Conductance Fluctuations: From Amorphous Silicon to the Cerebral Cortex

1. Conductance Fluctuations: From Amorphous Silicon to the Cerebral Cortex James Kakalios School of Physics and Astronomy The University of Minnesota Kakalios@umn.edu

2. Why make noise the signal? • As semiconductor devices become smaller - fundamental noise mechanisms in materials limit device performance • Studies of noise processes provide information concerning electronic transport and defect kinetics not accessible by other means • Unique probe to elucidate fundamental nature of complex systems

3. All noise is not created equal

4. 1/f noise characteristic of complex, messy systems • Metal, semiconducting resistors • Spin Glasses • Sunspot activity • X-ray emissions from Cygnus X-1 • Flood levels of the Nile • Traffic Jams Khera and JK, Phys Rev B 56 (1997)

5. Fluctuations with a Single Lifetime t <I(t)I(0)> ~ exp[-t/ t] have a Lorentzian Power Spectrum S = 4t / 1 + (2pft)2

6. Replotted as f x (Noise Power) against frequency f x S = 4t f / 1 + (2pft)2

7. Two separate fluctuators with lifetimes t1and t2

8. An Ensemble of Fluctuators S x f = Const.

9. Leads to a 1/f spectra when replotted as Noise Power against Frequency S x f = Const. S = Const. / f

10. Material system investigated hydrogenated amorphous silicon (a-Si:H) • Alloy of silicon and hydrogen • Prototypical disordered semiconductor • Hydrogen diffusion leads to fluctuations in defect structure and electronic conductance • Technological applications include solar cells and TFT’s

11. Hydrogenated amorphous silicon synthesized inRF capacitively coupled glow discharge deposition system

12. Co-planar conductance measurements • N-type doped a-Si:H • Films typically ~ 1.0 mm thick • Ohmic I-V characteristics • 1/f measurements in dark, under vacuum from 300 to 450 K

13. Measurement configuration

14. Spectral density of current fluctuations has 1/f frequency dependence rms average 1000 FFT traces

15. Time dependence of resistance

16. Random Telegraph Switching Noise (RTSN) in a-Si:H

17. Telegraph Noise varies at fixed voltage and temperature

18. RTSN due to current microchannels ? • Hydrogenated amorphous silicon (a-Si:H) is well known to contain Long Range Disorder (LRD) (1- 100 nm) due to compositional morphology and potential fluctuations • Influence on electronic properties indirect since Linelast ~ 5 Å • LRD leads to inhomogeneous current filaments

19. Simulations show current filaments arise from spatial variations of activation energy X-Y Grid of Resistors R = Roexp[Ea/kT] Quicker and JK, Phys Rev B 60 (1999)

20. Dynamical percolation model simulates effect of H motion on inhomogeneous current filaments

21. Simulated current fluctuations show both RTSN and 1/f noise Lust and JK, Phys Rev E (1994); Phys Rev Lett 75 (1995)

22. Consistent with measured current fluctuations

23. Interactions between fluctuators lead to time dependent variations in power spectra • Changes in spectral slope of power spectra reflect variations in ensemble of Lorentzian fluctuators • Interactions between Lorentzian fluctuators reflected in correlations in power spectra across frequencies

24. 1/ f noise in n-type a-Si:H

25. Noise power per octave fluctuates in time Interactions between fluctuators reflected in Correlation Coefficients

26. Correlation coefficients quantify interactions across frequency octaves rij = S (NPi - <NPi>)(NPj - <NPj>) (K - 1)si sj NPi = Noise Power in Octave i (i = 1 - 7) <NPi> = Average Noise Power in Octave i si = Standard Deviation of Average Noise Power in Octave i K = 1 – 1024 FFT’s

27. Correlation coefficients for a-Si:H

28. Free standing amorphous silicon nanodots in an insulating matrix Synthesized in Inductively coupled HPCVD system Z. Shen, et al J. Appl. Phys 94 (2003); 96 (2004)

