Bonds and Bands in Semiconductors
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Bonding forces arise from a quantum mechanical interaction between the shared electrons. Both electrons belong to each bond, are indistinguishable, and have opposite spins. No free electrons available at 0 K, however, by thermal or optical excitation, electrons can be excited out of a covalent bond and can participate in current conduction important feature of semiconductors. Ionic character of bonding becomes more prominent as the constituent atoms move further away in the periodic table, e.
Energy Bands As isolated atoms are brought together to form a solid, the electron wave functions begin to overlap. Various interactions occur, and, at the proper interatomic spacing for the crystal, the forces of attraction and repulsion find a balance. Due to Pauli exclusion principle, the discrete energy levels of individual atoms split into bands belonging to the pair instead of to individual atoms.
In a solid, due to large number of atoms, the split energy levels for essentially continuous bands of energy. Imaginary formation of a diamond crystal from isolated carbon atoms. Each atom has two 1s states, two 2s states, six 2p states, and higher states. For N atoms, the numbers of states are 2N, 2N, and 6N of type 1s, 2s, and 2p respectively. With a reduction in the interatomic spacing, these energy levels split into bands, and the 2s and 2p bands merge into a single band having 8N available states. As the interatomic spacing approaches the equilibrium spacing of diamond crystal, this band splits into two bands separated by an energy gap , where no allowed energy states for electrons exist forbidden gap.
The upper band called the conduction band and the lower band called the valence band contain 4N states each. At 0 K, the electrons will occupy the lowest energy states available to them thus, the 4N states in the valence band will be completely filled, and the 4N states in the conduction band will be completely empty. Metals, Semiconductors, and Insulators For electrons to move under an applied electric field, there must be states available to them.
A completely filled band cannot contribute to current transport; neither can a completely empty band. Thus, semiconductors at 0 K are perfect insulators. With thermal or optical excitation, some of these electrons can be excited from the valence band to the conduction band, and then they can contribute to the current transport process. At temperatures other than 0 K, the magnitude of the band gap separates an insulator from a semiconductor, e.
Number of electrons available for conduction can be increased greatly in semiconductors by reasonable amount of thermal or optical energy. In metals, the bands are either partially filled or they overlap thus, electrons and empty states coexist great electrical conductivity. Direct and Indirect Semiconductors In a typical quantitative calculation of band structures, the wave function of a single electron traveling through a perfectly periodic lattice is assumed to be in the form of a plane wave moving in the x-direction say with propagation constant k, also called a wave vector.
In quantum mechanics, the electron momentum can be given by The space dependent wave function for the electron is 2. Allowed values of energy, while plotted as a function of k, gives the E-k diagram. Since the periodicity of most lattices is different in various directions, the E-k diagram is a complex surface, which is to be visualized in three dimensions. Direct band gap semiconductor: In a solid, electrons can become mobile if the electrons can be promoted to unfilled orbitals in the conduction band of the solid.
How can we account for the electrical conductivity of metals? Think again about an individual Na atom, containing only one valence electron in the 3s orbital recall Figure 3. This atom has a half-filled 3s orbital because the 3s orbital can hold up to 2 electrons and three unfilled 3p orbitals, as you will learn later in Chem All of these are valence orbitals and combine with those from other atoms in the solid to form the band of "mixed" orbitals described above. However, the number of electrons contained in the valence band is much smaller than the number the band is capable of containing.
The reason the band is filled much less than its capacity is that each atom contributes only one electron to the band, but contributes four orbitals to the band; hence, the band is capable of holding up to eight electrons per atom. The filled and unfilled portions of the band are continuous recall Figure 3 ; no band gap is present like in carbon and other nonmetal solids. Therefore, electrons can easily i. Therefore, metals conduct electricity because the partially-filled band of orbitals allows electrons to move easily throughout the sample.
We know that nonmetallic solids form two distinct bands. The lower-energy band, known as the valence band, contains all of the valence electrons the band is filled with electrons , while the higher-energy band, the conduction band, contains no electrons recall Figure 4. Electrons in the filled valence band cannot move to other orbitals within the band because all of the orbitals are already filled. No motion of electrons occurs in the conduction band because it is empty. Now, recall that these bands are separated by a large band gap.
Therefore, a large amount of input energy is required to promote an electron from the filled lower-energy valence band to the unfilled higher-energy conduction band.
Thus, without the high-energy input to promote an electron from the lower-energy band to the higher-energy band, there are no mobile charge carriers, and the nonmetallic solid cannot conduct electricity. As you should observe in lab, semimetalssuch as silicon Si have intermediate properties between those of metals and nonmetals. The band gap in semimetals is small enough recall Figure 5 that an electron can be promoted from the filled lower-energy band to the unfilled higher-energy band with a moderate input of energy such as the thermal energy that dissipates in the solid when electrical current is passed through it.
Then, the lower-energy valence band is no longer completely filled and the higher-energy conduction band is no longer completely empty; i. In the valence band, electrons can move between orbitals and thus throughout the solid once some of the orbitals have become vacant. Promotion of electrons to the conduction band allows the electrons to move easily between the band's many empty orbitals. Hence, semimetals can conduct electricity with a moderate input of energy. In a semiconductor, the band gap is small enough that electrons can be moved from the orbitals in the valence band to the orbitals in the conduction band.
This leaves both bands partially filled, so the material can conduct electricity. Adding small, controlled amounts of "impurities" that have roughly the same atomic size, but more or fewer valence electrons than the semimetal can increase the conductivity of semiconductors like Si.
