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Quantity in solid state thermodynamics
The Fermi level of a solid-state body is the thermodynamic work required to add one electron to the body. It is a thermodynamic quantity usually denoted
Fermi_level
Highest particle energy in a Fermi gas at absolute zero
the Fermi level and Fermi energy, at least as they are used in this article: The Fermi energy is only defined at absolute zero, while the Fermi level is
Fermi_energy
Term used in quantum mechanics
A quasi Fermi level is a term used in quantum mechanics and especially in solid state physics for the Fermi level (chemical potential of electrons) that
Quasi_Fermi_level
Statistical description for the behavior of fermions
Fermi–Dirac statistics is a type of quantum statistics that applies to the physics of a system consisting of many non-interacting, identical particles
Fermi–Dirac_statistics
Abstract boundary in condensed matter physics
In condensed matter physics, the Fermi surface is the surface in reciprocal space which separates occupied electron states from unoccupied electron states
Fermi_surface
Type of electrical junction
referred to as "Fermi level pinning" caused some point of the band gap, at which finite DOS exists, to be locked (pinned) to the Fermi level. This made the
Metal–semiconductor_junction
Describes the range of energies of an electron within the solid
potential of electrons, or Fermi level (in semiconductor physics, this quantity is more often denoted EF). The Fermi level of a solid is directly related
Electronic_band_structure
Electron energy bands which determine the electrical conductivity of a material
physics, the valence band and conduction band are the bands closest to the Fermi level, and thus determine the electrical conductivity of the solid. In nonmetals
Valence_and_conduction_bands
Phenomenon observed in semiconductors
conduction band which pushes the Fermi level to higher energy. In the case of degenerate level of doping, the Fermi level lies inside the conduction band
Moss–Burstein_effect
Intentional introduction of impurities into an intrinsic semiconductor
denoted x. The Fermi level is also usually indicated in the diagram. Sometimes the intrinsic Fermi level, Ei, which is the Fermi level in the absence
Doping_(semiconductor)
Type of material
properties are all associated with having electrons available at the Fermi level, as opposed to nonmetallic materials which do not. Metals are typically
Metal
Type of field-effect transistor
Intrinsic level will start to cross the Fermi level and when the voltage reaches the threshold voltage, the intrinsic level does cross the Fermi level, and
MOSFET
Measure of a substance's ability to resist or conduct electric current
The characteristic energy level up to which the electrons have filled is called the Fermi level. The position of the Fermi level with respect to the band
Electrical resistivity and conductivity
Electrical_resistivity_and_conductivity
Diagram plotting electron energy levels
a band diagram is a diagram plotting various key electron energy levels (Fermi level and nearby energy band edges) as a function of some spatial dimension
Band_diagram
Potential energy barrier in metal–semiconductor junctions
n-type and its conduction band minimum (CBM) is higher in energy than the Fermi level of the metal, and when the semiconductor is p-type and its valence band
Schottky_barrier
Electromagnetic effect in physics
remains constant when the Fermi level is in a clean spectral gap, this situation corresponds to one where the Fermi level is an energy with a finite
Quantum_Hall_effect
Material of moderate electrical conductivity
states with energies near their Fermi level. Insulators, by contrast, have few partially filled states, their Fermi levels sit within band gaps with few
Semiconductor
Model of electrons within a metallic solid
Sommerfeld, who combined the classical Drude model with quantum mechanical Fermi–Dirac statistics and hence it is also known as the Drude–Sommerfeld model
Free_electron_model
How the term nonmetal is used in many disciplines
the energy levels of the electrons at the Fermi level. In contrast, a metal would have at least one partially occupied band at the Fermi level; in a semiconductor
Nonmetallic_material
Concept in condensed matter physics
e^{2}{\frac {\partial n}{\partial \mu }},} where μ is the chemical potential (Fermi level), n is the electron concentration and e is the elementary charge. For
