Introduction

Semiconductor devices form the backbone of modern electronics and are crucial to the functioning of numerous electronic devices such as computers, mobile phones and solar cells. These devices exploit the special properties of materials that are neither good conductors nor good insulators, but lie somewhere in between – so-called semiconductors. The following section discusses how they work, starting with the band model, which describes the energy states in solids. Based on various properties, other semiconductor materials and their applications are explained. A fundamental concept that plays a key role is the pn junction, which forms the basis for a wide range of components. In this context, the second part discusses various semiconductor components such as diodes and transistors and explains their functions.

1 Band model

The band model is a fundamental concept in solid state physics that describes the physical properties of solids. It provides a theoretical basis for understanding the electrical, optical and magnetic properties of materials. The model organises the energy states of electrons into so-called energy bands. These bands have a significant influence on the electronic behaviour of the material. The band model makes it possible to understand and explain complex phenomena such as conduction, insulation, semiconductor behaviour and the formation of surface and interface states. The following section explains the basic principles and takes a look at charge carrier transport.

To understand the band model, we must first establish a connection to Bohr’s atomic model, which is familiar from school physics. In Bohr’s atomic model, the energy levels of electrons in an atom are assumed to be discrete. According to this model, electrons are located on defined orbits around the atomic nucleus, which are referred to as shells. Each shell has a characteristic energy level. These energy levels are quantised in relation to the distance from the atomic nucleus, with electrons in the inner shells having lower energy levels than electrons in the outer shells. The relationship between the Bohr atomic model and the band model is shown in Figure 2.

In a single atom, the possible energy states are clearly defined. If at least two atoms are brought together so that they interact electrically, their energy states overlap. However, due to the Pauli principle, also known as the exclusion principle, two electrons cannot assume exactly the same state, which is why the states shift minimally in relation to each other. As the number of atoms increases, so does the number of different energy states in a solid. Since these levels are very close to each other, they are grouped together into energy bands. This relationship is shown in Figure 3.

Electrons can only assume fixed values within the energy bands. No charge carriers can move freely in the gaps between the bands. These gaps are referred to as the ‘forbidden region’ or band gap. The size of these gaps determines the electrical properties of the material. The energy difference between the bands corresponds to the energy absorbed or emitted during the absorption or emission of photons.

1.1 Classification of materials

Two bands are particularly relevant for charge transport and thus for electrical properties: the valence band (VB) and the conduction band (CB). The valence band is the band that contains the highest energy levels occupied by electrons when the material is at a temperature of \({0}\,\mathrm {K}\). These electrons are tightly bound to the atomic nuclei and do not contribute to the electric current. The conduction band lies above the valence band and contains empty states in which electrons can be easily excited, for example by increasing the temperature. Electrons in the conduction band can move relatively freely through the material, thus enabling the flow of electric current. The three basic classes of conductors, semiconductors and insulators can be defined by the distance (band gap) between these two relevant bands. The following figure shows the band model of a material at \({0}\,\mathrm {K}\), with the relevant quantities and designations.

The occupation of the bands with electrons depends on other factors besides temperature. Conductivity can be influenced primarily by targeted contamination with foreign atoms, a process known as doping. The foreign atoms introduce free charge carriers and lead to additional energy levels within the band gap, from which, for example, light charge carriers can change bands (see section 3). In addition to the energy levels shown so far, the Fermi level is another important quantity. This indicates the energy value at which electrons have a probability of \(1/{1}{2}\) of being present. In an undoped semiconductor, the level lies midway between the valence and conduction bands, while in doped semiconductors, the level shifts towards the respective doping band.

Conductors are materials whose valence and conduction bands are adjacent or overlap, meaning that electrons can easily move between the bands. This proximity enables high conductivity, as electrons can move freely through the material. Metals such as copper and aluminium are typical examples of conductors.

Semiconductors have a small band gap that lies between that of conductors and insulators. This band gap is so large that no electric current flows in the material at low temperatures, as electrons do not have enough energy to be excited into the conduction band. However, conductivity can be significantly increased by raising the temperature or introducing foreign atoms. Semiconductors such as silicon and germanium are frequently used materials in the electronics industry.

Insulators have a large band gap, which means that the valence band is completely filled and the conduction band is empty. This makes it difficult for electrons to be excited into the conduction band, even with high energy input. Insulators such as glass and ceramics therefore exhibit very low conductivity.

The following are examples of band models with the valence and conduction bands of the three classes mentioned above.

2 semiconductor materials

The lattice structures of semiconductor materials play a decisive role in terms of their electronic and mechanical properties. The lattice structures of silicon and gallium arsenide (GaAs) are considered below. Silicon is the most widely used semiconductor material due to its high availability and the associated low price. In addition, it is very easy to process and its electrical properties can be easily influenced. Gallium arsenide, on the other hand, serves as an example of a compound semiconductor consisting of an element from the III and V main groups of the periodic table; accordingly, such a semiconductor is also referred to as a III/V compound semiconductor. The individual elements do not exhibit semiconductor behaviour; only when arranged in a specific way and with a specific atomic ratio does the semiconductor behaviour develop. Silicon has a diamond lattice structure in which each silicon atom is surrounded by four neighbouring atoms in a tetrahedral arrangement. This structure results in a stable and robust crystal structure with high mechanical stability. In addition, the arrangement allows high mobility of the free electrons in all spatial directions.

In contrast, in gallium arsenide, the gallium and arsenic atoms are arranged in such a way that they form two interlocking cubic face-centred lattices, known as the zinc blende lattice structure. The resulting arrangement is identical to the diamond lattice structure, but with regular alternation between two types of ions. This structure allows for a small band gap, resulting in low excitation energy required to shift electrons between the valence and conduction bands.

