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

3. 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)) 0.3 0.1 0.03 T (K) 100 10 1 0.1 (Hz) 10 100 1 0.110 -2 10 0 10 2 10 4 10 6

4. 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

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

6. 1/f noise in operation regime T~0.1K Goal: Develop the general theory to account for the universal 1/f-noise

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

8. 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) r E ErEr E1E1 E2E2

9. Previous work - 3 Trap noise, high T

10. Trap noise, low T Previous work - 4 One charge with energy e 2 /r per volume r 3 (Efros, Shklovskii, 1975) r e 2 /r 2e 2 /r

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

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

13. Hypothesis: Involvement of multi-electron tunneling (1) 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 (2) Clusters can be formed due to long-range interaction (Burin, Kagan, 1995, 1996) (3) We exploit the most straightforward case of “random order”, i. e. Wigner crystal like configuration formed statistically (4)External noise source (atomic tunneling, etc.) is less probable because of the correlation of noise with metal-insulator transition

14. Chessboard cluster r

15. 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

16. Transition of chessboard cluster: tunneling Tunneling

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

18. Statistics of transition rates

19. Statistics of transition rates - 2 Main contribution comes from the crossover regime N~N c r rcrc

20. Deviations from 1/f statistics Practically unlimited applicability at low temperature T<0.1e 2 /a

21. Conductivity noise e 2 /T

22. Hooge constant, comparison with experiment

23. Results, for higher temperature, lower dimension

24. Conclusions 1.Correlated transitions in coupled many-electron clusters account for the 1/f noise in a hopping conduction 2.Clusters are made of ordered “crystalline” configurations formed due to fluctuations of a random potential

25. Acknowledgements 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 Coworkers: Veniamin Kozub Yuri Galperin Valery Vinokur Funding: