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9.4.C - Semiconductors


Semiconductors are electrical conductors that will conduct electricity only under certain conditions. At very low temperatures they tend not to conduct at all and at high temperatures they conduct as normal conductors do. In between these extremes, their conductivity depends on temperature or other forms of energy and it is this property that makes them useful in electronics. The most common semiconductor in use today is silicon but germanium also has the properties of a semiconductor.

Band Theory is a model for explaining the conducting behaviour of semiconductors and why some substances are considered conductors and others are semiconductors or insulators.

The current carrying capacity of semiconductors can be enhanced by the addition of small amounts of impurities in a process known as doping. Doping produces n-type or p-type semiconductors that are better able to conduct negative and positive currents, respectively. Sandwiching a layer of n-type semiconductor with a p-type semiconductor is called a p-n junction and this is the most fundamental of all components in microcircuits and solid-state electronics. The discovery and application of semiconductors revolutionized the field of electronics, and paved the way for smaller and cheaper radios, calculators, and computers.

In this unit you will:

  • Use Band Theory to describe the electrical behaviour of conductors, insulators and semiconductors
  • Describe the process of conduction by electrons and holes in semiconductors
  • Explain how doping enhances the current carrying capacity of semiconductors
  • Outline the use of semiconductors in solid-state electronics and their advantages over thermionic devices
  • Evaluate the impact of the invention of the transistor on society


Band Theory

In the first half of the twentieth century, quantum physics had provided an enhanced understanding of how electrons were arranged in atoms. Electrons were classified into energy levels (shells) around the nucleus, defined not by their distance from the nucleus, but rather the energy an electron possessed. This also meant that electrons could not have any and every value for energy but only discrete energies allowed by the atom of that particular element. There were rules about how many electrons were allowed to occupy each energy level but for our discussion we are only interested in the fact that an electron in a particular atom was only allowed to possess certain values for energy and never anything in between. You should also recall that in any atom, the valence electrons are the electrons in the highest energy level (with the most energy) and it is almost always these valence electrons that are the ones that do the conducting.

Conductors are able to conduct electricity because they have free electrons. This means that their electrons are not bound to the nucleus by the electrostatic attraction of its positively charged protons. In some conductors such as metals, the valence electrons are not bound to the nucleus so they are free to conduct. In semiconductors, the valence electrons are bound to the positive nucleus and some energy is required to free them for conduction. In insulators, too much energy is needed to free the valence electrons for conduction so they cannot conduct (unless subjected to extreme energy conditions such as high voltages).



A diagram showing the relative energy levels for the valence and conducting states of an electron in a (a) single
atom, (b) two atoms, (c) five atoms and (d) a solid with billions of atoms.

 

In (a) of the diagram above, the first horizontal line represents the allowed energy for an electron in the highest (valence) energy level of a single atom. If this atom were  the semiconductor silicon, there would be four electrons in the valence energy level, each with this amount of energy. If one of these electrons was given enough energy to overcome the attraction of the nucleus it would be free to conduct and the other higher horizontal line represents the energy an electron would have if it were in this state and free of the nucleus.

A diagrammatic representation of Band Theory showing the relative size of the energy gap
for insulators, conductors and semiconductors.

The laws of quantum mechanics tell us that when atoms are placed next to one another, such as they are in a solid, the allowed energy values for electrons split. In (b) of the diagram you can see two allowed energy levels for two atoms close to one another and (c) for five atoms. When there are billions of atoms packed together neatly in a crystalline solid, billions of hyperfine allowed energy values result that are so close together that they form a band of allowed energies (d). In this regard, an electron in the valence band (or conducting band) of a solid semiconductor such as silicon can have a range or band of energies rather than one discrete value for energy and this is the basis for Band Theory. This theory explains why certain materials are conductors while others are semiconductors or insulators.

This graph shows the relationship between the energy gap and atomic radius for elements in
Group IV of the Periodic Table. Note that only silicon and germanium possess an energy
gap that makes them acceptable semiconductors.

For insulators, the energy gap between electrons in the valence band and the conduction band is large. This means that the electrons in the valence band of the insulating material must gain significant energy before they are free from the nucleus and have the energy required to conduct. This large energy gap is the reason why insulators are not able to conduct electricity.

