Defect levels

Fig. 1. The energy levels in a semiconductor. Shown are the valence and conduction bands and the forbidden gap in between where represents an occupied level, ie, electrons are present O, an unoccupied level and -3- an energy level arising from a chemical defect D and occurring within the forbidden gap. The electrons in each band are somewhat independent, (a) A cold semiconductor in pitch darkness where the valence band levels are filled and conduction band levels are empty, (b) The same semiconductor exposed to intense light or some other form of excitation showing the quasi-Fermi level for each band. The energy levels are occupied up to the available voltage for that band. There is a population inversion between conduction and valence bands which can lead to optical gain and possible lasing. Conversely, the chemical potential difference between the quasi-Fermi levels can be connected as the output voltage of a solar cell. Fquilihrium is reestabUshed by stepwise recombination at the defect levels D within the forbidden gap.

Measures to minimize safety problems must be initiated at the start of the life cycle of any product, but too often determinations of criticality are left to production or quality control personnel who may have an incomplete knowledge of which items are safety critical (Hammer, 1980). Any potential non-conformity that occurs with a severity sufficient to cause a product or service not to satisfy intended normal or reasonably foreseeable usage requirements is termed a defect (Kutz, 1986). The optimum defect level will vary according to the application, where the more severe the consequences of failure the higher the quality of conformance needs to be. 

To further characterize the event it is first necessary to identify critical features of the initial configuration that will strongly influence the process. For powder compacts, the most obvious features are the morphological characteristics of the powders, their microstructures, and the porosity of the compact. For solid density samples, the grain structure, grain boundaries, defect level, impurities, and inclusions are critical features. 

The various studies of shock-modified powders provide clear indications of the principal characteristics of shock modification. The picture is one in which the powders have been extensively plastically deformed and defect levels are extraordinarily large. The extreme nature of the plastic deformation in these brittle materials is clearly evident in the optical microscopy of spherical alumina [85B01]. In these defect states their solid state reactivities would be expected to achieve values as large as possible in their particular morphologies greatly enhanced solid state reactivity is to be expected. 

At present, defect-free silicon crystals have been achieved at only at diameters of 200 mm. Comparisons of crystal quality were made among three techniques a typical conventional Czrochralski crystal growth technique, a slow-cooled controlled reaction and the perfect silicon process. The quality levels achieved in D-defect levels of the material is... 

There are several reports of the use of directed ion sources to hydrogen passivate both shallow impurities (Horn et al., 1987 Martinuzzi et al., 1985) and deep defect levels in silicon (Dube and Hanoka, 1984 Hanoka... 

The adequacy of the spin-averaged approach has been confirmed in self-consistent spin-density-functional calculations for H in Si by Van de Walle et al. (1989). The deviation from the spin-averaged results is expected to be largest for H at the tetrahedral interstitial (T) site, where the crystal charge density reaches its lowest value. For neutral H at the T site, it was found that inclusion of spin polarization lowered the total energy of the defect only by 0.1 eV. The defect level was split into a spin-up and a spin-down level, which were separated by 0.4 eV. These results are consistent with spin-polarized linearized-muffin-tin-orbital (LMTO) Green s-function calculations (Beeler, 1986). 

It is important to realize that each of the electronic-structure methods discussed above displays certain shortcomings in reproducing the correct band structure of the host crystal and consequently the positions of defect levels. Hartree-Fock methods severely overestimate the semiconductor band gap, sometimes by several electron volts (Estreicher, 1988). In semi-empirical methods, the situation is usually even worse, and the band structure may not be reliably represented (Deak and Snyder, 1987 Besson et al., 1988). Density-functional theory, on the other hand, provides a quite accurate description of the band structure, except for an underestimation of the band gap (by up to 50%). Indeed, density-functional theory predicts conduction bands and hence conduction-band-derived energy levels to be too low. This problem has been studied in great detail, and its origins are well understood (see, e.g., Hybertsen and Louie, 1986). To solve it, however, requires techniques of many-body theory and carrying out a quasi-particle calculation. Such calculational schemes are presently prohibitively complex and too computationally demanding to apply to defect calculations. 

Defect levels typically contain both valence- and conduction-band character. If the relative position of these bands is inaccurate, the position of the defect level will also be uncertain. We thus see that, at this point in time, none of the theoretical methods is able to make accurate predictions for positions of defect levels in the band gap. However, it should be noted that, while the absolute position of defect levels is uncertain, their relative motion induced by displacements of the impurity or by changes in the charge state is quite reliable. These observations generally allow the derivation of reliable qualitative conclusions about defect levels, such as deep... 

The defect levels discussed so far represent the most dramatic effects of the presence of the impurity. The levels introducted in the gap region are schematically illustrated in Fig. 6. However, these are by no means the only changes to the band structure induced by the presence of H. Important changes indeed occur down to energies far below the energy gap, as found by Katayama-Yoshida and Shindo (1985), who investigated the effect on the density of states of introducing H (or muonium) at T in Si. 

