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The Application and Calculation of Bond Orbital Model on Quantum Semiconductor

The Application and Calculation of Bond Orbital Model on Quantum Semiconductor. 鍵結軌道理論在量子半導體之應用與計算. Introduction. Why is the choosing the BOM?. a hybrid or link between the k.p and the tight-binding methods combining the virtues of the two above approaches

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The Application and Calculation of Bond Orbital Model on Quantum Semiconductor

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  1. The Application and Calculation of Bond Orbital Model on Quantum Semiconductor 鍵結軌道理論在量子半導體之應用與計算

  2. Introduction

  3. Why is the choosing the BOM? • a hybrid or link between the k.p and the tight-binding methods • combining the virtues of the two above approaches --the computational effort is comparable to the k.p method --avoiding the tedious fitting procedure like the tight-binding method --it is adequate for ultra-thin superlattice --the boundary condition between materials is treated in the straight-forward manner --its flexibility to accommodate otherwise awkward geometries

  4. The improvement of the bond orbital model (BOM): • the (hkl)-oriented BOM Hamiltonian • the BOM Hamiltonian with the second-neighbor interaction • the BOM in the antibonding orbital framework • the BOM with microscopic interface perturbation (MBOM) • the k.p formalism from the BOM

  5. Bond Orbital Model

  6. What is the bond orbital model? • a tight-binding-like framework with the s- and p-like basis orbital • the interaction parameters directly related to the Luttinger parameters

  7. Zinc-blende Lattice Structure:

  8. The BOM matrix elements: where ：The interaction parameters Es and Ep: on-site parametersEss, Esx, Exx, Exy, and Ezz: the nearest-neighbor interaction parameters

  9. H(k)= where with The BOM matrix:

  10. - H(k)= - - where and Taking Taylor-expansion on the BOM matrix:(up to the second order)

  11. /3 Relations between BOM parameters and Luttinger parameters

  12. Bulk Bandstructure:(001)-orientation

  13. Superlattice Bandstructure:(001)-orientation

  14. The orthogonal transformation matrix: where the angles and are the polar and azimuthal angles of the new growth axis relative to the primary crystallographic axes.

  15. Bulk InAs Bandstructure:(111), (110), (112), (113), and (115)-orientation

  16. InAs/GaSb Superlattice Bandstructure:(111), (110), (112), (113), and (115)-orientation

  17. H(k)= Where and The second-neighbor bond orbital (SBO) model:

  18. Bulk Bandstructure:With the Second Nearest Neighbor Interaction:

  19. Bulk Bandstructure in the Antibonding Orbital Model:

  20. Bond Orbital Model with Microscopic Effects

  21. For the common atom (CA) heterostructure eg: (AlGa)As/GaAs, InAs/GaAs • For the no common atom (NCA) heterostructure eg:InAs/GaSb, (InGa)/As/InP --InAs/GaSb with In-Sb and Ga-As heterobonds at the interfaces --(InGa)As/InP with (InGa)-P and In-As heterobonds at the interfaces

  22. The (001) InAs/GaSb superlattice： the planes of atoms are stacked in the growth direction as follows ．．．Ga Sb Ga Sb In As In As．．．． for the one interface; and ．．．In As In As Ga Sb Ga Sb．．．． for the next interface.

  23. = ( + - - ), = ( + + + ), = ( - + - ), = ( - - + ), (R) + ), The extracting of microscopic information: • the s- and p-like bond orbitals expanded in terms of the tetrahedral (anti)bonding orbitals and • instead of scalar potential by potential operator ~this is the so-called modified bond orbital model (MBOM) ~

  24. V4X4(Rz)=V+ 0 0 0 0 0 0 0 0 0 0 The potential term of the MBOM: • a potential matrix form, but not a scalar potential V

  25. InAs/GaSb Superlattice Bandstructure:(calculated with the BOM and MBOM)

  26. Orientation Dependence of Interface Inversion Asymmetry Effect on InGaAs/InP Quantum Wells

  27. Inversion asymmetry effect: • the microscopic crystal structure: Dresselhaus effect • the macroscopic confining potential: Rashba effect • the inversion asymmetry between two interfaces: NCA heterostructures --the zero-field spin splitting --in-plane anisotropy

  28. The 73-Å-wide (25 monolayers) (001) InGaAs/InP QW: • A and • the planes of atoms are stacked in the growth direction as follows: M+1 C D C D C D AB A B A B  Mfor the (InGa)P-like interface; andN+1 A B A B A B CD C D C D  Nfor the InAs-like interface, where A=(InGa), B=As, C=In, and D=P. The Mth (or Nth) monolayer is located at the left (or right) interface, where N=M+25.

