本論文主要以WKB漸近展開法研究光調制光譜學中的樣品在中強電場調制下其調制光譜中所出現的法蘭茲—凱爾迪西(Franz—Keldysh effect)的理論，同時進行光調制光譜的實驗以驗證所得的理論。首先，根據光學，電磁學及量子力學的基本理論推導光調制光譜的物理機制﹐並藉由中高電場下電子電洞對的薛丁格方程式來求得在中電場調制下介電常數虛部的調制量﹐可用Airy函數平方的積分式表示之。

接著，對Airy函數的數學特性做了一系列的分析與推導，並引入了WKB漸近展開法來求出介電常數虛部的調制量，再經由K－K relation求出介電常數的實部並與低電場下的Aspnese三階微分公式擬合， 即可決定合適的Seraphin係數並求出反射率的改變量﹐即 ，所得之公式與一般用以擬和及分析實驗數據的公式是一致的；此外，在許多文獻資料中用以表示中電場下介電係數虛部的譜圖在光子能量高於能隙值時會有遞增振盪而發散的現象，但是實際調制光譜的實驗數據都顯示出譜圖的振盪應是隨光子能量的增加而衰減的，因此我們在計算介電係數時，對光子能量引入了增寬參數的修正，經計算後發現經由增寬參數修正過的介電係數由於指數衰減的壓制，的確不會隨著光子能量的增加而發散了。

最後，我們量測本質砷化鎵基板與砷化鎵表面本徵 摻雜結構（ ）兩種樣品在不同激發光強度（改變光壓）的光調制光譜，而分析PR光譜譜線所得的結果與我們推導出的公式所預測的趨勢是一致的。

Modulation spectroscopy of photoreflectance has been widely employed in studies of the photoelectric properties of semiconductors and semiconductor microstructures. However, to our knowledge, completed derivations of the equations used in analyzing the PR spectra have never been presented in literature or textbooks. In this study, the Franz-Keldysh oscillation of the spectra of the modulation spectroscopy of photoreflectance (PR) or electroreflectance (ER) is analyzed theoretically in detail and demonstrated experimentally. The relative formulae are derived in detail. Based on the fundamental theories of optics, electromagnetism and quantum mechanics, the Schrodinger equation of the electron-hole pair modulated with a moderate electric field is expressed by an Airy function while the imaginary part of the dielectric constant can be expressed as an integration of the square of the Airy function over the photon energy. The WKB approximation is employed to execute the integration of . The real part of the dielectric constant is then obtained from via the Kramer-Kronig relation. By comparing the variations of and as a function of electric field at low field limit with Aspenese third derivative formula, the Seraphine coefficients are obtained and thus the formula for the PR spectra, which agrees with equations widely used in analyzing experimental data of photoreflectance and electroreflectance.

The equation for the variation in the imaginary part of the dielectric constant has been presented in various literature and textbooks. The equation represents an oscillation function of photon energy and becomes divergent as the photon energy increases, which apparently violate its nature as a physical quantity. In this study, a broadening parameter is introduced in the derivation of . An oscillation function with exponential

decay is obtained for the variation of , which is not only consistent with its fundamental nature as a physical quantity but also agrees with the features observed experimentally.

The PR spectra of intrinsic GaAs wafer and surface intrinsic-N+ (SIN+) structures are measured with various pump beam intensities. The variation of the PR spectra observed experimentally agrees with expectations of the theoretically derived formulae. In addition, the electro-optical properties obtained from the analysis of the experimental data are consistent with that observed in previous studies.

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