Insulators and semiconductors

When each atom provides two electrons, the 2N electrons fill the N orbitals of the s band. The Fermi level now lies at the top of the band (at T = 0), and there is a gap before the next band begins (Fig. 20.55). As the temperature is increased, the tail of the Fermi–Dirac distribution extends across the gap, and electrons leave the lower band, which is called the valence band, and populate the empty orbitals of the upper band, which is called the conduction band. As a consequence of electron promotion, positively charged ‘holes’ are left in in the valence band. The holes and promoted electrons are now mobile, and the solid is an electrical conductor. In fact, it is a semiconductor, because the electrical conductivity depends on the number of electrons that are pro moted across the gap, and that number increases as the temperature is raised. If the gap is large, though, very few electrons will be promoted at ordinary temperatures and the conductivity will remain close to zero, resulting in an insulator. Thus, the conventional distinction between an insulator and a semiconductor is related to the size of the band gap and is not an absolute distinction like that between a metal (incomplete bands at T = 0) and a semiconductor (full bands at T = 0). Figure 20.55 depicts conduction in an intrinsic semiconductor, in which semicon duction is a property of the band structure of the pure material. Examples of intrinsic semiconductors include silicon and germanium. A compound semiconductor is an intrinsic semiconductor that is a combination of different elements, such as GaN, CdS, and many d-metal oxides. An extrinsic semiconductor is one in which charge carriers are present as a result of the replacement of some atoms (to the extent of about 1 in 109) by dopant atoms, the atoms of another element. If the dopants can trap electrons, they withdraw electrons from the filled band, leaving holes which allow the remaining electrons to move (Fig. 20.56a). This procedure gives rise to p-type semiconductivity, the p indicating that the holes are positive relative to the electrons in the band. An example is silicon doped with indium. We can picture the semiconduction as arising from the transfer of an electron from a Si atom to a neighbouring In atom. The electrons at the top of the silicon valence band are now mobile, and carry current through the solid. Alternatively, a dopant might carry excess electrons (for example, phosphorus atoms introduced into germanium), and these additional electrons occupy otherwise empty bands, giving n-type semiconduc tivity, where n denotes the negative charge of the carriers (Fig. 20.56b). The prepara tion of doped but otherwise ultrapure materials was described in Impact I6.2. Now we consider the properties of a p–n junction, the interface of a p-type and n type semiconductor. Consider the application of a ‘reverse bias’ to the junction, in the sense that a negative electrode is attached to the p-type semiconductor and a positive electrode is attached to the n-type semiconductor (Fig. 20.57a). Under these conditions, the positively charged holes in p-type semicondutor are attracted to the negative electrode and the negatively charged electrons in the n-type semiconductor are attracted to the positive electrode. As a consequence, charge does not flow across the junction. Now consider the application of a ‘forward bias’ to the junction, in the sense that the positive electrode is attached to the p-type semiconductor and the negative electrode is attached to the n-type semiconductor (Fig. 20.57b). Now charge flows across the junction, with electrons in the n-type semiconductor moving toward the positive electrode and holes moving in the opposite direction. It follows that a p–n junction affords a great deal of control over the magnitude and direction of current through a material. This control is essential for the operation of transistors and diodes, which are key components of modern electronic devices. As electrons and holes move across a p–n junction under forward bias, they recombine and release energy. However, as long as the forward bias continues to be applied, the flow of charge from the electrodes to the semiconductors will replenish them with electrons and holes, so the junction will sustain a current. In some solids, the energy of electron–hole recombination is released as heat and the device becomes warm. This is the case for silicon semiconductors, and is one reason why computers need efficient cooling systems.

We have already remarked (Impacts I9.1, I9.2, and I19.3) that research on nano metre-sized materials is motivated by the possibility that they will form the basis for cheaper and smaller electronic devices. The synthesis of nanowires, nanometre-sized atomic assemblies that conduct electricity, is a major step in the fabrication of nanodevices. An important type of nanowire is based on carbon nanotubes, which, like graphite, can conduct electrons through delocalized π molecular orbitals that form from unhybridized 2p orbitals on carbon. Recent studies have shown a correlation between structure and conductivity in single-walled nanotubes (SWNTs) that does not occur in graphite. The SWNT in Fig. 20.45 is a semiconductor. If the hexagons are rotated by 90° about their sixfold axis, the resulting SWNT is a metallic conductor. Carbon nanotubes are promising building blocks not only because they have useful electrical properties but also because they have unusual mechanical properties. For example, an SWNT has a Young’s modulus that is approximately five times larger and a tensile strength that is approximately 375 times larger than that of steel. Silicon nanowires can be made by focusing a pulsed laser beam on to a solid target composed of silicon and iron. The laser ejects Fe and Si atoms from the surface of the target, forming a vapour that can condense into liquid FeSin nanoclusters at sufficiently low temperatures. The phase diagram for this complex mixture shows that solid silicon and liquid FeSin coexist at temperatures higher than 1473 K. Hence, it is possible to precipitate solid silicon from the mixture if the experimental conditions are controlled to maintain the FeSin nanoclusters in a liquid state that is supersatur ated with silicon. It is observed that the silicon precipitate consists of nanowires with diameters of about 10 nm and lengths greater than 1 µm. Nanowires are also fabricated by molecular beam epitaxy (MBE), in which gaseous atoms or molecules are sprayed onto a crystalline surface in an ultra-high vacuum chamber. The result is formation of highly ordered structures. Through careful control of the chamber temperature and of the spraying process, it is possible to deposit thin films on to a surface or to create nanometre-sized assemblies with specific shapes. For example, Fig. 20.58 shows an AFM image of germanium nanowires on a silicon surface. The wires are about 2 nm high, 10–32 nm wide, and 10–600 nm long. Direct manipulation of atoms on a surface also leads to the formation of nanowires. The Coulomb attraction between an atom and the tip of an STM can be exploited to move atoms along a surface, arranging them into patterns, such as wires.

Fig. 20.55 (a) When 2N electrons are present, the band is full and the material is an insulator at T = 0. (b) At temperatures above T=0, electrons populate the levels of the upper conduction band and the solid is a semiconductor.

Fig. 20.56 (a) A dopant with fewer electrons than its host can form a narrow band that accepts electrons from the valence band. The holes in the band are mobile and the substance is a p-type semiconductor. (b) A dopant with more electrons than its host forms a narrow band that can supply electrons to the conduction band. The electrons it supplies are mobile and the substance is an n-type semiconductor.

Fig. 20.57 A p–n junction under (a) reverse bias, (b) forward bias.

Fig. 20.58 Germanium nanowires fabricated on to a silicon surface by molecular beam epitaxy. (Reproduced with permission from T. Ogino et al. Acc. Chem. Res. 32, 447 (1999).)

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مواضيع ذات صلة

Light emission by solid-state lasers and light-emitting diodes

Light absorption by molecular solids, metallic conductors, and semiconductors

The occupation of orbitals

The formation of bands

Molecular solids and covalent networks

Energetics

Structure

Close packing

Structure refinement

The phase problem

Bragg’s law

X-ray diffraction