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In this chapter we have introduced the wide class of materials referred to as and we have mentioned the large range of structural and physical properties they can have. Most of the semiconductors used in science and modern technology are single crystals, with a very high degree of perfection and purity. They are grown as bulk three-dimensional crystals or as thin, two-dimensional epitaxial layers on bulk crystals which serve as substrates. Among the techniques for growing bulk crystals that we have briefly discussed are the Czochralski and Bridgman methods. Epitaxial techniques for growing two-dimensional samples introduced in this chapter include chemical vapor deposition, molecular beam epitaxy, and liquid phase epitaxy. Self-organized two-dimensional lattices of quantum dots can also be grown with epitaxial techniques.

A semiconductor sample contains a very large number of atoms. Hence a quantitative quantum mechanical calculation of its physical properties constitutes a rather formidable task. This task can be enormously simplified by bringing into play the symmetry properties of the crystal lattice, i. e., by using group theory. We have shown how wave functions of electrons and vibrational modes (phonons) can be classified according to their behavior under symmetry operations. These classifications involve of the group of symmetry operations. The translational symmetry of crystals led us to theorem and the introduction of Bloch for the electrons. We have learnt that their eigenfunctions can be indexed by wave vectors (Bloch vectors) which can be confined to a portion of the reciprocal space called the first zone. Similarly, their energy eigenvalues can be represented as functions of wave vectors inside the first Brillouin zone, the so-called electron . We have reviewed the following main methods for calculating energy bands of semiconductors: the method, the or (LCAO) method and the method. We have performed simplified versions of these calculations in order to illustrate the main features of the energy bands in diamond- and zinc-blende-type semiconductors.

Although the atoms in semiconductors are not stationary, their motion is so slow compared to that of electrons that they were regarded as static in Chap. 2. In this chapter we have analyzed the motion of atoms in semiconductors in terms of . Instead of calculating from first principles the for these quantized oscillators or , we have studied models based on which these force constants can be deduced from experimental results. The usefulness of these models is judged by the minimum number of parameters they require to describe experimental . The more successful models typically treat the interaction between the electrons and ions in a realistic manner. The assumes that the valence electrons are localized in deformable shells surrounding the ions. regard the solid as a very large molecule in which atoms are connected by bonds. Interactions between atoms are expressed in terms of and force constants. In covalent semiconductors charges are known to pile up in regions between adjacent atoms, giving rise to . So far, models based on bond charges have been most successful in fitting experimental results.

In this chapter we have also studied the different ways electrons can be affected by phonons, i. e., . These interactions have a significant effect on the optical and transport properties of electrons in semiconductors. We showed how long-wavelength acoustic phonons can change the energy of electrons via their strain field. These interactions can be described in terms of . Optical phonons can be regarded as giving rise to “internal strain” and their interactions with electrons can likewise be described by . In polar semiconductors both long-wavelength acoustic and optical phonons can generate electric fields through the charges associated with the moving ions. These fields can interact very strongly with electrons, giving rise to for acoustic phonons and the for optical phonons. Electrons located at band extrema near or at zone boundaries can be scattered from one valley to another equivalent valley via .

This chapter dealt with the study of the electronic properties of defects in semiconductors because electrically active defects play an important role in the operation of many semiconductor devices. Since defects come in many different forms we restricted our discussions to only. These are separated into and and further divided into or and . For shallow centers we introduced the for calculating their energies and wave functions. Properties of shallow centers were shown to be very similar to those of the hydrogen atom except for effective mass anisotropy and other corrections arising from the host crystal lattice. Hence energy levels of shallow centers are sometimes referred to as hydrogenic levels. Many defect centers cannot be understood within this approximation and they are referred to as . Properties of deep centers are often determined by potentials, localized within one unit cell, known as . These localized potentials are difficult to handle. We have, therefore, presented only a rather rudimentary approach to calculating deep center energies. This approach was applied to explain the chemical trends of deep levels in tetrahedrally bonded semiconductors and to the special case of (substitutional nitrogen) impurities in GaAsP alloys. A very serious limitation of our approach is the neglect of , which are often associated with deep centers.

In this chapter we have discussed the transport of charges in semiconductors under the influence of external fields. We have used the to treat the as having classical charge and renormalized masses. We first considered the case of weak fields in which the field does not distort the carrier distribution but causes the entire distribution to move with a . The drift velocity is determined by the length of time, known as the , over which the carriers can accelerate in the field before they are scattered. We also defined as the constant of proportionality between drift velocity and electric field. We calculated the scattering rates for carriers scattered by . Using these scattering rates we deduced the . Based on this temperature dependence we introduced as a way to minimize scattering by ionized impurities at low temperatures. We discussed qualitatively the behavior of carriers under high electric fields. We showed that these do not obey Ohm’s law. Instead, their drift velocities at high fields saturate at a constant value known as the saturation velocity. We showed that the saturation velocity is about 107 cm/s in most semiconductors as a result of energy and momentum relaxation of carriers by scattering with optical phonons. In a few n-type semiconductors, such as GaAs, the drift velocity can the saturation velocity and exhibit . This is the result of these semiconductors having secondary conduction band valleys whose energies are of the order of 0.1 eV above the lowest conduction band minimum. The existence of negative differential resistance leads to spontaneous current oscillations at microwave frequencies when thin samples are subjected to high electric fields, a phenomenon known as the . Under the combined influence of an electric and magnetic field, the transport of carriers in a semiconductor is described by an antisymmetric second rank . One important application of this tensor is in explaining the . The provides the most direct way to determine the sign and concentration of charged carriers in a sample.

