Semiconductors Fermi energy

The electrochemical potential of the solution and semiconductor, see Fig. 3.6, are determined hy the standard redox potential of the electrolyte solution (or its equivalent the standard redox Fermi level, Ep,redo, and the semiconductor Fermi energy level. If these two levels do not lie at the same energy then movement of charge across the semiconductor - solution interface continues until the two phases equilibrate with a corresponding energy band bending, see Fig. 3.8. 

Figure 9.8(a) shows how the conduction band C and the empty valence band V are not separated in a conductor whereas Figure 9.8(c) shows that they are well separated in an insulator. The situation in a semiconductor, shown in Figure 9.8(b), is that the band gap, between the conduction and valence bands, is sufficiently small that promotion of electrons into the conduction band is possible by heating the material. For a semiconductor the Fermi energy E, such that at T= 0 K all levels with E < are filled, lies between the bands as shown. 

Band gap engineetring confined hetetrostruciutres. When the thickness of a crystalline film is comparable with the de Broglie wavelength, the conduction and valence bands will break into subbands and as the thickness increases, the Fermi energy of the electrons oscillates. This leads to the so-called quantum size effects, which had been precociously predicted in Russia by Lifshitz and Kosevich (1953). A piece of semiconductor which is very small in one, two or three dimensions - a confined structure - is called a quantum well, quantum wire or quantum dot, respectively, and much fundamental physics research has been devoted to these in the last two decades. However, the world of MSE only became involved when several quantum wells were combined into what is now termed a heterostructure. 

A semiconductor can be described as a material with a Fermi energy, which typically is located within the energy gap region at any temperature. If a semiconductor is brought into electrical contact with a metal, either an ohmic or a rectifying Schouky contact is formed at the interface. The nature of the contact is determined by the workfunction, (the energetic difference between the Fermi level and the vacuum level), of the semiconductor relative to the mclal (if interface effects are neglected - see below) 47J. 

Adsorption related charging of surface naturally affects the value of the thermoelectron work function of semiconductor [4, 92]. According to definition the thermoelectron work function is equal to the difference in energy of a free (on the vacuum level) electron and electron in the volume of the solid state having the Fermi energy (see Fig. 1.5). In this case the calculation of adsorption change in the work function Aiqp) in... 

The electrochemical potential of an electron in a solid defines the Fermi energy (cf. Eq. 3.1.9). The Fermi energy of a semiconductor electrode (e ) and the electrolyte energy level (credox) are generally different before contact of both phases (Fig. 5.60a). After immersing the semiconductor electrode into the electrolyte, an equilibrium is attained ... 

The potential which controls the photoelectrochemical reaction is generally not the photopotential defined by Eqs (5.10.20) and (5.10.21) (except for the very special case where the values of v, REdox and the initial Fermi energy of the counterelectrode are equal). The energy which drives the photoelectrochemical reaction, eR can be expressed, for example, for an n-semiconductor electrode as... 

Direct splitting of water can be accomplished by illuminating two interconnected photoelectrodes, a photoanode, and a photocathode as shown in Figure 7.6. Here, Eg(n) and Eg(p) are, respectively, the bandgaps of the n- and p-type semiconductors and AEp(n) and AEF(p) are, respectively, the differences between the Fermi energies and the conduction band-minimum of the n-type semiconductor bulk and valence band-maximum of the p-type semiconductor bulk. lifb(p) and Utb(n) are, respectively, the flat-band potentials of the p- and n-type semiconductors with the electrolyte. In this case, the sum of the potentials of the electron-hole pairs generated in the two photoelectrodes can be approximated by the following expression ... 

Manipulating surface states of semiconductors for energy conversion applications is one problem area common to electronic devices as well. The problem of Fermi level pinning by surface states with GaAs, for example, raises difficulties in the development of field effect transistors that depend on the... 

Figure 12.6 Plot showing the formation of semiconductor surface band bending when a semiconductor contacts a metal (Ec, the bottom of conduction band Ev, the top of valence band EF, the fermi energy level SC, semiconductor M, metal Vs, the surface barrier). (From Liqiang, J. et al., Solar Energy Mater. Solar Cells, 79, 133, 2003.)...

Fig. 2-20. Electron state density and ranges of Fermi energy where electron occupation probability in the conduction band of an electron ensemble of low electron density (e.g., semiconductor) follows Boltzmann function (Y i)or Fermi function (y > 1) y = electron activity coeffident ET =transition level from Y 4= 1 to Y > 1 0(t) = electron energy state density CB = conduction band. [From Rosenberg, I960.]...

Fermi level of standard redox electrons in complexed redox particles Fermi level of standard redox electrons in adsorbed redox particles Fermi level of n-type or p-type semiconductor electrodes quasi-Fermi level of electrons in semiconductor electrodes quasi-Fermi level of holes in semiconductor electrodes energy of a particle i... 

