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Coulomb Forces in Excitonic Solar Cells
Published in Sun Sam-Shajing, Sariciftci Niyazi Serdar, Organic Photovoltaics, 2017
The other primary difference is the small Bohr radius of carriers, rB, in XSCs compared to CSCs. For a hydrogen atom in its ground state, the Bohr radius, r0 = 0.53Å, is the average distance between the electron wavefunction and the positively charged nucleus. In a semiconductor with hydrogen-like wavefunctions (such as silicon), the Bohr radius of the lowest electronic state is [8] rB=r0ε(me/meff) where me is the mass of a free electron in vacuum and meff is the effective mass of the electron in the semiconductor (usually less than me in ISCs but greater than me in OSCs). The effective mass decreases as the carrier becomes more delocalized and its transport becomes more wave-like. Thus increasing ε and decreasing meff lead to a greater average distance between the charges.
Tools For Analysis
Published in James J Y Hsu, Nanocomputing, 2017
The order of magnitude analysis is an important process for sorting out physically related effects. Scientists and physicists in particular, are often concerned about the order of magnitude of a property, to gain relevant insight for a particular effect as measured by the said quantity. Suppose one is interested in altering the energy band gap of a carbon nano tube so as to change its electronic or optical properties. One obvious way is by applying an external electric field; but how much? The estimate is straightforward. The ionization energy or the energy band gap of a single atom is around a few eVs, while its size is on the order of a Bohr radius, which is about 0.5 Å. Thus, it implies that the internal electric field as experienced by the electrons would be around 100MV/cm. To alter the electron states of such will require an electrostatic field near this kind of magnitude, namely, 10V/nm. The mere order of magnitude estimate could accurately point out the underlying principles to rule in or rule out a conjecture. We are often quite satisfied with order of magnitude descriptions to gain insight into scientific inquiries. For example, as quoted from the book of Biology by Campbell, Reece and Mitchell,“Earth formed about 4.5 billion years ago, and life probably began only a few hundred million years later.”“Biologists have identified and named about 1.5 million species, including over 260,000 plants, almost 50,000 vertebrates and more than 750,000 insects.”“In the continuum of life spanning over 3.5 billion years, humans and apes have shared ancestry for all but the last few million years.”
Symbols, Terminology, and Nomenclature
Published in W. M. Haynes, David R. Lide, Thomas J. Bruno, CRC Handbook of Chemistry and Physics, 2016
W. M. Haynes, David R. Lide, Thomas J. Bruno
where is the wavelength, h is Planck's constant, c is the speed of light, k is the Boltzmann constant, and T is the temperature. Black hole - A very dense object, formed in a supernova explosion, whose gravitational field is so large that no matter or radiation can escape from the object. Bloch wave function - A solution of the Schrödinger equation for an electron moving in a spatially periodic potential; used in the band theory of solids. Bohr magneton (µB)* - The atomic unit of magnetic moment, defined as eh/4me, where h is Planck's constant, me the electron mass, and e the elementary charge. It is the moment associated with a single electron spin. Bohr, bohr radius (a0)* - The radius of the lowest orbit in the Bohr model of the hydrogen atom, defined as oh2/mee2, where o is the permittivity of a vacuum, h is Planck's constant, me the electron mass, and e the elementary charge. It is customarily taken as the unit of length when using atomic units. Boiling point - The temperature at which the liquid and gas phases of a substance are in equilibrium at a specified pressure. The normal boiling point is the boiling point at normal atmospheric pressure (101.325 kPa). Boltzmann constant (k)* - The molar gas constant R divided by Avogadro's constant. Boltzmann distribution - An expression for the equilibrium distribution of molecules as a function of their energy, in which the number of molecules in a state of energy E is proportional to exp(-E/kT), where k is the Boltzmann constant and T is the temperature. Bond strength - See Dissociation energy. Born-Haber cycle* - A thermodynamic cycle in which a crystalline solid is converted to gaseous ions and then reconverted to the solid. The cycle permits calculation of the lattice energy of the crystal. Bose-Einstein distribution - A modification of the Boltzmann distribution which applies to a system of particles that are bosons. The number of particles of energy E is proportional to [e(E-µ)/kT-1]-1 , where µ is a normalization constant, k is the Boltzmann constant, and T is the temperature. Boson - A particle that obeys Bose-Einstein Statistics; specifically, any particle with spin equal to zero or an integer. This includes
Density functionals for nondynamical correlation constructed from an upper bound to the exact exchange energy density
Published in Molecular Physics, 2019
Benjamin G. Janesko, Giovanni Scalmani, Michael J. Frisch
Our need for a predetermined length scale d in Equation (3) is not a special limitation of our approach. The Bohr radius is a ‘chemically relevant’ length scale arising from fundamental constants. Several widely used approximate correlation functionals incorporate the Bohr radius, as in the PBE correlation reduced density gradient [27]. Screened [66] and long-range-corrected [58] hybrids require a range-separation length , which is typically on the order of [67]. We slightly modify the choices made in existing correlation functionals, and choose length scale d to be the Bohr radius times an empirical prefactor on the order of .