Download F. (Francesco) Maddalena

500 nm
By Francesco Maddalena
1. Introduction
To uphold Moore’s 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
2. Principles of the SET
The simplest of the single-electron
tunneling devices is the single-electron box
(SEB)
Electrons 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:
(ne  VGC ) 2 (ne  Q ) 2
Ech (n, QG ) 
G
2(CJ  CG )

G
2C
2. Principles of the SET
(ne  QG ) 2
Ech (n, QG ) 
2C
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 T=0 (blue line)
At finite temperatures the Q/Vg
dependence will be smoothed or even
disappear
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
2. Principles of the SET
Drain
The SET is a relative
simple device to build
Source
Island
500 nm
Gate
The the SET can be constructed by using Electron-beam lithography
(EBL) and evaporations techniques such as evaporation at different
deposition angles
2. Principles of the SET
Similarly to the single electron box the island of the SET can be
charged by excess electrons on it
(ne  VGCG ) 2
EC (n, QG ) 
2C
(Q
G
 VGCG)
1 QG e 2
En1 (QG )  En (QG )  (n  
)
2 e C
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
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:
VDS ,T 
e
e

(CL  CR  CG ) C
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:
VG (VDS ,T
e
 0) 
2CG
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
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
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:
Q  SV (w ) / Zinw
Where SV(w) is the spectral density of the voltage noise, Zin the input
impedance and w the frequency
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
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
3. Charge Sensitivity
In the RF mode the
measured value is usually
the damping of an highfrequency 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
(EC>>kT)
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 (  100MHz  1GHz ) will
reduce the Flicker noise to values that can be ignored and at low
frequencies (  1MHz ) 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
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 autocorrelation function of the voltage noise:
 C
(1   )
SV (w ) 
eRVDS 
2
8
 CG
4



2
  2(CGVG  e) / CVDS
Coulomb blockade parameter
From SV we can then write an expression for the charge sensitivity:
(CJ 1  C J 2 ) (1   4 )
Q(w ) 
RVDS

8
3. Charge Sensitivity
2
For optimal parameters:   (neglects co-tunneling processes)
3
e and low temperatures (EC>> kT):
V 
DS
2C
Qoptimal  1.7 106 e / Hz
a factor 10 higher than the theoretical limit
Experimentally determined values of  Q are low as
1.2 105 e / Hz
can be reached, a factor 10 higher than the (theoretical) optimal value
2
1

10
e / Hz
FET theoretical optimal limit:
The SET is a factor 1000 better than the FET!
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
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