For semiconductors, the energy difference between the valence band and the conduction band is quite small. This means that the electrons can usually gain the additional energy from the semiconductor being heated or from light energy in order for the electron to be able to move from the valence to the conduction band and conduct. After the electron has moved into the conduction band it is free to move between one atom and the next, hence conduction can occur if a potential difference is applied.

For conducting solids such as metals, there is an overlap between the allowed energies of the valence band and the conducting band. This is because metals have delocalised valence electrons that are already free from the attraction of the nucleus. As a result, there is no energy gap as the delocalised electrons are already free for conduction.

  Conductors Semiconductors Insulators
Energy Gap
None
Small
Large
Valence Band
Partly Full
Full
Full
Conducting Band
Some Electrons
Some Electrons
Empty

 

Conduction in Semiconductors

Covalent bonding in silicon and germaniu.

The atoms of semiconducting elements have four unpaired electrons in their valence energy levels. Silicon and germanium are two most common semiconductor elements. There are four electrons in the valence energy level of each atom of the semiconductors. These four electrons are shared with the four adjacent atoms. Each of these four adjacent atoms shares its four valence electrons with another four atoms and so on to make up a giant crystal. This type of interaction between adjacent atoms is called covalent bonding.
 
At absolute zero (0 K), covalent bonding like this produces an empty conduction band and a full valence band. The electrons have no convertible kinetic energy at this temperature so the energy gap cannot be breached. As the temperature is increased, more and more electrons gain sufficient energy to enter the conduction band. Further input of energy as heat or light means that more electrons acquire sufficient energy to move into the conduction band. Under an applied potential difference, electrons in the conduction band are able to move freely towards a positive potential creating an electric current through the semiconductor, just as it would be in an equivalent metal conductor.  The important point here is that for semiconductors, their capacity to conduct increases with temperature and this is what makes them so useful.

Conduction in silicon occurs when electrons have sufficient energy to
cross the energy gap and enter the conduction band.

When an electron leaves the valence band for conduction, the atom loses that electron. The missing electron leaves a hole or a positive charge on that atom. Electrons from other adjacent atoms in the valence band move from one atom to the next to fill the holes left behind by conducting electrons. This creates a net movement of holes (positive charge) in the valence band that is towards the negative potential.

So there are two types of conduction going on in a semiconductor. Electrons with conduction band energy are moving towards the positive potential creating an electron (negative) current. The holes they leave behind migrate towards the negative potential as electrons in the valence band jump from atom to atom to fill the holes. This creates a hole (positive) current that moves in the opposite direction to the electron current. While electron current is conducted on the conduction band, hole current is conducted in the valence band.

Conduction in semiconductors where electrons in the
conduction band move towards the positive potential
and holes in the valence band migrate towards the
negative potential.

Hole current is slower than electron current because holes move by transferring from one atom to another thus making their movement through a material much slower. Excess free electrons in hot semiconductors can simply flow over adjacent atoms that don’t contain holes. Because electron flow is much faster than hole flow, electronic devices that use electron flow are chosen for applications that require high frequency current fluctuations.

In most cases the semiconductor materials operate at the prescribed limits when the semiconductor is conducting just the right amount of electrical current. Consequently the semiconductor cannot be allowed to become too hot otherwise it will conduct too much current. This occurs because the semiconductor itself like a regular conductor and the band gap is insufficient to stop it conducting larger currents along unintended pathways. To avoid this problem in electronic devices such as computers, silicon based chips are cooled by fans or are attached to heat sinks. Often these heat sinks are made from a conductive metal such as aluminium. The heat is conducted away from the chip to the heat sink that dissipates the heat to the environment.

 

Doping

Intrinsic semiconductors are those made from pure silicon or germanium. For general use, a pure semiconductor material has too few free electrons and holes to be useful in electronic devices. In order to increase the number of charge carriers, certain impurities are added to the pure semiconductor in a process called doping. Doping a semiconducting material vastly increases the number of free electrons or holes and the energy gap for the donor or acceptor impurities. This enhances the current carrying capacity of the semiconductor.

N-Type Semiconductors


Doping with a Group V element to produce an
n-type semiconductor.

