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Conductance Fluctuations: From Amorphous Silicon to the
Cerebral Cortex
James Kakalios
School of Physics and Astronomy
The University of Minnesota
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?
vo
lta
ge
(a
rb. u
nits)
R032-2003-05-30
1768.1 1768.3 1768.5 1768.7 1768.9 1769.10
10
20
30
sp
ee
d (
cm
/se
c)
time (sec)
1768.5 1768.54 1768.58 1768.62 1768.66 1768.7 time (sec)
vo
lta
ge
(a
rb. u
nits)
vo
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ge
(a
rb. u
nits)
R032-2003-05-30
1768.1 1768.3 1768.5 1768.7 1768.9 1769.10
10
20
30
sp
ee
d (
cm
/se
c)
time (sec)
1768.5 1768.54 1768.58 1768.62 1768.66 1768.7 time (sec)
vo
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(a
rb. u
nits)
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