異質結構半導體元件在電磁場中, 電子能階之量子效應

Abstract

於異質半導体對稱量子井及單一位障結構中，外加磁場方向垂直在長晶的 方向上，我們嚴密地將電子能階推導出來並且利用數值分析反覆求解的方 法計算出能階數值的大小。我們引進一個臨界距離及臨界磁場來描述電子 在臨界條件時於量子井或單一位障中間能階將被藍道能階所主導。所謂臨 界距離定義為電子在磁場中迴轉半徑邊緣與位障邊界之間的距離此時電子 幾乎不受位能障影響。基於這個推導，我們可以預測在量子井或單一位障 的中間藍道能階主導的臨界磁場之大小，與理論推導數值計算的結果比較 顯示出預測值具有相當高的準確度。其次對於非對稱之量子井及非對稱雙 位障之異質量子結構，我們也將電子能階予以嚴密地推導。針對非對稱之 量子井及非對稱雙位障之結構，我們討論能障大小，量子井寬度，位障寬 度及橫向電場對單電子基態與激發態能階之量子效應。對於量子井寬度大 小所造成能階特性圖上的主要差異也加以探討。在較寬的量子井中低能階 會被藍道能階所主導而較窄的量子井中能階會被提昇的特性也得到解釋。 我們也發現在量子井中電子密度分布函數受到非對稱量子井的能階組態及 外加橫向電場的大小影響很大。 The energy spectra of a symmetric quantum well and single barrier within an in-plane magnetic field are exactly derived and the numerical results are calculated by iteration. A critical dis- tance between the edge of electron spiral radius and the barrier boundary is introduced to describe the relation of well or width and the critical magnetic field beyond which the Landau levels will dominate. We can predict by a simple equation when bulk Landau levels will dominate in the middle of the well or barrier region. The energy spectra of an electron in an asym- metric quantum well and an asymmetric quantum double barrier within in-plane magnetic field and electric field perpendicular to the barrier interfaces are exactly derived and the numerical results are calculated by iteration. The ground and excited are calculated for various asymmetric potential barriers, well widths, barrier widths and electric fields. Major different cha- racteristics of energy spectra between wide and narrow wells are discussed. The behaviors of bulk Landau level in well region of a larger well and the elevation of the ground state in a smaller well width are explained. It is found that the density distribu- tion of electrons in a large well region is strongly affected by the asymmetric potential configuration and electric field in the growth direction. The characteristics of the energy spectrum are discussed by the superposition of well-and barrier- potential sub- systems. Major different characteristics of energy spectra with variation of wire radius and potential configuration are The behaviors of bulk Landau levels under large perpendicular netic field are explained. The characteristics of crossing points within neighboring modes is explained by the combined effect of well-and barrier-subsystems.