The following table provides an overview of some of the most important semiconductor materials and compound semiconductors, as well as their key properties and applications. These materials play a crucial role in modern electrical engineering and are used in a wide range of applications, from microchips and solar cells to high-frequency circuits and LED lighting. The table contains information about the band gap, charge carrier density (intrinsic conductivity), electron and hole mobility, and characteristic properties and applications of each material. Mobility is the speed at which charge carriers move through a medium due to an electric field. Holes are quasi-partial states that are considered positive charge carriers. They are not actual positive charge carriers, but rather local areas that can be considered positively charged due to a missing electron.

3 Load carrier transport

At a temperature of \(\mathrm {0\,K}\) (absolute zero), semiconductors such as silicon have a completely filled valence band with the energy level \(E_\mathrm {V}\) and an empty conduction band with the energy level \(E_\mathrm {L}\). This means that all electrons are bound in the valence band and there are no free charge carriers. The band model shows a distinct band gap between the valence band and the conduction band. When the temperature is raised above \(\mathrm {0\,K}\), the mobility of the electrons in the crystal lattice increases. Some electrons in the valence band can gain energy through thermal excitation and transition to the conduction band, creating free electrons and holes. These free charge carriers contribute to the conductivity of the semiconductor.

When phosphorus is added to silicon, the phosphorus atom contributes five valence electrons (n-doped), one more than silicon. In this case, the excess electron is loosely bound to the crystal lattice and can be easily removed by external energy sources, making it a donor of free electrons. These electrons are located in the donor band (\(E_\mathrm {D}\)), immediately below the conduction band. At temperatures above \(\mathrm {0\,K}\), thermal excitation gives the electrons enough energy to overcome the band gap and enter the conduction band. The electrons provided by the phosphorus facilitate this process. This increases the conductivity of the material.

When boron is added to silicon (p-doped), the boron atom has only three valence electrons, one less than silicon. This creates a hole in the valence band of the crystal lattice, which acts as an electron acceptor. At \({0}\,\mathrm {K}\), however, there are no thermally generated holes. At temperatures above \({0}\,\mathrm {K}\), the thermal energy causes electrons to move from the valence band to the acceptor band (\(E_\mathrm {A}\)), leaving holes in the valence band. These holes act as positive charge carriers and increase the conductivity of the material.

In addition to the aforementioned processes within the crystal lattice, which enable charge carrier transport through additional charge carriers, two other important variables are drift current and diffusion current. Drift current in a semiconductor occurs due to the movement of charged particles under the influence of an external electric field. When an electric field is applied to a semiconductor, a force acts on the free charge carriers (electrons and holes), accelerating or decelerating them in the direction of the field, depending on their sign or charge. For electrons in the conduction band, this means that they drift towards the positive electrode (anode) under the influence of the electric field. For holes in the valence band, this means a drift towards the negative electrode (cathode). For better comparability, the hole is shown as a positive charge carrier in the following figure. The drift velocity of the charge carriers depends on the strength of the applied electric field and on the mobility of the charge carriers in the semiconductor material. It is important to note that the drift current only accounts for part of the total current in a semiconductor.

The other part of the current is caused by diffusion, which is the movement of charge carriers due to concentration differences. In many semiconductor devices, such as diodes and transistors, drift and diffusion currents work together to determine the behaviour of the device. In diffusion current, free electrons or holes move from areas of high concentration to areas of low concentration, similar to the diffusion of particles in a concentration gradient. In the case of electrons in an n-doped semiconductor, electrons move from regions of high electron concentration to regions of low electron concentration. Conversely, in a p-doped semiconductor, holes move from regions of high hole concentration to regions of low hole concentration.

Finally, this section examines charge transport in the band diagram when a voltage is applied. Until now, the band diagram has been analysed exclusively in a state of thermodynamic equilibrium. The general case is considered, in which a current flows through the semiconductor. A homogeneous, n-doped semiconductor serves as an example. Initially, no voltage is applied to the semiconductor, which means that no electric current flows. The band diagram over the location x therefore shows a curve similar to that in Figure 13 on the left, where possible edge effects at the contacts are not taken into account. The bands of a semiconductor without applied voltage are aligned horizontally. However, as soon as a voltage is applied, the band diagram shifts, causing the electrons to migrate towards lower energy.

4 pn-junction

The pn junction is the central element of semiconductor devices such as diodes and transistors. It is created by connecting two differently doped semiconductor layers, a p-doped layer and an n-doped layer. The transition between these layers is called a pn junction. Free charge carriers diffuse in the pn junction: electrons from the n-doped layer diffuse to the p-doped layer and holes from the p-doped layer diffuse to the n-doped layer. This diffusion process leads to the formation of a so-called space charge region (SCR) in the junction region. This process is illustrated in Figure 14. The SCZ is a narrow region around the pn junction in which positive ions from the n layer and negative ions from the p layer remain after diffusion is complete. There are no free charge carriers in this zone, as the positive and negative charges neutralise each other. This creates an electric field (\(\vec {E}\)) that generates a drift current and suppresses the diffusion of further charge carriers. The space charge zone acts as a barrier layer and prevents current flow in the reverse direction.

When a voltage is applied in the forward direction (see Figure 15 on the left), the RLZ is reduced and the junction becomes conductive. Electrons from the n-doped side migrate to the p-doped side, while holes diffuse from the p-doped side to the n-doped side. This creates a current flow through the pn junction. Conversely, a voltage applied in the reverse direction increases the RLZ (see Figure 15 on the right). The free charge carriers are balanced by the voltage source. The pn junction is therefore a key element in semiconductor devices that controls the direction and strength of the current flow. Its properties are influenced by the doping concentration, the size of the space charge zone and the applied voltage.