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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
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 "hydrogen like" energy level schemes for the single bound electron/hole, with binding energies in the order of 10 meV. The PTIS technique is based on the two-step photothermal ionization process where the electron/hole is excited from the impurity groundstate to a higher level by the FIR radiation, and then subse quently thermally ionized into the band continuum, where it contributes to the electrical conductivity. Therefore, in the photoconductivity line spectra, which reflect the discrete energy level structure of the impurity, the line intensity will be temperature dependent. Up to now little was known about the detailed mechanism of this thermal ionization, nor was the temperature dependence exactly known. The ad hoc assumption often mentioned in the literature of a simple exponential behaviour seems not to fit the experimental results. Therefore the statistical problem was studied in detail (i.e. the transition from a localized impurity state to a delocalized bandstate); we have been able to show that a detailed theoretical understanding is possible and gives very good agreement with our experimental observations. An expression was derived for the temperature
2 dependence, which includes not only the energy difference between band edge and excited level, but also the degeneracy of the relevant level and the band. Moreover it contains a factor proportional to the impurity concentration. Preliminary results are given in chapter IV, section IV.2 and Ref. 17. In section IV.3 (Ref. 18) very accurate values for the ground state energies of the ΑΙ, В and Ρ impurities in germanium are derived from the temperature dependence. These values are in excellent agreement with existent theories (19 20) ' . In addition, the ratio of the concentrations of the two acceptors present in our sample, is derived. This ratio is in accordance with the value obtained from the concentration profile in the original crystal from which our sample was cut. The determination of this profile is explained in section IV.4. In section IV.5 (Ref. 21) a detailed theoretical derivation of the temperature dependence is given, not only for the line intensity in a photo- thermal conductivity spectrum, but also for the signal strength in a photo conductivity experiment. Photoconductivity measurements in magnetic fields are described in section IV.6 (Ref. 22). The linear and quadratic Zeeman terms are determined for all lines of the boron excitation spectrum. In the literature ' only values for the lowest levels are available; the corresponding values of our investigation agree with these. Some of the lines showing up in a magnetic field can be identified as states associated with light-hole Landau levels. Values for the magnetic field dependence of these Landau levels, derived from (25) the measurements, agree very well with values from the literature
References.
1. T.Y. Chang, IEEE Trans. Microwave Theory and Tech. MTT-22, 983 (1974). 2. D.T. Hodges, Infrared Phys. 18, 375 (1978). 3. M.J. Huijben, CG.C.M. de Kort, J.H.M. Stoelinga and P. Wyder, Infrared Phys. 19, 257 (1979). 4. M. Tinkham, Science 145, 240 (1964). 5. J.H.M. Stoelinga en P. Wyder, Nederlands Tijdschrift voor Natuurkunde ¿6, 107 (1970). 6. M.V. Dorigo, J.H.M. Stoelinga and P. Wyder, Z. f. angew. Math. u. Phys. 20, 565 (1969). 7. J. Strong and G.A. Vanesse, J. Opt. Soc. Am. 50, 113 (1960). 8. R.C. Milward, Infrared Phys. 6, 59 (1969).
3 9. G.W. Chantry, H.W. Evans, J. Chamberlain and H.A. Gebbie, Infrared Phys. 9, 85 (1969). 10. H.W.H.M. Jongbloets, M.J.H. van de Steeg, E.J.C.M. van der Werf, J.H.M. Stoelinga and P. Wyder, accepted for publication in Infrared Phys. (1980). 11. T.M. Lifshits and F. Ya. Nad', Sov. Phys. Doklady 10, 532 (1965). 12. Sh. M. Kogan and T.M. Lifshits, Phys. Status Solidi A39, 11 (1977). 13. T.M. Lifshits, N.I. Likhtman and V.l. Sidorov, Sov. Phys. Semicond. 2, 652 (1968). 14. S. Dana Seccombe and D.M. Korn, Solid State Commun. 11, 1539 (1972). 15. E.M. Bykova, L.A. Goncharov, T.M. Lifshits, V.l. Sidorov and R.N. Hall, Sov. Phys. Semicond. 9, 1223 (1976). 16. P.E. Simmonds, J.M. Chamberlain, R.A. Hoult, R.A. Stradling and C.C. Bradley, J. Phys. C: Solid St. Phys. 2. 4164 (1974). 17. H.W.H.M. Jongbloets, J.H.M. Stoelinga, M.J.H. van de Steeg and P. Wyder, Physica 89B, 18 (1977). 18. H.W.H.M. Jongbloets, J.H.M. Stoelinga, M.J.H. van de Steeg and P. Wyder, Phys. Rev. В 20, 3328 (1979). 19. R.L. Jones and P. Fisher, J. Phys. Chem. Solids 26, 1125 (1965). 20. J.H. Reuszer and P. Fisher, Phys. Rev. 1_35, A1125 (1965). 21. H.W.H.M. Jongbloets, M.J.H. van de Steeg, J.H.M. Stoelinga and P. Wyder, accepted for publication in J. Phys. C: Solid St. Phys. (1980). 22. H.W.H.M. Jongbloets, M.J.H. van de Steeg, J.H.M. Stoelinga and P. Wyder, submitted for publication. 23. A.P. Soepangkat and P. Fisher, Phys. Rev. В 8, 870 (1973). 24. J. Broeckx, P. Clauws, K. van den Steen and J. Vennik, J. Phys. C: Solid St. Phys. 12, 4061 (1979). 25. J.С Hensel and K. Suzuki, Phys. Rev. В 9, 4219 (1974).
4 CHAPTER II INSTRUMENTATION
1. Introduction.
For all far infrared spectroscopic experiments described in this thesis the technique of Fourier transform spectroscopy (FTS) was used. The principle of FTS involves the recording of interference fringes formed by radiation which has propagated through an interferometer. This interferogram is a function of path difference between two optical beams formed in the interfero meter, and is uniquely related to the spectral distribution of the radiation. This information is recovered by the process of Fourier transformation (see chapter III). The FTS technique offers several advantages over conventional dispersive techniques : 1. The multiplex advantage, first pointed out by Fellgett .that each spectral element is observed for the whole duration of the experiment. The signal-to-noise ratio of an interferometric system will therefore be superior to that of a dispersive system (at least as long as detector noise is the dominant source of noise). (2) 2. Jacquinot showed that the information throughput of cylindncally symetrical systems such as an interferometer, could be much higher than in systems where a slit has to be used. 3. An interferometer is mechanically extremely simple as compared with a grating instrument. And it has the added advantage that the problem of stray light is not very severe, because only radiation that has undergone interfer ence contributes to the interferogram. Once the problem of transforming interferograms into spectra was overcome with the advance of modern computers, the advantages mentioned before made the FTS technique the most widely applied technique in far infrared spectroscopy. Extensive reviews of FTS have been given by Chantry and Bell ; a short summary of the most important aspects is given in chapter III (section III.l).
2. Spectrometer hardware
A typical far infrared interferometric spectrometer consists of the following sub-systems: a). A broad band source of far infrared radiation, and optics for beam co11 imation.
5 Control Water unit DC-Supply cooling
,,•• to computer ( optional ) Fan Photocell *- Source Tape- Chopper• punch Reference generator
Interfero Stepping Scanner- Detector meter motor Control unit
D.VM. Vibrating mirror Multiplexer Pre amplifier I I I L analog inputs
Driver Amplitude Oscillator meter
Ampi.mod. J Phase mod
Ref Τ input Signal Lock-in Recorder input amplifier
SCHEMATIC DIAGRAM OF FOURIER SPECTROMETER
Figure 1
6 F.I.R. MICHELSON INTERFEROMETER
Φ Collimator mirrors ® Lightpipe (polished brass) φ Reference signal generator ® Brass cone (D Chopper motor ® TPX Fresnel lens © Chopper © Vibrating mirror (D Medium pressure mercury lamp © Beamsplitter (mylar film) © Water-cooled lamp mount © Moving mirror © Transmission fitter © Micrometer (D Black polyethylene window © Stepping motor
Ргдиге 2
7 b). The interferometer itself to create the necessary interferograra-function from the broad band radiation. c). A far infrared detector and signal amplifying system for recording analogue interferogram signals. d). A Scanner-Control Unit to drive the interferometer and containing a digital data system to digitize interferogram signals and store the data, so that they can be processed by a computer. These subsystems can easily be recognized in the schematic diagram (figure 1) of the Fourier spectrometer, which was used for the experiments described in this thesis. The interferometer is of the Michelson type, with a thin film dielectric beamsplitter (figure 2). This modular instrument was developed at the National Physical Laboratory (Teddington, England) and manufactured by Grubb Parsons Company . Several details of this basic machine have been modified and improved in our laboratory.
a) Source
The medium pressure mercury arc lamp is still the best continuous broad band far infrared source available today, particularly at wave numbers below 100 cm where emission from the hot electron plasma predominates. Unfortuna tely its power output is rather low. In the whole 10 - 300 cm band it deli- -2-1 -1 . . vers ^5 mW.cm .sterad . Above 100 cm , strong absorption and reemission from the fused quartz outer mantle takes place, which makes the total radia tive output extremely sensitive to effects of convective cooling. For high stability, the lamp operates on d.c, under constant vacuum and in a water- cooled jacket. The special d.c. power supply for the Philips HPK 125 W mercury lamp was custom-built by Heinzinger ; it uses a photo-cell feed-back circuit to stabilize the radiation output of the source. The radiation can be chopped by a cylindrical chopper around the lamp (amplitude modulation; see chapter III, section III.l), and the emergent beam is collimated by a combination of a concave and convex mirror.
b) Michelson interferometer
The radiation from the source is divided by the beamsplitter into two beams, which are sent to two plane mirrors. One mirror can be translated over a distance of 2 cm by a micrometer screw driven by a stepping motor (Slo-Syn SS25-1002). The beams are reflected by the mirrors and, as they are mutually coherent, interference will occur as they are recombined at the beamsplitter
8 and travel to the detector. The emergent beam is focussed on the entrance of a polished brass lightpipe by a TPX Fresnel lens. A low-pass transmission filter and a vacuum-tight black polyethylene window remove the unwanted part of the Planck-spectrum of the source. The division of the incident wavefront into two is achieved by a free standing dielectric film beamsplitter; Mylar films of thicknesses between 6 ym and 100 ym are available, covering the spectral range of 5-350 cm (For a description of the properties of thin film beamsplitters: see Ref. 3, chapter 3). An alternative way of modulating the radiation is the so-called phase modulation (see chapter III, section III.l), achieved by a sinusoidal varia tion of the optical path difference. For this purpose, one of the plane mir rors is mounted on a vibration generator manufactured by Ling Dynamic Systems Ltd(8). c) Far infrared detector
The important criteria for a detector for use in combination with a far infrared interferometer are that it should have a high sensitivity (low noise equivalent power, NEP) and high responsivity, a uniform spectral response over a wide wave number range, and a high linearity of output over a wide dynamic range of input signals. In practice these criteria are only met by thermal detectors, which use the heating by the radiation to measure the absorbed power. Most commercial far infrared interferometers use a room temperature Golay detector , which has the disadvantage of a moderate NEP ("ь 10 W.Hz ) and slow response time ('v 30 msec). Low was the first to describe a germanium bolometer operated at liquid helium temperatures. Nowadays both germanium and silicon bolometers are used, and often a He cooling system (12) -12 is employed to reach a temperature of 0.35 К , yielding a NEP of 10 -14 -h • 10 W.Hz . An extensive review of these cryogenic semiconductor bolometers (13) was given by Pankratov and Korotkov Figure 3 shows a typical example of a basic detection system; various modifications for specific experiments are used in our laboratory. The FIR radiation enters the system via a black polyethylene window, which blocks out all visible and near infrared radiation. A lightpipe directs the radiation through a cooled low-pass filter (removing room temperature radiation) and a conical lightpipe to an integrating cavity wherein the bolometer has been CRYOSTAT WITH FAR INFRARED DETECTOR
12.6 V ω Incident radiation ® Light pipe (stainless steel) © Polyethylene window Figure 3 10 CRYOSTAT FOR PHOTOTHERMAL CONDUCTIVITY MEASUREMENTS JL -±- lj5Mмп^r © 126V ι _f—*H D HD φ Incident radiation ® Superconducting magnet (D Polyethylene window © Germanium sample (5) Electrical connections for Ge-sample @ To amplifier (Z) Electrical connections for s.c magnet © Load resistor (5ΜΩ) © To helium pump © Cavity (gold plated copper) (6) Liquid helium dewar ® Clamp © Liquid nitrogen dewar ® Thermometer (8) Light pipe (stainless steel) © Heater (9) Sapphire filter (fê) Tufnol insulation (© Cone ( gold plated copper ) Ггаиге 4 11 mounted. The absorbed radiation causes an increase in temperature of the bolometer element; this temperature change manifests itself as a change in the electrical conductance. The bolometer is connected to an electric circuit which delivers a bias current provided by a 12.6 Volt mercury battery via a 5 MÜ cooled load resistor. The variation in the voltage drop across the bolometer, due to the chopped radiation, is measured with a lock-in amplifier. d) Scanner-Control Unit The Scanner-Control Unit contains a preset indexer to drive the stepping motor a preset number of steps for discrete sampling of the interferogram. The step-length (i.e. the number of steps between two consecutive interfero gram points) is chosen appropiate to the spectrum high wave number cutoff (see also chapter III). The waiting time between sampled points is about twice the integration time of the detector lock-in amplifier. A digital volt meter (4? digit), preceded by a 4-channel multiplexer, digitizes the analogue output of the lock-in amplifier, and eventually the data are punched on papertape. The data are processed on a PDP-12 (DEC) laboratory computer, linked to a Houston incremental plotter. The relevant computer program is shown in an appendix to this thesis. 3. Experimental arrangement for photo-conductivity measurements. For the photoconductivity experiments, described in chapter IV, no bolo meter is needed, as the sample itself is the detector. Figure 4 shows the cryostat insert. As can be seen, the construction is almost identical to that of the bolometer system (figure 3). Only the semispherical cavity at the end of the conical lightpipe is enlarged so that it can contain the cubic sample 3 of dimensions 1 χ 1 χ 1 cm . The sample is clamped onto the base of the cavity with only a small heat leak to the base. The clamp and the sample can be heated above the temperature of the surrounding helium bath by a resistance wire wrapped around the mount ing stud. The temperature of the sample is measured with an Allen Bradley carbon resistor and can be stabilized within 0.1 K. Electric contacts are made by pressing flat copper disks against two sides of the sample which are wetted with a mixture of In-Hg (50-50). The sample is connected to an electric circuit, identical to the bolometer circuit, so the variation of the conduc tivity due to chopped radiation can be measured with a lock-in amplifier. 12 References 1. P. Felgett, J. de Physique C.2 28. 165 (1967). 2. P. Jacquinot, J. Opt. Soc. Am. 44, 761 (1954). 3. G.W. Chantry, Submillimetre Spectroscopy, Academic Press, N.Y. (1971). 4. R.J. Bell, Introductory Fourier Transform Spectroscopy, Academic Press, N.Y. (1972). 5. G.W. Chantry, H.H. Evans, J. Chamberlain and H.A. Gebbie, Infrared Phys. 9, 85 (1969). 6. Sir Howard Grubb Parsons and Company Limited, Walkergate, Newcastle upon Tyne NE62YB, England. 7. Heinzinger Regel- und Messtechnik, 82 Rosenheim, Happingerstr. 71, We s t Ge rmany. 8. Ling Dynamic Systems Limited, Royston Herts SG85BQ, England. 9. M.J.E. Golay, Rev. Sei. Instrum. 20, 816 (1949). 10. F.J. Low, J. Opt. Soc. Am. 5J.» 1300 (1961). 11. I.F. Silvera and G. Birnbaum, J. Opt. Soc. Am. 58, 718 (1968). 12. H.D. Drew and A.J. Sievers, Appi. Opt. 8, 2067 (1969). 13. N.A. Pankratov and V.P. Korotkov, (Sov. Phys.) Opt. Technology JL4, 106 (1974). 