Title: Many electron theory of 1/f Noise in doped semiconductors
1(No Transcript)
2Many electron theory of 1/f Noise in doped
semiconductors
Alexander Burin Tulane University
3Motivation (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
0.1
10-2
0.03
0.1
0.3
0.1
10
1
100
T (K)
? (Hz)
4Motivation (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
5Universal 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
61/f noise in operation regime T0.1K
Goal Develop the general theory to account for
the universal 1/f-noise
7Previous 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
8Previous 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
9Previous work - 3
Trap noise, high T
10Previous work - 4
Trap noise, low T
2e2/r
One charge with energy e2/r per volume r3 (Efros,
Shklovskii, 1975)
e2/r
r
11Previous work - 5
Exponent reaches 1 for the variable-range hopping
rate
12Problems of trap model
I
0.1
10
100
1
? (Hz)
13Hypothesis 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
14Chessboard cluster
r
15Probability to form chessboard cluster of N sites
Structure close to that of the Wigners crystal
Site energy reproduces that of Wigners crystal
16Transition of chessboard cluster tunneling
Tunneling
17Transition of chessboard cluster thermal
activation
Thermal activation of domain boundary
18Statistics of transition rates
19Statistics of transition rates - 2
Main contribution comes from the crossover regime
NNc
?
r
rc
20Deviations from 1/f statistics
Practically unlimited applicability at low
temperature Tlt0.1e2/a
21Conductivity noise
e2/T
22Hooge constant, comparison with experiment
23Results, for higher temperature, lower dimension
24Conclusions
- 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
25Acknowledgements
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