Basics of Semiconductors

Semiconductors are materials that have a conductivity between conductors (usually metals) and non-conductors or insulators (such as most ceramics). Semiconductors can be pure elements, such as silicon or germanium, or compounds such as gallium arsenide or cadmium selenide. In a process called doping, small amounts of impurities are added to pure semiconductors, causing large changes in the conductivity of the material.

A semiconductor is a material whose resistivity is between that of a conductor and an insulator. The property of resistivity is not only what decides a material to be a semiconductor, but some of its properties are as follows.

• Semiconductors have resistivity which is less than insulators and higher than conductors.
• Negative temperature is co-efficient in semiconductors. The resistance in semiconductors increases with a decrease in temperature.
• The conducting properties of a semiconductor change when a suitable metallic impurity is added to it, which is a very important property.

Semiconductor devices are widely used in the field of electronics. Transistors replaced bulky vacuum tubes, reducing the size and cost of devices, and the revolution continued to accelerate, leading to new inventions such as integrated electronics.

Gallium arsenide, germanium, and silicon are some of the most commonly used semiconductors. Silicon is used in electronic circuit manufacturing and gallium arsenide is used in solar cells, laser diodes, etc.

Holes and Electrons in Semiconductors

Holes and electrons are a type of charge carriers for the flow of current in a semiconductor. Holes (valence electrons) are positively charged electrical charge carriers whereas electrons are negatively charged particles. Both electrons and holes are equal in magnitude but opposite in polarity.

Mobility of electrons and holes

In semiconductors, the mobility of electrons is higher than that of holes. This is mainly due to their different band structures and scattering mechanisms.

Electrons travel in the conduction band while holes travel in the valence band. When an electric field is applied, holes cannot move as freely as electrons because of their restricted motion. Holes are formed in semiconductors as electrons move from their inner shell to the higher shell. Since a stronger nuclear force is experienced by the nucleus than the electrons in the holes, the mobility of the holes is low.

The mobility of a particle in a semiconductor is high if;

• The effective mass of the particles is less.
• The time between scattering events is greater.

Conduction in Semiconductors

Having some knowledge about electrons, we learned that the outermost shell contains valence electrons that are loosely attached to the nucleus. An atom that has valence electrons when brought close to another atom, the valence electrons of these two atoms combine to form “electron pairs”. This bond is not that strong and hence it is a covalent bond.

For example, a germanium atom has 32 electrons. 2 electrons in the first orbit, 8 in the second orbit, 18 in the third orbit, and 4 electrons in the last orbit. These 4 electrons are the valence electrons of the germanium atom. These electrons combine with the valence electrons of adjacent atoms, forming electron pairs, as shown in the following figure.

Creation of Hole

Due to the thermal energy supplied to the crystal, some electrons move out of their positions and break the covalent bonds. These broken covalent bonds result in free electrons that spin around randomly. But the electrons that have moved away from an empty space, or valence, behind which is called a hole.

This hole which represents a missing electron can be considered as the unit of positive charge whereas an electron is considered as the unit of negative charge. Free electrons move randomly but when some external electric field is applied, these electrons move in the opposite direction of the applied field. But the holes formed due to the absence of electrons move in the direction of the applied field.

Hole Current

It is already understood that when a covalent bond is broken, a hole is formed. In fact, semiconductor crystals have a strong tendency to form covalent bonds. So, a hole does not exist in the crystal. This can be better understood by the following figure, showing a semiconducting crystal lattice.

An electron, when transferred from position A, creates a hole. Because of its tendency to form covalent bonds, one electron from B gets transferred to A. Now, in order to re-equilibrate the covalent bond at B, an electron is transferred from C to B. It continues to build the path. In the absence of an applied area, this motion of the hole is random. But when the electric field is applied, the hole flows along with the applied field, creating a hole current. This is called hole current but not electron current, because the hole’s motion contributes to the flow of current.

When in random motion the electrons and holes can encounter each other to form pairs. This recombination results in the release of heat, which breaks another covalent bond. When the temperature increases, the rate of formation of electrons and holes increases, thus increasing the rate of recombination, resulting in an increase in the density of electrons and holes. As a result, the conductivity of the semiconductor increases, and the resistivity decreases, which means a negative temperature coefficient.

Band Theory of Semiconductors

Band theory originated during the quantum revolution in science. Walter Hitler and Fritz London discovered the energy band.

We know that electrons exist at different energy levels in an atom. When we try to assemble the lattice of a solid with N atoms, each level of the atom must be divided into N levels in the solid. This division of fast and tightly packed energy levels forms the energy band. The distance between adjacent bands that represent a range of energies that do not contain any electrons is called the band gap.

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Valence Band and Conduction Band in Semiconductors

Valence Band:

The energy band comprising the energy levels of the valence electrons is known as the valence band. This is the highest occupied energy band. When compared with insulators, semiconductors have a smaller bandgap. This allows the electrons in the valence band to jump to the conduction band upon receiving any external energy.

Conduction Band:

It is the lowest empty band that contains the energy levels of either positive (hole) or negative (free electron) charge carriers. There is the conduction of electrons in it which results in the flow of current. The conduction band has a high energy level and is usually empty. In semiconductors, the conduction band accepts electrons from the valence band.

