Basics notions about solids

In order to understand the electrochemistry of semiconductors some
basics notions about solids are nevessary.

2.1.1 Basics notions about solids

The properties of semiconductor electrodes can be understood by examining their electronic structure. Due to the essentially infinite number of atoms that must be considered, the electronic structure of these solids is typically discussed in terms of energy bands [13]. The band model stems directly from the picture of atomic energy levels. The theory and experiment show that when the atoms are brought close enough to each other, so that they form a solid, the valence electrons interact with each other in a such a way that their sharp atomic energy levels are broadened into wider regions called energy bands.

A solid is nothing else than a collection of interacting atoms. According to the energy band theory, from each atomic level a huge number of different energy levels is generated due to interaction between atoms. The "new" levels are only slightly different from the original atomic levels. A schematic splitting of atomic levels by decreasing the distance between the atoms is presented in Figure 2.1.

 A schematic representation of the splitting of atomic energy levels into bands by decreasing the distance between the atoms (d) up to several Angstroms.

Figure 2.1: A schematic representation of the splitting of atomic energy levels into bands by decreasing the distance between the atoms (d) up to several Angstroms.

From the point of view of solid state physics there are two atomic levels which are of considerable importance: the last occupied and the first unoccupied by electrons. These two atomic levels give rise to two different bands in the solid. The band resulting from the last occupied level is called the valence band (Ev) and that resulting from the first unoccupied level is called the conductance band (Ec) [14]. Thus, the valence band will be totally occupied by electrons, whereas the conduction band will be partially or totally free of electrons. The metallic, semiconductor or dielectric properties of a solid are determined by the fact how the two bands are filled by electrons.

  • A solid has metallic properties if the valence and conduction bands overlap, or if the valence and conduction bands do not overlap but the conduction band is only partially filled with electrons at T = 0 K (see Figure 2.2a);
  • A solid has semiconductor properties when the valence and conduction bands do not overlap and the conduction band is free of electrons at T = 0 K. The difference between the top of Ev and bottom of Ec is called the electronic band gap (Eg). Usually if the band gap between valence and conduction bands is smaller than 3 eV then the material is considered a semiconductor (Figure 2.2b);
  • The same is true for dielectrics, however the band gap should be larger than 3 eV (Figure 2.2c). Note that there is no strict separation between semiconductors and dielectrics regarding the electronic band gap. For example, GaN with a band gap of 3.3 eV is still considered a semiconductor.

A schematic band occupation by electron in metals, semiconductors and dielectrics.

Figure 2.2: A schematic electron population in metals, semiconductors and dielectrics.

The electrons behave differently within the two bands. A way to consider the behaviour of electrons is by considering their moving properties, usually referred to as conductivity. An electron can move in a band if it has partially filled or free states in its neighbourhood. This is much easily done in the conduction band, where a high number of unoccupied states is available. The metals fulfil this condition very well and therefore they have the highest conductivity.

For insulators, the band gap is sufficiently large and under normal conditions the electrons can not be transferred from the valence to the conduction band. Thus, the conduction band remains unoccupied and as a result the conductivity in insulators is very low.

On the other hand, in semiconductors the band gap is not so large and the electrons can be transferred into the conduction band, e.g. by thermal excitation. The transferred electrons will behave like electrons in a metal, however, the number of electrons in the conduction band of semiconductors will be much lower as compared with metals. The interesting issue is that the excitation of electrons leaves positively charged vacancies in the valence band of semiconductor. These positively charged vacancies are mobile as well and are normally called 'holes'. A hole is an empty level in the valence band, or in other words, a valence bond with a missing electron. As a result the current in semiconductors is made up of two components [15]:

  • The mobile electrons in the conduction band;
  • The mobile holes in the valence band.

In the general case, the electrons can be excited into the conduction band either electrically, thermally, or optically. However, there is another efficient approach for generating charge carriers in semiconductors, referred to as doping. Doping involves the addition of tiny amounts of a different chemical element into the semiconductor. The simplest example is the introduction of a group V element (donor, e.g., P) or a group III element (acceptor, e.g., B) into a group IV crystal (host, e.g., Si).

The addition of P into Si introduces occupied energy levels into the band gap close to the edge of the conduction band, thereby allowing an easy promotion of electrons from the group V atom into the conduction band of the group IV crystal. On the other hand, e.g. the addition of B introduces vacant energy levels into the band gap close to the edge of the valence band, which facilitates the transfer of electrons from the valence band to group III atoms. Thus, by doping the semiconductor accordingly, an additional number of electrons or holes can be generated.

For III-V materials, impurity species like Si, Sn, Te, Se, and S are suitable candidates as donor species. Acceptor impurities include Be, C, Zn, Cd, and Mn. Other metal species such as Cr, Ni, Fe tend to produce mid gap deep level states with high resistivity or semi-insulating characteristics [16].

Undoped semiconductors are known as intrinsic, while doped semiconductors are called extrinsic semiconductors. Doped semiconductors with the dominant charge carriers being the electrons are referred to as n-type semiconductors (donor doped), whereas those where the holes make the majority are referred to as p-type semiconductors (acceptor doped).

The three types of semiconductors: a) Intrinsic semiconductors. b) n-type semiconductors. c) p-type semiconductors.

Figure 2.10: The three types of semiconductors: a) Intrinsic semiconductors. b) n-type semiconductors. c) p-type semiconductors.

A very important concept used to describe the thermodynamical equilibrium of charges in solid state materials is the so called Fermi level [16]. The Fermi level is defined as the energy level where the probability of population by an electron is equal to 0.5. For metals at T = 0 K the Fermi level represents the energy level separating the occupied from the unoccupied by electrons levels. In semiconductors, on the other hand, the occupied and unoccupied levels are separated by a band gap and for example, for an intrinsic semiconductor the Fermi level lies (at T = 0) at the mid point of the band gap (Figure 2.3a).

As it was already mentioned, doping changes the energy distribution of electrons, hence, changes the position of the Fermi level as well. For n-type semiconductors the Fermi level lies just below the conduction band (Figure 2.3b), whereas for p-type semiconductors is just above the valence band (Figure 2.3c). Such semiconductors are called non-degenerated. However, at very high doping levels the Fermi level can move into the conduction or valence band respectively. In such a case the semiconductor is said to be degenerated.

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