Holes and electrons, in solids

Figure 13. Voltage relaxation method for the determination of the diffusion coefficients (mobilities) of electrons and holes in solid electrolytes. The various possibilities for calculating the diffusion coefficients and from the behavior over short (t L2 /De ) and long (/ L2 /Dc ll ) times are indicated cc h is the concentration of the electrons and holes respectively, q is the elementary charge, k is the Boltzmann constant and T is the absolute temperature.

The diffuse layer of excess electrons and holes in solids is called the space charge layer and the diffuse layer of excess hydrated ions in aqueous solution is simply called the diffuse layer and occasionally called the Gouy layer [Gouy, 1917]. The middle layer of adsorbed water moleciiles, between the diffuse layer on the aqueous solution side and the space charge layer on the soUd side, is called the compact or the inner layer. This compact or inner layer is also called the Helmholtz layer [Helmholtz, 1879] or the Stem layer [Stem, 1924] the plane of the closest approach of hydrated ions to the solid surface is called the outer Helmholtz plane (OHP) [Graham, 1947]. 

Clearly, a large subfield of radiation chemistry has grown up around the phenomena observed during radiolysis in the presence of solids. It depends upon the behavior of electrons and holes in solids and their interactions with adsorbed molecules, and therefore has a general connection with catalytic reactions on the same solids. Further developments may reveal points of closer and more specific common interest. 

An electrical double layer is usually formed at a semiconductor-electrolyte interface, as well as at the boundary between two solids. This layer consists of plates carrying opposite charges, each being located in one of the phases in contact. In the semiconductor the charge in the region near the surface is formed due to redistribution of electrons and holes in the electrolyte solution, due to redistribution of ions, which form the ionic plate of the double layer. 

A photomultiplier tube is a sensitive detector of visible and ultraviolet radiation photons cause electrons to be ejected from a metallic cathode. The signal is amplified at each successive dynode on which the photoelectrons impinge. Photodiode arrays and charge coupled devices are solid-state detectors in which photons create electrons and holes in semiconductor materials. Coupled to a polychromator, these devices can record all wavelengths of a spectrum simultaneously, with resolution limited by the number and spacing of detector elements. Common infrared detectors include thermocouples, ferroelectric materials, and photoconductive and photovoltaic devices. 

Photovoltaic Devices. For many inorganic semiconductors, absorption of light can be used to create free electrons and holes. In an organic semiconducting solid, however, absorption of a photon leads to the formation of a bound electron—hole pair. Separation of this pair in an electric field can... 

Apart from the wider band gaps, electrons and holes in ionic solids have mobilities several orders lower than those in the covalent semiconductors. This is due to the variation in potential that a carrier experiences in an ionic lattice. 

Because of the dependence of the PL intensity of TiC>2 on the nature of the gas-phase molecules introduced (alcohols) and its reversibility upon elimination of the molecules by flowing dinitrogen, there is hope that such an effect can be applied to gas sensors. With the combined use of several techniques (PL, time-resolved femtosecond diffuse reflectance spectroscopy, multiple internal reflection IR absorption), the dynamics and role of photogenerated electrons and holes in the absence or presence of metals (notably platinum) are now better understood, at both the gas-solid and liquid-solid interfaces. It is also likely that not only TiOz, but other types of semiconductors will be more thoroughly investigated in the future. 

Refs. [i] Shockley W (1950) Electrons and holes in semiconductors. Van Nostrand, New York [ii] Blakemore JS (1987) Semiconductor statistics. Dover, New York [Hi] Rhoderick EH (1978) Metal-semiconductor contacts. Clarendon Press, Oxford [iv] Ashcroft W, Mermin ND (1976) Solid state physics. Saunders College, Philadelphia [v] SeegerK (1991) Semiconductor physics - an introduction. Springer, Berlin... 

Fig. 7.9 shows some of the SAW data for electrons and holes in doped a-Si H (Takada and Fritzsche 1987). The mobility data are not proportional to the measured because the attenuation coefficients depend on the dc conductivity, which is temperature-dependent. The solid lines are calculated fits to the data assuming an exponential density of tail states. The results are similar to the time-of-flight data on undoped a-Si H and the deduced values of the free carrier mobilities are also similar. The electron mobility decreases at high doping levels. 

To describe the conductivity of an intrinsic semiconductor sample quantitatively, we need to calculate the concentrations of both types of charge carriers in the solid. The key quantity that controls the equilibrium concentration of electrons and holes in an intrinsic semiconductor is the band gap. Because the thermal excitation energy required to produce an electron and a hole is equal to Eg, the intrinsic carrier concentrations can be related to Eg using the Boltzmann relationship ... 

This equation states that the electrical conductivity due to a free carrier is the product of the charge on the carrier, q, its concentration in the solid, and its mobility, fx. Since semiconductors have two different types of mobile charge carriers, electrons, and holes, the total sample conductivity, a, is simply the sum of the individual conductivities due to each carrier type. It should be noted that the conductivity depends only on the absolute number of carriers, and therefore is not affected by the signs of the carriers themselves. Carrier mobilities for electrons and holes in a variety of semiconductors can be measured experimentally. These values have been tabulated in various reference books and are available for many semiconductors of interest. Doping of a semiconductor therefore allows precise control over the conductivity of the semiconductor sample. 

Sinitsky D., Assaderaghi F., Orshansky M., Bokor J. and Hu C. (1997), Velocity overshoot of electrons and holes in Si inversion layers , Solid-State Electr. 41, 1119-1125. 

The above set of equations must be augmented by an energy balance for the solution and/or the solid phase if temperature effects are important. An example is high rate etching or deposition effected by a laser beam [265]. Also, potential depended transport of charge carries (electrons and holes) in the semiconductor must be accounted for in photochemical and photoelectrochemical etching [266, 267]. 

This chapter first discusses the fundamentals of energy states in crystals, a subject necessary for understanding the creation and movement of electrons and holes in a solid. The properties of semiconductors are discussed next, with special emphasis given to the properties of silicon and germanium. The principle of construction and operation is accompanied by a description of the different types of detectors available in the market. Future prospects in this field are also discussed. 

Figure 12.23 shows that, in small molecules, electrons occupy discrete molecular orbitals whereas in macroscale solids the electrons occupy delocalized bands. At what point does a molecule get so large that it starts behaving as though it has delocalized bands rather than localized molecular orbitals For semiconductors, both theory and experiment tell us that the answer is roughly at 1 to 10 nm (about 10—100 atoms across). The exact number depends on the specific semiconductor material. The equations of quantum mechanics that were used for electrons in atoms can be applied to electrons (and holes) in semiconductors to estimate the size where materials undergo a crossover from molecular orbitals to bands. Because these effects become important at 1 to 10 nm, semiconductor particles with diameters in this size range are called quantum dots. 

For the application of the image charges method, similarly to [41], the model of continuous media characterized by dielectric permittivity and the effective mass approximation was used for the wave functions calculations. These two characteristics could be sufficient for the description of the principal differences between the solid and its ambience as well as between electrons and holes in dielectrics and semiconductors. 

To understand and describe the electrical and optical properties of a semiconductor, it is essential to have knowledge of its electronic band structure, which exhibits the relation between energy and momentum E k) of electrons and holes in the different possible states of the conduction and valence bands at the various symmetry points of the first Brillouin zone of the reciprocal lattice. In particular, the band gap between the valence and conduction bands is important, because it determines, e.g., the optical transition energy and the temperature dependence of the intrinsic conductivity. In the case of the complex boron-rich solids with large numbers of atoms per unit cell, the agreement between theoretical calculations of the band gaps and the experimental results has not yet been satisfactory. 

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