Application of Circuit Theory to Synthesis of New Materials Using Quantum Effect

本研究计划的目的是展示半导体超晶格的新合成方法，以及利用量子效应获得物理新特性的多势垒和阱结构。获得了以下结果。(I)在双势垒共振隧穿器件中，共振态寿命被定义为渡越时间，用来估计器件的工作速度，它与合理能级的能量宽度有关。本文提出利用电路理论中的拉普拉斯参数的复能量来计算寿命。我们表明，我们很容易获得的寿命多势垒和阱结构。(II)通过得到异质界面的复等效电路，我们分析了第二类和第三类的伽马-X混合和量子威尔斯。通过得到边界条件的复等效电路，我们得到了量子阱的本征能量和GaAs/Al _xGa_ As，InAs/GaSb构成的周期势的能带结构<1-x>。在给定电子转移特性的条件下，得到了一种包含δ势的一维势结构的综合方法。我们还得到了Kane提出的两带模型的等效电路，用以描述GaSb，InAs，AlSb组成的RIT（Resonant Interband Tunnel）的波形特性。(III)为了更有效地制作共振隧穿二极管，我们提出了在费米能级以下的导带中获得共振隧穿能级的合成方法。我们还展示了一种使用深井威尔斯的有效方法。(IV)我们讨论量子摩擦。电摩擦相当于能量损失。由于我们从薛定谔方程导出电报员型方程，我们得到了对应于波函数的电压和电流的两个波。通过使用这两种波，我们可以将量子摩擦分析为电损耗。(V)用狄拉克算符给出了一些量子波。通过对Dirac算子的等价电路的研究，揭示了Dirac算子的一些基本性质.

The objective of this research projects is to show new synthesis methods of semiconductor superlattices, and multiple barrier and well structures deriving physically new characteristics utilizing quantum effect. The following results are obtained.(I) Since the lifetime of the resonant state is defined as the transit time to estimate operation speed in double barrier resonant tunneling devices, it is related to the energy width of reasonant level. We propose to obtain the lifetime by utilizing the complex energy of Laplace parameter used in the circuit theory. We show that we easily obtain the lifetime for multiple barrier and well structures.(II) By obtaining complex equivalent circuits for heterointerfaces, we analyze GAMMA-X mixing and quantum wells of Type II or III.By obtaining complex equivalent circuits for boundary conditions, we obtain eigenenergy of quantum well and mini-band structure of periodic potential constituted by GaAs/Al _xGa_<1-x> As, InAs/GaSb. We obtain a synthesis method of one-dimentional potential structure including delta potential with given electron transfer characteristics. We also obtain the equivalent circuit for the 2-band model prposed by Kane, to represent wave characteristics of RIT (Resonant Interband Tunneling) consituted with GaSb, InAs, AlSb.(III) In order to make resonant tunneling diodes more effectively, we propose synthesizing methods to obtain a resonant tunneling level in the conduction band under the Fermi level. We also show an efficient method using deep wells.(IV) We discuss quantum friction. Electrical friction corresponds to energy loss. Since we derive Telegrapher's type equation from Schrodinger equation, we obtain two waves of voltage and current corresponding to wave function. By using these two waves, we can analyze quantum friction as electrical loss.(V) Some quantum waves are presented by Dirac operator. We show some fundamental characteristics of Dirac operator by obtaining the quivalent circuit.