13 CHAPTER HI THE FAR INFRARED MICHELSON INTERFEROMETER III.l GENERAL INTRODUCTION 1. The interferogram-function. In a Michelson interferometer radiation from the source is divided into two beams, one is sent to a fixed mirror, and the other is sent to another mirror which can be driven along one arm of the interferometer (Fig. 1). Assume the source to be monochromatic, emitting radiation of amplitude /s (intensity S) and of wave number σ(=1/λ). This radiation falls onto a dielectric beam divider to which can be assigned a complex reflectivity f and transmissivity t; these functions are complex because of the phase shifts introduced into the optical beam by the phenomena that occur in the # Source Detector Sample Ж/////Ш/Ж ?ig. 1 : The division of oomplex amplitudes in a Michelson interferometer; $ and t are the complex reflectivity and transmissivity of the dielectric film beam splitter (B.S.). 14 beam divider. (See e.g. Chantry , chapter 3.) Therefore î and t can be written as f = г.еІ i, α) t = fe . A displacement x/2 of the moving mirror in one arm of the interferometer produces a phase delay Δ between the two beams, given by Δ = 2irax . (2) From Fig. 1 it can easily be seen that the amplitude â, of the recombined det beam going to the detector, and the amplitude â of the beam eoing r source & back to the source, are given by â, _ = /S(?t+tf-eiA) det ? 9 ίΛ (3) 2 2 lA â = /s(t +î .e ) . These equations illustrate the dissymmetry of the two beams. For the one travelling towards the detector, the beams traversing the two arms each suffer one transmission and one reflection at the beam splitter; for the other case one beam is reflected twice and the other transmitted twice. Using equation (1) this leads to iA i(e ) â, , = /Srt(l+e )e ^ det (4) 2 ia, 2 i2e iA â source = ^(t .e +r .e .e ) . The intensity of the beams is given by the square of the modulus of the com plex amplitude. Therefore, one gets at the detector and at the source res pectively I. .. = 2r2t2S(l+cosA) det (5) I = S[r4+t4+2r2t2'cos(2e-2^+A)] . source 15 In the case of a non-absorbing beam splitter it can be shown (Chantry .chap ter 3) that 2В-Ър = (2η+1)π η = 1,2,3,... . (6) This leads to I = S(r4+t4-2r2t2-cosn) . (7) source The properties of the beam splitter can be combined in two parameters A and В given by A = At4 2 2 (8) В = 2r t . The quality В is often called the efficiency of the beam splitter. If a sample with energy transmission-coefficient Τ is placed into the beam going to the detector (see Fig. 1), the intensity of the relevant beams can finally be expressed as Ι. ίΔ) = TSB(l+cosA) det (9) Ι (Δ) = S(A-B'COsA) source So far the source was assumed to be monochromatic with wave number σ and intensity S. If the source emits a broad spectrum with distribution S(a), the total intensity I'(x) reaching the detector can be found by integrating Ι, (Δ) over all wave numbers σ. It has to be noted that the quantities A, det В and Τ are function« of σ as well. The interferogram-function I'(x) for a broad spectrum is thus found to be іЧх) = ƒ T(a)-S(a)-B(a)-(l+cos2wax)-da о (10) = 2 ƒ C!(a)'(l+cos2TOx)-do , о where Q(a) Ξ ^ τ(σ)·5(σ)·Β(σ). 16 2. Amplitude and phase modulation. Since the intensity of the source in the far infrared region is very weak, the voltage output of the detectors is very small. Therefore it is necessary to modulate the radiation and to use phase sensitive detection (PSD) techniques. In a Michelson interferometer this modulation can be done in two ways: 1) Amplitude Modulation (AM), where the light beam emerging from the source is chopped; 2) Phase Modulation (PM), where the optical path difference between the two interfering beams is modulated. This is achieved by a vibration with small amplitude a of one of the mirrors in the inter ferometer. The modulation frequency ω for AM and PM is optimized with respect to the response time of the detector. In the previous section the unmodulated interferogram-function I'(x) was calculated and is given by equation (10). When some form of periodic modulation is used, the interferogram-function becomes time-dependent and the intensity reaching the detector can be resolved into Fourier components. Since phase sensitive detection selects out only the fundamental Fourier- component of the signal, the ideal form of modulation is a pure sine-function of time. Obviously, the resulting interferograms and spectra will depend on which of the two modulation techniques, AM or PM, is used. When AM is used the source intensity 5(σ) in equation (10) becomes time-dependent. If the modulation has the ideal sine-form, the intensity Ilw(x>t) reaching the detector becomes AM l!M(x,t) = I'ixMl+sinot) . (11) AM After PSD, the registered interferogram-function will be proportional to I' (x) = h Ι'(χ) AM (12) = h ƒ 2Q(a)'(l+cos2Trax)-da . о This proportionality-factor is determined by the detector sensitivity and the amplification of the phase sensitive detector (lock-in amplifier). If a more practical square function is used for the modulation, the factor \ in equation (12) has to be replaced by 2/π. The actual spectral information is contained in the x-dependent part of equation (12), called the interferogram. 17 This interferogram I (χ) is obtained from expression (12) by subtracting the , constant level ƒ Q(a) da) leading to I^U) = h ƒ 2Q(a)'cos(2waxWa . (13) о Notice that I.w(x) is an even function of xl AM When PM is applied the optical path difference χ is modulated. If a sinusoidal modulation of amplitude a is used, in equation (10) χ has to be replaced by x+a*sinu)t. Using the Bessel series expansions of cos(z'sinO) and sin(z'sin6), the cos-term in equation (10) can be written as CO cos[ 2πσ(χ+Ε·8ΪηωΟ ] = У J (2waa),cos(2iTax+müt) . (14) u m ms-» Since phase sensitive detection is used, only the component with the funda mental frequency hhaa s to be considered. The intensity I' (x,t) of this com ponent is given by I' (x,t) = ƒ 2Q(a)'(.-2JA2iíaa.))'sÍTt2T¡ax'sinb¡fda , (15) о where the relation J (z) = (-1) J (z) has been used. After PSD, the regis- -m m tered interferogram is therefore proportional to 00 I™(x) = ƒ 2Q(a)'(-2J.(2w0a))-sin2wax'do . (16) PM 1 о Notice that this interferogram is an odd function of χ and that this ex pression has no constant term as in equation (12). 3. Spectra calculated by Fourier transformation. Expressions for the observed interferograms were given in equations (13) and (16) for the case of AM and PM respectively. An extension can be made to negative wave numbers by stating that Q(-a) = Q(a) . Since J^(-2ixaa) = -J1(2woa) it follows that -2J.(г-са)'Q(a) is an odd function of σ. With this 18 extension equations (13) and (16) can be rewritten in a complex form as i2TOX lmM = h ƒ Q(a)-e -da (17) -2 r «ζ \ . /•-! \ i2iroTOXx Ірм(х) = ^ ƒ Q(a)-J1(2waa)-e^ -do . From these equations it is clear that the interferograms I...(x) and Ι,,,.ίχ) AM PM have a Fourier-type of relationship with the spectral functions h Q(o) and -τ- Q(o)'J.(2wca) respectively. The latter two functions can be recovered from I,..(x) and I„.,(x) by an inverse complex Fourier transform. Since in AM PM practise a complex Fourier transform yields a complex spectrum, one usually calculates the modulus of this spectrum, i.e. 2πίσχ Ρ(σ) = | ƒ ΐ(χ)·6" Μχ| , (18) yielding Ρ.Μ(σ) = % Q(a) and AM ΡρΜ(σ) = 2|J (2πσβ)|·ς(σ). From these considerations, some advantages of PM are immediately evident: 1. In order to obtain the spectral information from the interferogram- function I' (x) (equation (12)), the constant term in this expression has to be subtracted. Fluctuations in the source intensity and detector sensiti vity affect this constant term and therefore can falsefy the spectrum. Since the expression for I (x) (equation (16)) contains no constant term, greater immunity from fluctuations in source intensity and detector sensi tivity is obtained with PM. 2. The ratio of Ρ„.Χσ) and Ρ...(σ) is 4| J, (2тгоа) I . This factor is wave PM AM ' 1 ' number dependent and is > 1 for wave numbers between 0.08/a and 0.51/a. It reaches zero at σ = 0.611/a and has a maximum of 2.3 at σ = 0.29/a. This о max means that in case of PM the signal-to-noise ratio exceeds that of AM over 75% of the range between 0 and σ and is twice as high near σ . A physical ь о ь max ^ ' 19 way of looking at this is that there is no chopper to interrupt the optical beam, so that the detector views the source for a greater length of time with PM, thus leading to an increase in the signal-to-noise ratio. 3. The wave number dependent multiplicative factor 4|j..(2waa)| can be used to act as a non-absorbtive filter. The Bessel function falls to zero when σ = 0.611/a. By an appropriate choice of the modulation amplitude a, a certain spectral region can be suppressed. Thus in combination with suited low-pass transmission filters an effective suppression of radiation with high wave numbers can be achieved. A more detailed description of AM and PM was given by Chamberlain ' ' and Chantry , 4. Effects due to sampling of the interferogram over a finite length. The optical path difference χ is usually assumed to be a continuous variable ranging from -"> to +<». Actually, however, interferograms are recor ded in discrete steps Δχ, over a finite range. If N datapoints are recorded symmetrically around zero path difference, i.e. χ ranging from -L to +L with L = (Ν/2)·Δχ> then expression (18) for the modulus spectrum has to be modi fied into +N/2 . 2πισηΔχ Ρ(σ) = Δχ- Ι ΐ(ηΔχ).ε" . (19) η=-Ν/2 This expression relates Ρ(σ) uniquely with ΐ(ηΛχ) for a limited range of values for σ only. This can be seen by considering the source to be monochro matic with wave number σ = (1/λ ). According to equation (9), this results in a cosine-like interferogram. To determine the value of σ from the inter- o ferogram, the sampling theorem states that at least two points have to be sampled within one wave length. Therefore, this leads, for a given value of Δχ, to a limit for the highest wave number σ , given by σ = 1/(2Δχ). 0 max 0 J max However, it is obvious that an infinite number of waves with higher wave numbers will also fit through the points in the range of observation. There fore, the information contained in the interferogram can be attributed to higher wave numbers as well; this phenomenon is called "aliasing" (Chantry , chapter 3). If low pass filters are used, which block out the radiation with wave numbers above σma x , usingo rexpressio n (19) the original ospectrur m can be 20 recovered uniquely from the recorded interferogram. In addition, the limitation of recording the interferogram over a finite range of x-values, -L < χ < L, also confines the spectral resolution. It can easily be shown (Chantry , chapter 3), that the power spectrum of a truncated interferogram of a monochromatic line is proportional to 8ίη2π(σ -a)L 2л(а0-о)Ь · (20) о This function has a half-width of approximately 1/(2L)( and has large and slowly decaying sidelobes. If the resolution is taken as the minimum wave number distance at which another line of equal intensity can just be observed in the transformed discrete spectrum, then one gets a resolution of 1/(2L). Therefore, spectra with a higher resolution can be obtained simply by moving the mirror over a longer distance, parallel to its original position. In practice, the resolution is restricted by the signal-to-noise-ratio, the finite aperture of the source and detector, and by tilt adjustments (i.e. the image of one mirror in the beam splitter is not perfectly parallel to the surface of the other). The sidelobes mentioned above can easily be mistaken for real spectral features. If the recorded interferogram is multiplied with a so-called apodization-function, these sidelobes can be suppressed effectively. Usually a cosine squared function (which is 1 at χ = 0 and 0 at χ = +_ L) is chosen; this is also done in our computer program, described in the Appendix. It should be noted however, that this procedure broadens the central line, degrading the resolution by a factor 1.5. An example of an interferogram of a monochromatic line, recorded with amplitude modulation, is shown in figure 2a. This line originated from a home-built grating monochromator, described in refs. 5 and 6. Figure 2b shows the corresponding power spectrum, calculated with equation (19). From figure 2a it can be seen that the interference pattern decays within the interferogram length; therefore figure 2b represents the actual lineshape. In fact, the lineshape is determined by the width of the exit-slit of the grating monochromator. From the interferogram, the wavelength λ is seen to have a value of 0.370 mm, while the central position σ of the line in . . -1 0 the spectrum is situated at 27 cm . So for these values the relation σ = Ι/λ holds. о о 21 ω '.hi с 'ι φ Ι (α) ί 11 ', ί ! - ίί ' ' ' ι' ΓΙ' ' '' ', ! ,' , ι Μ ! ι ι Ι' ι, , ,", Ν -,Ι 1 ' , ι Ι' 'Ι , ι ι , 4 ' - " " , ! h ,, '· •' ' '/ у ι ι· Ί ч, !, ; ι . ι Ί,' υ ·/ i Ί Ι· ., ' '! . ι , ν ' ,1 ίι ι' . " ι. ' ' 'ί ϊ г -5 -25 Ο 25 5 Optical path difference ( mm ) (Л с (Ы Φ _L_i_. 25 50 75 100 125 150 Wave number (cm"1) Fig. 2 : Figure (a) and (b) show respectively the interferogram and speatmm of a ntonoohro^atia line, originating fren a grating monoahro^ator. 22 w с (α) φ —^Λι'/Υ- \ ι -10 12 Optical path difference ( mm ) λ ω с Á \ (b) Φ M Ι' ι I1 i Л^Л I í > I > / 1 í u V 50 100 150 200 250 300 350 Wave number (cm"1) '.•'ig. 3 : Figure (a) and (b) show respectively the interferogram and speatrur, of a continuous broad band spcctriov. The structure is determined by the efficiency of the 50 \m Mylar beamsplitter. 23 In the previous section it was demonstrated that the spectral output was determined by the properties of the thin film beam splitter as well. The disadvantage of these thin films is that due to standing wave interference effects, caused by multiple reflections within the thin transparant films, the beam splitter efficiency Β(σ) is a periodic archlike function of wave number, reaching zero at multiple values of l/(2ndcos9'). Here d is the thickness of the film, η the refractive index and Θ' the angle of the re fracted beam inside the film. The function Β(σ) was first introduced in equation (8); its exact form has been calculated by several authors An example of the influence of a beam splitter is shown in figure 3a and 3b, where a Mylar beam splitter of 50 μπι thickness was used, with an angle of incidence for the broad band radiation of 45 . Using η = 1.72 the wave numbers where Β(σ) reaches 0, are found to be multiple values of 64 cm , in accordance with figure 3b. Interferograms such as in figure 2a and 3a, which are recorded symmetri cally around zero path difference, are called double-sided interferograms. In principle, if the interferogram is exactly symmetrically sampled, it is sufficient to record one side only (single-sided interferograms). Actually, often the sampling comb is not positioned so as to record an ordinate at exactly zero path difference. It can easily be shown (Chantry , chapter 3) that this does not affect the modulus spectrum of a dobble-sided interfero gram. In case of a single-sided interferogram symmetry must be restored by numerical computation ' . Single-sided interferograms (not used in the (13) present investigations) are treated in details in textbooks (see Bell or Vanasse and Sakai ). 24 References. 1. G.W. Chantry, Submillimetre Spectroscopy, Academic Press, New York (1971). 2. J. Chamberlain, Infrared Physics 11, 25 (1971). 3. J. Chamberlain and H.A. Gebbie, Infrared Physics VL, 57 (1971). 4. J. Chamberlain, J. Haigh and M.J. Hine, Infrared Physics 1A, 75 (1971). 5. M.V. Dorigo, J.H.M. Stoelinga and P. Wyder, Z. ang. Math. Phys. (ZAMP) 20, 565 (1969). 6. J.H.M. Stoelinga and P. Wyder, Nederlands Tijdschrift voor Natuurkunde 36, 107 (1970). 7. D.J. James and J. Ring, J. Phys. (Paris) 28, 150 (1967). 8. E.V. Loewenstein and A. Engelsrath, J. Phys. 28, 153 (1967). 9. D.R. Smith and E.V. Loewenstein, Appi. Opt. 14, 2473 (1975). 10. D.A. Naylor, R.T. Boreiko and T.A. Clark, Appi. Opt. 17, 1055 (1978). 11. M.L. Forman, W.H. Steel and G.A. Vanasse, J. Opt. Soc. Am. 56, 59 (1966). 12. H. Sakai, G.A. Vanasse and M.L. Forman, J. Opt. Soc. Am. 58, 84 (1968). 13. R.J. Bell, Introductory Fourier Transform Spectroscopy, Academic Press, New York (1972). 14. G.A. Vanasse and H. Sakai, Progress in Optics, E. Wolf ed., 6, 259 (1967), North Holland, Amsterdam. 25 III.2 SPECTRUM DISTORTION IN FAR-INFRARED FOURIER SPECTROSCOPY BY MULTIPLE REFLECTIONS BETWEEN SAMPLE AND MICHELSON INTERFEROMETER ABSTRACT In far-infrared Fourier spectroscopy with a Michelson interferometer deviations in the measured transmission spectra of samples with non- negligible reflection can be observed. This effect is investigated both theoretically and experimentally. It is shown that the spectral element at a certain wave number contains contributions of subharmonics of that wave number. 