In this paper, we have constructed a sequence of soft points in one soft set with respect to a fixed soft point of another soft set. The convergence and boundedness of these sequences in soft ∆-metric spaces are defined and their properties are established. Further, the complete soft ∆-metric spaces are introduced by defining soft ∆-Cauchy sequences.
Atomically thin MoSe2 is of interest from the perspective of estimating the layer-dependent material properties necessary for the translation of two-dimensional materials into devices. This work presents Raman spectroscopic protocols to determine a multitude of material parameters of two-dimensional MoSe2 films, including the layer thickness as well as the layer-dependent thermal conductivity, interlayer interactions, and anharmonicity. The Davydov splitting (factor-group splitting) observed in an out-of-plane A1g Raman mode, being layer-dependent in both the number and the peak positions, provides a method for estimating the number of layers. Furthermore, this work demonstrates the determination of the thermal conductivity ( K) from the temperature-dependent Davydov split Raman modes of the multi-layers. The measurement of K by conventional methods is otherwise challenging for the micrometer sizes of the two-dimensional materials. The value of K thus determined increases significantly from 9 W m−1 K−1 for a four-layer thick MoSe2 film to 52 W m−1 K−1 for a monolayer. The diminishing effect of anharmonicity observed in the monolayer as compared to multi-layer MoSe2 supports the layer-dependent trend in the thermal conductivity. Overall, the findings are relevant for the applications of 2D MoSe2 in low power electronic, optoelectronic, and thermoelectric devices.
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