Bandgap pressure dependence

Fig. 27.11 Temperature dependence of a the Young s modulus [7] and b the Raman shifts at the atmospheric pressure for ZnO with confirmation of = 310 K and derivative of = 0.75 eV per bond, which is in accordance with that derived from T-dependent bandgap change (inset b [111-114]) of ZnO [19]. Pressure dependence of c elastic modulus [115] and d optical modes [Ei(LO), E2(high), Ei(TO), Ai(TO), and Bi(LO)] for ZnO [109, 110] with derivative of the binding energy density (Ej) of 0.097 eV/A (reprinted with permission from [19])...

In Figure 10.7 the center of the graph is at the oxygen partial pressure that is in equilibrium with the stoichiometric oxide MjOi. The value of the equilibrium constants and depends on the reaction heat for oxidation or reduction of the oxide. Ki depends exponentially on the bandgap. This figure shows how oxygen pressures affect the electic behavior of the oxide ... 

A factor which has to be taken into consideration, especially in the MBE growth of layered systems, is the influence of effective pressure and strain on the vibronic properties of the semiconductors. Strain effects arise because of the differences in the lattice constants. This difference leads to a distortion of the crystal lattice, which causes a shift of the bandgap energy and, thus, directly affects the optical properties of the layered systems. Therefore, it is important to investigate strain effects quantitatively. The compression (expansion) of the lattice constants by strain effects is equivalent to a change in the interatomic distances and therefore leads to a shift of the LO-phonon frequency. Compressive (tensile) strain leads to a blueshift (redshift) of the phonon wave number. The amount of this shift is proportional to the strain. Strain shifts can mask confinement shifts or compositional shifts. Therefore, it is necessary to separate the strain-induced part of the shift from the other parts. In addition to the dependence on the difference in the lattice constants, the strain shows also a dependence on the thickness of the layer. The strain increases with increasing layer thickness up to a critical thickness. From this thickness onward, the strain decreases because of the formation of misfit dislocations. The appearance of misfit dislocations can be observed in the Raman spectra as an increase in the intensity of the symmetry-forbidden TO-phonon peak as well as a broadening of the LO-phonon peak. 

The lattice constants change with temperature, as will be discussed in Section 1.6.1, and with pressure as already mentioned in Section 1.2. Consequently, the electronic band structure changes with temperature and pressure. The bandgap (at F point) shrinks with increasing temperature and the dependence is given by the empirical relationship [62]... 

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