# Composition Dependence of Transport Properties in YSi Thermometric Films

L- H- H. To, F. Pallier, L. Bergé, L. Dumoulin, S. Marnieros, C.

Marrache-Kikuchi, Shamashis Sengupta

► To cite this version:

L- H- H. To, F. Pallier, L. Bergé, L. Dumoulin, S. Marnieros, et al. Composition Dependence of Transport Properties in YSi Thermometric Films. Journal of Low Temperature Physics, 2022, 209 (5-6), pp.1104-1110. 10.1007/s10909-022-02717-9. hal-03884808

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# *Composition-dependence of transport properties in YSi thermometric films*

L. H. H. To, S. Sengupta, F. Pallier, L. Bergé, L. Dumoulin, S. Marnieros, C. Marrache-Kikuchi

IJCLab, Université Paris-Saclay, 91400 Orsay, France

**Abstract:**

We report on the low-temperature study of thick YSi films that are of potential interest for applications in low temperature thermometry. Thick amorphous $Y_xSi_{1-x}$ films (300 to 600 Å) have been synthesized, and the temperature variation of their resistance studied as a function of the stoichiometry of the alloy. These measurements show that $Y_xSi_{1-x}$ can exist in various states: insulating, metallic and superconducting. We have determined a preliminary phase diagram for the 3D $Y_xSi_{1-x}$ alloy. On the superconducting side, the $Y_{30}Si_{70}$ film shows a sharp transition at about 1K. This superconducting compound therefore is a promising candidate for Transition-Edge Sensors (TES).

Understanding the influence of disorder on the electronic transport properties is still an open question in the field of condensed matter physics. Indeed, in disordered materials, there is, at low temperature, a competition between disorder-induced quantum interferences (eventually leading to the localization of charge carriers [1]), the enhancement of Coulomb interactions due to impaired screening [2], the reduction of electron-phonon interactions with temperature (which tend to favor delocalized states, thanks to a decrease in the scattering rate [3]), and, in some cases, superconductivity. As a consequence, disorder is known to be one of the parameters that can induce a transition from a superconducting to a metallic ground state (SMT) [4,5] or a metal-insulator transition (MIT) [6].

In addition, over the past decades, disordered materials, such as TiN [7], NbSi [8], NbN [9], gr-Al [10] etc. have been used as thermal or radiation sensors for numerous astrophysical or astroparticle applications. If superconducting, they can be used as Transition Edge Sensors (TES) [11], and their large kinetic inductances, resulting precisely from their large normal state resistance, have made these materials particularly interesting for Kinetic Inductance Detectors (KIDs) [12]. In the insulating regime, disordered systems have also been widely used as resistive thermal sensors [13,14].
In this paper, we present the low temperature electronic transport properties of another disordered material, a-$Y_xSi_{1-x}$ (YSi). The ground state of this material, like similar alloys, such as a-$Nb_xSi_{1-x}$ or NbN, is controlled both by its stoichiometry x and by the film thickness d, rendering it extremely versatile for applications. Actually, electronic transport in this compound has previously been studied at low temperature, but investigations mainly focused on the metal-to-insulator transition at $x \approx 0.15$ [15-20]. Moreover, thermal transport and specific heat measurements have been performed, showing excess vibrational modes [21,22], and no sign of superconductivity above 100 mK for $x = 0.65$. To the best of our knowledge, this paper is the first report of superconducting YSi films [22,23]. Through the control of both x and d, the surface impedance of the film can be tuned to match the vacuum impedance $Z = 337\Omega/\square$ for maximum photon absorption [24]. Moreover, we expect that it should have a lower specific heat than any Nb-based alloy, due to a lower nuclear specific heat [25]. When these films are used as thermal sensors, the typical change in temperature $\Delta T$ to an energy input E is governed by the specific heat $C_V$: $\Delta T = E/C_V$, so that YSi should be a promising candidate for these applications.

The samples were synthesized under ultrahigh vacuum by e-gun co-deposition. Yttrium and Silicon were simultaneously evaporated from separate sources using two e-guns. The films were patterned via mechanical masks. The film thickness *d* was typically chosen between 300 and 600 Å, and the film composition was varied in the range of 0.05 < *x* < 0.32, and controlled in-situ by a pair of piezoelectric quartz microbalance for each source, allowing for a separate control of the deposition rate [26].

