氮化銦、氮砷化銦及磷化銦鎵鋁薄膜的紅外線光譜研究

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(1)物理學系. 國立臺灣師範大學碩士論文. 氮化銦、氮砷化銦及磷化銦鎵鋁薄膜的紅外光譜研究徐經瑋撰一百零一年八月. 國立臺灣師範大學物理學系碩士論文 Department of Physics, National Taiwan Normal University Master Thesis 指導教授：楊遵榮博士 Advisor：Tzuen-Rong Yang, Ph. D.. 氮化銦、氮砷化銦及磷化銦鎵鋁薄膜的紅外線光譜研究 Infrared Spectroscopy Studies of InN/sapphire, InAsN/InP and InGaAlP/GaAs. 研究生：徐經瑋撰 Graduate Student：Ching-Wei Hsu. 中華民國一百零一年八月 August 2012.

(2) 誌謝這篇論文的完成，首先要感謝的當然是楊遵榮教授。由於楊老師這兩年來細心的指導，不厭其煩的指正，另外也學生在論文的寫作上，益加辛勤指正，使整篇論文更加言詞達意。而對學生的影響不僅是在研究上，也在學業及生活上收穫良多，對學生在處理事情的態度上也有很大的影響。也感謝楊老師給我接觸其他實驗室的機會，讓我除了紅外線光譜實驗以外，也能增加其它的經驗。在碩士求學的兩年期間，我學會了要更主動的學習，才能更增強自己的能力，在社會後能更有競爭力。遇到問題的時候，要自己去尋找答案，對我解決問題的能力也有相當增加。老師對我來說是一個表率。在此，謹獻上對楊老師深深地的謝意。再來也要感謝論文口試委員林浩雄教授及盧志權教授對於論文上所有的諸多指教。這裡也特別感謝馮哲川教授給我研究上的協助，也常教導我們做研究的態度要積極，處理事情要迅速、面面俱到，而培養了我積極的處事觀念，並且提供我許多學習及做事的新觀念，謝謝馮老師。也感謝吳文欽教授、林豐利教授、張明哲教授和李沃龍教授在課業上的教導，以及系上所有老師的教誨，學生都發自內心的感激。在這兩年的研究生學習中，學習到好多、無法用言語一一的說明。只期望在這兩年期間所學習到的任何事物，在出社會後，可以學以致用。最後要感謝我的父母以及關心我的所有人，你們是我這兩年來最大的支柱，使我無任何的後顧之憂，我非常感激你你們。在此，願將一切成果獻給我所感謝的人。. 最深的感謝經瑋 2012. 7.. i.

(3) 摘要. 關鍵字: 紅外線光譜、氮化銦、氮砷化銦、磷化銦鎵鋁、光學聲子、傳輸載子在我的論文中，我們藉由分析半導體材料的紅外線光譜圖，來研究它們的光學特性，而不同濃度參雜的成長在藍寶石基板上的氮化銦薄膜、成長在磷化銦基板上的氮砷化銦 (參雜氮)薄膜及成長在砷化鎵基板上的磷化銦鎵鋁薄膜都是本次實驗的研究樣品。紅外線光譜學是一種非破壞性的量測方法，可以在不破壞樣品的情況下，利用晶格的震盪特性，取得樣品的資訊。本研究使用傅立葉式紅外線光譜儀(FTIR) Bruker IFS 66 v/S，進行一系列的室溫(300K)的遠紅外線反射光譜測量。我們並利用介電方程式分析由實驗得到的遠紅外線反射光譜，藉由光譜的模擬，計算出光學聲子及載子特性。從氮化銦的紅外光譜中，我們利用擬和的方法，在大約 473~478 (cm−1) 找到了一個氮化銦的 E1 聲子模。從氮砷化銦的紅外光譜中，它的兩個類聲子模(氮化銦、砷化銦)頻率都隨著氮含量的增加而增加且載流子濃度與有效質量隨著氮含量的增加而增加，但遷移率是減少的。從磷化銦鎵鋁的紅外光譜中，發現有四個明顯的鋒值，一個來自砷化鎵基底而另外三個磷化銦鎵鋁薄膜，但也發現了第五個鋒值，其原因可能來自於磷化銦鎵鋁形成 Cu-Pt 結構而導致峰值的分裂。以及磷化銦與磷化鎵之間發生強烈的耦合導致峰值的結合，使得鋒值只剩三個。這個研究也界定了這些樣品的高頻介電常數、載子濃度、遷移率、有效質量及薄膜厚度。而我們同樣的也可計算出樣品的導電度。希望研究結果對於這些材料特性的資訊建立有些貢獻，也可做為這些材料在應用上的參考依據。. ii.

(4) ABSTRACT Key Word : Infrared Spectroscopy、InN、InAsN、InGaAlP、Optic phonon、 Transport Carrier In this thesis, we study the optical properties of semiconductor materials, especially on infrared reflectance spectra, the InN films grown on sapphire substrates, different compositions of series of InAs1-xNx films grown on InP substrates and In0.5(Ga1-xAlx)0.5P films grown on GaAs substrates were used in this study. Infrared spectroscopy is a non-destructive measurement which can get the information from the lattice vibrations of the samples without doing any damage. Fourier transform infrared (FTIR) Bruker IFS 66 V/S were employed to do a series measurements. A dielectric response model was used to determine the optical and transport properties of the semiconductors. From infrared spectra of InN/sapphire, we found the E1 (TO) phonon mode frequencies were obtained at 473~478 cm−1 by dielectric response function fitting. From infrared spectra of InAs1-xNx/InP, the InAs-like TO phonon mode increases with the increase of N composition x and the InN-like TO phonon mode also increases with the increase of N composition x. With increasing x, the effective mass and carrier concentration increase greatly but mobility decrease greatly. From infrared spectra of In0.5(Ga1-xAlx)0.5P/GaAs, there are apparently four main peaks. And we also could define the four TO frequency peak from low frequency to higher frequency are the GaAs phonon mode, InP-, GaP- and AlP-like phonon mode that similar with reference. However, there is a fifth phonon mode that is the Cu-pt type ordered characteristics affect the TO-phonon peak split into two TO mode. And the InP and GaP mode combine into one mode that the effects are made possible by. iii.

(5) the strong coupling between the Ga-P and In-P vibrations. In my works, we also have analyzed the high-frequency dielectric constant, carrier concentration, mobility and effective mass and the thickness of the films of these materials. Conductivity had been calculated, too. This study established a data base of these materials and provides a reference for their applications.. iv.

(6) TABLE OF CONTENTS 誌謝 …………………..…………………………………………..…….….……….. i 摘要 ………………………………………………………………………...……… ii ABSTRACT …………..…………...………………………………..….………... iii TABLE OF CONTENTS ………..……………………………………….……. v LIST OF TABLES ……..……………………………………………….........… vii LIST OF FIGURES …………..………………………………………….......… ix 1. INTRODUCTION ……..………...…………….……………......….. 1 2. THE OPTICAL CONSTANTS AND REFLECTANCE SPECTRA OF SEMICONDUCTOR .…………....………………….….. 4 2.1 Propagation of Electromagnetic Waves ……….………………..….......…….... 4 2.2 Kramers-Kronig Relations …………………………..……………………...… 8 2.3 The Dielectric Response Model ………………………….………...…….….. 12 2.4 Harmonic Oscillator Model for Phonons and Plasma …………..…..…......… 12 2.5 The Dielectric Response Function and Reflectivity ………………..…….….. 16. 3. INFORMATION OF INSTRUMENTS AND SAMPLES …......... 19 3.1 Fourier Transform Infrared (FTIR) Spectrometer …………………..…...…... 19 3.2 Principles of FTIR Spectroscopy ………….……..…….……..…...…...……. 27 3.3 Fourier Transform …………………..……………………………………….. 30 3.4 Sample Preparation ……………………..…………………………………… 31 3.5 Experiment Procedure ……………………………………………..………… 34. 4. EXPERIMENT RESULTS AND DISCUSSIONS ………....…….. 39 4.1 Middle Infrared Spectrum Analysis of InN/sapphire ..………………............. 40 4.2 Far ( &Middle ) Infrared Spectrum Analysis of InAs1-xNx/InP ……….....…... 54. v.

