Fermi level doping dependence

All in all, the equilibrium concentration of neutral hydrogen species will depend on nd temperature, but not on Fermi level, doping or oxygen activity (at constant p fj. The concentrations will probably not be very high, but also not very low either. Their temperature dependences are probably not very strong. 

Evidence on this question may be taken by the behavior of the electrical conductivity CT as a function of temperature. A thermally activated process T dependence on log(CT), Arrhenius plot) is expected if doping takes place, whereas j -i/4 dependence, characteristic of a variable range hopping at the Fermi level is expected for a nondoping situation. 

Schematic representation of how doping can lead to (a) w-type and (b) / -type semiconductors. Note that the exact position of the Fermi level is temperature-dependent.

Contrary to silicon, very little work has been done in germanium regarding quantitative hydrogen diffusion or electric field drift studies. Such experiments may be complicated by the fact that ultra-pure germanium becomes intrinsic already at temperatures near 200 K. It would be worthwhile to explore the possibility of using lightly doped germanium for such studies in order to explore Fermi level dependent effects. 

Most impurities can occur in different charge states we will see that H in Si can occur as H+, H°, or H. Which charge state is preferred depends on the position of the Fermi level, with which the defect can exchange electrons. Relative formation energies as a function of Fermi level position can be calculated and tell us which charge state will be preferred in material of a certain doping type. Section V will discuss charge states in detail. 

The analytical solutions to Fick s continuity equation represent special cases for which the diflusion coefficient, D, is constant. In practice, this condition is met only when the concentration of diffusing dopants is below a certain level ( 1 x 1019 atoms/cm3). Above this doping density, D may depend on local dopant concentration levels through electric field effects, Fermi-level effects, strain, or the presence of other dopants. For these cases, equation 1 must be integrated with a computer. The form of equation 1 is essentially the same for a wide range of nonlinear diffusion effects. Thus, the research emphasis has been on understanding the complex behavior of the diffusion coefficient, D, which can be accomplished by studying diffusion at the atomic level. 

In a metal, the Fermi level is located within the conduction band. In a semiconductor, this level usually is found in the forbidden gap between the valence band and the conductivity band by doping it can be shifted up or down relative to the band edges. The activation energy of a catalyzed reaction depends on the distance of the Fermi level from the band edges for acceptor reactions it is related to the distance from the conduction band, for donor reactions to the distance from the valence band. The exact theory will not be presented here it has been given by Hauffe (6) and by Steinbach (9). 

The oxide layer of a metal such as copper may be seen as a semiconductor with a band gap, which may be measured by absorption spectroscopy or photocurrent spectroscopy and photopotential measurements. Valuable additional data are obtained by Schottky Mott plots, i.e. the C 2 E evaluation of the potential dependence of the differential capacity C. For thin anodic oxide layers usually electronic equilibrium is assumed with the same position of the Fermi level within the metal and the oxide layer. The energetic position of the Fermi level relative to the valence band (VB) or conduction band (CB) depends on the p- or n-type doping. Anodic CU2O is a p-type semiconductor with cathodic photocurrents, whereas most passive layers have n-character. 

Electronic surface properties including Fermi level positions, work functions, and ionization potentials of sputter-deposited ZnO and Al-doped ZnO films in dependence on deposition parameters. The results provide insight into aspects of doping, surface chemistry, and terminations. 

The work functions and ionization potentials of sputter-deposited ZnO and ZnO Al films are shown in Fig. 4.13. The different Fermi level positions of ZnO and ZnO Al for deposition at room temperature in pure Ar are also observed in the work function. The undoped films prepared under these conditions have a work function of 4.1eV, while the Al-doped films show values of 3.2eV. The difference is almost of the same magnitude as for the Fermi level position and, therefore, explained by the different doping level. Also the ionization potentials are almost the same under these preparation conditions. The work function of the undoped material is close to the value reported by Moormann et al. for the vacuum-cleaved Zn-terminated (0001) surface [20], The same authors report a work function of 4.95 eV for the oxygen terminated ZnO(OOOl) surface, which is in good agreement with the values obtained for films deposited with >5% oxygen in the sputter gas. Since the Fermi level position of the undoped ZnO films does not depend on the oxygen content in the sputter gas (Fig. 4.12), the different work functions correspond to different ionization potentials. 

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