- Open Access
Strained donor-bound excitons in
Phys. Rev. B 113, 075203 – Published 17 February, 2026
DOI: https://doi.org/10.1103/g6yl-q9bl
Abstract
We present a comprehensive experimental study of the neutral donor to donor-bound exciton transition () in isotopically enriched , focusing on the group V donors P, As, and Sb under finely tuned uniaxial stress along the [100] and [110] crystal axes and magnetic fields from 3.5 mT to 1.7 T. From these measurements, donor-specific deformation potentials are extracted. The uniaxial electron deformation potential is found to be significantly larger than values reported for other states or transitions in silicon and shows clear dependence on the donor species, indicating an increased sensitivity of the state to strain and central-cell effects. We also observe a magnetic field dependence of the hole shear deformation potential , suggesting a more complex strain coupling mechanism than captured by standard theory. Diamagnetic shift parameters determined from Zeeman spectra show good agreement with earlier measurements. Our results provide a refined parameter set critical for the design of silicon quantum devices based on transitions.
Physics Subject Headings (PhySH)
Article Text
References (71)
- B. E. Kane, A silicon-based nuclear spin quantum computer, Nature (London) 393, 133 (1998).
- A. Morello, J. J. Pla, P. Bertet, and D. N. Jamieson, Donor spins in silicon for quantum technologies, Adv. Quantum Technol. 3, 2000005 (2020).
- J. Koch, T. M. Yu, J. Gambetta, A. A. Houck, D. I. Schuster, J. Majer, A. Blais, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, Charge-insensitive qubit design derived from the Cooper pair box, Phys. Rev. A 76, 042319 (2007).
- F. A. Zwanenburg, A. S. Dzurak, A. Morello, M. Y. Simmons, Lloyd C. L. Hollenberg, G. Klimeck, S. Rogge, S. N. Coppersmith, and M. A. Eriksson, Silicon quantum electronics, Rev. Mod. Phys. 85, 961 (2013).
- H. Haffner, C. Roos, and R. Blatt, Quantum computing with trapped ions, Phys. Rep. 469, 155 (2008).
- S. R. Schofield, N. J. Curson, M. Y. Simmons, F. J. Rueß, T. Hallam, L. Oberbeck, and R. G. Clark, Atomically precise placement of single dopants in Si, Phys. Rev. Lett. 91, 136104 (2003).
- B. Andreas, Y. Azuma, G. Bartl, P. Becker, H. Bettin, M. Borys, I. Busch, M. Gray, P. Fuchs, K. Fujii, H. Fujimoto, E. Kessler, M. Krumrey, U. Kuetgens, N. Kuramoto, G. Mana, P. Manson, E. Massa, S. Mizushima, A. Nicolaus, A. Picard, A. Pramann, O. Rienitz, D. Schiel, S. Valkiers, and A. Waseda, Determination of the Avogadro constant by counting the atoms in a crystal, Phys. Rev. Lett. 106, 030801 (2011).
- A. M. Tyryshkin, S. Tojo, J. J. L. Morton, H. Riemann, N. V. Abrosimov, P. Becker, H.-J. Pohl, T. Schenkel, M. L. W. Thewalt, K. M. Itoh, and S. A. Lyon, Electron spin coherence exceeding seconds in high-purity silicon, Nat. Mater. 11, 143 (2012).
- M. Steger, K. Saeedi, M. L. W. Thewalt, J. J. L. Morton, H. Riemann, N. V. Abrosimov, P. Becker, and H.-J. Pohl, Quantum information storage for over 180 s using donor spins in a Si-28 “semiconductor vacuum”, Science 336, 1280 (2012).
- K. Saeedi, S. Simmons, J. Z. Salvail, P. Dluhy, H. Riemann, N. V. Abrosimov, P. Becker, H.-J. Pohl, J. J. L. Morton, and M. L. W. Thewalt, Room-temperature quantum bit storage exceeding 39 minutes using ionized donors in silicon-28, Science 342, 830 (2013).
- S. Asaad, V. Mourik, B. Joecker, M. A. I. Johnson, A. D. Baczewski, H. R. Firgau, M. T. Mądzik, V. Schmitt, J. J. Pla, F. E. Hudson, K. M. Itoh, J. C. McCallum, A. S. Dzurak, A. Laucht, and A. Morello, Coherent electrical control of a single high-spin nucleus in silicon, Nature (London) 579, 205 (2020).
