Conductance Fluctuations: From Amorphous Silicon to the

Cerebral Cortex

James Kakalios

School of Physics and Astronomy

The University of Minnesota

Kakalios@umn.edu

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

All noise is not created equal

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)

Fluctuations with a Single Lifetime <I(t)I(0)> ~ exp[-t/ ]

have a Lorentzian Power Spectrum

S = 4 / 1 + (2f)2

Replotted as f x (Noise Power) against frequency

f x S = 4 f / 1 + (2f)2

Two separate fluctuators with lifetimes and

An Ensemble of FluctuatorsS x f = Const.

Leads to a 1/f spectra when replotted as Noise Power

against Frequency

S x f = Const.

S = Const. / f

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

Gas Inlet

To Pump

Matching Network

RF 13.56MHz

RF Showerhead Electrode

Grounded Electrode

Substrates

Plasma

Hydrogenated amorphous silicon synthesized in RF capacitively coupled

glow discharge deposition system

Co-planar conductance measurements

• N-type doped a-Si:H

• Films typically ~ 1.0 m thick

• Ohmic I-V characteristics

• 1/f measurements in dark, under vacuum from 300 to 450 K

Measurement configuration

Spectral density of current fluctuations has 1/f frequency dependence

rms average 1000 FFT traces

Time dependence of resistance

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

Telegraph Noise varies at fixed voltage and temperature

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

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)

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

Simulated current fluctuations show both RTSN and 1/f noise

Lust and JK, Phys Rev E (1994); Phys Rev Lett 75 (1995)

Consistent with measured current fluctuations

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

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

Noise power per octave fluctuates in time

Interactions between fluctuators reflected in Correlation Coefficients

Correlation coefficients quantify interactions across frequency octaves

ij = (NPi - <NPi>)(NPj - <NPj>)

(K - 1) i j

NPi = Noise Power in Octave i (i = 1 - 7)

<NPi> = Average Noise Power in Octave i

i = Standard Deviation of Average Noise Power in Octave iK = 1 – 1024 FFT’s

Correlation coefficients for a-Si:H

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)

Device FabricationDevice Fabrication

Top electrode 1 mm x 1 mm will cover

~ 10, 000 a-Si:H nanoparticles

1/ f noise in a-Si:H nanoparticles

Correlation coefficients for a-Si:H nanoparticles

Belich, Shen, Blackwell, Campbell, JK MRS (2005)

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

Recording apparatus

• Local field potentials– Reflection of activity

over a large population of neurons

• 12 electrodes over an ~ 1.4 mm

hexagonal

array

Coherent oscillations in local field potentials

• 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?

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1768.1 1768.3 1768.5 1768.7 1768.9 1769.10

10

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d (

cm

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time (sec)

1768.5 1768.54 1768.58 1768.62 1768.66 1768.7 time (sec)

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R032-2003-05-30

1768.1 1768.3 1768.5 1768.7 1768.9 1769.10

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time (sec)

1768.5 1768.54 1768.58 1768.62 1768.66 1768.7 time (sec)

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Voltage Traces from Local Field Potential Measurements

Each Time Slice Yields a Power Spectrum

Average of 1024 Consecutive Power Spectra

Transient oscillations

• 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

Correlation coefficients for all frequencies

• Calculate the standard correlation matrix

ji ff

K

kjjkiik

ij K

fSfSfSfS

)1(

))()()()()((1

fi,j

frequency (Hz)

fre

qu

en

cy (

Hz)

1 50 100 1501

50

100

150

0

0.1

0.2

0.3

0.4

0.5

corr

ela

tion

fi,j

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.

Simulation

• 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

100

101

102

103

104

105

frequency (Hz)

no

ise

po

we

r (

V2 /H

z)

100

101

102

103

104

105

frequency (Hz)

no

ise

po

we

r (

V2 /H

z)

frequency (Hz)

fre

qu

en

cy (

Hz)

1 50 100 1501

50

100

150

0

0.1

0.2

0.3

0.4

0.5

frequency (Hz)

fre

qu

en

cy (

Hz)

1 50 100 1501

50

100

150

0

0.1

0.2

0.3

0.4

0.5

Simulationunmodified modified

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)

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.

Time = 0 when 50 Hz oscillation observed

Masimore, Schmitzer-Torbert, JK and Redish, NeuroReport (2005)

50 signal sensitive to drugs that affect striatal dopamine receptors

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

Acknowledgements• 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