Figure 6, Schematic showing energy correlations for photoassisted electrolysis of water using n-type TiOg as a photoanode and a metal cathode. Symbols as in Figures 3, 4, and 5, except Epis Fermi level for metal contact to TiO and E/ is higher Fermi level in metal cathode, polarized by an external source to a potential negative to the semiconductor anode. EF(Hi) and Ep(02) are abbreviated forms for Fermi energies for redox systems of Figure 3 (13j.

As shown in Fig. 3.6, for intrinsic (undoped) semiconductors the number of holes equals the number of electrons and the Fermi energy level > lies in the middle of the band gap. Impurity doped semiconductors in which the majority charge carriers are electrons and holes, respectively, are referred to as n-type and p-type semiconductors. For n-type semiconductors the Fermi level lies just below the conduction band, whereas for p-type semiconductors it lies just above the valence band. In an intrinsic semiconductor tbe equilibrium electron and bole concentrations, no and po respectively, in tbe conduction and valence bands are given by ... 

Similarly, one can derive an equation for a p-type semiconductor, where the distance between the Fermi energy level and the valence band is a logarithmic function of acceptor impurity concentration. As the acceptor impurity increases so too does the hole concentration in valence band, with the Fermi level moving closer to the valence band. 

Fig. 7.1 Position of band edges and photodecomposition Fermi energies levels of various non-oxide semiconductors. E(e,d) represents decomposition energy level by electrons, while E(h,d) represents the decomposition energy level for holes vs normal hydrogen electrode (NHE). E(VB) denotes the valence band edge, E(CB) denotes the conduction band edge. E(H2/H20) denotes the reduction potential of water, and (H2O/O2) the oxidation potential of water, both with reference to NHE.

Fig. 14 (a) Equilibrium energy diagram for a pn junction in an inorganic semiconductor material with intrinsic Fermi energy Ep , conduction band energy E, valence band energy The quantity Vu... 

Figure 6.11 Energy bands of an intrinsic semiconductor Ef is the Fermi energy level Ec is the lower edge of the conduction band is the upper edge of the valence band and Eg is the band gap. From Z. Jastrzebski, The Nature and Properties of Engineering Materials, 2nd ed. Copyright 1976 by John Wiley Sons, Inc. This material is used by permission of John...

For a semiconductor like Ge, the pattern of electronic interaction between the surface and an adsorbate is more complex than that for a metal. Semiconductors possess a forbidden gap between the filled band (valence band) and the conduction band. Fig. 6a shows the energy levels for a semiconductor where Er represents the energy of the top of the valence band, Ec the bottom of the conduction band, and Ey is the Fermi energy level. The clean Ge surface is characterized by the presence of unfilled orbitals which trap electrons from the bulk, and the free bonds give rise to a space-charge layer S and hence a substantial dipole moment. Furthermore, an appreciable field is produced inside the semiconductor, as distinct from a metal, and positive charges may be distributed over several hundred A. 

Fig. 1.13 Electron density of states N(E) in a cubic material F denotes the Fermi energy (a) normal metal (b) semimetal (c) insulator, (d) n-type degenerate semiconductor.

The concept of a mobility edge has proved useful in the description of the nondegenerate gas of electrons in the conduction band of non-crystalline semiconductors. Here recent theoretical work (see Dersch and Thomas 1985, Dersch et al. 1987, Mott 1988, Overhof and Thomas 1989) has emphasized that, since even at zero temperature an electron can jump downwards with the emission of a phonon, the localized states always have a finite lifetime x and so are broadened with width AE fi/x. This allows non-activated hopping from one such state to another, the states are delocalized by phonons. In this book we discuss only degenerate electron gases here neither the Fermi energy at T=0 nor the mobility edge is broadened by interaction with phonons or by electron-electron interaction this will be shown in Chapter 2. 

Interaction of electrons with phonons, and the fact that the presence of a trapped electron can deform the surrounding material, allows the radius of an empty localized state to change when the state is occupied. Also, in a condensed electron gas phonons lead to a mass enhancement near the Fermi energy, or in some circumstances to polaron formation. For the development of the theory, and comparison with experiment, it is therefore desirable to begin by choosing a system where these effects are unimportant. The study of doped semiconductors provides such a system. This is because the radius aH of a donor is given, apart from central cell corrections, by the hydrogen-like formula... 

On the other hand, although the reorganization energy is a construct (like the Fermi energy of electrons in an intrinsic semiconductor in the middle of a region with no electrons), it is easy to imagine. Thus, in Fig. 9.24 at D, the ferrous ion would just have been formed by a vertical electronic transition and be with all the solvent structure of the ferric ion. But not C the ferrous ion has its solvation shell, teoiganized from that of the ferric ion. 

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