1. Introduction. One of the most widely used instruments in far-infrared spectroscopy is the Michelson interferometer with thin film beamsplitter. An extensive review of the Fourier spectroscopic technique on which this instrument is based has been given by Chantry . In order to determine the transmission spectrum of some sample one usually performs two measurements: 1) A sample interferogram with a sample in the light-path between interferometer and detector, and: 2) A background interferogram without the sample. These interferograms are Fourier transformed, and the ratio of the two obtained spectra then yields the desired transmission spectrum. However, it should be noted that a non-negligible amount of radiation can be reflected back into the interferometer system by a reflecting sample. This can lead to significant distortions in the spectra. This effect seems to have escaped notice until now. It is the purpose of this paper to present results of a theoretical and experimental investigation into the effect of this reflected radiation on the measured transmission spectrum. 26 * Source Detector Sample '////////////////M Fig. 1 : Schevatie diagram of a Viihelscn interferone ter in a con figura tion for transmission measurements. The energy reflection ana transnission coefficients of the beamsplitter are R-, and T, respectively, those of the sample are Ρ and T. 2. Theory. Fig. 1 shows schematically a Michelson interferometer with an inci dent beam of radiation. There are two emergent beams, one towards the sample and detector, the other towards the source. In the following cal culations we neglect the effect of absorption in the beamsplitter, which is a good approximation for the first lobe of the interference pattern (2) of a Mylar beamsplitter We assume the source to be monochromatic with wave number σ and in tensity S, and the optical path difference between the two arms of the interferometer to be x. Then the phase difference between the beams recombining at the beamsplitter will be Δ = 2ιτσχ, the energy I arriving at the sample will be given by Ι (Δ) = SB(l + cosA) , о (1) and the energy I' returning to the source by 27 Ι'(Δ) = S(A - B'cosA) . (2) о (3) (See for instance: Loewenstein and Engelsrath .) The beamsplitter pro- 2 2 perties are represented by the quantities A = R + T. and Β = 2Κ,Τ, , where R, and T, denote the energy reflection and transmission coefficients of the beamsplitter respectively. For a non-absorbing beamsplitter we have R, + T, = 1 and A + В = 1. The quantity В is often called the efficiency of the beamsplitter. The sample will transmit a fraction Τ of the incident radiation to wards the detector, and will reflect a fraction R back into the inter ferometer (R < 1). To simplify the calculations it will be assumed that the reflected radiation has a random phase relation with the original beam, so that no interference will occur and one can simply add the in tensities. The sample can then be considered as an extra radiation source with intensity RI (Δ). According to Eq. (2) a fraction with energy І.Ш = RI (Δ)(Α - B'cosA) 1 о will return to the sample, and will again be partly reflected, etc. The total energy I reaching the detector, after transmission through the sample, will therefore be œ Ι(Δ) = TSBd + cosA) I Rn(A - B-cosA)" . (3) n=0 The term in the infinite sum is < 1 (because R < 1 and A + В = 1), so the geometrical series can be summed. Introducing the quantity C, defined as c=r^Rl· (4) the summation of Eq. (3) yields: Ι(Δ) = ψ [l - , * ' C . ] . (5) R 1 + С'созЛ 28 It follows from Eq. (4) that 0 < С < 1. In order to perform the Fourier transform it is convenient to write Eq. (5) in the form of a Fourier series. It is shown in the Appendix that the function ί(Δ) = (1 + C-cosA)"1 can be represented by a Fourier series a «> £(Δ) = -£ + У a 'COsCnA) 2 -i n n=l with coefficients a given by 2 2 1 n f^J - ΐ . (6) иг: ,2 Defining the coefficients В as: В - i-ll - (1 - C) -£] (7.a) о R l 2 В = C Г 1 »a for η = 1,2,3, (7.b) η nR η ' the Fourier series representation of ΐ(Δ) can be expressed as: Ι(Δ) = TS [ В + LУ В ·η·οο3(ηΔ) ] . (8) о η=.1 η Fig. 2 shows the calculated В , B., B_ and B, as functions of R for various values of the beamsplitter efficiency B. It can easily be shown that for R -* 0 the values В -»· В, В, -»· В and В -> 0 for η > 2, so that ol η in this limit Eq. (8) reduces to the well known form of Eq. (1) lim Ι(Λ) = TSBd + cosA) . R+0 29 OC 02 0¿ R- - Вз Fig. 2 : The ealaulated values of the quantities В , В j S and В as o i ¿ о functions of R for various values of the beamsplitter efficiency В (non-absorbing beamsplitter). 30 It is obvious from Eq. (8) that the interferogram-function ΐ(Δ) contains higher harmonics of the basic frequency due to the reflected radiation. So far the source was assumed to be monochromatic with wavenumber σ and intensity S. If the source emits a broad spectrum 5(σ), the total energy I'(x) reaching the detector can be found by integrating Ι(Λ) over all wavenumbers σ. In doing so one has to take into account that the quantities Α,Β,Τ,Κ,Ο and В may also be functions of σ. The interferogram- function I'Cx) for a broad spectrum is thus found to be oo I'Cx) = ƒ τ(σ)·8(σ)·Β о(o)'d a о' (9) œ œ + ƒ У Τ(σ)·8(σ)·Β (σ)·η·ΰθ8(2πησχ)«do . ι n ο n=l The first integral in Eq. (9) is independent of x, and corresponds to the average of l'(x) over all x. The second integral in Eq. (9) is the proper interferogram iCx), which, by changing the variable σ to σ/η, can be written as CO 00 I(x) = ƒ Уи Τ(-)·8(-)·Β (-).οο8(2πσχ)·ασ . (10) ο' η=,1 η η η η In most experiments the intensity of the source is chopped and the detector provides a signal proportional to I'Cx). After phase-sensitive detection and subtraction of the average level one obtains an interfero gram proportional to l(x). The spectrum one is interested in is then cal culated as the Fourier transform of this interferogram. One sees immedia tely from Eq. (10) that this spectrum Ρ(σ), omitting multiplicative con stants, is given by: oo Ρ(σ) = I T(^)-S(2.).B A . (11) η=*·1, η η η η This means that the spectral element with wavenumber σ contains not only information about the sample, source and instrument for wavenumber σ, but 31 also for a series of subharmonics of σ. For small values of R Eq. (11) reduces to the well known undistorted spectrum: lim Ρ(σ) = Τ(σ)·8(σ)·Β(σ) . R-+0 The background spectrum (without the sample) is simply 8(σ)·Β(σ)) so that for R-+0 the transmission spectrum, calculated as the ratio of the sample and background spectrum, is indeed equal to Τ(σ). However, for non-negli gible values of R one does not obtain the proper transmission spectrum in this simple way, and the corrections discussed above have to be taken into account. 3. Experiment. In order to test the analysis of section 2 we performed some experi ments in which the transmission spectra of samples with high reflection were measured and compared with the known transmission. A modular FTR (4) interferometer , manufactured by Grubb Parsons Company, was employed with a 12.5 um Mylar beamsplitter. One of the modifications allowed the use of both the standard broadband source (i.e. a mercury lamp) or an external monochromatic source (i.e. a FIR-laser or a monochromator). A TPX lens focussed the radiation emerging from the interferometer onto the entrance hole of a lightpipe which contained the sample-holder. The reflected radiation re-entered the interferometer along the reversed path, while the transmitted power was detected at the exit of the lightpipe. a. Monochromatic_source. The properties of an interferometer are most clearly studied by em ploying a monochromatic source. In our experiments this was an optically pumped FIR laser, operating at the 118.8 ym (σ = 84.2 cm ) transition (5) . . . 0 . of methanol . The radiation was coupled into the interferometer via a lightpipe and collimated by a TPX lens; the emerging power was measured with a Molectron P3 pyro-electric detector. A 750 lines/inch nickel mesh (manufactured by Buckbee and Mears Company, Minnesota) was used as re flecting sample; the measured transmission coefficient at 84.2 cm was Τ = 0.15. 32 750 l/inch Ni-mesh (a) Hl·- No sample (b) Hl·- ooL 100 200 300 Wave number (cm*1) The tr>ansrri3siûn apee trun of а /Ь0 linee/inoh nickel neah, chjiäing ine effect on the Ь^тг s formed opeotpun of the reflected raáiui,ion (7). "he source wac mono car ovati в vith radiation wave —2 nuròer σ„ - 84.2 an ; the background specie J."I Is s noun as c;rve (bj. The traronlssion of ^ie sarcle at 3Λ.? »η * is " = 0.15. 33 The measured background interferogram was an almost perfect cosine of which the Fourier transform yields the monochromatic peak at σ = 84.2 cm shown in Fig. 3b. A very small harmonic component at 2σ can be seen which may be due to a reflection at the detector or to a possible non-linearity of the detector sensitivity. The small side-peaks at 10 cm to the left and right of the main peak are caused by a small periodical pitch error in the micrometer screw of the mirror drive of the interferometer The measured transmission spectrum (see Fig. 3a) of the sample shows very clearly the peaks at harmonics of σ as predicted by the theory of section 2. As our computer program calculated the modulus of the complex transformed spectrum, the negative sign of the peaks at even multiples of σ does not show up in Fig. 3a. The intensities of the peaks relative to the background peak are given in Table 1. We also calculated the re lative peak intensities with the formula Τ(σ )·Β (σ )/Β(σ ) given by the ο η о о theory; the results are also given in Table 1, where the negative signs for the even peaks have been omitted. In the calculations a loss of 5% of the radiation was assumed so that the effective reflection coefficient of the sample was taken as R = 0.8. In calculating the efficiency of the beamsplitter the polarization (2 3) properties have to be taken into account ' . The originally polarized radiation of the laser proved to be totally depolarized by entering the interferometer through a lightpipe and collimator lens. The calculations were performed separately for the parallel and perpendicularly polarized components of the incident radiation, and the results were averaged. For a non-absorbing 12.5 ym Mylar beamsplitter and 45 angle of incidence, the calculated efficiency of the two components was found to be B« = 0.11 and B. = 0.46 respectively. As can be seen from Table 1 the agreement between theory and experi ment is rather good. It is interesting to note that the efficiency of the beamsplitter has a minimum at 250 cm so that without the reflection effect discussed in this paper there could not be a noticeable intensity in the region where peak no. 3 is located. b. Broadband source. In order to investigate the influence of the reflection effect on broadband spectra, we measured the transmission of polished brass disks 34 'i'áble 1 : The experimentally and theoretically determined relative peak intensitbes in the transmission speetrum of a 750 lines/inch nickel mesh with a monochromatic source of wave number 84.2 cm ". peak no. 1 2 3 A Experiment 0.19 0.024 0.012 0.002 Theory 0.19 0.026 0.006 0.002 150 200 250 Wave number (cm"1) Fig. 4 : The measured (solid curves) and calculated (dashed cvroes) transmission spectra of polished brass disks from which sectors of 90 j 180 and 270 were removed. The deviation due to the reflection effect from the ideal constant transmission coeffi cients Τ - 0.25, 0.50 and 0.75 respectively is clearly demonstrated. 35 from which sectors of 90 , 180 , and 270 were removed. The broadband source was a medium pressure mercury lamp (Philips HPK 125 W). An IR50 Golay cell was used as detector. Without the reflection effect under study, the expected transmission spectra should have a constant level at Τ = 0.25, 0.50, and 0.75 respectively. But, as can be seen in Fig. 4, the experimen tal results exhibit a distinct deviation from this ideal behaviour. Only the spectrum with the lowest reflection (T = 0.75) approximates the real transmission spectrum almost up to the regions near 0 cm and 250 cm , where the ratio of sample and background spectrum becomes inaccurate be cause of the minima in the beamsplitter efficiency. However, the measured transmission spectra conform very well to the calculated spectra (dashed curves in Fig. 4) if the reflection effect is included. In these calcula tions effective reflection coefficients were chosen by assuming a loss of 5% of the radiation, yielding R = 0.70, 0.45, and 0.20 respectively. The beamsplitter efficiency Β(σ) was calculated as in Ref. 2, ignoring absorp tion, and averaging over all polarization directions. The combination of source-spectrum and transmission of the present filters and windows was approximated by an analytical function S(o), which fitted the experimental curve within 10%. As the spectral level at wavenumber σ is mainly determined by the first two terms of the infinite series of Eq. (11), i.e. Τ(σ)·5(σ)•B1(σ) and Τ(^σ)·5(^σ) ·Β.(ΐίσ), the main result of the reflection effect will be 1 -1 an increase of the level for low wavenumbers, and a decrease near 250 cm This is due to the maximum in the beamsplitter efficiency at 125 cm , and the minima at 0 cm and 250 cm 4. Conclusions. We have shown theoretically and experimentally that due to reflections from the sample the measured transmission spectrum can exhibit a substan tial deviation from the real spectrum if a Michelson interferometer is employed. The best way to avoid this effect is to arrange the optical set-up in such a way that the reflected radiation is prevented to re-enter the interferometer. 36 Appendix. In this appendix the calculation will be given of the coefficients of the Fourier series representation of the function: ί(Δ) = (1 + C-cosA)"1 , (Al) where 0 < С < 1. This function f(A) is a bounded periodic function of period 2π (i.e. f(A + 2π) = f(A)), and satisfies the Dirichlet conditions: a) In any period f(A) is continuous; b) In any period f(A) has only a finite number of maxima and minima. In addition, f(A) is even (i.e. f(-A) = f(A)). Then f(A) may be represented by a Fourier series a œ f(A) = -%- + I a -cosinA) (A2) n=l where a - - ƒ f(A)-cos(nA)-dA . (A3) η π J -π Writing the Euler definition for the cosine, and using the fact that f(A) is even one obtains the complex form of a : r η π ιηΔ a i f e_^ _dn -π 2 + C(e + e ) Substituting ζ = e and integrating along the unity circle yields: а = I f Ξ . d£ . (A4) n π 1 1Z 2 + C(z + z" ) Introducing the quantities E and F, defined as: 37 2 E = (^0(1 + Vi - С ) (A5a) F = (^)(1 - Vi - С2) (A5b) Eq. (A4) can be written as: 4 1 n an = С ' 2ÏT ^ (z - EKz - F) dZ · (A6) Since 0 < С < 1 we have E < -1 and -1 < F < 0, so that F lies inside the unity circle and E does not. The residu theorem is stated as ι f lí£)_dz = g(a) if a lies inside the closed integration path, and g(z) does not have any singularities inside this path. This can be applied to Eq. (A6) by sub stituting a = F and η Z g(z) = ζ - E ' yielding: _ 4 F an С " F - E or, using the definitions for E and F: f- f - Г . (A7) n vnt 38 References. 1. Chantry G.W., Submíllimetre Spectroscopy, Academic Press, London and New York (1971). 2. Naylor D.A., R.T. Boreiko & T.A. Clark, Appi. Opt. Ц, 1055 (1978). 3. Loewenstein E.V. & A. Engelsrath, J. de Phys. 28, C2-153 (1967). 4. Chantry G.W., H.M. Evans, J. Chamberlain & H.A. Gebbie, Infrared Phys. 9, 85 (1969). 5. Chang T.Y. , T.J. Bridges & E.G. Burkhardt, Appi. Phys. Lett. 1_7, 249 (1970). 6. Steeg M.J.H, van de, H.W.H.M. Jongbloets, J.H.M. Stoelinga, R.W. van der Heijden, R.J.M, van Vucht & P. Wyder, to be published. 39 CHAPTER IV PHOTOTHERMAL IONIZATION SPECTROSCOPY OF SHALLOW IMPURITIES IN ULTRA-PURE GERMANIUM IV.1 INTRODUCTION TO PHOTOTHERMAL IONIZATION SPECTROSCOPY (PTIS) 1. General introduction. In the last decade extensive investigations into the ultrapurification of germanium have taken place, mainly with the purpose of fabrication of (1 2 3) nuclear radiation detectors ' ' As criterion for the purity of germanium is currently used the total concentration of shallow donors and acceptors (i.e. elements like As, Sb, P, Li, ΑΙ, В, etc.). One of the difficulties which were met for many years was that while the net concentration of the residual donors and acceptors in the Ge crystals could be measured, one had very little information about the chemical identities of these impurities. However, a knowledge of the chemical identities is obligatory for the improvement in the technology of preparation of ultrapure germanium. Here a new technique, developed by Russian scientists ' ' , came to the rescue, which could be used to detect and identify impurities in 9 -3 germanium m concentrations down to the 10 cm range and possibly even lower. This technique of photothermal ionization spectroscopy (PTIS) is based on two experimentally established facts: 1) Under very definite con ditions the spectrum of the extrinsic photoconductivity is a line spectrum which reflects the energy level structure of the impurities; 2) The magni tude of the photoresponse is independent of the concentrations of the impurities down to very low concentrations. A recent review of the PTIS technique was given by Kogan and Lif shits1· ' '. Since 1970 many experi mentalists have used PTIS for the investigation of ultra-pure Ge. (See for instance Refs. 3*8-13.) In our laboratory we have performed measurements on ultra-pure germa nium samples obtained from Dr. H.J.A. van Dijk of Philips Research Labora tories in Eindhoven. Before explaining the PTIS technique a brief review will be given of the essential details of the theory of shallow donors and acceptors in germanium. 