Nanoelectronics:

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Nano-electronics
500 nm
Single Electron Transistor Ultrasensitive
Electrometer
By Francesco Maddalena
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1. Introduction
To uphold Moores Law in the future a new
generation of devices that fully operate in the
quantum realm is needed NANODEVICES
One of the most interesting types of nanodevices
is the Single-Electron Transistor The
Single-Electron Transistor can perform the same
functions as a common transistor yet it will
probably not replace the nowadays FETs Instead
it can be used as ultra-sensitive electrometer
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2. Principles of the SET
The simplest of the single-electron tunneling
devices is the single-electron box (SEB) Electron
s can tunnel though the junction from the source
to the island putting excess electrons on it
By changing the gate voltage one can add or
subtract single electrons from the island The
number of excess electrons depend on the
electrostatic energy of the SEB
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2. Principles of the SET
The energy of the SEB varies quadratcally with
QG at the degeneracy points tunneling will occur
The charge Q on the island will depend on the
voltage Vg and it will increase discretely at T0
(blue line) At finite temperatures the Q/Vg
dependence will be smoothed or even disappear
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2. Principles of the SET
The single-electron transistor (SET) is an
expansion of the SEB
The SET has a drain, a source and a gate
electrode (as a normal FET) and a island
contained between two tunneling
junctions The current flow between the drain
and the source and the charge on the island is
regulated by the gate voltage VG via the Coulomb
Blockade
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2. Principles of the SET
Drain
The SET is a relative simple device to
build The the SET can be constructed by
using Electron-beam lithography (EBL) and
evaporations techniques such as evaporation at
different deposition angles
Source
Island
Gate
500 nm
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2. Principles of the SET
Similarly to the single electron box the island
of the SET can be charged by excess electrons on
it
If adding an extra excess electron on the island
(by tunneling) causes the energy to increase the
system will be then energetically forbidden This
represents a barrier for adding excess electrons
and is defined as the Coulomb blockade
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2. Principles of the SET
The SET allows a current between the drain and
source electrodes if the value of the
drain-source voltage is higher than a critical
threshold voltage VT If there are no excess
electrons on the island and the gate voltage is
zero then the threshold voltage is equal
to By changing the gate voltage we can lower
the threshold voltage since the energy of the
system depends on the gate charge The gate
voltage for which the threshold voltage is zero
is equal to
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2. Principles of the SET
We can plot the I/V characteristics of the SET
We can also plot the value of the threshold
voltage against the value of the gate
voltage This is called the Stability Diagram of
the SET
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2. Principles of the SET

• The performance of the SET is altered by external
  parameters
• At finite temperatures the Coulomb blockade of
  the SET is thermally whashed out.
• For a good performance the charging energy of
  the SET must be much higher than the thermal
  energy
• Most SETs work properly only at temperatures
  close to liquid Helium temperatures, however room
  temperature SETs have been made
• External charges influence the SET, shifting the
  threshold voltage, and can be seen as an extra
  gate charge

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3. Charge Sensitivity
The SET has many applications it can function
as a regular transistor, memory storage device
and has great potential in metrology as
ultra-sensitive electrometer with an high charge
sensitivity The SET can be seen as a linear
amplifier The charge sensitivity for an
amplifier is defined as Where SV(w) is the
spectral density of the voltage noise, Zin the
input impedance and w the frequency
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3. Charge Sensitivity

• Charge sensitivity is limited by different types
  of noise
• Thermal Noise Johnson-Nyquist noise depended on
  the impendance and temperature of the system
  
• Shot Noise generated by random tunneling of
  electrons across the island junctions
• Flicker Noise (a.k.a. Pink Noise or 1/f-noise)
  still an ill-understood process with different
  possible causes
• For the SET the Flicker noise is originated
  principally from

1-Mobility fluctuations in conductors 2- Charge
fluctuations at the surface in contact with the
oxide layer in semiconductors
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3. Charge Sensitivity
The SET can be used as charge meter either in DC
or RF mode
In the DC mode the current or the conductance are
measured
Maximum sensitivity is achieved by setting VG
such that the current is at half maximum
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3. Charge Sensitivity
In the RF mode the measured value is usually the
damping of an high-frequency resonant circuit
The RF mode has the advantage to eliminate 1/f
noise at high frequencies The resonant circuit
and the SET can be physically separated
permitting the SET to be independently cooled at
low temperatures (ECgtgtkT)
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3. Charge Sensitivity
If we operate the SET at low temperatures the
Johnson-Nyquist noise due to thermal effects will
be negligible We can also reduce the Flicker
noise (proportional to 1/f) to negligible values
if we operate the SET in the rf-domain Operating
the SET at high frequencies (
) will reduce the Flicker noise to
values that can be ignored and at low frequencies
( ) a feedback can compensate for
the noise Under the above mentioned conditions
the only significant noise source is the
Shot-noise caused by the random tunneling
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3. Charge Sensitivity
With the shot noise as significant noise source
the spectral density of the voltage noise SV is
given by the Fourier transform of the
auto-correlation function of the voltage noise
Coulomb blockade parameter
From SV we can then write an expression for the
charge sensitivity
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3. Charge Sensitivity
For optimal parameters (neglects
co-tunneling processes)
and low temperatures (ECgtgt kT) a factor 10
higher than the theoretical limit
Experimentally determined values of d Q are low
as can be reached, a factor 10 higher than the
(theoretical) optimal value FET theoretical
optimal limit
The SET is a factor 1000 better than the FET!
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4. Conclusions
The Single-electron transistor is capable of
controlling the movement of single elementary
charges Technologically it is quite easy to
build It has various applications, some of them
equal to the classical transistors used
nowadays but will probably be the replacement of
the Field-effect transistor It has an high
charge sensitivity, a factor 1000 better than the
FET and it is a very good candidate for
ultra-sensitive charge measurements
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5. References
Devoret M.H. and Schoelkopf R.J.- Nature (2000),
vol 406, p.1039 Schoelkopf et. al.- Science
(1998), 280 (5367), p1238 Zimmerli et. al.-
Appl. Phys. Lett. (1992), 61 (2), p237