How do we relate this picture to what we know about energy levels in atoms? As you know, atoms have many atomic orbitals that hold the atom's electrons. Like atoms, molecules can be thought of as containing energy levels that hold electrons. These energy levels are associated with molecular orbitals just as atomic energy levels are associated with atomic orbitals. Like atomic orbitals, each molecular orbital can hold just two electrons. Electrons fill the lowest energy molecular orbital available (two electrons per orbital). Additional molecular orbitals are empty and reside at higher energies.

Molecular orbitals consist of combinations of atomic orbitals. In simple molecular orbital (MO) theory, a number of atomic orbitals will combine to form the same number of molecular orbitals. For example, "n" atomic orbitals will combine to form "n" molecular orbitals.

To see what this means for molecules, consider the simple molecule H₂. Each H atom has an electron in a 1s orbital. These electrons must come together to form a bond, and they do that through overlap of their 1s orbitals.

However, because we started with two atomic orbitals, one on each H, the overlap actually creates two molecular orbitals. A molecular orbital diagram shows the relative energies of molecular orbials in a molecule. For H₂ it looks like the following:

Note the blue drawings of the molecular orbitals on the right side of the figure above. Each of the molecular orbitals has its own character. The lowest orbital will contain H₂'s two electrons. It also has a shape that makes the electrons spend more time between the two atoms. That is, there is an enhancement of electron density between the two atoms. Because of this, this is considered a bonding orbital - one in which electrons are shared between the two atoms.

The other orbital (the one at higher energy) is empty and has a shape that would lead to electrons spending more time away from the region between the two atoms. This is indicated in the drawing by the lack of a blue region in between the atomic centers. Because of this lack of electrons between the two atoms, this orbital is considered an anti-bonding orbital. In a sense, an antibonding orbital is the opposite of a bonding orbital.

More complex systems have more complex molecular orbital structures. There are a number of computational methods that allow us to use computers to generate descriptions of the molecular orbitals in a molecule. However, with a few simple qualitative rules, we can determine a lot about the electronic structure of a molecule without doing complex calculations. For example:

• The number of atomic orbitals in all the atoms in the molecule = number of molecular orbitals in the molecule.
• Electrons fill the lowest energy molecular orbitals first.
• Filled orbitals are often bonding in character, whereas empty orbitals are often antibonding.
• Electrons can jump from lower energy orbitals to higher energy ones through the absorption of light.

Band Theory

In extended solids, the number of atomic orbitals is quite large due to the large number of atoms. Bringing a lot of atomic orbitals together for such a large compound leads to many, many molecular orbitals in a small energy region. There are so many orbitals, in fact, that the spacing between them becomes essentially negligible. In this case, it no longer makes sense to talk about molecular orbitals with discrete (separated) energy levels. Instead, we call these overlapping levels "bands".

As you can imagine, it would be difficult to talk about 10²³ molecular orbitals individually, so this different model is needed! It is called band theory and is used widely in chemistry, physics, materials science and engineering.

Conductors, Insulators and Semiconductors

• Conductors - conduct electricity in response to a very small applied voltage difference. Electrical current is essentially a flow of electrons across the material. Metals, as well as some compounds, are considered conductors. Conductors have very low electrical resistivity (resistance to electrical conduction) and resistivity generally increases as temperature increases. Resistivity in the range of 10^-8 Ohm-meters is not uncommon. Common conductors include familiar metals like copper, gold and aluminum.

• Insulators - do not conduct electricity. In contract to conductors, applying a voltage difference across an insulator results in negligible electric current. Insulators have a very high resistivity, in the 10⁺⁸ Ohm-meter range. Resistivity generally decreases with increasing temperature, but this is not enough to produce appreciable current. Common insulators include many plastics, rubber and glass.

• Semiconductors - are essentially intermediates between conductors and insulators. They conduct better than insulators, but not as well as conductors. Their resistivity decreases as temperature increases, and substantial currents can be produced. Probably the semiconducting materials that are most familiar to you are silicon and germanium. Some semiconductors can also be made to conduct electricity by other means, such as by the absorption of light.

To understand the differences between these compounds, we must look back at band theory. The electronic structure of solids can be described as a series of bands. The valence band is the highest energy band that contains electrons. Just as in atoms, these valence electrons are the most weakly bound. The valence band becomes extremely important in describing conductors, insulators and semiconductors.

In conductors, the valence band is partially filled with electrons. This is indicated by the shaded region in the diagram. The upper part of the valence band is empty.

Electrons are able to flow across the material in response to an applied voltage, because they can move into the open part of the band. In this region, electrons are not bound to any one atomic center, but are free to flow across the the material. The open part of the band is called the conduction band. (It is said that the valence band and conduction bands overlap. )

In insulators, the valence band is completely filled, thus the electrons are essentially "stuck". There is no where for them to move. There are conduction bands (empty bands) at higher energies, but the band gap between the valence and conduction bands is too large. A lot of energy would be required to promote electrons up into the conduction band, where they could move freely. Thus, little current will be produced.