40 2. Theoretical considerations. Kittel and Mitchell and Kohn and Luttinger presented the first comprehensive theoretical model for shallow donors in germanium; the so- called "effective mass approximation". The model is based on the following qualitative picture: The group V donor has five electrons outside of closed shells. Four of these complete the bonds with neighbouring Ge atoms. The fifth finds itself in the Coulomb field of the singly-charged impurity ion. A series of quantum states can be assigned to this additional electron similar to those of the single electron in the hydrogen atom, but with some important modifications. First, the "hydrogenic" impurity is not in a vacuum but in a lattice with dielectric constant, ε, so that all binding-energies 2 emerging from the hydrogen atom are reduced by a factor e and the linear dimensions of the wave functions are increased by a factor ε. Furthermore, the electric charge moving in the field of the impurity ion does not have the mass m of the free electron but has an effective mass m , which is о anisotropic. The dielectric constant and the reduced mass together result in approximately 1000 times smaller energies than in the hydrogen atom. The wave functions of the excited states extend over thousands of crystal cells, but are zero in the central cell occupied by the impurity. The corresponding energy levels are therefore almost insensitive to the chemical nature of the impurity atoms, and the "effective mass theory" provides a very accurate description of the excited levels. The differences that make the identification of the individual impuri ties possible are due to departures of the lowest levels from the effective mass approximation. The ground state wave function has a maximum in the crystal central cell. Therefore the ground state energy is sensitive to the form of the crystal field in the central cell and depends on the chemical nature of the impurity. This "central cell correction" to the effective mass approximation causes a "chemical shift" of the ground state level, characteristic for the impurity in question. Theoretical calculations were performed by Philips , while Reuszer and Fisher deduced the chemical shifts for various donors from measured absorption spectra. Most of the considerations above apply mutatis mutandis also to accep tors in Ge. On the other hand, acceptor states represent a rather different situation, because of the special structure of the top of the valence band. (18) The acceptor problem was first formulated by Kohn , while numerical calculations were performed by Schechter , Mendelson and James and 41 .(21 22) more recently by Baldereschi and Lipari ' . A very extensive review of (23) the theory of acceptors and donors in Ge was given by Bassani et al. The chemical shifts of the ground states of several shallow acceptors (24) in germanium were determined by Jones and Fisher from transmission 15 -3 measurements on samples with impurity concentrations of 10 cm . The ab sorption peaks they observed were interpreted as optical transitions from the ground state of the impurities to bound excited states. From a combina tion of theory and experiment they deduced the energy level schemes shown in Fig. 1. As can be seen the higher excited states of all acceptors are virtually the same, as was predicted by the effective mass theory. Only the SJ VALENCE BANDÌ 0 1 I A" 2 - u ce Egs. Egs. Egs.- 11 BORON ALUMINUM 10.47 meV 10.80 meV GALL|UM Egs. 12 INDIUM 10.97 meV 11.61 meV 13 Egs.- THALLIUM 13.10 meV Fig. 1 : The bound states of some shallou acceptors in germanium, as deter- (24) mined by Jones and Fisher . The numbers in the figure give the ground state energies (E ) of the impurities relative to the g.s. valence band. most strongly bound states, and especially the ground state Ε , differ among different impurities. The resulting absorption spectra therefore have the same structure but are shifted versus each other, the shifts depending on the differences in ground state energies. 42 The disadvantage of using transmission spectroscopy for the study of impurities is that this technique asks for samples with a high impurity con centration. However, the size of the wave functions then produces a severe overlapping between the impurity atoms, resulting in a relatively low reso lution in the spectra. In contrast with this PTIS on very pure samples, where the impurity atoms are far apart, produces spectra with very narrow lines. 3. Photothermal ionization spectroscopy (PTIS). In PTIS one measures the change in conductivity of a sample under illumination with radiation in the same region as used in transmission spec troscopy. For shallow donors and acceptors in germanium this is the far infrared region (wave number 10 - 200 cm ). As an example we show in Fig. 2 the photoconductivity spectra at several temperatures of a polycrystalline sample, containing residual im purities in a concentration of ^ 10 - 10 cm . It is seen that above a temperature of 5 К a photoconductivity spectrum with a distinct line struc ture arises for photon energies below the impurity ionization energy (i.e. the onset of the continuum at ^ 85 cm ). The positions of the peaks on the energy scale coincide with the peaks in the optical absorption spectrum of (24) the boron and aluminum acceptors known from the literature . This proves that the lines are due to optical transitions of the charge carriers from the ground state to bound excited states of the impurity. However, in order to contribute to the conductivity the charge carriers must be released into the free band. We see in Fig. 2 that the heights of the peaks increase with increase in temperature. This suggests that the ionization of the impurity is a two-step process: 1) charge carriers in the ground state are optically excited to some intermediate state; 2) Subsequently a fraction of these excited charge carriers may be promoted thermally into the free band, producing an increase in conductivity of the sample. This is why the name of photothermal ionization was introduced for this two-step process. In order to obtain enough phonons of sufficient energy one would like to keep the Ge sample at high temperatures, while to keep most of the impurities in their ground state low temperatures would be prefered. This leads to an experimentally-determined optimum temperature of around 8 К for observation of shallow impurities in germanium. 43 в DC7—ішіши» ~^| ' Ес9' Α DC» ι іиіішші · >. о R78B 80 100 120 Wavenumber 'cm ! Fig. 2 : Photooonduativity spectra at several temperatures of a polyarystal- Ыпе Ge sample, containing aluminum and boron in a concentration of ъ IO10 - IO11 cm'2. The most important and essential difference between PTIS and other analysis methods is that the recorded signal does not decrease with decrease of impurity concentration down to a very low concentration . This is a consequence of the fact that both the average number of current carriers, n, and the change Δη under illumination depend equally on the concentration of the impurities. The voltage sensitivity of the photo-response is proportional to the relative change of the carrier concentration Δη/η. This enables one to detect the impurities even if their concentration is extremely low and undetectable by all other analysis methods. As the positions of the spectral lines reflect the energy spectrum of the impurity atoms PTIS enables the determination of the chemical nature of 44 К Hb ч| о 'w|lJ д^ ί \ уft •Г И J^ 1 ν V 'г, [ 20kG^I IJ, Vi ' Ι' , ι Μ; 1' • Ν! 1 17 5 kG ι Ι, Ι ' -'' i Α •Ι ' ' i ι и ι Ли Λ ^ Ι 1 U Ζ 15 kG ,/,"ί.!Μ '\ !-^, i'ιJ' Ι Λ 12 5 kG, ,-Ίι^,ν V' Il * ν ' - чЛлчЛЛ-АлЛ> ' V ΙΑ , 1Ι1" · ι', ι 'Ιι ι ,. »Ί 7 5kG ;¡; .1||ч ." ;и::.; f \і*\ 100 120 Wavenumber (cm-') Fig. 3 : Photoconduetivity spectra at 7.5 К of shallow aoaeptors in germanium for several values of the applied magnetio field (same sample as in Fig. 2). 45 the impurities. Accurate spectra for a number of donors and acceptors can be found in the literature (for instance in Refs. 8,9 and 10). The identifica tion of the impurities in the spectra of Fig. 2 was done by comparison with (9) the В and Al spectra given by Haller and Hansen ; these spectra are shown in the top of Fig. 2. 4. Applications of PTIS. Originally the PTIS technique was only used as an analytical tool in the production of ultra-pure germanium. However, the inherent advantages over other analysis methods, such as the much better spectral resolution, have predicted PTIS to become one of the most powerful tools for the study of the basic physical aspects of germanium and a variety of other semicon ductors . The research subjects in which we have been engaged are: 1. An accurate determination of the ground state energies of some impurities from the temperature dependence of the peak intensities in the photocon ductivity spectra; 2. The influence of a magnetic field on the energy level scheme of acceptors in germanium. Figure 2 showed the effect of the temperature on the intensity of the peaks in a spectrum, whereas Fig. 3 shows the effect of a magnetic field on the same spectrum. As can be seen from Fig. 3 the spectrum not only exhibits a splitting or shift of the peaks below the continuum onset, but also develops a set of peaks in the continuum. The results of our investigations will be presented in the form of a set of papers. Preliminary results are presented in Section IV.2, while in Sections IV.3 and IV.5 the temperature effect is explained in more detail. Section IV.4 is a supplement to Section IV.3. In Section IV.6 we present measurements in a magnetic field on a monocrystalline sample, where the orientation was known. The experimental results will be discussed in terms of existing theories about Zeeman effect and Landau levels in germanium. 46 References. 1. R.D. Baertsch and R.N. Hall, IEEE Trans. Nucl. Sci. 17, 235 (1970). 2. R.N. Hall and T.J. Soltys, IEEE Trans. Nucl. Sci. 18, 160 (1971). 3. R.N. Hall, R.D. Baertsch, T.J. Soltys, and L.J. Petrucco, Annual Report No. 6 (Aug. 73), General Electric Co. 4. T.M. Lifshits and F.Ya. Nad', Sov. Phys. Doklady 10, 532 (1965). 5. V.l. Sidorov and T.M. Lifshits, Sov. Phys. Solid State 8, 2000 (1967). 6. T.M. Lifshits, N.I. Likhtman, and V.l. Sidorov, Sov. Phys. Semicond. 2, 652 (1968). 7. Sh.M. Kogan and T.M. Lifshits, Phys. Status Solidi A 39, 11 (1977). 8. S. Dana Seccorabe and D.M. Korn, Solid State Commun. 1Λ, 1539 (1972). 9. E.E. Haller and W.L. Hansen, Solid State Commun. LS, 687 (1974). 10. M.S. Skolnick, L. Eaves, R.A. Stradling, T.C. Portal and S. Askenazy, Solid State Commun. 21, 1403 (1974). 11. E.E. Haller, W.L. Hansen and F.S. Goulding, IEEE Trans. Nucl. Sci. NS-22, 127 (1975). 12. E.M. Bykova, L.A. Goncharov, T.M. Lifshits, V.l. Sidorov, and R.N. Hall, Sov. Phys. Semicond. 9, 1223 (1976). 13. E.E. Haller, Phys. Rev. Letters 40, 584 (1978). 14. С Kittel and A.H. Mitchell, Phys. Rev. 96, 1488 (1954). 15. W. Kohn and J.M. Luttinger, Phys. Rev. 98, 915 (1955). 16. J.C. Phillips, Phys. Rev. Bl_, 1540 (1970). 17. J.H. Reuszer and P. Fisher, Phys. Rev. 135, A1125 (1965). 18. W. Kohn, Solid-State Physics, Vol. 5, p. 257 (ed. by F. Seitz and D. Turnbull), Academic Press, New York (1957). 19. D. Schechter, J. Phys. Chem. Solids 23, 237 (1962). 20. K.S. Mendelson and H.M. James, J. Phys. Chem. Solids 25, 729 (1964). 21. A. Baldereschi and N.O. Lipari, Phys. Rev. B8, 2697 (1973). 22. A. Baldereschi and N.O. Lipari, Phys. Rev. B9, 1525 (1974). 23. F. Bassani, G. ladonisi and B. Preziosi, Rep. Prog. Phys. _У7, 1099 (1974). 24. R.L. Jones and P. Fisher, J. Phys. Chem. Solids 26, 1125 (1965). 47 IV.2 MAGNETO-OPTICAL DETERMINATION OF THE GROUND STATE Li VI·LS OF SOME SHALLOW IMPURITIES IN HIGH PURITY GERMAMLM H W H M JONGBLOETS, J H M SIOFl INGA, M J H VAN Db STFFG and Ρ WYDER Ph\su s I aborali>r\ and lit\earih íns/iíw/t for Material* Vmter\it\ of Ntfnufun Tturnootutii Nijmtíí«" The Netherlands Wc determine Ihe impurity ground state levels of aluminium boron find phosphor in permanium from very iccunte medsurements of the photo thermal conductivit> as a function of the frequency of the incident radiation the temper Uure and the magnetic field strength From our magnetic data mfornation is obtained on the field dependence of even the highest levels observed up to now 1. Introduction and experimental method Hallet and Hansen [S] on the other hand determine the energy difference of the ground During the last decade there has been con state energy and the band edge from the shape siderable interest in the study of the energy of the onset of the continuum observed in their levels of the impurity states m germanium and photo thermal conductivity data They assume silicon The experimental techniques used fall that this shape is due to the Fermi distribution mainly into two groups far infrared trans of the electron energy at the top of the (valence) mission measurements using spectrometers or band Their obtained values for the ground state interferometers on samples containing im energies are about 1 cm ' higher than the purities at concentrations of ~10',-10"'at/cm', theoretical values from the literature However, and photo-thermal conductivity measurements since the shape of the onset of the continuum, which enable investigation of high-purity sam according to our observations, does not change ples with 10IO-10" impunties/cm' Here also far with the temperature between 2 and 8 K, this infrared grating spectrometers or inter shape cannot be due to the Fermi distribution ferometers and sometimes lasers are used The but may be caused for instance by an averaging experimental results of these two methods are over к space by the effect of two phonon in good agreement both with each other and processes in the thermal process Although the with theoretical calculations For a review see frequency of the onset of the continuum gives Bassani et al [Ι] information over the ground state energy its However, up to now the precise deter value cannot be obtained from this with high mination of the ground state levels of the accuracy impurities has met difficulties Seccombc and It is our aim to derive the right temperature Korn [21 assume that the two step photo dependence of the photo thermal conductivity thermal conductivity process has a relative response and to obtain accurate values for the ionization probability which varies as ground state energies for some shallow ac P, п(Г)*ехр{-(Е„-Еі)ДГЬ where Fi is the ceptors and donors in high purity germanium energy of the intermediate level and EB is the from detailed measurements of the photo- energy of the banded higher energy levels bom thermal conductivity as a function of the tem the measured temperature dependence they find perature For the determination of the ground activation energies Ей-F, which lie about state levels the degeneracy of the intermediate 3 cm ' below the ionization energy of the levels has to be known This degeneracy is isolated impurity which is attributed to impurity obtained from measured level splittings m a banding The same temperature dependence has magnetic field up to 20 kG The field depen been assumed by Simmonds et al Π] and pre dencies of the energy levels are compared with viously by Nagasaka (4] whereby the latter current theories of both the low and high field remarks that the measured temperature depen region dence deviates from an exponential behaviour The measurements were performed both on This is tentatively attributed to the effect of polycrystallme and on monocrystallme samples clustering of the impurities obtained from the same ingot of high purity Physica 89B (1977) IH-21 © North Holland 48 energy-difference between the intermediate I ¡МЩЩІ level and the band, g is the degeneracy of the excited level and g' is the degeneracy of the 1 ,IIJ¡J.n,J ** ι band at к =0. The factor A is proportional to the concentration of the impurity and to the Hb optical transition probability of the spectral line. We measured the temperature dependence of the line intensities at temperatures ranging from 2 to 10 K. As an example some of these spectra are shown in fig. 1. All spectra were corrected ІцДі-*^- for the spectral background of the far infrared interferometer and were normalized to the same continuum height. This continuum is caused by LJVAAAAÍWA и direct optical excitations to the band edge. The relative line intensities were plotted on a lo Ur^ garithmic scale versus 10/T as is shown in fig. 2 ^j^M^i for boron in the monocrystalline sample J78A. In this figure the solid curves represent com *• AiU/^i puter fits of the experimental data to eq. (1) •О 100 120 using ΔΕ and A as parameters. The degeneracy Wov«numb«r cm ι factors g were deduced from the measured level Fig 1 Photoconductivity spectra at several temperatures of splittings in a magnetic field (see the next sec a Ge sample containing both donors (P) and acceptors (B tion). The degeneracy of the conduction band of and ΛΙ) The ΛΙ and В spectra at the top are after Mailer and germanium is g' = 1 and that of its valence band Hansen 15), the Ρ spectrum after Seccombe [2) is g' = 2. As is shown in fig. 2 the measured temperature dependencies of the line intensities germanium containing aluminium, boron and are fully m agreement with eq. (1) within the phosphor in concentrations ranging from 10'° to experimental error. 