Three types of samples were simultaneously synthesized. One, on a sapphire substrate, was dedicated to transport measurements, whereas the two others, respectively on a Si and an a-C substrate, were for additional characterization. The sample deposited on the Si substrate was used to check ex-situ the film composition and thickness by Rutherford BackScattering (RBS). *x* and *d* determined by this method agreed with the nominal composition and thickness within $\Delta x \sim \pm 0.7\%$. The sample deposited on the a-C substrate was dedicated to structural characterization, by Transmission Electron Microscopy (TEM) and Atomic Force Microscopy (AFM).

AFM measurements, performed systematically on all samples, confirmed the sample thickness measured by the in-situ quartz microbalance and ex-situ by RBS. Moreover, the sample thickness was homogeneous on the size of the samples (a few mm) and the surface roughness was determined to be smaller than 4 Å. Preliminary TEM measurements have shown that the films were amorphous, with no observable crystallite on the scale of 2 nm.

To perform the electronic transport measurements, our samples were measured in a dilution refrigerator which allows to continuously measure samples down to 10 mK. Resistance measurements were performed using a dedicated low noise TRMC2 resistor bridge providing a square wave signal at 25 Hz. Specific care was taken not to heat the
samples through the measurements.

We are here considering 3D films, i.e., films in which the thickness is large compared to all other relevant lengths. For insulating samples, the localization length should be of the order of 100-200 Å [17]. For metallic films, the reported coherence lengths are of the order of 600 Å at 450 mK [17]. We will also see that the superconducting coherence length [27] for our superconducting samples exceeds the film thickness.

The temperature dependence of the resistance for the various $Y_xSi_{1-x}$ samples is presented in Fig. 1. As can be seen, the $R(T)$ behavior strongly depends on the composition $x$ of a $Y_xSi_{1-x}$. The extrapolation to zero temperature defines the system's ground state. YSi can therefore exist in the superconducting, metallic or insulating state, as $x$ decreases. The MIT occurs between $x = 10\%$ and $x = 15\%$, similar to what has previously been reported [15], and the SMT at about $x = 21\%$.

On the superconducting side, the critical temperature $T_c$ increases as $x$ increases in the probed composition range ($T_c = 672$ mK for $x = 26\%$ and $T_c = 932$ mK for $x = 32\%$). However, we expect this trend not to hold for larger $x$, since pure yttrium is not superconducting. This issue will be the subject of future investigations. For these two samples, the superconducting coherence length at zero temperature can be calculated in the dirty limit: $\xi_0 = \sqrt{\frac{\hbar v_F}{1.76 k_B T_c}} l$, where $l$ is the mean free path which can be taken to be of the order of the interatomic distance $l \approx 5$ Å in these amorphous films, the Fermi velocity can be estimated from the published diffusion constant $D = (1/3) v_F l = 4 \times 10^{-5} \text{ m}^2\cdot\text{s}^{-1}$ [17]: $v_F \approx 2 \times 10^5 \text{ m}\cdot\text{s}^{-1}$. From this, we can estimate that $\xi_0 \approx 270$ Å for $x = 26\%$, and $230$ Å for $x = 32\%$, smaller than the sample thickness. The $x = 26\%$ sample presents a sharp transition of width $\Delta T \sim 10$ mK for $T_c = 672$ mK. This would yield a sensitivity of $\alpha = \frac{1}{R} \times \frac{dR}{dT} \approx 100$, which is comparable to state-of-the-art TES [28,29].

For applications, the electron-phonon coupling is an important parameter to consider, as it is for theoretical reasons [30]. It plays a crucial role in the performances of hot electron detectors [31], single photon detectors [32,33], kinetic inductance detectors [34], or heat flow measurements [35]. In thermometric thin films, the relaxation time back to the bath's temperature after an energy deposition is typically $\tau_{e-ph} = \frac{c_V}{G_{e-ph}}$, where $G_{e-ph} = \Gamma_{e-ph}\beta T^{\beta-1}$ is the electron-phonon coupling constant, $T$ the temperature and $\beta$ a constant of the order of 5 [25,36,37]. In the following, we have assumed $\beta = 5$. Moreover, $G_{e-ph}$ can also limit the Noise Equivalent Power NEP = $\sqrt{4k_B T^2 G_{e-ph}}$ [8].

