利用Kane模型計算閃鋅礦半導體之泰拉赫茲光整流信號

Abstract

在本論文中，我們利用量子力學的密度矩陣形式，推導一階線性極化及二階差頻極化。並經由Kene模型來表示能帶結構，以計算閃鋅礦半導體之砷化鎵與磷化銦的折射率與二階差頻介電係數。我們由計算的結果得知，二階差頻介電係數有與線性吸收相同的特性，且其值等於入射光頻率往低頻平移二分之一差頻之光整流係數。折射率之數值模擬，不僅可以計算出在能隙附近躍遷對折射率的影響，加上非共振區域折射率之經驗公式後，即可以與實驗數據有很好的擬合度。

In this thesis, the linear and the difference frequency polorizations were obtained by density matrix formalism of quantum mechanics. Based on Kane model to describe band-structure of zinc-blende semiconductors, GaAs and InP, we have calculated the refractive index and the second-order difference frequenncy susceptibility of these materials. It is shown that the second-order difference frequency susceptibility has absorptionlike behavior, In addition, respect to the incident photon energy, its distribution is similar to the optical rectification coefficient but shifted one half of the THz radiation frequency toward the lower energy. Not only the refractive index around the band gap transition can be calculated but also by including the empirical formula for that of nonresonant region match the experimental data quite well.