BASIC SEMICONDUCTOR PRINCIPLES

1.8.1 Band energy

The electronic properties of solids are usually described by the molecular orbital theory in terms of the ‘band model’. The band model describes energy bands encompassing a range of energies that electrons can have in a solid. In a single atom, electrons exist in discrete energy levels, but in a crystalline

solid because the atoms are close together the orbitals of their electrons overlap so that they now form continuous energy bands (Figure 1.8.1). Each band represents a large number of allowed quantum states (Smith, 1990).

Energy

Vacant conduction band

Anti - bondUvi

Padnddcmi%ion Filled valence band

Bonding

1.8.2 Metals

In a metal the bonding and anti-bonding molecular orbitals (valence and conduction bands) overlap so that the conduction band is also partially filled. The loosely bound electrons form a mobile ’electron gas’ where an electron can move easily between the filled and vacant electronic energy levels of the valence and conduction band at virtually the same energy (Figure 1.2.3.a). The number of readily available electrons able to impart electrical conductivity (when an electric field is applied) is high in metal lattices. This number of available electrons is not increased significantly with increased temperatures. In fact, electrical conductivity in metals decreases with increased temperature as the mobility of the electrons in the conduction band falls. Because of this, high conductivity in metals is best achieved at normal temperatures.

1.8.3 Semiconductors

The bonding energy levels of atoms in a semiconductor are almost filled by electrons and form the valence band, whilst the anti-bonding energy levels are almost empty and form the conduction band. These two bands are separated by a forbidden region, a region where no allowed energy levels exists for electrons (Figure 1.2.3.a). This forbidden region gives rise to a band gap energy Eg, an energy which an electron must surpass to be able to move from the valence band to the conductance band to impart semiconducting capability (Figure 1.8.1). Electrons under thermal or photo excitation, traverse the band gap and so move from the valence band to the conduction band. Under an applied electric field the material will now conduct. Electrical conductivity of semiconductors, unlike metals, rapidly increases with increasing temperature. The reason for this is that more electrons leave the valence band and enter the conduction band than would occur at normal temperatures. Because of this, the slight fall in electron mobility with increased temperature can be neglected when considering semiconductors as conducting materials.

Electrical conduction occurs as a result of a net movement (under the influence of temperature and an applied electric field) of electrons from the filled valence band into the empty conduction band where the electrons are now able to move freely, leaving

behind holes in the nearly full valence band, which also now move freely. A hole behaves as if it were an electron with a positive charge.

1.8.3.1 Intrinsic semiconductors

Semiconducting materials which produce equal numbers of electrons and positive holes in conduction and valence bands by thermal excitation are called intrinsic semiconductors i.e. Silicon. Pure silicon has a band gap, = 1.1 eV and is an insulator at room temperature (Figure 1.8.3. La), only acting as a semiconductor at higher temperatures (Figure 1.8.3. l.b). Silicon is an insulator at room temperature because the band gap energy is too large for electrons to attain and cross at room temperature, higher temperatures being required to excite electrons from the valence band into the conduction band to impart semiconducting capability. Materials with band gap energies Eg> 1.5 eV are insulators because few if any electrons can be excited to jump from the valence band to the conduction band simply by thermal excitation (Guinier and Jullien, 1989).

Valence baad

Figure 1.8.3.1.a shows the intrinsic semiconductor silicon has a perfect crystal lattice where all electrons are confined to the valence band and no positive holes exist. Figure 1.8.3.l.b shows that at higher temperature, electrons are promoted to the conduction band,leaving positive holes in the valence band and broken lattice bonds.

1.8.3.2 Extrinsic semiconductors

Semiconductors also exist in which the number of electrons and positive holes produced after thermal excitation are not equal. These are called extrinsic semiconductors and have been doped with impurity atoms. The type of conduction that predominates here depends on the number and valence of the impurity atoms present.

Silicon atoms have a valence of four. If impurity atoms of valence five, such as arsenic, antimony, or phosphorus, are added to the lattice a further energy level E^, very close to the bottom of the conduction band of pure silicon will be introduced. At room temperature most of the dopant will be ionized, and free electrons will be introduced into the conduction band. Therefore, the electron density (n) in the conduction band does not reflect the hole density (p) in the valence band, since the remaining dopant are fixed in the energy level Ep and not the valence band. Thus, extrinsic semiconductors of this type give rise to crystals with electrons as major cause of conductivity, the so-called n-type semiconductors (Figure 1.8.3.2.a).

Ga

Valance bole

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Valenoe band

Figure 1.8.3.2.a shows the energy bands and representation of the extrinsic semiconductor crystal lattice for doped n-type semiconductor and Figure 1.8.3.2.b for doped p-type semiconductor.

Similarly, if the impurity atoms have a valence of three, such as boron, aluminium, or gallium, an energy level is created close to the top of the valence band, thus allowing electrons to be thermally excited from the valence band of silicon into this new lower energy level Ey^, leaving positive holes in the valence band. Conductivity in this instance can be attributed to the positive hole density in the valence band, the so called p-type semiconductors (Figure 1.8.3.2.b) (Guinier and Jullien, 1989).

1.8.4 Fermi level

The Fermi level is the energy in a solid at which the average number of particles per quantum state is 0.5; i.e. one half of the quantum states are occupied. The Fermi level of conductors such as metals lies in the conduction band, in insulators such as diamond it lies in the valence band, and in semiconductors it lies in the gap between the valence band and the conductance band (Figure 1.8.3.l.b). It will be closer to the conductance band than the valence band in n-type semiconductors (Figure 1.8.3.2.a) and visa versa for p- type semiconductors (Figure 1.8.3.2.b). At absolute zero all the electrons would occupy energy levels up to the Fermi level and no higher levels would be occupied (Solymar and Walsh, 1993).