To estimate the value of the electron-phonon coupling in $Y_xSi_{1-x}$, we used the hot electron model. The central assumption of this model is that, at high electrical power and at low temperatures, electrons can thermally decouple from phonons. In a steady state, for disordered materials, we could obtain $\Gamma_{e-ph}$ by solving the heat-balance equation [37]:
$$P = \Gamma_{e-ph} \Omega (T_{el}^{\beta} - T_{ph}^{\beta}) \quad \dots \dots (1)$$

where $\Omega$ is the sample volume, $T_{el}$ is the electronic temperature, and $T_{ph}$ is the temperature of the phonon bath. This equation implies that the electrical power input $P$ due to the measurement eventually relaxes towards the phonons. In our case, the heat flow through the phonons and then the copper holder, with which the sample is in good thermal contact, dominates over the heat flow through the leads which are made of Niobium (these are superconducting typically below 8 K) [38].

<figure><img src="image_2.png" /><figcaption>**Fig. 1.** Resistance as a function of temperature for a-Y$_{x}$Si$_{1-x}$ films obtained by a modification of the composition x. Inset: Schematic representation of a typical sample: the YSi films are deposited on top of Nb electrodes, themselves connected to gold pads, and wire-bonded from there to the sample holder [26]. The typical sample length is of 14 mm, and its width 1 mm.</figcaption></figure>
<figure><img src="image_3.png" /><figcaption>**Fig. 2.** Measurement of the R(T) characteristics at different AC (25 Hz) bias voltages, for the 300 A°-thick α-Y₂₀Si₈₀ film. Inset: Electrical power P per unit volume as a function of Tₑl⁵ – Tₚh⁵ for different temperatures. The slope of this curve gives the electron phonon coupling constant Γₑ⁻ₚh. The typical value of 7x10⁷ W/m³. K⁵ is indicated by the dashed line.</figcaption></figure>

We used the method described in reference [25] to extract Γₑ⁻ₚh using equation (1), for the Y₂₀Si₈₀ sample (Fig. 2). Let us first note that the resistance R only depends on Tₑl. When measuring the resistance R at very low bias voltage (10 μV), we assumed that the electrons and the phonons were at thermal equilibrium. This is confirmed by the fact that doubling the bias voltage does not affect the measurement: P does not heat the electron bath. Then, we performed the same measurement at higher bias (40 and 80 μV). The phonon temperature was then assumed to be the same as the substrate's, given by the cryostat's thermometer. The electronic temperature was derived from the resistance measurement, using the curve at low bias to convert the resistance into Tₑl. By this procedure, we found an electron-phonon coupling coefficient that is almost temperature-independent below 50 mK, and which value is of 6-8 ×10⁷ W/m³. K⁵ which is weaker than values in NbSi (15 ×10⁷ W/m³. K⁵) [25]. This is promising for the application of YₓSi₁₋ₓ thin films to thermometry, and could further improve the performances of resistive thermometers based on these alloys below 10⁻¹² W/Hz¹/² at temperatures of the order of 20 mK. As an element of comparison, Planck's CMB background power was of the order of the pW [25]. For samples farther in the insulating regime, the value of Gₑ⁻ₚh could further be decreased.
Conclusions

During this work, we have studied the transport properties of amorphous YₓSi₁₋ₓ films at low temperatures in order to establish the first preliminary phase diagram in 3D. The R(T) characteristics on amorphous YSi samples have already shown interesting properties: tunability, sharp superconducting transitions, low electron-phonon coupling, which makes it a potential candidate for applications as low temperature sensor (TES, thermoresistive sensors and sensitive radiation sensors). To further assess the potentiality of this material, we plan to continue investigating its properties at larger x and lower d. Indeed, decreasing d should allow to decrease C_v without impairing the material's tunability as well as the corresponding electron-phonon decoupling [18].