Semiconductors also have band gaps. However, in the case of semiconductors, the band gap is small. Thus, only a small amount of energy is needed to promote electrons to the conduction band. In many cases, room temperature provides enough thermal energy to excite a significant number of electrons, resulting in appreciable current. Raising the temperature will increase the number of electrons in the conduction band, resulting in lower resistivity.

In addition, empty spaces, or "holes", are created in the valence band when electrons are promoted into the conduction band. These holes are considered to be positively charged due to the absence of the electrons. A hole residing on an atom can move - a neighboring electron can move into the hole, thus creating a new hole in the electron's place. Thus, these holes in the valence band are also considered to be charge carriers that contribute to conductivity.

Electrons in semiconductors may also be excited by other means, such as the absorption of light. This type of process is the physics behind photosensitive switches used in many modern devices.

In summary, the three different types of solids viewed together look like the following. Insulators have large gaps between the valence and conduction bands, semiconductors have small gaps, and in conductors, the two bands overlap and are one in the same.

Why are Metals Shiny?

It turns out that this strong absorption allows for high reflectivity. "What?" you might say. "How can absorption of light lead to its reflectance?" A very good question! It turns out that by exciting electrons into the conduction band, we create an electrical current on the surface of the metal. This current, in turn, re-emits the light. This re-emitted light is the metallic luster we are familiar with in gold, silver, copper and other metals.

"What about the color?" you may ask. The color of different metals is the result of different absorption profiles. For example, copper and gold absorb more poorly at the blue end of the spectrum, thus these wavelengths do not reflect as well. That means that reflected light appears rich in the red-orange-yellow regions, giving gold and copper their familiar colors. Interestingly, if you pound gold into a very thin sheet known as gold leaf, the color it transmits is blue-green (as blue does not absorb and therefor doesn't reflect well).

Doped Semiconductors - and Eventually LEDs

Silicon atoms have four valence electrons. These four electrons fill the valence band of the material. So pure silicon has a band structure as follows:

Phosphorous has five valence electrons. When a small amount of phosphorous is incorporated into silicon's crystal lattice, four of the electrons go into the valence band. The extra electron must go somewhere, so it resides in what is called a donor band. This band lies just below the higher energy conduction band, making it easy for these electrons to jump into the conduction band. Thus, adding a small amount of phosphorous dramatically increases the number of charge carriers in the conduction band, leading to increased conductivity. Semiconductors enhanced in this way are known as N-type semiconductors.

Boron, on the other hand, has three valence electrons. When a small amount of boron is incorporated into silicon's crystal lattice, it is essentially one electron short. Thus, an acceptor band will be produced just above the valence band. Thus, the valence band electrons can easily be promoted to this acceptor band, leaving empty sites at the valence band, referred to as "holes". These holes increase the conductivity of the material. Adding a small amount of boron dramatically increases the number of charge carriers (in this case the holes) leading to increased conductivity. Semiconductors enhanced in this way are known as P-type semiconductors.

LEDs

How LEDs Work - From HowStuffWorks.com

Diamonds

Blue diamonds, such as the famous Hope diamond (or the fictional blue diamond in the movie Titanic), are the result of doping with boron. Boron contains only three valence electrons. Just like in the case of silicon, the incorporation of boron into the crystal leads to the production of acceptor band just above the valence band. The energy difference between the top of the valence band and the bottom of the acceptor band is only 0.4 electron volts. Thermal energy at room temperature is enough to promote electrons into the acceptor band, making blue diamonds conductive.

The blue color is the result of the absorption of light by electrons in the valence band. Electrons in the lower region of the valence band can absorb energy. In this process, they are promoted into the holes left behind by the electrons that moved into the acceptor band. Absorption is stronger in the red region, giving these diamonds their blue color.

In a similar fashion, nitrogen gives rise to yellow diamonds. Nitrogen atoms have five valence electrons, thus a nitrogen impurity in diamond leads to the creation of a donor band below the conduction band. In this case, however, the energy difference between the donor band and the conduction band is still quite large, so yellow diamonds are classified as insulators. However, electrons can be promoted from the donor band into the conduction band by the absorption of blue and violet light. The result is the yellow color of yellow diamonds.

Metal Color, Semiconductor and Diamond Links

• Color in Metals - from Professor Neff at CalPoly.
• Blue Diamonds - specific information about blue and yellow diamonds from webexhibits.org.
• Diamonds - general diamond info from the free on-line encyclopedia Wikipedia.org. This is user-modified, so be sure to double checks facts found here.
• Fancy Colored Diamonds - a good resource from Takara Diamonds - a producer of laboratory grown diamonds.
• Just for fun: Enlightened Illuminated Clothing - Bioengineer and clothing designer Janet Hansen sells custom clothing containing LEDs.

References

• Nassau, K. The Physics and Chemistry of Color: The Fifteen Causes of Color; 2nd ed.; Wiley: New York 2001.
• Webexhibits.org, Blue Diamonds (accessed May 2005).

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