10" at./cm'. The concentrations of the im purities of the two monocrystalline samples J78A and J78B were (2x10" at./cm' B, 4.7 χ 100 10 1 IO at./cm' Al, 1.9 χ 10'° at./cm Ρ) and (1.5 χ B0R0N 10" at./cm' Ρ, 4.7χ IO10 at./cm5 Al), respec X tively. These concentrations were determined \ with the method outlined in ref. 6 where also the -A J78A experimental details will be given. •>^ As is shown in fig. 1 with this method both κ^ν*^ donor and acceptor impurities present in the ^>4 ^\ same sample can be investigated. Using a \\Γ ^^^ . superconducting coil magnetic fields up to 20 kO ю-• could be applied. >κ" о χ\ 2. Determination of the ground state energy \ * с \ \\ Generalizing the calculations of Spenke [7] it о в \\ ^Χ can be shown that the thermal ionization me Ατ chanism associated with the two-step photo- Α; thermal conductivity process leads to a line intensity ƒ given by: , ι , I i .... ι ... . 15 20 25 30 35 / = Α Γΐ + (—) exp (ΔΕ/ΛΤ)1 (1) ίο/τ ÍK Ί Fig 2 Logarithmic plot of the relative line intensities ver sus 10/T for several boron lines in sample J78A The solid for both donors and acceptors. Here ΔΕ is the curves represent computer fits to eq (1) 49 For each transition observed the sum of ΔΕ and the energy of the transition E as obtained from the measured spectra yields the energy of the ground state ERS of the impurity involved In this way we obtain for the ground state Г-1- ^ energies of aluminium, boron and phosphor the values presented in table I As is shown in this table these values are in excellent agreement with the theoretically deduced values for Al and I ' В of Jones and Fisher [8] and the value for Ρ of Reuszer and Fisher (9] 1" i г* 'VV If I, i' "·' .' -»'I >. J Table 1 The ground stale energies of ΑΙ В and Ρ in germanium in ' . ' fv (this work) 81 1 * 0 4 84 « + 0 1 I02 9JLO^ £, (refs 8 and 9) »ι 1 » 0 2 84 S i 0 2 1029*01 i' I 'Л, U 3. The effect of a magnetic field •·* ι t ι' < -ν,ν, _'V*f ~'·ι ', ' ^ Ь'* In a low magnetic field, in the low field limit, the Zeeman term connected with the magnetic field produces a linear splitting of the /*0 levels while the diamagnetic term gives a quadratic correction On the other hand, in the high field limit the impurity potential produces a wn Ν ч^ ^ τι set of sublevéis associated with each I andau big 1 Photoconductivity spectra of sample J78A at 7 ^ К level Again we refer to the review of Bassani et for several values of the magnetic field with B//(1001 Im purity concentrations 2 χ 10' at lem' В 4 7 χ ю' at /cm' al [I] Al 1 9 ж 10 'at/cm' Ρ The labelling at the top shows the Experimentally Boyle et al [10] investigated boron spectrum with the Zeeman splitting and the first four As donors in germanium by measuring the far Landau levels with their associated sublevéis at ISkG infrared transmission of samples containing ~ I 5 χ 10" árceme atoms/cm' in magnetic fields up to 40kG Horn et al [II] did the same for shows that the general behaviour sketched arsenic and antimony up to 46 kG. while Soe- above manifests itself in these spectra on a very pangkat et al [12] studied boron and thallium clear and illustrative way After a shift and acceptors in germanium in magnetic fields up to splitting of the hydrogen like levels lying below 20kG using the same method Nisida et al [Π] the band edge to higher energies in low fields, investigated germanium containing antimony these levels are forced up to energies higher and arsenic impurities by measuring the pho than the band edge energy in higher fields At toconductivity m a varying magnetic field up to these fields the continuum above the band edge 40 kG under the influence of intraband radiation changes more and more in a number of peaks of a laser source the Landau levels with their associated su In our experiment we measured the photo- blevéis By plotting the resonance frequencies thermal conductivity response of our high- as function of the magnetic field each line could punty germanium samples as a function of the easily be followed and identified In this way the frequency of the far infrared radiation at several identification indicated in fig Λ has been per values of the magnetic field up to 20 kG hig Я formed 1 he notation is that of Jones and Fisher 50 [8] From the energy differences of the first four References I andau levels which can be identified we obtain |1| h Bassani O Iddonisi and В Pre/iosi Rep Progr an effective mass of m*lm =0 08 ±0 04 which Phys V (1974) 1099 has to be compared with the effective mass |2] S Dana Seccombe and D M Korn Solid Stale Com m*/m =0 04 of the light hole, cf Sze |I4] The mun II 119-2) i^9 inaccuracy is caused by the non linearity of the |4) Ρ Ь Simmonds J M Chamberlain R A Houli R A shift of the I andau levels with the magnetic Stradlmg ind С С Bradley J Ph>s С Solid Mate field m this region since the high field limit is not Ph>s 7 (1974)4164 [4| К Ndgasdka and S Narita Solid State Commun 7 entirely reached For the lower levels, our (1969) 467 results are in accordance with those of the au І^] I F Hiller and Wl Hansen Solid State Commun И thors mentioned above However, in contrast to (1974) Ш these authors, we obtained also information (6| H W H M Jongbloets J H M Stoelmga M J H Van de about the higher levels More quantitative Steeg Ρ Wydcr and H J A van Dijk (o be published 171 [ Spenke FlcUronic Semiconductors (McGraw Hill results about these magnetic data will be pu Book С ompany Ine №8) ρ 187 blished separateli [15] |81 R I Jones and Ρ Hsher J Phys Chcm Solids 26 (I96S) 1124 We thank Dr H J A van Dijk, Philips |9| J Η Reiiszer and Ρ Fisher Phys Rev 13S (|%S) A I12S Research Laboratories, for providing the Ge [101 W S Boyle and Rb Howard J Phys Chem Solids 19 samples and performing the impurity concen (1961) 181 tration analysis This work was performed as [III К Horn and Y Nisida J Phys Soc Jap 11(1971)781 part of the research program of the Stichting [121 HP SoepmkatandP Fisher Phys Rev 88(1971)870 voor Fundamenteel Onderzoek der Materie (ΠΙ Y Nisida and К Muro Suppl Progr Theor Phys 41 (FOM) with financial support from the Neder (I97Í) 77 1I4| SM Sie Physics of Semiconductor Devices (John landse Organisatie voor Zuiver Wetenschap Wiley and Sons Ine 1969) ρ 20 pehjk Onderzoek (ZWO) I И] H W H M Jongbloets J H M Stoelmga M J H Van de Stceg Ρ Wydcr to be published 51 PHYSICAL REVIEW В VOLUME 20, NUMBER 8 15 OCTOBER 1979 IV. 3 Temperature dependence of the photothermal conductivity of high-purity germanium containing very low concentrations of ΑΙ, В, and Ρ Η W H M Jongbloets, i H M Stoelmga, M J H van de Steeg, and Ρ Wyder Research institute for Materials University of Nijmegen, Toernooiveld Nijmegen The Nethertands (Received 7 February 1979) The temperature dependence of the photothermal conductivity in the far-infrared region (10 to 200 cm"') is studied in pure germanium containing —IO'0 atoms/cmJ of Al, В, and Ρ A theoretical expression for the temperature dependence of the intensities is given which is in ex cellent agreement with the experimental results From these very detailed spectra, reliable values for the ground-state energies of the impurities are obtained and a quantitative chemical analysis of the impurity concentration as a function of the position in a Czochralski-grown single crystal is achieved I INTRODUCTION analyzed It will be shown that the measurements are in very good agreement with our calculations of The photothermal conductivity in the far-infrared the temperature dependence of the photothermal region of very pure germanium containing residual response Finally, a qualitative and a quantitative impurities of very low concentrations ( —IO" chemical analysis of the samples will be given, based atoms/cm1) has been the subject of several studies in on the photoconductivity data This analysis will be the past '"* A recent review of this subject was given compared with results based on Hall-effect measure by Kogan and Lifshits ' However, surprisingly ments on the same ingot from which the samples enough, the temperature dependence of this effect were obtained Preliminary results of these investiga has drawn little attention so far tions have been published before ' It is generally believed that, in order to get a pho tothermal response, the donors or acceptors are ion ized through a two-step process First, the electrons II SAMPLE PREPARATION AND (or holes) are excited from their ground state to a EXPERIMENTAL DETAILS higher bound state by irradiation with light in the far-infrared region (10-200 cm"') Then, a subse All our germanium samples were cut from the quent excitation to the free conduction (or valence) same boule These ultrapure samples were kindly band occurs by interaction with thermal phonons supplied by Dr H J A van Dijk of the Philips The photoconductivity is measured as a function of Research Laboratories, who also performed Hall- the radiation frequency, whereas the sample tempera effect measurements to determine the residual im ture is held constant, typically between 2 and 10 К purity concentration The polycrystallme samples, At higher temperatures the photoconductivity signal R78/4 and R78Ä, were obtained from both of the decreases due to the increase of the carrier density in ends of the high-purity zone-refined ingot Then, the free band, while lower temperatures provide too from the remaining ingot, a single crystal was grown few thermal phonons necessary for the second step of with the Czochralski method Again from both ends the process Although the influence of the tempera of this crystal two monocrystalline samples ¡HA and ture on the effect is thus qualitativley well under J78B were cut Figure 1 shows the variation of the stood, the precise temperature dependence has never impurity concentration along this single crystal as cal been studied in a quantitative way Most authors as culated from Hall-effect measurements, assuming sume a temperature dependence typically of the form aluminum, boron, and phosphorus as the main impur ехр(-Д£/<:Г), where Af is the energy difference ities and using the known segregation properties of between the excited level and the conduction (or these elements 2 J valence) band edge ' ' However, the agreement The samples used for the photoconductivity meas with experimental results is rather poor, and esti urements were cubes with dimensions of mates for the binding energy of the impurities yield ~1 χ I χ 1 cm3 The cubes were polished and etched, 5 values which are about 3 cm"' too low and then electrical contacts were produced by wetting In this paper, we will concentrate upon this aspect with a mixture of In-Hg (50 50) Although these In Sec II the experimental details will be described, contacts were not entirely ohmic, we found no evi while in Sec III the results will be presented and dence that the contacts had any effect on the data 20 3328 52 20 TEMPERATURE DEPENDENCE OF THE PHOTOTHERMAL 3329 CRYSTAL τ τ 1 пикник Al O i > -Т--Г- 08 Froc tion W^-4rt FIG 1 Disinbution of phosphorus, boron and alumi num impurities along a germanium single crystal, calculated from Hall-effect measurements (Segregation coefficients FIG 2 Photoconductivity spectra of the polycrystallme germanium samples R78/4 and Я1ІВ containing boron and used Ρ The samples were positioned in a semisphencal cavity wherein the chopped far-infrared radiation en at a temperature of 7 S К Indicated are also the ex tered through a conical light pipe Thermal contact pected transitions for boron and aluminum known 4 5 was made by clamping the sample onto the base of from the literature From these spectra one can the cavity The clamp and the sample could be heat conclude that R78/I contains В and Al in about equal ed above the temperature of the surrounding helium amounts, while in sample R780the Al concentration bath with an electronically controlled heater system exceeds the В concentration as is expected in a The temperature of the sample was stabilized within zone-refined ingot Figure 3 shows similar data for OIK An Allen-Bradley carbon resistor was used as the monocrystallme samples, ¡HA contains both В a thermometer and Al, with В having the highest concentration, while in sample J78ß, apart from phosphorus, some Using standard lock-in techniques, the photocon lithium is present as well3 s In addition, indicated by ductivity was measured as a function of the wave an asterisk in the figure, in 1780 some other transi number of the incident radiation produced by a tions, with an origin not entirely known, are found, Grubb-Parson Michelson interferometer operating these transitions may be due to a LiO complex l0 with phase modulation at 90 Hz The data were The wave numbers where the transitions are observed punched on tape, and subsequently handled and agree within 0 2 cm"1 with the expected ones from analyzed on a PDP-12 laboratory computer linked to the literature3"5, however, due to the limited resolu a plotter All spectra were corrected for the varying tion, the A and / transitions of aluminum and boron spectral background of the interferometer by dividing are not fully resolved in these spectra The continu through a spectrum obtained by replacing the Ge um in the spettra is caused by direct optical transi sample with a Si bolometer tions from the ground state into the valence (or con duction) band In this context, it is interesting to III RESULTS AND DISCUSSION note that with the method of pholothermal ionization both donor and acceptor impurities can be seen Figure 2 shows the photothermal response as a simultaneously in one sample function of the wave number of the incident radia The strength of a spectral line is proportional to the tion for the polycrystallme samples R78/1 and R78B thermal ionization probability of the excited states 53 3330 JONGBLOETS, STOELINGA, van de STEEG, AND WYDER 20 _ f«· t ¿ ¿ ¿ ^«и«, —ι 1 1 щи urn ι Al 9 ¿ - ¿ ;^«і!^ о с в Τι ι ιι ιιιιιι il В >. J78A ° t в » , 1 Eg5 Hb 0 * С 0 ιΚ α • Λ) lil ^ ε « о e .с J78B α. -II- i г-і tl ι η-m » il № I ifV Wove numbtr {cm I FIG 3 Photoconductivity spectra at Γ-7 5 К of the monocryslalline germanium samples ПІА, containing boron and aluminum, and J780, containing phosporus, lithium, 60 80 100 120 and probably a LiO complex The spectra at the top are WAVE NUMBER (cm'] from Refs 3, 4, 5, and 10 FIG 4 Photoconduc^iviiy spectra at several temperatures of the monocryslalline germanium sample Л8Л Impurity concentration В 2 1 x 10" atoms/cm3. Al 4 3 χ IO10 atoms/cm3 and this can be studied by comparing the line intensi ties at various temperatures with the height of the continuum 2 Figure 4 shows the spectrum of sample equilibrium is found in the usual way by optimizing ПІА, containing aluminum and boron, at different the number of possibilities for ionization at constant temperatures All these spectra are corrected for the total energy Hereby the strong Coulomb interaction spectral background of the interferometer and are of electrons in an excited state has to be taken into normalized to the same continuum height Similar account which can be done m a similar way as in con measurements were also performed on a sample con siderations regarding donor and acceptor ionization taining phosphorus 2 probabilities ' In this manner the line intensity /, From the voltage drop across the sample, the which is proportional to the average number of ioni current through the sample and the measured change zations is found to be given by in voltage in a typical experiment, it is possible to get a rough estimate of the number of carriers involved Typical data yield for the ntftnber η of the free car l=A 1 -f-iyexp (1) riers in the band η ~ 10' (cm"') and the change Δη gg in carriers due to photothermal ionization Δη ~ 10s (cm-3) This means that η and Δη are small com for both donors and acceptors Here, ΔΕ is the ener pared with the total number of impurity states gy difference between the intermediate level and the Therefore the average number of optical excitations band edge, g is the degeneracy of the excited level, to one of the excited levels may be considered as in and g' is the degeneracy of the band The factor A is dependent of temperature at very low temperature proportional to the concentration of the impurity and Since the excited levels are very localized in к to the optical transition probability for the spectral space," thermal ionization from this level will at low line under consideration For donor states, where temperatures only take place to the nearest band ex- spin-orbit interaction is small, thermal processes with tremum The average number of ionizations in spin flip may be neglected so that g' is the band de- 54 20 TEMPERATURE DEPENDENCE OF THE PHOTOTHERMAL 3331 generacy apart from spin, thus g' — 1 for german 1 1 ' ' ' ' ' ' ium Although for acceptor states the situation is less obvious, the degeneracy of the valence band in •\ germanium will be taken only as the effective-mass degeneracy at к-0, yielding g' -2 ;\ « Is —2p Figure 5 shows the relative line intensities for the о Is -Зр. phosphorus spectrum, plotted on a logarithmic scale, 0 1s -¡.p. as a function of the inverse temperature The solid » 1s -4f. curves in this figure represent computer fits of Eq (1) to the experimental data, using Δ£ and A as adjust able parameters The degeneracy factors g were de έ 10!