Bonds, Bands, and Doping: Periodic Trends Experiment |
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Authors: Rachel Casiday and Regina Frey Department of Chemistry, Washington University St. Louis, MO 63130 |
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For information or comments on this tutorial, please contact K. Mao at mao@wustl.edu. Please click here for a pdf version of this tutorial. |
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Light-emitting diodes (LEDs) (Figure 1) are found in many ordinary objects that we use on a daily basis. Common examples of LEDs include the digital display (i.e., the bars and dots that make up the numbers) on your alarm clock, the tiny light that indicates whether your iron, computer, or electric razor is on, the scanners on grocery-store checkout counters, and the red lights on the back of some children's tennis shoes that flash when the child takes a step. Pocket laser pointers and the lasers used to scan CD's are also based on LED technology. (Lasers have LEDs in combination with optical devices (e.g., mirrors) to give a specially directed beam of light.) Although they are now commonplace, LEDs that give off visible light were actually invented relatively recently. In 1962, Nick Holonyak, Jr., while working for General Electric, discovered that the chemical composition of earlier diodes could be changed to make them give off visible light for use in digital displays and indicators. LEDs operate by a completely different mechanism from other sources of light, such as light bulbs and the sun. Furthermore, LEDs release only one particular color of light, and they produce very little heat. In contrast, the "white" light produced by a light bulb or the sun is really a blend of many different colors, and these sources also typically produce a large amount of heat. Hence, LEDs are much more efficient for producing small quantities of light of a particular color than other light sources. Because of this efficiency, scientists and engineers are hard at work to develop designs that will allow LEDs to be used for many new applications, from traffic lights to atmospheric-haze detectors. It has been estimated that replacing all the incandescent traffic lights in the United States with LED traffic signals would save almost 2.5 billion kilowatt hours per year (roughly equivalent to $200 million, or 5 billion pounds of CO2 (from burning fossil fuels to make electricity) released into the atmosphere)!
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| Figure 1
This diagram shows the principal components of a typical LED, such as the one you used in the experiment to test conductivity. The plastic lens encapsulating the LED takes up most of the space in this device, while the actual LED chip is only about 0.25 mm2. |
Just what, then, is a light-emitting diode? LEDs are semiconductor devices that can convert electrical energy directly into light, due to the nature of the bonding that occurs in the semiconductor solid. As we shall see, the type of bonding in a solid is directly related to the conductivity of the solid. Metals, nonmetals, and semimetals have different bonding properties that lead to the differences in conductivity that can be observed among these categories of elements. LEDs rely on special conductivity properties in order to emit light. Hence, to understand LEDs we must first look at bonding in elemental solids.
Bonding in Elemental Solids
In the introduction to the experiment, you learned that metals are electrically conducting because their valence electrons (the outermost electrons of an atom) "swim" in an electron "sea". This picture is useful for imagining how metals have sufficiently mobile charged particles to conduct electricity, but it does not fully explain the difference in conductivity among the various elements. To explain the difference in the properties of metals, semimetals, and nonmetals, and hence to understand how LEDs work, we need to understand the bonding of solids in more detail. Throughout this course (and science, in general), different models (theories) are used to describe a phenomenon (e.g., electrical conductivity). It is important to remember that all models are approximations and will fail at some point, but all have their own usefulness and advantages in describing a phenomenon of interest.
You read in the introduction to the experiment that the electronegativity of elements increases from the left side of the periodic table (metallic elements) to the right side (nonmetallic elements). (Electronegativity is the ability of an atom in a compound to attract electrons to itself (away from its neighbor).) Because atoms with low electronegativity (i.e., metals) do not hold their valence electrons tightly, their valence-electron orbitals are diffuse and may extend to large distances away from the nucleus. Highly electronegative atoms (i.e., nonmetals) do hold their electrons tightly, and so their valence-electron orbitals are less diffuse and smaller. (To help visualize how high electronegativity makes orbitals less diffuse and smaller, think of a dog on a leash: if you pull harder on the leash, you bring the dog closer to you so that its movement is restricted to a smaller area.)