(7) 4.3 Far Infrared Spectrum Analysis of In0.5(Ga1-xAlx)0.5P/GaAs ………...….…… 65. 5. CONCLUSIONS ……………....…………………...….…….......… 80 REFERENCE ………………….………………….……..…..….......... 83 APPENDIX A ………………………………..……………..…….…... 88 APPENDIX B ………………………………..……….…………..…... 94. vi.

(8) LIST OF TABLES TABLE 3.1.1: The information of interferometer compartment …………................ 21 TABLE 3.1.2: The information of component ……………......……….…………… 22 TABLE 3.1.3: The effective frequency of beam splitters …………………..…...….. 23 TABLE 3.1.4: Light sources and wavenumber range ………………….………..…. 24 TABLE 3.1.5: Detectors and detect range ……………………………………….…. 25 TABLE 3.1.6: Windows and the transmitting range ……………………………….. 26 TABLE 3.4.1: Growth conditions of InN on Sapphire substrate ……..………….… 32 TABLE 3.4.2: Growth conditions and nitrogen composition of InAsN on InP substrate …………………………………..…………………..…….. 33 TABLE 4.1.1: Classical oscillator parameters for sapphire o-ray ……………….…. 44 TABLE 4.1.2: Optical constants of InN by dielectric response function fitting …… 51 TABLE 4.1.3: Transport properties of InN films by Hall measurement and electric response function fitting …………………………………………..... 52 TABLE 4.2.1: Optical parameters and high-frequency dielectric constant of InP substrate at 300K by fitting ……………………………………….... 56 TABLE 4.2.2: Optical parameters and high-frequency dielectric constant of InAs1-xNx/InP at 300K by fitting …………………………………..... 61 TABLE 4.2.3: Transport and electrical parameters of InAs1-xNx/InP at 300K by fitting ………………………………………………………………... 63 TABLE 4.3.1: Optical parameters and high-frequency dielectric constant of InGaAlP/GaAs for T-series at 300K by fitting ……………………... 73 TABLE 4.3.2: Transport and electrical parameters of InGaAlP/GaAs for T-series at 300K by fitting ……………………………………………………... 73. vii.

(9) TABLE 4.3.3: Optical parameters and high-frequency dielectric constant of InGaAlP/GaAs for E-series at 300K by fitting …………………..… 74 TABLE 4.3.4: Transport and electrical parameters of InGaAlP/GaAs for E-series at 300K by fitting ……………………………………………………... 74 TABLE 4.3.5: All parameters of GaAs substrate for T-series at 300K by fitting ….. 75 TABLE 4.3.6: All parameters of GaAs substrate for E-series at 300K by fitting ….. 75. viii.

(10) LIST OF FIGURES FIGURE 2.1.1: Wave propagation in a bulk ………………………………...………. 6 FIGURE 2.1.2: Wave propagation in a film/substrate ………………………...…….. 7 FIGURE 2.2.1: Integral diagram of residue theorem …………………………..……. 9 FIGURE 3.1.1: The Bruker IFS 66 v/S …………………………………….........…. 20 FIGURE 3.1.2: Interferometer compartment and optical path (Dotted Line). © Bruker ……………………………………………………......…. 21 FIGURE 3.1.3: Optical path (dotted line) for sample compartment spectrum Acquisition. © Bruker ……..……………………….……….…….. 21 FIGURE 3.1.4: Beamsplitter. © Bruker ……...………………………………….…. 22 FIGURE 3.1.5: Spectrum Range of Beam Splitters. © Bruker ………………….…. 23 FIGURE 3.1.6: Spectrum Range of IR Light Source. © Bruker ……………...……. 24 FIGURE 3.1.7: Spectrum Range of IR Detectors. © Bruker ……….……..….......... 25 FIGURE 3.2.1: A configuration of the Michelson Interferometer ……………...….. 28 FIGURE 3.5.1: The background of middle infrared spectrum …………………..…. 35 FIGURE 3.5.2: The background of far infrared spectrum …………………………. 35 FIGURE 3.5.3: Fitting program of dielectric response model by Fortran …………. 37 FIGURE 3.5.4: Fitting program of dielectric response model by Matlab ……….…. 38 FIGURE 4.1.1: Middle Infrared reflectance spectra of InN/sapphire from 400 cm-1 to 1000 cm-1 ………………………………………………….…….… 41 FIGURE 4.1.2: Middle Infrared reflectance spectra of InN/sapphire from 400 cm-1 to 4000 cm-1 ………………………………………………………….. 42 FIGURE 4.1.3: Middle Infrared reflectance spectra of Sapphire substrate from 400 cm-1 to 1050 cm-1 ………………………………………………….. 42. ix.

(11) FIGURE 4.1.4: Middle infrared reflectance spectrum and fitting of Sapphire substrate ………………………………………………………….... 44 FIGURE 4.1.5: Middle infrared reflectance spectrum and fitting of InN/sapphire CC-21 ……………………………………….……………..……… 45 FIGURE 4.1.6: Middle infrared reflectance spectrum and fitting of InN/sapphire CC-28 …………………………………………………………..…. 45 FIGURE 4.1.7: Middle infrared reflectance spectrum and fitting of InN/sapphire CC-30 ………………………………………………………….….. 46 FIGURE 4.1.8: Middle infrared reflectance spectrum and fitting of InN/sapphire CC-40 ……………………..………………………………...…..… 46 FIGURE 4.1.9: Middle infrared reflectance spectrum and fitting of InN/sapphire CD-2 ………………………………………………………………. 47 FIGURE 4.1.10: Middle infrared reflectance spectrum and fitting of InN/sapphire CD-7 ……………………………………….………………..…… 47 FIGURE 4.1.11: Middle infrared reflectance spectrum and fitting of InN/sapphire CD-8 …………………………………………………………...… 48 FIGURE 4.1.12: Middle infrared reflectance spectrum and fitting of InN/sapphire CD-9 ………………………………………………………….….. 48 FIGURE 4.1.13: Middle infrared reflectance spectrum and fitting of InN/sapphire CD-10 ……………………………………………………………. 49 FIGURE 4.1.14: Middle infrared reflectance spectrum and fitting of InN/sapphire CD-14 ……………………………………………………………. 49 FIGURE 4.1.15: Middle infrared reflectance spectrum and fitting of InN/sapphire CD-15 ……………………………………………………….…… 50 FIGURE 4.1.16: Middle infrared reflectance spectrum and fitting of InN/sapphire CD-16 ……………………………………………………………. 50. x.

(12) FIGURE 4.1.17: A comparison between the IR carrier concentrations and that obtained from Hall measurements …………………………….…. 51 FIGURE 4.2.1: Far infrared reflectance spectra of different N composition of InAs1-xNx/InP …………………………………………………...…. 54 FIGURE 4.2.2: Far infrared reflectance spectrum of InP substrate ……………...… 55 FIGURE 4.2.3: Far infrared reflectance spectrum and fitting of InP ………………. 56 FIGURE 4.2.4: Far infrared reflectance spectrum and fitting of InAs0.998N0.002/InP . 57 FIGURE 4.2.5: Far infrared reflectance spectrum and fitting of InAs0.978N0.022/InP . 57 FIGURE 4.2.6: Far infrared reflectance spectrum and fitting of InAs0.976N0.024/InP . 58 FIGURE 4.2.7: Far infrared reflectance spectrum and fitting of InAs0.97N0.03/InP … 58 FIGURE 4.2.8: Far infrared reflectance spectra and TO frequencies of different N composition of InAs1-xNx/InP ……………………………………... 59 FIGURE 4.2.9: TO and LO frequencies versus N composition x of InAs1-xNx/InP by fittings and calculations ………………………………………….... 60 FIGURE 4.2.10: Phonon oscillator strength versus N composition x of InAs1-xNx/InP …………………………………………………….. 60 FIGURE 4.2.11: Effective mass versus N composition x of InAs1-xNx/InP ………... 61 FIGURE 4.2.12: Carrier concentration and mobility versus N composition x of InAs1-xNx/InP …………………………………………………….. 62 FIGURE 4.2.13: Conductivity versus N composition x of InAs1-xNx/InP …………. 62 FIGURE 4.3.1: Far infrared reflectance spectra of InGaAlP/GaAs for T-series at 300K …………………………………………………………..…. 66 FIGURE 4.3.2: Far infrared reflectance spectra of InGaAlP/GaAs for E-series at 300K …………………………………………………………...… 66 FIGURE 4.3.3: Far infrared reflectance spectrum and fitting of InGaAlP/GaAs T382 ……………………………………………………………..... 68. xi.

