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Describe the optical response of semiconductors
The semiconductor Bloch equations (abbreviated as SBEs) describe the optical response of semiconductors excited by coherent classical light sources, such
Semiconductor_Bloch_equations
Photoexciation and similar effects
effects in semiconductors and semiconductor nanostructures. After an introduction into the basic principles, the semiconductor Bloch equations (abbreviated
Coherent effects in semiconductor optics
Coherent_effects_in_semiconductor_optics
Model of a quantum/optical system
equivalent to) the Bloch equations which describe the motion of the nuclear magnetic moment in an electromagnetic field. The equations can be derived either
Maxwell–Bloch_equations
Wannier equation considerably. The resulting generalized Wannier equation can be determined from the homogeneous part of the semiconductor Bloch equations or
Wannier_equation
Theory of laser diodes
semiconductor optical gain. Hartree Fock approximation: To describe an interacting carrier system at any density, the semiconductor Bloch equations (SBEs)
Semiconductor_laser_theory
Physical equations of light emission in semiconductors
The semiconductor luminescence equations (SLEs) describe luminescence of semiconductors resulting from spontaneous recombination of electronic excitations
Semiconductor luminescence equations
Semiconductor_luminescence_equations
How semiconductor lasers work
recent years, the microscopic many-body model based on the semiconductor Bloch equations (SBE) has been very successful. The model is based on the SBE
Semiconductor_optical_gain
Topics referred to by the same term
SBE may refer to: Sacred Books of the East Semiconductor Bloch equations Social, behavioral, environmental and medical sciences Society of Broadcast Engineers
SBE
German theoretical physicist
this approach, he was one of the key players to develop the semiconductor Bloch equations (abbreviated as SBEs). Ever since this breakthrough, the SBEs
Stephan_W._Koch
Phenomenon from solid state physics
Schmitt-Rink, S. (1992-09-15). "Optical investigation of Bloch oscillations in a semiconductor superlattice". Physical Review B. 46 (11): 7252–7255. Bibcode:1992PhRvB
Bloch_oscillation
Light emission from substances after they absorb photons
light excites a polarization that can be described with the semiconductor Bloch equations. Once the photons are absorbed, electrons and holes are formed
Photoluminescence
High-temperature expansion in statistical mechanics
applied in semiconductor quantum optics and it can be applied to generalize the semiconductor Bloch equations and semiconductor luminescence equations. Quantum
Cluster_expansion
Fundamental theorem in condensed matter physics
In condensed matter physics, Bloch's theorem states that solutions to the Schrödinger equation in a periodic potential can be expressed as plane waves
Bloch's_theorem
Route Bloch, at CERN (Meyrin site) Bloch Auditorium, Hewlett Teaching Center room 201, Stanford University Bloch Beamline at MAX IV Laboratory Bloch Fellowship
List of things named after Felix Bloch
List_of_things_named_after_Felix_Bloch
Formula for solid emission and absorption
microscopically using, e.g., the semiconductor Bloch equations (abbreviated as SBEs) or the semiconductor luminescence equations (abbreviated as SLEs). One
Elliott_formula
Optical filter
frequency as in equation (1.1.3). On the other hand, k0 in the equations above comes from the assumed Bloch wave solution given by equations (1.2.1) & (1
Frequency_selective_surface
Molecule investigation technique
for solid emission and absorption Semiconductor Bloch equations – Describe the optical response of semiconductors Terahertz nondestructive evaluation –
Terahertz_spectroscopy
Measure of a substance's ability to resist or conduct electric current
fields. This equation, along with the continuity equation for J and the Poisson's equation for E, form a set of partial differential equations. In special
Electrical resistivity and conductivity
Electrical_resistivity_and_conductivity
Periodic structure of layers of two or more materials
the band structure of the original bulk semiconductors. It is straightforward to solve 1D Schrödinger equations in each of the individual layers, whose
Superlattice
Generalization of laser spectroscopy in quantum optics
Photon antibunching Resonance fluorescence Semiconductor Bloch equations Semiconductor luminescence equations Ultrafast laser spectroscopy Kira, M.; Koch
