An efficient approach to improve the thermoelectric performance of materials is to converge their electronic bands, which is known as band engineering. In this regard, lots of effort has been made to further improve the thermoelectric efficiency of bulk and exfoliated monolayers of Bi2Te3 and Sb2Te3. However, ultrahigh band degeneracy and thus significant improvement of the power factor have not yet been realized in these materials. Using first-principles methods, we demonstrate that the valley degeneracy of Bi2Te3 and Sb2Te3 can be largely improved upon substitution of the middle-layer Te atoms with the more electronegative S or Se atoms. Our detailed analysis reveals that in this family of materials, two out of four possible valence band valleys merely depend on the electronegativity of the middle-layer chalcogen atoms, which makes the independent modulation of the valleys’ position feasible. As such, band alignment of Bi2Te3 and Sb2Te3 largely improves upon substitution of the middle-layer Te atoms with more electronegative, yet chemically similar, S and Se ones. A superior valence band alignment is attained in Sb2Te2Se monolayers where three out of four possible valleys are well aligned, resulting in a giant band degeneracy of 18 that holds the record among all thermoelectric materials. As a result, an outstanding power factor for the hole-doped monolayers is achieved, indicating a highly efficient p-type thermoelectric material.

Invasion occurs in environments that are normally spatially disordered, however, the effect of such a randomness on the dynamics of the invasion front has remained less understood. Here, we study Fisher’s equation in disordered environments both analytically and numerically. Using the Effective Medium Approximation, we show that disorder slows down invasion velocity and for ensemble average of invasion velocity in disordered environment we have $$\bar{v}=v_0 (1-|\xi |^2/6)$$ v ¯ = v 0 ( 1 - | ξ | 2 / 6 ) where $$|\xi |$$ | ξ | is the amplitude of disorder and $$v_0$$ v 0 is the invasion velocity in the corresponding homogeneous environment given by $$v_0=2\sqrt{RD_0}$$ v 0 = 2 R D 0 . Additionally, disorder imposes fluctuations on the invasion front. Using a perturbative approach, we show that these fluctuations are Brownian with a diffusion constant of: $$D_{C}= \dfrac{1}{8} \xi ^2\sqrt{RD_0 (1-|\xi |^2/3)}$$ D C = 1 8 ξ 2 R D 0 ( 1 - | ξ | 2 / 3 ) . These findings were approved by numerical analysis. Alongside this continuum model, we use the Stepping Stone Model to check how our findings change when we move from the continuum approach to a discrete approach. Our analysis suggests that individual-based models exhibit inherent fluctuations and the effect of environmental disorder becomes apparent for large disorder intensity and/or high carrying capacities.

In this research, efficiency enhancement of dye-sensitized solar cell (DSSC) with Ag doped TiO 2 core-shell (C-S) as plasmonic photoanode structure, abbreviated as Ag@TiO 2 , was investigated using Sol-Gel-Dr Blade method. Different amount of Ag in two different thick of photoanode were applied to enhance the light absorption for high-performance DSSCs. The localized surface plasmonic resonance (LSPR) effect of Ag@TiO 2 showed an improvement in light trapping and power conversion efficiency (PCE) of developed DSSCs. Conforming to the conclusions under AM 1.5 spectrum, the prepared plasmonic solar cells exhibited 21.9% and 41.46% increase in PCE for 13 μm and 8.4 μm thick of photoanode, respectively.