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ELECTRONIC STRUCTURE of DEEP LEVELS in SILICON a Study of Gold, Magnesium, and Iron Centers in Silicon

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ELECTRONIC STRUCTURE of DEEP LEVELS in SILICON a Study of Gold, Magnesium, and Iron Centers in Silicon ELECTRONIC STRUCTURE OF DEEP LEVELS IN SILICON A Study of Gold, Magnesium, and Iron Centers in Silicon AnnaLena Thilderkvist DEPARTMENT OF <• j SOLID STATE PHYSICS UNIVERSITY OF LUND SWEDEN 1994 r- Organization Document name LUND UNIVERSnY DOCTORAL DISSERTATION Department of Solid State Physics Date of Box 118 Februarv 22, 1994 S-221 00 Lund CODEN: Sweden LUFTD2/TFFF-0039/1-160 Authors) Spo&somt| of (auizatioB AnnaLcna Thilderkvist Title ind sobtitle ELECTRONIC STRUCTURE OF DEEP LEVELS IN SILICON A Study of Cold, Magnesium, and Iron Centers in Silicon Abstract In this thesis, the electronic structure of gold, magnesium and iron related deep centers in silicon is investigated. Their deep and shallow levels are studied by means of Fourier transform spectroscopv. combined with uniaxial stress and Zeeman spectroscopv. The neutral substitutional geld center in silicon is investigated and the center is paramagnetic. S=l/2, with g||-2.8 and gi-0, and has a static <100> distortion. Reorientation between different equivalent distortions is observed even at 1.9 K. A gold pair center in silicon is studied and several line series, with a zero-phonon line followed by several phonon replicas, are observed. Uniaxial stress and Zeeman results reveal a trigonal symmetry of the center, which ogether with the high dissociation energy of 1.7 eV suggests that the center consists of two nearest-neighbor substitutional gold atoms. A divacancv model is employed to explain the electronic properties of the center. The interstitial magnesium double donor in silicon in its two charge states Mg° and Mg+ is investigated. Deviations in the binding energies of the excited states from those calculated within the effective-mass theory fEMT) are found and explained by a perturbation in the central-cell region. The quadratic Zeeman effect of shallow donors in silicon is analyzed within the framework of the EMT using a numerical approach. The wave functions are calculated on a discrete radial mesh and the Zeeman Hamiltonian has been evaluated for the lowest excited states for fields up to 6 T. The neutral interstitial iron defect in silicon gives rise to two sets of line spectra. The first set arises when an electron is excited to a shallow donor like state where the electron is decoupled from the Fe+ core 4 which has a T, ground state term. The second set arises when an excited electron of at symmetry is is coupled by exchange interaction to the core, yielding a *Ti final state. Experiments determine the multiplet splitting of the 4Tj and 5Tj states due to spin-orbit interaction. Large deviations from the I.amitf inter"!)! rule are observed. Preliminary results strongly support a dynamical Jahn-Teller distortion to be the dominant mechanism responsible for the non-Landi behavior. si Key word» silicon, deep levels, shallow donor stales, effective mass theory, EMT, Fourier transform spectroscopy, uniaxial stress, Zeeman spectroscopy, quadratic Zeeman effect, spin-orbit interaction, Jahn- Teller effect, Au, Mg, Fe. Claatfkatkra system and/or index terns (if any) Supptanentiry bibliographical inlonoMtioa Ua«ua«t English ISSN and key title BBN 91-628-1179-7 Reapient's notes Number of pages Price Security classification Distribution by (name and address) Department of Solid State Physics, Lund University, Box 118, S-221 00 Lund, Sweden I, the undersajDed, being the copyright owner of (he abstract of (he above-mentioned dissertation, hereby grant to all reference sources permission to publish and disseminate the abstract of the above-mentioned dissertation. February 22,1994 Data ELECTRONIC STRUCTURE OF DEEP LEVELS IN SILICON A Study of Gold, Magnesium, and Iron Centers in Silicon av AnnaLena Thilderkvist civ. ing., Kristianstads nation AKADEMISK AVHANDLING SOM FÖR AVLÄGGANDE AV TEKNISK DOKTORSEXAMEN VID TEKNISKA FAKULTETEN VID j UNIVERSITETET I LUND KOMMER ATT OFFENTLIGEN FÖRSVARAS I FYSISKA j INSTITUTIONENS FÖRELÄSNINGSSAL B FREDAGEN DEN 25 MARS 1994, KL. 10.15 mm. ELECTRONIC STRUCTURE OF DEEP LEVELS IN SILICON A Study of Gold, Magnesium, and Iron Centers in Silicon AnnaLena Thilderkvist Lund 1994 • l Department of Solid State Physics Lund University Box 118 S-221 00 Lund Sweden © AnnaLena Thilderkvist ISBN 91-628-1179-7 KF-Sigma, Lund 1994 Printed in Sweden Cover Picture: A shallow donor 4f0 wave function in silicon, calculated for eleven values of the magnetic field, between 1 and 6 Tesla. For details, see section 23 in this thesis. Contents 1. Introduction 2 1.1 List of Papers 5 2. Shallow Donor States in Silicon 7 2.1 The Effective Mass Theory 7 2.1.2 Vanatwnal Method 2.1.2 Numerical Method 2.2 Deviations from EMT 12 2.3 Zeeman Effect 13 