(13) FIGURE 4.3.4: Far infrared reflectance spectrum and fitting of InGaAlP/GaAs T383 ………………………………………………………………. 68 FIGURE 4.3.5: Far infrared reflectance spectrum and fitting of InGaAlP/GaAs T453 ………………………………………………………………. 69 FIGURE 4.3.6: Far infrared reflectance spectrum and fitting of InGaAlP/GaAs T454 ………………………………………………………………. 69 FIGURE 4.3.7: Far infrared reflectance spectrum and fitting of InGaAlP/GaAs E260 ………………………………………………………………. 70 FIGURE 4.3.8: Far infrared reflectance spectrum and fitting of InGaAlP/GaAs E261 ..……………………………………………………………... 70 FIGURE 4.3.9: Far infrared reflectance spectrum and fitting of InGaAlP/GaAs E264 ………………………………………………………...…….. 71 FIGURE 4.3.10: Far infrared reflectance spectrum and fitting of InGaAlP/GaAs E269 ……………………………………………………………... 71 FIGURE 4.3.11: Far infrared reflectance spectrum and fitting of InGaAlP/GaAs E270 ………………………………………………………….….. 72 FIGURE 4.3.12: Far infrared reflectance spectrum and fitting of InGaAlP/GaAs E271 ……………………………………………………………... 72. xii.

(14) CHAPTER 1. INTRODUCTION In this thesis, three kinds of semiconductor have been studied by infrared (IR) reflectance spectra which are InN films grown on sapphire with twelve samples, InAsxN1-x film grown on InP with four samples distributed in 0.002≦x≦0.03 and In0.5(Ga1-xAlx)0.5P (x ~ 0.24 and 0.18) films grown on GaAs with ten samples. First, several models were used to analyze the IR reflectance spectra such as a phonon-phonon model [1,2], a Plasmon-phonon model [3,4,5], a phonon-phonon model with multi-layers [6,7,8] and a Plasmon-phonon model with multi-layers [9,10]. In this thesis, we used a multi-layer dielectric response model to study the IR reflectance spectra. The details of the derivations of the dielectric response model will be introduced in chapter 2. Second, we will introduce the Fourier Transform Infrared (FTIR) spectrometer. The FTIR spectrometer is a non-destructive technique so it is preferred over the traditional filter spectrophotometer. The FTIR Bruker IFS 66 v/S has been employed to do these series of infrared reflectance measurements to study the optical phonon behavior and transport properties of these samples. We had analyzed the IR spectra by the dielectric response model and fitting program. The details of the instrument and analysis procedures are presented in the chapter 3. Third, to analyze these IR reflectance spectra, the optical parameters such like transverse-optical phonon mode frequency, strength, damping and the transport properties such as free carrier concentration, mobility and effective mass and high-frequency dielectric constant and thickness of the film are characterized by fittings. And we also could compare these results to Hall or Raman measurements. All. 1.

(15) the discussions of reflectance spectra will be presented in the chapter 4. Finally, we combined these discussions and give conclusions for these samples in a new chapter. I hope all experiment analysis results are useful. And it provides a reference for the application of these materials and infrared reflectance spectrum studies. The conclusions of our works will be presented in chapter 5.. About InN Films Grown on Sapphire For many devices applications, indium nitride (InN) is an important III-nitride semiconductor [11]. It is a potential material for optoelectronic devices, such as low-cost solar cells with high efficiency, optical coatings, and various types of sensors because a wurtzite crystal structure and a direct band gap of 1.9 eV [12]. Moreover, It also has a particular advantages in high-frequency centimeter and millimeter wave devices and the electrochromic effect [13] because the transport characteristics of InN are better than GaN and GaAs [14,15].. About InAs1-xNx Films Grown on InP Low-nitrogen-content zincblende III–V alloys have received much attention in the recent years [16-18]. Owing to InAs has a narrow band gap of 0.36 eV at room temperature the indium arsenide nitride (InAsN) should be a potential material for infrared technology. Using InAsN to substitute InAs can alleviate the critical thickness limitation of the quantum well because of its small lattice constant. In addition, the band-gap energy of the quantum well can also be reduced further because of the huge bowing effect. These two features reveal the possibilities of extending the wavelength of lasers on InP substrates to the longer infrared range [19]. Up to now, there were only very limited efforts directed to this alloy [20-22].. 2.

(16) About In0.5(Ga1-xAlx)0.5P Films Grown on GaAs Indium gallium aluminium phosphide (InGaAlP), the quaternary alloy In0.5(Ga1-xAlx)0.5P, lattice-matched to GaAs, has a direct band gap transition in the wavelength range between green and red and it is useful for optoelectronic applications such as visible laser diodes (LDs) [23-27], light emitting diodes (LEDs) [28,29], and heterojunction bipolar transistors [30]. It has been used for bulk and quantum well active and confinement layers [23-25], layers in distributed Bragg reflectors for visible vertical cavity surface emitting lasers [26], high-power and reliable LDs for large-memory-capacity optical disk drives [27], and high brightness visible LEDs for large area displays [28,29].. 3.

(17) CHAPTER 2. THE. OPTICAL. CONSTANTS. REFLECTANCE. SPECTRA. AND OF. SEMICONDUCTOR. Anyone can not just use eyes to see what happened in the solids. Electromagnetic wave is the useful technique to study the crystal solids. In this thesis, we used the infrared spectroscopy to study the semiconductor films and dielectric response model to analyzing the infrared reflectance spectrum. The infrared reflectance spectrum comes from the vibration of the lattice, impurity, electrons, holes, phonons and free carriers, and so on. Because of we must to explain the infrared principle a dielectric response model has been established for analyzing the reflectance spectrum. Infrared spectroscopy exploits the fact that molecules absorb specific frequencies that are characteristic of their structure. These absorptions are resonant frequencies, i.e. the frequency of the absorbed radiation matches the frequency of the bond or group that vibrates. We could use the shape of the molecular potential energy surfaces, the masses of the atoms and the associated vibronic coupling to determine the energies.. 2.1 PROPAGATION OF ELECTROMAGNETIC WAVES. Maxwell’s Equations Maxwell's equations are a set of four linear partial differential equations that,. 4.

(18) together with the Lorentz force equation, form the foundation of classical electrodynamics, classical optics and electric circuits theory. These equations can be used to explain and predict all macroscopic electromagnetic phenomena [31]. Maxwell's equations:.   D  . (2.1.1).    D  H  j  t   B  E   t   B  0. (2.1.2) (2.1.3) (2.1.4). Where.     j  E , D  E. (2.1.5). Now we consider that if the sample medium is conducting. From the eq. (2.1.2).    and eq. (2.1.5) and the general solution for plane waves E  E0 e i qr t  , we could get    ∇× H = j + iωεE  = (σ + iωε ) E = iω(ε +. σ  )E iω.  = iω~ εE. (2.1.6). σ ~ ε =ε+ iω. (2.1.7). Where. We could get the dielectric constant for the sample medium is conducting. The eq. (2.1.5) and eq. (2.1.7) will be used more in section 2.4.. Reflection Coefficient and Reflectivity The reflection coefficient is used in physics and electrical engineering when. 5.

(19) wave propagation in a medium containing discontinuities is considered [32]. The results are. r. E r n1  n2  Ei n1  n2. (2.1.8). Here Er and Ei are the electric field strength of the reflected wave and incident wave. And the complex refractive index n is a complex value and could be expressed to a real part and an imaginary part.. n j  n j  i j. (2.1.9). With n is refractive index and k is extinction coefficient.. FIGURE 2.1.1: Wave propagation in a bulk.. We already know the n1  1 ,  1  0 in a space of vacuum and the complex refractive index of medium n2  n2  i 2 will be defined. Replace these parameters into eq. (2.1.9), then. r. n2  1  i 2 n2  1  i 2. R  rr* . n2  12   2 2 n2  12   2 2. Where R is the reflectivity for bulk. Considering different conditions: (1) When n2  1 and  2  1 ,. 6. (2.1.10). (2.1.11).

