Lesson Explainer: Pure Semiconductors Physics • 9th Grade

In this explainer, we will learn how to describe the electrical bonds in pure semiconductor materials.

We are already familiar with the term conductor, which describes a class of materials that allows electrons to flow easily through them. Most metals are good conductors; for instance, copper is one of the most common materials used in electric wires, because it allows charge to flow freely through it. A material that does not allow charge to flow easily is known as an insulator, such as wood.

In terms of electrical conductivity, insulators and conductors are opposites, but some materials have properties that fall somewhere in between the two categories. Such materials are classified as “semiconductors.” The conductivity of a semiconductor can be controlled in ways that would not be possible for a conductor. Although the specifics will not be covered in this explainer, it should be noted that semiconductors are very useful in electronics because of their specialized properties.

Copper is one of the most well-known conductors. On the other hand, silicon is the most common semiconductor. An example of an insulator would be a piece of wood.

There are ways to create semiconductors by mixing two or more elements together, but for now we will focus on pure semiconductors that are composed of only one element. The element silicon (Si), shown above, is one of the most common semiconducting materials, as it is very plentiful on Earth and has atomic properties that make it an ideal semiconductor. Although there are several other semiconductive elements, such as germanium and tin, we will purely focus on silicon in this explainer.

Let us first examine a single silicon atom, which has atomic number 14 and has three occupied electron energy levels. A Bohr model diagram of a neutral Atomsbonded silicon atom is shown below.

We can learn the most from an element’s outermost layer of electrons, as these electrons will most readily interact with outside influences, such as neighboring atoms and charges. We are most interested in these electrons, so, for the remainder of this explainer, we will depict Si atoms by showing the nucleus and only the electrons in the outer shell, like in the diagram below. The outermost shell of a silicon atom can contain up to eight electrons, but a neutral Si atom has only four electrons in its outermost shell.

While it is important to understand the composition of a single Si atom, we are even more interested in many atoms coming together to form a complete material. Covalent bonds are key to such a formation.

For a quick review of covalent bonds, let us first examine an interaction between two neutral hydrogen atoms, since they have the simplest possible atomic structure. In the diagram below, the atoms are shown side by side, but not yet bonded. Note that each atom has one electron in its electron shell.

Recall that a covalent bond is the sharing of a pair of electrons between two atoms. The diagram below shows a covalent bond between two hydrogen atoms. Because of this bond, each atom now has two electrons in its shell.

Now, let us return to silicon atoms. When groups of Si atoms come together, they create a regular arrangement, called a lattice, by forming covalent bonds with adjacent atoms. For simplicity, the diagram below only shows one internal, or central, atom surrounded by an atom on each side. Also, remember that only the electrons in the outermost shell of each atom are shown. However, it should be noted that any macroscopic material, such as an electrical component, is made of many billions of atoms. Understanding the lattice pattern and how the groups of atoms’ outermost electrons interact is key to learning how a semiconducting material like silicon works.

Notice that there is an overlap in the outermost electron layers between neighboring atoms—this illustrates the covalent bonds that hold these atoms together in lattice formation. An electron in a covalent bond is simultaneously attracted to two nuclei that are very close together, so we will see these bonds form between adjacent atoms. This concept is illustrated below.

An internal silicon atom, like the one shown above, has four covalent bonds: one with the neighbor to its top, bottom, left, and right. Because of this, an internal Si atom contains eight outermost electrons, which constitutes a full set. However, it should be noted that the atoms in the lattice remain electrically neutral. The overall charge has not changed because no electrons were added or taken away from the lattice; they have simply been rearranged. This unlocks some of the semiconducting properties that make silicon so useful. Let us explore this in an example.

Example 1: Covalent Bonds in a Pure Semiconductor Lattice

An atom of Si is part of an object made of Si atoms, as shown in the diagram. Only the electrons in the outermost shells of the atoms are individually represented. How many of the electrons in the outermost shell of an atom in the object form covalent bonds with adjacent atoms?

Answer

As shown in the diagram above, a single Si atoms has four electrons in its outermost shell. When groups of these atoms come together and arrange themselves in a lattice, they develop covalent bonds that help keep them in this regular pattern. This means that neighboring atoms “share” a pair of electrons, with each atom contributing one electron to the bond.