- I. Fernández de Fuentes, T. Botzem, M. A. I. Johnson, A. Vaartjes, S. Asaad, V. Mourik, F. E. Hudson, K. M. Itoh, B. C. Johnson, A. M. Jakob, J. C. McCallum, D. N. Jamieson, A. S. Dzurak, and A. Morello, Navigating the 16-dimensional Hilbert space of a high-spin donor qudit with electric and magnetic fields, Nat. Commun. 15, 1380 (2024).
- X. Yu, B. Wilhelm, D. Holmes, A. Vaartjes, D. Schwienbacher, M. Nurizzo, A. Kringhøj, M. R. van Blankenstein, A. M. Jakob, P. Gupta, F. E. Hudson, K. M. Itoh, R. J. Murray, R. Blume-Kohout, T. D. Ladd, N. Anand, A. S. Dzurak, B. C. Sanders, D. N. Jamieson, and A. Morello, Schrödinger cat states of a nuclear spin qudit in silicon, Nat. Phys. 21, 362 (2025).
- A. Morello, J. J. Pla, F. A. Zwanenburg, K. W. Chan, K. Y. Tan, H. Huebl, M. Möttönen, C. D. Nugroho, C. Yang, J. A. van Donkelaar, A. D. C. Alves, D. N. Jamieson, C. C. Escott, L. C. L. Hollenberg, R. G. Clark, and A. S. Dzurak, Single-shot readout of an electron spin in silicon, Nature (London) 467, 687 (2010).
- J. J. Pla, K. Y. Tan, J. P. Dehollain, W. H. Lim, J. J. L. Morton, F. A. Zwanenburg, D. N. Jamieson, A. S. Dzurak, and A. Morello, High-fidelity readout and control of a nuclear spin qubit in silicon, Nature (London) 496, 334 (2013).
- M. T. Mądzik, A. Laucht, F. E. Hudson, A. M. Jakob, B. C. Johnson, D. N. Jamieson, K. M. Itoh, A. S. Dzurak, and A. Morello, Conditional quantum operation of two exchange-coupled single-donor spin qubits in a MOS-compatible silicon device, Nat. Commun. 12, 181 (2021).
- M. T. Mądzik, S. Asaad, A. Youssry, B. Joecker, K. M. Rudinger, E. Nielsen, K. C. Young, T. J. Proctor, A. D. Baczewski, A. Laucht, V. Schmitt, F. E. Hudson, K. M. Itoh, A. M. Jakob, B. C. Johnson, D. N. Jamieson, A. S. Dzurak, C. Ferrie, R. Blume-Kohout, and A. Morello, Precision tomography of a three-qubit donor quantum processor in silicon, Nature (London) 601, 348 (2022).
- A. Yang, M. Steger, D. Karaiskaj, M. L. W. Thewalt, M. Cardona, K. M. Itoh, H. Riemann, N. V. Abrosimov, M. F. Churbanov, A. V. Gusev, A. D. Bulanov, A. K. Kaliteevskii, O. N. Godisov, P. Becker, H.-J. Pohl, J. W. Ager, and E. E. Haller, Optical detection and ionization of donors in specific electronic and nuclear spin states, Phys. Rev. Lett. 97, 227401 (2006).
- M. Steger, T. Sekiguchi, A. Yang, K. Saeedi, M. E. Hayden, M. L. W. Thewalt, K. M. Itoh, H. Riemann, N. V. Abrosimov, P. Becker, and H.-J. Pohl, Optically-detected NMR of optically-hyperpolarized neutral donors in , J. Appl. Phys. 109, 102411 (2011).
- C. C. Lo, M. Urdampilleta, P. Ross, M. F. Gonzalez-Zalba, J. Mansir, S. A. Lyon, M. L. W. Thewalt, and J. J. L. Morton, Hybrid optical–electrical detection of donor electron spins with bound excitons in silicon, Nat. Mater. 14, 490 (2015).
- P. Ross, B. C. Rose, C. C. Lo, Mike L. W. Thewalt, A. M. Tyryshkin, S. A. Lyon, and John J. L. Morton, Electron spin resonance of P donors in isotopically purified detected by contactless photoconductivity, Phys. Rev. Appl. 11, 054014 (2019).
- W. Schmid, Auger lifetimes for excitons bound to neutral donors and acceptors in Si, Phys. Status Solidi B 84, 529 (1977).
- P. Conti, S. Dhomkar, P. Ross, J. Mansir, and J. J. L. Morton, Donor-bound-exciton strain microscopy in silicon devices, arXiv:2408.17382.
- R. Rahman, J. Verduijn, Y. Wang, C. Yin, G. D. Boo, G. Klimeck, and S. Rogge, Bulk and sub-surface donor bound excitons in silicon under electric fields, arXiv:1510.00065.