(20) R. n2  12 n2  12. (2.1.12). (2) When  2  n2 , or     0 that means n2  0 , R 1. (2.1.13). (3) Consider the interference between the reflect wave from medium 1 to medium 2 and the reflect wave from medium 2 to medium 3 in Figure 2.1.1. The reflectivity will become. R' . 4 R sin 2 . 1  R . 2 2.  4 R sin 2 . (2.1.14). Where  is the phase shift between the two reflect waves and could be expressed as. . nd c. (2.1.15). And d is the thickness of the material [33-35]. Now, to consider the reflectance of a thin film grown on a substrate, we used a three-medium “air-film-substrate” system. To compare the Figure 2.1.1, we should add a complex refractive index of substrate n3 = n3 + iκ 3. FIGURE 2.1.2: Wave propagation in a film/substrate.. 7.

(21) The reflection ~ r123 [36] at normal incidence for such an film of thickness d can be written as ~ r ~ r e i 2  ~ r123  12 ~ ~23 i 2  1  r12r23e. (2.1.16). n~i  n~ j Where ~ rij  ~ ~ are the Fresnel coefficients and β = 2πdω n2 + iκ 2 is a phase ni  n j multiplier. The reflectivity for film/substrate as [37]. ~ r ~ r e i 2  2 R   ~ r123  12 ~ ~23 i 2  1  r12r23e. 2. (2.1.17). 2.2 KRAMERS-KRONIG RELATIONS. Kramers-Kronig Relations The Kramers–Kronig relations, named for Ralph Kronig and Hendrik Anthony Kramers, are bidirectional mathematical relations, connecting the real and imaginary parts of any complex function that is analytic in the upper half-plane [38]. These relations enable us to find the real part of the response of a linear passive system if we know the imaginary part of the response at all frequencies, and vice versa [39]. The    be a complex function which is composed of a real part and an imaginary part as.      '    i ' '  . (2.2.1). And  '   is an even function and  ' '   is an odd function. That means.  '      '   ,  ' '       ' '   Given any analytic function    , then. 8. (2.2.2).

(22)   .  d '  '  0. (2.2.3). FIGURE 2.2.1: Integral diagram of residue theorem. The residue theorem for any contour within this region. We choose the contour to trace the real axis, a hump over the pole at ω = ω' and a semicircle in the upper half plane at infinity..   '.   '.   '.   '.   '.  d' '   d'  '  d' '  d' '  d' '  0 1. 2. 3. (2.2.4). 4. And the fourth term.   '. lim  d '  '  0. (2.2.5). R  c. By variable transformation, we could get  '    e i and leads d '  ie i d ,  '  e i. (2.2.6). Where  is an infinitesimal displacement of the pole. Therefore, replace the eq. (2.2.6) to the second term and it will become. lim.  d '. R 0, 0 c. 0   '    e i  i  lim  d ie  i    ' R0, 0  e i. On the other hand, the first and third terms will become. 9. (2.2.7).

(23)  d ' 1.    '   '   '   d '  P  d '  ' 3  '  ' .  i    i  '    i ' '  . (2.2.8). Where P is Cauchy principal value which could avoid the singularity. To divide eq. (2.2.8) into a real part and an imaginary part..  '   . 1. .  ' '    . . P  d ' . 1. . .  ' '  '  '. P  d ' .  '  '  '. The eq. (2.2.9) and eq. (2.2.10) multiplied by. (2.2.9) (2.2.10).  ' . Then the real part and  '. imaginary part of the susceptibility will become.  ' '  ' '  2   '  ' '  '  P  d ' 2 2 2 2    0  '   '  1   '  ' '  2   '  '  ' '     P  d '   P  d ' 2 2 2 2    0  '   '   '   . 1. . P  d '. (2.2.11) (2.2.12). So far, the well-known Kramers-Kronig relations have been derived [34,39].. Complex Refractive Index and Dielectric Constant However, we only obtained the reflectivity by measurement. We should find out the relationship between R  and θ (ω) that the refractive index n and extinction coefficient  will be defined. The reflection coefficient could be expressed as. r    R e i  rr    iri  . (2.2.13). Where R  is the reflectivity and  is the wavenumber of the incident light. Here, we do logarithmic transformation to eq. (2.2.13). ln r    Using the K-K relations, substitute. 1 ln R   i   2. (2.2.14). 1 ln R    '   and      ' '   into eq. 2. 10.

(24) (2.2.12) and that we gets.     . 2. . . P. 1 2. . . 0. . 0. 1 ln R  2 d ' 2 2  ' . d ' ln.  ' d ln R  d '  ' d '. (2.2.15). We could get that the real part R(ω) has relation with imaginary part θ (ω) and using the eq. (2.2.11) also has the same result. Then back to eq. (2.2.13) that the reflection coefficient could also be represented by its amplitude and phase terms r. Ereflection Eincident. . n  i  1  R cos   i sin   n  i  1. (2.2.16). With n is the refractive index and  is the extinction coefficient. Then we could get n  .    . 1  R . 1  R   2 R  cos  2 R  sin . 1  R   2 R  cos . (2.2.17). (2.2.18). Finally, we use the dielectric constant to connect the complex refractive index n  n  i  . (2.2.19).    1  i 2  n 2   2  2in. (2.2.20). 1  n 2   2. (2.2.21).  2  2n. (2.2.22). To use those relations, we could calculate the complex refractive index, refractive index, extinction coefficient and dielectric constant of the materials [33,34,39].. 11.

(25) 2.3 THE DIELECTRIC RESPONSE MODEL. Dielectric Response Model Aquanovich, Kravtsov and Cohen have been described the dielectric response model in long wavelength (Infrared) region. The dielectric response function could be expressed as.      fc     pl     int er     int ra  . (2.3.1). The right four terms are dielectric response function, but origin different.[33,34] These parameters from eq. (2.3.1) are.  fc   : Contribution from free carriers.  pl   : Contribution from phonons.  int er   : Contribution from interband electron transitions.  int ra   : Contribution from intraband electron transitions.. 2.4 HARMONIC OSCILLATOR MODEL FOR PHONONS AND PLASMA. Plasma-Phonon Coupling Start from the simple harmonic motion of electrons [39] in an electric field is   d 2x (2.4.1) m 2  eE dt    Then to solve this equation, we already now that E  E0 e i qr t  and get solution. 12.

(26)   eE x m 2. (2.4.2).  And the electric dipole moment P could be derived as    ne 2 E P  nex   m 2. (2.4.3). From the eq. (2.1.5), the dielectric constant    also could be expressed as.   D  P   1        0 E    0 E    1. ne 2  0 m 2.  ~ p 2     1  2     . (2.4.4). Where    is the high-frequency dielectric constant and  p is the plasma frequency could be defined as. p2 . ne 2  0m. (2.4.5). Consider the different frequency of incident light:. ~ =>   0 (1)    p This frequency region of light could not propagate in the medium which means the light will all reflect from the sample.. ~ =>   0 (2)    p From eq. (2.1.11), the longitudinal mode frequency could be defined as ~ LO   p. .. ~ =>   0 (3)    p This frequency region of light could propagate in the medium. The Drude model predicted carrier behavior when we consider the effective mass of electrons m* and relaxation time  . Now, let us consider the effect of damping. 13.

(27) The equation of motion for free carriers could become  2  * d x * 1 dx m  m   e E  dt dt 2. (2.4.6). Where m* is effective mass of electrons and  is relaxation time. By variable   dv transformation, we could get x = that replaced to the eq. (2.4.6) and get dt    dv v (2.4.7) m*     eE dt  The general solution is  v m. *. .  eE 1  i. .  eE  *  m 1  i . (2.4.8).    The current density j = σE = nev , then  nev ne 2     * m 1  i  E. (2.4.9). Using the eq. (2.1.7) and we could get.  ( )   () . p2   . i. . . (2.4.10). Phonon-Phonon Oscillation and Damping Considering the oscillation of phonons, the equation of motion [39] for TO phonons is   d 2x 2  m 2  TO mx  eE dt. To solve the equation, we obtained the general solution is  eE  x 2 m 2   TO. (2.4.11). (2.4.12). Where TO is the transverse-optical phonon mode frequency. Substituting the  electric dipole moment P into eq. (2.4.12) then. 14.