In n-type semiconductors, small amounts of atoms with five valence electrons are substituted for a small number of the semiconductor atoms with four valence electrons. These impurity atoms come from Group V in the Periodic Table such as phosphorous. This results in an increased number of free electrons in the crystal lattice but no increase in net negative charge. Every impurity atom that is added still has the same number of protons as electrons so no net charge is added to the semiconductor. An n-type semiconductor just has more electrons available for conduction.

The impurity atoms are chosen so that their valence band energy level is close the conduction band allowed energies for the semiconductor. In this way, less energy is needed to get an electron from the donor impurity valence energy level to the conduction band than from the semiconductor valence band to the conduction band. This enhances the electron current carrying capacity of the semiconductor.

 

P-Type Semiconductors

Doping with a Group III element to produce an
n-type semiconductor.

In p-type semiconductors, some atoms with three valence electrons are substituted for some atoms of the semiconductor. This creates an increased number of holes in the crystal lattice but again does not add any net positive charge. Each impurity atom that is added has an equal number of protons and electrons so the net charge on the semiconductor is still zero.

In these semiconductors the impurity atoms have an acceptor valence energy level that is slightly different to the semiconductor atom. The impurity atoms are chosen so that their valence energy level is close to the valence energy band of the semiconductor. This means that only a small amount of energy is needed to get an electron from the valence energy level of the semiconductor to fill a hole in an impurity atom. This enhances the hole current carrying capacity of the semiconductor.

 

 

 



Very little energy is needed to get an electron from a donor atom in a p-type semiconductor to the conduction
band. Similarly, there is only a small energy gap between the valence band of an acceptor impurity atom and
the valence band of the semiconductor atom.

 

N-Type
P-Type
Doped with Group V elements
Doped with Group II elements
Increases the number of electrons in conduction band
Increases the number of holes in the valence band
Creates a new donor impurity energy level
Creates a new acceptor impurity level
Enhances negative conduction capability
Enhances positive conduction capacity

 

Diodes

Combinations of p and n-type semiconductors are used to make all modern electronic devices, ranging from the simple remote control to the sophisticated computer microprocessor . The basis of this technology is a result of the properties of the junction between a layer of p and n type semiconductor materials that are sandwiched together. This is known as a p-n junction and is the basis of all modern electrical components.

The formation of the depletion layer across a p-n junction creates a potential difference
that in a diode will only allow current to flow in one direction.

The p-n junction is used in the most basic electronic device, the diode. The function of a diode is to allow current to flow in one direction only. At the junction between p and n-type layers, electrons from the n-type layer move across to fill holes in the p-type layer. This creates what is known as a depletion layer. A potential difference is created across the depletion layer that blocks current in one direction only.

A depletion layer is like two parallel plates with equal and opposite charges on them resulting in an electric field and potential difference across the space between them. The energy that created the electric field or potential difference essentially came from the thermal (kinetic) energy of the charge carriers. Electrons that diffused across and combined with holes cannot easily drift back since they lost energy as they fell into the holes. Similarly, holes that diffused combine with electrons from the n-type material. The trapping of the diffused holes and electrons has resulted in the conversion of thermal energy into the electrostatic energy stored in the electric field region.

When current flows in one direction (forward bias) the depletion layer is reduced in size and current can flow. When current flows in the opposite direction (reverse bias) the depletion layer expands and prevents the flow of current.

 

Thermionic Devices

A thermionic diode in use before solid-state electronics which allowed current to flow
in one direction only.

Before the discovery and use of semiconductor materials in solid-state electronics, thermionic devices were used in electric circuits. These looked like light bulbs and were also called valves. The diode equivalent was a vacuum tube with a filament for the cathode and a vacuum between the cathode and anode, much like a cathode ray tube. When the device was turned on, the filament heated up and electrons were burned off the filament through a process known as thermionic emission. They then travelled towards the anode and current was allowed to flow. When the current direction was reversed, there was no filament as the originating electrode so electrons could not be released to travel across the vacuum. In this way the thermionic diode would also only allow current to flow in one direction.

Thermionic valves and solid-state devices do the same job, however, solid-state devices have a number of advantages, which is why they were invented. The advantages and disadvantages are oultined below.

  • Solid-state devices are much more reliable and have a consistent performance for a longer time.

