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来源:上海文忠翻译作者:文忠翻译公司

2.5  THE HALL EFFECT AND HALL DEVICES

An important phenomenon that we can comfortably explain using the "electron as a particle" concept is the Hall effect, which is illustrated in Figure 2.16. When we apply a magnetic field in a perpendicular direction to the applied field (which is driving the current), we find there is a transverse field in the sample that is perpendicular to the direction of both the applied field Ex and the magnetic field Bz, that is, in the y direction. Putting a voltmeter across the sample, as in Figure 2.16, gives a voltage reading VH. The applied field Ex drives a current Jx in the sample. The electrons move in the -x direction, with a drift velocity vdxBecause of the magnetic field, there is  a force (called the Lorentz force) acting on each electron and given by Fy = -evdxBz. The direction

of this Lorentz force is the -y direction, which we can show by applying the cork-screw rule, because, in vector notation, the force F acting on a charge q moving with a velocity v in a magnetic field B is given through the vector product

F= qv× B                                  [2.29]   Lorentz force

   All moving charges experience the Lorentz force in Equation 2.29 as shown schematically in Figure 2.17. In our example of a metal in Figure 2.16, this Lorentz force is the -y direction, so it pushes the electrons downward, as a result of which there is a negative charge accumulation near the bottom of the sample and a positive charge near the top of the sample, due to exposed metal ions (e.g., Cu+).

霍尔效应与霍尔器件

如图2.16所示的霍尔效是我们可以用“粒子化电子”概念解释的一个重要现象。当我们在垂直于外加电场的方向上施加一个磁场,我们发现在样品内产生一横向的电场,该电场垂直于外加电场Ex 和磁场Bz,即在y方向上。如图2.16所示,当一个电压表跨接在样品上,则会给出一电压读数VH。样品内外加的电场Ex产生一电流Jx 。电子沿-x方向以漂移速度vdx运动。在磁场的作用下,每个电子收到洛伦兹力的作用,为Fy = -evdxB。-

该洛伦兹力的方向为-y方向,这我们可以用螺旋法则表示。用矢量标记时,在磁场B中的一个以速度为v运动的电荷所受到的力F为矢量积

F = qv×B                             [2.29]  洛伦兹力

   如图2.17所示,所有移动的电荷都受到式(2.29)的洛伦兹力作用。在我们图2.16所示的一个金属例子中,该洛伦兹力为-y方向,将推电子向下偏转。因此在样品的底部会有负电荷的积累,而在上部由于留下金属离子(如Cu+)而有正电荷的积累。


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