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.

Approach to Determine the Density‐of‐States Effective Mass with Carrier Concentration‐Dependent Seebeck Coefficient

The density of states of electrons is a simple, yet highly-informative, summary of the electronic structure of a material. Here, some remarkable features of the electronic structure that are perceptible from the density of states are concisely reviewed, notably the analytical E vs. k dispersion relation near the band edges, effective mass, Van Hove singularities, and the effective dimensionality of the electrons, all of which have a strong influence on physical properties of materials. We emphasize that appropriate parameters in electronic structure calculations are necessary to obtain even a sufficient-quality density of states exhibiting fine features of the electronic structure. 

https://doi.org/10.1016/j.mtelec.2022.100002

How to analyse a density of states

Thermoelectric materials possess the potential for refrigeration and power generation due to their ability to directly convert heat and electricity. Carrier mobility and the Seebeck coefficient are key properties of thermoelectric materials. Improving the effective mass is the most effective and frequent way to optimize the Seebeck coefficient. However, carrier mobility deteriorates dramatically with increasing effective mass and thus limits further improvement of thermoelectric performance. Here, the focus is on the importance of modifying the scattering factor (r) to enhance the electrical properties, and it is found that the anisotropic scattering factor enhances the carrier mobility and Seebeck coefficient of anion‐doped n‐type tin selenide crystals along the out‐of‐plane direction, indicating the potential of modifying r to improve electrical properties. Following this strategy, the average dimensionless figure of merit (ZTave) for iodine‐doped SnSe crystals is significantly improved from 0.84 to 1.57 in 300–773 K. The results emphasize the critical role of scattering factor and propose a new perspective for enhancing carrier mobility, providing a novel strategy to optimize thermoelectric performance.

Enhancing Carrier Mobility and Seebeck Coefficient by Modifying Scattering Factor

The thermoelectric (TE) performance of Molybdenum disulpide (MoS2) can be improved by the incorporation of nanomaterials. MoS2 has been reported as promising thermoelectric materials due to their large bandgap and low thermal conductivity. In the present work, n-type MoS2 was successfully synthesized by facile hydrothermal route with an excellent thermoelectric performance by introducing rhenium (Re) dopant. The structural and morphological analyses confirmed the incorporation of Re into Mo (Molybdenum) lattice. The thermoelectric results showed that both the electrical conductivity (σ) and Seebeck coefficient (S) has been increased with the increase in Re content (2.5, 5, 7.5 and 10 at%) and temperature (303 K to 700 K), while the thermal conductivity (κ) was low. Doping with Re on MoS2 enhances the electrical conductivity through band engineering, improving carrier concentration and shifting the Fermi level to the conduction band. Introducing a heavy atomic element can reduce the total thermal conductivity by facilitating mass fluctuation. The maximum Seebeck coefficient was obtained as -100 μVK-1 at 500 K for Re 5 at% sample, which is 3.7 times greater than undoped MoS2. In addition, introducing electrons through Re doping induced bipolar conduction. These enhancements have increased the power factor of 8 μWm-1K-2 at 650 K. 

Multiple approaches of band engineering and mass fluctuation of solution-processed n-type Re-doped MoS2 nanosheets for enhanced thermoelectric power factor

An ideal thermoelectric material requires the multi‐valley and strong dispersion band structure, for relieving the competition between thermopower and electrical conductivity, whereas the two features barely coexist in natural compounds. Here, the significantly improved thermoelectric performance in n‐type PbSe‐xAgSbS2 with the purposefully renormalized conduction band structure is reported. It is shown that the strong spin‐orbit coupling effect splits the single valley at “L” point into three individuals delicately, as the Dirac point is shifted away from the high symmetry point by the decreasing lattice constant. Compared with the common PbSe‐based compounds, the renormalized system exhibits a range of distinctive properties, such as the 2–3 times larger band gap, 5–10 times lower optimal carrier concentration, and weakly temperature‐dependent Seebeck coefficient. Owing to the achieved giant band convergence and the low thermal conductivity, a high peak zT of 1.75 at 850 K and an outstanding average zT of 1.04 are obtained. Furthermore, the mechanical property and thermal stability of PbSe are considerably improved for the introduced high entropy effect and lattice shrinkage. This study reveals the remarkable impact of spin‐orbit coupling on thermoelectric performance, and suggests that the optimized PbSe material holds great promise for practical applications.

Giant Band Convergence and High Thermoelectric Performance in n‐Type PbSe Induced by Spin‐Orbit Coupling

Engineering semiconductor devices requires an understanding of the effective mass of electrons and holes. Effective masses have historically been determined in metals at cryogenic temperatures estimated using measurements of the electronic specific heat. Instead, by combining measurements of the Seebeck and Hall effects, a density of states effective mass can be determined in doped semiconductors at room temperature and above. Here, a simple method to calculate the electron effective mass using the Seebeck coefficient and an estimate of the free electron or hole concentration, such as that determined from the Hall effect, is introduced mS∗me=0.924(300KT)(nH1020cm−3)2/3[3(exp[|S|kB/e−2]−0.17)2/31+exp[−5(|S|kB/e−kB/e|S|)]+|S|kB/e1+exp[5(|S|kB/e−kB/e|S|)]] here mS∗ is the Seebeck effective mass, nH is the charge carrier concentration measured by the Hall effect (nH = 1/eRH, RH is Hall resistance) in 1020 cm−3, T is the absolute temperature in K, S is the Seebeck coefficient, and kB/e = 86.3 μV K−1. This estimate of the effective mass can aid the understanding and engineering of the electronic structure as it is largely independent of scattering and the effects of microstructure (grain boundary resistance). It is particularly helpful in characterizing thermoelectric materials.

Effective Mass from Seebeck Coefficient

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Effective Mass from Seebeck Coefficient