Fermi level semiconductors

A semiconductor laser takes advantage of the properties of a junction between a p-type and an n-type semiconductor made from the same host material. Such an n-p combination is called a semiconductor diode. Doping concentrations are quite high and, as a result, the conduction and valence band energies of the host are shifted in the two semiconductors, as shown in Figure 9.10(a). Bands are filled up to the Fermi level with energy E. ... 

Fig. 1. Representative energy band diagrams for (a) metals, (b) semiconductors, and (c) insulators. The dashed line represents the Fermi Level, and the shaded areas represent filled states of the bands. denotes the band gap of the material.

Instead of plotting the electron distribution function in a band energy level diagram, it is convenient to indicate the Fermi level. For instance, it is easy to see that in -type semiconductors the Fermi level Hes near the valence band. 

Fig. 2. Representation of the band edges in a semiconductor p—n junction where shallow donor, acceptor energies, and the Fermi level are labeled Ejy E, and E respectively, (a) Without external bias is the built-in potential of the p—n junction (b) under an appHed forward voltage F. ...

Fig. 1. The energy levels in a semiconductor. Shown are the valence and conduction bands and the forbidden gap in between where represents an occupied level, ie, electrons are present O, an unoccupied level and -3- an energy level arising from a chemical defect D and occurring within the forbidden gap. The electrons in each band are somewhat independent, (a) A cold semiconductor in pitch darkness where the valence band levels are filled and conduction band levels are empty, (b) The same semiconductor exposed to intense light or some other form of excitation showing the quasi-Fermi level for each band. The energy levels are occupied up to the available voltage for that band. There is a population inversion between conduction and valence bands which can lead to optical gain and possible lasing. Conversely, the chemical potential difference between the quasi-Fermi levels can be connected as the output voltage of a solar cell. Fquilihrium is reestabUshed by stepwise recombination at the defect levels D within the forbidden gap.

The degree of surface cleanliness or even ordering can be determined by REELS, especially from the intense VEELS signals. The relative intensity of the surface and bulk plasmon peaks is often more sensitive to surface contamination than AES, especially for elements like Al, which have intense plasmon peaks. Semiconductor surfaces often have surface states due to dangling bonds that are unique to each crystal orientation, which have been used in the case of Si and GaAs to follow in situ the formation of metal contacts and to resolve such issues as Fermi-level pinning and its role in Schottky barrier heights. 

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. 

Figure 13-4. Encigy level diagnim of a single-layer OLED, where the organic malerial is depicted as a fully depleted semiconductor. The valence band Ey corresponds to the HOMO and the conduction band Ec corresponds to the LUMO. Tile Fermi levels of the two metal electrodes are marked as Et-. Upon contact a built-in potential is established and needs to be compensated for, before the device will begin to operating.

In the case of negative bias, the Fermi level moves closer to the valence band edge. Consequently, the concentration of the majority of carriers (holes) at die insulator-semiconductor interface becomes laiger than in the bulk. This corresponds to the accumulation regime. When a positive bias is applied to die metal, the... 

Figure 7.13. The definitions of ionization potential, Ie, work function, , Fermi level, EF, conduction level, Ec, valence level Ev, and x-potential Xe without (a) and with (b) band bending at the semiconductor-vacuum interface.

Singh P, Singh R, Gale R, Rajeshwar K, DuBow J (1980) Surface charge and specific ion adsorption effects in photoelectrochemical devices. J Appl Phys 51 6286-6291 Bard AJ, Bocarsly AB, Pan ERF, Walton EG, Wrighton MS (1980) The concept of Fermi level pinning at semiconductor/liquid junctions. Consequences for energy conversion efficiency and selection of useful solution redox couples in solar devices. J Am Chem Soc 102 3671-3677... 

