Single Electron Phenomena and Single Electron Transistor

SINGLE ELECTRON PHENOMENA AND SINGLE ELECTRON TRANSISTOR

SINGLE ELECTRON PHENOMENA

Theory

In electronics, the transistor is a king. Computers uses transistors to compute. Also, transistors are used as tiny switches for tunning on and off. It is also used in transferring and amplifying signals, making logical decisions, etc. Today, microchips have a billion transistors, each one turning on and off a billion times every second. These chips require manufacturing processes with roughly 100-nm resolution. Every year this resolution drops, manufacturing even small transistors. Thus, each transistor is reduced to a few atoms or even a single atom.

In 1970, silicon transistors required about 10 million electrons. Current transistors requires closer to 10,000 electrons.

In fact, we here already built single-atom and single-electron transistors. We can use single-electron transistors to make sensitive amplifiers, electrometers, switches, oscillators and other digital electron circuits. All these instruments will be operated by using single electrons or quantum dots.

Condition for single electron phenomena to occur

For single electron phenomena to occur, we have to keep the single electron or quantum dot in isolation.

If any electron on one side of the barrier could just junnel across it, there would not be any isolation. The dot would not be a quantum dot because it would still essentially be part of the bulk, so we need to control the addition and subtraction of electrons.

Rules for single electron phenomena to occur

There are two rules for preventing electrons from tunneling back and forth from a quantum dot. When we follow these rules, they help to ensure that the dot remains isolated and quantized.

The rules are

Rule 1: The coulomb Blockade

Rule 2: Overcoming uncertainty

Rule 1: The coulomb Blockade

We know that the coulomb blockade can prevent unwanted tunneling. Hence we can keep the quantum dots isolated. The condition for this is given by

 …….. (1)

Rule 2: Overcoming uncertainity

For the second condition, to keep quantum dots electronically isolated, we look to the uncertainty principle.

According to uncertainty principle

…....(2)

Energy uncertainty

……..(3)

Here, h is the Planck's constant and Δt is the measurement time. Since, quantum dot is a tiny capacitor then the measurement time Δt is capacitor's time constant.

The time constant for a capacitor is RC, where R is the resistance and C is the capacitance.

We can write the time constant as

……..(4)

Substituting Eqn. (4) in Eqn. (3), we get

……..(5)

Where R_t = tunneling resistance and

C_dot = capacitance dot.

Our aim is to keep electrons from tunneling freely back and forth to and from the dot. To ensure this, the uncertainty of the charging energy must be less than the charging energy itself.

For maintaining electron isolation in quantum dot, we need

……..(6)

Substituting Eqn. (3) and Eqn. (1) in equation (6), we get

……..(7)

Substitute Eqn.(4) in Eqn.(7), we get

…….(8)

In other word we can write the Eqn. (8) as

…… (9)

Substituting the values for h = 6.625 × 10^-34 Js and E = 1.6x 10^-19 C, we get

h/e² = 25878 is the resistance quantum.

This high resistance value is like a thick insulating material surrounding the quantum dot.

Thus, we keep the quantum dots electronically isolated.

Conditions for tunneling

The two tunneling conditions are

When these conditions are met and the voltage accross the quantum dot is scanned, then the current jumps in increments everytime the voltage changes by the value of equation  

This is called a coulomb blockade because the electrons are blocked from tunneling except at the discrete voltage change positions.

The two conditions or rules which explain the single electron phenomenon will help to build a single electron transistor.

SINGLE ELECTRON TRANSISTOR [SET]

Definition

A transistor made from a quantum dot that controls the current from source to drain one electron at a time is called single electron transistor.

Difference between ordinary and single electron transistor

The single electron transistor [SET] is built like a conventional FET. The difference is that instead of a semiconductor channel between the source and drain electrodes, there is a quantum dot.

This dot can be a particle on an insulating surface, a disk sandwiched between insulators or even just a section of semiconducting material where electric fields effectively isolate electrons.

