可变空隙度量子超晶格中的隧穿
Tunnelling in quantum superlattices with variable lacunarity
摘要：
量子分形超晶格是由一系列两种半导体材料交替沉积在衬底上的薄层组成的微电子器件，它们遵循分形集的构造规则，这里是对称的多矢康托分形。电子在这些超晶格中的散射性质可以用分段常势阱中的量子粒子的散射性质来模拟。表示反射系数作为空隙度参数的函数的扭曲图示出了具有完全透明的隧道效应的黑色曲线的外观，其可以被分类为垂直、弧形和条纹零点。利用传递矩阵法导出了这些无反射曲线的近似解析公式。通过与数值计算结果的比较，表明了其良好的精度.
英文摘要：
Quantum fractal superlattices are microelectronic devices consisting of a series of thin layers of two semiconductor materials deposited alternately on each other over a substrate following the rules of construction of a fractal set, here, a symmetrical polyadic Cantor fractal. The scattering properties of electrons in these superlattices may be modeled by using that of quantum particles in piecewise constant potential wells. The twist plots representing the reflection coefficient as function of the lacunarity parameter show the appearance of black curves with perfectly transparent tunnelling which may be classified as vertical, arc, and striation nulls. Approximate analytical formulae for these reflection-less curves are derived using the transfer matrix method. Comparison with the numerical results show their good accuracy.
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