Computational Approaches Computational Approaches Theoretical Theoretical and and Computational Approaches Computational Approaches for Identifying and Optimizing Novel Thermoelectric Materials for Identifying and Optimizing Novel Thermoelectric Materials David J.Singh Theoretical and Computational Approaches for Identifying and Optimizing Novel Thermoelectric Materials David J.Singh 第一原理計算そしてバンド計算を元にした熱電についての Hiromi Okubo

Thermoelectric Effect The Seebeck effect The Peltier effect The Thomson effect Advantage Products Performance index Performance index ZT ZT Guideline of Design Guideline of Design CHEVREL PHASES Mo8Se6 Industrial material Bi2Te3/Sb2Te3 Future Future

Thermoelectric Effect In Thomas seebeck １８２３ A temperature gradient A voltage drop Peltier effect Seebeck effect V V＝S・ΔT ΠとSにはこのような関係があります Q＝π・ I V T H T C Seebeck coefficient Peltier coefficient T H T C π＝ TS

Peltier device

Advantage Products Exhaust gas Heat generation from the engine Energy and environmental issues ・Generation by waste heat ・Cooling without Freon ・maintenance free ・longevity Products Mobile refrigerator in the car 熱電変換 固体の熱電気現象で熱と電気を相互変換 熱電素子 長寿命 メンテナンスフリー 直接変換 （老廃物なし) 廃熱による発電 フロンなしの冷却 エネルギー・環境問題 に資する Cooling machine of the CPU of the computer Thermoelectricity watch Exhaust gas Heat generation from the engine

ZT S σ Z =  Performance index 2 Electric conductivity Figure of Merit Electric conductivity Z = Seebeck coefficient  Thermal conductivity A.F.Ioffe, semiconductor Thermoelements and Thermoelectric cooling , Infosearch Ltd London(1957)

ZT σ S Z =  Performance index 2 Ohm's law Fourier's law Electric conductivity Z = Seebeck coefficient  Thermal conductivity A.F.Ioffe, semiconductor Thermoelements and Thermoelectric cooling , Infosearch Ltd London(1957)

ZT S σ Z =  Performance index 2 Electric conductivity Seebeck coefficient  Thermal conductivity A.F.Ioffe, semiconductor Thermoelements and Thermoelectric cooling , Infosearch Ltd London(1957)

Boltzmann equation ＋ Band Theory Conductivity tensor

ZT σ S Z =  Performance index 2 Electric conductivity Figure of Merit Electric conductivity Z = Seebeck coefficient  Thermal conductivity A.F.Ioffe, semiconductor Thermoelements and Thermoelectric cooling , Infosearch Ltd London(1957)

σ σ Metals Z =  Insulators  semiconductor S S 2 σ  S Carrier concentration 2 σ S  Metals Z = low Seebeck coefficient large electronic contribution to the thermal conductivity Insulators large Seebeck coefficient small electronic contribution to the thermal conductivity Too few carriers semiconductor A carrier concentration of about 1019cm-3

G ε Large S  を最小にするには 元素固溶・重い元素・ラットリング 重要な点 格子の熱伝導率はが大きいとZT小さい 格子の熱伝導率の低い物質a low lattice thermal conductivity 単位格子内の原子数が多いものA large number of atoms in the unit cell 　　　平均の原子量が大きいもの　A large average atomic mass 一原子あたりの平均配位数が大きい結晶構造を有するものCrystal structures that result in a high average coordination number per atom かご状の構造を有し、内部に弱く結合した原子や分子が存在してガラガラのように鳴る構造を有すもの Cagelike structures in which a weakly bound atom or molecule in the cage “rattles” The ability of the lattice to conduct heat is only slightly affected by changes in the carrier concentration

