鍺中三價受子和雙共振腔於兆赫波源之理論研究

Abstract

在本論文中我們分兩個部份分別討論兩種不同的半導體的兆赫波光源。第一個是摻雜三價受子的鍺。其可藉由電洞從鍺三價受子的激發態到基態的電隅極躍遷（electric-dipole transition）放出的兆赫頻段的電磁波。第二個是搭配兩種不同特性的共振腔所形成的拋物量子井雷射。我們預期在低溫下其可成為高功率的兆赫波光源。 在第一個部份中我們探討應力對鍺受子能階的電子結構（electronic structure）以及其電隅極躍遷的效應。而我們的計算是建立在等效質量理論（effective mass theory）並考慮了一個半經驗的雜質位能。這個雜質位能考慮了波向量q相關介電函數所造成的屏蔽效應以及中心核修正（central-cell correction）。 我們可以從受子態的成份來瞭解應力對電子結構和電隅極躍遷所造成的影響。在應力約小於3 kbar時受子態的束縛能會隨應力增加而快速地下降。此外我們發現偶對稱的受子態對於壓縮應力（compressive stress）和對伸張應力（tensile stress）展現出非對稱的特性。這是因為偶對稱的受子態重電洞（heavy-hole）和輕電洞（light-hole）的成份有很大的差異所造成。隨著應力的增加重電洞能帶和輕電洞能帶的隅合越來越小，且其在高應力（>3 kbar）的情況機乎可以乎略。此時受子態機乎是由單純的重電洞或是單純的由輕電洞所組成。這會造成受子態會有額外簡併的行為，且電隅極躍遷會有額外的選擇定則（selection rule）。我們針對低能量的激發態和基態間的躍遷在無應力和低應力（<0.35 kbar）的情況下做詳細的討論並且發現我們的結果與實驗比較達到定量的一致。至於高應力的情況目前並無實驗可供對照，我們也討論了理論模型在高應力下的適用性。 在第二個部份中我們提出並以理論証實一種雙共振腔的高功率的拋物量子井兆赫波雷射。當量子井與光子晶體-金屬-金屬共振腔共振時可以將載子次能帶間發光躍遷率（intersubband radiative transition rate）提高幾個數量級，而當量子井與法布利-培若（Fabry-Perot）共振腔產生共振會提高載子的帶間躍遷率（interband transition rate）。當這兩個共振腔同時與量子井共振，載子數和熱都會明顯地降低。此時，熱機乎不隨注入電流的增加而增加但兆赫波的發光強度卻可隨著注入電流呈線性地增加。我們預期這個系統可以有很好的發光效率且發光功率可輕易地達到10 W/cm^2。

In this dissertation, we study two types of semiconductor terahertz source. 1. The group-III acceptors in Ge under uniaxial stress. It can radiate terahertz electromagnetic wave through the electric-dipole transitions from the excited to the ground acceptor states. 2. The parabolic quantum wells laser with heterogeneous cavities. We expect it can be a high-power terahertz emitter. In the first part of the dissertation, we study stress effect on the electronic structures and the electric-dipole transitions for group-III acceptors in Ge. The calculation is based on the effective mass theory with a semi-empirical impurity potential which considers the q-dependent screening and the central-cell correction. The stress effect on the electronic structures and the electric-dipole transi-tions can be undertood by connecting with the composition of the acceptor states. We find that the binding energies decrease rapidly with the stress in the low-stress region, and for even-parity states they exhibit remarkable asymmetry between the compressive and the tensile stress due to the large difference between the heavy-hole and the light-hole compositions. The coupling between the heavy-hole and the light-hole bands decreases with increasing stress and is almost negligible in the high-stress region (>3kbar). In this case, the acceptor states are almost pure heavy-hole or light-hole states. This causes the appearance of extra degeneracy of the acceptor states and additional selection rules of the electric-dipole transitions. In addition, we study in detail the electronic structures of the low-lying acceptor states and the electric-dipole transitions in the low-stress region. The results are in agreement with the currently available experimental data. However, because of the lack of the experimental data in the high-stress region, a justification is made for the applicability of our calcu-lation for the case of high stress. In the second part of the dissertation, we propose and demonstrate theoretically a scheme for high-efficiency terahertz lasing from parabolic quantum wells resonant coupled with two different cavities. An in-resonance photonic crystal metal-metal cavity can increase the intersubband radiative transition rates by several orders; an in-resonance Fabry-Perot cavity can increase the interband transition rate. Simultaneous interband and intersubband lasings can significantly reduce the carrier density and heat generation due to nonradiative processes. In this case, the heat generation remains low and constant, independent of the injection current but the terahertz emission power increases linearly with current. With the present scheme, terahertz emission power of 10 W/cm2 can easily be achieved, accompanied by high intersubband quantum efficiency.