- C^^T^\ l duced from measured level splittings due to magnetic >— fields Here our own observations' 13 confirmed the splittings found in the literature for the lower levels of the donors" and acceptors,'4 1S and extended the results to higher levels As is shown in Fig 5, the measured temperature dependence of the line mten- sitie; is within experimental accuracy in agreement with Eq (1) Similar results were obtained for the Al and В spectra of sample Л$А Table 1 collects the numerical results of the computer fits for the param eters A and Δ£ In the fitting procedure also the pro duct gg' was varied by integer values It was not pos sible however to obtain a reasonable fit for other values of gg' than those quoted which supports the FIG 5 Logarithmic plot of the relative line intensities vs assumption of the neglect of spin in the band degen lO/Tfor several phosporus lines The solid curves represent eracy made above computer fits to Eq (1) (See also Table I ) The energy of the ground state Ets of the impurity involved is now simply the sum of Δ£ and the energy from this table, these experimentally found values of the optical transition £,„„, (as obtained from the are in excellent agreement with the theoretically de measured spectra) In this way it is possible to obtain duced values of Jones and Fisher" for В and Al and the ground-state energies of boron, aluminum and of Reuszer and Fisher" for Ρ phosphorus as presented in Table II As can be seen As a factor A is proportional to the impurity con- TABLE I Values of A and A£as obtained from a computer fit from the temperature depen dence of various lines in the B, Al, and Ρ spectra [see bq (1)1 Transition „(cm"1) A (arb units) dEtcm-') Boron D 64 0 ±0 2 450 ±15 20 5 ±0 2 С 70 1 265 ±8 144±02 078,4) В 75 2 44 ±1 93±02 Аг 77 9 123 ±3 66±02 Αι 78 9 78 ±2 56±02 Aluminum D 66 7 + 0 2 70 ±7 20 5 ±0 6 С 72 8 41 ±3 14 Ι ±0 5 078,4) h 8S0 36 ±2 23±05 Phosphorus υ— 2/1+ 90 0+0 2 285 ± 10 12 9+0 2 ls-3/ч. 95 5 44 ±3 75+02 1.-4/,+ 97 9 26 ±2 53+03 Is-4/+ 99 0 33 ±3 40±03 33Î2 JONGBLOETS, STOELINGA, v«n de STEEG, AND WYDER 20 TABLE 11 Energies of Ihe ground state of B, Al, and Ρ in germanium, measured in cm" В Al £^5 (experimental, this work) 84 5 ±0 2 87 1+0 3 103 0 ±0 2 E„ (theoretical, Refs II and 17) 84 5 ±0 2 87 1 ±02 1029±03 centration, it is in principle possible to get some in dence of the photoconductive response which is in formation on the relative impurity content from a excellent agreement with our experimental results determination of A Assuming the same transition The values found from these data for the ground- probability for transitions between similar states of state energies of various impurities confirm theoreti different donors or acceptors, the ratio of the A fac cal calculations very well In addition, we have tors for corresponding lines will therefore indicate the shown that the concentration ratios of the impurities ratio of the concentrations of the impurities For as obtained from photoconductive measurements are sample J78/4 one finds for the ratio of the A factors in reasonable agreement with values obtained from for the С and D transitions of boron and of alumi Hall-effect measurements num a value of 6 4 ± 0 5 This value can be com pared with the concentrations obtained from Hall- effect measurements as presented in Fig 1 From ACKNOWLEDGMENTS this figure one concludes that for sample ПІА the ra tio of the concentrations of В and Al is Part of this work has been supported by the Stich (2 1 x 10" cm-J)/(4 3 x 10'° cm"') -5 ± 1 , ting voor Fundamenteel Onderzoek der Materie (FOM) with financial support from the Nederlandse which is in good agreement with the value obtained Organisatie voor Zuiver Wetenschappelijk Onderzoek from the photoconductivity measurements (ZWO) We thank Dr Η J A van Dijk, Philips In conclusion we can remark that we have given a Research Laboratories, for providing the Ge samples theoretical expression for the temperature depen and performing the impurity-concentration analysis 'T M Lifshits and F Ya Nad', Sov Phys Dokl 10, 532 'H W H M Jongbloets, J H M Stoelmga, M J H van (1965) de Steeg, and Ρ Wyder, Physica (Utrecht) В 89, 18 2T M Lifshits, N I Likhtman, and V I Sidorov, Sov (1977) Phys Semicond 2, 652 (1968) ,0R L Aggarwal, Ρ Fischer, V Mourzme, and A К Ram 3S Dana Seccombe and D M Korn, Solid State Commun das, Phys Rev Ш, A882 (1965) И, 1539 (1972) "F Bassani, G ladomsi, and В Preziosi, Rep Prog Phys 4E E Haller and λν L Hansen, Solid State Commun 15, 37, 1099 (1974) 687 (1974) 12E Spenke, Electronic Semicondtutors (McGraw Hill, New 'M S Skolnick, L Eaves, R A Stradlmg, J С Portal, and York, 1958), ρ 387 S Askenazy, Solid Slate Commun 15, 1403 (1974) "H W H M Jongbloets, J H M Stoelmga, M J H van 'Ε M Bykova, L A Goncharov, Τ M Lifshits, V I de Steeg, and Ρ Wyder (unpublished) Sidorov, and R N Hall, Sov Phys Semicond 9, 1223 MH Ρ Soepangkat and Ρ Fisher, Phys Rev |, 870 (1973) (1976) I5E Ρ Kartheuser, S Rodriguez, and Ρ bisher, Phys Status 'S M Kogan and Τ M Lifshits, Phys Status Solidi A 39, Solidi В 64, Il (1974) 11 (1977) "R L Jones and Ρ Fisher, J Phys Chem Solids 26, 1125 'P E Simmonds, J M Chamberlain, R A Houli, R A (1965) Stradlmg, and С С Bradley, J Phys С 7, 4164 (1974) "J Η ReuszerandP Fisher, Phys Rev J35, A1125 (1965) 56 IV.4 DETERMINATION OF THE IMPURITY CONCENTRATION PROFILE IN A Ge SINGLE CRYSTAL GROWN WITH THE CZOCHRALSKI METHOD Figure 1 of the preceding paper (Section IV.3) showed the distribution of the phosphorus, boron and aluminum impurities along the germanium crystal, from which our samples J78A and J78B were cut. In this section it will be shown how this figure was obtained from Hall effect measurements, performed by Dr. H.J.A. van Dijk of Philips Research Laboratories. The variation of the impurity concentration along a crystal which is grown by the Czochralski method, is caused by the segregation of dissolved ...... (1 2) impurities during non-equilibrium solidification ' . For low impurity concentrations the ratio of the concentration С in the just solidified material and the concentration С in the remaining liquid will be a constant L K, the so-called segregation coefficient. If the location in the crystal is denoted by the weight fraction g of the original melt that was solidified at that point, the distribution of (3) every impurity along the crystal can be described by : 1 Cs(g) = CgCOXl-g)^ , (1) where С (0) is the concentration at the head of the crystal (i.e. g=0). The number of uncompensated holes N.-N is determined by the net impurity concentration [NA-ND] (g) = I c£(g) - I c£(g) , (2) where A and D denote acceptors and donors respectively. The value of KA"N_ at various positions in the crystal can be deduced from Hall effect measure- ment s The photothermal conductivity spectra of samples J78A and J78B (Fig. 3, Section IV.3) reveal that the Al and В acceptors and Ρ donor are the most important residual impurities in our crystal. From the measured values of N.-N for three different locations g, indicated in Fig. 1 by small circles, ΑΙ Β Ρ equations (1) and (2) can be solved for С (0), С (0) and С (0). The con centration profile for ΑΙ, В and Ρ can then be calculated with Eq. (1). These 57 solutions are represented in Fig. 1 (Section IV.3) by the solid curves, whereas the dashed curve shows the calculated profile of N.-N,. . 'AD' As a check the values of K.-N were also measured for three intermediate positions, indicated in Fig. 1 (Section IV.3) by crosses; they fit very well to the calculated IN.-ÍLI curve. 1 A D' The segregation coefficient used for these calculations were: Κ^=0.1, ^=5.7 and K. =0.9. Aluminum has normally a segregation coefficient В Al1 К =C (0)/C (0)=0.1) but when a crystal is grown with the Czochralski method (5) Al shows only a small segregation , so that in Eq. (1) we have used К =0.9. (6) However, in the zone-refining process used for the purification of the original Ge ingot, one has Кд1=0.1. We find boron and aluminum in about equal amounts in the region where the zone is started (sample R78A was cut from this region). Near the opposite end the boron concentration is reduced but aluminum is increased (sample R78B). References. 1. The structure and properties of materials. IV: Electronic properties. Ed. John Wiley & Sons, New York (1966), pp. 146-154. 2. R.N. Hall and T.J. Soltys, IEEE Trans. Nucl. Sci. 18, 160 (1971). 3. E.M. Bykova, L.A. Goncharov, T.M. Lifshits, V.l. Sidorov, and R.N. Hall, Sov. Phys. Semicond. 9, 1223 (1976). 4. C. Kittel; Introduction to solid state physics, 4 edition, John Wiley & Sons, New York (1971), p. 288. 5. H.J.A. van Dijk, private communication. 6. W.G. Pfann; Zone melting, John Wiley & Sons, New York (1958), p. 211. 58 IV.5 TEMPERATURE DEPENDENCE OF THE PHOTOTHERMAL CONDUCTIVITY OF SEMICONDUCTORS AT LOW TEMPERATURES ABSTRACT A careful analysis has been made of the temperature dependence of the signal strength in a photoconductivity experiment in a semi conductor. The temperature dependence of the line intensity in a photothermal conductivity spectrum has been calculated. The results are in excellent agreement with measurements on high purity germa nium containing boron, aluminum and phosphorus as residual impurities (ъ 10 atoms/cm ;. 59 1. Introduction. Photothermal conductivity spectroscopy is of considerable in terest for the study of impurity states in semiconductors (Lifshits and Nad' 1965). It offers the most sensitive method of analysis of impurities at very low concentrations (10 -10 atoms/cm ) in semiconductors. The method is sensitive enough to investigate subtle features such as the magnetic field dependence of central cell cor rections (Stoelinga et al 1978). A lot of work has been done related to this subject. A recent review has been given by Kogan and Lifshits (1977, further referred to as Ref. I). However, the well known strong temperature dependence of the photothermal conductivity signal has met relatively little attention so far. Frequently a simple exponential behaviour, ехр(-ДЕ/кТ), has been assumed for the relative ionization probability of the two-step photothermal conductivity process (Lifshits et al 1968, Seccombe and Korn 1972, Stillman et al 1972, Simmonds et al 1974, Bykova et al 1976, Ref. I). Here ΔΕ is the energy difference between the band edge and the intermediate level to which optical excitation from the ground state takes place followed by thermal ionization from this level to the band edge. The experimental results do not agree very well with this assumption; this has been tentatively attributed to the effect of clustering of the impurities (Nagasaka and Narita 1969). In this paper we will analyze the temperature dependence of the photothermal conductivity in semiconductors in detail, and derive a theoretical expression for this temperature dependence which accor ding to our measurements on shallow impurities in high purity germa nium is in excellent agreement with the experimental results. This 60 0.7¿ Eg s - Etrans + ΔΕ •• /ч/ ч^ hv=Etran s 0.73 J gs DONOR ACCEPTOR gs. 0.01 > hv = Etl О) >- о cc kr^in-i) к=(000) 1 : Illustration of the mechanism for photothermal ionization. Shown is part of the band structure of germanium along the (111) direction in к space, with the conduction band (C.B.), the valence band (V.B.) and some shallow donor and acceptor levels, i.e. the impurity ground state (g.s.) and the excited levels. expression enables one to determine the ground state levels of the impurities very accurately from photothermal conductivity experiments (Jongbloets et al 1977 and 1979, further referred to as Ref. II and III). In analyzing the experimental data it will become clear why photothermal conductivity spectroscopy is applicable only in a relatively small temperature region (2-10 K). 2. Signal formation in a photoconductivity experiment. In photothermal conductivity spectroscopy, electrons (or holes) are excited from their ground state with binding energy E to an excited state by radiation of energy hv equal to the transition energy E , as illustrated in figure 1. The radiation frequency ν is usually in the far infrared region (10-200 cm ). While being in such an excited state, the extra energy ΔΕ needed to overcome the remaining part of the binding energy is gained by interaction with thermal phonons. This ionization can be observed as an increase in the electric conductivity of the sample. The photoconductivity is usually measured as a function of the radiation frequency at constant temperature, typically between 2 and 10 K, yielding characteristic "hydrogen-like" excitation spectra for the various shallow impurities (Refs. I, II and III). In the measured spectra one can distinguish between a continuum, caused by direct photo-ionization from the bound ground state into the free band, and sharp peaks due to the two-step photothermal ionization process via bound intermediate states. In order to analyze the temperature dependence of the photo- thermal ionization process, we will treat a typical experiment as an example, the results are of general validity however. In such an 62 experiment the source for the chopped excitation radiation is usually a Michelson interferometer. The sample is connected to an electric circuit so that a bias current is provided by a battery (V„) via a load resistor (R. ) in series with the sample. The change in voltage drop across the sample due to the radiation is measured at various temperatures, using standard lock-in techniques. The electric conductance of a sample of area A and length I is given by Aepn/Ä, where η is the free carrier concentration, μ is the mobility and e is the charge of the carrier. Introducing the quan tity a = RjAe/Ä the d.c. voltage drop V across the sample may be written as 1 V = Vn(l + αμη)" . (1) Without the chopped excitation radiation the number of ionizations, n, will be determined by the background radiation and by the few phonons of sufficient energy available at low temperature. The chop ped radiation causes a change Δη of the free carrier concentration, and thus a change in the conductivity of the sample. Assuming Δη << η the photoconductive response will be an a.c. voltage with amplitude Д = ν_βμ·Δη(1 + αμη)" (2) В so that Л is directly proportional to Δη. One now has to distinguish between the change in free carrier density Δη due to photothermal ionization via an intermediate level Ρ and the change Δη due to direct photo-ionization. The "continuum" carrier density variation Δη is expected to be independent of tem perature in the temperature region of present interest. However, it 63 will be shown below that the "peak" carrier density variation Δη is Ρ strongly temperature dependent, and that this temperature dependence can be investigated by looking at the ratio Д /ÛV . 3. Derivation of the temperature dependence of the photothermal ionization process. As will be shown in section 4 in a typical experiment the free carrier densities η, Δη and Δη are small compared to the total number of impurity states, so that most of the impurities remain in their ground state. The average number N of optical transitions to one of the excited states may therefore be treated as independent of temperature at the low temperatures at which these experiments are usually carried out, so that only the subsequent thermal ionization needs to be considered. N is directly proportional to the impurity concentration. In electron-phonon interaction the longitudinal acoustic phonons are most important. At the low thermal energies (< 10 K) where the experiments under consideration take place these phonons have a small wave vector k. Since the excited states are very localized in k-space (Bassani et al 1974), ionization by phonons from these levels will only take place to the nearest band extremum. Generally the excited state is g-fold degenerated, so the strong Coulomb interaction of electrons (holes) in such a state has to be taken into account. This can be done by stating that an excited level can be occupied by only one electron (hole) but in g different ways (Spenke 1958). The number of ways, g', in which a particle can be transferred from one of the g degenerate excited states to a band state depends on the degeneracy of the band and on the selection rules for such transitions via a 64 phonon. The number of ways W in which Δη particles can be transferred from the N optical excited levels to a band state is then given by: Δη , W = (gg*) Ρ·Ν: [Δη !