When atoms interact together, their valence orbitals overlap to form bonds between the atoms. You have already learned from the experiment that electronegativity differences are very important in determining the types of bonds that form between atoms of different elements. Electronegativity also plays an important role in determining the properties of bonds between atoms of the same element in a solid (for which the difference in electronegativity is zero). How can electronegativity help us to understand the behavior of metals, semimetals, and nonmetals?
Metals: Weak Covalent Bonding (Metallic Bonding)
Let us first consider the example of sodium (Na). Na has one valence electron, which is in the 3s orbital. When two Na atoms bond to form a gaseous Na2 molecule, the two valence electrons (one from each Na atom) are found primarily between the two Na nuclei. To make a crystalline solid, many atoms are packed together in a regular pattern. In metal solids (Figure 2a), the atoms adopt a "closest packed" configuration, in which the atoms are equally spaced, and space between the atoms is minimized. Electrons in diffuse orbitals are not tightly constrained to a small space, and hence the interactions between one Na atom and an adjacent Na atom, or "nearest neighbor," are weak. At the same time, each atom in a metallic solid has many (up to 12) "nearest neighbors," i.e., each atom interacts with many other atoms. Thus, although the individual interactions between atoms are weak, there are many interactions, and the aggregate effect is a well-bonded metallic solid. (To illustrate this point, think of how a woven cloth is held together. Although the individual threads may be quite weak, when many threads are woven together, they form a strong cloth.)
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Figure 2a. This is a representation of the three-dimensional structure of a crystalline metal, in which each atom has 12 nearest neighbors (closest-packed configuration). The bonding in this structure is described above in the section, "Metals: Weak Covalent Bonding." b. This is a representation of the three-dimensional structure of a crystalline nonmetal, in which each atom has only 4 nearest neighbors. The bonding in this structure is described below in the section, "Nonmetals: Strong Covalent Bonding." Note: The crystal structures were drawn using PowderCell for Windows, and the images were rendered using POV-Ray (see References ). |
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The large number of nearest neighbors for metal atoms in a solid effectively causes the atoms to be surrounded in all directions by other atoms' valence-electron orbitals. Recall that when atoms are packed in a solid and interact, their valence orbitals overlap. Thus, in a metallic solid such as sodium, each atom's valence orbital can overlap with many other valence orbitals in virtually all directions. Each Na atom is affected (perturbed) by its many neighbors and therefore, the valence atomic orbitals of all of the Na atoms "mix" to form an almost continuous band of orbitals that are very close in energy. Because these valence atomic orbitals have lost their individual identity in this aggregate of Na atoms, the band formed is called the valence band (Figure 3). (You may find it helpful to think about what happens to the individual identities of voters in an election. Going into the voting booth, each voter decides for himself or herself how to vote, just as a solitary atom has its own valence orbitals with a certain number of electrons. However, when the results are tallied, the individual identities of the voters are lost; the voters are simply divided into those who voted for one candidate and those who voted for the other candidate. Similarly, when many atoms bond together, the individual identities of the orbitals are lost; they form continuous bands that are divided into the filled and unfilled orbitals.)
The low-electronegative metal atoms "give up" their valence electrons, allowing them to be found throughout the "mixed" orbitals of the valence band. Hence, the band of orbitals is filled to a certain energy according to the number of valence electrons provided by all of the Na atoms in the solid. Because electrons are shared among atoms in these "mixed" orbitals, they form covalent bonds between the atoms in the solid. Each atom shares electrons with all its many neighbors in all directions, so these bonds are weak covalent bonds. Because the orbitals are large and diffuse, the bonds formed are not confined between two atoms. Another term frequently used to describe this type of bonding is "metallic bonding." Solids with this type of bonding exhibit metallic properties and are therefore categorized as metals. As we shall see later in the tutorial, elements with metallic bonding are very good conductors of electricity because of the nondirectionality of the orbitals (i.e., electrons can easily move in any direction). Metallic elements are not used in LEDs, although they are important components of the circuits used to power LEDs.