(28) . .  ne 2  2   2  TO P  E m. (2.4.13). Combine it with eq. (2.4.4). ne 2         2 m  2  TO. . . (2.4.14). If   0 and eq. (2.4.14) becomes.  0     . ne 2 2 mTO. (2.4.15). We could replace eq. (2.4.15) to eq. (2.4.14) and gets.  ( )     . TO 2  0      2  TO 2. (2.4.16). ~ and eq. (2.4.16) becomes If   0 ,   LO   p. TO 2  0      ( LO )      0  LO 2  TO 2 We get the Lyddane-Sachs-Teller (LST) Relation [40]  0    . (2.4.17). LO 2 . TO 2. Now, let us consider the effect of damping. The equation of motion could become m.    d 2x dx 2   m   TO mx  eE 2 dt dt. To solve the equation, we obtained the general solution is  eE  m x 2   i  TO 2. (2.4.18). (2.4.19). So, to combine the eq. (2.4.4), eq. (2.4.15) and LST relation that the dielectric function becomes .       1  . LO 2  TO 2  TO 2   2  i . 15.

(29)     .     . TO 2  0     TO 2   2  i STO. 2. (2.4.20). TO 2   2  i. Where S is the oscillation strength of TO phonon. And adding the contribution from free carrier (eq. (2.4.10)), the dielectric function will becomes. p STO          2 2 TO    i     i      2. 2. (2.4.21). Actually, the eq. (2.4.21) is the main equation of the dielectric response model [33,34].. 2.5 THE DIELECTRIC RESPONSE FUNCTION AND REFLECTIVITY. Dielectric Response Function According to Aschcroft, Dixon and Jackson inference, we replaced the eq. (2.4.21) into the eq. (2.3.1)..           j. S j TO j. 2. TO 2   2  i j j. . p2 i       .  int er     int ra  . These parameters from eq. (2.5.1) are.  : The frequency (wavenumber) of incident light.     : The high-frequency dielectric constant. TO : The frequency of jth transverse-optical phonon mode. j. 16. (2.5.1).

(30) S j : The oscillator strength of jth phonons. γj : The damping constant of jth phonons.  p : The plasma frequency.  : The relaxation time. m*  Note the relaxation time   , where m * is the effective mass of electrons and e. e is the charge of an electron. And from the eq. (2.4.10), the Plasma frequency  P. could be expressed as. P 2 . 4ne 2 m * 0. (2.5.2). Where  0 is the vacuum dielectric constant [33-35].. Reflectivity for the Bulk Let us back to the eq. (2.2.19). The relation between dielectric response function and complex index of refraction is.     n  n  ik. (2.2.19). With n is refractive index and k is extinction coefficient. The reflectivity R and absorption coefficient  of infrared spectra could be expressed by refractive index and extinction coefficient as. R( ) . n  12  k 2 n  12  k 2 2k c. . (2.5.3). (2.5.4). The eq. (2.5.3) is the reflectivity of the bulk [33,34].. Reflectivity for Two Layer System To consider the reflectance of a thin film grown on a substrate, we used a. 17.

(31) three-medium “air-film-substrate” system with dielectric response functions ε1 = 1 (air), ε 2 = ~tf (thin film), and ε 3 = ~s (substrate). Following Cadman and Sadowski [36], the reflection ~ r123 at normal incidence for such an epilayer of thickness d can be written as ~ r ~ r e i 2  ~ r123  12 ~ ~23 i 2  1  r12r23e. (2.5.5). n~i  n~ j Where ~ rij  ~ ~ are the Fresnel coefficients and   2d ~( ) 2 is a phase ni  n j multiplier [37]. The power reflection R(ω) are simply given by ~ r ~ r e i 2  2 R   ~ r123  12 ~ ~23 i 2  1  r12r23e. 2. (2.5.6). If the incident light is perpendicular to the sample, eq. (2.5.3), eq. (2.5.4) and eq. (2.5.6) will be suitable for use. In our experiment, we measure the reflectivity of the infrared light from sample. And we fitted the spectra and analyzed it by the relation between reflection coefficient and dielectric response function.. 18.

(32) CHAPTER 3. INFORMATION OF INSTRUMENTS AND SAMPLES. Fourier transform infrared (FTIR) spectroscopy is a technique which is used to obtain an infrared spectrum of absorption, emission, photoconductivity or Raman scattering of a solid, liquid or gas [44]. FTIR spectroscopy has been a workhorse technique for the materials analysis. We do a series measurement by the FTIR Bruker IFS 66 v/S in this thesis. The Bruker 66 v/S configuration contains beam splitter, light source, detector, aperture changer, window, vacuum system and low temperature system. This chapter will introduce the principle and the configuration of the FTIR Bruker IFS 66 v/S, the information of samples and the experiment procedures.. 3.1 FOURIER TRANSFORM INFRARED (FTIR) SPECTROMETER. The FTIR Bruker IFS 66 v/S was employed to do the series measurements in this thesis. FTIR spectrometer is preferred over the traditional filter spectrophotometer for several reasons: • It is a non-destructive technique. • It provides a precise measurement method which requires no external calibration. • It can increase speed, collecting a scan every second.. 19.

(33) • It can increase sensitivity – one second scans can be co-added together to ratio out random noise.. FIGURE 3.1.1: The Bruker IFS 66 v/S.. The Figure 3.1.1 and Figure 3.1.2 show the optical path of the Bruker IFS 66 v/S. The infrared light is emitted from the light source (Element A in Figure 3.1.1). After once reflection, the infrared light passes the aperture wheel (Element B in Figure 3.1.1). Through the aperture wheel, the light hits the beam splitter (Element D in Figure 3.1.1), and then the light is split into two parts at the beam splitter. One beam through the beam splitter to a mirror and the others reflect from the beam splitter to another mirror. Next, both beams recombine into a new light and produce interference at interferometer (part C of Figure 3.1.1). After interference, the light will through a window (Element F in Figure 3.1.1) and propagates to the sample (Part C in Figure 3.1.2). We could select a transmission or reflection measurement that depend which holder be used. After that, the light thought into the detector (Element D in Figure 3.1.2). The signal will be processed under Fourier Transform by computer and finally get the spectrum. The detail of each element will be introduced one by one below [34].. 20.

(34) FIGURE 3.1.2: Interferometer compartment and optical path (dotted line) © Bruker. TABLE 3.1.1: The information of interferometer compartment. Description. Description. A. Globar Source. D. Beamsplitter. B. Aperture Wheel. E. Vacuum Manifold. C. Interferometer. F. Window or shutter. FIGURE 3.1.3: Optical path (dotted line) for sample compartment spectrum acquisition. © Bruker. 21.

(35) TABLE 3.1.2: The information of component. Component. Component. A. Source “0” (a Globar). C. Sample holder position. B. Interferometer. D. DLATGS detector. Beam Splitter Different splitter will produce different interference frequency (wavenumber). The details are listed in Table 3.1.3. In our works, the Mylar 6 and KBr were chosen in our measurements.. FIGURE 3.1.4: Beamsplitter. © Bruker. 22.

(36) FIGURE 3.1.5: Spectrum Range of Beam Splitters. © Bruker. TABLE 3.1.3: The effective frequency of beam splitters. Beam Splitter. Wavenumber (cm-1). Mylar 125 (μm). 10 ~ 35. Mylar 23 (μm). 30 ~ 100. Mylar 6 (μm). 60 ~ 450. Mylar 3.5 (μm). 100 ~ 720. KBr. 400 ~ 4800. CaF2. 1000 ~ 10000. Quartz. 8000 ~ 25000. Light Source There are three types of light source: Far-infrared (FIR), Middle-infrared (MIR), Near-infrared (NIR), which are listed in Table 3.1.4. In this thesis, far and middle infrared reflectance spectra were measured, so the Mercury lamp and Globar will be. 23.