(Ν-Δη )l]'L . (3) The equilibrium state is now easily obtained in the well known manner by demanding that W is maximal under the condition that the energy: U = Ν·Ε^ + Δη ·ΔΕ trans ρ is a constant. Maximizing (with respect to Δη ) of: Ρ In W + e(U - Ν·Ε^ - Δη ·ΔΕ) trans ρ using Stirling's formula yields: Δη = N[1 + (J-OexpCß.AE)]"1 , (4) Ρ gg where β = 1/кТ. The intensity I of a line in the photothermal con ductivity spectrum relative to that of the continuum is now given by: I - Л /Л = Δη /Δη pc pc = A [ 1 + (-i-ïOexpUE/kT) Γ1 , (5) gg where equation (2) has been used. Here A contains the optical tran sition probability of the line under consideration. Since both Δη and Δη are proportional to the impurity con centration the intensity I is independent of the latter. If a sample contains several impurities the various Δη 's add up in forming one continuum band in the spectrum. The ratios of the intensities of corresponding peaks, all compared with the intensity of the combined continuum band, yield a measure of the ratios of the concentrations 65 of these impurities in the sample, cf. the experimental work of Ref. III. As argued above, in equation (5) g is the degeneracy of the excited bound state while g' is partly determined by the selection rules for transitions via phonons from this state to the nearest band extremum. For donor states in germanium and silicon, where the spin-orbit interaction is small, thermal processes in which spin flips occur may be neglected and the selection rule simply converts to that of spin conservation. In this case g' is the band degeneracy apart from spin, thus g' = 1 for germanium and silicon. Although for acceptor states, where spin-orbit interaction is not negligible, the situation is less obvious the degeneracy of the valence band at к = 0 will be taken in analogy only as the effective mass degenera cy, yielding g' = 2 for germanium and silicon. 4. Comparison with experimental results. In this section the analysis of the previous sections will be compared with experimental results obtained on high purity germanium samples. These samples contained aluminum, boron and phosphorus as residual impurities in concentrations of 10 -10 atoms/cm (Refs. II and III). The dimensions of the cube-shaped samples were 3 Ixlxl cm . The bias voltage V was provided by a 12.6 Volt mercury battery over a load resistor R. of 5 ΜΩ in series with the sample. The quantity о introduced in section 2 has thus a value of 8xlO"13[V-cm-s]. The photoconductive signal strength Д and Д , corresponding with the change in carrier density Δη and Δη respectively, can be deduced from the measured spectra by taking the area of a peak and of 66 6 8 Temperature (К) F-íg. 2 : For a germanium sample with impurity oonaentration 2.1x10 aioms/om are shewn as a function of temperature: the voltage drop V across the sample, the contribution Δ/ of the continuum to the photoconduaiive signal, and the contribution &V of the peak belonging to the C-transition of the boron spectrum. 67 10 ι 1 1 1 1 r Fig. Ζ : The values for μη, μ·Δη and van as a function of iemperatui aalaulated from figure 2 with equations (1) and (2). Here μ is the carrier mobility, η the carrier concentration, an the variation of the latter by photothermal ionization vie an excited state and Δη its variation by direct photo-ionizai 68 the continuum. In figure 2 this is shown as a function of temperature for the C-transition peak and continuum of the boron spectrum from a 11 3 sample with impurity concentration 2.1x10 atoms/cm . Also shown in figure 2 is the d.c. voltage-drop V across the sample. It is seen that ÛV decreases very rapidly above 7 К whereas V decreases more slowly. The peak strength Д increases with temperature as expected, but above 7 К Д decreases along with Д . ρ с The values for μη, ν·Δη and μ·Δη can now be calculated from с ρ the measured V, Δν and Л with equations (1) and (2); the results ' с ρ м are presented in figure 3. The precise temperature dependence of μ is not known but according to Debye and Conwell (195A) typical S f\ 9 values for ν lie between 10 -10 [cm /V-s] in this temperature range and for this impurity concentration. As the "continuum" carrier density variation Δη is expected to be independent of temperature, the shape of the μ·Δη curve in figure 3 will reflect the tempera ture dependence of μ. 5 -3 We thus conclude from figure 3 that Δη * 10 [cm ] and с that the strongly temperature dependent value of Δη is of the 4 -3 order of 10 [cm ]. The mean free carrier concentration η approaches an assymptotic value for low temperatures, probably due to ionization by background radiation. For temperatures above 7 Κ η increases because of thermal ionization. In the considered temperature region 8 -3 the value of η is of the order of 10 [cm ]. We may conclude from all this that although Δη does not change with temperature, the photoconductive signal (i.e. Δν and Л ) decreases very rapidly above 7 К due to the increase of n, according to equation (2). Furthermore we see that η, Δη and Δη are very small compared with 11 3 the impurity concentration (2.1x10 atoms/cm ), so that practically 69 most impurities remain in their ground states. The temperature depen dence of the photothermal ionization process can now be studied by comparing the measured peak strength Д at various temperatures with the area of the continuum ÛV , so by studying: I = Д MV = Δη /Δη . pc pc In references II and III where equation (5) was already pro pounded, it was shown that experimental results on boron, aluminum and phosphorus dopes in high purity germanium were in excellent agreement with this equation. This is illustrated in figure 4 for two lines of the phosphorus spectrum. These results justify the assump tion made about g' in section 3. The line intensities were taken from spectra which were normalized to the same continuum area. The solid curves in this figure represent least square computer fits of equation (5) to the experimental data, using ΔΕ and A as adjustable parameters. The degeneracy g of the intermediate levels was deduced from measured level splittings due to a magnetic field (Bassani et al 1974). The numerical results of these fits for ΔΕ are presented in table 1, together with the ground state energies (E ) calcula- g.s. ted as : E = E,. + ΔΕ . (6) g.s. trans The values for E found in this way from the various spectral g.s. lines are consistent with each other within experimental accuracy and, as is shown in reference III, agree with data obtained by other means. As an illustration that the simple exponential behaviour Ι α ехр(-ДЕ/кТ) , (7) 70 100 ι I I 1 | I 1 I I | ι ι 1 1 | 1 1 1 1 (Л 'с PHOSPHORUS " 4 ι- Δ Ο 1s — 2p ι_ ± S ν 1s—Af. JD \ >- _ _ I- »—I со ζ ^ц» LU 10- — < ω CL - \^- 1 I Fig. 4 : Logarithmic plot of the relative line intensities versus 10/T for two phosphorus lines. The solid curves represent least square computer fits to equation (b), the dotted lines those to equation (7). (See also table 1.) 71 Table 1 : Values of AE and E as obtained from sommter fits of equations (h) and (7) from the temperavure dependence of tuo lines of the phospho-ms spectrun. With Eq. (5) With Eq. (7) transition E^ (cm ) g ДЕСст ) E (cm ) UE(cm ) E (cm ) trans β g.s. g.s. Is + 2p+ 90.0+0.2 4 12.9+0.2 102.9+0.2 9.5+0.4 99.5+0.4 Is -»- 4f 99.0 + 0.2 2 4.0 + 0.3 103.0 + 0.3 2.6 + 0.5 101.6 + 0.5 frequently assumed ad hoc in the literature, does not yield very reliable results equation (7) was also fitted to the experimental data. The results are shown in figure 4 (dotted lines) and in table 1. As can be seen from figure 4 the fit is not as good as with equation (5) and the calculated values for E are not consistent g.s. with each other. Summarizing we may conclude that the theory about the line intensity in a photoconductivity spectrum, as outlined above, is in excellent agreement with the experimental results. 73 References. Bassani F, ladonisi G and Preciosi В 1974 Rep. Prog. Phys. 37 1099-210 Bykova Ε M, Goncharov L A, Lifshits Τ M, Sidorov V I and Hall R N 1976 Sov. Phys. - Semicond. 9_ 1223-7 Debye Ρ Ρ and Conwell E M 1954 Phys. Rev. 93 693-706 Jongbloets li W H M, Stoel inga J H M, Steeg M J H van de and Wyder Ρ 1977 Physica 89B 18-21 1979 Phys. Rev. 20 3328-32 Kogan S M and Lifshits Τ M 1977 Phys. Stat. Solidi 39 11-39 Lifshits Τ M and Nad' F Ya 1965 Sov. Phys. - Doklady 1£ 532-3 Lifshits Τ M, Likhtman N I and Sidorov V I 1968 Sov. Phys. - Senicond. 2 652-5 Nagasaka К and Nar ita S 1969 Solid St. Commun. _7 467-70 Seccombe S D and Korn D M 1972 Solid St. Commun. 11_ 1539-45 Simmonds Ρ E, Chamberlain J M, Hoult R A, Stradling R A and Bradley С С 1974 J. Phys. С: Solid St. Phys. T_ 4164-84 Spenke E 1958 Electronic Semiconductors (McGraw-Hill Book Company, Inc.) ρ 387 Stillman G E, Wolfe С M and Korn D M 1972 Proc. XI Int. Conf. Semi cond. Phys. (Warsaw) ρ 863 Stoelinga J H M, Larsen D M, Walukiewicz W, Aggarwal R L and Bozler С 0 1978 J. Phys. Chem. Solids 39 873-7 74 IV.6 MAGNETIC FIELD DEPENDENCE OF PHOTOTHERMAL CONDUCTIVITY SPECTRA IN THE FAR INFRARED OF THE BORON ACCEPTOR IN GERMANIUM ABSTRACT Photothermal conductivity spectra in the far infrared (10 - 200 cm ) of boron doped germanium (dopant concentration 10 3 ъ 10 atoms/cm ) have been obtained in magnetic fields В up to 2 Τ (B//[001]) at a temperature of Τ = 7.5 К. The coefficients of the linear and quadratic field dependence of the Zeeman splittings and the resulting g values of the associated levels have been determined for the well known D and С transitions, and for the В and several A and I transitions as well. Moreover the field dependence has been studied of transitions to final states which could be identified as I, like states associated with light-hole Landau levels. The results are discussed in terms of existing theories. 75 1. Introduction. From a theoretical point of view, transitions between impurity states of semiconductors like GaAs and InSb are easier to discuss than those in Ge and Si because of the less complicated band struc ture of the former materials. However, in Ge and Si interactions between the impurity states are easier to avoid since impurity con io 3 centrations of ^ 10 atoms/cm can be achieved, while the lowest impurity concentration in a material like GaAs is of the order of 10 atoms/cm , where interactions cannot be excluded (Larsen 1976, Stoelinga et al. 1978). Impurity states have been studied mostly by measuring the transmission in the far infrared region (see the review article by Bassani et al. 1974). Soepangkat and Fisher (1973, further referred to as SF) employed this technique to investigate the Zeeman effect of lower levels of the boron and thallium impurities in germanium. For this type of measurements, relatively high impurity concentra tions are needed. By measuring the photothermal conductivity, samples of much higher purity can be used, yielding very narrow line widths of the spectra. This method was used by Lifshits and Nad (1965) for the first time and a recent review of this subject was given by Kogan and Lifshits (1977). In a set of previous papers (Jongbloets et al. 1977, 1979 and 1980, further referred to as I, II and III) it has been shown how very accurate values for the ground state energies of the impurities can be deduced from the temperature dependence of the peaks in the spectra, obtained with the technique of photothermal ionization spectroscopy. Broeckx et al. (1979, further referred to as BCSV) 76 used this technique to investigate the Zeeman effect of the D and С transitions of the aluminum acceptor in germanium. Here, experi mental results will be presented, not only for the D and С transi tions, but also for the В and several A and I transitions of the boron acceptor in germanium. The labeling of the transitions is the same as used by Haller and Hansen (1974). The Zeeman term connected with the magnetic field produces a linear splitting of the levels, whereas the diamagnetic term gives a quadratic correction. In addition, the impurity potential produces a set of sublevéis associated with each Landau level (for detailed references, see the review article of Bassani et al. 1974). In this paper, the splitting of one of the zero-field levels into sublevéis associated with Landau levels is studied. Taking into account the magnetic field dependence of this zero-field level, values of the magnetic field dependence of the light-hole Landau levels are obtained. This dependence is in excellent agree ment with theoretical considerations. 2. Experimental details. The measurements were performed on a germanium sample contain ing 2.1x10 atoms/cm boron and 4.3x10 atoms/cm aluminum. The photothermal conductivity spectrum of the sample was measured as function of the wave number of the far infrared excitation radiation, using a Grubb Parsons Cube interferometer. The position of the peaks in the spectra were determined with an accuracy of 0.2 cm .A mag netic field of up to 2 Tesla could be applied with a superconducting solenoid (Oxford Instruments). Most of the experimental details were given in reference II. 77 В// [001] Boron spectrum for B = 15 Tesla О С В A I S"^ ab CìS\ •a lb lc l<¡ ι il ι—ι ι ι ІІІІЧІІ|-Г- r- r- 1- D eg st Ι Ο Hb ^ σι -(I 2.0 Τ о f! ж ^''iv ^ Û. ш(Л er •AAJ ' ™ ^^Апм 1-от ^^IrAfW-,^ 0.5 Т от 100 120 КО WAVE NUMBER (cm"1) Photothezmal conductivity spectra at 7.5 К of shallou acceptors in germanivm for several values of the magnetic field В // [001 ]. 11 7 10 3 Impurity concentrations: 2.1x10 at./am B, 4.2x10 at./cm Al. The labelling at the top shous the boron spectrum at 1.5 Tesla including the Zeeman splitting and four satellite peaks of the I. transition associated with Landau levels. 6 Figure 1 shows some of the measured spectra for several values of the magnetic field with B//[001]. The sample was held at a tem perature of 7.5 K. The labeling of the lines of the boron spectrum at 1.5 Tesla is shown in the upper part of figure 1. The zero-field band edge corresponds with the ground state binding energy Ε , as g. s. determined by the method outlined in references II and III. The continuum above E in the zero-field spectrum is due to direct g.s. photo-ionization from the impurity ground state into the free band, whereas the peaks below E are caused by the two-step photother- g. s. mal ionization process. It is clearly visible in figure 1 that on applying a magnetic field the spectra not only exhibit a splitting or shift of the peaks below E , but also develop a set of peaks in the continuum. These two types of peaks will be discussed separately in the following sections. 3. Field dependence of the peaks below E In figure 2 the transition energies of the peaks with wave numbers below the continuum onset E are plotted as a function g.s. r of the magnetic field. As a linear and a quadratic Zeeman term is expected for each transition, a quadratic polynomial E(B) = E(0) + aB + ЬВ2 (1) was fitted to the experimental data. The solid curves in figure 2 calculated in this way, show an excellent fit to the data. The parameters a and b for the various spectral lines are summarized in table 1. A similar procedure was applied by SF to the D and С lines of boron, and by BCSV to the D and С lines of aluminum. BCSV used 79 11 h Ge(B) B//I001] I I I I 0 1 2 MAGNETIC FIELD (Τ) F-ìg. 2 : Zeeman effeat in the photothermal conduotivity spectrum of the boron acceptor in germanium with В // [ 001 ] . The curves are least square fits of a quadratic polynomial to the experimental data. (See also table 1.) 