It follows from the Franck-Condon principle that in electrochemical redox reactions at metal electrodes, practically only the electrons residing at the highest occupied level of the metal s valence band are involved (i.e., the electrons at the Fermi level). At semiconductor electrodes, the electrons from the bottom of the condnc-tion band or holes from the top of the valence band are involved in the reactions. Under equilibrium conditions, the electrochemical potential of these carriers is eqnal to the electrochemical potential of the electrons in the solution. Hence, mntnal exchange of electrons (an exchange cnrrent) is realized between levels having the same energies. 

These two groups of excited carriers are not in equilibrium with each other. Each of them corresponds to a particular value of electrochemical potential we shall call these values pf and Often, these levels are called the quasi-Fermi levels of excited electrons and holes. The quasilevel of the electrons is located between the (dark) Fermi level and the bottom of the conduction band, and the quasilevel of the holes is located between the Fermi level and the top of the valence band. The higher the relative concentration of excited carriers, the closer to the corresponding band will be the quasilevel. In n-type semiconductors, where the concentration of elec-ttons in the conduction band is high even without illumination, the quasilevel of the excited electrons is just slightly above the Fermi level, while the quasilevel of the excited holes, p , is located considerably lower than the Fermi level. 

Because of the excess holes with an energy lower than the Fermi level that are present at the n-type semiconductor surface in contact with the solution, electron ttansitions from the solution to the semiconductor electrode are facilitated ( egress of holes from the electrode to the reacting species ), and anodic photocurrents arise. Such currents do not arise merely from an acceleration of reactions which, at the particular potential, will also occur in the dark. According to Eq. (29.6), the electrochemical potential, corresponds to a more positive value of electrode potential (E ) than that which actually exists (E). Hence, anodic reactions can occur at the electrode even with redox systems having an equilibrium potential more positive than E (between E and E ) (i.e., reactions that are prohibited in the dark). 

The electrons produced in the conduction band as a result of illumination can participate in cathodic reactions. However, since in n-type semiconductors the quasi-Fermi level is just slightly above the Fermi level, the excited electrons participating in a cathodic reaction will almost not increase the energy effect of the reaction. Their concentration close to the actual surface is low hence, it will be advantageous to link the n-type semiconductor electrode to another electrode which is metallic, and not illuminated, and to allow the cathodic reaction to occur at this electrode. It is necessary, then, that the auxiliary metal electrode have good catalytic activity toward the cathodic reaction. 

The band edges are flattened when the anode is illuminated, the Fermi level rises, and the electrode potential shifts in the negative direction. As a result, a potential difference which amounts to about 0.6 to 0.8 V develops between the semiconductor and metal electrode. When the external circuit is closed over some load R, the electrons produced by illumination in the conduction band of the semiconductor electrode will flow through the external circuit to the metal electrode, where they are consumed in the cathodic reaction. Holes from the valence band of the semiconductor electrode at the same time are directly absorbed by the anodic reaction. Therefore, a steady electrical current arises in the system, and the energy of this current can be utilized in the external circuit. In such devices, the solar-to-electrical energy conversion efficiency is as high as 5 to 10%. Unfortunately, their operating life is restricted by the low corrosion resistance of semiconductor electrodes. 

The photoelectrolysis of H2O can be performed in cells being very similar to those applied for the production of electricity. They differ only insofar as no additional redox couple is used in a photoelectrolysis cell. The energy scheme of corresponding systems, semiconductor/liquid/Pt, is illustrated in Fig. 9, the upper scheme for an n-type, the lower for a p-type electrode. In the case of an n-type electrode the hole created by light excitation must react with H2O resulting in 02-formation whereas at the counter electrode H2 is produced. The electrolyte can be described by two redox potentials, E°(H20/H2) and E (H20/02) which differ by 1.23 eV. At equilibrium (left side of Fig. 9) the electrochemical potential (Fermi level) is constant in the whole system and it occurs in the electrolyte somewhere between the two standard energies E°(H20/H2) and E°(H20/02). The exact position depends on the relative concentrations of H2 and O2. Illuminating the n-type electrode the electrons are driven toward the bulk of the semiconductor and reach the counter electrode via the external circuit at which they are consumed for Hj-evolution whereas the holes are dir tly... 

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