# Bright Hub Engineering

## Wavefunctions and Visualization of Quantum Dots

written by: Aggeliki K. • edited by: Lamar Stonecypher • updated: 9/24/2010

This article describes the physics of Quantum Dots, their amazing optical properties, and how these tunable properties can be observed and used for bioimaging and other applications as well.

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### Introduction

Quantum Dots or QDs are artificial clusters of semi-conductive atoms, usually in the range of 2-50 nm, that are also known as fluorescent semiconductor nanocrystals. In these sizes, the material of the QD behaves differently than in the bulk state. This is due to the quantum confinement, meaning that the energy states of the electrons lose their continuity and become discrete. This affects the absorption and emission of light when electrons move from one state to another. The new optical properties that materials acquire in this 3D confinement state make them appropriate for various imaging applications.

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### Energy States and Wavefunctions of Quantum Dots

In a bulk semiconductor, the electrons occupy multiple energy levels in the valence band that appear continuous. When an external stimulus is applied (e.g. photon absorption), the electrons will move to higher energy levels of the conduction band that appear continuous as well. So after relaxation has occurred, the semiconductor will emit photons (light) of a wide and continuous wavelength range. The quantum confinement of the dot makes these energy levels discrete, and thus it will only emit light with wavelengths corresponding to the energy difference among these discrete states. The motion of a 3D confined electron in space and time can be described by a quantum mechanics defined wavefunction ψ. These wavefuctions describe how the electron behaves when being in a specific energy state.

The absolute value square of this function |ψ|2 gives us the probability density P of the electron's position:

P= ∫ |ψ(x,y,z)|2 dV

where x, y, z are the spatial dimensions and V the volume of the dot. The remarkable thing about this function is that it may be altered by tuning the quantum dot size or volume. So, the adjustment of the electron's energy levels inside the QD can lead to the adjustment of the photon's wavelength emitted by the QD.

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### Visualization of Quantum Dots and Optical Imaging

As described above, the QD emits photons or light in a specific wavelength that depends only on its size. As the size increases, there is a shift towards longer wavelengths, meaning that the light reaches the red end of the visible spectrum. Another fact is that the dot may remain fluorescent (keep emitting light) long after the external stimulus has stopped. These optical properties made QDs suitable for many applications including biological labelling, in whichh they substituted organic dyes.

The visualization of QDs is made possible through traditional fluorescence techniques or AFM imaging and sometimes a combination of both methods is used to give clearer results. QD visualization is possible through optical and electron microscopy as well. Another proposed method suggests the use of silver deposition onto the surface of QDs in order to amplify their size and make them visible for detection. This method could be ideal for the detection of non-fluorescent QDs.

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### Summing Up

The fact that Quantum Dots exhibit such remarkable and tunable optical properties makes them excellent candidates for biological imaging applications. Their electrical properties are also on the spotlight, and researchers are already exploiting them. We have yet to see many more applications, and QDs are very promising in this direction.

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### Sources:

Imaging Quantum Dots on the Surface of Cells", K. Poole, JPK Application Report

Visualizing Quantum Dots in Biological Samples Using Silver Staining", L.Y.T.Chou, H.C.Fischer,S.D.Perrault,W.C.W.Chan, 2009

"Introduction to Quantum Mechanics", D.L. Griffiths, 2004