Fermi Level in Semiconductors

The Fermi level (denoted by EF) exists between the valence and conduction bands. It is the most occupied molecular orbital at absolute zero. In this state, the charge carriers have their own quantum states and generally do not interact with each other. When the temperature rises above absolute zero, these charge carriers will begin to occupy states above the Fermi level.

In a p-type semiconductor, there is an increase in the density of the incomplete states. Thus, accommodating more electrons at lower energy levels. However, in an n-type semiconductor, the density of the states increases, therefore, accommodating more electrons at higher energy levels.

Properties of Semiconductors

Semiconductors can conduct electricity under better conditions or circumstances. This unique property makes it an excellent material for conducting electricity in a controlled manner as needed.

Unlike conductors, charge carriers in semiconductors arise only due to external energy (thermal movement). This causes a certain number of valence electrons to cross the energy gap and jump into the conduction band, leaving an equal amount of empty energy states, that is, holes. The conduction due to electrons and holes is equally important.

• Resistivity: 10^-5 to 10⁶ Ωm.
• Conductivity: 10⁵ to 10^-6 mho/m.
• Temperature coefficient of resistance: Negative.
• Current Flow: Due to electrons and holes.

Types of Semiconductors

There are two types of semiconductors:

• Intrinsic Semiconductor
• Extrinsic Semiconductor

Intrinsic Semiconductors

A semiconductor in its purest form is called an intrinsic semiconductor. The properties of this pure semiconductor are as follows:

• Electrons and holes are created entirely by thermal excitation.
• The number of free electrons is equal to the number of holes.
• The conductivity is small at room temperature.

In order to increase the conductivity of intrinsic semiconductors, it is better to add some impurities. This process of adding impurities is called doping. Now, this doped intrinsic semiconductor is called an extrinsic semiconductor.

Germanium (Ge) and silicon (Si) are the most common types of intrinsic semiconductor elements. They have four valence electrons (tetravalent). They are bonded to the atom by covalent bonds at absolute zero temperature.

When the temperature rises, due to collisions, some electrons are unbound and free to move through the lattice, thus creating an absence in their original state (hole). These free electrons and holes contribute to the conduction of electricity in a semiconductor. Negative and positive charge carriers are equal in number.

The thermal energy is able to ionize some of the atoms in the lattice, and therefore their conductivity is low.

Pure silicon semiconductor lattice at different temperatures:

• At absolute zero Kelvin temperature: At this temperature, the covalent bonds are very strong and there are no free electrons and the semiconductor behaves as an ideal insulator.
• Above absolute temperature: With the increase in temperature, some of the valence electrons jump into the conduction band and hence it behaves like a poor conductor.

Doping

The process of adding impurities to semiconductor materials is called doping. The added impurities are generally pentavalent and trivalent impurities.

Pentavalent Impurities

• Pentavalent impurities are those that have five valence electrons in their outermost orbitals. Example: bismuth, antimony, arsenic, phosphorus
• The pentavalent atom is called a donor atom because it donates an electron to the conduction band of a pure semiconductor atom.

Trivalent Impurities

• Trivalent impurities are those that have three valence electrons in their outermost orbitals. Examples: Gallium, Indium, Aluminum, Boron
• A trivalent atom is called an acceptor atom because it accepts an electron from a semiconductor atom.

Extrinsic Semiconductor

An impure semiconductor, which is formed by doping a pure semiconductor, is called an extrinsic semiconductor. There are two types of extrinsic semiconductors based on the type of impurity. They are n-type extrinsic semiconductors and p-type extrinsic semiconductors.

N-Type Extrinsic Semiconductor

A small amount of pentavalent impurity is added to a pure semiconductor resulting in the formation of an N-type extrinsic semiconductor. The additional impurity has 5 valence electrons.

For example, if an arsenic atom is added to a germanium atom, four valence electrons attach to the Ge atoms while one electron remains as a free electron. It is shown in the following figure.

All these free electrons form the electron stream. Therefore, when added to a pure semiconductor, the impurity provides electrons for conduction.

• In N-type extrinsic semiconductors, as electrons conduct through, electrons are the majority carriers and holes are the minority carriers.
• Since there is no sum of positive or negative charges, the electrons are electrically neutral.
• When an electric field is applied to an n-type semiconductor to which a pentavalent impurity is added, the free electrons travel towards the positive electrode. This is called negative or N-type conductivity.

P-Type Extrinsic Semiconductor

A small amount of trivalent impurity is added to the pure semiconductor to result in a P-type extrinsic semiconductor. The additional impurity has 3 valence electrons. For example, if a boron atom is added to a germanium atom, three valence electrons join with Ge atoms to form three covalent bonds. But, in germanium one more electron remains without any bond. Since there are no electrons left in the boron to form a covalent bond, the space is treated as a hole. It is shown in the following figure.

The boron impurity, when added in small amounts, provides many pores that help conduction. All these holes form the hole stream.

• In P-type extrinsic semiconductors, as in through holes, holes are the majority carriers while electrons are the minority carriers.
• The impurity added here provides holes that are called acceptors because they accept electrons from germanium atoms.
• Since the number of mobile holes is equal to the number of acceptors, the Ptype semiconductor remains electrically neutral.
• When an electric field is applied to a P-type semiconductor to which a trivalent impurity is added, holes move toward the negative electrode, but at a slower rate than electrons. This is called P-type conductivity.
• In this p-type conductivity, valence electrons move from one covalent bond to another, unlike in the n-type.