以數值法及解析法進行共振型半導體元件之研究

Abstract

本論文中,我們利用超晶格的結構提出兩種嶄新且近乎理想的量子能量帶 通濾波器.其一的特性為在長晶方向的位能障壁呈高斯函數的變化,而另一 則為其位能障壁與位能井之厚度呈漸近式的變化.當入射電子的能量位於 濾波器的導通帶時,電子可以近百分之百的通過.相反的,若入射電子的能 量位於截止帶內時,電子將會被完全的反射回來.我們可以藉由調變設計帶 通濾波器的結構參數,而得到各種不同的輸出特性．們利用了ＷＫＢ法來 解釋這種濾波器特有的穿透機率特性.另一方面,我們也以數值法進行了波 包的時間演化模擬.其結果可以很清楚的闡明帶通濾波器完全穿射的行為. 利用電子波阻抗匹配的觀念,可讓我們更進一步的了解電子完全穿射帶通 濾波器的物理意義.在進行波包對時間演化的同時,我們也一並的探討電子 穿隧時間的問題．因為理想帶通濾波器能提供電子波一個完全穿透的環境 ，所以由測不準原理所衍生出的種種的不確定性也因而消弭.數值分析的 結果指出不論電子的入射能量為何,其穿隧時間都將會大於當位能障壁不 存在之時.另外在本論文中,我們以Fabry-Perot模型結合QMWI與蒙地卡羅 法討論散射效應對共振型穿隧二極體穿透機率的影響.結果顯示:穿透機率 曲線變寬了,峰值減小了,峰值位置產生位移且聲子輔助穿隧的效應顯現. 藉由QMWI法所計算出電子在位能井中的停留時間與散射時間作一比較,我 們可以量化的方式來判別電子穿隧共振型二極體的行為是否為共諧模式亦 或為接續模式.本論文的最後一部份是探討光場強度分佈對共振加強型光 二極體頻率響應之影響.由於電子與電洞在光二極體內的飽合速率通常是 不同的,考慮此一因素,在我們舉的例子中,我們發現共振加強型光二極體 設計於使其最大光場分佈發生於靠p+時,元件將會有最佳的反應速度.脈衝 響應,步階響應計算的結果都在在的顯示了光場強度的考量對高速光通訊 元件設計的重要性. In this thesis, two novel quantum-mechanical energy band-pass filter (EBPF) using superlattice structures with a Gaussian envelope profile or gradually changing barrier and well width have been proposed. Such structures allow the incident electrons to be nearly totally transmitted when the impinging electron energy is in the passband. On the other hand, a complete reflection occurs when the impinging energy is in the stopband. By adjusting the parameters of the potential profile and the superlattices, the desired passband and stopband of such filter can be obtained. The WKB approximation is applied to demonstrate the phenomena of abrupt change of transmission profile. Time evolutiion of electron wavepacket moving through such structures is calculated by numerically solving the time-dependent Schrodinger equation. The numerical simulations clearly demonstrate the characteristics of total transmission and reflection. The generalized concept of matched quantum- mechanical wave impedance (QMWI) analogous to transmission line theory is presented to explained the occurrence of no reflection. At the same time we perform numerical simulation of wavepacket moving through the EBPF to investigate the electron tunneling time. By simulating the movement of a totally transmitted wavepacket, the ambiguity in the determination of the tunneling time from the uncertainty of a partially transmitted wavepacket is avoided. Numerical results indicate that the electron tunneling time is greater than the free particle time for all the incident energies. We have also studied the scattering effects on the transmission spectrum of a resonant tunneling diode (RTD) by employing the Fabry-Perot model, QMWI and Monte Carlo method. Our results indicate: the transmission spectrum is broadened, the peak amplitudes is decreased, the peak position is shifted and phonon-assisted tunneling happens. The resonant time calculated from QMWI method is compared with the scattering time to detrmine whether the tunneling mechanism is coherent or sequential tunneling. In the last part of the thesis, we present a theoretical study of the effects of light field distribution on the frequency response of a resonant cavity enhancee photodetector. Taking account of the difference in velocity of the carriers, and of the nonuniform generation of carriers in the i region, the results of our work indicate that when the maximum of light field intensity happens near the p+ edge of the depletion layer, the device shows optimum speed performance. The calculated impulse response and step response also indicate that device design with such intensity profile consideration is suitable for high bit rate communication systems.