(37) chosen in our experiments.. FIGURE 3.1.6: Spectrum Range of IR Light Source. © Bruker. TABLE 3.1.4: Light sources and wavenumber range. Light. Light Source. Wavenumber (cm-1). FIR. Mercury lamp. 50 ~ 400. MIR. Globar. 160 ~ 5000. NIR. Tungsten lamp. 3000 ~ 25000. Detector When a light reflect from these materials into the detector, it will induce an electrical potential or a current. Then the intensity of light could be measured from the induced current. The different detectors will be used with different light frequency range. The detectors and those detect range are listed in Table 3.1.5. Because of the. 24.

(38) DIGS 201 is good accuracy at room temperature it was chosen in our works.. FIGURE 3.1.7: Spectrum Range of IR Detectors. © Bruker. TABLE 3.1.5: Detectors and detect range. Detector. Detect Range (cm-1). Bolometer 2041. 5 ~ 50. Bolometer 2248. 50 ~ 400. DIGS 201. 30 ~ 720. MCT (D313). 800 ~ 6000. InSb. 1850 ~ 9000. Silicon Diode. 8000 ~ 25000. Aperture The aperture controls the intensity and cross section of the light. If the aperture is too small, the signal will be too weak. On the other hand, the aperture is too large and. 25.

(39) over the area of sample, the signal will not be precisely. The aperture has 16 types to be chosen to use (0.25, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0 and 12.0 mm).. Window Because of the window should have a good transmittance it not damage the light too much. The different windows will be used with different light frequency range. The windows and the transmitting range are listed in Table 3.1.6. The Polythene window was chosen in our measurements.. TABLE 3.1.6: Windows and the transmitting range. Window. Transmittance (%). Transmitting Range (μm). Spectrosil B. 90. 0.2 ~ 2.5. Spectrosil WF. 80. 0.2 ~ 4. Sapphire. 80. 0.2 ~ 5.4. Calcium Fluoride. 90. 0.2 ~ 9. KRS5. 60. 0.6 ~ 36. Zinc Selenide. 60. 0.6 ~ 20. Polythene. 80. 209 ~ 1000. Clear Mylar. >50. 0.1 ~ 0.8 or >100. Vacuum System The water molecule will affect the accuracy of IR experiment. In the spectrometer and sample room, the degree of vacuum should be controlled under 0.05 torr. Furthermore, to avoid the air condense on the sample or window at the low temperature, the degree of vacuum should be controlled more carefully. At the low temperature, the pressure of the sample room could reach below 10-6 torr.. 26.

(40) Low Temperature System To study the phonons, carriers and energy gap of the sample in different temperature. A low temperature system is necessary. The low temperature system is used for conductive cooling of small samples in low-temperature research in the temperature range of 2K to 300K. Cooling is accomplished by the controlled transfer of liquid helium (or nitrogen) through a high-efficiency transfer line to a heat exchanger adjacent to the sample interface.. 3.2 PRINCIPLES OF FTIR SPECTROSCOPY. The Michelson Interferometer The Michelson interferometer is the most common configuration for optical interference instruments and was invented by Albert Abraham Michelson [45]. The Michelson Interferometer is an important configuration of the FTIR instrument. An optical path diagram of a Michelson Interferometer is shown in Figure 3.2.1. A Michelson interferometer consists of two highly polished mirrors (stationary mirror and moving mirror). A light source emits light (Ei) that hits a beam splitter, and then the light is split into two parts (E1 and E2) at the beam splitter. One beam is transmitted through to moving mirror while the other is reflected in the direction of stationary mirror. Both beams recombine into a new light (E) at beam splitter to produce an interference pattern visible to the observer at detector. These processes will produce interference because of the different phases of two split lights. The derivation of the interference has been derived below [34, 46].. 27.

(41) E1. Ei. Light Source. Beam Splitter. Stationary Mirror Fixed mirror E2. E = E1 + E 2. Moving Mirror. Detector. FIGURE 3.2.1: A configuration of the Michelson Interferometer.. Optical Interference In physics, interference is a phenomenon in which two waves superimpose to form a resultant wave of greater or lower amplitude. Interference usually refers to the interaction of waves that are correlated or coherent with each other, either because they come from the same source or because they have the same or nearly the same frequency. Assume a single frequency light and it’s intensity as. Ei  E0  f ei 2f0 xt . (3.2.1). I i  E0  f . (3.2.2). 2. The transmittance and the reflectivity of the beam splitter are T and R . The reflectivity of the stationary mirror and moving mirror are r1 and r2 . Thus, the E1 and E2 could be expressed as. E1  TRr1 E0  f ei 2f0 xt . 28. (3.2.3).

(42) E2  TRr2 E0  f ei 2f0  x t . (3.2.4). Where  is the phase difference between E1 and E2. The E and it’s intensity I as. . . E  TR E0  f  r1  r2 ei 2f0 ei 2f0  x t . . (3.2.5). . (3.2.6). . (3.2.7). I    TRE0  f  r1  r2  2 r1r2 cos2f 0  2. If the incident light is multi-frequencies light, it’s intensity as . . I     TRE0  f  r1  r2  2 r1r2 cos2f 0  df 2. 0. If the reflectivity of the two mirrors are r1  r2  1 , then the eq. (3.2.7) could be a simplified form as . I    2 TRE0  f 1  cos2f 0 df 2. (3.2.8). 0. The eq. (3.2.8) is an even function, so the integral could be regard as . I     TRE0  f 1  cos2f 0 df 2. (3.2.9). . If the phase difference approaches infinity, the E1 is not associated with E2 . Then the light intensity will becomes . I     TRE0  f df 2. . (3.2.10). Replace eq. (3.2.10) into eq. (3.2.9) . I    I    TRE0  f cos2f 0 df 2. . (3.2.11). Finally, we do a Fourier cosine transform to the eq. (3.2.11) and get. S f   . . . I    I cos2f 0 d  TRE0 2  f . (3.2.12). Where S  f   TRE0  f  is the intensity of the signal from the sample. [33,34] 2. 29.

(43) 3.3 Fourier Transform. Fourier Transform The Fourier transform (FT) is named in the honor of Joseph Fourier, is a mathematical transform with many applications in physics, engineering and chemistry. Very commonly, it expresses a mathematical function of time as a function of frequency, known as its frequency spectrum. Assume a light intensity as I t   F 1 I   . 1 2.   I  e d. I    F I t  . 1 2.  I t e. . i t.  . . it. dt. (3.3.1) (3.3.2). The eq. (3.3.1) is performed over all contributing frequencies to give a signal. I t  in the time domain and I   is the spectrum to be determined. Using the relationship between eq. (3.3.1) and eq. (3.3.2) that converting spectra from time domain to frequency domain by the Fourier transform.. Correction Experiment Assume the moving mirror moves d cm in each step and the detector gets one signal in every n step. So the phase difference between the two signals will be 2nd cm in the interferogram. In a N data points symmetry interferogram, the phase difference changes from  Nnd cm to Nnd cm. Define the total displacement of the moving mirror L  Nnd cm and the phase difference  will be  L ~ L not  ~  .. Then the resolution will be. 1 cm-1 just concern with the total displacement L 2L. of the moving mirror. The finite optical path difference will cause data distortion. We. 30.

(44) should correct data and the resolution will become to fifty percent. That means the resolution will reduce to. 1 cm-1. Because of we get the signal is not continuous the L. integral of eq. (3.2.12) could be approached as S f   C. N 2.  I  cos2f   m. N 2. ap. Where the C is a constant and the. m. 0. m. (3.3.3). I ap  m  is the interferogram. However,. this is the time-consuming calculation. The Cooley–Tukey Fast Fourier Transform (FFT) algorithm could solve the problem, but only apply for the data points N  2 n ( n is any integer) [47,48]. This method became a standard process of Fourier transform and we used it in our experiments, too [33,34].. 3.4 SAMPLE PREPARATION. Growth of InN Films on Sapphire InN films were grown by plasma-assisted MBE, using a SVTA model SVT-V-2 [49], with various N2-plasma power levels in the range of 200 to 400W on sapphire substrates after nitridation process. The InN growth was proceeded in several steps. First, the substrate temperature was risen to 800℃ for 30 min for cleaning the impurities on the surface of the substrate in the growth chamber, and consequently, the indium source cell was risen to 850℃ for this cleaning procedure. Second, the nitridation process has been applied for the surface pretreatment and modification, at 200℃ and under 5×10-5 Torr with the N2-plasma power of 400W for 30-minutes, which also forms a thin AlN buffer layer of around few nm thick. Finally a series of InN thin films was grown with different plasma powers, under growth. 31.

