Extrinsic semiconductor donors

Figure 6.1 Schematic band structures of solids (a) insulator (kT ,) (b) intrinsic semiconductor (kT ,) (c) and (d) extrinsic semiconductors donor and acceptor levels in n-type and p-type semiconductors respectively are shown, (e) compensated semiconductor (f) metal (g) semimetal top of the valence band lies above the bottom of the conduction band.

In an extrinsic semiconductor, tlie conductivity is dominated by tlie e (or h ) in tlie CB (or VB) provided by shallow donors (or acceptors). If tlie dominant charge carriers are negative (electrons), tlie material is called n type. If tlie conduction is dominated by holes (positive charge carriers), tlie material is called p type. 

The carrier concentrations in doped or extrinsic semiconductors to which donor or acceptor atoms have been added can be deterrnined by considering the chemical kinetics or mass action of reactions between electrons and donor ions or between holes and acceptor ions. The condition for electrical neutraHty is given by equation 6. When the predominant dopants are donors, the semiconductor is... 

The position of the Fermi level in an extrinsic semiconductor depends upon the dopant concentrations and the temperature. As a rough guide the Fermi level can be taken as half way between the donor levels and the bottom of the valence band for n-type materials or half way between the top of the valence band and the acceptor levels for p-type semiconductor, both referred to 0 K. As the temperature rises the Fermi level in both cases moves toward the center of the band gap. 

Extrinsic Semiconductors are materials that contain donor or acceptor species (called doping substances) that provide electrons to the conduction band or holes to the valence band. If donor impurities (donating electrons) are present in minerals, the conduction is mainly by way of electrons, and the material is called an n-type semiconductor. If acceptors are the major impurities present, conduction is mainly by way of holes and the material is called a p-type semiconductor. For instance in a silicon semiconductor elements from a vertical row to the right of Si of... 

The Fermi level, e, at the surface can be derived in the same way as the interior Fermi level of extrinsic semiconductors shown in Eqns. 2-22 and 2-24 to give Eqn. 2-35 for the surface with a donor surface state at the energy level e , ... 

The most probable donor level, ered, the most probable acceptor level, eox, and the standard Fermi level, e redox) of redox electrons are characteristic of individual redox particles but the Fermi level, e m dox), of redox electrons depends on the concentration ratio of the reductant to the oxidant, which fact is similar to the Fermi level of extrinsic semiconductors depending on the concentration ratio of the donor to the acceptor. 

Extrinsic Semiconductors. Impurity levels can be either donor levels near the empty zone (normal or n-type), or acceptor levels near the filled band (abnormal or p-type). Conductivity in n-type conductors will be due to electrons in the empty band donated by the impurity levels, and in p-type conductors, to positive holes in the previously filled band, arising from the transition of electrons to the impurity acceptor levels. 

The presence of an impurity such as an As or a Ga atom in silicon leads to an occupied level in the band gap just below the conduction band or a vacant level just above the valence band, respectively. Such materials are described as extrinsic semiconductors. The n-type semiconductors have extra electrons provided by donor levels, and the p-type semiconductors have extra holes originating from the acceptor levels. Band structures of the different types of semiconductors are shown in Fig. 4.3.4. 

Extrinsic semiconductors ate those in which the carrier concentration, either holes or electrons, are controlled by intentionally added impurities called dopants. The dopants are termed shallow impurities because their energy levels lie within the band gap close to one or other of the bands. Because of thermal excitation, -type dopants (donors) are able to donate electrons to the conduction band and p-type dopants (acceptors) can accept electrons from the valence band, the result of which is equivalent to the introduction of holes in the valence band. Band gap widening/narrowingmay occur if the doping changes the band dispersion. At low temperamres, a special type of electrical transport known as impurity conduction proceeds. This topic is discussed in Section 7.3. 

Figure 8. Sketch of the density of electron states as a function of energy for a typical n-type extrinsic semiconductor, (a) 0 K, the donor atoms correspond to localized filled states just below the conduction band edge (b) T > 0 K, each donor atom is thermally ionized, this leads to a considerable density of electrons at the bottom of the CB the electrochemical potential is not far below the CB edge.

