半導體量子井及超晶格中紅外線吸收光譜之理論研究

Abstract

本論文研究三個與半導體量子井及超晶格中次能帶間吸收光譜相關的 問題: (一) N型半導體超晶格中橫電場(TE)和橫磁場(TM)吸收光譜之 比較.利用8x8超晶格K-cenetr-dot-p 理論模型,我們計算了N型砷化鎵/砷 化鋁鎵和砷化銦鎵/砷化鎵超晶格之橫電場及橫磁場吸收光譜.在超晶格波 向量為零處之橫電場吸收是起源於導電電子次能帶中s和p狀態互相混合. 由於某些矩陣元素項正負號相反而產生相互抵消的效應使得在超晶格波向 量為零處的橫電場矩陣元素(momentum matrix element)變得很小.隨著波 向量值的增加,橫電場矩陣元素也增加.此現象表示當電子濃度愈高時,橫 電場之吸收也愈大.雖然如此,橫電場吸收與橫磁場吸收相較之下仍是可以 忽略不計的. (二) P型超晶格中應力(strain)對橫電場吸收之影響.我 們同樣使用在(一)中所提之理論模型計算P型無應力砷化鎵/砷化鋁鎵和有 應力砷化銦鎵/砷化鎵超晶格之價電子次能帶結構,包絡波函數(envelope wave function),矩陣元素和吸收光譜等物理量.存在於砷化銦鎵/砷化鎵 超晶格之井層的應力增大了HH1和LH1次能帶間的能量間隔.我們也發現在 有應力超晶格中橫電場吸收光譜之強度增強了.因此之故,應力效應有益於 紅外線量子井光偵測器之應用. (三) P型量子井中方位對橫電場吸收 之影響.我們利用軸近似(axial approximation)4x4 Luttinger-Kohn 漢 彌頓量理論計算(100),(111)和(112)砷化鎵/砷化鋁鎵量子井價電子次能 帶結構.我們發現方位顯著地影響了重電洞(heavy hole)有效質量,因而改 變重電洞和輕電洞(light hole)次能帶相對位置和結構.比較各方位量子 井之橫電場吸收的計算結果,顯示(100)量子井具有較大的吸收強度.此外, 依據對矩陣元素的理論分析,我們設計了窄井結構(narrow-well structure)的(112)量子井以求改善吸收強度.然而計算結果顯示一般 的(100)量子井吸收強度仍是較大. In this thesis, three main topics related to intersubband absorptionspectra in semiconductor quantum wells and superlattices are studied: (1) Comparison of TE amd TM absorption spectra in N-type superlattices.We have calculated explicitly the TE and TM intersubband absorption in N-typeGaAs/ Al0.3Ga0.7As and In0.4Ga0.6As/GaAs superlattices by using 8x8 super-lattices K-center-dot-p theory. The origin of TE absorption at K=0 resultsfrom the mixing of s and p states in the conduction subbands. Due to the cancellation resulting from opposite signs of some bulk momentum matrix elements, the zone- center TE momentum matrix elements are small quantities.Away from the zone center, the enhancement of TE momentum matrix elementsindicates that the higher doping concentration produces the larger TEabsorption. Nevertheless, TE absorption is negligible compared to TM absorption. (2) Strain effects on TE absorption of P-type superlattices. We usethe 8x8 superlattice K-center-dot-p theory for P-type non-strained GaAs/ Al0.3Ga0.7As and strained In0.4Ga0.6As/GaAs superlattices to calculate thevalence subband structures, envelope wave functions, momentum matrix elements, and absorption spectra. The biaxial compressive strain in the welllayer of In0.4Ga0.6As/GaAs superlattice enlarges the energy-level separationbetween HH1 and LH1 subbands. We find that the peak of bound-to- continuumabsorption coefficient is enhanced in strained superlattice. Therefore, thestrain effects are useful for the device application of quantum well infraredphotodetectors. (3) Analysis of the orientational effects on TE absorption spectra inP-type quantum wells. We calculated the valence subband structures in (100),(111), and (112) oriented GaAs/Al0.3 Ga0.7As quantum wells, by solving the 4x4Luttinger-Kohn Hamiltonian with axial approximation. It is found that theorientational effects significantly influence the heavy-hole effective mass.Therefore, energy-level position and subband dispersion of heavy- and light-hole are largely changed with respect to different orientations. The TE intervalence subband absorption spectra are calculated and compared, demonstrating the larger absorption coefficient in (100)-oriented quantumwells. According to the theoretical analysis of zone- center momentum matrixelements we design a narrow-well structure of (112) quantum well to improvethe bound-to-quasi-bound and bound-to-continuum absorption spectra. However,our calculations show the general (100) quantum wells still have largerabsorption coefficient.