Large S ε G  を最小にするには 元素固溶・重い元素・ラットリング 重要な点 格子の熱伝導率はが大きいとZT小さい 格子の熱伝導率の低い物質a low lattice thermal conductivity 単位格子内の原子数が多いものA large number of atoms in the unit cell 　　　平均の原子量が大きいもの　A large average atomic mass 一原子あたりの平均配位数が大きい結晶構造を有するものCrystal structures that result in a high average coordination number per atom かご状の構造を有し、内部に弱く結合した原子や分子が存在してガラガラのように鳴る構造を有すもの Cagelike structures in which a weakly bound atom or molecule in the cage “rattles” The ability of the lattice to conduct heat is only slightly affected by changes in the carrier concentration

Low dimension Large S Large S ε G  を最小にするには 元素固溶・重い元素・ラットリング 重要な点 格子の熱伝導率はが大きいとZT小さい 格子の熱伝導率の低い物質a low lattice thermal conductivity 単位格子内の原子数が多いものA large number of atoms in the unit cell 　　　平均の原子量が大きいもの　A large average atomic mass 一原子あたりの平均配位数が大きい結晶構造を有するものCrystal structures that result in a high average coordination number per atom かご状の構造を有し、内部に弱く結合した原子や分子が存在してガラガラのように鳴る構造を有すもの Cagelike structures in which a weakly bound atom or molecule in the cage “rattles” The ability of the lattice to conduct heat is only slightly affected by changes in the carrier concentration

Low  A large number of atoms in the unit cell A large average atomic mass Cagelike structures in which a weakly bound atom or molecule in the cage “rattles”  を最小にするには 元素固溶・重い元素・ラットリング 重要な点 格子の熱伝導率はが大きいとZT小さい 格子の熱伝導率の低い物質a low lattice thermal conductivity 単位格子内の原子数が多いものA large number of atoms in the unit cell 　　　平均の原子量が大きいもの　A large average atomic mass 一原子あたりの平均配位数が大きい結晶構造を有するものCrystal structures that result in a high average coordination number per atom かご状の構造を有し、内部に弱く結合した原子や分子が存在してガラガラのように鳴る構造を有すもの Cagelike structures in which a weakly bound atom or molecule in the cage “rattles” The ability of the lattice to conduct heat is only slightly affected by changes in the carrier concentration

Guideline of Design semiconductor Cagelike structures Low dimension σ 2 σ  S Carrier concentration semiconductor Between metal and insulator A carrier concentration of about 1019cm-3 Cagelike structures Low dimension Layered material A large atomic mass Low  Large S

Bi Te Sb Te / Industrial material ZT=1 ZT=1 Refrigerator ZT=3 4 2 3 / Sb Te 2 3 ZT=1 Carnot efficiency ZT=1 about 10% Refrigerator Carnot efficiency ZT=3 About 30% 4

ZT  Performance index ZT = f (βEg,B) B = N ・μ・ m ( ) ＊ The degeneracy of the band extrema The carrier mobility The density of states band mass 状態密度 の有効質量 3 2  B = N ・μ・ m ＊ ( ) γ ph G.D.MAHAN SOILD STATE PHYSICS,vol,51 P81

CHEVREL PHASES S Se Te Mo X Chalcogen Large voids in the crystal structure シェブレル Chalcogen S Se Te Mo X 6 8

CHEVREL PHASES Pb Mo X M Mo X Low  Metal Large voids in the crystal structure A large atomic mass Low  Pb Metal シェブレル Mo X M Mo X 6 8 6 8

CHEVREL PHASES Mo Se Mo - Se p d LAPW method (linearized augmented plane wave method) Mo Se d p - シェブレル Mo Se 8 6

CHEVREL PHASES LAPW method (linearized augmented plane wave method) degeneracy flat Mo Se 8 6 シェブレル

CHEVREL PHASES LAPW method (linearized augmented plane wave method) degeneracy flat Mo Se 8 6 Doping シェブレル N-type

CHEVREL PHASES LAPW method (linearized augmented plane wave method) degeneracy flat Mo Se 8 6 Doping シェブレル N-type

Future Future Layered material Low dimensional compound and Thermoelectric calculation and material Design A calculation of the figure of merit ZT based on Bloch- Boltzmann Formula used First-principles studies