Two types of materials are currently used to build solar cells: namely inorganic and organic materials. To understand the performance of solar cells, it is necessary to become familiar with the properties of these materials. In the case of inorganic materials, the crystal structure in which atoms or groups of atoms form a crystal lattice is largely responsible for their properties. The atoms in a crystal lattice are so close together that interactions between them create electron energy bands in place of the quantized energy levels in the isolated atoms.
A simplified model of the energy bands is shown in Fig. 1. It consists of a valence band, an excited band and a conduction band. The valence band (VB) is completely filled with electrons that are not allowed to move in it (the Pauli exclusion principle). The bandgap (so-called energy gap \( E_{g} \)) is an area where electrons cannot reside because there are no energy levels in it. There are no electrons in the conduction band (CB) in the ground state of the atom. When an electron is transferred from the valence band to the conduction band, the possibility of electron transport arises.
Using this model, materials can be divided according to the size of their energy gap \( E_{g} \). Materials for which the energy gap \( E_{g} \) = 0 are called conductors. Materials with a gap \( E_{g} \) < 3.5 eV are called semiconductors, and insulators are materials with a very large energy gap \( E_{g} \) > 3.5 eV.

In the energy band model, it is useful to use the concept of the Fermi level. The Fermi level \( E_{F} \) is the theoretical value of the energy of an electron in a semiconductor such that the probability of occupying the VB and CB bands is \( 50\% \). In a dopant-free (self-consistent) semiconductor, the Fermi level lies halfway between VB and CB.
This simplified model is presented for easier understanding of the behavior of electrons in the crystal lattice of a semiconductor. The detailed model describing the electron behavior is more complex.
Current conduction in semiconductors in the bandgap model can be represented as follows. Electrons are strongly bonded in the lattice and it takes considerable energy to release them from the valence band. This is equal to the bandwidth of the excited band \( E_{g} \). An electron released from the valence band can move under the influence of an applied electric field. A positively charged ion remains after the released electron. The positive charge thus formed can move in the crystal lattice from atom to atom as the missing electron can be replenished from the adjacent bond and so on. Such movement of positive charges is called hole motion. Electron transport takes place in the conduction band where electrons can move freely. The transport of holes takes place in the valence band. Without an external electric field, the motion of charges is chaotic and disorderly. Application of an external electric field brings order to the movement of holes and electrons, causing current to flow.
Semiconductor materials are, for example, crystals of atoms in group 4 of the periodic table and the compounds shown in Fig. 2. The table in the figure also presents the properties of these compounds, namely the magnitudes of the energy gap, their electron mobility and hole mobility, which are the basic parameters that characterize semiconductors (the data for the table are taken from [1]). Properties of diamond are also given for comparison. The mobility of charge carriers is expressed by the relationship between the drift velocity of the charges and the intensity of the external electric field.

The mobility of holes in semiconductors is much smaller than that of electrons. This is due to the electrons being bonded to atoms, making it difficult for them to jump to another atom (the hole therefore has a larger so-called effective mass and moves slower - a simplified explanation). The magnitude of the energy band gap of the absorbed \( E_{g} \) indicates the minimum energy of a quantum of radiation that can be absorbed by a semiconductor.
Example:
The maximum wavelength that can be absorbed by a semiconductor can be calculated from :

where \( E_{g} \)– energy break \( \left [ eV \right ] \), \( \lambda \)– wavelength \( \left [ nm \right ] \), 1240 \( \left [ eV\cdot nm \right ] \).

Using this formula and the Si energy gap, one can easily calculate up to what wavelength solar radiation will be absorbed in a silicon semiconductor. For example, for \( E_{g} \)=1.12 eV the maximum wavelength absorbed by a Si semiconductor is \( \lambda_{max} \)=1100 nm.
The physical properties of semiconductors strongly depend on temperature, e.g., resistivity decreases with increasing temperature.
If the semiconductor crystal is perfect, we say that we are dealing with an intrinsic semiconductor. In an intrinsic semiconductor, the number of electrons in the conduction band is equal to the number of holes in the valence band. The replacement of an atom in the crystal lattice of a semiconductor by another atom is called doping.

The physical properties of semiconductors strongly depend on temperature e.g., the resistance decreases with increasing temperature. If a semiconductor crystal is perfect, we say that we are dealing with an intrinsic semiconductor. In an intrinsic semiconductor, the number of electrons in the conduction band is equal to the number of holes in the valence band. The replacement of an atom in the crystal lattice of a semiconductor by another atom is called doping. The properties of semiconductors depend very strongly on the degree of doping, that is, the number of atoms introduced into the crystal lattice of the semiconductor. The atomic dopants from group 3 of the periodic table introduced into the semiconductor crystal cause electron deficiency and electron capture from the neighboring atom in which the positive charge remains (so-called hole). Such a semiconductor is called a p-type. It conducts via holes, which are majority charges (holes in p-type semiconductors, electrons in n-type semiconductors).
The introduction of p-type dopants creates an energy level in semiconductors, called the acceptor level, in which electrons from the valence band are bound. These electrons leave behind a gap in the valence band that can move and thus is considered a positive charge carrier ( Fig. 3 ). This results in lowering the position of the Fermi level.

The doping with atoms from group 5 of the periodic table into the crystal of an intrinsic semiconductor results in an n-type semiconductor ( Fig. 3 ). Excess electrons are released and form an additional band in the excited region near the conduction band. Such a semiconductor conducts current with electrons that are majority charges. The Fermi level is displaced towards the conduction bands compared to an intrinsic semiconductor.

Fig. 3 shows the changes in energy levels produced by the introduction of doped atoms into the intrinsic semiconductor. The introduction of atoms from group 3 of the periodic table creates a p-type semiconductor with an additional energy level \( E_{A} \) – acceptor level (a), and the addition of group 5 atoms creates an n-type semiconductor with an additional energy level \( E_{D} \) – donor level (b). This causes a shift of the Fermi level \( E_{F} \) towards the valence band for doping with atoms from group 3 of the periodic table and towards the conduction band for n-type semiconductors. For a p-type semiconductor, the resulting dopant energy level is called acceptor, and for an n-type semiconductor, the dopant energy level is called donor.