Unusual bandgap and bandedge bowing of Snx Ge

Unusual band-gap and band-edge bowing of Snx. Ge 1 -x 尹万健，龚新高 Department of Physics, Fudan University, Shanghai, China 魏苏淮 National Renewable Energy Laboratory, Golden, Colarado

Introduction • Snx. Ge 1 -x is the only direct band-gap material composed entirely of group IV elements. • Adding Sn in Ge can enhance both electron and hole mobility, making Snx. Ge 1 -x a promising material for device applications. • Despite extensive study in this system, there are still many unanswered questions – What is the origin of the unusually large band gap bowing of the Snx. Ge 1 -x alloy. – What is the individual contribution of the VBM and CBM states to the bowing. Can it be described by the band-edge distribution rule.

Band gap bowing of Snx. Ge 1 -x • Experimental value for Snx. Ge 1 -x is large • Previous theoretical calculation find small bowing parameters

Band Anticrossing Model Sn defect level Isovalent Sn defect level couples with bulk Ge VBM lead to large VBM bowing Band edge distribution rule • Can the band gap bowing be described by the BAC model? • Is it true that in this system VBM bowing is larger than CBM bowing? • Is it consistent with the band edge distribution rule? [K. Alberi et al, Phys. Rev. B 77, 073202(2008)]

Calculation methods • Density functional method (VASP) • PW 92 GGA • PAW pseudopotential Alloy calculation SQS-64 Natural band offset calculation Ge VBM Core level Ge’ Sn’ Sn

Band gap bowing Agreement with Exp. Bowing is composition Independent Indirect to direct transition occurs at x=0. 063 W. -J. Yin, X. -G. Gong and S. -H. Wei, Phys. Rev. B 78, 161203 (2008) G. He and H. A. Atwater, Phys. Rev. Lett. 79, 1937 (1997) V. R. D’Costa et al, Phys. Rev. B 73, 125207 (2006)

Band edge distribution Band edge bowing: The CBM bowing is much larger than VBM bowing although DEVBM > DECBM Why does band edge distribution rule large lattice mismatch large deformation potential of band edge levels (a)Natural band offset at their respective lattice constants (b)Band offset at alloy lattice constant break down

Conclusions (1) Our first-principles calculations revealed the mystery of the large band gap bowing of Snx. Ge 1 -x, showing that it is induced by the disordering effect. (2) The band offset of Ge, Sn and their alloys are determined by considering the absolute deformation potential of core levels. (3) We have determined the individual contributions of VBM/CBM states to band-gap bowing. (4) We show that the conventional band-edge distribution rule is invalid for system with large lattice mismatch and large deformation potential of band edge levels such as the Snx. Ge 1 -x.

Thanks for Your Attention!