http://nano-bio.ehu.es/files/articles/Gonze_CPC_2009_590.pdf

ABINIT: First-principles approach to material and nanosystem properties

(b) Write out the equations for the time dependence of ρ11, ρ22, ρ12 and ρ21 assuming that a light field interaction V = -μ12Ee iωt + c.c. couples only levels |1> and |2>, and that the excited levels exhibit spontaneous decay. (8 marks) (c) Under steady-state conditions, find the ratio of populations in states |2> and |3>. (3 marks) (d) Find the slowly varying amplitude ̃ ρ 12 of the polarization ρ12 = ̃ ρ 12e iωt . (6 marks) (e) In the limiting case that no decay is possible from intermediate level |3>, what is the ground state population ρ11(∞)? (2 marks) 2. (15 marks total) In a 2-level atom system subjected to a strong field, dressed states are created in the form |D1(n)> = sin θ |1,n> + cos θ |2,n-1> |D2(n)> = cos θ |1,n> sin θ |2,n-1>

The Quantum Theory of Light

Bound states in the continuum (BICs) are waves that remain localized even though they coexist with a continuous spectrum of radiating waves that can carry energy away. Their very existence defies conventional wisdom. Although BICs were first proposed in quantum mechanics, they are a general wave phenomenon and have since been identified in electromagnetic waves, acoustic waves in air, water waves and elastic waves in solids. These states have been studied in a wide range of material systems, such as piezoelectric materials, dielectric photonic crystals, optical waveguides and fibres, quantum dots, graphene and topological insulators. In this Review, we describe recent developments in this field with an emphasis on the physical mechanisms that lead to BICs across seemingly very different materials and types of waves. We also discuss experimental realizations, existing applications and directions for future work. The fascinating wave phenomenon of ‘bound states in the continuum’ spans different material and wave systems, including electron, electromagnetic and mechanical waves. In this Review, we focus on the common physical mechanisms underlying these bound states, whilst also discussing recent experimental realizations, current applications and future opportunities for research.

Bound states in the continuum

Light-Emitting Diodes. (Monographs in Electrical and Electronic Engineering.) By A. A. Bergh and P. J. Dean. Pp. viii+591. (Clarendon: Oxford; Oxford University: London, 1976.) £22.

/pdf/light-emitting-diodes-ubzde6g9qc.pdf

Light-emitting diodes

Two-dimensional (2D) materials, such as molybdenum disulfide (MoS2), have been shown to exhibit excellent electrical and optical properties. The semiconducting nature of MoS2 allows it to overcome the shortcomings of zero-bandgap graphene, while still sharing many of graphene’s advantages for electronic and optoelectronic applications. Discrete electronic and optoelectronic components, such as field-effect transistors, sensors, and photodetectors made from few-layer MoS2 show promising performance as potential substitute of Si in conventional electronics and of organic and amorphous Si semiconductors in ubiquitous systems and display applications. An important next step is the fabrication of fully integrated multistage circuits and logic building blocks on MoS2 to demonstrate its capability for complex digital logic and high-frequency ac applications. This paper demonstrates an inverter, a NAND gate, a static random access memory, and a five-stage ring oscillator based on a direct-coupled transistor logic...

/pdf/integrated-circuits-based-on-bilayer-mos2-transistors-4upkmi1qw5.pdf

Integrated Circuits Based on Bilayer MoS2 Transistors

Lasing is experimentally demonstrated in a direct bandgap GeSn alloy, grown directly onto Si(001). The authors observe a clear lasing threshold as well as linewidth narrowing at low temperatures.

/pdf/lasing-in-direct-bandgap-gesn-alloy-grown-on-si-515b98x7i8.pdf

Lasing in direct-bandgap GeSn alloy grown on Si

Please format your submission as a single PDF file according to the instructions in the syllabus and submit it on UBlearns before 11:59 pm on Sunday, April 6. 1. (17 points) A variational calculation of the ground state energy of the Hydrogen atom is discussed in Thijssen Section 3.2.2. Review this section and the lecture notes to understand the method. Write a code, or use the hydrogen codes, to do the Programming Exercise on page 36: Check 1 Fortunately, we again have an exact answer for the ground state energy: this should be equal to −0.5 hartree = 13.6058 eV, and, if your program contains no errors, you should find −0.499278 hartree, which is amazingly good if you realize that only four functions have been taken into account. Check 2 The soution of the eigenvalue problem not only yields the eigenvalues (energies) but also the eigenvectors. Use these to draw the variational ground state wave function and compare with the exact form ψ(r) = 2 a 3/2 0 e −r/a0. 2. (17 points) The Kronig-Penney model of a periodic potential in one dimension is discussed in Thijssen Problem 6.2 on pages 164-165. Write a code, or use the kronig-penney codes, also studied in PHY 410-505 last semester, to compute a plot a band structure diagram for the model.

