论文标题
将福勒 - 诺德海姆隧道理论概括为任意权力法律障碍
Generalizing Fowler-Nordheim Tunneling Theory for an Arbitrary Power Law Barrier
论文作者
论文摘要
在此，通过计算零温度的传输概率来扩展规范的福勒 - 诺德海姆理论，该概率是分数幂定律所描述的屏障的更一般情况。根据高斯高几何函数编写了一个精确的分析公式，该公式完全捕获了此广义问题的传输概率，包括与图像电位的筛选相互作用。首先，对迄今为止最先进的Fowler-Nordheim公式的近似质量，该公式是根据椭圆形积分给出的。在下文中，由于势力法给出了障碍，因此详细介绍了传输概率对权力法指数的依赖性。将形式主义与数值计算的结果进行了比较，并讨论了其可能的实验相关性。最后，讨论了如何在某些特定情况下与量子井问题的精确量子机械解决方案链接所提出的解决方案。
Herein, the canonical Fowler-Nordheim theory is extended by computing the zero-temperature transmission probability for the more general case of a barrier described by a fractional power law. An exact analytical formula is derived, written in terms of Gauss hypergeometric functions, that fully capture the transmission probability for this generalized problem, including screened interaction with the image potential. First, the quality of approximation against the so far most advanced formulation of Fowler-Nordheim, where the transmission is given in terms of elliptic integrals, is benchmarked. In the following, as the barrier is given by a power law, in detail, the dependence of the transmission probability on the exponent of the power law is analyzed. The formalism is compared with results of numerical calculations and its possible experimental relevance is discussed. Finally, it is discussed how the presented solution can be linked in some specific cases with an exact quantum-mechanical solution of the quantum well problem.