Thomas–Fermi_screening
Semiconductor diode based upon the p–n junction
are short-circuited, the Fermi half-occupancy level (dashed horizontal straight line) is situated at a constant level. This level ensures that in the field-free
P–n_diode
Term in semiconductor electrochemistry
electrode. In solid junctions, we can take as a reference the metal Fermi level, if the work function is known, which provides a full energy diagram
Mott–Schottky_plot
Noncontact variant of atomic force microscopy
of the higher to the lower Fermi level. This electron flow causes the equilibration of the probe and sample Fermi levels. Furthermore, a surface charge
Kelvin_probe_force_microscope
Type of energy
electrostatic potential in the vacuum nearby the surface, and EF is the Fermi level (electrochemical potential of electrons) inside the material. The term
Work_function
Semiconductor-electrolyte junction potential
consequence of the condition that the redox Fermi level of the electrolyte must be equal to the Fermi level of the semiconductor and therefore preventing
Flat_band_potential
Energy release on formation of anions
analogy does not hold since an added electron will instead go to the Fermi level on average. In any case, the value of the electron affinity of a solid
Electron_affinity
Physical model of non-interacting fermions
A Fermi gas is an idealized model, an ensemble of many non-interacting fermions. Fermions are particles that obey Fermi–Dirac statistics, like electrons
Fermi_gas
Microscopic theory of superconductivity
key background to BCS theory as follows: Evidence of a band gap at the Fermi level (described as "a key piece in the puzzle") the existence of a critical
BCS_theory
Phenomenon involving the change of conductivity in metallic layers
random orientations. For good conductors such as gold or copper, the Fermi level lies within the sp band, and the d band is completely filled. In ferromagnets
Giant_magnetoresistance
Discrepancy of the lack of evidence for alien life despite its apparent likelihood
The Fermi paradox is the seeming inconsistency between the lack of evidence of extraterrestrial civilizations and the apparently high likelihood of their
Fermi_paradox
Metal with a small negative indirect band-gap
small density of states at the Fermi level. A metal, by contrast, has an appreciable density of states at the Fermi level because the conduction band is
Semimetal
Imaging Instrument
bring an electron from an occupied level, the highest of which is the Fermi level (for metals at T = 0 K), to vacuum level. The electrons can tunnel between
Scanning_tunneling_microscope
Emission of electrons induced by an electrostatic field
Fowler–Nordheim tunneling from electron states close to the emitter Fermi level. (By contrast, in the Schottky emission regime, most electrons escape
Field_electron_emission
Category of chemical elements
the energy levels of the electrons at the Fermi level. In contrast, a metal would have at least one partially occupied band at the Fermi level; in a semiconductor
Nonmetal
Entropy of a system attributable to electrons' probabilistic occupation of states
thermodynamics of condensed phases, where the density of states at the Fermi level can be quite large, and the electronic entropy can thus contribute substantially
Electronic_entropy
of only two atomic layers, exhibits complete spin polarization at the Fermi level, as demonstrated by momentum and spin-resolved photoelectron spectroscopy
Half-metal
Electrical engineering equation
between the quasi-Fermi level of the holes at the junction and that of the electrons at the junction, the drop of the quasi-Fermi level of the electrons
Shockley_diode_equation
Effect in field-effect transistors
causing the unique Fermi level to split into two distinct quasi-Fermi levels: E F p {\displaystyle E_{Fp}} : the quasi-Fermi level for holes, anchored
Body_effect
Experimental technique to determine the distribution of electrons in solids
material's Fermi level, which can be read off of an ARPES spectrum. The work function is the difference between the Fermi level and the vacuum level where
Angle-resolved photoemission spectroscopy
Angle-resolved_photoemission_spectroscopy
Quantum effect in some non-metals
and topological insulators. In these materials, at energies near the Fermi level, the valence band and conduction band take the shape of the upper and
Dirac_cone
