FIGURE 22 1 Crystalline lattice of silicon, a=5.43 A at 300oC. energy level E= Fis allowed, and only one energy band is partially filled. (In metals like aluminum, the partially filled band in ig. 22. 2(a)may actually represent a combination of several overlapping bands. The remaining energy bands are either completely filled or totally empty. Obviously, the empty energy bands do not contribute the charge transfer. It is a fundamental result of solid-state physics that energy bands that are completely led also do not contribute. What happens is that in the filled bands the average velocity of electrons is equal to zero. In semiconductors (and insulators)the Fermi level falls within a forbidden energy gap so that two of he energy bands are partially filled by electrons and may give rise to electron current. The upper partially filled band is called the conduction band while the lower is known as the valence band the number of electrons in the conduction band of a semiconductor is relatively small and can be easily changed by adding impurities In metals, the number of free carriers is large and is not sensitive to doping A more detailed description of energy bands in a crystalline semiconductor is based on the Bloch theorem, which states that an electron wave function has the form(bloch wave) yo=uK(r) exp(ikr) (22.2) where r is the radius vector of electron, the modulating function uu(r)has the periodicity of the lattice, and the quantum state is characterized by wave vector k and the band number b. Physically,(22. 2)means that an electron wave propagates through a periodic lattice without attenuation For each energy band one can consider ne dispersion law E= E,(k). Since(see Fig 22. 2b)in the conduction band only the states with energies close to the bottom, E, are occupied, it suffices to consider the e(k)dependence near E The simplified band diagrams of Si and GaAs are shown in Fig. 22.3 Electrons and holes The concentration of electrons in the valence band can be controlled by introducing impurity atoms. For example, the substitutional doping of Si with As results in a local energy level with an energy about AW,=45 mev below the conduction band edge, E [Fig 22. 2(b)]. At room temperature this impurity center is readily ionized, and(in the absence of other impurities)the concentration of electrons is close to the concentration of As atoms. Impurities of this type are known as donors e 2000 by CRC Press LLC© 2000 by CRC Press LLC energy level E = F is allowed, and only one energy band is partially filled. (In metals like aluminum, the partially filled band in Fig. 22.2(a) may actually represent a combination of several overlapping bands.) The remaining energy bands are either completely filled or totally empty. Obviously, the empty energy bands do not contribute to the charge transfer. It is a fundamental result of solid-state physics that energy bands that are completely filled also do not contribute. What happens is that in the filled bands the average velocity of electrons is equal to zero. In semiconductors (and insulators) the Fermi level falls within a forbidden energy gap so that two of the energy bands are partially filled by electrons and may give rise to electron current. The upper partially filled band is called the conduction band while the lower is known as the valence band. The number of electrons in the conduction band of a semiconductor is relatively small and can be easily changed by adding impurities. In metals, the number of free carriers is large and is not sensitive to doping. A more detailed description of energy bands in a crystalline semiconductor is based on the Bloch theorem, which states that an electron wave function has the form (Bloch wave) Cbk = ubk(r) exp(ikr) (22.2) where r is the radius vector of electron, the modulating function ubk(r) has the periodicity of the lattice, and the quantum state is characterized by wave vector k and the band number b. Physically, (22.2) means that an electron wave propagates through a periodic lattice without attenuation. For each energy band one can consider the dispersion law E = Eb(k). Since (see Fig. 22.2b) in the conduction band only the states with energies close to the bottom, Ec, are occupied, it suffices to consider the E(k) dependence near Ec. The simplified band diagrams of Si and GaAs are shown in Fig. 22.3. Electrons and Holes The concentration of electrons in the valence band can be controlled by introducing impurity atoms. For example, the substitutional doping of Si with As results in a local energy level with an energy about DWd ª 45 meV below the conduction band edge, Ec [Fig. 22.2(b)]. At room temperature this impurity center is readily ionized, and (in the absence of other impurities) the concentration of electrons is close to the concentration of As atoms. Impurities of this type are known as donors. FIGURE 22.1 Crystalline lattice of silicon, a = 5.43 Å at 300°C. a