Doped-semiconductor

When a semiconductor is doped with donor or acceptor atoms (see Fig. 1.10), then corresponding energy levels are introduced within the forbidden zone, as shown on the left side of Fig. 1.14. The donor level is usually close to the conduction band and the acceptor level close to the valence band. A donor level is defined as being neutral if filled by an electron, and positive if empty. An acceptor level is neutral if empty, and negative if filled by an electron. Depending on the distance of the donor and acceptor levels with respect to the corresponding bands, electrons are thermally excited into the conduction band and holes into the valence band. 

In the presence of impurities, the Fermi level must adjust itself to preserve charge neutrality. The latter is given for an n-type semiconductor by 

Introducing Eqs. (1.28), (1.30) and (1.34) into (1.33), the Fermi level, Ep, can be calculated. According to Eq. (1.34), it is clear that all donors are completely ionized if the Fermi level occurs below the donor level, as shown on the right side of Fig. 1.14. On the other hand, if the donor concentration is increased then the electron density also rises. 

In this case Ep may be located between E and , but then not all of the more highly concentrated donors are ionized. Similar relations can be derived for acceptor states in a p-type semiconductor. 

At extremely high impurity concentrations, the Fermi level may pass the band edge. In this case the semiconductor becomes degenerated, and most of the relations derived above are no longer applicable. The semiconductor then shows a metal-like behavior. 

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Jeon T I and Grischkowsky D 1998 Characterization of optically dense, doped semiconductors by reflection THz time domain spectroscopy Appl. Rhys. Lett. 72 3032-4... 

Instead of plotting tire electron distribution function in tire energy band diagram, it is convenient to indicate tire position of tire Fenni level. In a semiconductor of high purity, tire Fenni level is close to mid-gap. In p type (n type) semiconductors, it lies near tire VB (CB). In very heavily doped semiconductors tire Fenni level can move into eitlier tire CB or VB, depending on tire doping type. 

Gallium wets glass or porcelain and forms a brilliant mirror when it is painted on glass. It is widely used in doping semiconductors and producing solid-state devices such as transistors. 

Fig. 1. Band-edge energy diagram where the energy of electrons is higher in the conduction band than in the valence band (a) an undoped semiconductor having a thermally excited carrier (b) n-ty e doped semiconductor having shallow donors and (c) a -type doped semiconductor having shallow acceptors.

For insulators, Z is very small because p is very high, ie, there is Htde electrical conduction for metals, Z is very small because S is very low. Z peaks for semiconductors at - 10 cm charge carrier concentration, which is about three orders of magnitude less than for free electrons in metals. Thus for electrical power production or heat pump operation the optimum materials are heavily doped semiconductors. 

Finally, an electric current can produce injection luminescence from the recombination of electrons and holes in the contact 2one between differendy doped semiconductor regions. This is used in light-emitting diodes (LED, usually ted), in electronic displays, and in semiconductor lasers. 

Ion implantation is a method commonly used for doping semiconductors. Because the concentrations of the dopants (mostly B and P) are very low, a dynamic range of more than five orders of magnitude is often necessary. Measurement of is more difficult than that of B, because of the mass interference of °Si H. High mass resolution of m/Am = 5000, or an energy offset of 300 V, is necessary. 

A celebrated derivation of the temperature dependence of the mobility within the hopping model was made by Miller and Abrahams 22. They first evaluated the hopping rate y,y, that is the probability that an electron at site i jumps to site j. Their evaluation was made in the case of a lightly doped semiconductor at a very low temperature. The localized states are shallow impurity levels their energy stands in a narrow range, so that even at low temperatures, an electron at one site can easily find a phonon to jump to the nearest site. The hopping rate is given by... 

