Dielectric Suppression

Compared with Eq. (18.4), the traditional form of size-dependent (m) varies with the Eg and the incident beam energy  

The absorption coefficient, a, the refractive index, n (= s ), and the complex dielectric function are correlated as follows a( u) = 2ns[ co)/nX, and the transmittance of light is given as T oc exp (—ox), where x is the thickness of the medium for light transmission. This relation leads to the size-induced change of a as 

The traditional form [Ax( f)/x(oo) = —2Ah] discriminates the direct and indirect Eg transition by the a, while the BOLS form [Ax K)/x oo) = Ad Ah- BAg-p)] counts the contribution from e-p coupling, lattice relaxation, and crystal binding. 

It is possible to discriminate the dielectric contribution of the nanosolid Si backbone from the measured effective Se of p-Si by matching the prediction with the measured impedance spectra. P-Si samples were prepared, and their impedance was measured at ambient temperature in the frequency range of 50 Hz-1.0 MHz under 100 mV potential. Silver paste is generally used for an ohmic contact. 

The impedance behavior can be described by Debye s formula for a serial-parallel resistor-capacitor (RC) circuit [27] with elements that correspond to the dielectric behavior of different components. The high-temperature impedance behavior can be described by a series of triple parallel RC circuit elements [27] 

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Pan LK, Ee YK, Sun CQ, Yu GQ, Zhang QY, Tay BK (2004) Band-gap expansion, core-level shift, and dielectric suppression of porous silicon passivated by plasma fluorination. J Vac Sci Technol B 22(2) 583-587... 

The Eq expansion suppresses the complex dielectric constant of a nanometric semiconductor [24]. The dielectric suppression enhances the Coulomb interaction among electrons, holes, and ionized shallow impurities in nanometric devices and enhances the exciton binding energy [25]. 

The modified models [7, 8] suit only the cases where AEc K)/Eg oo) <0.5, otherwise, y < 0, which is physically forbidden. Generally, the Eq often expands beyond this critical value such as the case of Si nanorods with Eg = 3.5 eV [15]. Therefore, understanding of dielectric suppression of nanosolid semiconductors is still under debate. Furthermore, the size dependence of the imaginary part of the dielectric constant and of the photoabsorption coefficient needs yet to be established. Therefore, deeper and consistent insight into the origin and a clearer and complete expression for the size dependence of the complex dielectric constant of a nanosolid semiconductor is necessary. 

Figure 18.3 compares the 8 a o-si derived herein and other sophisticated calculations of nanosolid Si and the third-order dielectric susceptibility of Ag nanodots. Although the dielectric susceptibility does not follow the BOLS prediction, it shows the suppressed trend. Consistency in trends between BOLS predictions and the measured results evidences that the BOLS correlation describes adequately the true situation in which atomic CN imperfection dictates the 8 ano-si Suppression. Other factors may contribute to dielectric suppression, which makes the prediction deviate from measurement compared with other... 

It should be mentioned that as well as for metals the passivation of semiconductors (particularly on Si, GaAs, InP) is also a subject of intense investigation. However, the goal is mostly not the suppression of corrosion but either the fonnation of a dielectric layer that can be exploited for devices (MIS stmctures) or the minimization of interface states (dangling bonds) on the semiconductor surface [63, 64]. 

It was reported that high selectivity can be achieved with addition of small amount of O2, which increases the etch rate of metal electrode [4] while suppresses the etch rate of dielectrics [5]. Figure 2 shows the comparison of residues formation after etching between in (a) CI2 and (b) CI2/O2. Agglomerated residues were observed after etching in CI2/O2, indicating that addition of O2 (1%) enhances residues formation on the etched surface. 

It is thought that small additions of hydrocarbon solvents tend to enhance the formation of Ru(C0)3, whereas larger concentrations seriously decrease the dielectric constant of the solvent so that the formation of ionic species in solution is suppressed. 

The partial racemization of isolated 2-octanol suggests that the hydrolysis may proceed via ionization of optically active substrates as in the Sjjl hydrolysis in homogeneous solution. The hydrolysis via ionization may be suppressed in media with low dielectric constant like micelles (Okamoto and Kinoshita, 1972), resulting in net retention. The ineffectiveness of the stereochemical influence of the CTAB micelle may be interpreted as a consequence of the mutual repulsion of the positively charged head groups of [46] and CTAB, so there is need for molecules of solvent to be incorporated between surfactant head groups (Sukenik et al., 1975). An appreciable increase in retention was also observed in a reversed micellar system (Kinoshita and Okamoto, 1977). 

Experimentally, the retention time of ibuprofen was found in fact to be 12.23 min. This reflects the fact that the pATa of the drug may not be exactly as given in the literature under the conditions used for chromatography and the fact that the low dielectric constant of the mobile ptese in comparison with water suppresses ionisation so that the drug is less ionised than predicted. However, the calculation gives a reasonable approximation of the behaviour of ibuprofen. 

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