V. Yazdanpanah Tel: 575-7660, Office: Phys129 Email: yazdan@uark

1. Nanostructure Modeling Superlattice Structure Modeling V. Yazdanpanah Tel: 575-7660, Office: Phys129 Email: yazdan@uark.edu

2. Nanostructure Modeling • Course Content: • Questions and solutions in modeling. • Introduction to Mathematica programming. • Different Theoretical methods for nanostructure modeling. • Quantum well (QW) superlattice structure modeling and analyzing the results. • The Empirical Tight Binding Method (ETBM). • Quantum well superlattice energy band modeling and analyzing the results. • Advanced superlattice structure modeling.

3. HOW TO START MODELING? • Superlattice Constant • Superlattice Period • Superlattice Mismatch

4. Structure of III-V Bulk Semiconductors

5. c a b b g a Seven Crystal Systems Simple Cubic (SC) Seven Crystal Systems: Cubic: a=b=c, α=β=γ=90 Tetragonal: a=bc, α=β=γ=90 Orthorhombic: abc, α=β=γ=90 Rhombohedra: abc, α=β=γ90 Hexagonal: a=bc, α=β=90, γ=120 Monoclinic: abc, α=γ=90β Triclinic: abc, αβγ90 Simple Tetragonal (ST) Simple Orthorhombic (SO)

6. Crystalline Parameters Bravais Lattice: An infinite arrays of discrete points with an arrangement and orientations that appears exactly the same, from whichever of the points the array is viewed. Unite Cell: A region that just fills space without any overlapping when translated through some subset of the vectors of a Bravais lattice. Lattice Constant: The “cube” edge of a unite cell.

7. Crystalline Structure of III-V Bulk Semiconductors • There are two basic crystal structure for III-V bulk material: • Wurtzite Structure. • Zinc Blend Structure. • A. Wurtzite Structure • Consists of two hexagonal close-packed (hcp) • The Bravais lattice is hexagonal • The common structure for Nitrides semiconductors such as AlN, GaN,and InN.

8. z y x Zinc Blend Structure for Bulk Semiconductors • B. Zinc Blend • Zinc Blend is the structure of semiconductor compound which consist of group III:Al, Ga, and In and group V: P, As, and Sb. • The Lattice is two face-centered cubic (fcc) together • The basis consist of two different atoms displaced from each other by a quarter of the cube body diagonal.

9. A F ΔL E= Young’s Modulus F= The Force (N) A= The Cross-Sectional Area (m2) L= The Natural Length (m) Stress, Strain, and Young’s Modulus Stress is the force (F) normalized by the cross-sectional area (A) of the material. σ=F/A L Strain is the change in length of the fiber normalized by the initial length. ε=ΔL/L

10. εII= In Plain Strain ε= Strain in Growth Direction aII= In Plain Lattice Constant (Å) a= Lattice Constant in Growth Direction (Å) ai= Bulk Lattice Constant of Material “i” (Å) Cij= Elastic Constant All in Van De Walle Notation Strain in SLS

11. The Residual Net Strain Lattice Constants in Hetroepytaxy Growth Gi= Shear Modulus (Å-1) hi= The Respective Thickness (Å) aII= In Plan Lattice Constant (Å)

12. Strain Parameters Binary, Ternary and Quaternary Lattice Constants x = Composition of a given Material y = Composition of a given Material n = The nth layer

13. 120o c a c a c a a c Position of Atoms in Bulk Material z y a c x The unit cell for bulk zinc-blende crystal and their nearest neighbors. “a” denotes anion, “c” denotes cation.

14. c a c a Strained c a a c Non-Strained and Strained Radial Position of Atoms in Bulk Material a c Non Strained

15. Angular Position of Atoms The angles between τ1 and X, Y, Z axes.

16. Superlattice Structure

17. y 3D As As As As Sb Sb As As As Sb Sb y In In Ga Ga As As Sb Sb As As x Sb As As Sb Sb In In In In x As As Sb Sb As As In As As In In Sb Sb In In As As Sb Sb As As Ga Ga Origin Origin In In As As Sb Sb Ga As As Sb Sb Origin Origin Ga Ga In In In In In In z As As Sb Sb As As In In In In τn z In In As As Sb Sb As As Sb Sb In In Ga Ga As As Sb Sb As As As As Sb Sb In In In In One Superlattice Period of [-(InAs)2-InSb-(GaSb)1-InSb-]N As As Sb Sb As As As As In In Sb Sb In In As As As As Sb Sb Ga Ga In In As As Sb Sb As As Sb Sb As As 2D IF2 IF1 IF1 Transition form GaSb to InAs IF2  Transition form InAs to GaSb [-(InAs)1-InSb-(GaSb)2-]N Superlattice Period The Symmetry is Simple Tetragonal (ST)

18. Orthorhombic Symmetry Tetragonal Symmetry IF2 InSb IF2 GaAs GaAs InSb As Sb In IF1 InSb IF1 InSb Ga Tetragonal Symmetry Orthorhombic Symmetry Two Symmetry Systems in Type II SLS General Combination of Two Interfaces

19. Superlattice Parameters The Parameter for Non Segregated Case With InSb Interfaces: m = Layers of InAs (ML) n = Layers of GaSb (ML) MSL= Superlattice Mismatch

20. References • Solid State Physics, Neil W. Ashcroft, N. David Mermin. • Fundamentals of Solid State Engineering, Manijeh Razeghi. • Type II InAs/GaSb Superlattices For Infrared Detectors, Dissertation, H. Mohseni. • Type II InAs/GaSb Superlattice Photodiodes and Infrared Focal Plan Arrays, Dissertation, Y. Wei. • http://www.chemicool.com/definition/spin_orbit_coupling.html • http://hyperphysics.phy-astr.gsu.edu/hbase/permot3.html • JAP, 89, 5815. (For Band Structure) • PRB, 39,1871. and, PRB,61,10782. • Superlattices and Microstructures, 27, 519 • Semiconductor Devices an Introduction, Jasprit Singh, 1994. • http://www.ioffe.rssi.ru/SVA/NSM/Semicond/

21. Supporting Slides