**Acknowledgements:** This work has been partially funded by the French National Agency (ANR-19-CE30-0014-03).

References:

1. E. Abrahams, P.W. Anderson, D.C. Licciardello, and T.V. Ramakrishnan, Phys. Rev. Lett. 42, 673-676, (1979), DOI:10.1103/PhysRevLett.42.673.

2. M. Ma and P.A. Lee, Phys. Rev. B 32, 5658-5667, (1985), DOI:10.1103/PhysRevB.32.5658.

3. N.W. Ashcroft and N.D. Mermin, Solid state physics, (1976), New York: Holt, Rinehart and Winston.

4. S.L. Sondhi, S.M. Girvin, J.P. Carini and D. Shahar, Rev. Mod. Phys. 69, 315-333, (1997), DOI:10.1103/RevModPhys.69.315.

5. V.F. Gantmakher and V.T. Dolgopolov, Physics-Uspekhi 53, 1-49, (2010), DOI:10.3367/ufne.0180.201001a.0003.

6. B.I. Shklovskii and A.L. Efros, Electronic Properties of Doped Semiconductors, (1998). Springer-Verlag.

7. S. Doyle, P. Mauskopf, J. Zhang, A. Monfardini, L. Swenson, Jochem J.A. Baselmans, Stephen J.C. Yates and M. Roesc, Proc. SPIE - The International Society for Optical Engineering 7741, 77410M, (2010), DOI:https://doi.org/10.1117/12.857341.

8. S. Marnieros, L. Dumoulin, A. Benoit, L. Bergé, P. Camus, S. Collin, A. Juillard and C.A. Marrache-Kikuchi, J. Phys.: Conf. Ser. 150, 012027, (2009), DOI:10.1088/1742-6596/150/1/012027.

9. W. Miao, W. Zhang, K.M. Zhou, Z.H. Lin, Q.J. Yao, Y. Delorme, R. Lefevre and S.C Shi, Proc. SPIE, Infrared, Millimeter Wave, And Terahertz Technologies 7854, 70-75, (2010), DOI:10.1117/12.871759.

10. F. Levy-Bertrand, T. Klein, T. Grenet, O. Dupré, A. Benoit, A. Bideaud, O. Bourrion, M. Calvo, A. Catalano, A. Gomez, J. Goupy, L. Grunhaupt, U.V. Luepke, N. Maleeva, F. Valenti, I.M. Pop and A. Monfardini, Phys. Rev. B 99, 094506, (2019), DOI:10.1103/PhysRevB.99.094506.
11. K. Irwin and G. Hilton, Transition-Edge Sensors. In: Enss C. (eds) Cryogenic Particle Detection. Topics in Applied Physics 99, 63–150, (2005), Springer, Berlin, Heidelberg, DOI:https://doi.org/10.1007/10933596 3.

12. J. Baselmans, J Low Temp Phys 167, 292–304, (2012),
DOI:https://doi.org/10.1007/s10909-011-0448-8.

13. L. Dumoulin, L. Bergé, J. Lesueur et al., J Low Temp Phys 93, 301–306, (1993), DOI:https://doi.org/10.1007/BF00693437.

14. A. Ricci, A. Garcia-Fornes, D. Weyns, J. Such, J. Alberola, M. Pechoucek, V. and Botti, Proceedings of The Third International Workshop on INFRASTRUCTURES AND TOOLS FOR MULTIAGENT SYSTEMS ITMAS, (2012), DOI:10.13140/2.1.2049.7285.

15. F. Hellman, M.Q. Tran, A.E. Gebala, E.M. Wilcox and R.C. Dynes, Phys. Rev. Lett. 77, 4652–4655, (1996), DOI:https://doi.org/10.1103/PhysRevLett.77.4652.

16. P. Hernandez, F. Ladieu, M. Sanquer and D. Mailly, Physica B: Condensed Matter 194-196, 1141-1142, (1994), DOI: https://doi.org/10.1016/0921-4526(94)90900-8.

