NS, B3H 4R2, Canada 4) Physical and Life Sciences Directorate, Lawrence Livermore National Laboratory, Livermore, California 94550,

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1 Electronic Supplementary Material (ESI) for Journal of Materials Chemistry. This journal is The Royal Society of Chemistry 9 Supporting Information: Origins of Ultralow Thermal Conductivity in -- Quaternary Selenides Jimmy Jiahong Kuo, Umut ydemir, Jan-Hendrik Pöhls, Fei Zhou, Guodong Yu,, lireza Faghaninia, 7 Francesco Ricci, Mary nne White,, 8, 9 Gian-Marco Rignanese, Geoffroy Hautier, nubhav Jain, 7 and G., a) Jeffrey Snyder ) Department of Materials Science and Engineering, Northwestern University, Campus Drive, Evanston, IL-8, US ) Department of Chemistry, Koç University, Sariyer, Istanbul,, Turkey ) Department of Physics and tmospheric Science, Dalhousie University, PO BO, Coburg Rd, Halifax, NS, BH R, Canada ) Physical and Life Sciences Directorate, Lawrence Livermore National Laboratory, Livermore, California 9, US ) Institute of Condensed Matter and Nanosciences (IMCN), Université Catholique de Louvain, Chemin des Étoiles 8, B-8 Louvain-la-Neuve, Belgium ) School of Physics and Technology, Wuhan University, Wuhan 7, China 7) Energy Technologies rea, Lawrence Berkeley National Lab, Cyclotron Rd,Berkeley, C, US 8) Clean Technologies Research Institute, Dalhousie University, PO BO, Coburg Rd, Halifax, NS, BH R, Canada 9) Department of Chemistry, Dalhousie University, PO BO, Coburg Rd, Halifax, NS, BH R, Canada (Dated: December 8) I. ELECTRON BND STRUCTURES First-principles electronic band structures were computed using Vienna ab initio Simulation Package (VSP),. See Section IV E (Computational Details) in the main text for more detials. The calculation results are shown in Figure S. More details are available under Computational parameters reported by Ricci et al. II. RESULTS OF ELECTRONIC TRNSPORT CLCULTIONS In Table S, the complete results of our electronic transport calculations are presented using a hypothetical charge carrier concentration of cm and temperature of K as well as thermal conductivity values calculated at room temperature. III. DDITIONL DEFECT DIGRMS IV. PHONON BND STRUCTURES ND DYNMIC INSTBILITY OF BCU GESE Phonon dispersion curves and density of states are shown in Figure S. Similar to SnSe, all dispersion curves have low-frequency optical modes to suppress the acoustic modes and reduce the Debye temperature. a) Electronic mail: jeff.snyder@northwestern.edu TBLE S: The calculated p-type transport properties at the hypothetical carrier concentration of cm, temperature of K and a constant relaxation time of τ = s. Thermal conductivity values are reported at room temperature. MPID stands for the Materials Project ID and the computed data can be found at The GG band gap is in ev, power factors in µwcm K, electrical conductivity, σ, in S cm, Seebeck coefficient, S, in µv K, κ is in W m K and the bulk modulus, B, is in GPa. SnSe Cu SnSe Cu GeSe SrCu GeSe MPID mp-9 mp mp-7 mp-79 gap σ S P F P F xx...7. P F yy P F zz κ min.... κ SE....8 B In Cu GeSe, the phonon modes along the or [] direction are predicted to be soft and become unstable closer to, suggesting that this system is mechanically unstable at T =. Proper computational treatment of finite-temperature properties of Cu GeSe therefore requires more elaborate phonon renormalization calculations and is beyond the scope of the present study.

2 (a) SnSe (b) CuSnSe (c) CuGeSe (d) SrCuGeSe FIG. S: Calculated band structures. The compound formula are indicated under the figures. V. CHILL S GLSSY LIMIT The glassy limit of lattice thermal conductivity is calculated by using the following formula : π / T Z θi /T x ex κcahill = kb n/ vi dx, θi (ex ) i (S) where the subscript i represent the three sound modes (i.e. two transverse and one longitudinal) with the speed of sound v, the number density of atom n and the Debye temperature θi = vi (~/kb (π n)/ ). where Cv is the heat capacity at constant volume, αl and αv are the linear and volumetric coefficient of thermal expansion. VII. EQUTION TO CLCULTE DEFECT FORMTION ENERGY The formation energy of the defect with charge q was calculated by: E f [ q ] = Etot [ q ] Etot [bulk] ni µi + qef + Ecorr, i VI. GRU NEISEN PRMETER Gru neisen parameter can be calculated using γ= αl B v αv = s, CV CP (S) (S) Here, Etot [ q ] and Etot [bulk] are the total energies of the defect with charge q and the perfect crystal respectively. The integer ni indicates the number of atoms of type i that have been added to (ni > ) or removed from (ni < ) the supercell to form the defect, and the µi are the corresponding chemical potentials

3 CuSnSe (b) total Sn Cu Se 7 DOS (THz-) (a) SrCuGeSe 7 (d) total Sr Cu Ge Se S R Z Y S R Z Y 8 DOS (THz-) Energy (THz) (c) Energy (THz) 8 (e) 8 CuGeSe M K L H FIG. S: Calculated phonon dispersion curves and phonon density of states of Cu SnSe ((a) and (b)) and SrCu GeSe ((c) and (d)). (e) Phonon dispersion curves of Cu GeSe. Phonon density of state is not shown due to the dynamic instability at T = K. of these species. Ef is the Fermi energy, namely the chemical potential of the electrons. Ecorr is the correction of the defect formation energy. G. Kresse and J. Furthmu ller, Comput. Mater. Sci., (99). Kresse and J. Furthmu ller, Phys. Rev. B, 9 (99). F. Ricci, W. Chen, U. ydemir, G. J. Snyder, G.-M. Rignanese,. Jain, and G. Hautier, Scientific data, 78 (7). D. G. Cahill, S. K. Watson, and R. O. Pohl, Physical Review B, (99). G.

4 Sn (a) Se SnSe Se Se (b) 8 SnSe SnSe Se SnSe Vac Vac (c) 8 SnSe SnSe SnSe SnSe (d) Se 8 SnSe SnSe Vac Vac (e) 8 SnSe SnSe SnSe (f) Se SnSe Se (g) SnSe Se SnSe (h) SnSe 7 Sn Se SnSe SnSe

5 Sn Sn (i) Se 8 SnSe SnSe Se (j) Se SnSe Se Se Sn Sn (k) SnSe SnSe Se Se (l) SnSe SnSe Se Se Vac (m) SnSe 7 Sn Se SnSe Se (n) SnSe SnSe SnSe SnSe (o) 7 Sn Se SnSe Se SnSe (p) SnSe SnSe Se SnSe FIG. S: HSE refinement of intrinsic defect formation energy diagrams of SnSe. The phase regions are indicated under the figures. The positively charged nterstitials ( ) act as hole killers near the VBM. has the highest formation energy at VBM (most favorable) in part (p) (i.e., SnSe SnSe Se SnSe region of the phase diagram) but still very low relatively