The quantum mechanics of electric conduction in crystals
The quantum mechanics of electric conduction in crystals
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DOI：
10.1119/1.3436664
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发表时间：
2010-08
影响因子：
0.9
通讯作者：
R. Olsen;G. Vignale
中科院分区：
文献类型：
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作者：
R. Olsen;G. Vignale
我们引入了一个入射在一维周期性电势上的电子模型，并表明传导是电子波不同部分干涉的结果，电子波通过一系列电势多次反弹，最终被传输或反射。推导了简单的迭代方程来确定周期系统的透射和反射系数。我们发现电子的全反射发生在某些能量范围内，以及可以发生完全透射的能量范围内。发生传输的能量范围相当于传统上使用布洛赫定理发现的导带。这些方程通过数值求解，可以具体演示传导。无序的情况也得到解决。
We introduce a model of electrons incident on a one-dimensional periodic potential and show that conduction is a result of the interference of different parts of an electron wave that bounce multiple times through a series of potentials, ultimately being transmitted or reflected. Simple iterative equations are derived that determine the transmission and reflection coefficients of a periodic system. We find that total reflection of the electron occurs in certain energy ranges, as well as ranges of energy within which complete transmission can occur. The energy ranges in which transmission occurs are equivalent to the conduction bands traditionally found using Bloch’s theorem. These equations are solved numerically, allowing a concrete demonstration of conduction. The disordered case is also addressed.