應用於深紫外發光二極體與光色轉換表面電漿子耦合的模擬研究

Simulation Studies on Surface Plasmon Coupling Applications to Deep-ultraviolet Light-emitting Diode and Light Color Conversion

張文彥(Wen-Yen Chang)

指導教授 ： 江衍偉

共同指導教授 ： 楊志忠(Chih-Chung Yang)

國立臺灣大學/電機資訊學院/光電工程學研究所/博士(2019年)

https://doi.org/10.6342/NTU201902573

摘要

本論文中，我們利用半古典模型與電磁理論探討量子發射體、量子吸收體與表面電漿子間的耦合效應，以及表面電漿子的共振特性。經數值模擬，可瞭解表面電漿子在深紫外發光二極體之放光、量子井與量子點間光色轉換、氮化鎵上銀光柵之光特性等三方面所扮演的角色。
為探討表面電漿子耦合效應對深紫外發光二極體效能的影響，我們建立一套三能級系統之理論模型，藉數值模擬法，探討受空氣/氮化鋁鎵介面散射與表面鋁奈米粒子之表面電漿子耦合效應之影響下，氮化鋁鎵量子井的橫電與橫磁兩種偏振發光的Purcell效應。合理選擇氮化鋁鎵量子井內的鋁含量範圍，使其發出深紫外光，我們發現橫電(橫磁)偏振光之增強(減弱)主要係來自表面電漿子耦合(介面散射)效應。不同於兩二能級之模型，在三能級系統中，橫電與橫磁兩種偏振發光彼此會競爭高能階(用以模擬導電帶)中的共用電子，因此介面散射或表面電漿子耦合效應將稍減弱。在頗寬的發光波長範圍內，即使原本深紫外發光二極體之放光係以橫磁偏振為主，藉由介面散射與表面電漿子耦合效應，增強的橫電偏振將可成為主要的偏振。此種以橫電偏振為主的發光亦可提升深紫外發光二極體之光萃取效率。
其次我們也使用二能級系統來分析表面電漿子如何增強量子井與量子點間的光色轉換效率。數值模擬時，我們將短波長發光的量子井與長波長發光的量子點各視為一個電偶極，並在二電偶極間置入一顆具有兩種表面電漿子共振模態的銀奈米粒子，其一共振對應於量子井的發光波長，另一共振對應於量子點的發光波長。短波長的共振可以增加量子井與量子點間的能量轉換，亦即增強量子點吸收，長波長的共振可以增強量子點的輻射。總光色轉換效率則比例於此二機制相乘的結果。我們亦針對不同大小的銀奈米粒子所造成的表面電漿子增強效果作比較。
除了表面電漿子的耦合效應外，表面電漿子的基礎特性也很重要。一般金屬光柵結構是藉動量匹配來激發表面電漿極化子，但實際上侷域表面電漿子也存在於金屬光柵結構中，其耦合效應可用於發光二極體。因此我們特地研究存在於氮化鎵與銀光柵交界面之侷域表面電漿子與對向傳播的表面電漿極化子的特性。計算結果顯示，侷域表面電漿子的共振行為不只受制於金屬光柵的寬度與高度，還受週期影響，尤以小週期為甚。若光柵中的每一個突起物偏高、寬、或陡峭，侷域表面電漿子共振所造成的表面電荷分佈會橫跨在突起物之間。此時共振波長與突起物寬度較無關聯而表面電荷分佈較廣，可與發光二極體中的量子井作有效耦合。因為表面電漿極化子的消逝波涵蓋範圍小，由對向傳播之表面電漿極化子所造成的侷域震盪現象較不利耦合。故在發光二極體的應用上，侷域表面電漿子的效果略勝一籌。