Quantum-optical_spectroscopy
Conceptual opposite of an electron
leaves a net positive charge at the hole's location. Holes in a metal or semiconductor crystal lattice can move through the lattice as electrons can, and act
Electron_hole
Electronic states at the surface of materials
stated by Bloch's theorem, eigenstates of the single-electron Schrödinger equation with a perfectly periodic potential, a crystal, are Bloch waves Ψ n
Surface_states
Semi-analytic method of computational electromagnetism
solutions of periodic differential equations can be expanded with Floquet functions (or sometimes referred as a Bloch wave, especially in the solid-state
Rigorous coupled-wave analysis
Rigorous_coupled-wave_analysis
Solid-state physics model
same periodicity as the crystal lattice. Bloch's theorem proves that the solutions to this differential equation can be written as follows: ψ n , k ( x
K·p_perturbation_theory
Describes the range of energies of an electron within the solid
symmetry. The single-electron Schrödinger equation is solved for an electron in a lattice-periodic potential, giving Bloch electrons as solutions ψ n k ( r )
Electronic_band_structure
Law of electrical current and voltage
resulting in the free electron model. A year later, Felix Bloch showed that electrons move in waves (Bloch electrons) through a solid crystal lattice, so scattering
Ohm's_law
Mass of a particle when interacting with other particles
valence band in many semiconductors (Ge, Si, GaAs, ...), and the lowest energies of the conduction band in some semiconductors (GaAs, ...), the band
Effective mass (solid-state physics)
Effective_mass_(solid-state_physics)
Theory for waves passing through multiple obstacles
way. The MST equations can be derived with different wave equations, but one of the simplest and most useful ones is the Schrödinger equation for an electron
Multiple_scattering_theory
Branch of physics focused on matter in the solid state
the existence of conductors, semiconductors and insulators. The nearly free electron model rewrites the Schrödinger equation for the case of a periodic
Solid-state_physics
Boltzmann transport equation model has been the main tool used in the analysis of transport in semiconductors. The BTE equation is given by[citation
Monte Carlo methods for electron transport
Monte_Carlo_methods_for_electron_transport
State of matter
Devices made from semiconductor materials are the foundation of modern electronics, including radio, computers, telephones, etc. Semiconductor devices include
Solid
Physical model of non-interacting fermions
the crystal structure of metals and semiconductors, where electrons in a crystal lattice are substituted by Bloch electrons with a corresponding crystal
Fermi_gas
Branch of physics
Swiss physicist Felix Bloch provided a wave function solution to the Schrödinger equation with a periodic potential, known as Bloch's theorem. Calculating
Condensed_matter_physics
Number of available physical states per energy unit
electrons at the band edge between the valence and conduction bands in a semiconductor, for an electron in the conduction band, an increase of the electron
Density_of_states
Smooth curve outlining the extremes of an oscillating signal
eigenfunction for a mobile charge carrier in a crystal can be expressed as a Bloch wave: ψ n k ( r ) = e i k ⋅ r u n k ( r ) , {\displaystyle \psi _{n\mathbf
Envelope_(waves)
Transition rate formula
{\displaystyle |i\rangle } and | f ⟩ {\displaystyle |f\rangle } are the Bloch wavefunction of the initial and final states. Here the transition probability
Fermi's_golden_rule
Maximilian Bircher-Benner, invented modern muesli Felix Bloch, (nobel prize) discovered Bloch equations Johann Georg Bodmer Daniel Bovet (nobel prize), discovered
List of Swiss inventors and discoverers
List_of_Swiss_inventors_and_discoverers
State of matter
Peletminskii equations are valid for any finite temperatures below the critical point. Years after, in 1985, Kirkpatrick and Dorfman obtained similar equations using
Bose–Einstein_condensate
shallow potential, Bloch waves, as well as quantum tunneling, become of importance. The general solution of the above differential equation for a given value
Quantum_pendulum
Transfer of a bound electron to a more energetic state
by introducing Bloch waves into the Schrödinger equation with applying periodic boundary conditions. Solving this eigenvalue equation, one obtains sets
Electron_excitation
Quasiparticle form phonon and photon coupling
