“effective mass(symbol: m*)”的概念、定义、翻译、参考文献-科学参考

effective mass(symbol: m*)

Electronics and Electrical Engineering

The motion of electrons in free space is given by a classical Newtonian relationship,
$E = \frac{p^{2}}{(2 m_{0})}$
where E, p, and m₀ are the energy, momentum, and mass of the electron. In a crystal, the local potential due to the atoms will modify the dynamic behaviour of the electrons. The motion of electrons in a crystalline solid can be found using quantum mechanics; this results in the energy band structure of the crystal, which is the relationship between electron energy and momentum, E and p, in the crystal. The motion of an electron in the energy bands due to an applied electric field (a force) can be found in a semiclassical manner, as follows. The quantum mechanical part describes the velocity of the electron in the crystal: the group velocity of the electron de Broglie wave is
$v = \frac{\partial E}{\partial p}$
The energy dE gained by the electron in travelling a distance vdt under the influence of the force F is
$d E = F v d t = F (\frac{\partial E}{\partial p}) d t$
The acceleration due to the force is
$\frac{d v}{d t} = (\frac{d}{d t}) . (\frac{\partial E}{\partial p}) = (\frac{d p}{d t}) . (\frac{\partial^{2} E}{\partial p^{2}})$
But since force is the rate of change of momentum, the term $\partial^{2} E / \partial p^{2}$ has the units of (1/mass). The reciprocal of this term is the effective mass of the electron in the energy band of the crystal. The electron is seen to behave like a particle with this effective mass in response to an applied force, such as an electric field. The value of the effective mass is determined by the detailed shape of the energy band structure.

单词	effective mass(symbol: m*)
释义	effective mass(symbol: m*) Electronics and Electrical Engineering The motion of electrons in free space is given by a classical Newtonian relationship, $E = \frac{p^{2}}{(2 m_{0})}$ where E, p, and m₀ are the energy, momentum, and mass of the electron. In a crystal, the local potential due to the atoms will modify the dynamic behaviour of the electrons. The motion of electrons in a crystalline solid can be found using quantum mechanics; this results in the energy band structure of the crystal, which is the relationship between electron energy and momentum, E and p, in the crystal. The motion of an electron in the energy bands due to an applied electric field (a force) can be found in a semiclassical manner, as follows. The quantum mechanical part describes the velocity of the electron in the crystal: the group velocity of the electron de Broglie wave is $v = \frac{\partial E}{\partial p}$ The energy dE gained by the electron in travelling a distance vdt under the influence of the force F is $d E = F v d t = F (\frac{\partial E}{\partial p}) d t$ The acceleration due to the force is $\frac{d v}{d t} = (\frac{d}{d t}) . (\frac{\partial E}{\partial p}) = (\frac{d p}{d t}) . (\frac{\partial^{2} E}{\partial p^{2}})$ But since force is the rate of change of momentum, the term $\partial^{2} E / \partial p^{2}$ has the units of (1/mass). The reciprocal of this term is the effective mass of the electron in the energy band of the crystal. The electron is seen to behave like a particle with this effective mass in response to an applied force, such as an electric field. The value of the effective mass is determined by the detailed shape of the energy band structure.
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