Before constructing an electrode for microwave electrochemical studies, the question of microwave penetration in relation to the geometry of the sample has to be evaluated carefully. Typically only moderately doped semiconductors can be well investigated by microwave electrochemical techniques. On the other hand, if the microwaves are interacting with thin layers of materials or liquids also highly doped or even metallic films can be used, provided an appropriate geometry is selected to allow interaction of the microwaves with a thin oxide-, Helmholtz-, or space-charge layer of the materials. 

The relatively large band gaps of silicon and germanium limit their usefulness in electrical devices. Fortunately, adding tiny amounts of other elements that have different numbers of valence electrons alters the conductive properties of these solid elements. When a specific impurity is added deliberately to a pure substance, the resulting material is said to be doped. A doped semiconductor has almost the same band stmeture as the pure material, but it has different electron nonulations in its bands. 

Figure 10-53 shows band-gap diagrams of n-type and p-type semiconductors. Electrical current flows in a doped semiconductor in the same way as current flows in a metal (see Figure 10-501. Only a small energy difference exists between the top of the filled band and the next available orbital, so the slightest applied potential tilts the bands enough to allow electrons to move and current to flow.

The two extremes of ordering in solids are perfect crystals with complete regularity and amorphous solids that have little symmetry. Most solid materials are crystalline but contain defects. Crystalline defects can profoundly alter the properties of a solid material, often in ways that have usefial applications. Doped semiconductors, described in Section 10-, are solids into which impurity defects are introduced deliberately in order to modify electrical conductivity. Gemstones are crystals containing impurities that give them their color. Sapphires and rubies are imperfect crystals of colorless AI2 O3, red. 

In case of the doped semiconductor of -type under consideration the situation gets simple due to large thickness of SCR if compared to the free path length of the carriers. Therefore, substituting expression (1.42) into (1.41) under condition of applicability of the Boltzmann statistics for the free electrons and holes leads to expression... 

Thus, for a broad-band doped semiconductor of n-type which stays in equilibrium with outside medium containing oxygen with partial pressure Pq the neutrality equation acquires the shape... 

V.L. Bonch-Bruevich, Proceedings in Electron Theory of Highly Doped Semiconductors, VINITI Publ., Moscow, 1965... 

B. l. Shklovski and A.L. Efros, Electron Properties of Doped Semiconductors, Nauka Publ., Moscow, 1979... 

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. 

For doped semiconductors, it is assumed that the charge density in the semiconductor, e.g. of type ny is... 

Some insulating oxides become semiconducting by doping. This can be achieved either by inserting certain heteroatoms into the crystal lattice of the oxide, or more simply by its partial sub-stoichiometric reduction or oxidation, accompanied with a corresponding removal or addition of some oxygen anions from/into the crystal lattice. (Many metal oxides are, naturally, produced in these mixed-valence forms by common preparative techniques.) For instance, an oxide with partly reduced metal cations behaves as a n-doped semiconductor a typical example is Ti02. 

Although the role of rare earth ions on the surface of TiC>2 or close to them is important from the point of electron exchange, still more important is the number of f-electrons present in the valence shell of a particular rare earth. As in case of transition metal doped semiconductor catalysts, which produce n-type WO3 semiconductor [133] or p-type NiO semiconductor [134] catalysts and affect the overall kinetics of the reaction, the rare earth ions with just less than half filled (f5 6) shell produce p-type semiconductor catalysts and with slightly more than half filled electronic configuration (f8 10) would act as n-type of semiconductor catalyst. Since the half filled (f7) state is most stable, ions with f5 6 electrons would accept electrons from the surface of TiC>2 and get reduced and rare earth ions with f8-9 electrons would tend to lose electrons to go to stabler electronic configuration of f7. The tendency of rare earths with f1 3 electrons would be to lose electrons and thus behave as n-type of semiconductor catalyst to attain completely vacant f°- shell state [135]. The valence electrons of rare earths are rather embedded deep into their inner shells (n-2), hence not available easily for chemical reactions, but the cavitational energy of ultrasound activates them to participate in the chemical reactions, therefore some of the unknown oxidation states (as Dy+4) may also be seen [136,137]. 

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