光激砷化鎵中之全量子動力學

Abstract

本論文理論地探討光激砷化鎵中之非熱平衡電子-電子碰撞及超快熱電子藉極性縱光聲子釋能的現象，其中的方法包括使用非熱平衡格林函數所建立的全量子動力理論及量子相位解調後的半古典波茲曼理論。庫倫碰撞率之奇異點在全量子動力理論的消失有助於比較動態遮蔽強度在不同維度空間的表現。迥於以往的研究結論，低維度空間的遮蔽強度應較高維度的空間強。該現象不僅在電子-電子碰撞成立，電子-極光聲子作用亦有相同的表現。這原因與低維度的庫倫作用力較強有關。此外，量子相位的存在也將使得電子分佈函數隨時間的演化具有記憶的行為。本論文首度發現在量子動力區間內，電子分佈函數將會由於電子-電子碰撞而有振盪的現象。該結果可成功地解釋過去超快同調光子解相時間隨電子濃度關係在量子井及塊材所得不同實驗結果的矛盾。 雖然過去超快熱電子釋能的研究已漸趨飽和，但關於釋能現象在不同空間維度的差異一直沒有一致的結論。本論文使用準二維的聲子模型精確地估計並比較熱電子能量損耗率在量子井及塊材的差別，並發現當電子濃度高於一臨界值2 1018cm-3時，塊材的熱電子釋能速率將明顯快於量子井。該維度的關係在電子-電子碰撞亦有相同的結論，根據計算的結果，非熱平衡的電子在塊材比量子井更快達到準熱平衡的狀態。這是由於電子在高維度的空間具有較多的碰撞路徑使然。另外，過去的認知一向認為熱聲子效應是抑制熱電子釋能的主因。然而，本研究發現量子井中高電子濃度下的動態遮蔽亦有相同抑制熱電子釋能的能力。電漿子-聲子耦合的效應也在計算中考慮，並發現在面電荷密度1011cm-2附近會明顯加速熱電子釋能速率，該現象與電子-電漿子碰撞有關。電子-極光聲子作用隨量子井結構改變的影響也將討論並與過去實驗的結果比較且有相當吻合的趨勢。

We theoretically studied the non-equilibrium carrier-carrier scattering in the quantum kinetic regime and the ultrafast hot-carrier relaxation through the Fröhlich interaction in photoexcited GaAs by solving the Generalized Kadanoff-Baym equation and the semi-classical Boltzmann equation, respectively. The singularity of scattering rate at the vanishing wave vector can be eliminated in the quantum kinetic theory. With the advantage, the difference of screening strength between a bulk and a quantum well can be compared. In contrast to the earlier understanding, the screening strength is shown to be stronger in a lower dimensional structure and this is an evidence for a stronger Coulomb interaction in a quantum well. The screening dependence is also held for the Fröhlich interaction. In the quantum kinetic regime, the Markovian approximation for the scattering process is no longer available due to the carrier’s quantum coherence. The resulting memory effect is firstly demonstrated to be impact on the carrier’s evolution. The carrier-carrier scattering leading to a burning hole on the carrier’s distribution is shown at the early stage and is suggested to oscillate as the time further evolves. The theoretical result can successfully explain an earlier contradiction from the distinct measured power laws of the density dependence of photon-echo dephasing time in two different sample’s dimensions. Among the plenty of investigation on the hot carrier relaxation, the discrepancy from the dimensionality is clarified. With the dielectric continuum model, the hot carrier’s energy-loss rate in a quasi-two dimensional structure was strictly calculated. Above the density of 2 1018cm-3, the hot carrier is shown to be significantly faster in a bulk than a 10nm-wide quantum well due to the higher density of states. The dimensional dependence is also in consistent with the carrier-carrier scattering which shows a faster thermalization in a bulk. In addition, the dynamical screening in a quantum well on the shielding carrier-phonon interaction is demonstrated to be as important as the hot phonon effect when the carrier density is high. This rebuts the earlier argument where the dynamical screening can be neglected. The plasmon-phonon coupling was considered in the calculation and is shown to enhance the energy-loss rate around the density of 1011cm-2 due to the carrier-plasmon scattering. The structure effect on the Fröhlich interaction was also presented and compared to earlier experimental results where a very good agreement can be obtained.