利用FDBPM研究半導體量子結構中的量子效應

Abstract

我們利用FDBPM解等效質量近似之薛丁格方程式，藉以瞭解電子波在半導 體量子侷限結構中的量子效應及電子於量子傳輸結構之行徑。利用BPM及 部分維度空間模型，我們計算出激子在量子井的束縛能及史塔克效應。此 等結果與既有的其它理論計算值實驗數據皆相當吻合。另外我們模擬電子 波在共振穿隧結構中的運動情形,並計算電子穿隧時間且考慮電子在量子 井中堆積的影響。最後考慮一些量子結構如寬窄結構，寬窄寬窄寬結構等 之量子傳輸特性。模擬計算的結果，我們可清楚地觀察並分析電子波在這 些量子結構的運動情形及量子效應。 We use the finite difference beam propagation method (FDBPM) to solve the effective-mass approximation Schrdinger equation to investigate the electronic properties of the semiconductor quantum-confinement structures and electron behavior in a quantum-transport structures. By using FDBPM accompanied with fractional-space model, both the binding energy of exciton in the quantum-well and the Stark effect can be calculated. The propagation of electron wave packet in the double-barrier resonant-tunneling diode (RTD) is clearly illustrated and the lifetime is estimated, too. The factors that affect the lifetime are discussed. In the structure, we also compare the dwell time, the phase time, and the transmitted time. The influence of space charge accumulation in the well to the characteristic times are also considered. Special quantum- transport structures are artificially constructed by various combination of wide/narrow geometries. The time evolution of electron wave packet in these structures are displayed and analyzed to compare with the conventional RTD structures.