Investigation of the electronic and thermoelectric properties of hydrogenated monolayer germanene under biaxial tensile and compressive strains by DFT approach

Highlights

• Electronic and thermoelectric properties of hydrogenated germanene are studied.

• The biaxial strain is applied to the nanosheet.

• Combination of first-principles calculations and semiclassical Boltzmann transport theory is used.

• In the p-type doping, increasing the tensile strain would result in increasing the power factor.

• In the n-type doping, increasing the compressive strain increases the power factor.

Abstract

Two-dimensional materials possess a great potential in thermoelectric devices. In this work, by using a combination of first-principles calculations and semiclassical Boltzmann transport theory, a systematic investigation of electronic and thermoelectric properties of hydrogenated monolayer germanene under biaxial strain is presented. The results show that in all cases, the thermoelectric performance of the n-type doping on the germanene is substantially superior than that of the p-type doping. In the p-type doping, increasing the tensile strain would result in increasing the power factor, and the strain +3% creates the highest power factor. However, in the n-type doping, increasing the compressive strain increases the power factor, and the strain −6% leads to the highest power factor. Under the strain of −6%, the peak of the power factor for n-type doping equals to 32.3⨯10¹⁰ W/K²ms; while this amount equals to 12.2⨯10¹⁰ W/K²ms for the pristine case, which in fact has increased as 2.8 times. The mentioned peak will reach 57.21⨯10¹⁰ W/K²ms at the temperature 800 K, which is very significant. These results show the enormous potential of hydrogenated monolayer germanene in the thermoelectric industry.

Introduction

Thermoelectric materials can directly convert the wasted heat into electricity. In recent decades, due to the global warming crisis, the interest in these materials has increased [[1], [2], [3]]. The performance of thermoelectric materials is evaluated by using a dimensionless quantity $ZT=S^2\sigma T/\kappa$ which is called figure-of-merit, where S, σ and T are respectively Seebeck coefficient, electrical conductivity and absolute temperature [4,5]. Here, κ is the same as thermal conductivity of the material, which is consisted of two parts of electronic κ_e and lattice κ_p. The above equation shows that materials with extremely high electrical conductivity and low thermal conductivity are suitable for thermoelectric usage. In other words, to increase the thermoelectric efficiency, we need to increase the power factor and decrease the thermal conductivity. However, based on the Wiedemann-Franz law, these parameters are dependent [6]. Thus, the mentioned parameters cannot be improved easily. For example, Seebeck coefficient and electrical conductivity are inversely proportional to each other [7,8].

The power factor and efficiency of thermoelectric material can be increased by several strategies such as chemical functionalization [9], hydrogenation [10], halogenation [11], applying mechanical strain [[12], [13], [14], [15], [16], [17]], structural defects [[18], [19], [20]], heterostructure [21], etc. Among the mentioned strategies, applying mechanical strain is one of the most popular techniques for tuning the thermoelectric properties of materials. For instance, in monolayer WS_2, by applying uniaxial strain, a 77% increase in the power factor of the n-type doping was observed [22], and in monolayer ZrS_2, under 6% strain, the maximum ZT for the p-type doping equals 2.4, which is 4.3 times bigger than the pristine case [23].

Materials in two-dimensional form have a superior thermoelectric performance than their bulk state, because they possess a bigger power factor in two-dimensional form [24]. Graphene, as one of the most important two-dimensional materials [25], has a zero band gap, high mobility and electrical conductivity [26,27]. The unique properties of graphene motivated a large number of scientists to investigate the physical properties of other monolayers of the IV group, like silicene [28], germanene [29] and stanene [30]. However, the important disadvantage of these monolayers is their zero band gap which makes them an unsuitable choice for optic and thermoelectric usage. This weakness has been solved using hydrogenation and halogenation [31,32]. In other words, the band gap of the mentioned monolayers opens by using this method, which is followed by a long list of applications. Hydrogenated germanene is a stable semiconductor and has an extremely high mobility [33,34]. Hence this monolayer can be highly advantageous for thermoelectric usage.

Houssa et al. [31] investigated the effect of hydrogenation on the electronic properties of silicene and germanene by suing the first principle calculations. It was shown that for both of the silicene and germanene, adsorption of the hydrogen atoms results in opening an energy gap. The electronic and magnetic properties of the hydrogenated germanene and silicene were studied by Wang et al. [35]. They adsorbed the H atoms only on one side of the nanosheets on half of the atoms and showed that the resulted structures are stable. The energy gaps of these semi-hydrogenated silicene and germanene were computed as 1.74 eV and 1.32 eV, respectively. Using the DFT calculations, the effect of hydrogenation on the interactions between a layer and an Al substrate were studied by Marjaoui et al. [36]. It was shown that hydrogenation results in decreasing the interaction energy between the germanene layer and the Al substrate. The effects of hydrogenation and fluorination on the structural, electronic and optical properties of the germanene were evaluated by Shu et al. [37]. Liu et al. [38] showed that the one-side semi-hydrogenated germanene is a 2D half-semimetal material. Li et al. [10] investigated the thermoelectric properties of pure and hydrogenated multilayer (from one to five layers) silicene using density functional theory. They claim that hydrogenation can effectively modify the electronic band structure of multilayer silicene. Once the layer number is larger than two, hydrogenation improves the electronic figure of merit ZT of multilayer silicene. They also offer that by combining the adjustment of the hydrogenation ratio with changing the geometric structure, a high thermoelectric performance can be realized in multilayer silicene.

Moreover, it has previously been shown that the strain does not have significant influence on the electronic structure of pure germanene and cannot induce a suitable band gap for thermoelectric properties [39]. Hence, it can be deduced that hydrogenation can change the influence of the strain on the thermoelectric properties of the germanene.

Here, the dependence of thermoelectric properties of hydrogenated monolayer germanene on mechanical strain is studied. The influence of the compressive and tensile strains on the electronic and thermoelectric properties of the pure and hydrogenated germanene is evaluated. The strain is considered in the range of −6% (maximum compressive strain) to +3% (maximum tensile strain).