- J. J. Pla, A. Bienfait, G. Pica, J. Mansir, F. A. Mohiyaddin, Z. Zeng, Y. M. Niquet, A. Morello, T. Schenkel, J. J. L. Morton, and P. Bertet, Strain-induced spin-resonance shifts in silicon devices, Phys. Rev. Appl. 9, 044014 (2018).
- Y. Fang, P. Philippopoulos, D. Culcer, W. A. Coish, and S. Chesi, Recent advances in hole-spin qubits, Mater. Quantum. Technol. 3, 012003 (2023).
- T. Peach, K. Homewood, M. Lourenco, M. Hughes, K. Saeedi, N. Stavrias, J. Li, S. Chick, B. Murdin, and S. Clowes, The effect of lattice damage and annealing conditions on the hyperfine structure of ion implanted bismuth donors in silicon, Adv. Quantum Technol. 1, 1800038 (2018).
- M. L. W. Thewalt and J. A. Rostworowski, Effects of uniaxial stress on the luminescence lines due to multiexciton complexes bound to phosphorus in silicon, Phys. Rev. Lett. 41, 808 (1978).
- V. A. Karasyuk, A. G. Steele, A. Mainwood, E. C. Lightowlers, G. Davies, D. M. Brake, and M. L. W. Thewalt, Ultrahigh-resolution photoluminescence studies of excitons bound to boron in silicon under uniaxial stress, Phys. Rev. B 45, 11736 (1992).
- T. Loippo, A. Kanniainen, and J. T. Muhonen, Strain effects in phosphorus bound exciton transitions in silicon, Phys. Rev. Mater. 7, 016202 (2023).
- M. P. Ross, Bound exciton-assisted spin-to-charge conversion of donors in silicon, Ph.D. thesis, University College London, 2017.
- W. Kohn and J. M. Luttinger, Theory of donor states in silicon, Phys. Rev. 98, 915 (1955).
- W. P. Mason, Physical Acoustics and the Properties of Solids, Bell Telephone Laboratories Series (Van Nostrand, Princeton, New Jersey, 1958).
- G. L. Bir, E. I. Butikov, and G. E. Pikus, Spin and combined resonance on acceptor centres in Ge and Si type crystals—I: Paramagnetic resonance in strained and unstrained crystals, J. Phys. Chem. Solids 24, 1467 (1963).
- G. Kirczenow, A new model for bound multiexciton complexes, Solid State Commun. 21, 713 (1977).
- J. M. Luttinger, Quantum theory of cyclotron resonance in semiconductors: General theory, Phys. Rev. 102, 1030 (1956).
- A. K. Bhattacharjee and S. Rodriguez, Group-theoretical study of the Zeeman effect of acceptors in silicon and germanium, Phys. Rev. B 6, 3836 (1972).
- Unless both stress and magnetic field are aligned with the same [100] crystal axis, which is not the case in our work.
- K. L. Litvinenko, J. Li, N. Stavrias, A. J. Meaney, P. C. M. Christianen, H. Engelkamp, K. P. Homewood, C. R. Pidgeon, and B. N. Murdin, The quadratic Zeeman effect used for state-radius determination in neutral donors and donor bound excitons in Si:P, Semicond. Sci. Technol. 31, 045007 (2016).
- J. M. Cherlow, R. L. Aggarwal, and B. Lax, Raman scattering and photoluminescence in boron-doped and arsenic-doped silicon, Phys. Rev. B 7, 4547 (1973).
- Uncorrelated electron and hole energy fluctuations could yield substantial inhomogeneous broadening even when .
- G. Feher, Electron spin resonance experiments on donors in silicon. I. Electronic structure of donors by the electron nuclear double resonance technique, Phys. Rev. 114, 1219 (1959).
- D. P. Franke, Nuclear spins of heavy donors in silicon, Ph.D. thesis, Technische Universität München, 2018.
- A. Kaminskii, V. Karasyuk, and Y. E. Pokrovskii, Luminescence of excitons bound to phosphorus atoms in silicon subjected to a magnetic field, Zh. Eksp. Teor. Fiz. 79, 422 (1980) [Sov. Phys. JETP 52, 211 (1980)].
- C. Jagannath, Z. W. Grabowski, and A. K. Ramdas, Linewidths of the electronic excitation spectra of donors in silicon, Phys. Rev. B 23, 2082 (1981).
- I. Balslev, Influence of uniaxial stress on the indirect absorption edge in silicon and germanium, Phys. Rev. 143, 636 (1966).
