Electronic conductivity intrinsic semiconductors

In an intrinsic semiconductor, tlie conductivity is limited by tlie tlieniial excitation of electrons from a filled valence band (VB) into an empty conduction band (CB), across a forbidden energy gap of widtli E. The process... 

The effective masses of holes and electrons in semiconductors are considerably less than that of the free electron, and die conduction equation must be modified accordingly using the effective masses to replace tire free electron mass. The conductivity of an intrinsic semiconductor is then given by... 

Electric current is conducted either by these excited electrons in the conduction band or by holes remaining in place of excited electrons in the original valence energy band. These holes have a positive effective charge. If an electron from a neighbouring atom jumps over into a free site (hole), then this process is equivalent to movement of the hole in the opposite direction. In the valence band, the electric current is thus conducted by these positive charge carriers. Semiconductors are divided into intrinsic semiconductors, where electrons are thermally excited to the conduction band, and semiconductors with intentionally introduced impurities, called doped semiconductors, where the traces of impurities account for most of the conductivity. 

The description of the properties of this region is based on the solution of the Poisson equation (Eqs 4.3.2 and 4.3.3). For an intrinsic semiconductor where the only charge carriers are electrons and holes present in the conductivity or valence band, respectively, the result is given directly by Eq. (4.3.11) with the electrolyte concentration c replaced by the ratio n°/NA, where n is the concentration of electrons in 1 cm3 of the semiconductor in a region without an electric field (in solid-state physics, concentrations are expressed in terms of the number of particles per unit volume). 

The electronic band structure of a neutral polyacetylene is characterized by an empty band gap, like in other intrinsic semiconductors. Defect sites (solitons, polarons, bipolarons) can be regarded as electronic states within the band gap. The conduction in low-doped poly acetylene is attributed mainly to the transport of solitons within and between chains, as described by the intersoliton-hopping model (IHM) . Polarons and bipolarons are important charge carriers at higher doping levels and with polymers other than polyacetylene. 

Semiconductors are materials that contain a relatively small number of current carriers compared to conductors such as metals. Intrinsic semiconductors are materials in which electrons can be excited across a forbidden zone (bandgap) so that there are carriers in both the valence (holes, p-type) and conduction (electrons, ra-type) bands. The crucial difference between a semiconductor and an insulator is the magnitude of the energy separation between the bands, called the bandgap (Eg). In the majority of useful semiconducting materials this is of the order of 1 eV some common semiconductors are listed in Table 1. 

Degenerate semiconductors can be intrinsic or extrinsic semiconductors, but in these materials the band gap is similar to or less than the thermal energy. In such cases the number of charge carriers in each band becomes very high, as does the electronic conductivity. The compounds are said to show quasi-metallic behavior. 

Figure 7.1 Band structure of an intrinsic semiconductor. At T = 0 the valence band is completely filled and the conduction band is empty. At higher temperatures the conduction band contains a low concentration of electrons, the valence band an equal concentration of holes. Bands with a lower energy, one of which is shown, are always completely filled.

The band gap Eg of semiconductors is typically of the order of 0.5 - 2 eV (e.g., 1.12 eV for Si, and 0.67 eV for Ge at room temperature), and consequently the conductivity of intrinsic semiconductors is low. It can be greatly enhanced by doping, which is the controlled introduction of suitable impurities. There are two types of dopants Donors have localized electronic states with energies immediately below the conduction band, and can donate their electrons to the conduction band in... 

An Intrinsic Semiconductor is characterized by an equal density of positive and negative charge carriers, produced by thermal excitation i.e., the density of electrons in the conduction band, nj, and of holes in the valence band, Pi, are equal... 

The energy of the Fermi level, Ef, is defined as that energy where the probability of a level being occupied by an electron is V2 (i.e., where it is equally probable that the level is occupied or vacant). For an intrinsic semiconductor Ef lies essentially midway between the cb and vie. For a n-type solid Ef lies slightly below the conduction band, while for a p-type solid Ef lies slightly above the valence band. 

In intrinsic semiconductors, the concentration of electrons, n, in the conduction band is equal to the concentration of holes, p, in the valence band as shown in Eqn. 2-13 ... 

Fig. 2-16. Electron state density distribution and electron-hole pair formation in the conduction and valence bands of intrinsic semiconductors Cf > Fermi level of intrinsic semiconductors.