need the four Maxwell's equations in matter. Since, macroscopically, the crystal is uncharged and there is no current, the equations can be simplified. A
Phonon_polariton
Schrödinger equation with a one-electron periodic potential. The problem is further simplified with the use of group theory and in particular Bloch's theorem
Korringa–Kohn–Rostoker_method
Disordered magnetic state
by the de Almeida-Thouless curve, The curve is the solution set to the equations x 2 = 1 ( 2 π ) 1 / 2 ∫ d z e − 1 2 z 2 sech 4 ( q 1 / 2 z + y x )
Spin_glass
Early radio receiver component
sound in the earphones. It was the first type of semiconductor diode, and one of the first semiconductor electronic devices. The most common type was the
Crystal_detector
difference occurs because these states cannot be described with periodic Bloch waves due to the change in electron potential energy caused by the missing
Carrier_scattering
Theoretical model describing interacting fermions in a one-dimensional conductor
interactions. In 1963, J.M. Luttinger reformulated the theory in terms of Bloch sound waves and showed that the constraints proposed by Tomonaga were unnecessary
Luttinger_liquid
Quantum mechanical waves describing matter
1926, Schrödinger published the wave equation that now bears his name – the matter wave analogue of Maxwell's equations – and used it to derive the energy
Matter_wave
bother with a differential equation for a function already analytically obtained, but as will be demonstrated, this equation can also be generalized for
Path integrals in polymer science
Path_integrals_in_polymer_science
Form of magnetism
n\mu L\left({\frac {\mu _{0}H\mu }{k_{\text{B}}T}}\right)} In the above equations: n is the density of nanoparticles in the sample μ 0 {\textstyle \mu _{0}}
Superparamagnetism
Conglomeration of discrete solid, macroscopic particles
at the top of the silo z = 0 {\displaystyle z=0} . The given pressure equation does not account for boundary conditions, such as the ratio between the
Granular_material
Electromagnetic waves that travel along an interface
2}c}}} . A wave of this form satisfies Maxwell's equations only on condition that the following equations also hold: k z 1 ε 1 + k z 2 ε 2 = 0 {\displaystyle
Surface_plasmon_polariton
Periodic optical nanostructure that affects the motion of photons
X-ray diffraction and that the atomic lattices (crystal structure) of semiconductors affect their conductivity of electrons. Photonic crystals occur in nature
Photonic_crystal
American physicist (1931–2019)
After working out a theoretical problem of electrical conduction on semiconductor surfaces, Schrieffer spent a year in the laboratory, applying the theory
John_Robert_Schrieffer
State of matter of many bosons
longer support this many particles, at lower temperatures). The above equation can be solved for the critical temperature: T c = ( N ζ ( α ) ) 1 / α E
Bose_gas
Change in optical absorption by a semiconductor when an electric field is applied
The Franz–Keldysh effect is a change in optical absorption by a semiconductor when an electric field is applied. The effect is named after the German
Franz–Keldysh_effect
Effect in quantum electronics
{\displaystyle u(\mathbf {r} )} is a periodic Bloch function for the energy band edge in the bulk semiconductor and ϕ n ( z ) {\displaystyle \phi _{n}(z)}
Quantum-confined_Stark_effect
Study of classical optics using Fourier transforms
In the case of differential equations, as in the case of matrix equations, whenever the right-hand side of an equation is zero (For example, a forcing
Fourier_optics
Quasiparticle of mechanical vibrations
{\displaystyle j=1\dots N} . Substitution into the equation of motion produces the following decoupled equations (this requires a significant manipulation using
Phonon
Structure that repeats in time; a novel type or phase of non-equilibrium matter
when the lowest-energy state of a system is less symmetrical than the equations governing the system. In the crystal ground state, the continuous translational
Time_crystal
Quantum electromechanical process
electromagnetic field, the Heisenberg equation and Maxwell's equations can be used to find the resulting equations of motion for R k ^ ( t ) {\displaystyle
Resonance_fluorescence
Mathematical model in quantum mechanics
which are laser diodes consisting of one semiconductor “well” material sandwiched between two other semiconductor layers of different material . Because
Particle_in_a_box
Field of physics that studies polymers
