By Francesco Maddalena500 nm

1. IntroductionTo uphold Moores Law in the future a new generation of devices that fully operate in the quantum realm is needed:NANODEVICESOne 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 SETThe 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 islandThe number of excess electrons depend on the electrostatic energy of the SEB:

The energy of the SEB varies quadratcally with QG

at the degeneracy points tunneling will occurThe 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 disappear2. 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

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

2. Principles of the SET500 nmDrainGateSourceIsland

Similarly to the single electron box the island of the SET can be charged by excess electrons on it

2. Principles of the SETIf 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

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:

2. Principles of the SET

We can plot the I/V characteristics of the SET:2. Principles of the SETWe can also plot the value of the threshold voltage against the value of the gate voltageThis is called the Stability Diagram 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

2. Principles of the SET

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 frequency3. Charge Sensitivity

3. Charge SensitivityCharge 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 causesFor 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 SensitivityThe SET can be used as charge meter either in DC or RF modeIn 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 SensitivityIn the RF mode the measured value is usually the damping of an high-frequency resonant circuitThe 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 SensitivityIf 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

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:3. Charge SensitivityCoulomb blockade parameterFrom SV we can then write an expression for the charge sensitivity:

3. Charge SensitivityFor optimal parameters: (neglects co-tunneling processes) and low temperatures (EC>> 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!

4. ConclusionsThe 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 FETand it is a very good candidate for ultra-sensitive charge measurements

5. ReferencesDevoret 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