Theoretical Study For Thermoelectric Performances Of Two-Dimensional XI₂（X=Ge,Sn,Pb） Structures

Thermoelectric（TE）materials are popular cleaning materials,which can realize the con-version between thermal and electrical energy,convert waste heat into electricity,and effec-tively alleviate the energy crisis,providing a feasible thought for energy renewable issues.At present,research in the field of thermoelectric power has lasted for more than 100 years,and the low efficiency of thermoelectric conversion has become the main bottleneck of thermoelec-tric conversion technology.In the 1990s,Hicks and Dresselhaus proposed that reducing the material dimension can greatly improve their thermoelectric properties.Since then,vigorous excavations for the thermoelectric performances of many two-dimensional（2D）materials have been obtained.As the new members of 2D family,the thermoelectric properties of group-IV diiodides including GeI₂,SnI₂and PbI₂have intrigued researchers recently.PbI₂in particu-lar has been proven to be a potential thermoelectric material experimentally.In this paper,we performed a systematic calculation to explore the effects of the number of layers and biaxial compressive strains on the TE performance of 2D XI₂:（1）Using density functional theory and Boltzmann transport theory,we calculated the thermoelectric properties of monolayers XI₂（X=Ge,Sn,Pb）.The thermal conductivities of GeI₂,SnI₂and PbI₂at 300 K are 1.14 Wm^-1K^-1,0.78 Wm^-1K^-1and 0.63 Wm^-1K^-1,respec-tively.Using the PBE functional,we calculated the band structures and projected density of state（PDOS）of XI₂.All the structures have an indirect band gap with the value a little smaller than 2 eV.In the valence band,all the band structures have two energy peaks located betweenΓ-M and K-Γ,whose energy differences are less than 0.1 eV.Such band convergences will help producing large Seebeck coefficient and greatly improving the thermoelectric performance of p-type XI₂.The electron mobilities of XI₂are isotropic,while the hole mobilities have ob-vious direction dependence.The hole mobilities in the zigzag direction are much higher than that in the armchair direction,hence,it shows better electrical transport properties in the zigzag direction.According to the obtained electric and thermal transport parameters,we calculated the thermoelectric merit（ZT）of XI₂in the zigzag direction,the results show the ZT values of p-type XI₂are significantly better than that of n-type XI₂.At the optimal doping level,the ZT values of p-type GeI₂,SnI₂and PbI₂reach 2.91(n=4.06×10¹³cm^-2),4.76(n=3.58×10¹³cm^-2)and 3.98(n=4.96×10¹³cm^-2)at 700 K,respectively.These results show that the monolayer XI₂（X=Ge,Sn,Pb）are promising thermoelectric materials.（2）The TE performances of the bilayer XI₂（X=Ge,Sn,Pb）were explored.The lattice thermal conductivity of bilayer GeI₂,SnI₂,and PbI₂at 300 K is 1.74 Wm^-1K^-1,1.25 Wm^-1K^-1,and 1.05 Wm^-1K^-1,which is about 1.6 times that of the monolayer XI₂,respectively.Bilayer XI₂are indirect bandgap semiconductors with bandgap values between 1.84 e V～1.96 e V,simi-lar to the bandgap values of the corresponding monolayer structures.In addition,the XI₂bilay-ers have much higher electron mobility and relaxation time than the corresponding monolayers and exhibit nearly isotropic TE performance and have higher ZT values for n-type doping than the monolayers.The highest n-type ZT values reach 0.40(n=3.78×10¹²cm^-2),0.58(n=3.32×10¹²cm^-2),and 0.95(n=4.23×10¹²cm^-2)at 300 K for Ge I₂,SnI₂and PbI₂bilay-ers,respectively.The dramatic difference between the monolayer and bilayer indicates that the inter-layer interaction plays an important role in the TE performance of XI₂,which provides the tunability on their TE characteristics.（3）We explored the TE performance of the monolayer XI₂（X=Ge,Sn,Pb）at 300 K under a biaxial compressive strain of 3%,6%and 9%.The TE performances in the zigzag direction of n-type GeI₂and SnI₂have the most significant improvements when strain reaches 9%.The highest power factors（PF）of n-type GeI₂and SnI₂reach 10.31 mWm^-1K^-2(n=4.23×10¹³cm^-2)and 7.27 mWm^-1K^-2(n=4.95×10¹³cm^-2),respectively.Compared to the PF values when no strain is applied(GeI₂～1.10 mWm^-1K^-2,SnI₂～1.02 mWm^-1K^-2),the PF values of n-type GeI₂and SnI₂under the strain of 9%are increased by 6～8 times.The changes of the conduction bands of GeI₂and SnI₂under 9%strain result in an increase of Seebeck coefficient and electronic conductivity.Hence,the TE performances of the n-type GeI₂and SnI₂along zigzag direction are greatly improved.Similarly,the PF values of p-type GeI₂and SnI₂along zigzag direction are also increased for the improved hole mobility.However,the maximum P F values of n-and p-type PbI₂when strain is applied are always lower than that when no strain is applied,because neither the Seebeck coefficient nor the electronic conductivity of PbI₂increases.Hence,only the TE performances of Ge I₂and SnI₂have improved when the strain is applied.