Electronic Band Structures for Magnesium Silicide. Dr. HoSung Lee March 26, 2015

Transcription

1 Electronic Band Structures for Magnesium Silicide Dr. HoSung Lee March 26, 2015

2 Peter Lee (1964) Dept. of Physics, University of Chicago Fig. Atomic arrangement in Mg2Si Gerstein et al. (1967) Fig. Brillouin zone for face-centered cubic lattice.

3 Peter Lee (1964) (1954)

4 Morris et al. (1958) Dept. of Physics, Iowa State College R = Hall coefficient r = resistivity Experiments: m n = 0.46 m o m p = 0.87m o

5 Busch and Winkle (1954) Zurich, Schweiz

6 Au-Yang and Cohen (1969) Dept. of Physics, UC Berkeley Arnaud and Alouani (2001)- Universite Louis Pasteur, France Indirect energy gap = 0.53 ev LDA: Local density approximation. GW: In this approximation the electron self-energy operator is approximated by the product of the Green s function G and the screened Coulomb interaction W.

7 Aymerich and Mula (1970) Istituto di Fisica dell Universitu, Cagliari and Gruppo Nazionale di Strullura della Materia del C.N.R.

8 Zaitsev et al. (2006) Ioffe Physico-Technical Institute of the Russian Academy of Sciences Experiments

9 Zhou et al. (2010) Dept. Mechanical Engineering, University of Colorado

10 Boulet et al. (2011)- Universite Aix Marseille, France

11 Boulet et al. (2011)- Universite Aix Marseille, France

12 Satyala and Vashaee (2012) Oklahoma State University

13 Satyala and Vashaee (2012)

14 Satyala and Vashaee (2012) Oklahoma State University

15 Satyala and Vashaee (2012) Oklahoma State University

16 Wang et al. (2012) National Center for Nanoscience Technology of China

17 Bahk et al. (2014) Birck Nanotechnology Center, Purdue University

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19 Kutorasinski et al. (2014) Physics and Applied Computer Science, Poland

20 Experiments, Morris et al. (1958) Ab initio calculation, Boulet et al. (2011) Satyala and Vashaee (2012) Model fit to Tani and Kido (2008) Bahk et al. (2014) model fit to Tani and Kido (2008) and Zaitsev et al. (2006) Semiclassical Nonparabolic Two-Band Kane Model (fit to measurements of Tani and Kido (2008)) Band edge LCB HVB LCB HVB LCB HVB LCB HVB LCB HVB First band, Second band Degeneracy of first band, Degeneracy of second band, DE (ev) ev 0.4 ev - Band gap, E g (ev) x10-4 T x10-4 T x10-4 T Single DOS effective mass Integral DOS effective mass 0.46 m o 0.87 m o 0.27m o 0.25 m o 1.0m o 2.0m o 0.38m o 0.49m o 1.0m o 1.5m o 0.55 m o 0.99 m o m o 2.5 m o LCB: Lowest conduction band HVB: Highest valence band Note: This work assumes that the multiple bands are equal to multiple valleys. 20

21 Non-parabolic two band model for n-type Mg2Si by Dr. HoSung Lee on 8/26/2014 e c C k B J m K e kg J s h p N 2 A N v 4 o 20 0 inf Satyala (2012) m eff_e0 1.4 m e density-of-state effective mass of electron for multiple valleys m eff_h 2.5 m e density-of-state effective mass of hole for multiple valleys m eff_e ( T) m eff_e0 T 0 ( 300K ) m d_e ( T) N v m eff_e ( T) m d_h N v 2 3 m eff_h m I_e ( T) m d_e ( T) m I_h m d_h m* e m* h At 300 K Tani and Kido (2008) 1.1 Estimation from measurements Akasaka et al. (2008) Prediction Morris (1958) Measurements This work Prediction

22 Carrier density (cm^-3) n e n 1 T i T i n 1 cm 3 n h n 1 T i T i n 1 cm Holes (This work) Electrons (This work) Temperature (K) n = 1.9 x10^19 cm^-3 n = 2.9 x 10^19 cm^-3 T i T (K)

23 V/K) ( T (K) n=4.3 x 10^17 cm^-3, Present model n=1.1 x 10^20 cm^-3, Present model n=4.3 x 10^17 cm^-3, Tani and Kido (2005) n=1.1 x 10^20 cm^-3, Tani and Kido (2005) Present model Present model Tani and Kido (2005) Tani and Kido (2005)

24 k (W/m*K) Total thermal conductivity Electronic thermal conductivity Lattice thermal conductivity Tani and Kido (2005) Phonon Relaxation Time (ps) T(K) Umklapp Point Defects Electron-Phonon Total Frequaency (THz) Prediction, this work Experiment, Gerstein (1967)) Cv (J/mol.K) T (K)

25 The End