This process is known as doping. An impurity with fewer valence electrons such as Al; see the periodic table takes up space in the solid structure, but it contributes fewer electrons to the valence band, thus generating an electron deficit Figure 8. This type of dopant creates a space or "hole" in the lower-energy valence band, making room for electrons to travel.
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Hence, the electrons in the valence band can move from one orbital to another within this band with only a small input of energy smaller than required for the semiconductor without the doping. In this way, the electrons can move throughout the solid. Alternately, an impurity with more valence electrons such as P; see the periodic table contributes extra electrons to the band Figure 9. Since the valence band is already filled by the semimetal, the extra electrons must go into the higher-energy conduction band.
These electrons now occupy a partially-filled band the conduction band and can move easily between the orbitals of this band. This allows the electrons to move easily throughout the solid. Semiconductors whose conductivity has been enhanced with valence-electron-deficient dopants are known as p -type semiconductors p for "positive" because it is deficient in negatively-charged electrons.
Semiconductors whose conductivity has been enhanced with valence-electron-enriched dopants are known as n -type semiconductors n for "negative" because it is enriched with negatively-charged electrons. Now we know that LEDs are doped semiconductors and hence conduct electricity with a small input of energy i.
However, we have not yet answered the questions, how does an LED give off light, and why does an LED give off only one specific color of light?
Bonds and Bands in Semiconductors deals with bonds and bands in semiconductors and covers a wide range of topics, from crystal structures and covalent and. Bonds and Bands in Semiconductors. by Jim Phillips. Publisher: Momentum Press. Release Date: November ISBN: View table of.
Figure 8 A schematic diagram showing the solid crystal-lattice structure and bands for silicon doped with aluminum, a p -type semiconductor. Figure 9 A schematic diagram showing the solid crystal-lattice structure and bands for silicon doped with phosphorus, an n -type semiconductor.
In order to convert electrical current into light, an LED must have a p -type semiconductor in contact with an n -type semiconductor. This combination of the two types of semiconductors is known as a p-n junction , or a diode. When a p - n junction is placed in a circuit with an external power source e. How does this lead to the emission of light in the LEDs? Recall that the p -type semiconductor Figure 8 has extra space for electrons in its valence band and no electrons in its conduction band.
On the other hand, the n -type semiconductor Figure 9 has a full valence band no space and extra electrons in its conduction band. If the circuit is constructed such that electrons flow into the n -type side of the p - n junction from the power source Figure 10 , the electrons will occupy the conduction band, since there is no space in the valence band of an n -type semiconductor.
As electrons continue to come into the conduction band, they will be pushed to the p -type side of the p - n junction, which has more space to hold electrons you can think of the "positive" side attracting the negatively-charged electrons. The electrons go into the empty conduction band of the p -type side, since they already occupy the higher-energy band in the n -type side. However, once the electrons are in the higher-energy band of the p -type side, they will fall to the lower-energy band if there is space available for the electrons to occupy in the valence band.
Electrons falling from the higher-energy band of orbitals conduction band to the lower-energy band of orbitals valence band in the p -type semiconductor result in the atoms going from a higher-energy state to a lower-energy state i. As the electrons cross the band gap, energy related in magnitude to the size of the band gap is released in the form of light. The diagram on the left depicts a circuit composed of an LED, a resistor, and a battery.
Bonds and Bands in Semiconductors - Second Edition
The diagram on the right shows the path of electrons moving through a circuit containing a p-n junction. Electrons flow from the negative pole of the battery to the n-type semiconductor, where they occupy the conduction band. The electrons then move into the conduction band of the p-type semiconductor and fall into the empty orbitals of the valence band, which releases energy in the form of light. The electrons then move through the wire back to the positive pole of the battery, and they re-circulate. This picture has been simplified to follow the discussion presented here.
A more complete picture would show a potential energy barrier to electrons moving from the n-type to the p-type semiconductor must be overcome using the voltage from the battery; known as "biasing". For more information, see Elllis et. Click on the pink buttons to view a QuickTime movie showing the flow of electrons through the circuit and the light emitted by the LED. Click the link to download QuickTime and click on the pink button to view a QuickTime movie showing the inflation of dual airbags when a head-on collision occurs. The color of the light emitted depends on the size of the band gap.
The LEDs used in the experiment are made of a combination of semiconducting materials specially chosen to have the right size band gap for yellow light to be emitted. LEDs that emit red light, which are used in many digital alarm clocks, have a different-size band gap, and therefore a different amount of energy is released in the form of light Figure Later in the semester you will learn that light of different colors has different energies.
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LEDs that emit infrared rather than visible light are common in remote controls for televisions and stereos. The color of light emitted by an LED depends on the size of the band gap in the doped semiconductors. Summary and a Look to the Future In this tutorial, you learned that LEDs contain p- type and n- type semiconductors that are side-by-side. Semiconductors conduct electricity because of small band gaps between the valence and conduction bands, which allow electrons to move throughout the material with a moderate input of energy. The LED emits light when the electrons fall from the conduction band to the valence band.
Today's LEDs use inorganic material in the semiconductor.
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In , the next generation of light-emitting material, the light-emitting polymer LEP , was discovered. LEPs are organic carbon-based semiconducting materials. LEPs are based on the same chemical concepts taught in this tutorial. LEP's can be used in more diverse applications than LEDs because polymers are flexible and can be shaped to different forms, for example flat-panel color displays are made of LEP materials.
At this time, technology and applications based on LEPs are still in developmental stage. Fron Indicators to Illumination?
Rensselaer Polytechnic Institute, Chemical Bonding in Solids, New York: Oxford University Press, American Chemical Society, Smithsonian Museum of Natural History.