1. Combining indirect-gap materials (Si,Ge) to yield a direct-gap structure: a combinatorially impossible proposition ? Alex Zunger Mayeul d’ Avezac, Jun-Wei Luo National Renewable Energy Laboratory Funded by: Office of Science,Energy Frontier Research Center on Inverse Design

2. A single system with all needed knobs…. Strained,alloyed, ( nano) superlattice A single system with all needed knobs…. Strained,alloyed, ( nano) superlattice Substrate: [001] Si x Ge 1-x Si GeGe Alloying Strain Artificial Periodicity Inner Motif Hybridization:

3. Objective: Find Superlattice which folds the Bands and engineers wavefunctions Objective: Find Superlattice which folds the Bands and engineers wavefunctions Single repeat motifs already explored Si n Ge m /Si n Ge m How about allowing each segment to differ ? Si n 0 Ge m 0 /.../Si n N Ge m N There are 2 N such motifs: Need search method.

4. Inverse Band Design Method Semi-empirical pseudo-potential hamiltonian Optical “strength” from dipole matrix elements: Search with Bitstring Genetic Algorithm Each bit is an atomic-monolayer. Enumerate [001] substrate lattice constants between Si and Ge Enumerate number of monolayers: N=10, 20

5. Genetic Search of Superlattices += 1. Create Population of superlattices. 2. Breed best superlattices. 3. Remove unfit superlattices (small dipole moment) Add newly generated offspring.

6. A Magic Sequence: SiGe 2 Si 2 Ge 2 Si 2 Ge n Active Pattern Ge buffer Wavevector Direct:

7. SiGe 2 Si 2 Ge 2 Si 2 Ge n Active Pattern Ge buffer Optical transition at threshhold:

8. Superlattice switches to direct past a critical substrate lattice constant ( 60 % Ge) Superlattice switches to direct past a critical substrate lattice constant ( 60 % Ge) Active Pattern Ge buffer

9. Origin of the transition in k -space Active Pattern Ge buffer Significant Hybridization V. Weak Hybridization No Hybridization Γ X

10. Origin of the transition in r -space Active Pattern Ge buffer

11. Wave-vector Direct Superlattice. Active Pattern Ge buffer