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  • Letter
  • Open Access

On-chip quantum confinement refrigeration overcoming electron-phonon heat leaks

S. Autti1,*, J. R. Prance1, and M. Prunnila2

  • *Contact author: s.autti@lancaster.ac.uk
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Phys. Rev. B 111, L161404 – Published 14 April, 2025

DOI: https://doi.org/10.1103/PhysRevB.111.L161404

Abstract

Circuit-based quantum devices rely on keeping electrons at millikelvin temperatures. Improved coherence and sensitivity as well as discovering new physical phenomena motivate pursuing ever lower electron temperatures, accessible using on-chip cooling techniques. Here we show that a two-dimensional electron gas (2DEG), with the sub-band populations manipulated using gate voltages, works as an on-chip cooler only limited by a fundamental phonon heat leak. The 2DEG can, for example, be realized in a silicon-based double-gate complementary metal oxide semiconductor (CMOS) transistor. A single-shot 2DEG cooler can reduce the electron temperature by a factor of 2 with a hold time up to a second, achieved by expanding the electron gas into an additional sub-band. Integrating an array of such coolers—using, e.g., CMOS fabrication techniques—to obtain continuous cooldown may allow reaching down to microkelvin device temperatures.

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References (42)

  1. J. S. Xia, E. D. Adams, V. Shvarts, W. Pan, H. L. Stormer, and D. C. Tsui, Ultra-low-temperature cooling of two-dimensional electron gas, Phys. B: Condens. Matter 280, 491 (2000).
  2. N. Samkharadze, A. Kumar, M. J. Manfra, L. N. Pfeiffer, K. W. West, and G. A. Csáthy, Integrated electronic transport and thermometry at milliKelvin temperatures and in strong magnetic fields, Rev. Sci. Instrum. 82, 053902 (2011).
  3. D. I. Bradley, R. E. George, D. Gunnarsson, R. P. Haley, H. Heikkinen, Yu. A. Pashkin, J. Penttilä, J. R. Prance, M. Prunnila, L. Roschier, and M. Sarsby, Nanoelectronic primary thermometry below 4 mK, Nat. Commun. 7, 10455 (2016).
  4. A. T. Jones, C. P. Scheller, J. R. Prance, Y. B. Kalyoncu, D. M. Zumbühl, and R. P. Haley, Progress in cooling nanoelectronic devices to ultra-low temperatures, J. Low Temp. Phys. 201, 772 (2020).
  5. L. V. Levitin, H. van der Vliet, T. Theisen, S. Dimitriadis, M. Lucas, A. D. Corcoles, J. Nyéki, A. J. Casey, G. Creeth, I. Farrer, D. A. Ritchie, J. T. Nicholls, and J. Saunders, Cooling low-dimensional electron systems into the microkelvin regime, Nat. Commun. 13, 667 (2022).
  6. S. Autti, F. C. Bettsworth, K. Grigoras, D. Gunnarsson, R. P. Haley, A. T. Jones, Yu. A. Pashkin, J. R. Prance, M. Prunnila, M. D. Thompson, and D. E. Zmeev, Thermal transport in nanoelectronic devices cooled by on-chip magnetic refrigeration, Phys. Rev. Lett. 131, 077001 (2023).
  7. D. I. Bradley, A. M. Guénault, D. Gunnarsson, R. P. Haley, S. Holt, A. T. Jones, Yu. A. Pashkin, J. Penttilä, J. R. Prance, M. Prunnila, and L. Roschier, On-chip magnetic cooling of a nanoelectronic device, Sci. Rep. 7, 45566 (2017).
  8. M. Palma, C. P. Scheller, D. Maradan, A. V. Feshchenko, M. Meschke, and D. M. Zumbühl, On-and-off chip cooling of a Coulomb blockade thermometer down to 2.8 mK, Appl. Phys. Lett. 111, 253105 (2017).
