Al/AlO${}_x$/Al tunnel junctions, also known as Josephson Junctions, are key components of many established and emerging electronic devices. They are an essential component of superconducting qubits. A major drawback is a lack of understanding of how the amorphous AlO${}_x$ barrier influences the electron transport properties. In this work we combined Tight Binding Density Functional Theory (DFTB) with Non Equilibrium Greens Function (NEGF) to study computationally several Al/AlO${}_x$/Al with different barrier lengths. The simulations reveal a weak exponential relationship between barrier length and resistance of the device. However, considerable variability is found between junctions of similar barrier length. The calculations provide evidence of an “effective” barrier length significantly smaller than the actual (physical) barrier length. The resistance and effective barrier is found to be sensitively influenced by the local atomic structure of the amorphous barrier, which explains the junction to junction variability.

铝/氧化铝${}_X$/Al 隧道结，也称为约瑟夫森结，是许多成熟和新兴电子设备的关键组件。它们是超导量子比特的重要组成部分。一个主要缺点是缺乏对非晶 Al2O 的理解${}_X$势垒影响电子传输特性。在这项工作中，我们将紧结合密度泛函理论 (DFTB) 与非平衡格林函数 (NEGF) 相结合，在计算上研究了几种 Al/Al2O${}_X$/Al 具有不同的势垒长度。模拟揭示了势垒长度和器件电阻之间的弱指数关系。然而，在类似势垒长度的结之间发现了相当大的可变性。计算提供了“有效”屏障长度明显小于实际（物理）屏障长度的证据。发现电阻和有效势垒受到非晶势垒的局部原子结构的敏感影响，这解释了结到结的可变性。