In intrinsic semiconductors, considerable effects are possible, provided that the concentration of charge carriers remains small in comparison with the values of 10 and 10 just cited. Depending on whether the donor or acceptor type of defect is predominant, transformation may result into n- or p-type extrinsic semiconductor. 

This always holds when the semiconductor is clean, without any added impurities. Such semiconductors are called intrinsic. The balance (4.126) can be changed by adding impurities that can selectively ionize to release electrons into the conduction band or holes into the valence band. Consider, for example, an arsenic impurity (with five valence electrons) in gennanium (four valence electrons). The arsenic impurity acts as an electron donor and tends to release an electron into the system conduction band. Similarly, a gallium impurity (three valence electrons) acts as an acceptor, and tends to take an electron out of the valence band. The overall system remains neutral, however now n p and the difference is balanced by the immobile ionized impurity centers that are randomly distributed in the system. We refer to the resulting systems as doped or extrinsic semiconductors and to the added impurities as dopants. Extrinsic semiconductors with excess electrons are called n-type. In these systems the negatively charged electrons constitute the majority carrier. Semiconductors in which holes are the majority carriers are calledp-type. 

The differences in properties between semiconductors and conductors explained by the interaction of the whole lattice. Intrinsic and extrinsic semiconductors and donor/acceptor bands. Simple example of band theory in action. 

Extrinsic semiconductors are materials containing foreign atoms (FAs) or atomic impurity centres that can release electrons in the CB or trap an electron from the VB with energies smaller than Eg (from neutrality conservation, trapping an electron from the VB is equivalent to the release of a positive hole in the otherwise filled band). These centres can be inadvertently present in the material or introduced deliberately by doping, and, as intrinsic, the term extrinsic refers to the electrical conductivity of such materials. The electron-releasing entities are called donors and the electron-accepting ones acceptors. When a majority of the impurities or dopants in a material is of... 

To quantify the conductivity of an extrinsic semiconductor, consider an -type semiconductor doped with a concentration Nj) of dopant atoms. The ionization reaction of the donor can be written as... 

In the preceding subsection, the number of electronic defects was fixed by the doping level, especially at lower temperatures, and the concepts of donor and acceptor localized levels were discussed. The band picture for nonstoichiometric electronic semiconductors is very similar to that of extrinsic semiconductors, except that the electronic defects form not as a result of doping, but rather by varying the stoichiometry of the crystal. 

Figure 13.9 (a) (i) Donor impurity in a crystal of an extrinsic semiconductor and (ii) the associated energy-band diagram donor impurities add donor energy levels below tbe conduction band, (b) (i) Acceptor impurity in a crystal of an extrinsic semiconductor and (ii) the associated energy-band diagram acceptor impurities add acceptor energy levels above the valence band... 

In extrinsic semiconductors the carrier concentrations are perturbed such that n = p. Again the analogy with the addition of an acid or base to water is quite instructive here. Consider the case when donor impurities are added to a neutral semiconductor. Since the intrinsic carrier concentrations are so low (sub-parts per trillion), even additions in parts per billion levels can have a profound electrical effect. This process is known as doping of the semiconductor. In this particular case, the Fermi level shifts toward the CB edge (Fig. 4b). When the donor level is... 

We shall consider next the theory of condition 2 for an extrinsic photoconductor, then the theory of G RA for condition 3, and finally the dependence of t on material parameters. We shall analyze the geometrical model of Fig. 4.8 and assume a simple energy level model of an n-type extrinsic semiconductor consisting of a photoionizable donor level and a compensating acceptor level properties of a corresponding p-type model would be analogous. This material is extrinsic as both a photoconductor and semiconductor. 

In the case of extrinsic semiconductors for which traces of impurities are added intentionally by doping in order to modify their electrical properties, the concentration of donors (e.g., P, As, or Sb) is denoted hyN, while the concentration of acceptors (e.g., B, Al, or Ga) is denoted by Nj. To calculate the carrier concentration in this kind of semiconductor, it is necessary to use the equation of electrical-charge neutrality ... 

---