(45) pressure of 2~5×10-5 Torr, with the substrate temperature of 320℃ and indium flux of 0.9~1.2×10-5 sccm at temperatures between 821 and 835℃, for 60-minutes. These InN films all were grown by Prof. Feng’s group [50]. Detailed growth conditions are summarized in Table 3.6 and described elsewhere [50, 51].. TABLE 3.4.1: Growth conditions of InN on Sapphire substrate. [50] Samples. Plasma Power. In. Substrate. Number. ( Bias voltage (V) ). Temperature. Temperature. (W). (℃). (℃). CC-21. 350. 826. 320. CC-28. 230. 849. 320. CC-30. 200. 840. 360. CC-40. 200. 836. 360. CD-2. 80. 835. 360. CD-7. 350 (bias:400). 846. 360. CD-8. 350 (bias:500). 846. 360. CD-9. 350 (bias:600). 846. 360. CD-10. 150 (bias:400). 840. 360. CD-14. 350 (bias:400). 840. 360. CD-15. 350 (bias:400). 843. 360. CD-16. 200. 842. 300. Growth of InAs1-xNx Thin Films on InP The samples were grown on semi-insulating (100) InP substrates using a VG V-80H GSMBE system. Elemental In source and thermally cracked AsH3 and PH3 sources were used. The active N species were generated from an EPI UNI-bulb RF plasma source. The RF power and nitrogen flow rate used for these growths ranged from 300W to 480W and from 0.5 to 1.9 sccm, respectively. These InAsN films all were grown by Prof. Lin’s group [19,52,53]. Detailed growth conditions are. 32.

(46) summarized in Table 3.5 and described elsewhere [52]. To start the growth, the InP substrate was desorbed at 500℃ under P2 flux. Then, a 0.3-mm-thick undoped InP buffer layer was deposited at 460℃ at a rate of 1.5 mm/h. A 2-mm-thick undoped InAs(N) was subsequently over grown on the buffer layer without growth interruption and the AsH3 flow rate was fixed at 4 sccm. High-brightness mode N2 plasma was ignited for the N-containing growth. The RF power was turned off immediately after finishing the InAsN growth [53].. TABLE 3.4.2: Growth conditions and nitrogen composition of InAsN on InP substrate. [52] Sample Name. RF plasma power. Flow rate of N2. Nitrogen Composition. (W). (sccm). (%). B. 300. 1.2. 0.2. C. 480. 1.8. 2.2. D. 400. 1.2. 2.4. E. 480. 1.2. 3.0. Growth of In0.5(Ga1-xAlx)0.5P Films on GaAs Low pressure (LP) MOCVD was used to grow In0.5(Ga1-xAlx)0.5P layers on (100) n+-GaAs substrates oriented 15° off towards (110). Two systems (Emcore D180 and E400) with the vertical growth configuration and a high speed rotating disk able to handle multiple wafers were used. The system design was made according to hydrodynamic symmetry and flow dynamics of the rotating disk reactor (RDR), which ensures growth to be laterally uniform, abruptly switchable, and robust against variations in process parameters. High. purity. trimethyindium. (TMIn),. trimethygallium. (TMGa). and. trimethyaluminum (TMAl) metalorganic sources were used to supply In, Ga and Al,. 33.

(47) respectively, and PH3 was used for the P source. High purity H2 was used as the carrier gas. These InGaAsP films all were prepared by Prof. Feng’s group. Detailed growth conditions are described elsewhere [54].. 3.5 EXPERIMENT PROCEDURE. Preprocedure In FTIR reflectance spectrum measurements, the Mylar 6, Mercury lamp and DTGS 201 will be chosen for its beamsplitter, far IR light source and detector that for the InGaAlP/GaAs samples. And the KBr, Globar and DTGS 301 will be chosen for its beamsplitter, middle IR light source and detector that for the InN/sapphire. The pressure of the sample room contains at about 10-6 torr in the experiment process. Then, these InAs1-xNx/InP were measured by Prof. Hung [53]. When we start to measure these samples, we should confirm the IR background that the MIR and FIR background spectra were presented in Figure 3.5.1 and Figure 3.5.2.. 34.

(48) MIR-background Vacuum 300 K. 1000. 2000. 3000. 4000. 5000. 6000. 7000. Wavenumber (cm-1) FIGURE 3.5.1: The background of middle infrared spectrum.. FIR-background Vacuum 300 K. 100. 200. 300. 400. 500. 600. 700. Wavenumber (cm-1) FIGURE 3.5.2: The background of far infrared spectrum.. 35.

(49) Spectra Analysis After the measurements, the spectra could be fitted by the fitting program which was written by Fortran or Matlab and is showing below with its directions. We used the dielectric response function to analysis the infrared spectra. From the spectral peak positions, the phonon modes frequency all could be fined approximately. However, it is impossible for us to find the other parameters without a calculating program. Therefore the multi-layer fitting model is employed to analysis the infrared spectra. The multi-layer fitting model is based on the non-linear least squares fitting. It is the form of least squares analysis which is used to fit a set of m observations with a model that is non-linear in n unknown parameters (m > n). It is used in some forms of non-linear regression. The basis of the method is to approximate the model by a linear one and to refine the parameters by successive iterations. There the parameter  2 could be expressed as. 1 N El  Tl     N l 1  l 2. 2. 2. (3.5.1). Where N is the total number of the data points, El is the experiment values, Tl is the theoretical values.. l2 . 1 N El  El 2  N l 1. (3.5.2). 1 N  El N l 1. (3.5.3). El . The  l is the standard deviation and El is the mean value of these observations [33-35]. All the fitting parameters from eq. (2.5.1) are.   : High-frequency dielectric constant. S : Phonon oscillator strength.. TO : Transverse-optical (TO) phonon frequency. 36.

(50)  : Phonon damping constant. n : Free carrier concentration..  : Free carrier mobility. m * : Effective mass of free carrier.. d : Thickness of the film. The details of the program operation procedures are presented in the appendix.. FIGURE 3.5.3: Fitting program of dielectric response model by Fortran.. 37.

(51) FIGURE 3.5.4: Fitting program of dielectric response model by Matlab.. 38.

(52) CHAPTER 4. EXPERIMENT RESULTS AND DISCUSSIONS The results of infrared reflectance spectra measurements were presented in this chapter. At the beginning, let we recall the dielectric response model and its relations with refractive index, extinction coefficient and the reflectivity from chapter 2..           j. S jTO j. 2. TO 2   2  i j. . j. p2 i       .  int er     int ra  . (2.5.1).     n  n  ik. (2.5.2). n  12  k 2 n  12  k 2. (2.5.3). R( ) . ~ r ~ r e i 2  R   12 ~ ~23 i 2  1  r12r23e. 2. (2.5.6). With. n~i  n~ j ~ rij  ~ ~ ,   2d ~( )2 ni  n j From these equations, the reflectivity of bulk or two-layer films could be expressed by dielectric response function and analyze these spectra by the fitting program. After fitting, several parameters will be defined by dielectric response function fitting such as high-frequency dielectric constant, transverse-optical (TO) phonon frequency, strength, damping, free carrier concentration, mobility, effective mass and the thickness of the sample. However, there are some parameters undefined such as the longitudinal-optical (LO) phonon mode frequency, conductivity and force constant between cations and. 39.

