A Far-Infrared Michelson Interferometer and Its Application to the Study of Photoconductivity in Ultra-Pure Germanium
Total Page：16
File Type：pdf, Size：1020Kb
PDF hosted at the Radboud Repository of the Radboud University Nijmegen The following full text is a publisher's version. For additional information about this publication click this link. http://hdl.handle.net/2066/147901 Please be advised that this information was generated on 2021-10-06 and may be subject to change. A FAR-INFRARED MICHELSON INTERFEROMETER AND ITS APPLICATION TO THE STUDY OF PHOTOCONDUCTIVITY IN ULTRA-PURE GERMANIUM H.W.H.M. JONGBLOETS A FAR-INFRARED MICHELSON INTERFEROMETER AND ITS APPLICATION TO THE STUDY OF PHOTOCONDUCTIVITY IN ULTRA-PURE GERMANIUM PROMOTOR: PROF.DR.P. WYDKR CO-REF:I:RENT DR. J.H.M. STOELINGA A FAR-INFRARED MICHELSON INTERFEROMETER AND ITS APPLICATION TO THE STUDY OF PHOTOCONDUCTIVITY IN ULTRA-PURE GERMANIUM PROEFSCHRIFT TER VERKRIJGING VAN DE GRAAD VAN DOCTOR IN DE WISKUNDE EN NATUURWETENSCHAPPEN AAN DE KATHOLIEKE UNIVERSITEIT TE NIJMEGEN, OP GEZAG VAN DE RECTOR MAGNIFICUS PROF. DR. P.G.A.B. WIJDEVELD, VOLGENS BESLUIT VAN HET COLLEGE VAN DECANEN IN HET OPENBAAR TE VERDEDIGEN OP DONDERDAG 13 MAART 1980 DES NAMIDDAGS TE 4.00 UUR door HENDRIKUS WILHELMUS HUBERTUS MARIA JONGBLOETS geboren te Nijmegen 1980 Druk: Krips Repro Meppel The investigations described in this thesis have been carried out in the group "Experimentele Natuurkunde IV" of the Research Institute for Materials of the Faculty of Science at the Catholic University of Nijmegen under the direction of Prof. Dr. P. Wyder. Part of this work has been supported by the "Stichting voor Fundamenteel Onderzoek der Materie" (FOM) with financial support from the "Nederlandse Organisatie voor Zuiver Wetenschappelijk Onderzoek" (ZWO). We acknowledge the permission to reprint previously published papers, obtained from the publishers of Physica and Physical Review. Лап mijn ouders Op deze plaats wil ik allen bedanken die op enigerlei wijze hebben bijgedragen aan de totstandkoming van dit proefschrift. In het bijzonder wil ik vermelden dr. H.J.A. van Dijk van het Philips Natuurkundig Laboratorium te Eindhoven, die door het beschikbaar stellen van een aantal ultra-zuivere germanium prepa raten het onderzoek, beschreven in hoofdstuk IV van dit proefschrift, mogelijk heeft gemaakt. Verder dank ik Martien van de Steeg, die als doctoraal-student op uiterst ple zierige wijze heeft meegewerkt bij veel van de hier beschreven experimenten, en die ook in de laatste fase van het schrijven van dit manuscript is bijge- sprongen. Zeer bijzonder ook Riki Gommers, die het meeste type-werk voor haar rekening heeft genomen. Zeer zeker ook Evert-Jan van der Werf die als student uiterst geduldig een enorme reeks metingen heeft verricht die ons uiteindelijk het vertrouwen gaven dat het reflectie-effect, beschreven in hoofdstuk III, geen hersenschim was. En natuurlijk dank ik de medewerkers van de dienstverlenende afdelingen van de faculteit der wiskunde en natuurwetenschappen en, last but not least, alle medewerkers van Experimentele Natuurkunde IV, met wie ik jarenlang op uiterst plezierige wijze heb mogen samenwerken. In dit verband wil ik in het bijzonder noemen de technische medewerkers. Kees Beers en Jan Herrasen. CONTENTS CHAPTER I GENERAL INTRODUCTION 1 References 3 CHAPTER II INSTRUMENTATION 5 1. Introduction 5 2. Spectrometer hardware 5 3. Experimental arrangement for photoconductivity measurements 12 References 13 CHAPTER III THE FAR INFRARED MICHELSON INTERFEROMETER 14 111.1 GENERAL INTRODUCTION 14 1. The interferogram-function 14 2. Amplitude and phase modulation 17 3. Spectra calculated by Fourier transformation 18 4. Effects due to sampling of the interferogram over a finite length 20 References 25 111.2 SPECTRUM DISTORTION IN FAR INFRARED FOURIER SPECTROSCOPY BY MULTIPLE REFLECTION BETWEEN SAMPLE AND MICHELSON INTERFEROMETER 26 Abstract 26 1. Introduction 26 2. Theory 27 3. Experiment 32 4. Conclusions 36 Appendix 37 References 39 CHAPTER IV PHOTOTHERMAL IONIZATION SPECTROSCOPY OF SHALLOW IMPURITIES IN ULTRAPURE GERMANIUM 40 IV.1 INTRODUCTION TO PHOTOTHERMAL IONIZATION SPECTROSCOPY (PTIS) 40 1. General introduction 40 2. Theoretical considerations 41 3. Photothermal ionization spectroscopy (PTIS) 43 4. Applications of PTIS 46 References 47 MAGNETO-OPTICAL DETERMINATION OF THE GROUND STATE LEVELS OF SOME SHALLOW IMPURITIES IN HIGH PURITY GERMANIUM 48 1. Introduction and experimental method 48 2. Determination of the ground state energy 49 3. The effect of a magnetic field 50 References 51 TEMPERATURE DEPENDENCE OF THE PHOTOTHERMAL CONDUCTIVITY OF HIGH- PURITY GERMANIUM CONTAINING VERY LOW CONCENTRATIONS OF ΑΙ, В AND Ρ 52 1. Introduction 52 2. Sample preparation and experimental details 52 3. Results and discussion 53 References 56 DETERMINATION OF THE IMPURITY