電子於磁性和非磁性超晶格之傳輸特性

Abstract

本論文研究電子在半導體超晶格、磁子晶體和磁性穿隧接面奈米結構中傳輸之特性。對於半導體超晶格，本文利用能帶圖方法，研究類周期超晶格在不同基底和階數下碎狀迷你能帶的分裂規則。類周期超晶格的能帶分裂可分為好幾個區域，每個區域存在著相同數量的允帶和禁帶。研究發現對於費布那西超晶格結構來說，每個區域的能帶分裂一定會有二個主要禁帶。此主要禁帶的中心和寬度在階數上升時會收斂至常數。除了主要的禁帶之外，大多數禁帶的寬度在系統階數上升時會下降。本文也發現類周期超晶格能帶分裂的不變條件。 關於磁子晶體，本文發現在類周期磁子晶體中的自旋波存在完全傳輸。完全傳輸的位置正好對應於在能帶圖中的重疊能帶邊際。重疊能帶邊際點只會在特定的頻率和層厚度出現。然而，在階數大於3時， 重疊能帶邊際線對於任意的層厚度都會存在。利用布洛赫相位的餘弦可以求出在任意厚度與階數下系統的重疊能帶邊際線之頻率。當階數增加時，在較低階系統中出現重疊能帶邊際線依然會在高階系統中出現。完全傳輸的銳度在高階系統時會增加，可用來發展高品質，多通道的濾波器或共振腔。 本文計算結果顯示，共振峰值和半高寬的大小與類周期磁子晶體的階數有關。當階數上升時，共振峰值數量會成倍的增加。半高寬則是會隨階數的增加而下降。雖然半高寬在高階系統時非常的小，共振點仍因為完全傳輸的特性而保持在1。研究發現共振點的位置和特徵函數cos (KL) 有關。本文提出的填充因子和半高寬之關係可以藉由改變材料厚度來最佳化超窄帶通濾波器的設計。 本文也提出了一個使用超晶格為位障的磁性穿隧接面來提升穿隧磁阻，其中超晶格由非磁性金屬與超薄的氧化鎂絕緣層所組成。相較於傳統用較厚氧化鎂絕緣層的磁性穿隧接面， 磁性穿隧接面的穿隧磁阻可以達到 。研究發現在反平行結構沒有自旋極化共振穿隧時，將會有非常高的穿隧磁阻。

Electron transport in nanostructures, including semiconductor superlattices, magnonic crystals, and magnetic tunnel junctions, is studied in this thesis. For semiconductor superlattices, the splitting rules for the fragmental miniband in quasiperiodic superlattices with arbitrary basis and generation orders are presented using a gap map diagram. The band splitting for the quasiperiodic superlattice can be divided into many regions. Every region has a similar pattern, with the same number of allowed and gap bands. The width of most of the gap bands, with the exception of the major gaps, decreases when the generation order increases. The invariant conditions for band splitting in the quasiperiodic superlattice for arbitrary generation orders are determined. The complete transport of spin waves in a quasiperiodic magnonic crystal is proposed. It is found that complete transport corresponds to the repeated bandedges in the bandedge map. These repeated bandedge points only occur at certain special frequencies and layer thicknesses. However, the repeated bandedge lines exist for arbitrary layer thicknesses, when the order of the quasiperiodic magnonic crystal is greater than 3. The frequency of the repeated bandedge lines for a system with an arbitrary layer thickness and an arbitrary order can be determined using the cosine of the Bloch phase. As the order increases, the repeated bandedge lines in systems with lower orders can also be maintained. The sharpness of the complete transport peaks increases for higher order systems, which is useful for the development of ultrahigh quality multichannel filters. The calculation results show that the number of resonant peaks and the magnitude of the full width half maximum are both dependent on the generation order of the quasiperiodic magnonic crystal. The number of resonant peaks increases exponentially as order of the system increases and the full width at half maximum decreases exponentially as order of the system increases. Even though the full width half maximum is quite small for a high order system, the resonance remains exactly at one, because of the properties of complete transport. It is found that the location of the resonant peaks is related to the eigenfunctions, cos (KL). The relationship between the filling factor and the full width at half maximum allows the optimization of the design of ultra-narrow band filters by changing the thickness of the materials. A magnetic tunnel junction with a superlattice barrier that is composed of nonmagnetic metals and ultrathin amorphous MgO insulators is also proposed to improve tunnel magnetoresistance. Compared to the traditional thick-MgO-based magnetic tunnel junctions, the tunnel magnetoresistance can reach over in magnetic tunnel junctions. The results indicate that an ultrahigh tunnel magnetoresistance is possible when there is no spin-polarized resonant tunneling in the anti-parallel configuration.