Coulomb Blockade Effect

COULOMB BLOCKADE EFFECT

Definition

The resistance to electron transport caused by electrostatic coulomb forces in certain electronic structures, including quantum dots and single electron transistors is called coulomb Blockade.

(or)

The prohibition or suppression of tunneling is called Coulomb Blockade.

In simple words, the suppression of electron flow is called coulomb blockade.

Explanation

Now let us see the explanation of Coulomb blockade. We know coulomb forces are electrostatic. If we have two or more charges near one another, they exert coulomb forces upon each other. If two charges are same, the force is repulsive.

In the case of a quantum dot, the charges are all negative electrons. Trying to bring them forcefully together creat coulomb forces.

It is a well known fact that that the isolated droplet of electrons does not Willingly accept another, but repels it.

This is Coulomb blockade and it helps prevent constant tunneling to and from a quantum dot.

Now we can measure the Coulomb blockade's effect. A quantum dot has a capacitance, 'C_dot', a measure of how much electric charge it can store.

 C_dot = Gɛd            …….. (1)

Where

 ɛ ⇒ permittivity of the material surrounding the dot

 d ⇒ diameter of the dot

 G⇒ geometrical term [ If the quantum dot is disk, G = 4, if it is spherical particle, G = 2π].

Here, the capacitance is not like the one between a pair of parallel plates but an object isolated in space which can store charge on its own and hence have a Capacitance.

The energy needed to add negatively charged electron to the dot is known as the charging energy E_c.

 E_c = e² / 2C_dot             ...(2)

Where e = charge on the electron

Hint:

 q = CV

 e = CV

 V = e/C

 E = ½ CV² = ½ e²/C

 Ec = e² / 2C_dot

Inference

From equation (2) we can see that E_c is inversely proportional to the dot's capacitance. In that case, a large capacitor can quite easily accomodate another electron without too much energy required.

However, in the opposite case, with extremely small capacitors [quantum dots], the charging energy can be substantial [large]. That is, small capacitors [quantum dots] are large enough to "block" tunneling electrons.

Energy required

Now, we have to know how much energy is necessary to block the tunneling electrons in the coulomb blockade.

The answer is that coulomb blockade needs more energy than a given electron can "spend" trying to tunnel in and out.

We know that a free electron in a solid has a certain amount of energy depending on which band it is in. Due to thermal vibrations of the atoms in the lattice, these free electrons will get extra energy to go to higher bands. The extra energy is equal to K_BT [k_B = B Boltzmann constant = 1.38 × 10^‒23 J/k]. With this extra an this extra energy, an excited electron might be able to tunnel through a small barrier.

The coulomb blockade can prevent unwanted tunneling, when the charging energy is much higher than the thermal energy of an electron.

Condition for coulomb blockade

The condition of the coulomb blockade is therefore

 E_C >> K_BT             ...(3)

 (or)

As a rule of thumb, E_C > 10K_BT. This criterion can be more easily acheivable if smaller the dot becomes.