2.3.1 General Aspects 2.3-2 Shallow Donors in Silicon 2.3.3 Double Donors in Silicon 2.4 Uniaxial Stress 19 3. Deep Levels in Silicon 20 3.1 Introduction 20 3.2 Transition Metal Impurities in Silicon 20 3.2.1 Ionic Model 3.2.2 Recent Theoretical Results 3.3 Many-Particle Effects 26 3.3.1 Electrostatic Interaction 3.3.2 Spin-Orbit Effects 3.3.3 Zeeman Effects 4. Jahn-Teller Effects 29 4.1 Introduction 29 4.2 Jahn-Teller Effects in Tj Symmetry 30 4.2.2 Molecular Model and the Hamiltonian 4.2.2 e®E Case 4.2.3 e®T2 Case 4.3 Jahn-Teller Distortions at the Lattice Vacancy in Silicon 33 5. Gold Doped Silicon 35 5.1 The Neutral Substitutional Gold Center, Aus° 35 5.7.2 Introduction 5.2.2 Uniaxial Stress 5.1.3 Combined Stress and Zeeman Experiments 5.2 The Trigonal Substitutional Gold-Pair Center, Au2S 38 6. Experimental Techniques 40 6.1 Fourier Transform Spectroscopy 40 6.2 Perturbation Techniques 41 6.2.2 Uniaxial Stress 6.2.2 Zeeman Measurements 7. Acknowledgments 43 8. List of References 44 1. Introduction It has been said that "The engineers involved with microelectronics are doing their part to make many of the authors of science fiction look like prophets" (Colclaser 1980). This becomes obvious when we consider the fast development of micro-electronic devices, which started in the mid-1950s. During the last three decades the improvement in manufacturing techniques and the immense amount of research that has been carried out in the field of semiconductor technology, have resulted in a vast change in our every day life. All of us come daily into contact with semiconductor devices, nicely hidden in, e.g., watches, hand-held calculators, television sets, cars, airplanes, medical apparatus, and of course personal computers. The list can be made long, and it will continue to grow in the future. The main reasons for this rapid development are the new techniques that make it possible to shrink the size of electronic devices, reduce costs, and simultaneously increase both performance and reliability. What is a semiconductor and why is it so well suited for the manufacturing of electronic devices? In the following I will give a short summary of the most important properties of elemental semiconductors, which will be followed by an introduction to the field of defects in crystalline materials. Fig. 1. The crystal structure of group IV semiconductors, such as silicon and ger- manium crystals. In a perfect crystalline semiconductor, the atoms are arranged in a regular periodic manner throughout the whole material. The most important elemental semiconductors are those made up of atoms from group IV of the periodic table, such as, e.g., silicon. These atoms have four valence electrons, and when they form a crystal, each of these four electrons will take part in a covalent bond to another atom, i.e., each atom binds four other atoms in a tetrahedral crystal structure, see Fig. 1. The valence electrons are tightly bound in their respective bond and occupy energy states within the valence band, which is completely filled with electrons at low temperatures. To make the material conductive, electrons have to be released from their respective covalent bonds. This corresponds to excitations of the electrons from the valence band, into the next empty energy band, called the conduction band. The conduction band is separated from the valence band by a forbidden band gap, Eg. The size of this band gap is different for different types of crystals, and for most semiconductors Eg < 3 eV. For silicon, studied in this thesis, Eg = 1.12 eV at room • 4 temperature. By doping the semiconductor crystal with foreign atoms, the conductivity of the material can be increased by several orders of magnitude. In general, impurity atoms can be situated either on subshtutional lattice sites, i.e., on sites formerly occupied by a host atom, or on interstitial sites, i.e., in between lattice sites. The simplest example considers an impurity from group V of the periodic table, which have five electrons outside filled shells. When, the group V atom enters a substitutional lattice site, four of the valence electrons are needed in the covalent bonds to the surrounding silicon atoms, while the fifth electron is only weakly bound to the impurity core by Coulomb attraction. The energy needed to ionize the impurity, i.e., to transfer the electron to the conduction band of the semiconductor, can be hundred times smaller than the band gap energy. Thus the impurity introduces new energy levels in the band gap, situated closely beneath the conduction band edge. These levels are called shallow donor levels. The fifth electron, moving in the central field of the impurity core, can be bound not only in its ground state, but also in several excited states, in analogy with the hydrogen atom. The theory describing these shallow donor states is called effective mass theory (EMT), and is outlined in section 2 of this thesis.
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