that the equations governing the behavior of a polymer chain were independent of the chain chemistry. What is more, the governing equation turns out
Polymer_physics
Model of electrons within a metallic solid
electron models came in 1928, with Felix Bloch dissertation, under the supervision of Werner Heisenberg. Bloch's theorem introduced the electron wave behavior
Free_electron_model
Quasiparticle in condensed matter physics
materials. The electron mobility in semiconductors can be greatly decreased by the formation of polarons. Organic semiconductors are also sensitive to polaronic
Polaron
State of matter with properties of both conventional liquids and crystals
detect electrically generated hot spots for failure analysis in the semiconductor industry. Liquid crystal lenses converge or diverge the incident light
Liquid_crystal
Adages and sayings named after a person
an explicit formula for the solution of a system of linear equations with as many equations as unknowns, valid whenever the system has a unique solution
List of laws named after people
List_of_laws_named_after_people
Distortion of the periodic lattice of a one-dimensional crystal
Kronig–Penney model, which helps to explain the origin of band gaps in semiconductors). If the ions each contribute one electron, then the band will be half-filled
Peierls_transition
Proposed quantum computer implementation
point by a restoring force, with the motion described by a set of Mathieu equations. This saddle point is the point of minimized energy magnitude, | E ( x
Trapped-ion_quantum_computer
Physical model for semiconductors
is the Pauli spin matrix vector. Substituting into the Schrödinger equation in Bloch approximation we obtain H u n k ( r ) = ( H 0 + ℏ m 0 k ⋅ Π + ℏ 2
Luttinger–Kohn_model
non-physics disciplines dominate the prize in recent decades, followed by semiconductor physics and magnetics. 1901 1910 1920 1930 1940 1950 1960 1970 1980
List of Nobel laureates in Physics
List_of_Nobel_laureates_in_Physics
Medical imaging technique
{1}{T_{2}}}=R_{2}} . Magnetization as a function of time is defined by the Bloch equations. T1 and T2 values are dependent on the chemical environment of the
Magnetic_resonance_imaging
Experimental technique to determine the distribution of electrons in solids
solid. The band structure determines if a material is an insulator, a semiconductor, or a metal, how it conducts electricity and in which directions it
Angle-resolved photoemission spectroscopy
Angle-resolved_photoemission_spectroscopy
Subdiscipline of condensed matter physics
theoretically in order to advance understanding of the physics of insulators, semiconductors, metals, and superconductors. The applied science of mesoscopic physics
Mesoscopic_physics
Model of electronic band structures of solids
G. E. Horowitz, while the LCAO method for solids was developed by Felix Bloch, as part of his doctoral dissertation in 1928, concurrently with and independent
Tight_binding
Emission of electrons when electromagnetic radiation hits a material
Bibcode:1887AnP...267..421H. doi:10.1002/andp.18872670707. ISSN 0003-3804. Bloch, Eugene (1914). "Recent developments in electromagnetism". Annual Report
Photoelectric_effect
Physical structure guiding light waves
distribution (step or gradient index), and material (glass, polymer, semiconductor). The basic principles behind optical waveguides can be described using
Waveguide_(optics)
Special state of wave and quantum systems in physics
solutions at infinity, are widely known (atoms, quantum dots, defects in semiconductors). For solutions in a continuum that are associated with this continuum
Bound_state_in_the_continuum
nuclear submarine pioneer Admiral Hyman G. Rickover (1963), Nobel-winning semiconductor inventor William Shockley (1966), and Internet 'founding father' Leonard
Charles P. Steinmetz Memorial Lecture
Charles_P._Steinmetz_Memorial_Lecture
Change between conductive and non-conductive state
case of a semiconductor, doping. The basic distinction between metals and insulators was proposed by Hans Bethe, Arnold Sommerfeld and Felix Bloch in 1928-1929
Metal–insulator_transition
German-born British physicist (1907–1995)
on deriving a series of wave equations similar to the Schrödinger equation for photons. Unfortunately, their equations, while complicated, were nonsensical
Rudolf_Peierls
Hexagonal lattice made of carbon atoms
million in 2012, with most of the demand from research and development in semiconductors, electronics, electric batteries, and composites. In 2022, the graphene
