在半導體奈米混和體中量子與電子力學的偶合現象

Abstract

近來在半導體技術的成長使得半導體奈米混和體同時包含擁有不同物理性質的成分變為可 能。他們在各新興領域的需求應用上展開了一扇非常有前瞻性的大門。 奈米混和體中的半導體部分控制了量子特性，而金屬部分提供了非常大的偏極化。這兩部分 彼此的交互作用造成非常強的非線性效應。這項效應表露出難得的機會去觀測和使用介於不 同力學間的相互作用。少數最近發現的現象被認為是量子和電子直接和反轉偶合的效應。不 幸的是，相對應知識的缺乏和沒有完備的理論可以在相關文獻中被找到。於是填補這個研究 領域的空缺就是此計畫的目標。反轉多重物理偶合問題的公式化和計算技術的發展將是首要 任務。 我們近來發展了兩種有效率的計算方法：混和多尺度法和映射法，藉由非常有效率的計算方 式去得到半導體奈米體中電子和電洞的能階和波函數；接著，去模擬和分析這些半導體奈米 體的各種特性。 我們特別關注三個觀點：偶合模型適當的公式和推導出非線性三維薛丁格-帕森-納維爾方程式 的全自滿足的解；詳細的分析並決定最佳的條件和系統；及對於進一步此效應的應用公式化 的陳述。

Recent advances in lithography, colloidal chemistry, and epitaxial growth techniques have made it possible to produce semiconductor based nano-hybrids containing material components with different physical properties, such as core-shell quantum dots, metal-semiconductor nano-hybrids, magnetic-functionalized nano-rods, etc., The nano-hybrids opened up a very promising domain for new urgent applications in modern optics, nano-biology, nano-medicine, quantum information technology, etc. Semiconductor components of the hybrids control quantum properties and metallic counterparts offer very large polarizabilities. The mutual interactions between the counterparts lead to strong nonlinear effects. The effects manifest unique opportunity to explore and use the interplay between quantum mechanics, nano-electro-mechanics, and electrodynamics. This is an important signature of the coupled phenomena’s ubiquity in the nano-hybrids. Strong non-linear interactions between the ionic and electronic sub-systems in nano-hybrids can generate the self-consistent inverse effects – the ionic subsystem reconfigurations and transformations. Few very recently discovered phenomena are suggested as intriguing realizations of the coupled direct and inverse quantum and electro-mechanical effects. Unfortunately, the corresponding knowledge is particularly weak and no comprehensive theories, models, or a thorough description of the quantum inverse electro-mechanical effects can be found in literature. It is the central aim of this project to fill the gap for this emergent research field. The inverse multi-physics coupled problem formulation and development of a computational technique for the problem solution will be put in first place in this theoretical study on semiconductor based nano-hybrids. We recently developed two efficient computational methods: the hybrid multiscale method and the mapping method with which we are able in a very efficient computational manner to obtain the energy states and wave functions of electrons and holes confined in semiconductor nano-objects with very sophisticated and flexible shapes, strain and material contents, and, then, to simulate and analyze quantum, electrical, magnetic, and electro-mechanical characteristics of the objects. On the base of that, in this project we plan to build a robust theoretical basement to the description of the quantum inverse electro-mechanical and similar effects in semiconductor based nano-hybrids. This requires addressing both fundamental and applied issues. In this framework three aspects will obtain our attention: proper formulation of the coupled physical and mathematical models of multi-component nano-hybrids and derivation of a computational technique for findings fully self-consistent solutions of the coupled non-linear 3D Schrödinger–Poisson–Navier equations including polaron and inverse pieso-electric effects; detailed analysis of the geometrical and physical characteristics of semiconductor based nano-hybrids in order to determine optimal conditions and systems for the inverse quantum electromechanical effect realizations; formulation of propositions for further applications of the effects.