Semiconductors, extrinsic

We have shown that the carrier concentration in intrinsic semiconductors is a strong function of temperature. This would allow us to make useful devices such as thermistors or other temperature-sensitive devices, but the property that makes semiconductors so indispensable for modem electronic applications is the ability to drastically alter the electronic properties of the host material by the addition of trace quantities of electrically active impurities called dopants. For example, the addition of a pentavalent (group V) element such as Sb, P, or As to Si results in an additional electron that is loosely bound to the impurity atom. You can think of the orbital for this impiu-ity atom as being similar to that of a hydrogen atom. Recall that the first ionization energy of a hydrogen atom is given by fi. If we replace the mass of a free electron with the effective mass 

The ionization energies of the donor and acceptor states for Si and for Ge are given in Table 20.3. The energies are referred to the nearest band edge (conduction band for donors valence band for acceptors). 

The deliberate addition of carefully chosen impurities to silicon, germanium and other semiconductors is called doping. It is carried out so as to modify the electronic conductivity, and the dopants are chosen so as to add either electrons or holes to the material. It is possible to gain a good idea of how this is achieved very simply. Suppose that an atom such as phosphoms, P, ends up in a silicon crystal. This can occur, for example, if a small amount of phosphorus impurity is added to molten silicon before the solid is crystallised. Experimentally the impurity atom is found to occupy a position in the crystal that would normally be occupied by a silicon atom, and so forms a substitutional defect. 

The simplest model to employ for the estimation of the energy needed to free the electron uses the Bohr theory of the hydrogen atom. To recall this model, a single electron is attracted to a 

The energy to liberate donor electrons and acceptor holes is about 8 x 10 J (0.05 eV). These values are comparable to room temperature thermal energy, and most extrinsic electrons and holes should be free at room temperature. In this state, the donors and acceptors are said to be ionised, and 

The number of holes and electrons present is not solely dependent on the number of donors and acceptors present. The equilibrium equation. 

Electrons or holes in these dopant states can be easily released into the bands if the energy of the state is within a small number of thermal energy units (i.e. keT) of the appropriate band edge (the valence band for acceptors, the conduction band for donors). The probability of finding a carrier is calculated based on the Fermi function and the separation of the dopant state from the band edge. Thus, for donors  

In these equations, Ed and Ea are the donor and acceptor energies, Ec and Ev are the conduction and valence band edge energies, and No and Na are the concentrations of donors and acceptors, respectively. The energy differences are the energies necessary to transfer a carrier from the dopant state to the band edge. These equations assume 

When one adds dopant to a pure semiconductor the Fermi level shifts, approaching the doping state energy. A brief examination of Equation 2.27 shows that if the Fermi energy rises in the band gap, the concentration of holes in the valence band must shrink. While the intrinsic condition n=p no longer holds, the condition 

---

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 equihbtium lever relation, np = can be regarded from a chemical kinetics perspective as the result of a balance between the generation and recombination of electrons and holes (21). In extrinsic semiconductors recombination is assisted by chemical defects, such as transition metals, which introduce new energy levels in the energy gap. The recombination rate in extrinsic semiconductors is limited by the lifetime of minority carriers which, according to the equihbtium lever relation, have much lower concentrations than majority carriers. Thus, for a -type semiconductor where electrons are the minority carrier, the recombination rate is /S n/z. An = n — is the increase of the electron concentration over its value in thermal equihbtium, and... 

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. 

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. 

Extrinsic detectors, 22 180 Extrinsic fiber-optic sensors, 11 148 Extrinsic photoconductors, 19 138 Extrinsic semiconductors, 22 236-237 Extrinsic wastes, 10 68 Extruded food packaging, 18 45 Extruded lead-copper alloys, 14 776 Extruded lead-tellurium alloys, 14 778 Extruded rigid foam, 23 404-405 Extruders... 

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... 

In doped silicon (an extrinsic semiconductor) the doping element has either three or five valence electrons (one electron less or one electron more than the four valence electrons of silicon). Substituting an arsenic or phosphorus atom (five valence electrons) for a silicon atom in a silicon crystal provides an extra loosely-bound electron that is more easily excited into the CB than in the case of the pure silicon. In such an n-type semiconductor, most of the electrical conductivity is attributed... 

Thus, it follows that the Fermi level of p-1ype semiconductors ascends from an energy level near ea toward the middle of the band gap with decreasing acceptor concentration, N. From Eqns. 2-22 and 2-24, we obtain in general that the Fermi level is located at levels higher for n-type semiconductors and lower for p-type semiconductors than the middle of the band gap. As described in the foregoing, the concentration of electrons, n, in the conduction band is different from the concentration of holes, p, in the valence band in extrinsic semiconductors... 

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. 

Calculate conductivity from charge carrier concentration, charge, and mobility. Differentiate between a conductor, insulator, semiconductor, and superconductor. Differentiate between an intrinsic and an extrinsic semiconductor. 

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... 

Figure 6.14 Schematic illustration of energy bands in a p-type, extrinsic semiconductor. From Z. Jastrzebski The Nature and Properties of Engineering Materials, 2nd ed. Copyright 1976 by John Wiley Sons, Inc. This material is used by permission of John WUey Sons, Inc.

Assuming that the mobilities are the same in both the intrinsic and extrinsic states, combine your information to solve for the electron and hole mobilities of this substance. Can you tell whether the substance is an n-type of p-type extrinsic semiconductor by looking at the data ... 

The properties of semiconductors are extremely sensitive to the presence of impurities at concentrations as low as 1 part in 10 °. For this reason, silicon manufactured for transistors and other devices must be very pure. The deliberate introduction of a very low concentration of certain impurities into the very pure semiconductor, however, alters the properties in a way that has proved invaluable in constructing semiconductor devices. Such semiconductors are known as doped or extrinsic semiconductors. Consider a crystal of silicon containing boron as an impurity. Boron has one fewer valence electron than silicon. Therefore, for every silicon replaced by boron, there is an electron missing from the valence band (Figure 4.10) (i.e., positive holes occur in the valence band and these enable electrons near the top of the band to conduct electricity). Therefore, the doped solid will be a better conductor than pure silicon. A semiconductor like this doped with an element with fewer valence electrons than the bulk of the material is called a p type semiconductor because its conductivity is related to the number of positive holes (or empty electronic energy levels) produced by the impurity. 

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.

It is convenient to distinguish between intrinsic and extrinsic semiconductors. The former contain stoichiometric amounts of the lattice constituents, whereas the latter depend on impurities present in solid solution. These impurities can be due either to foreign elements or to a stoichiometric excess of one lattice constituent (Figs. 17b and 17c). 

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. 

Dowden (27) in a theoretical approach similar to that used for metals, has examined the probability of positive ion formation on intrinsic and extrinsic semiconductors. The energy of activation of this process in intrinsic semiconductors is considered to be proportional to ) where / is the ionization potential of the activated complex (/ + Ab ) the activation energy decreases as (exit work function) increases and as AF decreases, — defining the Fermi level. In the case of n- and p-type semiconductors, the Fermi level will... 

---