Impurity theory, doped semiconductor

Impurities in semiconductors, which release either free electrons or free holes (the absence of an electron in an otherwise filled sea of electrons), also give rise to optical properties at low energies below the minimum band gap (e.g., 1.1 eV for Si) that are characteristic of the Drude theory. Plasma frequencies for such doped semiconductors may be about 0.1 eV. 

This process describes the scattering of free carriers by the screened Coulomb potential of charged impurities (dopants) or defects theoretically treated already in 1946 by Conwell [74,75], later by Shockley [10] and Brooks and Herring [76,77]. In 1969, Fistul gave an overview on heavily-doped semiconductors [78]. A comprehensive review of the different theories and a comparison to the experimental data of elemental and compound semiconductors was performed by Chattopadhyay and Queisser in 1980 [79]. For nondegenerate semiconductors the ionized impurity mobility is given by [79] ... 

Various other electronic transitions are possible upon light excitation. Besides the band-band transitions, an excitation of an electron from a donor state or an impurity level into the conduction band is feasible (transition 2 in Fig. 1.9). However, since the impurity concentration is very small, the absorption cross-section and therefore the corresponding absorption coefficient will be smaller by many orders of magnitude than that for a band-band transition. At lower photon energies, i.e. at ph < g, an absorption increase with decreasing ph has frequently been observed for heavily doped semiconductors. This absorption has been related to an intraband transition (transition 4 in Fig. 1.9), and is approximately described by the Drude theory [4]. This free carrier absorption increases with the carrier density. It is negligible for carrier densities below about 10 cm ... 

Ion intercalated crystalline W oxide films can be treated as strongly doped semiconductors. The inserted electrons make the material infrared reflecting, and the imavoidable ion-electron scattering hmits the metallic properties. Drade theory can be used for qualitative work, but is unable to give quantitative predictions. Instead, the Gerlach theory for ionized impurity scattering is of much value. Screening of the ions can be represented by the random phase approximation or an extension thereof This theory has been used before to model the optical properties of ITO in considerable detail. ... 

FIGURE 16.9. Computed spectral reflectance R for a 0.2-pm-thick slab of a material characterized by a theory for heavily doped semiconductors with ionized impurity scattering of the charge carriers. The electron density is denoted n,.. (From Granqvist, C., Handbook of Inorganic Electrochromic Materials, Elsevier Science, 1995. With permission.)... 

Among other applications of electrolyte solution theory to defect problems should be mentioned the application of the Debye-Hiickel activity coefficients by Harvey32 to impurity ionization problems in elemental semiconductors. Recent reviews by Anderson7 and by Lawson45 emphasizing the importance of Debye-Hiickel effects in oxide semiconductors and in doped silver halides, respectively, and the book by Kroger41 contain accounts of other applications to defect problems. However, additional quantum-mechanical problems arise in the treatment of semiconductor systems and we shall not mention them further, although the studies described below are relevant to them in certain aspects. 

Chapter 4 discussed semiconductivity in terms of band theory. An intrinsic semiconductor has an empty conduction band lying close above the filled valence band. Electrons can be promoted into this conduction band by heating, leaving positive holes in the valence band the current is carried by both the electrons in the conduction band and by the positive holes in the valence band. Semiconductors, such as silicon, can also be doped with impurities to enhance their conductivity. For instance, if a small amount of phosphorus is incorporated into the lattice the extra electrons form impurity levels near the empty conduction band and are easily excited into it. The current is now carried by the electrons in the conduction band and the semiconductor is known as fl-type n for negative). Correspondingly, doping with Ga increases the conductivity by creating positive holes in the valence band and such semiconductors are called / -type (p for positive). 

Photovoltaic devices made of selenium have been known since the 19th Century. Pioneering research in semiconductors, which led to the invention of the transistor in 1947, formed the basis of the modem theory of photovoltaic performance. From this research, die silicon solar cell was the first known photovoltaic device that could convert a sufficient amount of the sun s energy to power complex electronic circuits. The conventional silicon cell is a solid-state device in which a junction is formed between single crystals of silicon separately doped with impurity atoms in order to create n (negative) regions and p (positive) regions which respectively are receptors to electrons and to holes (absence of electrons). See also Semiconductors. The first solar cell to be demonstrated occurred at Bell Laboratories (now AT T Bell Laboratories) in Murray Hill, New Jersey in 1954. 

It has been demonstrated in earlier sections that the catalytic activity of nickel oxide in the room-temperature oxidation of carbon monoxide is related to the number and the nature of the lattice defects on the surface of the catalyst and that any modification of the surface structure influences the activity of the solid. Changes of catalytic activity resulting from the incorporation of altervalent ions in the lattice of nickel oxide may, therefore, be associated not only with the electronic structure of the semiconductor (principle of controlled valency ) (78) but perhaps also with the presence of impurities in the oxide surface or a modification of the surface structure because of this incorporation. In order to determine the influence of dopants on the lattice defects in the surface of the solid and on its catalytic activity, doped nickel oxides were prepared under vacuum at a low temperature (250°). Bulk doping is not achieved and, thence, one of the basic assumptions of the electronic theory of catalysis (79) is not fulfilled. 

Electrical measurements of ice are diflBcult to interpret because of polarization effects, surface conductivity, injection of defects and/or impurity atoms from sandwich electrodes, diffusion effects, differential ion incorporation, and concentration gradients due to nonsteady state impurity distribution. Theories formulated for pure ice and for ice doped with HF (KF and CsF) in terms of ion states and valence defects, qualitatively account for experimental data, although the problem of the majority and minority carriers in doped ice, as a function of concentration and temperature, requires further examination. The measurements on ice prepared from ionic solutes other than HF, KF, and CsF are largely unexplained. An alternative approach that treats ice as a protonic semiconductor accounts for results obtained for both the before-named impurities as well as ammonia and ammonium fluoride. 

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