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| Figure 3
When metal atoms interact together to form a solid, their atomic orbitals mix to form a continuous band of orbitals. In the representation of 1 Na atom (left-hand side of diagram), the blue dot represents an electron in the 3s orbital; in the representation of many Na atoms (center of diagram), the blue dots again represent electrons in the "mixed" orbitals that are formed when many atoms interact. This "mixing" of orbitals is better represented by a "band" of orbitals (right-hand side of diagram), in which the blue area represents orbitals that are filled with electrons. |
Nonmetals: Strong Covalent Bonding
Now consider the example of carbon (C), a nonmetal. Its electronegativity is high relative to that of sodium. Therefore, the valence orbitals of a C atom are not diffuse and are smaller than those of Na. When C atoms are packed together to make a solid, the valence orbitals overlap within a small volume, thus causing the electrons in these orbitals to be constrained to a small space. Some of the C atoms are drawn closer together, pulling them further away from others. This severely distorts the closest-packed structure (Figure 2a) and causes it to become a nonmetallic crystalline solid structure (Figure 2b). In order to form the nonmetallic solid structure, the highly electronegative atoms interact with only a few (usually four or less) nearest neighbors, and each valence orbital is oriented in the direction of the atom with whose valence orbital it overlaps. Hence, the interactions between those atoms that are drawn close together are strong. As in metal solids, the valence atomic orbitals lose their individual identity in the aggregate of C atoms, and these orbitals "mix" to form a band of orbitals that are close in energy.
Electrons are shared between atoms in these "mixed" orbitals, but the bonds are directional. Therefore, the bonds formed in nonmetal elemental solids are stronger and are called strong covalent bonds. In strong covalent bonds, a large energy gap arises between the orbitals that are formed, as you will see later in Chem 111. When many strong covalent bonds are present, as in the nonmetallic solid, two bands of "mixed orbitals" form, separated by an energy gap called the band gap (Figure 4). The lower-energy band consists of filled orbitals (i.e., orbitals containing electrons) and is known as the valence band; the higher-energy band consists of unfilled orbitals and is known as the conduction band. As you go across the periodic table, the band gap increases (as the electronegativity increases). Semimetals (Figure 5), which lie between metals and nonmetals on the periodic table, have an energy gap between the valence and conduction bands (band gap) similar to nonmetals (not a continuous band like metals), but the band gap for semimetals is smaller than for nonmetals.
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| Figure 4
When nonmetal atoms interact to form a solid, their atomic orbitals mix to form two bands of orbitals that are separated by a large band gap. |
Figure 5
When semimetal atoms interact to form a solid, their atomic orbitals mix to form two bands of orbitals that are separated by a small band gap. |
As we shall see later in the tutorial, elements with band gaps are less able to conduct electricity. (Recall that the metals described above are good conductors because they have no band gap.) As the size of the gap increases, the materials become better insulators (poorer conductors of electricity). Hence, nonmetals are usually classified as insulators. Semimetals are the elements used in LEDs. Why are semimetals, and not metals (good conductors) or nonmetals (insulators), used in LEDs? To answer this question, we need to discuss conductivity in terms of bonds. Before we discuss conductivity, we need to summarize the periodic trends described above.
· Why is electronegativity related to band gap size and directionality of bonds?
· Which element would you expect to have a larger band gap in the elemental solid, aluminum (Al) or sulfur (S)? Briefly explain your reasoning.
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| Figure 6
This is a representation of the periodic table showing the trends in the bonding properties of solids from the left-hand side to the right-hand side. |
These periodic trends in bonding properties are also related to the conductivity of the elements. The metals (on the left of the periodic table) tend to be good conductors of electricity, while the nonmetals (on the right of the periodic table) tend to be poor electrical conductors. The semimetals are typically classified as semiconductors because they conduct electricity (but not as efficiently as the metals). Recall from the discussion of LEDs above that LEDs are semiconductor devices whose light-emitting properties are dependent on the nature of the bonding in the semiconductor. Hence, the next step in understanding how LEDs work is to describe the relationship between bonding (and the bands that form when the atoms are bonded together) and the conductivity properties of the elements.
