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Universal 1/f Noise in Doped Semiconductors: Multi-Electron Tunneling and Cluster Formation

This study aims to develop a general theory to explain the universal 1/f noise observed in doped semiconductors. The research focuses on the involvement of multi-electron tunneling and the formation of clustered structures. The findings provide a deeper understanding of the nature of 1/f noise and its impact on semiconductor bolometers.

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Universal 1/f Noise in Doped Semiconductors: Multi-Electron Tunneling and Cluster Formation

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  1. Many electron theory of 1/f Noise in doped semiconductors Alexander Burin Tulane University

  2. Motivation (Fundamental) Understanding the nature of anomalously strong 1/f noise in hopping conduction (e. g. McCammon, 2000-2006; Savchenko, 2000-2003 (Si-P-B); G. Deville, 2006, (Ga-As)) 106 100 104 102 10 1 100 10-2 0.1 0.03 0.1 0.3 10 0.1 1 100 T (K)  (Hz)

  3. Motivation (Practical) 1/f-noise affects a performance of semiconductor bolometers (McCammon, 2000-2006; Gershenson, 2000-2003 (Si-P)) Bolometers detect absorption of single X-ray or cosmic particle and can measure its energy by means of the change in temperature affecting the semiconductor conductivity

  4. Universal low temperature conductivity in doped semiconductors (Shklovskii, Efros, 1978) ln Universal strong temperature dependence serves to define the small temperature variation induced by X-ray absorption T-1/2

  5. 1/f noise in operation regime T~0.1K Goal: Develop the general theory to account for the universal 1/f-noise

  6. Previous work - 1 1. 1/f noise is caused by tunneling (McWorter, (1957)) r/2 r Hopping through intermediate sites breaks down 1/f transition rate statistics

  7. Previous work - 2 2. 1/f noise is caused by tunneling from traps (Shklovskii, (2003); Yu, (2003); Kozub (1996) occasional configurations with no intermediate sites) E E2 E1 Er r

  8. Previous work - 3 Trap noise, high T

  9. Previous work - 4 Trap noise, low T 2e2/r One charge with energy e2/r per volume r3 (Efros, Shklovskii, 1975) e2/r r

  10. Previous work - 5 Exponent reaches 1 for the variable-range hopping rate

  11. Problems of trap model I 0.1 10 1 100  (Hz)

  12. Hypothesis: Involvement of multi-electron tunneling • Simultaneous tunneling of multi-electron (N-electron) coupled clusters is characterized by tunneling amplitude V ~ exp(-aN),  leads to 1/f noise if transition rates • Clusters can be formed due to long-range interaction (Burin, Kagan, 1995, 1996) • We exploit the most straightforward case of “random order”, i. e. Wigner crystal like configuration formed statistically • External noise source (atomic tunneling, etc.) is less probable because of the correlation of noise with metal-insulator transition

  13. Chessboard cluster r

  14. Probability to form chessboard cluster of N sites Structure close to that of the Wigner’s crystal Site energy reproduces that of Wigner’s crystal

  15. Transition of chessboard cluster: tunneling Tunneling

  16. Transition of chessboard cluster: thermal activation Thermal activation of domain boundary

  17. Statistics of transition rates

  18. Statistics of transition rates - 2 Main contribution comes from the crossover regime N~Nc  rc r

  19. Deviations from 1/f statistics Practically unlimited applicability at low temperature T<0.1e2/a

  20. Conductivity noise e2/T

  21. Hooge constant, comparison with experiment

  22. Results, for higher temperature, lower dimension

  23. Conclusions • Correlated transitions in coupled many-electron clusters account for the 1/f noise in a hopping conduction • Clusters are made of ordered “crystalline” configurations formed due to fluctuations of a random potential

  24. Acknowledgements Coworkers: Boris Shklovskii , special acknowledge for supporting my life and work in UMN in the Fall 2005 (where this work has been done) during the disaster in New Orleans Veniamin Kozub Yuri Galperin Valery Vinokur Funding:

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