CONCENTRATION PROFILE IN A Ge SINGLE CRYSTAL GROWN WITH THE CZOCHRALSKI METHOD 57 References 58 TEMPERATURE DEPENDENCE OF THE PHOTOTHERMAL CONDUCTIVITY OF SEMICONDUCTORS AT LOW TEMPERATURES 59 Abstract 59 1. Introduction 60 2. Signal formation in a photoconductivity experiment 62 3. Derivation of the temperature dependence of the photothermal ionization process 64 4. Сотрагьеоп with experimental results 66 References 74 MAGNETIC FIELD DEPENDENCE OF PHOTOTHERMAL CONDUCTIVITY SPECTRA IN THE FAR INFRARED OF THE BORON ACCEPTOR IN GERMANIUM 75 Abstract 75 1. Introduction 76 2. Experimental details 77 3. Field dependence of the peaks below E 79 4. Field dependence of the peaks in the continuum 85 5. Zeeman effect 85 6. Landau levels 88 References 92 APPENDIX COMPUTER PROGRAM "PHASE2" 94 SUMMARY 119 SAMENVATTING 121 CURRICULUM VITAE 123 CHAPTER I GENERAL INTRODUCTION In solid state physics, the relevant energies of many interesting effects correspond with temperatures of the order of 1 - 1000 degrees Kelvin. This range covers the binding energies of impurities in semiconductors, the ordering temperatures in ferromagnetism, antiferromagnetism and ferroelec- tricity, the transition temperatures of superconductors, phonon- and Debije- energies, etc. To study this interesting region, sometimes high magnetic fields can be applied. Field strengths up to 25 Tesla, corresponding to 16.7 K, are available at the Nijmegen High Magnetic Field installation. In this framework it is obviously very much worthwile to have electro magnetic radiation available of comparable energy. This is the far infrared (FIR) or submillimetre wave region (wave length range 50 - 1000 pm or wave number range 10 - 200 cm. ), which connects the optical and microwave parts of the electromagnetic spectrum. This is a most awkward regime because of the lack of broadband sources of sufficient power. It is true that nowadays FIR (1 2) lasers are available with output power up to 0.4 W ' , but these have the disadvantage of not being continuously tunable nor being very stable. The FIR region can also be approached from the microwave side by the technique of harmonic generation which offers a higher stability and so a higher resolu tion. With this method the range of 2 - 25 cm can easily be spanned with an -2 -fi output power decreasing from 10 to 10 W with increasing wave number. The most widely used technique is that where the FIR region is penetrated from the optical side by employing a broadband source (medium pressure mercury arc lamp) in combination with a dispersive optical device, such as a grating monochromator ' ' , or an interferometric device such as a lamellar grating (7 8) (9) interferometer ' or a Michelson interferometer . These instruments -9 deliver only a radiation power which at low wave numbers is less than 10 W within a bandwidth of 1 cm , but they cover the whole FIR region. In chapter II of this thesis the hardware of a modern commercial Grubb Parsons FIR Michelson interferometer system is described, originally developed (9) by Chantry et al. This system has been modified and improved in our laboratory by the author with the help of the instrument and electronics workshops of our Faculty. This instrument now covers the range 5 - 350 cm A short summary of the theory underlying the technique of Fourier spectroscopy is given in chapter III (section III.l). This more conventional part of the theory does not take into account the radiation which returns to the interfe rometer due to reflection of the sample. It is shown that this can lead to significant distortions in the spectra, as is analyzed both theoretically and experimentally in chapter III (section III.2) and Ref. 10. In an appendix to this thesis the computer programs, developed for the processing of the data and the execution of the Fourier transform needed to obtain a frequency spectrum, are collected. The application of the Michelson interferometer to the study of the properties of impurity states in semiconductors is described in chapter IV. This study has been stimulated greatly by the very advanced crystal growing techniques which exist nowadays. It has become possible to fabricate ultra- 10 3 pure crystals with impurity concentrations smaller than 10 atoms/cm . In 12 other words, only one out of every 10 atoms is an impurity. It is extremely difficult to identify these impurities by conventional methods, e.g. Hall effect measurements. However, photothermal ionization spectroscopy (PTIS) in the far infrared region, first developed by Russian scientists ' , offers a possibility to study the impurities both qualitatively and quantitatively. With this technique FIR spectroscopy can be used as a tool for chemical analysis. It is well known that the group V donor and group III acceptor impurities in group IV semiconductors (e.g. in germanium, silicon) exhibit