Semiconductor, intrinsic

An intrinsic semiconductor has no impurities and the number of electrons, n, in the conduction band exactly matches the number of holes, p, in the valence band, n=p. The number of electrons or holes is named the intrinsic carrier concentration ni. This carrier concentration is given by the probability that a state at energy E is filled (as given by the Fermi function. Equation 2.11) multiplied by the density of states at that energy (Equation 2.22 for free electrons) integrated over all energies at or above the conduction band edge  

This equation can be simplified by noting that the band edge energy is typically far from the Fermi energy in units of keT, in an intrinsic material. Therefore, the Boltzmann approximation (Equation 2.12) can be used. With the further definition  

We can circumvent the issue of the Fermi energy by noting that a similar definition can be made based ni=p, and with a similar definition for the effective valence-band density of states, Ny  

Taking the square-root gives a value for Ui which does not depend upon Ep  

The most important point to note about Equation 2.30 is that ni depends exponentially with temperature on half of the semiconductor energy gap. Narrow-gap semiconductors will have large intrinsic carrier concentrations while wide-gap materials will have fewer mobile carriers at a given temperature. 

It is possible to determine the number of electrons excited into the conduction band by thermal energy in an intrinsic semiconductor using Fermi-Dirac statistics (see Section 2.3.7 and Section S4.12). It is found that  

The total conductivity, cr, which is proportional to the number of electrons and holes, can be expressed in the form  

An alternative method of obtaining the magnitude of the band gap is via the absorption of radiation. In a semiconductor, almost all of the energy levels below the conduction band are occupied. This means that low-energy radiation directed at a crystal will not interact with the electrons, and the crystal 

Approximate values for the band gap in some semiconductors is given in Table 13.1. The band gap decreases as the atom size increases (i.e. as one moves down the relevant group in the periodic table). Thus, within the group of elements listed, diamond is best regarded as an insulator, whereas grey tin is regarded as a metal. The second group 

Note the band gap is normally given in electron volts in most compilations 1 eV is equal to 1.60219 x 10 J. 

Electrons thermally excited from the valence band (VB) occupy successively the levels in the conduction band (CB) in accordance with the Fermi distribution function. Since the concentration of thermally excited electrons (10 to 10 cm ) is much smaller than the state density of electrons (10 cm ) in the conduction band, the Fermi function may be approximated by the Boltzmann distribution function. The concentration of electrons in the conduction band is, then, given by the following integral [Blakemore, 1985 Sato, 1993]  

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  

The Fermi level, Cp, of intrinsic semiconductors is obtained from Eqn. 2-13 as shown in Eqn. 2-15  

Since Nc is nearly equal to N, the Fermi level of intrinsic semiconductors is located midway in the band gap as shown in Fig. 2-16. All the equations given in the foregoing are valid under the condition that rii Nc or Ny. this condition is frilfilled with usual intrinsic semiconductors. 

As shown in Figs. 2-17 and 2-18, semiconductors containing impurities are classified into the following two types n-type semiconductors with localized donor levels close to the conduction band, and p-type semiconductors with localized acceptor levels close to the valence band in the band gap. The liberation of electrons from the donor levels into the conduction band and the liberation of holes from the acceptor levels into the valence band are represented by the ionization processes of donor D and acceptor A, respectively, as shown in Eqns. 2-16 and 2-17  

The number of electrons occupying levels in the conduction band is given by 

According to Eq. (1.27) one obtains 5 x cm for the density of states within 1 kT above the lower edge of the conduction band, assuming an effective mass of m = 1 X Wo (wo = electron mass in free space). Since semiconductors with doping of less than 1 x 10 cm are used in most investigations and applications, the majority of the energy levels remain empty. 

Similarly, we can obtain the hole density near the top of the valence band. We have, then 

In order to preserve charge neutrality in an intrinsic semiconductor, the electron and hole densities must be equal. The position of the Fermi level can then be calculated from Eqs. (1.26) and (1.29). We then have 

Accordingly, the Fermi level Ey is close to the middle of the energy gap, or for 

The product of n and p is constant and the corresponding concentration is w = p = j, that is, is the intrinsic electron density. Equation (1.32) is called the mass law of electrons and holes, in comparison with chemical equilibria in solutions. The intrinsic concentration can be calculated from Eq. (1.32) if the densities of states are known. Assuming that m /niQ = 1, then 10 cm for a bandgap of g = 1 eV, that is, is a very small quantity. In the case of intrinsic material, the electron hole pairs are created entirely by thermal excitation. Since this excitation becomes very small for large bandgaps, decreases with increasing bandgaps as 

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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... 

CONTROLLED RELEASE TECHNOLOGY - PHARMACEUTICAL] (Vol 7) Intrinsic semiconductors... 

Intrinsic Semiconductors. For semiconductors in thermal equiHbrium, (Ai( )), the average number of electrons occupying a state with energy E is governed by the Fermi-Dirac distribution. Because, by the Pauli exclusion principle, at most one electron (fermion) can occupy a state, this average number is also the probabiHty, P E), that this state is occupied (see Fig. 2c). In equation 2, K... 

In an undoped, intrinsic semiconductor the equiHbrium concentrations of electrons, and holes,/), are described by a lever rule derived from the law of mass action (eq. 3) ... 

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... 

Table 3. Energy Gap (Eg) at Room Temperature for Intrinsic Semiconductors...

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). 

This polymer occurs as trans- or a less stable c/s-isomer. (The ds-isomer can be converted to trans- by heating.) Both isomers are intrinsic semiconductors with conductivities around 10 9S/cm (cis) and 10 6S/cm (trans). 

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. 

Pure Cr203 is an intrinsic semiconductor with a band-gap of approximately 3.3 eV. Generally, Cr203 shows little stoichiometric variation. On doping with Ti02, Ti4+ ions substitute on Cr3+ sites in the structure. The conductivity of the doped solid is n-type and has a dependence upon oxygen partial pressure. The three... 

If the donors and acceptors are present in equal numbers, the material is said to be a compensated semiconductor. At 0 K these materials are insulators, and it is difficult in practice to distinguish between compensated and intrinsic semiconductors. When all of the impurities are fully ionized so that either all the donor levels have lost an electron or all the acceptor levels have gained an electron, the exhaustion range has been reached. 

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... 

Intrinsically conducting polymers, 13 540 Intrinsic bioremediation, 3 767 defined, 3 759t Intrinsic detectors, 22 180 Intrinsic fiber-optic sensors, 11 148 Intrinsic magnetic properties, of M-type ferrites, 11 67-68 Intrinsic photoconductors, 19 138 Intrinsic rate expressions, 21 341 Intrinsic semiconductors, 22 235-236 energy gap at room temperature, 5 596t Intrinsic strength, of vitreous silica, 22 428 Intrinsic-type detectors, cooling, 19 136 Intrinsic viscosity (TV), of thermoplastics, 10 178... 

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. 

Explain how doping of an intrinsic semiconductor such as silicon leads to modification of its properties. 

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