17. P. Hernandez and M. Sanquer, Phys. Rev. Lett. 68, 1402–1405, (1992), DOI:10.1103/PhysRevLett.68.1402.

18. F. Ladieu, M. Sanquer and J.P. Bouchaud, Phys. Rev. B 53, 973–976, (1996), DOI:10.1103/PhysRevB.53.973.

19. F. Ladieu, D. L'Hote and R. Tourbot, Phys. Rev. B 61, 8108–8118, (2000), DOI:10.1103/PhysRevB.61.8108.

20. M. Sanquer, R. Tourbot and B. Boucher, Europhysics Letters 7, 635–640, (1988), DOI:https://doi.org/10.1209/0295-5075/7/7/011.

21. B.L. Zink, R. Islam, D.J. Smith. and F. Hellman, Phys. Rev. B 74, 205209, (2006), DOI:https://doi.org/10.1103/PhysRevB.74.205209.

22. T. Satoh and T. Otsuka, Physics Letters 20, 565-566, (1966), DOI:https://doi.org/10.1016/0031-9163(66)91115-2.

23. B.T. Matthias, E. Corenzwit and W.H. Zachariasen, Phys. Rev. 112, 89, (1958), DOI: https://doi.org/10.1103/PhysRev.112.89.

24. S. Marnieros, P. Ade, J.G. Alberro et al., J Low Temp Phys 199, 955-961, (2020), DOI:https://doi.org/10.1007/s10909-019-02304-5.

25. S. Marnieros, L. Bergé, A. Juillard and L. Dumoulin, Phys. Rev. Lett. 84, 2469–2472, (2000), DOI: 10.1103/PhysRevLett.84.2469.

26. V. Humbert, Etude des états fondamentaux dans des systèmes supraconducteurs désordonnés de dimension 2, PhD Thesis, Université Paris-Saclay
URL:http://www.theses.fr/2016SACLS149.

27. M. Tinkham, Introduction to superconductivity, (2004), Mineola, N.Y: Dover Publications.

28. S. Marnieros, Détecteurs cryogéniques et leurs applications en Astrophysique et Astroparticules, HDR, Université Paris Sud (2014), URL:http://hal.in2p3.fr/tel-01088881.

29. F. Giazotto, T.T. Heikkila, A. Luukanen, A.M. Savin and J.P. Pekola, Rev. Mod. Phys. 78, 217–274, (2006), DOI:https://link.aps.org/doi/10.1103/RevModPhys.78.217.

30. B.L. Altshuler, V.E. Kravtsov, I.V. Lerner and I.L. Aleiner, Phys. Rev. Lett. 102, 176803, (2009), DOI:https://doi.org/10.1103/PhysRevLett.102.176803.
31. B.S. Karasik, A.V. Sergeev and M.E. Gershenson, AIP Conference Proceedings 605, 75-78, (2002), DOI:https://doi.org/10.1063/1.1457599.

32. B.S. Karasik, S.V. Pereverzev, A. Soibel, D.F. Santavicca, D.E. Prober, D. Olaya and M.E. Gershenson, Applied Physics Letters 101, 052601, (2012), DOI:https://doi.org/10.1063/1.4739839.

33. P.J. De Visser, S.A.H. De Rooij, V. Murugesan, D.J. Thoen, J.J.A. and Baselmans Phys. Rev. Applied 16, 034051, (2021), DOI:https://doi.org/10.1103/PhysRevApplied.16.034051.

34. J. Baselmans, J Low Temp Phys 167, 292-304, (2012), DOI:https://doi.org/10.1007/s10909-011-0448-8.

35. R. Forster and E. Gmelin, Review of Scientific Instruments 67, 4246-4255, (1996), DOI:https://doi.org/10.1063/1.1147576.

36. F.C. Wellstood, C. Urbina and J. Clarke, Phys. Rev. B 49, 5942-5955, (1994), DOI:https://doi.org/10.1103/PhysRevB.49.5942.

37. N. Wang, F.C. Wellstood, B. Sadoulet, E.E. Haller, J. and Beeman, Phys. Rev. B 41, 3761-3768, (1990), DOI:10.1103/PhysRevB.41.3761.

38. M. Biassoni, C. Brofferio, P. Carniti et al., J Low Temp Phys 206, 80-96, (2022), DOI:https://doi.org/10.1007/s10909-021-02639-y.