Crystals

Silicon is an element that occupies a unique place in the periodic table due to its valence electron configuration. It has four valence electrons, which means that its valence shell is half-filled. This makes it distinct from other elements, which typically have either a completely filled or completely unfilled valence shell.

In its pure form, silicon is not a good conductor of electricity nor a good insulator. However, when arranged in a specific crystal structure, it can become a semiconductor. Silicon is not the only material that can be used for semiconductors, and other elements like germanium have also been used in the past. Nevertheless, silicon is the most commonly used material for semiconductor manufacturing today.

When arranged in a crystal lattice, silicon atoms form covalent bonds with their nearest neighbors by sharing valence electrons. Each silicon atom can share one electron with each of its four nearest neighbors, resulting in a tightly-bound, well-ordered structure. This arrangement ensures that there are no voids or breaks in the crystal lattice, resulting in a mono crystalline structure.

Due to the unique properties of silicon and its crystal structure, it has become a crucial element in the manufacturing of semiconductors. Its ability to form covalent bonds and share electrons with its neighbors is vital to the functioning of semiconductor devices such as diodes and transistors, which are used in a wide range of electronic products.

The unique property of silicon is its halffilled valence shell with four electrons, which allows it to become a semiconductor with some attention to detail. Although germanium and other materials are also used for semiconductors, silicon remains the primary source. Pure silicon can form a mono crystalline structure where each atom effectively shares an electron from its four closest neighbors through a covalent bond, which results in a tightly bound structure without any voids or breaks in the pattern. This sharing is illustrated in Figure 1.8 with the use of simplified Bohr models and color coding to represent it. It is important to note that as silicon has only four electrons in its valence shell, it requires four more electrons to achieve stability or eight electrons in the outer shell.

The energy diagram that we have been discussing is not meant to represent the movement of individual valence electrons between atoms in a literal sense. Instead, it provides a graphical representation of the energy levels and band gaps that are characteristic of a semiconductor crystal. In reality, a crystal is not a two-dimensional sheet, but rather a three-dimensional structure with varying thickness.

It’s important to keep in mind that the energy diagram in Figure 1.8 is not meant to show the exact movement of individual valence electrons between atoms, but rather to represent the overall energy levels of the electrons in the crystal. The diagram is drawn in a flat two-dimensional form, whereas in reality the crystal structure is three-dimensional with varying thickness. Drawing a highly accurate representation of individual atoms in the crystal would be impractical, but we can make a closer approximation by representing each silicon atom as a ball and the covalent bond as a connecting tube. Since each atom in the crystal must be bound to four others in a regular and equal pattern, the resulting structure resembles a cube, with an atom of silicon at the center of each face. This crystal structure is referred to as face centered cubic, as shown in Figure 1.9.

While it is impossible to draw an exact representation of atoms in a crystal, we can make certain approximations to create a more realistic drawing. In this case, we can represent each silicon atom as a ball and the covalent bond between them as a connecting tube. Since each silicon atom must be bound to four others in a regular, equal pattern, the resulting structure is essentially that of a cube, with an atom of silicon at the center of each face. This is known as a face-centered cubic crystal structure.

This type of crystal structure is common in many semiconductors, including silicon. It is an important aspect of the material’s properties, as it affects how electrons move through the crystal lattice and ultimately determine its conductivity. By understanding the structure of a semiconductor crystal, scientists and engineers can design and optimize electronic devices that rely on its unique properties.

The energy levels of a crystal are affected by the presence of neighboring atoms, causing slight variations that lead to discrete energy levels blurring into broader bands. The valence and conduction bands can be seen as continuous bands rather than discrete levels, as shown in Figure 1.10. However, there are still non-permissible zones between these regions known as band gaps.

The Fermi level, named after physicist Enrico Fermi, is the energy level in a material at which there is a 50% probability that it is filled with electrons. If the Fermi level is within a band, the material is a good conductor, while if it lies between widely separated bands, the material is a good insulator. If the Fermi level is between bands that are relatively close, the material is a semiconductor. These concepts are illustrated in Figure 1.11.

Figure 1.10 illustrates the energy bands for an intrinsic semiconductor, which refers to a crystal without any impurities. The region between the valence band and conduction band is a forbidden region or band gap. The amount of energy required to move an electron from the valence band to the conduction band is equal to the band gap. The value of the band gap varies depending on the particular material used for the semiconductor.

At absolute zero temperature and in isolation, the crystal lattice is stable and there is no electron movement through the crystal. However, as thermal energy is added, valence electrons can gain enough energy to jump up to the conduction band. At this point, the electron can move through the crystal in a manner similar to that shown in Figure 1.11.

In an intrinsic semiconductor, thermal energy can cause electrons to move from the valence band to the conduction band, leaving behind a hole. The hole can then be filled by another electron, and this process repeats with increasing temperature, resulting in thermally-induced electron movement. The same process can also be viewed as a flow of holes in the opposite direction. Figure 1.12 illustrates this process with horizontal bars containing four dots representing electrons. The leftmost electron in the top bar moves into an empty space (a hole), filling it and resulting in the second bar. This process repeats as electrons move right to left, eventually leading to four electrons packed together toward the left. The movement of the hole can be observed by focusing on the negative space between the dots, moving from top to bottom and left to right.

To understand the movement of holes, we can think of them as a movement of positive charge, in contrast to the movement of electrons which is a movement of negative charge. Therefore, the electron is the carrier of negative charge, while the hole is the carrier of positive charge. It is essential to note that in an intrinsic semiconductor, where there are no impurities, the number of thermally generated electrons and holes will be equal. Additionally, even at room temperature, the total number of thermally generated electrons and holes will be quite small when compared to the number of electrons in the crystal. This is important to keep in mind as we move on to the next section.

discussion resolved around the basics of semiconductor physics, specifically the concept of energy bands in intrinsic semiconductors like pure silicon crystals. Figure 1.10 was presented to illustrate the energy bands and the band gap that separates the valence and conduction bands. At absolute zero temperature, the crystal lattice is stable and there is no electron movement. However, as thermal energy is added, electrons can jump up to the conduction band, creating a hole in the valence band. The number of freed electrons and corresponding holes increases with temperature, leading to thermally-induced electron movement or hole flow.

The movement of electrons is considered a movement of negative charge, while the movement of holes is considered a movement of positive charge. In an intrinsic semiconductor, the number of electrons and holes produced by thermal energy will be equal, and even at room temperature, the total number will be relatively small compared to the number of electrons in the crystal.

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