半磁性奈米晶體多體理論之研究以及其自旋生醫元件的應用

Abstract

半導體奈米晶體[semiconductor nanocrystal (NC)]是利用所謂由下而上（bottom-up） 之化學製成法所合成的人造奈米顆粒，其尺寸僅約數個奈米，多年來實驗上已證實其優 異的發光及量子特性，而被視為新一代光電材料的明日之星。不僅如此，最新的摻雜技 術已成功地將磁性元素（例如錳）結合入這些奈米晶體，[1]在未來，這些具磁性的半 導體顆粒，其應用層面將可擴展至奈米生醫檢測，乃至和磁性息息相關的自旋電子學和 量子資訊技術。 半磁性(semi-magnetic)奈米晶體吸引人之處，在於其獨特的磁光特性。最近，法國實 驗團隊L.Besombes 等人已成功測得包含單一光激子及單一錳原子的單顆量子點瑩光光 譜，[2]實驗光譜中豐富的精細結構直接反應出量子點中光激子(exciton)與磁性雜質間複 雜的自旋交互作用，儘管多年來物理學家對於半磁性半導體塊材或薄膜已有廣泛的研 究，然而半磁性量子點方面的研究卻仍有限。一方面，傳統的能帶理論在面對如此微小 的固體系統將遇到瓶頸，另一方面，由於奈米晶體中強烈的量子侷限效應，粒子或磁性 雜質間的自旋交互作用變得強烈且更為複雜進而造成理論計算上的困難。 最近我們已對多個電子與單一磁性原子的交互作用以及半磁性奈米晶體的磁性進行相 關研究。[3]在本計畫中，我們將延伸該理論方法及計算技術研究光激子與磁性雜質間的 交互作用以及半磁性奈米晶體的光電及自旋特性，並探討利用該磁性奈米晶體結合光學 技術實現生醫感測元件的可能性。本計畫主要由下列主題構成: 1. 奈米晶體電子結構的計算 我們將採用多重尺度的方法計算奈米晶體的電子結構:包括k.p 法及假位能(empirical pseudopotential)法?雖然奈米晶體的尺寸僅數個奈米，其中卻包含了>103 個原子，採用微 觀理論的假位能法處理如此龐大的原子數目將是數值技術上一大挑戰。因此我們將先建 構一16 節點(nodes)的計算機叢集配備高容量的動態計憶體(>6G/node)，再採用Lanczos 演算法解決超大(>105 執105)哈密頓矩陣(Hamltonian matrix)的對角化問題。 2. 半磁性奈米晶體中多激子的研究 利用configuration interaction (CI) 的方法及矩陣對角化的技術我們將計算半磁性奈米晶 體中多激子的能譜和磁性, 其中激子-激子、激子-磁性離子、及離子-離子間的庫倫作用 力將被完整地考慮?由於庫倫交換作用力，激子與磁性離子間有可能互相吸引而形成一 新準粒子(quasi-particle)，即所謂exciton magnetic polaron (EMP)，最近的研究顯 示EMP 在量子點光譜和自旋特性中伴演重要角色，我們將研究EMP 在奈米晶體瑩光 (Photoluminescence), 瑩光激發(Photoluminescence excitation) 和時析(time resolved)光譜 所造成的影響? 3. 利用奈米晶體實現自旋及生醫感測元件 最後我們將探討利用半磁性奈米晶體來發展自旋及生醫感測元件，我們將研究一奈米晶 體外部的磁性生物分子如何對奈米晶體光譜產生影?，並找出其瑩光光譜圖像與磁矩交 互作用的?係作為感測磁性生物分子的依據，我們將儘可能分析影?元件特性的因素， 例如熱效應(thermal effect),自旋態的穩定性(stability)和動態響應(dynamics)。 參考書目: [1] D. J. Norris, et al, Nano Lett. 1, 3 (2001). [2] L. Besombes et al,Phys. Rev. Lett. 93, 207403 (2004). [3] S.J. Cheng, to be published in Phys. Rev. B (2006).__

Semiconductor nanocrystals (NCs) refer to the chemically synthesized crystallite particles with typical radius of only few nanometers. Due to the excellent optical properties, NCs are treated as promising candidates of material system for realizing the advanced photoelectrical devices for the next generation. In addition, the latest technology has successfully incorporated magnetic elements, typically Mn2+, into those nanocrystals.[1] It is thus expected that the application of those semimagnetic NCs can be in near future extended to the highly spin-related fields, e.g. bio-sensing devices, spintronics, and quantum information technology. Recently, Besombes et al have first successfully demonstrated the emission spectrum from a single semimagnetic dot containing only one exciton and one magnetic ion.[2] The measured spectrum exhibits fascinating fine structures which are attributed to the complex spin interaction between the exciton and the Mn2+ ion. Although semimagnetic bulk or thin film systems have been extensively studied for years, the studies of semimagnetic nanostructures are still limited. Semimagnetic NCs is actually a challenging subject of research. On one hand, the validity of applying the macroscopic band theories, e.g. the effective mass or k.p theory, to calculate the electronic structure of those nanostructures is still controversial. On the other hand, due to the strong confinement of NC, the Coulomb interaction between the particles in a NC turns out to be strong and complex. In the past year, we have developed a theory for semi-magnetic NCs containing interacting electrons and a single Mn2+ ion.[3] In this project, we shall extend the theory and numerical technique to study the photoexcited semimagnetic NCs and the interaction between multi-excitons and multi- Mn2+ ions.We shall also explore the possibility of utilizing those semimagnetic nanostructures to realized new spin and biosensing devices. This research project consists of the following three topics: 1. The electronic structure of semimagnetic nanocrystals We shall take multi-scale approaches to calculate the electronic structure of semimagnetic NCs, i.e. the macroscopic k.p theory and the microscopic empirical pseudopotential method. Applying the microscopic theory to the calculation of the electronic structure of nanostructures is however still a challenging task, since typically the number of the atoms constructing the nanostructures is greater than >103 corresponding to the Hamiltonian matrix with the typical size larger than >105 執105. In this topic, we shall build up a 16-node PC cluster system and take the Lanczos algorithm to solve the problem of diagonalization of matrix. 2. Multi-exciton complexes in semimagnetic NCs We shall calculate the energy spectra, excitonic and magnetic properties of photoexcited semimagnetic NCs by using configuration interaction method and exact diagonalization technique, in which the complete interactions between exciton-excion, excion-magnetic ion, and ion-ion are taken into account. Due to spin interaction, an exciton could bind several Mn ions and a new quasi-particle called exciton magnetic polaron (EMP) is formed.We shall study the emission, absorption, and time-resolved optical spectra of semimagnetic NCs and how EMP affects the feature of the spectra. 3. Toward the realization of spin and biosensing devices based on NCs We shall explore the possibility of employing semimagnetc NCs to realize the advanced devices applied in the fields of biosensing and spintronics.We shall propose device models based on the physics knowledge which we acquire in the studies of topics 1 and 2.We shall study the emission pattern of a semimagnetic NC attached to a magnetic biological molecule, and how to recognize the pattern as the fingerprint of the host molecule. The realistic effects which could affect the performace of the devices will be taken into account, like the thermal effect and the decoherence of spin. Reference: [1] D. J. Norris, et al, Nano Lett. 1, 3 (2001). [2] L. Besombes et al,Phys. Rev. Lett. 93, 207403 (2004). [3] S.J. Cheng, to be published in Phys. Rev. B (2006).