Working of SET

A generalized schematic of such a device and its operation is shown in Fig 5.20.

1. The purpose of SET is to individually control the tunneling of electrons into and out of the quantum dot. To do this, we must first stop random tunneling by choosing the right circuit geometry and materials. If an electron comes or goes from the dot, it will on purpose.

2. To control tunneling, we apply a voltage bias to the gate electrode. There is also a voltage difference between the source and the drain that dictates the direction for the current. Here we say that current and electron flow in the same direction and we will consider the electrode from which the electrons orginate.

3. This is similar to the working of an FET, where the gate voltage creates an electric field that alters the conductivity of the semiconducting channel below it, enabling current to flow in form source to drain.

4. Applying a voltage to the gate in an SET creates an electic field and change the potential energy of the dot with respect to the source and drain. This gate voltage-controlled potential difference can make electrons in the source attracted to the dot and, simultaneously electrons in the dot attracted to the drain.

For current to flow, this potential difference must be atleast large enough to overcome the energy of the coulomb blockade.

The energy 'E' needed to move a charge, Q, across a potential energy difference, V, is given by

E = VQ

Here Q → e → charge of an electron.

Hence, we get the energy needed equal to the energy of the coulomb blockade [E = Ec] and determine the voltage that will move an electron onto or off the dot:

…….. (1)

With this voltage applied to it, an electron can tunnel though coulomb blockade of the quantum dot.

Working for single-electron transistor (SET) in nutshell

A single-electron transistor (SET) is shown in Fig. 5.20. As opposed to the semiconductor channel in a field-effect transistor, the SET has an electrically isolated quantum dot located between the source and drain.

1. The SET in "OFF" mode. The corresponding potential energy diagram shows that it is not energetically favorable for electrons in the source to tunnel to the dot as shown in Fig. 5.20 (a).

2. The SET in "ON" mode. At the lowest setting, electrons tunnel one at a time, via the dot, from source to drain as shown in Fig. 5.20 (b).

3. This is made possible by first applying the proper gate voltage, Vgate = e/2C_dot so that the potential energy of the dot is made low enough to encourage an electron to tunnel through the Coulomb blockade energy barrier to the quantum dot.

4. Once the electron is on it, the dot's potential energy rises as shown in Fig. 5.20 (c).

5. The electron then tunnels through the Coulomb blockade on the other side to reach the lower potential energy at the drain as shown in Fig. 5.20 (d).

6. With the dot empty and the potential lower again, the process repeats as shown in Fig. 5.20 (e).

ELECTRICAL BEHAVIOR OF AN IDEAL SET (OPTIONAL)

The electrical behavior of an ideal SET is shown in Fig. 5.21. The number of electrons in the quantum dot is controlled using the gate voltage.

Fig. 5.21 also shows the spikes in current through the transistor (from source to drain), which occur at discrete gate voltages.

These ON and OFF states can be utilized to make an effective switch out of a Single electron transistor [SET].

Fig. 5.21 The electrical behavior of an ideal SET as a function of gate voltage.

Explanation of Electrical behavior of an ideal SET

The electrical behavior of an ideal SET as a function of gate voltage is shown in Fig. 5.21 and explanation is given below.

1. The number of electrons on the quantum dot is zero until the Coulomb blockade is overcome at V _coulomb at which point electrons tunnel one at a time from the source to the drain via the quantum dot.

2. Because the energy on the dot quantized, only discrete gate voltages enable the tunneling of electrons and consequent increases in the number of electrons in the dot. The seperation between these gate voltage is e/2C. This is the voltage necessary to increase the number of electrons on the dot by one.

3. The current-versus-voltage chart at the bottom shows the corresponding spikes in the source-to-drain current through the transistor at discrete gate voltages. Between the spikes, the number of electrons on the dot remains fixed.

Typical gate voltages for such a device are a few millivolts; typical source-to-drain currents are in the picoampere range.