Italian-American physicist (1901–1954)
Enrico Fermi (Italian: [enˈriːko ˈfermi]; 29 September 1901 – 28 November 1954) was an Italian and naturalized-American physicist, renowned for being the
Enrico_Fermi
Different states of quantum systems
energy levels in a crystal are the top of the valence band, the bottom of the conduction band, the Fermi level, the vacuum level, and the energy levels of
Energy_level
Repulsive force in quantum mechanics
degenerate energy levels, but to Fermi–Dirac statistics close to the zero-temperature limit (temperatures much lower than the Fermi temperature, which
Electron_degeneracy_pressure
Experiments used to map the Fermi surface
the Landau levels to pass over the Fermi surface, which in turn results in oscillations of the electronic density of states at the Fermi level; this produces
Quantum_oscillations
Physical phenomenon of electronic band structures
semiconductor Fermi level and increasing that of the metal. Under equilibrium the work function difference vanishes and the Fermi levels align across the
Band_bending
Phenomenon in solid-state physics of semiconductors
by the Fermi level and the temperature of the electrons. At absolute zero temperature, all of the electrons have energy below the Fermi level; but at
Carrier generation and recombination
Carrier_generation_and_recombination
Estimation problem in physics or engineering
A Fermi problem (or Fermi question, Fermi quiz), also known as an order-of-magnitude problem, is an estimation problem in physics or engineering education
Fermi_problem
Simple model of topological insulator
the bands do not touch, there is a band gap. If the gap lies at the Fermi level, then the system is considered to be an insulator. The tight binding
Su–Schrieffer–Heeger_model
Spectroscopic technique
is the binding energy of the electron measured relative to the sample Fermi level, Ephoton is the energy of the X-ray photons being used, Ekinetic is the
X-ray photoelectron spectroscopy
X-ray_photoelectron_spectroscopy
Fermi energy Fermi's four factor formula Fermi gas Fermi's interaction, an explanation of the beta decay Fermi level Fermi liquid theory Quasi Fermi level
List of things named after Enrico Fermi
List_of_things_named_after_Enrico_Fermi
State at which a Fermi surface has a partial energy gap in condensed matter physics
Nevill Mott in 1968 to indicate a minimum in the density of states at the Fermi level, N(EF), resulting from Coulomb repulsion between electrons in the same
Pseudogap
Change in energies of a thermodynamic system with respect to particle number
physics, the chemical potential of a system of electrons is known as the Fermi level. Particles tend to move from higher chemical potential to lower chemical
Chemical_potential
Applied electric field conductivity change
situation: below this Fermi level the states are more likely to be occupied, the conduction band moves closer to the Fermi level, indicating more electrons
Field_effect_(semiconductor)
Effect in electrochemistry
will flow from the metal with the higher Fermi level to the metal with the lower Fermi level until the Fermi levels in the two phases are equal. Once this
Volta_potential
Hamiltonian used in quantum physics
regimes that depend on the relationship of the impurity energy levels to the Fermi level E F {\displaystyle E_{\rm {F}}} : The empty orbital regime for
Anderson_impurity_model
low-dimensional materials or in metals that have high densities of states at the Fermi level N ( E F ) {\displaystyle N(E_{F})} . Other low-temperature ground states
Spin_density_wave
Semiconductor that has been doped
n-type silicon is phosphorus or arsenic. In an n-type semiconductor, the Fermi level is greater than that of the intrinsic semiconductor and lies closer to
Extrinsic_semiconductor
Phenomenon in condensed matter physics
surface. Without the field, the surface barrier seen by an escaping Fermi-level electron has height W equal to the local work-function. The electric
Schottky_effect
Type of electrical contact to semiconductors
electrons tends to pin the center of the band gap to the Fermi level, an effect known as Fermi level pinning. Thus, the heights of the Schottky barriers in
Ohmic_contact
Type of chemical bond in metals
three-dimensional k-space, the set of points of the highest filled levels (the Fermi surface) should therefore be a sphere. In the nearly-free model, box-like
Metallic_bonding
