Energy bands from atomic levels

Figure 2.25 The development of energy bands from atomic orbitals for sodium metal. Isolated atoms (left-hand side) have sharp energy levels. In a solid, these are broadened into energy bands. Outermost orbitals broaden more than inner orbitals...

Figure 2.23 The development of an energy band from delocalised molecular orbitals. Each atom in the molecule contributes one molecular orbital. An isolated atom has sharp energy levels (left-hand side). As the number of atoms increases, the number of discrete orbitals merges into a band of closely spaced energy levels (right-hand side)...

The impurity atoms used to form the p—n junction form well-defined energy levels within the band gap. These levels are shallow in the sense that the donor levels He close to the conduction band (Fig. lb) and the acceptor levels are close to the valence band (Fig. Ic). The thermal energy at room temperature is large enough for most of the dopant atoms contributing to the impurity levels to become ionized. Thus, in the -type region, some electrons in the valence band have sufficient thermal energy to be excited into the acceptor level and leave mobile holes in the valence band. Similar excitation occurs for electrons from the donor to conduction bands of the n-ty e material. The electrons in the conduction band of the n-ty e semiconductor and the holes in the valence band of the -type semiconductor are called majority carriers. Likewise, holes in the -type, and electrons in the -type semiconductor are called minority carriers. 

The interaction energy of the valence electron with the two atomic 3d electrons, with parallel spins, is accordingly —0.67 ev, and the width of the energy band that would be occupied by uncoupled valence electrons is 1.34 ev. The number of orbitals in this band can be calculated from the equation for the distribution of energy levels for an electron in a box. The number of levels per atom is... 

Figure 9.14 Kinetic current density (squares) at 0.8 V for O2 reduction on the Pt monolayer deposited on various metal single-crystal surfaces in a 0.1 M HCIO4 solution, and calculated binding energies (circles) of atomic oxygen (BEq), as a function of calculated d-band center (relative to the Fermi level, ej — sp) of the respective surfaces. The data for Pt(lll) were obtained from [Markovic et al., 1999] and are included for comparison. Key 1, PIml/ Ru(OOOl) 2, PtML/Ir(lll) 3, PtML/Rh(lH) 4, PtML/Au(lll) 5, Pt(lll) 6, PIml/ Pd(lll). (Reproduced with permission from Zhang et al. [2005a].)...

Formation of bands in solids by assembly of isolated atoms into a lattice (modified from Bard, 1980). When the band gap Eg kT or when the conduction and valence band overlap, the material is a good conductor of electricity (metals). Under these circumstances, there exist in the solid filled and vacant electronic energy levels at virtually the same energy, so that an electron can move from one level to another with only a small energy of activation. For larger values of Eg, thermal excitation or excitation by absorption of light may transfer an electron from the valence band to the conduction band. There the electron is capable of moving freely to vacant levels. The electron in the conduction band leaves behind a hole in the valence band. 

In order for an electron to travel from atom to atom (i.e., for electron conduction to take place), the electron must first be raised to an unoccupied, allowable higher energy level (or band). For assemblages of atoms this is called the conduction band. 

With conductors either the valence band is only partially filled (as with metals) or it overlaps with the next higher allowable empty band. Hence only small amounts of energy are required to raise a valence electron into a higher-level empty band where it is free to move from atom to atom. 

Fig. 9-8. Potential energy profile for ionization of surface atoms in two steps on a covalent semiconductor electrode c, = band giq> energy tfi s electron level in an intermediate radical S " Ag = activation energy for the first step of radical formation in the conduction band mechanism df = activation energy for the first step of radical formation in the valence band mechanism = activation energy for the second step of radical ionization in the conduction band mechanism Ag = activation energy for the second step of radical ionization in the valence band mechanism beR = CR-Ev. [From Gerischer, 1970.]...

When combustion proceeds under high pressure, separate atoms and molecules may no longer be regarded as isolated systems. Owing to their interaction, broad energy bands arise from the sharp energy levels of the atoms and molecules. The continuous spectra of flames... 

The hydrogen chain orbitals were made up from only one sort of atomic orbital—15— and one energy band was formed. For most of the other atoms in the Periodic Table, it is necessary to consider other atomic orbitals in addition to the I5 and we find that the allowed energy levels form a series of energy bands separated by ranges of forbidden... 

FIGURE 4.8 Energy bands formed from ns and np atomic orbitals for (a) a body-centred cubic crystal and (b) a crystal of diamond structure, depicting filled levels for 4iVelectrons. 

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