Chapters 6 and 7 are devoted to the study of the optical properties of semiconductors. In this chapter we have discussed those phenomena involving only one photon frequency. In processes like and an incident electromagnetic wave illuminates the sample and the frequency of the wave is unchanged by its interaction with the sample. In the following chapter we shall discuss phenomena in which the frequency of the incident wave is altered by the sample. The optical properties of the sample studied in this chapter can be completely described by its complex . A microscopic theory of this function shows that photons interact mainly with the electrons in semiconductors by exciting interband and intraband transitions. from the valence bands to the conduction bands produce peaks and shoulders in the optical spectra which can be attributed to in the valence-conduction band . These structures can be greatly enhanced by using the technique of , in which the derivatives of some optical response function with respect to either frequency or an external modulation (such as electric and stress fields) are measured. These optical measurements have provided an extremely sensitive test of existing electronic band structure calculations. Occasionally, disagreements between experimental and theoretical spectral peak positions and lineshapes have been found. These can be explained by the as a result of the Coulomb interaction between excited electrons and holes in the semiconductor. occur in doped semiconductors and their contribution to the optical properties can be obtained by using the proposed for free electrons in simple metals.

Transitions between the discrete levels of impurities in semiconductors can also contribute to absorption of photons in the infrared. Although these processes are much waker than those involving intrinsic electronic transitions, they can give rise to extremely sharp peaks and have been a very useful and highly sensitive probe of the electronic energy levels of impurities. Finally, in polar semiconductors, such as those with the zincblende crystal structure, photons can be absorbed and reflected as a result of interaction with optical phonons. The reflectivity becomes particularly high for photons with frequency between the TO and LO phonon frequencies, giving rise to a phenomenon known for a long time as . The coupling between infrared-active optic phonons and electromagnetic waves can be so strong that they cannot be separated inside the medium. Instead, they should be regarded as coupled waves or quasiparticles known as .

In this chapter we have studied light emission processes in semiconductors. In , external radiation excites electron-hole pairs in the sample. These relax to lower energy states by giving up their excess energy to phonons. As a result, the emission produced by the relaxed electron-hole pairs is characteristic of the bandgap of the semiconductor or of gap states associated with defects. Therefore, luminescence is a very useful technique for studying excitons, bound excitons, donors, acceptors and even deep centers (such as isoelectronic traps). Some of the radiation passing through a medium is always scattered by fluctuations in the medium. Such light scattering can also be understood in terms of spontaneous emission from polarizations induced in the medium by the incident radiation. When the induced polarization is modulated by phonons (both optical and acoustic) the incident light is inelastically scattered. These emission processes, known as , are very powerful tools for determining the frequency and symmetry of vibrational modes in condensed media. Their excitation spectroscopies (known as or ), in which one measures the scattering cross section as a function of the incident photon energy, are also extremely useful. We have shown that they can be used to determine electronic excitation energies, electron-phonon interaction and dispersion of excitons. Since real electron-hole pairs are excited in resonant Raman and Brillouin scattering as well as in photoluminescence, the distinction between the two starts to blur, leading to the suggestion that resonant light scattering processes, especially multiphonon ones, can be regarded as a form on nonthermalized luminescence or .

We have briefly discussed a wide range of spectroscopic techniques that involve the use of electrons and/or photons. These techniques yield very detailed information about occupied and empty electron energy bands and also core levels of semiconductors. The angle-resolved versions of photoemission and inverse photoemission have produced convincing pictures of the () dependence of bulk electronic states. They also have yielded information on surface states. We presented spectra of excitations of core levels and discussed the information that can be obtained from them. We also introduced the concepts of surface reconstruction, electronic surface states, and surface energy bands, and presented a few phenomena related to them, such as Fermi level pinning. This led to a brief discussion of the technologically important concepts of charge depletion and enrichment layers at semiconductor surfaces.

In this chapter we studied the effect of quantum confinement on electrons and phonons in semiconductors in synthetic layered structures, known as quantum wells and superlattices, that are usually fabricated with the technique of molecular beam epitaxy. Due to limited space, we have considered mainly the most studied systems composed of lattice-matched GaAs, AlAs and their alloys. However, this system is versatile enough to demonstrate much of the physics involved, such as formation of electronic subbands and minibands, the confinement of optical phonons, folding of acoustic phonons and the introduction of interface modes. We also illustrated the effect of confinement on the transport properties of carriers in these materials by studying the phenomena of resonant tunneling and the integral quantum Hall effect. The fractional quantum Hall effect has become one of the most exciting areas of current research.