郭宇軒臺灣大學:電子工程學研究所李銀順Li, Yin-ShunYin-ShunLi2010-07-142018-07-102010-07-142018-07-102009U0001-0707200920263400http://ntur.lib.ntu.edu.tw//handle/246246/189218光調變器是光通訊中極為重要的元件，其中最有效之調變機制為量子侷限史塔克效應(Quantum Confined Stark Effect)。於矽基板上成長之鍺/矽鍺化合物(Ge/SiGe)量子井中已證實有極大之量子侷限史塔克效應，可達高速調變，並可應用於長波長及商用通訊之C波段(~1530-1565 nm)之操作。此結果能有效應用在具高速調變、低驅動電壓、體積小之光電元件上；並可有效限低製作成本。本論文中，基於三種激子模型(二維、三維及非對稱性之三維)的變分法來探討Ge無限量子井及Ge/Si0.15Ge0.85有限量子井中基態直接能隙之電子與重電洞(e1-hh1)所形成之激子現象。對於有限量子井而言，導電帶之nonparabolicity效應在部份計算也有納入考慮。激子半徑、遷移能量、束縛能量及振子強度之值為針對不同量子井厚度於不同之垂直偏壓抑或是不同之垂直電場變化下計算所得。對於無限及有限量子井，在較寬的量子井厚度及較強的偏壓/電場下，激子都會變弱。種激子模型有進行比較，顯示三維模型可適用於無限量子井之模擬計算。而對於有限量子井(含nonparabolicity效應)而言，在較薄的量子井厚度下是較接近二維模型，隨厚度變寬則接近非對稱性之三維模型。且對此有限量子井，最小之激子半徑及最大之振子強度發生在1.6 nm，即證明此Ge/SiGe有限量子井系統即使在很薄的量子井厚度下也具有很強之量子侷限功能。對於沒有考慮nonparabolicity效應的有限量子井，利用三維模型探討其直接吸收比上非直接吸收之比率，證實有大範圍之量子井厚度區域(~5-15 nm)可以在長波長之操作範圍提供很穩定之激子吸收及對比比率。最後，nonparabolicity效應可強化激子效應，特別是對於較薄之量子井；且本研究之結果與其他實驗結果及模擬計算結果極為接近。The optical modulator is one of the most important devices for optical communication, and the strongest modulation mechanism, the quantum-confined Stark effect (QCSE), had been demonstrated in Ge/SiGe quantum wells on Si substrate. It is fully compatible with silicon electronics and can achieve the GHz-region operation for the long wavelength and C-band (1530–1565 nm) operation. The discovery can highly improve high-speed, low power, and small optical devices. n this thesis, the variational methods based on the 2-dimensional (2-D), 3-D and anisotropic 3-D exciton models are used to study the direct-band-edge ground-level electron-heavy-hole (e1-hh1) exciton behaviors in the infinite Ge quantum well and the finite Ge/Si0.15Ge0.85 quantum well structures. For the finite case, the effect of the conduction-band nonparabolicity effect on the exciton behavior is also investigated. The exciton radius, transition energy, binding energy, and optical oscillator strength are calculated for various quantum well thicknesses and “bias voltage” (or “vertical electric fields”). The exciton becomes weaker with thicker well and stronger bias voltage/electric field for both the infinite and finite well cases. he three exciton models are compared, indicating that the 3-D model is suitable for the infinite well modeling while the exciton in the finite well considered with the nonparabolicity effect case is nearly 2-D for thinner well and becomes anisotropic-3-D for wider well. The exciton radius minimum and oscillator strength maximum occur at 1.6 nm for the finite well case; therefore, this Ge/SiGe quantum well system shows a strong quantum-confinement even with a thin thickness. or the finite case without considering the nonparabolicity effect, the 3-D model is used to investigate the exciton effect. The relative direct-gap-to-indirect-gap absorption ratios are compared, indicating a broad thickness range of ~5–15 nm can provide moderate excitonic absorption and contrast ratio for long wavelength operation. inally, the nonparabolicity effect can enhance the exciton effect, especially in a thinner well. Also, our work agrees well with the experimental result and other calculation for the 10-nm Ge/SiGe quantum well case.Abstract (Chinese) Ibstract (English) IIIhapter 1: Introduction 1.1 Silicon photonics and the quantum-confined Stark effect in Ge/SiGe quantum well systems 1.2 Purpose of the study and discussion of theoretical calculations 3.3 Thesis organization 4hapter 2: Principle and Modeling 6.1 Principle 6.1.1 Exciton and excitonic absorption 6.1.2 Quantum confined Stark effect (QCSE) 7.2 Ge quantum well structures and its parameters 10.3 Modeling 16.3.1Airy function 16 2.3.2 Transfer matrix and tunneling resonance method 17.3.3 Exciton modeling and variational method 21.4 Algorithm and discussion issues 24.4.1 Algorithm 24.4.2 Oscillator strength and direct vs. indirect gap absorption 26.4.2.1 Oscillator strength 26.4.2.2 Direct vs. indirect gap absorption 27hapter 3: Results of the infinite Ge quantum well structure 28.1 The combined quantum well energy 28.2 The exciton binding using the 2-D and 3-D models 30.3 The exciton binding using the anisotropic 3-D model 32.3.1 The exciton radius and dimensionality 34.3.2 The oscillator strength 37hapter 4: Results of the Ge/Si0.15Ge0.85 quantum well structure 40.1 Results with the nonparabolicity effect 40.1.1 The exciton binding using the 2-D and 3-D models 40.1.2 The exciton binding using the anisotropic 3-D model 42.1.2.1 The exciton radius and dimensionality 42.1.2.2 The exciton binding energy and the oscillator strength 44.1.2.3 The strongest exciton effect in the Ge/Si0.15Ge0.85 quantum well structure 47.2 Results without the nonparabolicity effect 48.2.1 Exciton radius 49.2.2 Transition energy and binding energy 50.2.3 Oscillator strength and direct vs. indirect absorption 52. 3 Comparison between the parabolicity and nonparabolicity effects 56.4 Theoretical calculation Comparison 58hapter 5: Conclusions and Future Work 59.1 Conclusions 59.2 Future Works 61.2.1 The design and fabrication of optimal Ge/SiGe quantum well modulator 61.2.2 Absorption spectra simulation 63eferences 647290504 bytesapplication/pdfen-US量子侷限史塔克效應變分法激子nonparabolicity效應非對稱性之三維模型quantum-confined Stark effect (QCSE)variational methodexcitonnonparabolicity effectanisotropic 3-D modelthesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/189218/1/ntu-98-R96943056-1.pdf