1. Unusual band-gap and band-edge bowing of SnxGe1-x
尹万健，龚新高
Department of Physics, Fudan University, Shanghai, China
魏苏淮
National Renewable Energy Laboratory, Golden, Colarado

2. Introduction
SnxGe1-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 SnxGe1-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 SnxGe1-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.

3. Band gap bowing of SnxGe1-x
Experimental value for SnxGe1-x is large
Previous theoretical calculation find small bowing parameters

4. 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, (2008)]

5. Calculation methods Natural band offset calculation
Density functional method (VASP)
PW92 GGA
PAW pseudopotential
Alloy calculation
SQS-64
Natural band offset calculation
Sn’ Sn Ge
Ge’
Ge’
Sn’
VBM
Core level

6. 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, (2008)
G. He and H. A. Atwater, Phys. Rev. Lett. 79, 1937 (1997)
V. R. D’Costa et al, Phys. Rev. B 73, (2006)

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

8. Conclusions
(1) Our first-principles calculations revealed the mystery of the large band gap bowing of SnxGe1-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 SnxGe1-x.

9. Thanks for Your Attention!