For H at T in Ge, Pickett et al. (1979) carried out empirical-pseudopotential supercell calculations. Their band structures showed a H-induced deep donor state more than 6 eV below the valence-band maximum in a non-self-consistent calculation. This binding energy was substantially reduced in a self-consistent calculation. However, lack of convergence and the use of empirical pseudopotentials cast doubt on the quantitative accuracy. More recent calculations (Denteneer et al., 1989b) using ab initio norm-conserving pseudopotentials have shown that H at T in Ge induces a level just below the valence-band maximum, very similar to the situation in Si. The arguments by Pickett et al. that a spin-polarized treatment would be essential (which would introduce a shift in the defect level of up to 0.5 Ry), have already been refuted in Section II.2.d. 

Thus far, I have mainly discussed neutral impurities. From the treatment of the electronic states, however, it should be clear that occupation of the defect level with exactly one electron is by no means required. In principle, zero, one, or two electrons can be accommodated. To alter the charge state, electrons are taken from or removed to a reservoir the Fermi level determines the energy of electrons in this reservoir. In a self-consistent calculation, the position of the defect levels in the band structure changes as a function of charge state. For H in Si, it was found that with H fixed at a particular site, the defect level shifted only by 0.1 eV as a function of charge state (Van de Walle et al., 1989). 

The energy surface for H° was discussed in Section III. 1. The bond center was the lowest energy site, 0.3 eV lower in energy than the T site (Van de Walle etal., 1989). The corresponding defect levels were schematically illustrated in Fig. 6. 

Recent calculations of hyperfine parameters using pseudopotential-density-functional theory, when combined with the ability to generate accurate total-energy surfaces, establish this technique as a powerful tool for the study of defects in semiconductors. One area in which theory is not yet able to make accurate predictions is for positions of defect levels in the band structure. Methods that go beyond the one-particle description are available but presently too computationally demanding. Increasing computer power and/or the development of simplified schemes will hopefully... 

Schon, J. H. Bucher, E. 1999. Characterization of intrinsic defect levels in CuInS2. Phys. Stat. Sol. A 171 511-519. 

Abou-Elfotouh, F. A. Moutinho, FI. Bakry, A. Coutts, T. J. Kazmerski, L. L. 1991. Characterization of the defect levels in copper indium diselenide. Solar Cells 30 151-160. 

However, the pinhole density in the imaging layer has to be reduced. This can be done by searching among all the commercial novolak - based resists for an acceptable candidate or by setting an MLR specification for resist vendors improve their quality control. Because thin resists have been used for mask making with an acceptable defect level, no fundamental pinhole problem is anticipated. 

The year 2000 will mark 15 years since the initial CMP patents were filed by IBM. Opportunities for expanding use of CMP in existing chip technology continue to flourish. In addition, the challenges ahead for CMP technology to keep pace are formidable in this third wave of the evolution of the technology. Increasing concern about improved within-wafer nonuniformity, better planarity (flatter surfaces), and lower defectivity levels are all requirements for advanced, sub-0.25-micron devices. In addition. 

Nagahara et al, The Effect of Slurry Particle Size on Defect Levels for a BPSG CMP Process, Proceedings of 1996 VMIC Conference (June 1996), p. 443. 

One striking result [64] involves making a small change in regularity when one GC pair in a strand is simply inverted to CG, the local defect CG pair drops 0.6 eV below its previous position—that drop is 15 times the calculated bandwidth. This electrostatic stabilization means that the defect level is far from the conducting delocalized states, and corresponds to Anderson-type localization. With Anderson locahzation of this depth, the conductance is expected to decay exponentially. Indeed, exponential decay of conductance has been discussed in a number of measurements both on A-DNA and on poly(GC) sequences [65-67]. 

Recombination at and excitation from deep levels are emphasized. Nonradiative transitions at defect levels—Auger, cascade capture, and multiphonon emission processes—are discussed in detail. Factors to be considered in the analysis of optical cross sections which can give information about the parity of the impurity wave function and thus about the symmetry of a particular center are reviewed. 

In the system AJ5 3xAg+s+x 2xM04, the authors (96) reported that the dimensions of the unit cells of these scheelite phases vary significantly with changes in either type or number of cations in the A sites and that the number of A cation sites which can be vacant is less than approximately 15% before additional phases appear. The results for the oxidation of propylene over the composition Aj5ltrAo.5+x xMo04 (A+ = Li, Na, or Ag) showed that when x = 0 the activity is very low. The activity dramatically increased when 4% of the A cation sites were made vacant and continued to increase with the defect level until a two-phase mixture resulted in decreased activity. 

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