Band engineering is an effective strategy to improve the electronic transport properties of semiconductors. In thermoelectric materials research, density‐of‐states effective mass is an undoubted key factor in verifying the band engineering effect and establishing a strategy for enhancing thermoelectric performance. However, estimation of the effective mass is demanding or inaccurate depending on the methods taken. A simple equation is proposed, valid for all degeneracy: Log10 (md*T/300) = (2/3) Log10 (n) − (2/3) [20.3 − (0.00508 × |S|) + (1.58 × 0.967|S|)] that utilizes experimentally determined Seebeck coefficient (S) and carrier concentration (n) to determine the effective mass (md*) at a temperature (T). This straightforward equation, which gives an accurate analysis of the band modulation in terms of md*, is indispensable in designing thermoelectric materials of maximized performance.

Flat metasurfaces with subwavelength meta‐atoms can be designed to manipulate the electromagnetic parameters of incident light and enable unusual light–matter interactions. Although hydrogel‐based metasurfaces have the potential to control optical properties dynamically in response to environmental conditions, the pattern resolution of these surfaces has been limited to microscale features or larger, limiting capabilities at the nanoscale, and precluding effective use in metamaterials. This paper reports a general approach to developing tunable plasmonic metasurfaces with hydrogel meta‐atoms at the subwavelength scale. Periodic arrays of hydrogel nanodots with continuously tunable diameters are fabricated on silver substrates, resulting in humidity‐responsive surface plasmon polaritons (SPPs) at the nanostructure–metal interfaces. The peaks of the SPPs are controlled reversibly by absorbing or releasing water within the hydrogel matrix, the matrix‐generated plasmonic color rendering in the visible spectrum. This work demonstrates that metasurfaces designed with these spatially patterned nanodots of varying sizes benefit applications in anti‐counterfeiting and generate multicolored displays with single‐nanodot resolution. Furthermore, this work shows system versatility exhibited by broadband beam‐steering on a phase modulator consisting of hydrogel supercell units in which the size variations of constituent hydrogel nanostructures engineer the wavefront of reflected light from the metasurface.

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The density-of-states effective mass (m d*) is commonly obtained by fitting the equation, S = (8π2 k B 2/3eh 2)m d*T(π/3n)2/3 (S, T, and n are the Seebeck coefficient, temperature, and the carrier concentration, respectively), to n-dependent S measurement. However, n is not a measurable parameter. It needs to be converted from the measured Hall carrier concentration (n H) using the Hall factor (r H = n/n H). The r H of material can be estimated by Single Parabolic Band (SPB) model if the band that contributed to transport is approximated to be parabolic and acoustic phonons dominantly scatter its carriers. However, the measurable n H is often used instead of n when utilizing the above equation due to the complex Fermi integrals involved in the SPB model calculation. Consequently, the m d* estimated from the above equation while using n H would be inaccurate. We propose the equation r H = 1.17 – [0.216 / {1 + exp­(( |S| – 101) / 67.1)}] as a simple and accurate method to obtain the r H from the measured S to facilitate the conversion from n H to n and eventually increase the accuracy of m d* estimated from the above equation.

Recent studies have revealed the outstanding thermoelectric performance of Bi-doped n-type SnSe. In this regard, we analyzed the band parameters for Sn1−xBixSe (x = 0.00, 0.02, 0.04, and 0.06) using simple equations and the Single Parabolic Band model. Bi doping suppresses the carrier-phonon coupling while increasing the density-of-states effective mass. The n-type SnSe is known to have two conduction bands converge near 600 K. Bi doping changes the temperature at which the band convergence occurs. When x = 0.04, its weighted mobility maximized near 500 K, which indicated the possible band convergence. The highest zT of the x = 0.04 sample at mid-temperatures (473–573 K) can be attributed to the engineered band convergence via Bi doping.