Any one Si atom in the lattice is immediately surrounded by four atoms: one to its top, bottom, left, and right. As shown in the diagram, each atom shares one of its four electrons with one of its neighbors, so each atom then has four pairs of electrons, for a total of eight electrons surrounding a nucleus.

However, each atom still only actually contains its own four electrons. The Si atoms might now appear to have eight electrons, but the overall charge (and therefore number of electrons) of the Si atoms does not change when they arrange themselves in a lattice. If each atom did actually have eight outermost electrons, the extra four electrons per atom would need to be acquired from somewhere. A lattice configuration only changes the pattern of the electrons’ locations, not the overall number of electrons in the lattice.

Therefore, 4 electrons in the outermost shell form covalent bonds with adjacent atoms.

Until this point, we have seen very idealized diagrams of a silicon lattice, such that each atom has its full set of outermost electrons, and every electron stays set in place. However, this pristine arrangement of electrons is only realized when there is no thermal energy in the system, so that the temperature of the material measures 0 K, or absolute zero. More realistically, the materials we interact with in everyday life have a temperature above absolute zero, meaning that there is some thermal energy available to the atoms.

When enough energy is transferred to an electron, it will not remain confined to one atoms, and instead will move between lattice atoms. In this case, it is considered a “free” electron. A free electron comes from the outermost electron shell, and the lattice arrangement around it still exists. Thus, when an electron is freed, it leaves behind a vacant spot, or a hole, where it was previously bound. We have previously mentioned the overall neutral charge of the atoms, with an equal number of protons and electrons in the lattice. However, if an atom loses an electron, it loses a negative charge. Subtracting a 1 charge effectively creates a positive charge in its place, so we consider a hole left behind by a free electron to have an effective charge of +1. Let us explore this in an example.

Example 2: Free Electrons in a Pure Semiconductor

The diagram shows a lattice of Si atoms at a temperature of 300 K.

  1. Which of the features labeled in the diagram is a free electron?
  2. What is the effective relative charge of the feature labeled B?
    1. 1
    2. 0
    3. +1

Answer

Part 1

Here, we see a lattice of silicon atoms. The nuclei are represented by red circles and the small blue dots represent the outermost electrons that form covalent bonds among the atoms.

We know that when enough energy is added to such an atomic system, an electron from the outermost layer can become free and move throughout the material. A free electron leaves behind a “hole” in the lattice, which is represented by the blank space labeled B.

Therefore, the feature labeled A is a free electron.

Part 2

The feature labeled B represents the space an electron used to occupy but has since left behind. Because an electron has a negative charge, this hole represents the absence of a negative charge, effectively creating a positive charge.

Therefore, the feature labeled B has an effective relative charge of +1, and C is the correct answer.

It should be noted that the process of electrons being freed and leaving holes is widespread throughout the lattice. This is a continuing cycle of many electrons being freed, moving around, and filling vacancies. Typically, a hole is filled very quickly by another free electron in the lattice.

Recall that, for an electron to be freed, it must gain enough energy to leave its bound state. A similar process happens in reverse when a free electron fills a hole and becomes bound again. When a free electron reenters the outermost electron shell of an atom, it releases some energy so that it becomes bound to the atom. The energy released by this process is equal to the energy needed to break a bond. Often, this excess energy is transferred to another (bound) electron close to the hole so that it takes in this released energy and becomes freed itself. This balanced amount of transferred energy explains the balanced concentrations of free electrons and holes in the lattice.

This creates a cycle of energy being transferred around the lattice. As more thermal energy is available to a lattice, we can expect to see more electrons moving around and interacting. The availability of free electrons is what allows a semiconductor to have charge flow, or current, when a potential difference is applied.

Example 3: Free Electrons in a Pure Semiconductor

In a lattice of Si atoms, an electron in the outermost shell of an atom gains sufficient energy to become a free electron, leaving a vacancy in the shell. The vacancy is then filled by a different electron. Which of the following could be the source of the electron that fills the vacancy?