29. Device Fabrication Device Fabrication Top electrode 1 mm x 1 mm will cover ~ 10, 000 a-Si:H nanoparticles

30. 1/ f noise in a-Si:H nanoparticles

31. Correlation coefficients for a-Si:H nanoparticles Belich, Shen, Blackwell, Campbell, JK MRS (2005)

32. Noise in other complex systems • Random telegraph switching noise consistent with electronic conduction through inhomogeneous current filaments • Non-Gaussian nature of 1/f noise in amorphous silicon reflects correlations between fluctuators • Electronic conduction along neurons can be considered as spatially and temporally inhomogenous currents with varying correlations between currents

33. Local field potentials Reflection of activity over a large population of neurons 12 electrodes over an ~ 1.4 mm hexagonal array Recording apparatus

34. Voltage fluctuations in various brain structures show distinct oscillations. Known events range from long in duration (seconds-minutes) to very transient (tens of milliseconds). In 40 minutes of data, how can we tell if there’s something worth digging for? Coherent oscillations in local field potentials

35. Voltage Traces from Local Field Potential Measurements

36. Each Time Slice Yields a Power Spectrum

37. Average of 1024 Consecutive Power Spectra

38. Infinitely long periodic oscillations yield delta function peak in Fourier transform Oscillations that are transient in time will have FFT with finite frequency width Power spectra at peak will be positively correlated with neighboring frequencies - part of same wave packet Transient oscillations

39. Correlation coefficients for all frequencies • Calculate the standard correlation matrix fi,j fi,j

40. Correlation coefficients will reveal coherent oscillations • Transient frequencies will show up as regions of high correlation on the diagonal x=y axis. • Different transient frequencies that tend to occur at the same time will show up as regions of high correlation off of the center axis.

41. 3 different oscillations added 50 Hz, 100 ms 100 Hz, 75 ms 150 Hz, 50 ms Amplitude equal to rms value of voltage signal 50 Hz and 100 Hz added together 150 Hz added independently Parameters are in line with known transient oscillations Simulation

42. 5 5 10 10 /Hz) /Hz) 2 2 V V m m 4 4 10 10 noise power ( noise power ( 3 3 10 10 0 1 2 0 1 2 10 10 10 10 10 10 frequency (Hz) frequency (Hz) 0.5 0.5 0.4 0.4 150 150 0.3 0.3 frequency (Hz) frequency (Hz) 100 100 0.2 0.2 50 50 0.1 0.1 1 1 0 0 1 50 100 150 1 50 100 150 frequency (Hz) frequency (Hz) Simulation modified unmodified

43. Dorsal Striatum • Local field activity has not been studied in depth • Tight region of high correlation around 50Hz • Present on many animals (14), several tasks (3) • Figure from 5 animals, Take5 task Masimore, JK and Redish, J. Neurosci. Meth. (2003)

44. Behavioral task • Take 5 task • Rats ran around a rectangular track with feeders on each side. In order to receive food, rats had to run 5/4 around the track.

47. Time = 0 when 50 Hz oscillation observed Masimore, Schmitzer-Torbert, JK and Redish, NeuroReport (2005)

48. g50 signal sensitive to drugs that affect striatal dopamine receptors

49. Summary • Non-Gaussian 1/f Noise observed in a-Si:H • Random Telegraph Switching Noise consistent with conduction through inhomogeneous current filaments • Noise analysis has been applied to neurological data - enables identification of fundamental oscillation frequencies without a priori filtering

50. Collaborators Uwe Kortshagen (Mechanical Engineering) A. David Redish (Neuroscience) Steve Campbell (Electrical Engineering) C. Barry Carter (Chemical Engineering and Materials Science) Funding NREL - AAD NSF-NER NSF-IGERT - Nano NSF-IGERT - Neuro NIH MH68029 U of M IRCSA grant U of M Graduate School Grad Students Amorphous Silicon Craig Parmen Nathan Israeloff Lisa Lust Gautam Khera Peter West David Quicker T. James Belich Charlie Blackwell Neuroscience Beth Masimore Neil Schmitzer-Torbert Jadin Jackson Acknowledgements