¹ /¹)L, where o and n are slowly vary ing with alloy composition. The sensitivity de"ned by A "!d ln o/d ln ¹"n ln(o/o ) depends only on the resistivity. The correlation between A and the resistivity obtained from several samples composition between 7}8.5% and at 100}500 mK is in full agreement with previous measurements [3] made on sapphire substrates (Fig. 1). To optimize the thermometer shape, non-ohmic e!ects must be considered. Numerous analyses of previous experiments showed that the resistivity of NbSi alloys can be described by an electron} phonon decoupling model P"
0168-9002/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 9 0 0 2 ( 9 9 ) 0 1 4 1 4 - X
SECTION VIII.
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Ph. Camus et al. / Nuclear Instruments and Methods in Physics Research A 444 (2000) 419}422
where P ( , P" 5gX¹
Fig. 1. Correlation between the sensitivity under low bias power and the resistivity (the "lm geometry is 100 lm;400 mm and 100 nm thick).
o exp+¹ /¹(1!q ¸ E/2k .¹),L [3], where X *-! is the "lm volume, q the electron charge, E the electric "eld, k Boltzmann's constant and ¸ a characteristic localization length. The elec*-! trical "eld e!ect is classically described by o(E, ¹)"o(0, ¹) exp(!q ¸ E/k ¹) [2,4], where ¸ is a characteristic length for the hopping pro cess. At low electrical "eld (E;k ¹/q ), the two lengths are related by ¸ "¸ ) n/2 ) (¹ /¹)L. *-! 2. Optimization Due to the combined e!ect of the electron} phonon coupling and the electrical "eld, there is an optimal bias power value. Considering only the Johnson noise contribution, the equivalent substrate temperature noise is given by
4k ¹ (K/(Hz). AP ( Where A is the sensitivity of the resistivity relative to the substrate temperature and P the bias ( power. A simple calculation gives a model for the sensitivity A for a given bias power in the case of constant bias current: NET"
¹ *o A C A"! " , o *¹ 1#(5#A )P C
2k ¹E e" , q ¸ *-! 1!2e A "A . C eA #(1!e)\L There is a strong in#uence of the electrical "eld on sensitivity. The main parameter available to optimize the "lm is the ratio of the electrodes length (a) to the interelectrode distance (l). The thickness (e) has the same in#uence as the electrodes length. To avoid a 2D hopping process, the thickness must be maintained well above the hopping length (e<¸ , i.e. 10}20 nm). Table 1 lists the ideal performances of di!erent geometries and temperatures. As con"rmed by parametric studies for a 10 M) "lm, there is a #at optimum for a/l between 1 and 10 if e"100 nm. An increase of a/l, or thickness, is favourable at low temperature (100 mK). The optimal bias power increases from P /g ) ¹"0.08 at ( 100 mK to 0.20 at 300 mK and the e!ective sensitivity under polarization is 2.5}3.0. Heat capacity is an important parameter in millimeter wavelength bolometer applications where NTD-Ge thermometers yield the best results. Compared to NbSi layers, their performance is limited by the same variable-range hopping conduction process and non-ohmic e!ects [4]. A common value for the electron}phonon coupling in NTDGe at 100 mK is 10}20 W/Kcm, while around 100 W/Kcm in NbSi. The volume required for the same optimal bias power with a NbSi layer is 100 times less at 100 mK. NbSi has a rather constant speci"c heat (20;10\J/K/cm) between 100}300 mK, attributed to Nb nuclear moments and NbSi localized magnetic moments [2]. A common estimation for NTD-Ge heat capacity is 10\ T J/K/cm [4], leading to approximately the same heat capacity for a given power. The main di!erence is the volume required, which is precisely why NbSi is well adapted to thin "lm thermometric layers. 3. Thermometers construction and results Rotation of the supporting system during coevaporation assured a spatial homogeneity. Gold
Ph. Camus et al. / Nuclear Instruments and Methods in Physics Research A 444 (2000) 419}422
421
Table 1 Ideal performance of thermometric layer under optimal bias power
M-Type M-Type F-Type F-Type
1 (l)
e (nm)
a/l
¹ (mK)
A
NET (nK/Hz )
P (pW)
P/P (%)
100 100 400 400
300 100 300 100
4 4 4.25 4.25
100 300 100 300
3.08 2.41 3.08 2.39
92 44 22 11
0.69 130 11.7 2200
7.2 17 7.2 17
Note: e"100 nm, g"80 W/K/cm, ¸
*-!
"10 nm, R"10 M), P "g ) T
electrodes of 100}150 nm thickness have been used to "t the thermal link to the speci"c need in bolometers applications. Nb superconducting electrodes were also used to achieve the highest thermal insulation. Two thermometers were simultaneously evaporated, one 100;400 lm (M-Type) at the center of a 4 or 5 mm square Si N mem brane (100 nm thick), and one 400;1700 lm (F-Type) on the supporting Si frame. Gold wires were used for electrical contacts and thermalization of the frame with the cryostat. A DC method was used to determine the thermal response under low bias power (P(0.1 pW) in the required temperature range. Due to the high thermal coupling, the <(I) response of thermometers deposited on the frame were used to "t the g and ¸ parameters. The results, ranging between *-! 80}200 W/K/cm and 3}15 nm, are in good agreement with previous measurements made with sapphire substrates [3]. From <(I) responses of thermometers deposited on the membrane, an estimation of the local phonon temperature is obtained. Except for the lowest temperatures (100}150 mK), non-ohmic effects are dominated by the thermal link between the centre of the membrane and the frame. The latter is supposed to be at the cryostat temperature. The in#uence of the electrode material was investigated with 4 mm square membranes. The thermal conductance de"ned by dP/d¹ (P is the bias power and ¹ the phonon temperature at the centre of the membrane) is given in Fig. 2 for various samples. With gold electrodes, the thermal conductance is dominated by a metallic conduction-type (d ln P/d ln ¹+2). The gold contribution behaviour is roughly proportionnal to the electrode
Fig. 2. Thermal conductance between the thermometer and the outer frame (open symbols for 4;4 mm membrane; "lled symbols for 5;5 mm).
thickness (100}150 nm). Niobium electrodes were used to estimate the amorphous membrane contribution. The estimated contribution of phonon conduction in superconducting electrodes is negligible ((1%). A comparison is given for two membranes sizes (4 and 5 mm). The membrane conductance is compared to a theoretical estimate based on a thermal conductivity k"14.5;10\ T W/cm/K [5] (Fig. 2). The temperature dependence and the in#uence of the membrane size are not explained by this di!usive model. The conductance is signi"catively higher at 300 mK (800 pW/K for a 5 mm membrane). A millimeter wavelength bolometer made on such a membrane would be limited by phonon noise and adapted for medium background power (&100 pW) at 300 mK, which is adequate for selected ground-based applications.
SECTION VIII.
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Ph. Camus et al. / Nuclear Instruments and Methods in Physics Research A 444 (2000) 419}422
Acknowledgements This work has been partially funded under EEC contract TMR-ERBFMRXCT980167 and supported by an ESA doctoral fellowship.
References [1] L. Dumoulin, et al., Nucl. Instr. and Meth. 370 (1995) 211. [2] S. Marnieros, Phy. B 259}261 (1999) 826.
[3] S. Marnieros, Ph.D. Thesis, UniversiteH Paris-Sud France, 1998. [4] T.W. Kenny, et al., Phy. Rev. B. 39 (12) (1989) 8476. [5] M.M. Leivo, J.P. Pekola, Appl. Phy. Lett. 72 (11) (1998) 1305.