Electronic Band Structures for Tin Selenide Dr. HoSung Lee April 2, 2015 1 Car et al. (1978) – Istituto di Fisica del Politecnico, Milano Calculated bandgap: 2.1 eV Experimental value (Albers et al. (1962)): 0.9 eV 2 Soliman et al. (1995) – Dept. of Physics, Ain Shams University, Cairo 3 Lefebvre et al. (1998) – IEMN and LPMC, France 4 Makinistian and Albanesi (2009) – Universidad Nacional de Entre Rios, Argentina Indirect bandgap, C1-V1: 1.05 eV 5 Chen et al. (2012) – Tongji University, China Polycrystalline SnSe The band gap can be adjusted by doping element Te from 0.643 (no doping) to 0.608 eV (doping). Band gap: 0.643 eV 6 He et al. (2013) – Dept. of Material Science and Engineering, Nanjing Institute of Technology, China Direct energy gap: 0.8 eV Debye temperature: 215 K Gruneisen parameter: 2.98 7 Sun et al. (2013) – Chinese Academy of Sciences, China 8 Zhao et al. (2014) – Dept. of Chemistry, Northwestern University 9 Zhao et al. (2014) – Dept. of Chemistry, Northwestern University 10 Shi and Kioupakis (2015) – Dept. of Material Science and Engineering, University of Michigan 11 Shi and Kioupakis (2015) 12 Park et al. (2010) – Dept. of Physics, Missouri University of Science and Technology Scheidemantel et al. (2003) – Dept. of Physics, Pen State University 13 Shi and Kioupakis (2015) 14 Shi and Kioupakis (2015) 15 Experiments, Ab initio Experiments, Ab initio Semiclassical Soliman et al. Calculation, Zhao et al.(2014) Calculations, Shi and Nonparabolic Two-Band (1995) Chen et al. Kioupakis (2015) Kane Model (2012) (fit to measurements of Zhao et al. (2014)) Band edge LCB HVB LCB HVB LCB HVB LCB HVB LCB HVB First band, - - - - 1 1 1 1 1 1 Second band 1 1 Degeneracy of first band, - - - - - - 2 2 2 2 Degeneracy of second 2 2 (4) (4) band, DE (eV) = - - - - - First band – second band -4 Band gap, Eg (eV) 0.895 0.643 0.61-0.39 0.83-0.46 0.74 – 0.95x10 T Single DOS effective - - 4.02mo - - - 2.4mo 0.74mo 5.35 mo 0.47 mo mass (md) 1.06mo 3.0mo 0.34mo (3.3mo) (0.3mo) Integral DOS effective - - - - - - - - 8.5 mo 0.75 mo mass (m*) LCB: Lowest conduction band HVB: Highest valence band Note: This work assumes that the multiple bands are equal to multiple valleys. The effective 1/3 2/3 masses are calculated using the relationship of md = (mxmymz) and m* = Nv md. 16 Nonparabolic two-band model for p-type SnSe by Dr. HoSung Lee on 7/26/2014 2 4 12 A s 19 23 J 31 8.854 10 e 1.602110 C k 1.380610 m 9.1093910 kg 0 3 c B K e m kg 34 6.6260810 Js 23 h N 6.02213710 N 2 p 2 A v o 2900 Maldelung (1983) Thomas (1991) used 90 for Bi2Te3 meff_h0 0.75me density-of-state effective mass of hole for multiple valleys meff_e 8.5me density-of-state effective mass of electron for multiple valleys meff_h0 0 Bejenari (2008) used exponent 0.2 for Bi2Te3 and exponent 0.2 for Si by Barber (1967) and m (T) T eff_h 0 exponent of 0.8 for PbTe by Lyden (1964) (300K) 2 3 2 m (T) N m (T) d_h v eff_h 3 md_e Nv meff_e Lyden (1964) and Pei et al. (2012) mI_h(T) md_h (T) mI_e md_e Nv m* h m*e Chen et al. (2014) 2 0.75 SPB model calculation This work 2 0.75 Calculation Nv: multiplicity of valleys 17 Debye temperature θ =65K by Zhao et al. (2014), θ =215 K for SnSe by He et al. (2013) D 155K gm gm d 5.76 d 4.81 Mass density= mass/volume = molar mass/(NA*a^3), Sn 3 Se 3 cm cm Goldsmid (1964) and Maldelung (1983) Atomic (molecular) masses, Periodic table MSn 118.71gm MSe 78.96gm y 0.5 1 1 3 3 M M Sn 10 Se 10 aSn aSn 3.247 10 m aSe aSe 3.01 10 m NAdSn NAdSe 1 3 3 3 10 a aSn (1 y) aSe y a 3.133 10 m Atomic size, Vining (1991) Atomic size, 2.9x10^-8 cm used by Larson et al. (2000) Mean atomic mass MSnSe MSn(1 y) MSey MSnSe gm d d 5.339 mass density, d = 8.219 gm/cm^3 by Malelung (1983) 3 3 NAa cm 1 3 kB cm 2 5 Speed of sound, Zhao et al. (2014) gives 2.0 x 10^5 cm/s. vs 6 Da vs 1.631 10 hp s 18 20 110 Holes (This work) Electrons (This work) 2 Holes, Zhao et al. (2014)) 19 110 nhn1Ti Tin1 3 3 cm n n T T n 18 e 1 i i 1 110 3 cm 4 1 19 p_data 10 Carrier densityCarrier(cm^-3) 17 110 5 3 200 400 600 800 110 16 110 3 Temperature (K) 200 400 600 800 110 0 n = 3.3 x10^17 cm^-3 TiTip_data T (K) 19 600 0.8 500 0.6 ( V/K) 400 This work Zhao et al. (2014) 0.4 300 k (W/m*K) 3 200 400 600 800 110 T (K) 0.2 0 o 4.5ecV 3 100 200 400 600 800 110 This work Z 0.1 80 Zhao et al. (2014) T(K) Ka 1 Total thermal conductivity 60 Electronic thermal conductivity 1 1 Lattice thermal conductivity cm 40 Zhao et al. (2014) 20 0 3 200 400 600 800 110 20 800 300 K 900 K 800 niT1 T1ni 600 300 K niT1 T1ni V 1 1 K 900 K 600 cm 400 niT T ni niT T ni 3 3 400 3 3 V 1 1 cm K 200 200 0 0 16 17 18 19 20 110 110 110 110 110 ni 3 cm Shi and Kioupakis (2015) This work 21 3 This work 3 300 K Experiment, Zhao et al. (2014) 600 K ZT n T T n 900 K 2 i 1 1 i2 ZT niT2 T2ni ZT ZT niT T ni 3 3 1 1 0 16 17 18 19 20 0 110 110 110 110 110 3 200 400 600 800 110 ni 3 Temperature (K) cm 0.3 1.5 Parabolic model Kane model g E SPM i Ab Initio calc. He et al. (2013) 0.2 3 1 1 a ecV gSKM Ei 3 1 (J/g.K) Cv a ecV 0.1 0.5 E_DOSti Prediction, this work Experiment, Zhao et al. (2014) 0 0 3 3 2 1 0 1 2 3 0 200 400 600 800 110 Ei Ei ti T (K) 22 ecV ecV ecV The End 23.