(53) anions. We continued to discuss these equations. The conductivity was calculated from the relation with free carrier concentration and mobility as [39].   ne. (4.1). With  is conductivity, n is free carrier concentration, e is the charge of an electron and  is mobility. Furthermore, from the eq. (2.3.12), the phonon strength of TO1 and TO2 can be expressed as [41] S1T21   . ( L21  T21 )( L22  T21 ) T22  T21. (4.2). S 2T22   . ( L21  T2 2 )( L22  T2 2 ) T21  T22. (4.3). Where T 1 is the TO1 phonon frequency with strength S1 and  L1 is the LO1 phonon frequency. Similarly, the subscript “2” means the frequency and strength of TO2 and LO2 phonon modes. It also could be extended to TO3 and LO3. After fitting and calculation, these optical and transport properties parameters will be defined and their physical meanings also will be discussed.. 4.1 MIDDLE INFRARED SPECTRUM ANALYSIS OF InN/Sapphire. These are twelve InN films grown on Sapphire have been measured by Fourier transform far infrared spectrometer Bruker IFS 66 v/S with different grown conditions. The measured range of middle infrared reflectance spectra is from 400 cm-1 to 4000 cm-1 at 300K. We found a one mode behavior of InN but the effects from Sapphire substrate cannot be ignored. And we also found a four mode behavior of sapphire substrate at this range [55]. The experiment results are displaying below and the. 40.

(54) fitting results and discussions will be presented, too.. Middle Infrared Reflectance Experiment Results. 1.0. Reflectivity. 0.8 0.6 0.4. InN/sapphire 300K. 0.2 0.0 400. 500. 600. CC21 CC28 CC30 CC30 CD2 CD7 CD8 CD9 CD10 CD14 CD15 CD16. 700. 800. 900. 1000. Wavenumber (cm-1) FIGURE 4.1.1: Middle Infrared reflectance spectra of InN/sapphire from 400 cm-1 to 1000 cm-1.. 41.

(55) CC21 CC28 CC30 CC30 CD2 CD7 CD8 CD9 CD10 CD14 CD15 CD16. 1.0. Reflectivity. 0.8. InN/sapphire 300K. 0.6 0.4 0.2 0.0. 500. 1000. 1500. 2000. 2500. 3000. 3500. 4000. Wavenumber (cm-1) FIGURE 4.1.2: Middle Infrared reflectance spectra of InN/sapphire from 400 cm-1 to 4000 cm-1.. 1.0. Reflectivity. 0.8 0.6 Experiment. 0.4 Sapphire (substrate) 300K. 0.2 0.0 400. 500. 600. 700. 800. 900. 1000. Wavenumber (cm-1) FIGURE 4.1.3: Middle Infrared reflectance spectra of Sapphire substrate from 400 cm-1 to 1050 cm-1.. 42.

(56) The reflectance spectra measured at room temperature for the InN/sapphire samples and Sapphire substrate were presented in Figure 4.1.1-3. As shown in Figure 4.1.1-2, the spectra in the figure can be simply divided into two regions, i.e. the region between 400 cm-1 and 1000 cm-1 and above 1000 cm-1. All spectra display four peaks and we can see the position at the frequencies around of 444, 577 and 644 cm-1 that are the TO-phonon frequencies of the sapphire [56,57], and also at the frequency around of 483 cm-1 that is the E1(TO)-mode of the InN. Obviously the all peaks seem no shift and the sapphire substrate structures only appear between 400 cm-1 and 1000 cm-1. But M-IR structures of the InN/sapphire extend to 1500cm-1 even higher. We guess it will be contribution from the carrier concentration [58]. By the way, the characteristic plasma edge also can be seen. From the report of E. Frayssinet et al [58], the plasma edge will shifted towards higher frequencies with increasing electron concentration. So we could discussion this phenomenon at next section. The thickness of films can be determined by various interferometric methods [59]. In our work, we use the IR measurement and theoretical calculations to obtain the thickness of film.. 43.

(57) Fitting Results and Discussions. 1.0. Reflectivity. 0.8 0.6 Experiment Fitting. 0.4. Sapphire (substrate) 300K. 0.2 0.0 400. 500. 600. 700. 800. 900. 1000. Wavenumber (cm-1) FIGURE 4.1.4: Middle infrared reflectance spectrum and fitting of Sapphire substrate.. TABLE 4.1.1: Classical oscillator parameters for sapphire o-ray. [55]. γi ωi. Si. ωi. (cm-1). (cm-1). 1. 0.33. 384.3. 0.011. 2. 2.788. 438.9. 0.006. 3. 2.98. 568.2. 0.012. 4. 0.145. 633.6. 0.010. 5. 0.0185. 809.6. 0.157. 6. 0.65068713. 85723.7. 0.00001. 7. 1.4313993. 137621.4. 0.00001. i. 44.

(58) 1.0. Reflectivity. 0.8 0.6. Experiment Fitting. 0.4. 600. 800. 1000. 1200. 1400. InN/sapphire CC-21 300K. 0.2 0.0. 400. 500. 1000. 1500. 2000. 2500. 3000. 3500. 4000. Wavenumber (cm-1) FIGURE 4.1.5: Middle infrared reflectance spectrum and fitting of InN/sapphire CC-21.. 1.0. Reflectivity. 0.8 0.6 0.4. Experiment Fitting. 0.2. InN/sapphire CC-28 300K. 0.0. 500. 1000. 1500. 400. 2000. 600. 2500. 800. 1000. 3000. 1200. 3500. 4000. Wavenumber (cm-1) FIGURE 4.1.6: Middle infrared reflectance spectrum and fitting of InN/sapphire CC-28.. 45.

(59) Reflectivity. 1.0 0.8. Experiment Fitting. 0.6. InN/sapphire CC-30 300K 400. 600. 800. 1000. 0.4 0.2 0.0. 500. 1000. 1500. 2000. 2500. 3000. 3500. 4000. Wavenumber (cm-1) FIGURE 4.1.7: Middle infrared reflectance spectrum and fitting of InN/sapphire CC-30.. 1.0 Experiment Fitting. Reflectivity. 0.8. InN/sapphire CC-40 300K. 0.6. 400. 600. 800. 1000. 1200. 0.4 0.2 0.0. 500. 1000. 1500. 2000. 2500. 3000. 3500. 4000. Wavenumber (cm-1) FIGURE 4.1.8: Middle infrared reflectance spectrum and fitting of InN/sapphire CC-40.. 46.

(60) 1.0. Reflectivity. 0.8 Experiment Fitting. 0.6. InN/sapphire CD-2 300K. 0.4. 400. 600. 800. 0.2 0.0. 500. 1000. 1500. 2000. 2500. 3000. 3500. 4000. Wavenumber (cm-1) FIGURE 4.1.9: Middle infrared reflectance spectrum and fitting of InN/sapphire CD-2.. Reflectivity. 1.0 0.8. Experiment Fitting. 0.6. InN/sapphire CD-7 300K 400. 600. 800. 1000. 2500. 3000. 3500. 0.4 0.2 0.0. 500. 1000. 1500. 2000. 4000. Wavenumber (cm-1) FIGURE 4.1.10: Middle infrared reflectance spectrum and fitting of InN/sapphire CD-7.. 47.

(61) Reflectivity. 1.0 0.8. Experiment Fitting. 0.6. InN/sapphire CD-8 300K 400. 600. 800. 1000. 0.4 0.2 0.0. 500. 1000. 1500. 2000. 2500. 3000. 3500. 4000. Wavenumber (cm-1) FIGURE 4.1.11: Middle infrared reflectance spectrum and fitting of InN/sapphire CD-8.. 1.0 Experiment Fitting. Reflectivity. 0.8. InN/sapphire CD-9 300K. 0.6. 400. 600. 800. 1000. 2500. 3000. 3500. 0.4 0.2 0.0. 500. 1000. 1500. 2000. 4000. Wavenumber (cm-1) FIGURE 4.1.12: Middle infrared reflectance spectrum and fitting of InN/sapphire CD-9.. 48.

(62) 1.0. Reflectivity. 0.8 Experiment Fitting. 0.6. InN/sapphire CD-10 300K. 0.4. 400. 600. 800. 0.2 0.0. 500. 1000. 1500. 2000. 2500. 3000. 3500. 4000. Wavenumber (cm-1) FIGURE 4.1.13: Middle infrared reflectance spectrum and fitting of InN/sapphire CD-10.. 1.0. Reflectivity. 0.8. Experiment Fitting. 0.6. InN/sapphire CD-14 400 300K. 0.4. 600. 800. 0.2 0.0. 500. 1000. 1500. 2000. 2500. 3000. 3500. 4000. Wavenumber (cm-1) FIGURE 4.1.14: Middle infrared reflectance spectrum and fitting of InN/sapphire CD-14.. 49.