  9. N. Yurttagül, M. Sarsby, and A. Geresdi, Indium as a high-cooling-power nuclear refrigerant for quantum nanoelectronics, Phys. Rev. Appl. 12, 011005(R) (2019).
  10. L. G. C. Rego and G. Kirczenow, Electrostatic mechanism for cooling semiconductor heterostructures, Appl. Phys. Lett. 75, 2262 (1999).
  11. M. Prunnila, Electron–acoustic-phonon energy-loss rate in multicomponent electron systems with symmetric and asymmetric coupling constants, Phys. Rev. B 75, 165322 (2007).
  12. Q. Li, X. C. Xie, and S. Das Sarma, Calculated heat capacity and magnetization of two-dimensional electron systems, Phys. Rev. B 40, 1381 (1989).
  13. E. Grivei, J.-M. Beuken, G. Mariage, V. Bayot, and M. Shayegan, Heat capacity of a 2DEG, Phys. B: Condens. Matter 256–258, 90 (1998).
  14. M. Prunnila and J. Ahopelto, Two sub-band conductivity of Si quantum well, Physica E 32, 281 (2006).
  15. S. Zhao, G. Yuan, D. Zhang, Y. Liu, J. Lu, W. Han, and J. Luo, Electron transport characteristics in dual gate-controlled 30 nm-thick silicon membrane, J. Phys. D 55, 495105 (2022).
  16. L. Yang, X. Wang, T. Wang, J. Wang, W. Zhang, P. Quach, P. Wang, F. Liu, D. Li, L. Chen et al., Three subband occupation of the two-dimensional electron gas in ultrathin barrier AlN/GaN heterostructures, Adv. Funct. Mater. 30, 2004450 (2020).
  17. M. Cassé, B. Cardoso Paz, G. Ghibaudo, T. Poiroux, E. Vincent, P. Galy, A. Juge, F. Gaillard, S. de Franceschi, T. Meunier et al., Evidence of 2D intersubband scattering in thin film fully depleted silicon-on-insulator transistors operating at 4.2 K, Appl. Phys. Lett. 116, 243502 (2020).
  18. R. A. Davies and M. Pepper, Electron-electron scattering in silicon inversion layers, J. Phys. C 16, L353 (1983).
  19. S.-C. Lee and I. Galbraith, Intersubband and intrasubband electronic scattering rates in semiconductor quantum wells, Phys. Rev. B 59, 15796 (1999).
  20. L. Zheng and S. Das Sarma, Coulomb scattering lifetime of a two-dimensional electron gas, Phys. Rev. B 53, 9964 (1996).
  21. G. F. Giuliani and J. J. Quinn, Lifetime of a quasiparticle in a two-dimensional electron gas, Phys. Rev. B 26, 4421 (1982).
  22. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevB.111.L161404 for details on the numerical simulations, which includes Refs. [40, 41].
  23. R. Hull, Properties of Crystalline Silicon, Emis Series No. 20 (IET, London, 1999).
  24. A. Sergeev, M. Yu. Reizer, and V. Mitin, Deformation electron-phonon coupling in disordered semiconductors and nanostructures, Phys. Rev. Lett. 94, 136602 (2005).
  25. T. Ando, A. B. Fowler, and F. Stern, Electronic properties of two-dimensional systems, Rev. Mod. Phys. 54, 437 (1982).
  26. P. J. Heikkinen, S. Autti, V. B. Eltsov, R. P. Haley, and V. V. Zavjalov, Microkelvin thermometry with Bose–Einstein condensates of magnons and applications to studies of the AB interface in superfluid He3, J. Low Temp. Phys. 175, 681 (2014).
  27. J. J. Hosio, V. B. Eltsov, R. De Graaf, M. Krusius, J. Mäkinen, and D. Schmoranzer, Propagation of thermal excitations in a cluster of vortices in superfluid He3-B, Phys. Rev. B 84, 224501 (2011).