  • Thermionic devices are large and transistors can now be made extremely small. Millions of transistors making up complex circuits can be fitted onto microchips. The size of thermionic devices does not allow for the miniaturisation demanded from modem electronic devices.

  • Solid-state devices consume far less energy than thermionic devices and also produce far less heat energy as a waste product. Thermionic devices require a heater to stimulate the cathode to emit electrons.

  • Thermionic devices are much more expensive to produce than solid-state devices.

  • Thermionic devices are made from glass and are inherently fragile.

  • Thermionic devices have a longer warm up period while the filament is heated to make it give off electrons.

  • Silicon transistors typically do not operate at voltages higher than about 1000 V. In contrast, thermionic devices have been developed that can be operated at tens of thousands of volts so thermionic devices are better in high voltage applications.

 

Transistors

A transistor is a semiconductor device used to amplify and switch electronic signals and power. It is composed of a semiconductor material with a NPN junction and at least three terminals for connection to an external circuit. A voltage or current applied to one pair of the transistor's terminals changes the current flowing through another pair of terminals. Because the output power can be higher than the input power, a transistor can amplify a signal. Transistors are also able to act as switches to turn current on and off. Today, some transistors are packaged individually, but many more are found embedded in integrated circuits.

The thermionic triode, a vacuum tube invented in 1907, propelled the electronics age forward, enabling amplified radio technology and long-distance telephony despite it being such a fragile device that consumed so much power. Telephone companies were the ones in greatest need of a solid-state replacement for thermionic devices in the electronic circuitry they used. In 1947, John Bardeen and Walter Brattain Bell Labs in the United States, performed experiments and observed that when two gold point contacts were applied to a crystal of germanium, a signal was produced with the output power greater than the input power. This application of semiconductors with the potential to replace thermionic devices saw the birth of what is known as solid-state electronics and over the next few months much work was done to expand knowledge of semiconductors.

The first silicon transistor was produced by Texas Instruments in 1954. This was the work of Gordon Teal, an expert in growing crystals of high purity, who had previously worked at Bell Labs. This was important because there were significant problems with using germanium as a semiconductor. Although it was easier to purify than silicon it was not as abundant and because of its smaller energy gap, would conduct at lower temperatures. This caused significant problems in electronic circuits. When a technique for purifying more abundant silicon became viable, silicon replaced germanium as the preferred semiconductor material.

The transistor is the key active component in practically all modern electronics. Many consider it to be one of the greatest inventions of the twentieth century. Its importance in today's society rests on its ability to be mass produced using a highly automated process (semiconductor device fabrication) that achieves astonishingly low per-transistor costs. Although several companies each produce over a billion individually packaged (known as discrete) transistors every year, the vast majority of transistors are now produced in integrated circuits (microchips), along with diodes, resistors, capacitors and other electronic components, to produce complete electronic circuits. A logic gate consists of up to about twenty transistors whereas an advanced microprocessor can use as many as three billion transistors.

The transistor's low cost, flexibility, and reliability have made it a ubiquitous device. Such circuits have replaced electromechanical devices in controlling appliances and machinery. It is often easier and cheaper to use a standard microcontroller and write a computer program to carry out a control function than to design an equivalent mechanical control function. The transistor is also the fundamental building block of modern electronic devices and is fundamental in modern electronic systems. Following its development in the early 1950s, the transistor revolutionised the field of electronics and paved the way for smaller and cheaper radios, calculators, and computers.

 

Solar Cells

Solar cells use the properties of a p-n junction and the photoelectric effect to convert light directly into electricity. They are also called photovoltaic cells.

Solar cells are simply a p-n junction. The photons absorbed in the p-layer near the depletion layer produce conduction electrons. The n-type layer is usually made quite thin so that solar photons can pass through it easily to the p-type layer where most photoemission occurs. These electrons are swept across the depletion layer by the electric field into the n-type layer, leaving behind holes in the p-type layer. The potential difference across the depletion layer prevents the electrons travelling directly back across it to recombine with the holes. As such, electrons are forced to travel around an external circuit and back to the p-type layer where they recombine with the holes they left behind.

This creates an electric current and a source of useable electrical energy from the light energy from the Sun.