關鍵字

表面電漿子 ； 量子點 ； 深紫外線 ； 發光二極體 ； 光色轉換

並列摘要

In this dissertation, we propose numerical algorithms based on semi-classical model and electromagnetic theory to investigate the coupling between quantum emitters, absorbers and surface plasmon (SP) as well as resonance characteristics of SP. These algorithms are applied to discuss the roles of SPs in deep-ultraviolet (UV) light-emitting diodes (LEDs), in the light color conversion between quantum wells (QWs) and quantum dots (QDs), and at the interface between silver grating and GaN.
For discussing how SP coupling affects the performance of a deep-UV LED, the formulations and numerical algorithms derived from a three-level model for studying the Purcell effect produced by the scattering of an air/AlGaN interface and the SP-coupling effect induced by a surface Al nanoparticle (NP) in a two-polarization emission system to simulate the transverse-electric- (TE-) and transverse-magnetic- (TM-) polarized emissions in an AlxGa1-xN/AlyGa1-yN (y > x) QW are built. In reasonably selected ranges of Al content for an AlGaN QW to emit deep-UV light, the enhancement (suppression) of TE- (TM-) polarized emission is mainly caused by the SP-coupling (interface-scattering) effect. Different from a two two-level model, in the three-level model the TE- and TM-polarized emissions compete for electrons in the shared upper state, which is used for simulating the conduction band, such that either interface-scattering or SP-coupling effect becomes weaker. In a quite large range of emission wavelength, in which the intrinsic emission is dominated by TM polarization, with the interface-scattering and SP-coupling effects, the TE-polarized emission becomes dominant for enhancing the light extraction efficiency of a deep-UV light-emitting diode.
To investigate the mechanism of the color conversion, another theoretical model together with numerical algorithms of SP coupling are built for simulating SP-enhanced light color conversion from a shorter-wavelength radiating dipole (representing a QW) into a longer-wavelength one (representing a QD) through QD absorption at the shorter wavelength. An Ag NP located between the two dipoles is designed for producing strong SP couplings simultaneously at the two wavelengths. At the QW emission wavelength, SP couplings with the QW and QD dipoles lead to the energy transfer from the QW into the QD and hence the absorption enhancement of the QD. At the QD emission wavelength, SP coupling with the excited QD dipole results in the enhancement of QD emission efficiency. The combination of the SP-induced effects at the two wavelengths leads to the increase of overall color conversion efficiency. The color conversion efficiencies in using Ag NPs of different geometries or SP resonance behaviors for producing different QD absorption and emission enhancement levels are compared.
Apart from SP coupling effects, the fundamental characteristics of SPs are also important. Although a metal grating structure is usually fabricated for momentum-matching a surface plasmon polariton (SPP) with photon, for SP coupling application in an LED, localized surface plasmon (LSP) on such a structure also plays an important role. We numerically study the LSP resonance behaviors, including the localized resonance behavior of counter-propagating SPP interference, of an Ag grating on GaN. It is found that the resonance behaviors of LSP are controlled not only by the geometry of a grating ridge, but also by grating period, particularly when the grating period is small. In a grating with sharp ridge, large ridge height or width, LSP features of dense charge distributions around the boundaries between ridges and connecting valleys exist. The spectral positions of such LSP features are weakly dependent on the ridge width. Among such features, those with their mode field oscillations across a ridge and hence distributions in an extended space around the ridge can more strongly couple with the QWs of an LED. Because of the short coverage range of SPP evanescent field, the localized resonance feature caused by counter-propagating SPP interference has a shorter coupling range. For LED application, an LSP mode with field oscillation across a ridge is preferred.

並列關鍵字

Surface Plasmon ； Deep-ultraviolet Light-emitting Diode ； Light Color Conversion

參考文獻

1. S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, Berlin, 2007).

2. C. F. Bohren, “How can a particle absorb more than the light on it?” Am. J. Phys. 51, 323 (1983).

3. N. A. Azarenkov and N. K. Ostrikov, “Surface magnetoplasma waves at the interface between a plasma-like medium and a metal in a Voigt geometry,” Phys. Rep. 308, 333–428 (1999).

4. J. J. Sakurai, Advanced Quantum Mechanics (Addison-Wesley Publications, Boston, 1967).

5. K. C. Shen, C. Y. Chen, C. F. Huang, J. Y. Wang, Y. C. Lu, Y. W. Kiang, C. C. Yang, and Y. J. Yang, “Polarization dependent coupling of surface plasmon on a one-dimensional Ag grating with an InGaN/GaN dual-quantum-well structure,” Appl. Phys. Lett. 92(1), 013108 (2008).