Donor impurity concentration

For an n-type semiconductor, if the donor impurity concentration is much greater than the intrinsic carrier concentration, Nd >nj, then no Nd. Equation (3.4.9) can then be written as... 

A 50 mV drop in the potential of a ro = 6 nm colloidal Ti02 particle correlates to an ionized donor impurity concentration of 5 x lO cm , correlating to a Debye length Ld on the order of 10 m thus satisfying the condition ro Ld. 

Holm and Clark (34) noted the increase of the activity of A1203 specimens with increasing amount of the Si02 impurity (donor impurity) further increase in impurity concentration, however, diminishes the activity. 

Emphasis should here be placed on the observations of Holm and Clark (34), according to whom the reaction rate go passes through a maximum when the concentration of a donor impurity is monotonically increased. This maximum may be due, as shown in Fig. 8a, to the transition from the acceptor to the donor branch of the go = go ( [Pg.186]

At the same time Markham and Laidler (70) and also Veselovsky and Shub (71, 72) have shown that the photocatalytic activity of zinc oxide diminishes as a result of the calcination of specimens at high temperatures (around 1000°C) in the reduced atmosphere (such pretreatment results in an increase of the concentration of superstoichiometric zinc in the specimen). In other words, a donor impurity (zinc in excess of stoichiometry) retarded the reaction. 

Patel et al., 1974), but no effect is observed for neutral (Group IV) impurities in Ge or Si. Also, impurities that are electron-donors soften both Ge and Si at temperatures above about 450 °C whereas accepter type impurities soften Ge, but not Si. Another important point is that small impurity concentrations have little effect. The effects begin at concentrations of about 1018/cc. Since the atomic volume of Si is 20 A3, the critical ratio of impurity to Si atom is about 2 x 10 5. Therefore, the average lineal distance between impurity atoms is about one every 270 A. 

By varying the impurity concentration in the semiconductor, one may regulate not only the activity of the catalyst but its selectivity as well. Indeed, if the reaction proceeds along two parallel paths, one of which is of the acceptor type and the other of the donor type, then upon the monotonic displacement of the Fermi level (i.e., upon the monotonic change of Z) the reaction will be accelerated on one path and retarded on the other, as appears, e.g., from a comparison of Figs. 19a and 19b. Doping of the crystal may accelerate the reaction on one path and retard it on the other. 

Comparison of this luminescence intensity in different samples reveals that any correlation is absent any impurity concentration. Thus it was supposed that the mostly probable luminescence center is Ti, which presence is quite natural in Ti bearing benitoite. The wide occurrence of Ti " minor impurities in minerals was detected by EPR. Like the other d ions (V, Mo ), Ti ions occur often in minerals as electron center (Marfunin 1979). It may be realized in benitoite, which does have some natural exposure to gamma rays in its natural setting. There could be radiation centers, such as, for example, Ti + gamma ray + electron donor Ti + electron hole. Benitoite color does not change with gamma irradiation to quite high doses (Rossman 1997) but luminescence is much more sensitive compared to optical absorption and can occur from centers at such low concentration that they do not impact the color of a benitoite. 

Quite a different approach has been developed in some other works149, l52). It has been shown by extrapolation of the dependence of the initial reaction rate on the proton-donor concentration in the system to the zero concentration of the proton-donor that the initial reaction rate is expected to be equal to zero. The authors attempted to carry out precision vacuum cleaning and drying of the reagents and reaction vessels to remove proton-donor impurities. The results of this investigation are given in Fig. 14. As can be seen, even trace amounts of moisture have a great effect on the... 

We shall present here a calculation of the equilibrium adsorption when it is assumed that physically adsorbed molecules are the empty adsorption traps. This gives a temperature dependence of the high-temperature equilibrium adsorption. Assume again a simple surface barrier, produced by ionization of donor impurities of concentration Nd, a constant. Poisson s equation, using MKS units, becomes in the exhaustion region... 

The material has been found to be an W-type semiconductor at all temperatures (24-27). The donor impurities, as has been quite well established (24,28), are interstitial excess zinc atoms. Their concentration depends on the method of preparation of the sample, ranging from 10 cm.- to 10 cm.- (24,28). 

To summarize the various results which suggest the energy level diagram of Fig. 1, many authors have shown (24,26,28) that zinc oxide has interstitial zinc as a donor impurity. As determined by conductivity and Hall effect measurements, the energy level for single ionization of this interstitial zinc is of the order of several hundredths of an electron volt below the conduction band when the concentration of donors is of the order of 10 cm. . The energy level for double ionization, from optical absorption measurements, appears to be at about 3.2 e.v. below the con-... 

Figure 7. Donor impurity diffusion coefficient (Di) vs. electron concentration (electrons per cm3) showing regions of intrinsic and extrinsic diffusion. (Reproduced with permisssion from reference 119. Copyright 1981 Academic...

The Situation in Doped Semiconductors. There is an increasing belief amongst workers in the field that the M-NM transition is continuous, based on experimental measurements carried out at low temperatures down to 3 mK. In Figure 12, we show the experimental evidence in P-doped Si. Note that at a fixed (very low) temperature, the conductivity changes continuously with, for example, donor concentration. In addition, the extrapolated zero-temperature value of the conductivity (o(0)) varies continuously with impurity concentration. An example showing the variation of the extrapolated zero-temperature conductivity41 in the case of B-doped Si is... 

All the information needed to calculate the doping efficiency, T, of a-Si H from Eq. (5.2) is provided by the experiments discussed above, q is obtained by equating the excess electron concentration with the density of donors and is defined in terms of either the gas-phase or solid-phase impurity concentration. 

The number of electrons transferred, and the number of electrons transferred per metal atom, ejM, were estimated as a function of the mean diameter of the metal crystallites, d, employing two models pertaining to infinite and finite interfaces between the metal and the support [88]. The parameters employed correspond to metal with work functions of 5.0 or 6.0 eV (the corresponding contact potential differences, Vq, being 0.9 and 1.9 V, respectively), in contact with Ti02 doped with a donor impurity (W, for example) with donor concentration of 2 X 10 cm. The results obtained are shown in Figure 3, in which the number of transferred electrons, n, and the number of electrons transferred per metal atom, ejM, are plotted as a function of d [88]. The number of transferred electrons ranges from about 8000 for a 40-nm metal particle to approximately 60 electrons for a... 

From the latter equation, it is found that the electrical field in nano-sized semiconductors will usually be small and that high dopant levels are required to produce a significant potential difference between the center and the surface. For example [69], in order to obtain a 50 meV potential drop in a nanocrystalline Ti02 particle with R = 6 nm, a concentration of 5 x 1019 cur3 of ionized donor impurities is necessary. Undoped Ti02 nanocrystallites have a much lower carrier concentration and the band bending within the particles is therefore negligibly small. 

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