- F. J. Morin, T. H. Geballe, and C. Herring, Temperature dependence of the piezoresistance of high-purity silicon and germanium, Phys. Rev. 105, 525 (1957).
- J. E. Aubrey, W. Gubler, T. Henningsen, and S. H. Koenig, Piezoresistance and piezo-Hall-effect in -type silicon, Phys. Rev. 130, 1667 (1963).
- J. C. Hensel and G. Feher, Cyclotron resonance experiments in uniaxially stressed silicon: Valence band inverse mass parameters and deformation potentials, Phys. Rev. 129, 1041 (1963).
- D. K. Wilson and G. Feher, Electron spin resonance experiments on donors in silicon. III. Investigation of excited states by the application of uniaxial stress and their importance in relaxation processes, Phys. Rev. 124, 1068 (1961).
- V. J. Tekippe, H. R. Chandrasekhar, P. Fisher, and A. K. Ramdas, Determination of the deformation-potential constant of the conduction band of silicon from the piezospectroscopy of donors, Phys. Rev. B 6, 2348 (1972).
- L. D. Laude, F. H. Pollak, and M. Cardona, Effects of uniaxial stress on the indirect exciton spectrum of silicon, Phys. Rev. B 3, 2623 (1971).
- R. Ito, H. Kawamura, and M. Fukai, Anisotropic phonon scattering of electrons in germanium and silicon, Phys. Lett. 13, 26 (1964).
- G. D. Watkins and F. S. Ham, Electron paramagnetic resonance studies of a system with orbital degeneracy: The lithium donor in silicon, Phys. Rev. B 1, 4071 (1970).
- J. J. Hall, Electronic effects in the elastic constants of -type silicon, Phys. Rev. 161, 756 (1967).
- M. V. Fischetti and S. E. Laux, Band structure, deformation potentials, and carrier mobility in strained Si, Ge, and SiGe alloys, J. Appl. Phys. 80, 2234 (1996).
- M. M. Rieger and P. Vogl, Electronic-band parameters in strained alloys on substrates, Phys. Rev. B 48, 14276 (1993).
- C. Tserbak, H. M. Polatoglou, and G. Theodorou, Unified approach to the electronic structure of strained Si/Ge superlattices, Phys. Rev. B 47, 7104 (1993).
- C. G. Van de Walle and R. M. Martin, Theoretical calculations of heterojunction discontinuities in the Si/Ge system, Phys. Rev. B 34, 5621 (1986).
- M. Cardona and F. H. Pollak, Energy-band structure of germanium and silicon: The kp method, Phys. Rev. 142, 530 (1966).
- P. Friedel, M. S. Hybertsen, and M. Schlüter, Local empirical pseudopotential approach to the optical properties of Si/Ge superlattices, Phys. Rev. B 39, 7974 (1989).
- U. Schmid, N. E. Christensen, and M. Cardona, Calculated deformation potentials in Si, Ge, and GeSi, Solid State Commun. 75, 39 (1990).
- G. L. Bir and G. E. Pikus, Symmetry and Strain-Induced Effects in Semiconductors (Wiley, New York, 1974).
- U. Gerstmann (private communication).
- B. Hönerlage and I. Pelant, Symmetry and Symmetry-Breaking in Semiconductors, Springer Tracts in Modern Physics Vol. 279 (Springer, Cham, Switzerland, 2018).
- J. Mansir, The effects of strain on donor spin qubits in Silicon, Ph.D. thesis, University College London, 2019.
- P. J. Dean, W. F. Flood, and G. Kaminsky, Absorption due to bound excitons in silicon, Phys. Rev. 163, 721 (1967).
- D. Sleiter, N. Y. Kim, K. Nozawa, T. D. Ladd, M. L. W. Thewalt, and Y. Yamamoto, Quantum Hall charge sensor for single-donor nuclear spin detection in silicon, New J. Phys. 12, 093028 (2010).
- M. T. Uysal, L. Dusanowski, H. Xu, S. P. Horvath, S. Ourari, R. J. Cava, N. P. de Leon, and J. D. Thompson, Spin-photon entanglement of a single ion in the telecom band, Phys. Rev. X 15, 011071 (2025).
- S. Nur, H.-J. Lim, J. Elzerman, and J. J. L. Morton, Silicon photonic crystal cavities at near band-edge wavelengths, Appl. Phys. Lett. 114, 091101 (2019).
- K.-M. C. Fu, T. D. Ladd, C. Santori, and Y. Yamamoto, Optical detection of the spin state of a single nucleus in silicon, Phys. Rev. B 69, 125306 (2004).