The Brus equation or confinement energy equation can be used to describe the
emission energy of
quantum dot
Quantum dots (QDs) or semiconductor nanocrystals are semiconductor particles a few nanometres in size with optical and electronic properties that differ from those of larger particles via quantum mechanical effects. They are a central topic i ...
semiconductor
A semiconductor is a material with electrical conductivity between that of a conductor and an insulator. Its conductivity can be modified by adding impurities (" doping") to its crystal structure. When two regions with different doping level ...
nanocrystal
A nanocrystalline (NC) material is a polycrystalline material with a crystallite size of only a few nanometers. These materials fill the gap between amorphous materials without any long range order and conventional coarse-grained materials. De ...
s in terms of the
band gap energy
In solid-state physics and solid-state chemistry, a band gap, also called a bandgap or energy gap, is an energy range in a solid where no electronic states exist. In graphs of the electronic band structure of solids, the band gap refers to the ...
''E''
gap, the
Planck constant
The Planck constant, or Planck's constant, denoted by h, is a fundamental physical constant of foundational importance in quantum mechanics: a photon's energy is equal to its frequency multiplied by the Planck constant, and the wavelength of a ...
''h'', the radius of the quantum dot ''r'', as well as the effective mass of the
excited electron ''m''
e* and of the
excited hole ''m''
h*. The equation was named after
Louis E. Brus who independently discovered it.
The radius of the quantum dot affects the wavelength of the emitted light due to
quantum confinement
A potential well is the region surrounding a local minimum of potential energy. Energy captured in a potential well is unable to convert to another type of energy (kinetic energy in the case of a gravitational potential well) because it is captu ...
, and this equation describes the effect of changing the radius of the quantum dot on the
wavelength
In physics and mathematics, wavelength or spatial period of a wave or periodic function is the distance over which the wave's shape repeats.
In other words, it is the distance between consecutive corresponding points of the same ''phase (waves ...
''λ'' of the emitted light (and thereby on the emission energy , where ''c'' is the
speed of light
The speed of light in vacuum, commonly denoted , is a universal physical constant exactly equal to ). It is exact because, by international agreement, a metre is defined as the length of the path travelled by light in vacuum during a time i ...
). This is useful for calculating the radius of a quantum dot from experimentally determined parameters.
The overall equation is
:
''E''
gap, ''m''
e*, and ''m''
h* are unique for each nanocrystal composition.
For example, with
cadmium selenide
Cadmium selenide is an inorganic compound with the formula Cd Se. It is a black to red-black solid that is classified as a II-VI semiconductor of the n-type. It is a pigment, but applications are declining because of environmental concerns.
...
(CdSe) nanocrystals:
: ''E''
gap (CdSe) = = ,
: ''m''
e* (CdSe) = 0.13
''m''e = ,
: ''m''
h* (CdSe) = 0.45 ''m''
e = .
References
{{reflist
Quantum dots
Nanoparticles
Quantum electronics