| Topic: |
Science > Physics |
| User: |
"Sam Wormley" |
| Date: |
19 Jan 2005 10:35:13 PM |
| Object: |
Looking at electrons without touching |
Looking at electrons without touching (Jan 19)
http://physicsweb.org/article/news/9/1/11
Physicists in Canada have developed a new way to investigate
single-electron effects in quantum structures without the need to attach
leads to the system being studied. The method, dubbed electrostatic
force spectroscopy, relies on an atomic force microscope and has a
spatial resolution of 50 nanometres (R Stomp et al. 2005
arXiv/cond-mat/0501272).
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| User: "lingShangteng" |
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| Title: Re: Looking at electrons without touching |
20 Jan 2005 02:30:11 AM |
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The experiment is useful to single-electron device which is used for
display tech. with the development of measuring the properties of
single-electron, I think this multi-film model will become a good
device structure.
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| User: "Zigoteau" |
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| Title: Re: Looking at electrons without touching |
20 Jan 2005 02:50:59 PM |
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Hi, Sam and Ling,
Looking at electrons without touching (Jan 19)
http://physicsweb.org/article/news/9/1/11
Physicists in Canada have developed a new way to investigate
single-electron effects in quantum structures without the need to
attach
leads to the system being studied. The method, dubbed electrostatic
force spectroscopy, relies on an atomic force microscope and has a
spatial resolution of 50 nanometres (R Stomp et al. 2005
arXiv/cond-mat/0501272).
The experiment is useful to single-electron device which is used for
display tech. with the development of measuring the properties of
single-electron, I think this multi-film model will become a good
device structure.
I haven't any comments about your posts so much as about the whole idea
of the Coulomb blockade and single-electron effects. I had a
breakthrough in understanding these about a year ago, and I would like
to bounce it off any of you who may have thought deeply about it.
Perhaps you have a complementary insight to share.
First of all, the whole field was set in motion by Averin and Likharev
in their paper in J. Low Temp. Phys. 62 (1986) 345. I believe that
their analysis is widely misunderstood and does not have the mystic
significance often attributed to it. Anyway, I welcome comments from
all comers.
Understanding the paper is not helped by a misprint between equations 5
and 6, where they have the in-line equation H_T =3D (H_+)(H_-) followed
by equation 6
H_+ =3D Sigma_{k_1,k_2}{T_{k_1,k_2}*c=86_k_1*c_k_2}
This makes it look as if their Hamiltonian has fourth-order products of
creator and annihilator operators. These would correspond to
electron-electrom interactions, which are extremely complicated and
hard to get any intuition about. However if you go back to their source
reference, or read other papers by them, it is clear that the in-line
equation should in fact read H_T =3D (H_+)+(H_-). So their Hamiltonian
does not involve electron-electron interaction. This is justified for
electrons in metals because of the strong shielding, and makes the math
much simpler. Electrons move around independently of one another. To
get sensible results you have to assume that they are in thermodynamic
equilibrium, which is of course only achieved through electron-electron
interaction, but this may be assumed to have happened a long time ago
and far away.
The next funny thing they do is to use the charge Q on the metallic
nanoparticle as an independent variable. I agonized for a long time
over this, because a much more natural independent variable is the
potential V of the nanoparticle. In fact their Q is not the
instantaneous charge on the nanoparticle but the expectation value of
the charge for a given V, and I believe the apparently
counter-intuitive nature of their result is purely the result of their
strange choice of independent variable.
A common statement about the Coulomb blockade refers to the
small-voltage conductance between source and drain electrodes separated
by tunneling junctions from the nanoparticle, a so-called Single
Electron Transistor, SET. The SET is designed so that the charge on the
nanoparticle is more affected by the potential on a gate electrode,
from which electrodes cannot tunnel.
My revelations:
1=2E The nanoparticle has a spectrum of electron states. Since it is not
strongly coupled to two neighboring electrodes, each of these states
fills up over quite a narrow range of the nanoparticle potential V. The
range depends on kT/e and on the strength of the tunnel coupling. Q(V)
is the integral of a sum of Lorentzians. Since the states are so
narrow, Q(V) is like a sum of unit step functions. When V is exactly
aligned with the expectation energy of a state, Q(V) is half-integral.
2=2E The current between the two neighboring electrodes may be described
as resonant tunneling. When a nanoparticle state is more than kT/e
below the Fermi levels of both electrodes, it is fully occupied and
does not contribute to the current between them. If it is more than
kT/e above the Fermi levels of both electrodes, it is empty and does
not contribute to the current. Current only flows through a state if it
is close to the Fermi levels. Maximum current flows when the state is
aligned with the Fermi level. The expectation charge on the
nanoparticle is then half-integral.
The separation DeltaV between the states of the nanoparticle may be
considered to be DeltaV/C_diff, where C_diff is similar in nature to
the "diffusion capacitance" of a BJT base. It varies as the square of
the linear dimensions of the nanoparticle, and is typically much larger
than the "junction capacitance" of the nanoparticle to the gate
electrode. When controlling the charge on the nanoparticle by the
voltage on the gate electrode, to a first approximation essentially
only the junction capacitance need be considered. The junction
capacitance varies directly as the linear dimensions of the
nanoparticle. Hence if high precision is required, the diffusion
capacitance must also be considered, and the discrepancy is worst for
very small nanoparticles.
In a lot of the literature, the SET is described as a turnstile,
allowing electrons through one by one in a controlled manner. I can't
see that at all. Any quantization there may be is related to Q, and
that is an expectation charge, not the instantaneous charge on the
nanoparticle. AFAICS, the current between the source and drain flows
randomly, not in the regular manner suggested by the turnstile
metaphor. And for precision metrology, if you're expecting the
separation between conductance maxima to be determined by the
nanoparticle capacitance, your error with the smallest nanoparticles
may be as much as 10%.
Any complementary enlightment welcomed!
Cheers,
Zigoteau.
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