Fig. 8-16. Electron state density in a semiconductor electrode and in hjrdrated redox partides, rate constant of electron tunneling, and exchange redox current in equilibrium with a redox electron transfer reaction for which the Fermi level is close to the conduction band edge eF(sc) = Fermi level of intrinsic semiconductor at the flat band potential 1. 0 (tp.o) = exchange reaction current of electrons (holes) (hvp)) - tunneling rate constant of electrons (holes).

As shown in Fig. 3.6, for intrinsic (undoped) semiconductors the number of holes equals the number of electrons and the Fermi energy level > lies in the middle of the band gap. Impurity doped semiconductors in which the majority charge carriers are electrons and holes, respectively, are referred to as n-type and p-type semiconductors. For n-type semiconductors the Fermi level lies just below the conduction band, whereas for p-type semiconductors it lies just above the valence band. In an intrinsic semiconductor tbe equilibrium electron and bole concentrations, no and po respectively, in tbe conduction and valence bands are given by ... 

Conduction that arises from thermally or optically excited electrons is called intrinsic semiconduction. The conduction of intrinsic semiconductors usually takes place at elevated temperamres, since sufficient thermal agitation is necessary to transfer a reasonable number of electrons from the valence band to the conduction band. The elements that are capable of intrinsic semiconduction are relatively limited and are shown in Figure 6.12. The most important of these are silicon and germanium. 

In intrinsic semiconductors, the number of holes equals the number of mobile electrons. The resulting electrical conductivity is the sum of the conductivities of the valence band and conduction band charge carriers, which are holes and electrons, respectively. In this case, the conductivity can be expressed by modifying Eq. (6.9) to account for both charge carriers ... 

The mobilities of holes are always less than those of electrons that is fXh < Me- In silicon and germanium, the ratio [ie/[ih is approximately three and two, respectively (see Table 6.2). Since the mobilities change only slightly as compared to the change of the charge carrier densities with temperature, the temperature variation of conductivity for an intrinsic semiconductor is similar to that of charge carrier density. 

Equation (6.31) indicates that the conductivity of intrinsic semiconductors drops nearly exponentially with increasing temperature. At still higher temperamres, the concentration of thermally excited electrons in the conduction band may become so high that the semiconductor behaves more like a metal. 

A sequence may form and eventually meet a B sequence, as shown, but in doing so, a free radical, called a soliton, is produced. The soliton is a relatively stable electron with an unpaired spin and is located in a nonbonding state in the energy gap, midway between the conduction and valence bands. It is the presence of these neutral solitons which gives frany-polyacetylene the characteristics of an intrinsic semiconductor with conductivities of 10 to 10 (f2 cm) ... 

Chapter 4 discussed semiconductivity in terms of band theory. An intrinsic semiconductor has an empty conduction band lying close above the filled valence band. Electrons can be promoted into this conduction band by heating, leaving positive holes in the valence band the current is carried by both the electrons in the conduction band and by the positive holes in the valence band. Semiconductors, such as silicon, can also be doped with impurities to enhance their conductivity. For instance, if a small amount of phosphorus is incorporated into the lattice the extra electrons form impurity levels near the empty conduction band and are easily excited into it. The current is now carried by the electrons in the conduction band and the semiconductor is known as fl-type n for negative). Correspondingly, doping with Ga increases the conductivity by creating positive holes in the valence band and such semiconductors are called / -type (p for positive). 

From 3 to (say) 0.3 MPM the conductivity is not in the metallic range, but we believe that the material behaves like an intrinsic semiconductor, current being carried by electrons in the upper band. This, as we have seen, is not a Hubbard band, but the band formed from molecular orbitals for an extra electron on molecular dimers. In this range d In a jdT... 

When an electron is excited across the energy gap g to the conduction band in an intrinsic semiconductor, an unoccupied energy state, or hole, is left behind in the normally full valence band. This vacant state can be jumped into by another electron... 

The effect of an external electric field is to produce an acceleration of the electrons in the direction of the field, and this causes a shift of the Fermi surface. It is a necessary condition for the movement of electrons in the fc-space that there are allowed empty states at the Fermi surface hence electrical conductivity is dependent on partially filled bands. An insulating crystal is one in which the electron bands are either completely full or completely empty. If the energy gap between a completely filled band and an empty band is small, it is possible that thermal excitation of electrons from the filled to the empty band will result in a conducting crystal. Such substances are usually referred to as intrinsic semiconductors. A much larger class of semiconductors arises from impurities... 

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