  28. S. Autti, A. Casey, N. Eng, N. Darvishi, P. Franchini, R. P. Haley, P. J. Heikkinen, A. Jennings, A. Kemp, E. Leason, L. V. Levitin, J. Monroe, J. March-Russel, M. T. Noble, J. R. Prance, X. Rojas, T. Salmon, J. Saunders, R. Smith, M. D. Thompson et al., QUEST-DMC superfluid He3 detector for sub-GeV dark matter, Eur. Phys. J. C 84, 248 (2024).
  29. S. Autti, A. Casey, N. Eng, N. Darvishi, P. Franchini, R. P. Haley, P. J. Heikkinen, A. Kemp, E. Leason, L. V. Levitin et al., QUEST-DMC: Background modelling and resulting heat deposit for a superfluid helium-3 bolometer, J. Low Temp. Phys. 215, 465 (2024).
  30. O. Prus, M. Reznikov, U. Sivan, and V. Pudalov, Cooling of electrons in a silicon inversion layer, Phys. Rev. Lett. 88, 016801 (2001).
  31. A. Mittal, R. G. Wheeler, M. W. Keller, D. E. Prober, and R. N. Sacks, Electron-phonon scattering rates in GaAs/AlGaAs 2DEG samples below 0.5 K, Surf. Sci. 361, 537 (1996).
  32. Y. Y. Proskuryakov, J. T. Nicholls, D. I. Hadji-Ristic, A. Kristensen, and C. B. Sørensen, Energy-loss rate of a two-dimensional electron gas measured using a mesoscopic thermometer, Phys. Rev. B 75, 045308 (2007).
  33. N. J. Appleyard, J. T. Nicholls, M. Y. Simmons, W. R. Tribe, and M. Pepper, Thermometer for the 2D electron gas using 1D thermopower, Phys. Rev. Lett. 81, 3491 (1998).
  34. M. Prunnila, P. Kivinen, A. Savin, P. Törmä, and J. Ahopelto, Intervalley-scattering-induced electron-phonon energy relaxation in many-valley semiconductors at low temperatures, Phys. Rev. Lett. 95, 206602 (2005).
  35. J. R. Prance, C. G. Smith, J. P. Griffiths, S. J. Chorley, D. Anderson, G. A. C. Jones, I. Farrer, and D. A. Ritchie, Electronic refrigeration of a two-dimensional electron gas, Phys. Rev. Lett. 102, 146602 (2009).
  36. E. Mykkänen, J. S. Lehtinen, L. Grönberg, A. Shchepetov, A. V. Timofeev, D. Gunnarsson, A. Kemppinen, A. J. Manninen, and M. Prunnila, Thermionic junction devices utilizing phonon blocking, Sci. Adv. 6, eaax9191 (2020).
  37. A. V. Feshchenko, J. V. Koski, and J. P. Pekola, Experimental realization of a Coulomb blockade refrigerator, Phys. Rev. B 90, 201407(R) (2014).
  38. M. Yu. Melnikov, A. A. Shashkin, V. T. Dolgopolov, S.-H. Huang, C. W. Liu, and S. V. Kravchenko, Ultra-high mobility two-dimensional electron gas in a SiGe/Si/SiGe quantum well, Appl. Phys. Lett. 106, 092102 (2015).
  39. A. A. Shashkin and S. V. Kravchenko, Recent developments in the field of the metal-insulator transition in two dimensions, Appl. Sci. 9, 1169 (2019).
  40. J. T. Muhonen, M. J. Prest, M. Prunnila, D. Gunnarsson, V. A. Shah, A. Dobbie, M. Myronov, R. J. H. Morris, T. E. Whall, E. H. C. Parker et al., Strain dependence of electron-phonon energy loss rate in many-valley semiconductors, Appl. Phys. Lett. 98, 182103 (2011).
  41. F. Cardarelli, Materials Handbook: A Concise Desktop Reference (Springer, London, 2008).
  42. https://doi.org/10.17635/lancaster/researchdata/712.

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Phys. Rev. B 111, L161404– Published 14 April, 2025
  • Received 20 August 2024
  • Revised 6 December 2024
  • Accepted 26 March 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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