In this paper, using the compatible theory of differential invariants, a class of exact solutions is obtained for nonhomogeneous quasilinear hyperbolic system of partial differential equations (PDEs) describing rate type materials; these solutions exhibit genuine nonlinearity that leads to the formation of discontinuities such as shocks and rarefaction waves. For certain nonconstant and smooth initial data, the solution to the Riemann problem is presented providing a complete characterization of the solutions.
This paper reports on the steady state and transient photoconductivity of Ge20Se70−xIn10Bix (x = 2, 4, 6, 8, 10) thermally evaporated thin films. The dark conductivity (σd) increases with the increase in the Bi content. The value of σd increases slowly from x = 2 to x = 6, but for x ⩾ 8 the increase is quite abrupt. Photoconductivity (σph) also increases with the increase in the Bi content. The dark activation energy (ΔEd) decreases with the increase in the Bi content. There is a drop in the photosensitivity (σph/σd) of films with the increase in Bi addition. The result of the intensity dependent steady state photoconductivity (σph) follows the power law with intensity (F), i.e. σph α Fγ where the value of γ is close to 0.5, suggesting the predominance of bimolecular recombination in these materials. The rise and decay of photocurrent show the increase in the differential lifetime (τd), with the increase in the Bi content, indicating a delay in the recombination rate of photo-generated charge carriers. This change is governed by the photo-generated carriers trapped in the intrinsic defects or light induced defect creation through structural changes. One can therefore also expect that the density of states increases with the increase in the Bi content in amorphous thin films. The dispersion parameter (α) of the localized state energy distribution, determined from the decay curves, is also reported.
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