非完整超晶格中电子透射问题的计算机模拟

Simulation Research for Electronic Transmission of Disordered One Dimensional Finite Superlattices

采用转移矩阵方法 ,模拟研究了垒高无序和阱宽无序非完整超晶格的电子态问题。计算了垒高无序有限超晶格的透射谱和其局域态波函数以及阱宽无序有限超晶格的透射谱和本征值 ,直观地给出了垒高无序和阱宽无序非完整有限超晶格其电子态行为的物理图像。模拟结果表明 :垒高无序和阱宽无序这两种常见非完整一维有限超晶格的子带带隙间均存在强烈的电子运动定域化 ,且电子波的布喇格散射对周期性势场更敏感 ;这两种非完整性引起的局域 ,通过计算电子局域态波函数和有限系统的本征值得到了证实 ;对本文讨论的这种类型和周期的超晶格 ,如果控制阱宽在 9.1～ 1 0 .9nm间随机变化 ,即阱宽的值最大相差 1 8nm时 ,计算机模拟的结果是 ,阱宽的这种非周期性开始使子带的带隙消失。

The Kronig-Penney model has been widely used to explore the characteristics of electrons in a periodic potential as this model provides one with perhaps the simplest instance of Bloch states. This model and its relation with superlattices has also been used in recent times to provide an implementation of the physics of random and quasiperiodic systems. It is because of its importance and wide applicability that we focus our attention on the Kronig-Penney model to investigate the imperfect finite superlattices. There exist many theoretical methods developed for description of disordered systems such as Monte-Carlo simulation, truncated rate equation, perturbative approach, Wannier-Stark levels etc. However, provides an easy way (tranfer matrix) that is very valid for studying the electronic states of imperfect finite SLS. Tranfer matrix method can be turned out to be more convenient for computer than the conventional formalism, which is based on effective mass approximation and Bastard's boundary condition. The barrier and well can be represented by matrixes and the wave functions at any two positions inside the superlattice are connected by a product of transfer matrixes. The sequence of the matrixes matches the arrangement of the barriers and wells. No matter how the barrier and well change, we need only to modify the matrixes of barrier and well. We mainly discuss the electronic states of finite SLS with intentional random barriers or well widths by means of a transfer matrix method. The transmittance and its localized wave function of SLS with random potentials were calculated and also the transmittance and electronic eigenfunction of SLS with random well widths were calculated. The results are compared with those obtained from ordered SLS. We can observe discrete localized states of finite SLS with intentional random barriers or well widths. Our simulated results indicate that electronic states are sensitive to both the intentional random barriers and well widths. Especially when well widths randomly vary in a range of (9.1～10.9) nm for SLS discussed in this paper, we find that the subband begins to disappear. In recent decades the physical community and scientists in related fields have shown an increasing interest in the structure and properties of disordered condensed systems. It's clear that the method developed in this paper can be extended easily to solve some other kinds of problems caused by disordered systems such as localized states, extended states, mobility edges and so on.