  1. A bound electron from the outermost shell of the atom from which the free electron was produced
  2. A bound electron from a shell other than the outermost shell of the atom from which the free electron was produced
  3. A bound electron from the outermost shell of an atom bonded with the atom from which the free electron was produced
  4. A bound electron from a shell other than the outermost shell of an atom bonded with the atom from which the free electron was produced
  5. Another free electron in the lattice

Answer

It takes a very large amount of energy, and is therefore very difficult, to free an electron from an inner electron shell, so this would not happen naturally just to fill a hole in a lattice. Therefore, options B and D are incorrect.

Further, if an electron from the outermost shell of the same atom filled the free electron’s vacancy, there would still be a hole left behind from where that electron was before it moved to fill the original vacancy. Thus, an electron will not fill a vacancy in its own shell and choice A is incorrect.

In any case, electrons are “bound” if they are strongly attracted to the nucleus of an atom, so it takes some external energy to free a bound electron. Bound electrons cannot freely move around in a material, and therefore only a free electron in the lattice can be available to fill a hole. For this reason, choice C is also incorrect.

Therefore, holes are filled by free electrons in the lattice, and so E is the correct answer.

Recall that electrons become freed by absorbing energy, such as thermal energy, and, for this reason, a semiconductor at a higher temperature has more free electrons and holes than it would at a lower temperature. Further, when a material is in thermal equilibrium, the cycle is balanced, since there is an equivalent amount of energy released and gained by electrons leaving and joining atoms. Thus, there is an equal number of free electrons and holes, meaning that the overall charge remains neutral. This concept is explored in the next example.

Example 4: Free Electrons in a Pure Semiconductor as a Function of Temperature

In a pure semiconductor at a temperature of 320 K, the number of free electrons in the semiconductor is 𝑛. The temperature of the semiconductor is increased to 420 K. Which of the following correctly describes how 𝑛 changes? The semiconductor is in thermal equilibrium at both temperatures.

  1. 𝑛 remains constant.
  2. 𝑛 increases.
  3. 𝑛 decreases.

Answer

As thermal energy is made available to atoms in a pure semiconductor, some of the energy is transferred to electrons, allowing them to be freed from their bonds, which creates electron holes in the lattice structure. For this reason, we can expect to see a higher number of free electrons and holes in semiconductors at higher temperatures.

Therefore, if the temperature of a semiconductor is increased, the number of free electrons, 𝑛, also increases, and choice B is correct.

Example 5: Free Electrons in a Pure Semiconductor as a Function of Temperature

In a pure semiconductor at a temperature of 320 K, the number of free electrons in the semiconductor is 𝑛 and the number of holes in the semiconductor is 𝑛. The temperature of the semiconductor is reduced to 280 K. What is the ratio of 𝑛 to 𝑛? The semiconductor is in thermal equilibrium at both temperatures.

Answer

We can expect that as the temperature of the semiconductor decreases, so will the number of free electrons, 𝑛, and holes, 𝑛. We know that, at both temperatures, the pure semiconductor is in thermal equilibrium, which means that there is a balance between 𝑛 and 𝑛. Free electrons leave behind holes, so we know that each free electron must correspond to a hole somewhere in the lattice.

Therefore, the ratio of 𝑛 to 𝑛 is 1.

Let us finish by summarizing some important concepts.

Key Points

  • Semiconductors are a class of materials that has electrical properties between those of electrical insulators and electrical conductors. Silicon is the most commonly used semiconducting element.
  • A pure semiconductor has no added impurities; instead, its concentration of free charges is determined only by the properties and temperature of the semiconducting material.
  • A neutral silicon atom has four outermost electrons, and groups of silicon atoms arrange themselves in a lattice formation. This pattern allows adjacent atoms to share outermost electrons, forming covalent bonds.
  • If the temperature of an atomic lattice increases, the thermal energy transferred to bound electrons in the outer shells of atoms frees these electrons to move between lattice atoms.
  • When a bound electron in a lattice atom becomes a free electron, a vacancy, or a hole, is produced in the atom.
  • Vacancies in lattice atoms are filled by free electrons from the lattice.

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