局部性聲子對量子井中類氫原子態的影響

Abstract

在本論文中，我們考慮在外加磁場下，置於量子井中央的施體原子狀態。 對該施體原子所引起之局部性聲子可視之為施體在晶格中的諧振運動。在 此我們討論局部性聲子對施體原子之1s-2p+能態躍遷的影響。施體原子的 能階與波函數可由變分法對高斯基底展開而得。在此我們提出電子與局部 性聲子交互作用的漢彌頓量，計算1s-2 p+能態躍遷譜線上的分裂則是依 照White與Koonce所提出的方法。在以矽取代砷化鎵中的鎵原子成為施體 原子，量子井寬為１等效波耳半徑的情形下，我們發現在磁場為20.67特 斯拉附近，躍遷頻率的分裂約為0.15 1/cm。這個頻率分裂的值，或說電 子與局部性聲子的交互作用，預期在量子點中將會增強。 We consider a centered donor in a quantum well and in the the presence of a longitudinal magnetic field. The donor atom gives rise to a localized phonon mode which essentially has the donor along alone involved in a harmonic oscillation. In this thesis, we consider the effect of this localized phonon on the 1s-2p+ transition of the donor states. The donor states are calculated within a variation approach using a Gaussian basis set expansion. An electron-local-phonon inter- action hamiltonian is proposed and the splitting in the 1s-2p+ transition due to this interaction is calculated, following the method of White and Koonce. For the case when the Ga is substituted by a Si donor in a GaAs quantum well of width L=1 a(a=98.7), we find a frequency splitting to 1s-2p+ tran- sition △ν=0.15 1/cm at around B=20.67 Tesla. The splitting, or the electron-local- phonon coupling, is expected to be enhanced in the case of quantum dot.