Variation of threshold voltage in polycrystalline silicon materials
forms an SiOx layer. Moreover, there remains a high probability for Fermi level pinning to occur. So the effect with doped poly is an undesired reduction
Polysilicon_depletion_effect
Mass of a particle when interacting with other particles
effect, etc.) are restricted to only probe motion for energies near the Fermi level. In two-dimensional electron gases, the cyclotron effective mass is defined
Effective mass (solid-state physics)
Effective_mass_(solid-state_physics)
Schottky barrier solar cell
built-in voltage (a p-n junction). Due to differing energy levels between the Fermi level of the metal and the conduction band of the semiconductor, an
Schottky_junction_solar_cell
GPU microarchitecture by Nvidia
receives support for Microsoft's rendering API Direct3D 12 feature_level 11. Fermi was followed by Kepler, and used alongside Kepler in the GeForce 600
Fermi_(microarchitecture)
Electrical action produced by a non-electrical source
often expressed as a difference in Fermi levels in the two solids when they are at charge neutrality, where the Fermi level (a name for the chemical potential
Electromotive_force
Superconductive behavior at temperatures much higher than absolute zero
increased Tc resulting from two separate bands being present at the Fermi level. In 1991 Hebard et al. discovered Fulleride superconductors, where alkali-metal
High-temperature superconductivity
High-temperature_superconductivity
Measure of voltage induced by change of temperature
field effect. In semiconductors at low levels of doping, transport only occurs far away from the Fermi level. At low doping in the conduction band (where
Seebeck_coefficient
Number of available physical states per energy unit
atom results in a half-filled top band; there are free electrons at the Fermi level resulting in a metal. On the other hand, an even number of electrons
Density_of_states
technique. As inverse photoemission probes the electronic states above the Fermi level of the system, it is a complementary technique to photoemission spectroscopy
Inverse photoemission spectroscopy
Inverse_photoemission_spectroscopy
Equation in solid-state physics
where Ec is the energy of the conduction band, EF is the energy of the Fermi level, kB is the Boltzmann constant, T is the absolute temperature in kelvins
Mass_action_law_(electronics)
equation, i.e. electrons are moving towards higher fermi level or holes are moving towards lower fermi level. This is unusual: For example, in a normal silicon
Anomalous_photovoltaic_effect
ferromagnetism. In the Stoner model, a high density of states at the Fermi level makes the nonmagnetic state unstable. In SP calculations of covalent
Colossal_magnetoresistance
Proposed superconducting material
Alexandru Georgescu at Indiana University did not find flat bands at Fermi level, concluding that they related to an unfavored high-symmetry structure
LK-99
Chemical element with atomic number 14 (Si)
its highest occupied energy levels (the valence band) and the lowest unoccupied ones (the conduction band). The Fermi level is about halfway between the
Silicon
Intensive physical property of substances
voltmeters. The electron electrochemical potential is also known as the Fermi level of solid-state physics. In generic terms, electrochemical potential is
Electrochemical_potential
must match that of an electron in the metal at the interface. Since the Fermi levels of the two materials must match at the interface, there exists gap states
Metal-induced_gap_states
Relativistic interaction in quantum physics
a relatively more important role if we zoom in to bands close to the Fermi level ( E F {\displaystyle E_{\text{F}}} ). The atomic L ⋅ S {\displaystyle
Spin–orbit_interaction
Type of X-ray absorption spectrometry requiring a synchrotron radiation facility
metals, the photoelectron is excited to the first unoccupied level above the Fermi level. Therefore, its mean free path in a pure single crystal at zero
X-ray absorption near edge structure
X-ray_absorption_near_edge_structure
Synchrotron radiation-based spectroscopy
by the transition to the lowest unoccupied states: the states at the Fermi level in metals giving a "rising edge" with an arc tangent shape; the bound
X-ray_absorption_spectroscopy
Proposed state of matter in semiconductors
system behaves like an ordinary insulator and does not conduct when the Fermi level resides in the band-gap. When the sheet of HgTe is varied and made thicker