  29. 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Where Rz is the z component of lattice site r, i.e., R=R//+RzŽ, and also the U (for the conduction band) and the V (for the valence band) denote the difference of potential energy between the heterobond species and the host material at the interfaces.

  30. (001) InGaAs/InP Quantum Well Bandstructure:(calculated with the BOM and MBOM)

  31. Spin Splitting of the Lowest Conduction Subband:((001) InGaAs/InP Quantum Well)

  32. When the in-plane wave vector moves around the circle ( =0 2 ), the mixing elements in Eq. (4.2) should be strictly written as for the (3,5) and (4,6) matrix elements and for the (5,3) and (6,4) matrix elements. Therefore, the mixing strength depends on the azimuthal angle Moreover, the and terms equal to –1 for or and 1 for or .

  33. The 71-Å-wide (21 monolayers) (111) InGaAs/InP QW: • The same order of atomic planes as the (001) QW • A and

  34. 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 • the heterobonds in the [111] growth direction: • the heterobonds are the remaining three bonds other than the bond along the [111] direction:

  35. (111) InGaAs/InP Quantum Well Bandstructure:(calculated with the BOM and MBOM)

  36. Spin Splitting of the Lowest Conduction Subband:((111) InGaAs/InP Quantum Well)

  37. The 73-Å-wide (35 monolayers) (110) InGaAs/InP QW: • = + + + =- + + - =- +and = - • across perfect (110) interfaces, planes of atoms are arranged in the order of: M+1 D C D C B A B A   C D C D AB A B  Mfor the left interface and N A B A B C D C D   B A B A D C D C  N+1for the right interface, where N=M+35

  38. 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 where the upper sign is used for the Mth and Nth monolayer, and the lower sign is used for the (M+1)th and (N+1)th monolayer.

  39. (110) InGaAs/InP Quantum Well Bandstructure:(calculated with the BOM and MBOM)

  40. Spin Splitting of the Lowest Conduction Subband: ((110) InGaAs/InP Quantum Well)

  41. Dresselhaus-like Spin Splitting

  42. The degeneracy bands of the zinc-blends bulk are lifted except for the wave vector along the <001> and <111> directions, and this is the so-called Dresselhaus effect. • Dresselhaus effect:

  43. Subband Structure of (110) InAs/GaSb Superlattice:(calculated with the BOM and MBOM)

  44. MBOM Bandstructure of InAs/GaSb Superlattice(grown on the (001), (111), (113), and (115)-orientation)

  45. Microscopic Interface Effect on (Anti)crossing Behavior and Semiconductor-semimetal Transition in InAs/GaSb Superlattices

  46. This MBOM model is based on the framework of the bond orbital model (BOM) and combines the concept of the heuristic Hbf model to include the microscopic interface effect. The MBOM provides the direct insight into the microscopic symmetry of the crystal chemical bonds in the vicinity of the heterostructure interfaces. Moreover, the MBOM can easily calculate various growth directions of heterostructures to explore the influence of interface perturbation. • In this chapter, by applying the proposed MBOM, we will calculate and discuss the (anti)crossing behavior and the semiconductor to semimetal transition on InAs/GaSb SLs grown on the (001)-, (111)-, and (110)-oriented substrates. The effect of interface perturbation on InAs/GaSb will be studied in detail.

  47. (Anti)crossing Behavior of InAs/GaSb Superlattice

  48. (001) Semimetal Phenomenon:(calculated with the BOM and MBOM)

  49. (111) Semimetal Phenomenon:(calculated with the BOM and MBOM)

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