Impurity bands

The Bolir radius is very large, 3-5 nm, and tlie shallow impurity wavefunction extends over a large portion of the crystal. Doping up to tlie Tnetallic limit consists in implanting a sufficiently high concentration of donors so tliat tlie shallow-donor wavefunctions overlap, creating a half-filled impurity band in which tlie electrons move freely. 

Alternatively, as in Figure 9.9(b), a dopant with one valence electron fewer than the host contributes an impurity band 1 which is empty but more accessible to electrons from the valence band. An example of such a p-type semiconductor is silicon doped with aluminium KL3s 3p ) in which the band gap is about 0.08 eY... 

The testing of impnrities in active pharmacentical ingredients has become an important initiative on the part of both federal and private organizations. Franolic and coworkers [113] describe the utilization of PLC (stationary phase — silica gel and mobile phase — dichloromethane-acetonitrile-acetone (4 1 1, v/v)) for the isolation and characterization of impurities in hydrochlorothiazide (diuretic drug). This drug is utilized individually or in combination with other dmgs for the treatment of hypertension. The unknown impurity band was scraped off the plate and extracted in acetonitrile. The solution was filtered and used for LC/MS and NMR analysis. The proposed procedure enabled the identification of a new, previonsly nnknown impurity. It was characterized as a 2 1 hydrochlorothiazide-formaldehyde adduct of the parent drug substance. 

The most detailed NMR study of impurity band formation in a semiconductor in the intermediate regime involved 31P and 29 Si 7). line width and shift measurements at 8 T from 100-500 K for Si samples doped with P at levels between 4 x 1018 cm 3 and 8 x 1019 cm 3 [189], and an alternate simplified interpretation of these results in terms of an extended Korringa relation [185]. While the results and interpretation are too involved to discuss here, the important conclusion was that the conventional picture of P-doped Si at 300 K consisting of fully-ionized donors and carriers confined to extended conduction band states is inadequate. Instead, a complex of impurity bands survives in some form to doping levels as high as 1019 cm 3. A related example of an impurity NMR study of impurity bands is discussed in Sect. 3.8 for Ga-doped ZnO. 

One application of these formulae in 4his book is to impurity bands in doped silicon or germanium. Here the centres are distributed at random the appropriate formulae for this case are discussed in Section 7 and Chapter 6. 

In situations where V(x9y9z) is not periodic, as for instance in the impurity band of doped semiconductors and in non-crystalline materials, it is still true that if N(E ) vanishes then the material is an insulator at zero temperature, but the converse is not true. This is because a finite value of N(E )9 still within the context... 

Interacting Electrons in Non-Crystalline Systems. Impurity Bands and Metal-Insulator Transitions in Doped Semiconductors... 

Impurity conduction metal-insulator transitions in impurity bands... 

In our discussion we assume that for concentrations up to and some way beyond that at which the transition occurs the electrons remain in an impurity band separate from the conduction band. At higher concentrations, perhaps >3nc, the impurity band merges with the conduction band. This was first suggested by Alexander and Holcomb (1968). The evidence is summarized in Section 10. 

Evidence that the transition ties in an impurity band, and that the two Hubbard bands have merged... 

The assumption that the transition takes place in an impurity band does not necessarily mean that there is a gap between it and the conduction band. It means that the wave functions are such that, at the Fermi energy, p 2 is much greater in the dopant atoms than elsewhere. No sharp transition between the two situations is envisaged. 

In n-type GaAs Ming-Way Lee et al. (1988) used far-infrared optical absorption to show that, in the metallic state near the magnetic-field-induced transition, the ls-2p absorption by donors persists, giving evidence that the transition lies in an impurity band. 

The second question that we discuss in this section is whether the Hubbard U determines the concentration at which the transition takes place—a possibility that could occur only in an impurity band—or whether the transition is purely of... 

On the other hand, such a model would suggest an increase in AT for a specimen alloyed with V203, whereas the reverse seems to be the case (see Mott 1981). This may be due to an increase in the dielectric constant resulting from the formation of an impurity band, which decreases the term e2/icR,. 

In NaxW03-yFy Doumerc (1978) observed a transition that has all the characteristics of an Anderson transition similar phenomena are observed in NaxTayW3 y03. The results are shown in Fig. 7.14. It is unlikely that this transition is generated by the overlap of two Hubbard bands with tails (Chapter 1, Section 4) this could only occur if it took place in an uncompensated alkali-metal impurity band, which seems inconsistent with the comparatively small electron mass. We think rather that in the tungsten (or tungsten-tantalum) 5d-band an Anderson transition caused by the random positions of Na (and F or Ta) atoms occurs. The apparent occurrence of amiD must, as explained elsewhere, indicate that a at the temperature of the experiments. Work below 100 K, to look for quantum interference effects, does not seem to have been carried out. 

Hollinger et al (1985) have studied bronzes NaxW03 and Na2TayW1 y03 near the metal-insulator transition using photoelectron spectroscopy with synchrotron radiation. The results show that the transition is due to localization in an impurity band in a pseudogap. 

We now consider the nature of the transition. In compensated Si P the transition takes place in an impurity band for high concentrations of dopant this merges with the conduction band. In uncompensated Si P the many-valley structure of the conduction band leads to a kind of self-compensation so that N( F) is already finite at the transition (Chapter 5), and the transition is of Anderson type. Whether this is so for p-type material or for single-valley materials is not known. If not then the transition must be of Mott type (Chapter 4), occurring when B U. 

In the case discussed here a Mott transition is unlikely the Hubbard U deduced from the Neel temperature is not relevant if the carriers are in the s-p oxygen band, but if the carriers have their mass enhanced by spin-polaron formation then the condition B U for a Mott transition seems improbable. In those materials no compensation is expected. We suppose, then, that the metallic behaviour does not occur until the impurity band has merged with the valence band. The transition will then be of Anderson type, occurring when the random potential resulting from the dopants is no longer sufficient to produce localization at the Fermi energy. 

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