Graphene
Quantum computing implementation
node of the circuit network to obtain the system's equations of motion. Finally, these equations of motion must be reformulated to Lagrangian mechanics
Superconducting quantum computing
Superconducting_quantum_computing
equations. It is usually referred to as Hamilton's principle; when the equations in the original form are used they are known as Lagrange's equations
History of electromagnetic theory
History_of_electromagnetic_theory
Quasiparticle of charge oscillations in condensed matter
oscillations, most of their properties can be derived directly from Maxwell's equations. Plasmons can be described in the classical picture as an oscillation
Plasmon
Loss of quantum coherence
pure states on the surface of the Bloch sphere to mixed states within the Bloch sphere. This would contract the Bloch sphere by some finite amount and
Quantum_decoherence
Physical process of transition between basic states of matter
1038/ncomms10102. PMC 4686770. PMID 26626302. Eds. Zhou, W., and Fan. S., Semiconductors and Semimetals. Vol 100. Photonic Crystal Metasurface Optoelectronics
Phase_transition
Type of quantum state
the phase difference between the two states. This is also known as the Bloch sphere picture. We can then define uncertainty relations such as Δ J z ⋅
Squeezed_coherent_state
Magnetic storage technology
Terry W. McDaniel (2018). "Application of Updated Landau–Lifshitz–Bloch Equations to Heat-Assisted Magnetic Recording". IEEE Trans. Magn. 54 (2): 3000611
Heat-assisted magnetic recording
Heat-assisted_magnetic_recording
Classic textbook in by Charles Kittel
The book covers a wide range of topics in solid state physics, including Bloch's theorem, crystals, magnetism, phonons, Fermi gases, magnetic resonance
Introduction to Solid State Physics
Introduction_to_Solid_State_Physics
Scientific field of study
could not be resolved with the constant speed predicted by Maxwell's equations of electromagnetism. This discrepancy was corrected by Einstein's theory
Physics
German research award
Dresden) 2005: Peter Becker – cell biology/biochemistry (LMU Munich) Immanuel Bloch – quantum optics (University of Mainz) Stefanie Dimmeler – molecular cardiology
Leibniz_Prize
difference method for the Navier–Stokes equations. 1958: Xie Xide publishes the first book on semiconductor theory in China and establishes modern institutes
Women_in_physics
Condensed matter system
the d × d {\displaystyle d\times d} -dimensional unit matrix. In all equations, implicit summation over a {\displaystyle a} and μ {\displaystyle \mu
Dirac_matter
Class of chemical substance
Press. ISBN 978-1-78326-328-8. Sumida K, Rogow DL, Mason JA, McDonald TM, Bloch ED, Herm ZR, Bae TH, Long JR (February 2012). "Carbon dioxide capture in
Metal–organic_framework
Extended physical object in string theory
shapes in algebraic terms and solves geometric problems using algebraic equations. On the other hand, the Fukaya category is constructed using symplectic
Brane
of view of the new quantum theory, using the equations of Schrödinger and others. The derived equations for the line intensities are a decided improvement
Timeline_of_quantum_mechanics
American theoretical physicist (1908–2002)
Conwell–Weisskopf theory, which describes the movement of electrons through semiconductors and led to a better understanding of integrated circuits, knowledge
Victor_Weisskopf
P. H. (1999-08-15). "Full-potential KKR calculations for metals and semiconductors". Physical Review B. 60 (8): 5202–5210. doi:10.1103/PhysRevB.60.5202
Coherent potential approximation
Coherent_potential_approximation
Computer hardware technology that uses quantum mechanics
classical electrodynamics. In these computers, components, such as semiconductors and random number generators, may rely on quantum behavior; however
Quantum_computing
Clerk Maxwell summarizes the fundamental equations of electromagnetism into an early version of Maxwell's equations and relates electromagnetism to light
Timeline of condensed matter physics
Timeline_of_condensed_matter_physics
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SEMICONDUCTOR BLOCH-EQUATIONS
SEMICONDUCTOR BLOCH-EQUATIONS
SEMICONDUCTOR BLOCH-EQUATIONS
SEMICONDUCTOR BLOCH-EQUATIONS
SEMICONDUCTOR BLOCH-EQUATIONS
SEMICONDUCTOR BLOCH-EQUATIONS
SEMICONDUCTOR BLOCH-EQUATIONS
SEMICONDUCTOR BLOCH-EQUATIONS
SEMICONDUCTOR BLOCH-EQUATIONS
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