Question

3. What are the two rules for keeping the Quantum in Quantum Dot? Explain each rule.

Answer 1

A quantum dot is a semiconductor nano-structure that confines the motion of conduction band electrons, valence band holes, or excitons (bound pairs of conduction band electrons and valence band holes) in all three spatial directions.

The confinement can be due to electrostatic potentials (generated by external electrodes, doping, strain, impurities), the presence of an interface between different semiconductor materials (e.g. in core-shell nano-crystal systems), the presence of the semiconductor surface (e.g. semiconductor nano-crystal), or a combination of these.

A quantum dot has a discrete quantized energy spectrum.

Quantum dots exhibit “total confinement".

Tunneling is the way electrons cross both the physical barriers and the energy barriers separating a quantum dot from the bulk material that surrounds it. Yet the energy needed to tunnel is only part of the story. If any electron on one side of the barrier could just tunnel 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 be able to control the addition and subtraction of electrons. We can do this with voltage biases that force the electrons around. However, priority number one is ensuring that the electrons stay put when there is no voltage bias at all. There are two rules for preventing electrons from tunneling back and forth from a quantum dot. When followed, these rules help to ensure that the dot remains isolated and quantized.

Two Rules for Keeping the Quantum in Quantum Dot :

Rule 1: The Coulomb Blockade

Just from the name we can get an idea of what is happening. 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 the same, the force is repulsive. In the case of a quantum dot, the charges are all negative electrons. Trying to cram even just a few electrons into a tiny piece of real estate creates Coulomb forces. As we would expect, the isolated droplet of electrons does not willingly accept another electron, but repels it. This is the Coulomb blockade and it helps prevent constant tunneling to and from a quantum dot.

Rule 2: Overcoming Uncertainty

For the second condition that must be met in order to keep quantum dots electronically isolated, we look to the Uncertainty Principle. The central tenet of the Uncertainty Principle is: "the more precisely we know something’s position, the less precisely we can know its momentum". A corollary to this rule has to do with energy. It states that, "the uncertainty in the energy of a system is inversely proportional to how much time we have to measure it". Specifically, the energy uncertainty, ΔE, adheres to this relationship:

Where, h is Planck’s constant and Δt is the measurement time.

We have 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. It means that, if what we determine to be the amount of energy needed to add an electron to the dot can be off by as much as, or more than, the actual amount, random tunneling can occur without our knowledge.

Example - Imagine if an amusement park determined that people needed be at least 50 inch tall to ride a particular roller coaster safely, but the tool used for measuring height had a precision of plus-or-minus 75 inch. The park cannot be certain who ends up getting on the ride, or if they will be safe.