What about nonmetals? 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, semimetals such 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.e., both bands are partially filled (Figure 7). 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.
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| Figure 7
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. |
Now we know that LEDs are doped semiconductors and hence conduct electricity with a small input of energy (i.e., LEDs are very efficient). 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?
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| 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. |
· State whether each of the following could be used to dope arsenic (As): gallium (Ga), phosphorus (P) and selenium (Se). Explain your answer.· For each of the elements listed above that could be used to dope arsenic, state whether an n-type or p-type semiconductor is formed. Explain your answer.
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.e., becoming more stable). 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.
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Figure 10The diagram on the left schematically shows the path of electrons moving through a circuit containing a p-n junction. Electrons flow from the negative (shown in black) pole of the battery to the n -type semiconductor, where they occupy the higher-energy (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 (shown in copper) of the battery, and they re-circulate. ( Note: This picture has been simplified to follow the discussion presented here. A more complete picture would show the two doped semiconductors in equilibrium, in which the band gaps are "bent" and 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 on bending in diodes, see Elllis et. al in the References . The diagram on the right depicts a circuit composed of an LED, a resistor, and a power source (battery). The flow of electrons through this circuit is the same as that described above. The resistor in the circuit (which is not shown on the left for ease of viewing) is necessary to limit the current so that the LED does not "burn out" by receiving too much current from the battery. Click on the pink button below to view a QuickTime movie showing the flow of electrons through the circuit and the light emitted by the LED. Click here to download QuickTime 7.0 to view the movie.
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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 11). (Later in the semester you will learn that light of different colors has different energies.) LEDs that emit infrared rather than visible light are common in remote controls for televisions and stereos.
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| Figure 11
The color of light emitted by an LED depends on the size of the band gap in the doped semiconductors. For instance, LEDs that emit red light have a smaller band gap than LEDs that emit yellow light. |
Today's LEDs use inorganic material in the semiconductor. In 1990, 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. At this time, however, technology based on LEPs is still in the experimental stages.
• Bierman, A.; Narendran, N.; Bullough, J. "LEDs: Fron Indicators to Illumination?" Lighting Futures, Vol. 3, No. 4. Rensselaer Polytechnic Institute, 1998. URL: http://www.lrc.rpi.edu/programs/Futures/index.asp .
• Burdett, J. K. Chemical Bonding in Solids, New York: Oxford University Press, 1995.
• Ellis, A. B. et al. Teaching General Chemistry: A Materials Science Companion, Washington, D.C.: American Chemical Society, 1993.
• Cook, G. "What Is Lighting Efficiency?" Energy Efficiency & Environmental News: Facts on Energy and Energy Use. Florida Energy Extension Service, 1991. URL: http://edis.ifas.ufl.edu/BODY_EH334.
• Fury, M.A. "Electronic Products," in Electronic Materials Chemistry , H.B. Pogge, ed. New York: Marcel Dekker, Inc., 1996.
• Lemelson Center. "Inventors: Nick Holonyak, Jr. invented the first visible-spectrum light-emitting diode," The Quartz Watch. Smithsonian Museum of Natural History. URL: http://www.si.edu/lemelson/Quartz/inventors/holonyak.html .
• Porile, N.T. Modern University Chemistry, San Diego: Harcourt Brace Jovanovich, 1987.
• Persistence of Vision Ray Tracer (POV-Ray). URL: http://www.povray.org .
PowderCell for Windows. Kraus, W. and Nolye, G.; Bundesanstalt für Materialforschung und -prüfung (BAM) . URL: http://www.bam.de/php/loadframe.php?a=http://www.bam.de/service/publikationen/powdercell_i.htm .The development of this tutorial was supported by a grant from the Howard Hughes Medical Institute, through the Undergraduate Biological Sciences Education program, Grant HHMI# 71192-502004 to Washington University.
Copyright 1998, Washington University, All Rights Reserved.
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