Intrinsic semiconductor carriers

In an intrinsic semiconductor, charge conservation gives n = p = where is the intrinsic carrier concentration as shown in Table 1. Ai, and are the effective densities of states per unit volume for the conduction and valence bands. In terms of these densities of states, n andp are given in equations 4 and... 

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. 

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... 

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 ... 

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. 

Unlike intrinsic semiconductors, in which the conductivity is dominated by the exponential temperature aud band-gap expression of Eq. (6.31), the conductivity of extrinsic semiconductors is governed by competing forces charge carrier density and charge carrier mobility. At low temperatures, the number of charge carriers initially... 

This material, which has the corundum structure, is a semiconductor at low temperatures, the optical band gap being 0.2 eV (Lucovsky et al. 1979). We should probably consider it to be an intrinsic semiconductor, but the activation energy in the conductivity does not appear to be constant. The thermopower (Chandrasekhar et al. 1970) is about 900pVK 1 at 100K and 500pVK 1 at 200 K this would suggest an activation energy of about 0.06 eV, or less than half the band gap.f This makes it likely that one of the carriers is a small polaron the... 

When one examines the value of n = p, it turns out that the density of charge carriers in an intrinsic semiconductor (Table 6.16) at room temperature is in the range of 10 to 10 cm, compared with about 10 cm in a metal. It is this relatively low concentration of charge carriers in intrinsic semiconductors that is responsible for the most important differences between semiconductor electrodes and metal electrodes. 

Impurity Semiconductors, n-Type andp-Type. The discussion has been restricted so far to pure intrinsic semiconductors exemplified by germanium and silicon. In these substances, there is a low concentration of charge carriers (compared with metals). Further, the hole and electron concentrations are equal, and their product is a constant given by the law of mass action... 

The fact that n-type crystals thus grown are semi-insulating cannot be explained from the viewpoint of the phase diagram. The semi-insulating phase is regarded as a pseudo-intrinsic semiconductor, i.e. the concentration of free carriers is very low, due to the carrier compensation in some sense. Holmers et al. have concluded from their data that the concentration of free carrier called EL2 , Nq, is compensated for by that of acceptors derived from impurity carbon, Ta et carried out a similar investigation independently and reached the same conclusion. 

Carrier Concentrations. Intrinsic Carriers. The number of available carriers depends on thermally generated conduction band electrons and valence band holes, as well as carriers produced from the incorporation (intentional or unintentional) of impurities. In an intrinsic semiconductor, the thermally generated carriers dominate. The number of electrons (n) in the conduction band can then be calculated from the integral over the density... 

There are three basic types of semiconductor materials depending on their ability to conduct hole (p-type), electrons (n-type), or both (ambipo-lar) under different gate bias conditions. In semiconductor materials, reduction of the bandgap (Eg) will enhance the thermal population of the conduction band and thus increase the number of intrinsic charge carriers. The decrease of Eg can led to true organic metals showing intrinsic electrical conductivity. 

Intrinsic semiconductors have a band structure similar to that of insulators, except that the gap is smaller, usually in the range 0.5 to 3 eV. A few electrons may have sufficient thermal energy to be promoted to the empty conduction band. Each electron leaving the valence band not only creates a charge carrier in the conduction band but also leaves behind a hole in the valence band. This hole provides a vacancy which can promote the movement of electrons in the valence band. 

First, the drift current is calculated in the case of a constant electrical field, as one would expect for very thin bulk heterojunction solar cells. If the width W of the active layer is similar to the drift length of the carrier, the device will behave as a MIM junction, where the intrinsic semiconductor is fully depleted. The current is then determined by integrating the generation rate G = —dP/dx over the active layer, where P is the photon flux ... 

An undoped or pure semiconductor material is called an intrinsic semiconductor. Dopants (or impurities) are often added at very low concentration to modify the type and/or number of charge carriers in the material (i.e., adjust the Fermi level). There are two types of semiconductor materials, n-type in which the majority charge carriers are (negative) electrons, andp-fypein which the majority charge carriers are (positive) holes or electron deficiencies. Most (but not all) semiconducting metal oxides are of the n-type. 

If a semiconductor is so pure that impurities contribute negligibly to - charge carrier densities in the conduction and valence bands, it is called an intrinsic semiconductor and the intrinsic charge-carrier density dependence on temperature is given by n (T) oc T exp (-2 r)> where g is the band-gap energy and ks is the - Boltzmann constant. 

The equivalent circuit of Fig. 37 clearly demonstrates the main experimental difficulties encountered in determining Rac it is evident that only d.c. measurements are likely to prove practical else ZF will be too small and the semiconductor will be shunted by Rel (which is likely to be very small). The bulk resistor RB is only larger than Rac for intrinsic semiconductors and it has proved difficult to extend the technique to extrinsic materials as R becomes effectively shunted by RB. Evidently, only Rsc and Rel vary with potential applied across the semiconductor between the back contact and the reference electrode in solution however, the change in Rel is normally much smaller than Rsc as the mobility of the ions in solution is so much smaller than that of the carriers in the semiconductor. 

Hole an electronic vacancy in the valence band of a solid Indirect band gap semiconductors semiconductors in which the lowest energy electronic transition between the valence and conduction bands is formally optically forbidden Intrinsic semiconductor an undoped semiconductor Majority carrier the predominant charge carrier in the bulk of a doped semiconductor... 

To describe the conductivity of an intrinsic semiconductor sample quantitatively, we need to calculate the concentrations of both types of charge carriers in the solid. The key quantity that controls the equilibrium concentration of electrons and holes in an intrinsic semiconductor is the band gap. Because the thermal excitation energy required to produce an electron and a hole is equal to Eg, the intrinsic carrier concentrations can be related to Eg using the Boltzmann relationship ... 

---