Electronic structure of

The strong correlation between advancing the performance of Si microelectronics and their demand of low power consumption requires new ways of data communication. Photonic circuits on Si are already highly developed except for an eligible on-chip laser source integrated monolithically. The recent demonstration of an optically pumped waveguide laser made from the Si-congruent GeSn alloy, monolithical laser integration has taken a big step forward on the way to an all-inclusive nanophotonic platform in CMOS. We present group IV microdisk lasers with significant improvements in lasing temperature and lasing threshold compared to the previously reported nonundercut Fabry–Perot type lasers. Lasing is observed up to 130 K with optical excitation density threshold of 220 kW/cm2 at 50 K. Additionally the influence of strain relaxation on the band structure of undercut resonators is discussed and allows the proof of laser emission for a just direct Ge0.915Sn0.085 alloy where Γ and L valleys have the same energies....

/pdf/optically-pumped-gesn-microdisk-lasers-on-si-3ip1edabyn.pdf

Optically Pumped GeSn Microdisk Lasers on Si

Alloys of silicon (Si), germanium (Ge) and tin (Sn) are continuously attracting research attention as possible direct band gap semiconductors with prospective applications in optoelectronics. The direct gap property may be brought about by the alloy composition alone or combined with the influence of strain, when an alloy layer is grown on a virtual substrate of different compositions. In search for direct gap materials, the electronic structure of relaxed or strained Ge1−xSnx and Si1−xSnx alloys, and of strained Ge grown on relaxed Ge1−x−ySixSny, was calculated by the self-consistent pseudo-potential plane wave method, within the mixed-atom supercell model of alloys, which was found to offer a much better accuracy than the virtual crystal approximation. Expressions are given for the direct and indirect band gaps in relaxed Ge1−xSnx, strained Ge grown on relaxed SixGe1−x−ySny and strained Ge1−xSnx grown on a relaxed Ge1−ySny substrate, and these constitute the criteria for achieving a (finite) direct band gap semiconductor. Roughly speaking, good-size (up to ~0.5 eV) direct gap materials are achievable by subjecting Ge or Ge1−xSnx alloy layers to an intermediately large tensile strain, but not excessive because this would result in a small or zero direct gap (detailed criteria are given in the text). Unstrained Ge1−xSnx bulk becomes a direct gap material for Sn content of >17%, but offers only smaller values of the direct gap, typically ≤0.2 eV. On the other hand, relaxed SnxSi1−x alloys do not show a finite direct band gap.

/pdf/band-structure-calculations-of-si-ge-sn-alloys-achieving-6nvmt4zlyt.pdf

Band structure calculations of Si Ge Sn alloys: achieving direct band gap materials

Using empirical pseudopotential theory, the direct (Γ) and indirect bandgaps (L and X) of unstrained crystalline SixGe1−x−ySny have been calculated over the entire xy composition range. The results are presented as energy-contour maps on ternary diagrams along with a ternary plot of the predicted lattice parameters. A group of 0.2 to 0.6 eV direct-gap SiGeSn materials is found for a variety of mid-infrared photonic applications. A set of “slightly indirect” SiGeSn alloys having a direct gap at 0.8 eV (but with a smaller L-Γ separation than in Ge) have been identified. These materials will function like Ge in various telecom photonic devices. Hetero-layered SiGeSn structures are described for infrared light emitters, amplifiers, photodetectors, and modulators (free carrier or Franz-Keldysh). We have examined in detail the optimized design space for mid-infrared SiGeSn-based multiple-quantum-well laser diodes, amplifiers, photodetectors, and quantum-confined Stark effect modulators.

Zoran Ikonic

Papers

Lasing in direct-bandgap GeSn alloy grown on Si

Electronic structure of

Optically Pumped GeSn Microdisk Lasers on Si

Band structure calculations of Si Ge Sn alloys: achieving direct band gap materials

The direct and indirect bandgaps of unstrained SixGe1−x−ySny and their photonic device applications