Quantum_spin_Hall_effect
Direct conversion of temperature differences to electric voltage and vice versa
/ e {\displaystyle V=-\mu /e} , where μ {\displaystyle \mu } is the Fermi level. Peltier (1834). "Nouvelles expériences sur la caloricité des courants
Thermoelectric_effect
Nuclear shell model
In an odd, well-deformed nucleus, the single-particle levels are filled up to the Fermi level, and the odd particle's Ω and parity give the spin and
Nilsson_model
Mechanism of electrical conduction in disordered materials
{\displaystyle \textstyle {\mathcal {R}}} of some initial state at the Fermi level. For d {\displaystyle d} -dimensions, and under particular assumptions
Variable-range_hopping
Difference in electric potential between two points in space
negative of the difference of the electrochemical potential of electrons (Fermi level) divided by the electron charge and commonly referred to as the voltage
Voltage
Effect in semiconductor physics
its valence and conduction bands, which produces a phenomenon known as Fermi level pinning, causing, at its time, band bending and consequently the formation
Photo–Dember_effect
light of adequate wavelength to produce electric charge carriers. The Fermi level of an intrinsic semiconductor is exactly in the middle of the band gap
Organic photorefractive materials
Organic_photorefractive_materials
Screening phenomenon in metals
perturbations in a metallic or semiconductor system caused by a defect in the Fermi gas or Fermi liquid. Friedel oscillations are a quantum mechanical analog to electric
Friedel_oscillations
Smallest unit of a chemical element
electron orbitals across closely packed energy levels—the local density of the electronic states near the Fermi level. Because of the distances involved, both
Atom
Chemical reaction with gold
on the position of the d-band center such that a d-band closer to the Fermi level ( E F {\displaystyle E_{\mathrm {F} }} ) will result in stronger interaction
Heterogeneous_gold_catalysis
State of an immobilized atom in chemistry
difference in surface and bulk Fermi level causes surface band bending and the abundancy of surface states pins the Fermi level. For the compound semiconductor
Dangling_bond
Chemical element with atomic number 79 (Au)
relativistic interband energy between the top of the 5d band and the Fermi level in the half-filled 6s band, 2.4 eV, is close to the experimental value
Gold
Line integral of the electric field
quantity measured by a voltmeter is called electrochemical potential or fermi level, while the pure unadjusted electric potential, V, is sometimes called
Electric_potential
to align close to the interface. This is done to ensure that the Fermi energy level stays continuous throughout the two semiconductors. This alignment
Band_offset
there. The voltage measured is equal to the difference in the quasi Fermi levels of the majority carriers (electrons in the n-type portion and holes in
Theory_of_solar_cells
Statistical ensemble of particles in thermodynamic equilibrium
band edge ϵC plays the role of the vacuum energy level (replacing −qϕ), and µ is known as the Fermi level. Of course, the ionization energy and electron
Grand_canonical_ensemble
of the bands with energies close and approximately 10-15 eV below the Fermi level. These electrons are ejected from a solid when it is illuminated by monochromatic
Nano-ARPES
Form of diode
applied, the Fermi level in the cathode moves into the third band, and reflections of ballistic electrons starting around the Fermi level are minimized
Gunn_diode
Theories, models and concepts that go back to the quantum hypothesis of Max Planck
understood with quantum mechanics: As the confined state moves close to Fermi level, tunnel current increases. As it moves away, the current decreases. Quantum
Applications of quantum mechanics
Applications_of_quantum_mechanics
Weak, attractive magnetism possessed by most elements and some compounds
magnetic potential energy for spin-up and spin-down electrons. Since the Fermi level must be identical for both bands, this means that there will be a small
Paramagnetism
Thermodynamic potential used in statistical mechanics
University of Manchester. Retrieved 5 December 2016. Brachman, M. K. (1954). "Fermi Level, Chemical Potential, and Gibbs Free Energy". The Journal of Chemical
Grand_potential
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