80 Table 1 : Linear and quadratic Zeeman parameters for the spectral lines of the boron impuri by in germanium with В // [ 001 ] as deter mined from figure 2. Transition a (meV/T) b (meV/T ) D -0.205 + 0.005 0.031 + 0.004 a D -0.041 + 0.005 0.003 + 0.002 b D 0.050 + 0.005 0.020 + 0.004 с D 0.198 + 0.009 -0.027 + 0.006 d С -0.081 + 0.005 0.061 + 0.004 a C 0.094 + 0.003 0.032 + 0.001 b В -0.094 + 0.009 0.042 + 0.006 -0.17 + 0.01 0.103 + 0.006 A4 A -0.117 + 0.007 0.086 + 0.006 3 -0.175 + 0.005 0.124 + 0.004 A2 -0.07 + 0.01 0.08 + 0.01 Al h -0.09 + 0.01 0.082 + 0.007 h -0.057 + 0.007 0.084 + 0.005 h -0.079 + 0.007 0.108 + 0.006 h -0.07 + 0.01 0.12 + 0.01 81 polarized radiation in the Faraday configuration with the polariza- tion vector E 1 В, SF used the Voigt configuration with E 1 В and E//B. So the relative intensities of the peaks within one multi plet could be used for the identification of the transitions (see Bhattacharjee and Rodriguez, 1972). The experimental results of SF and BCSV for B//[ 001 ] are collected in table 2. The corresponding notations for the transitions, used by BCSV and SF, and in the present paper are also given there. In this experiment the sample was mounted inside a semispheri- cal integrating cavity; therefore it was not possible to use pola rized radiation. This was not a serious problem, however, because the only lines seen to be splitting into multiplets with B//[ 001 ] are the D and С transitions, for which the identification was already given by BCSV. Comparing table 1 and 2 a good agreement can be seen between the present values for the linear and quadratic Zeeman terms for the D and С transitions, and those of SF and BCSV. For the higher transitions (i.e. B, A and I lines) no compara ble experimental values are available from the literature. Compa rison with theory is also not possible because, as can be seen from figure 2, the theoretical assumption (Bhattacharjee and Rodriguez, 1972) that the unperturbed states at В = 0 are sufficiently well separated to treat the splitting of each state separately, does not hold for the higher lines any longer. The violence of this assump tion for the A and I-lines can be seen from the nearly similar values for b, which is a consequence of the mutual repulsion of these lines because of their narrow spacing. A common feature of the B, A and I lines is the negative sign for the values of a. 82 Table 2 : Linear and quadratic Zeeman parameLers a and Ъ with В // [ 00] ] for the D and С transition of the Al aooeptor in Ge3 as deter mined by BCS7 (Faraday aonfiguration, E 1 Β), together with the values for the В aooeptor in Ge, as determined by SF (Voigt configuration, E 1 В and 'È // В). This work BCSV values for Ge(Al) SF values for Ge(B) Trans. Trans, a (meV/T) b (meV/T2) Trans, a (meV/T) b (meV/T ) D -0.176 0.015 D D. -0.208 0.028 l a 4 D -0.163 0.014 2 D -0.045 0.005 DL D. -0.05A 0.009 D J 3 D -0.030 0.002 4 D D 0.055 0.017 D 0.057 0.019 0 6 с 2 D 0.046 0.021 5 D 0.185 -0.017 D,, D, 0.219 -0.030 8 α 1 D 0.187 -0.020 7 C -0.048 0.052 С С, , -0.066 0.062 2 а 4,3 C -0.064 0.055 l C 0.095 0.038 С, С, . 0.120 0.033 3 D /,1 C 0.107 0.037 4 Gel В) B//I001] 1 1 1 1 ι__ Ο 1 2 MAGNETIC FIELD (Τ) Fig. S : Magnetic field dependence in the photoconduativity spectra of the I- transition and four satellite transitions to bound states associated with Landau levels. The dashed line indicates the zero-field band edge. The curves are least square fits of a quadratic polynomial to the experimental data. (See table 3. ) 84 4. Field dependence of the peaks in the continuum. Apart from the peaks below the band edge, the photoconductivity spectra (figure 1) show a great number of peaks in the continuum that are almost impossible to identify unambiguously. However, some very pronounced peaks appear (labelled I , I, , I and I.) that can easily be recognized in every spectrum. The magnetic field depen dence of these peaks is shown in figure 3, together with the I, transition. Again a quadratic polynomial was fitted to the experi mental points, i.e. E (В) = E (0) + ρ В + q В2 , η = a,b,c,d . (2) η η "η ηη A very good fit can be obtained if the zero-field energy intercepts E (0) of the curves coincide with the zero-field I, transition η 6 energy; this has been plotted in figure 3. The parameters ρ and q of these fits are summarized in table 3. ^n This allows the conclusion that the I , I, , I and I, transi- a' b' с d tions are of the same type as I,, i.e. transitions from the impurity ground state to impurity excited states rather than valence band levels. Kaplan (1968) observed similar features in transmission spectra of boron in germanium and attributed the excited states tentatively to light-hole Landau states. The present very accurate experimental data support this conclusion (section 6). 5. Zeeman effect. Soepangkat and Fisher (1973) interpreted their absorption spectra of the boron impurity in germanium under the assumption that the Zeeman splitting of the ground level is of the same order of magnitude as that of the final state of the D transition. However, 85 Table S : Linear and quaâratia fit parameters for the magnetie field de pendence of the I , I,, J and Ij transitions of the boron impurity in germanium with В // [001] (see figure 3). Also listed are the differenaes between these parameters and those of the I„ transition. 6 Transition p q n n p„ - W % - "«V (meV/T) (meV/T2) (meV/T) (meV/T2) I 0.11 + 0.01 0.20 + 0.01 0.19 + 0.02 0.09 + 0.01 a h 1.28 + 0.03 0.24 + 0.03 1.35 + 0.03 0.13 + 0.03 l 2.46 + 0.04 0.16 + 0.03 2.53 + 0.04 0.05 + 0.03 c h 3.47 + 0.04 0.47 + 0.04 3.55 + 0.04 0.36 + 0.04 Table 4 : Calculated parameters for the linear Zeeman effect of the final state of the D and С transitions with Ъ // \001\ for Ge(B). Also shown are the values of BCSV for Ge(Al). 'Ill '3/2 this work 7.0+0.2 -0.52+0.04 -0.120+0.005 7.9+0.2 M BCSV 7.4 + 0.2 -0.63 + 0.07 -0.119 + 0.006 8.4 + 0.2 this work 3.0 + 0.1 1.01 + 0.04 -0.077 + 0.004 3.3 + 0.1 С { BCSV 3.2 + 0.2 1.07 + 0.07 - 1/13 3.5 + 0.2 Tokumoto and Ishiguro (1977) concluded from magnetoacoustic resonance attenuation measurements on Ga-doped Ge that the splitting of the ground state of shallow acceptors in Ge is much smaller than previous ly assumed. BCSV pointed out that the ground state splitting is in fact so small that the observed line-splittings in photothermal conductivity spectra would reflect the splittings in the final state of the transitions only. This simplifies greatly the interpretation of the spectra, BCSV proposed the assignment of both the D and С lines to Гй -*• Г. transition. We will proceed along the same line and compare our results for the Zeeman effect of the D and С transi tions of boron in germanium with В/Д 001 ] with the results of BCSV for aluminum. Using symmetry considerations Bhattacharjee and Rodriguez (1972) have shown that with B//[ 001 ] the energy shifts of the Zeeman levels of a Γ„ state are given by ΔΕ P (g'p + g^i3)B + Uj + gi/2 - gl Ü • D (4) g'/2 - gi (1 • 9r) , the linear part of equation (3) can be written as: AE+1/2 » І 1/2 Si/^B (5) ΔΕ 3/2 μ Β +3/2 - І δ3/2 Β 87 So the splitting of а Г„ level will be symmetrical relative to the zero-field energy for μ = -1/2, +1/2 and μ = -3/2, +3/2. BCSV assign to the D multiplet with B//[ 001 ] the transitions: D Γ 1/2 D Γ V +3/2 D Γ 3/2 and D Γ +1/2 a = 8 - - · b - 8 - > c - 8 - - d - 8 " · With this assignment the principal g-factors gì/, and go/9 can be deduced from the measured parameters a with equation (5), and from this gl and r can be calculated with equation (4). The results are shown in table 4, together with the results of BCSV. For the С multiplet BCSV give the assignment С =?„->• -3/2, -1/2 and C. = rD ->• +3/2, +1/2. This leads to the g-factors for the C-final D о state which are also summarized in table 4. As can be seen from table 4 there is a good agreement between our values and those of BCSV. 6. Landau levels. -»• In a uniform magnetic field В the continuum of states in the energy band coalesces into a set of discrete quantum states, the Landau levels. Usually these Landau levels form a "ladder" of equidistant energies with spacing ϋω defined by the classical cyclotron frequency ω = еВ/m , m being the effective mass of the charge carrier. However, for degenerate bands such as the valence band edge in Ge the situation is more complex. Using the quantum- mechanical effective mass formalism Luttinger (1956) predicted that the lowest Landau levels would have irregular spacings, while the higher levels tend to uniform intervals. Numerical values for the Landau energy levels in Ge were derived by Evtuhov (1962) from second order perturbation theory. 88 60 І//І001: 1 mie > α) Ι Ε 1 "о ДО (Л 'с >- 98- 97- О 87. 8б· er 7 . 20 76- 5 б5. 64- Зі. 32- 2о- Fig. 4 : Valenae-band Landau levels in germanium with В // [001] , as oaloulated by Hensel and Suzuki (1974). 89 Very extensive calculations have been carried out by Hensel and Suzuki (1974) who applied uniaxial stress to the Ge crystal as a means to uncouple the valence bands in order to decipher the com plicated quantum spectra. They found a separate Landau ladder for every value of the magnetic quantum number Μ , i.e. two heavy hole ladders (M = + 1/2) and two light hole ladders (M = + 3/2). Their results for B//[001] are plotted in figure 4. Boyle and Howard (1961) and Horii and Nisida (1971) have shown that in Zeeman transmission spectra of Ge donors every bound state with energy E(B) has a set of satellite states associated with con duction band Landau levels. The energy Ε (В) of these satellite states is given by E (В) = E(B) + L (Β) , η η where L (в) is the energy of the n-th Landau level relative to the zero-field band edge. Applying the same idea to acceptor spectra, the valence band Landau levels can be deduced from the experimental data of figure 3 and table 2 by subtracting the linear and quadratic fit parameters of the I, transition from those of the I , I. , I and I, transition i.e. d L (B) = [p - a(I,)]-B + [q - b(I,)]'B2 η = a.b.c.d . η По η Ό The results are listed in table 3. A comparison of the values of the linear field dependence with the calculations of Hensel and Suzuki (figure 4), yields that the value of (p - ad,)) for L has a fair agreement with Landau levels 1- and 0-, whereas the corresponding values for L, , L and L, agree excellently with the Landau levels 90 2Ì, 1. and 3n respectively. So apparently the spectral lines I , I, , I and I can be assigned to transitions from the boron ground state to I -like final states associated with light-hole Landau levels. b In conclusion it should be emphasized that the technique of photothermal ionization spectroscopy not only provides an excellent method for the study of the Zeeman effect of shallow impurities in germanium, but also for the analysis of the Landau level structure of the energy bands. It is shown that the results obtained with this technique are in excellent agreement with existing theories. 91 References. Bassani F, ladonisi G and Preciosi В 1974 Rep. Prog. Phys. 37 1099-210 Bhattacharjee A К and Rodriguez S 1972 Phys. Rev. B6 3836-56 Boyle W S and Howard R E 1961 J. Phys. Chem. Solids 19 181-8 Broeckx J, Clauws P, Van den Steen К and Vennik J 1979 J. Phys. C: Solid St. Phys. 12 4061-79 Evtuhov V 1962 Phys. Rev. 125 1869-79 Haller E E and Hansen W L 1974 Solid St. Commun. 15 687-92 Hensel J С and Suzuki К 1974 Phys. Rev. B9 4219-57 Horii К and Nisida Y 1971 J. Phys. Soc. Jap. 31 783-91 Jongbloets H W H M, Stoelinga J H M, Steeg M J H van de and Wyder Ρ 1977 Physica 89В 18-21 Jongbloets H W H M, Stoelinga J H M, Steeg M J H van de and Wyder Ρ 1979 Phys. Rev. B20 3328-32 Jongbloets H W H M, Steeg M J H van de, Stoelinga J H M and Wyder Ρ 1980 accepted for publication in J. Phys. С: Solid St. Phys. Kaplan R 1968 Phys. Rev. Letters 20 329-31 Kogan S M and Lifshits Τ M 1977 Phys. Stat. Solidi 39 11-39 Larsen D M 1976 Phys. Rev. ВП 1681-91 Lifshits Τ M and Nad' F Ya 1965 Sov. Phys. - Doklady 10 532-3 Luttinger J M 1956 Phys. Rev. 102 1030-41 Soepangkat Η Ρ and Fisher Ρ 1973 Phys. Rev. B8 870-93 Stoelinga J Η M, Larsen D M, Walukiewicz W, Aggarwal R L and Bozler С 0 1978 J. Phys. Chem. Solids 39 873-7 Tokumoto H and Ishiguro Τ 1977 Phys. Rev. Bl¿ 2099-117 92 APPENDIX COMPUTER PROGRAM "PHASE2" This appendix shows the computer program, that has been developed for the processing of the data from the interferometer equipment, described in Chapter II. It is intended for handling phase-modulated interferograms, but only minor modifications are necessary for amplitude-modulation. The program is written in assembler language for a PDP-12 (DEC) laboratory computer. But it is also suited for a PDP-8 system; only the instructions for reading and writing of magnetic tapes have to be adapted. The program is divided into two parts : 1. The main program "PHASE2", the structure of which is shown in Fig. A.l. 2. "FIRUTIL", a series of utily subroutines, such as: a software floating point system, a subroutine to type text strings, an incremental plotter subroutine, a subroutine to plot alphanumeric characters, a subroutine to read papertapes and convert codes, a subroutine to read or write magnetic tapes. The program "PHASE2" reads interferograms, which are punched on paper- tape. "PHASE2" can handle a single interferogram, or a combination of a sample- and background-interferogram. These sample- and background-interfero grams can be registered as separate measurements, but also simultaneously with a two-channel system. "PHASE2" has also the possibility to transform a series of interferograms and average the resulting spectra. Each interferogram is preceded by control data, such as step length and number of channels used, and a series of 30 BCD characters defined by the operator with thumbwheel switches on the scanner-control unit. These 30 charac ters are used to provide the program with an identification number for the spectrum, and information about the sensitivity of the detection system. This last information is necessary to calculate the correct average and ratio of spectra. The maximum number of interferometric data points that can be trans formed is N = 1024. The interferogram should ideally be double sided with approximately an equal number of data points on either side of zero path. However, there is no need to have exactly the correct amount as the program is arranged to either truncate or pad the data as necessary. 94 START No - Yes i ' HOW MANY SAMPLE ? HOW MANY ? BACKGR.? 1 ONE- OR TWO- BOLOMETER SYSTEM ? 1 -'. READ CONTROL DATA . - " Í READ INTERFEROGRAM REARRANGE DATA-POINT1 S ' APODIZE 1 FFT READ NEXT READ NEXT SAMPLE INT. I BACKGR. INT. 1 1 1 MODULUS '' ' AVERAGE SAMPLE- AVERAGE BACKGR.- SPECTRA SPECTRA WRITE ON TAPE WRITE ON TAPE I 1 No No ALL DONE ? Yes ALL DONE ? ¿Yes Yes RATIO SAMPLE/BACKGR. WRITE ON TAPE 'r 1 » CHANGE PLOT LIMITS - PLOT SAMPLE+BACKGR. " > SMOOTH1 E ? 1 . гыл of C^J KUN ^, EXIT Fig. A.l 95 After reading the entire interferogram the maximum positive and negative values of the data are located, and the data point in between is attributed to zero path difference. The average value of the entire data array is sub tracted from every data point to remove a possible D.C. offset present in the interferogram. The data array is then padded out to the maximum size of N = 1024 (if necessary) with zero's and then re-located such that the order is undisturbed but zero path is in the first location. The data array is then apodized from both ends towards the middle with a "cosine squared" function, after which the program calls for the "Fast Fourier Transform" (FFT). The FFT subroutine is based on a program written by P.L. Walton , which employs (2) a modifLcation of the Cooley-Tukey fast Fourier transform algorithm . The FFT program calculates the complex spectrum . N-l . Ρ(η·Δσ) = i l і(т-Дх)«ехр(-:^і'П'т) , η = 0,1, . . . ,Ν/2 . т=0 The spectrum points are equidistant with a frequency-interval Δσ = (Ν·Δχ) , where Δχ is the sampling interval of the interferogram points. Then the modulus-spectrum is calculated as |Ρ(η·Δσ)! = l/[Re(P)]2 + [ Im(P) ]2 , and stored on magnetic tape. If a number of spectra must be averaged, the relevant interferograms are now read one by one, transformed and averaged with the already stored spectrum. The same procedure is then repeated for possible background- spectra, and the ratio of the (averaged) sample- and background-spectrum is calculated. Finally the resultant spectrum is plotted on an incremental plotter, within wave number limits chosen by the operator. Noisy spectra can be improved somewhat (at the cost of resolution) by a mathematical smoothing procedure, and then plotted again. References. 1. P.L. Walton, "TOFAST-Fast Direct and Inverse Discrete Fourier Transform Routines.". DECUS Program Library: 8-260 (1970). 2. J.W. Cooley and J.W. Tukey, "An Algorithm for the Machine Calculation of Fourier Series.", Math, of Computers, 19, 297-301 (1965). 96 * 0 0J0> 0000 0000 /•mn',1 F.' UAK INI KA KI К INIIKM KOfif Π 0J06 1464 F NK· NR / 97 0J6'. 5Ϊ74 JMI bAHUlfl 0 .4,? 3074 Dl А МАЛ! UI /LUI AI HI« IIF M *ï/2 054/ 4407 hbNILh 03 /J 0607 CHFfM. , ГНЕСК OJZO 5120 Н.ЬТ * /READ SftMI-Lb IMTtRFFRObRAtt. 05"SJ -510 F ЫІ(. 1 A IL /S A< )ì OS/ Ï 4772 SAHPLE, • JMS I (HLCM /READ NPf STtF 0552 0000 FEX Г 0374 10Ï6 ГАП TF-FRSr OSSI Ι ΙΛΟ IAD HUR Г' 0175 Ϊ5ΪΪ [ICA I KIKTf /FIRST lAftDIOIK 0554 7 7=0 SFA SNA LLA / 0 ' 0374 4404 UKtTb 0555 5344 JMF . + 7 /NU OÎ77 1^13 rttbG9 /•SAMFIF:· 0554 4407 FFNTFR 0400 460^ № I L0( К /htAl' SfcNS 055/ 5510 FLU I Л И 0401 4210 тч чм 9 0560 Al^O FFUT S 'YIS. <; .Ì(J) 040J 4404 kt AD 0541 0000 FIX! 0403 4406 UFAD 0 -A ' 1106 IAI· 1 0404 Ίί -Ι JNf DATA /READ DATA 0·Α3 JO/5 DCA MINI OL /1 OIAIION III M 040·'. 0/*ΐ0 LOrK. Ι0ΓΚ1Ν 0S44 7'MO ЫА 040Λ 1003 CIINTKI, . rONTk «^45 lu M TAD NK /Il NK 1 'ι Kl 0407 742' NU * 7ft ' 2 /-IKM LI 15*4 /450 SNA /ЧКІІ HAIKGK. 0410 0000 '.KFV, 0 /SKÏF 9 LHAk. JMF .F4 0411 1217 'AH MV ГЛІ. RUN 0412 31^4 ПСА TOLKT Ь/Л HA 04 ίΐ 4406 Rf AH IMS SKFV 0414 .ΙΆ IS7 rOUHT JbZ ) c 041t. .21ï JMF , 2 1 I A С II 1 MA І1л 041A 5610 MF Ι ΆΓ9 'AD 1 ••41/ /?Α7 M» f /747 / 9 С 7/ 7440 SZA ι LA / ' IO ' 04'0 Οί,Ο/ ΙΜΙ-ΓΚ-Ί - ι HI 1 К О' 7/ 5267 IMI DAIAJ /№) 1 UN INI F /1 (ЛИ KM Kl F iilJND INFtKhhhOVv'Vl . 040( 440A KFAD /ΥΓ KIF KF .1 0421 7344 KKGKr STA III ΚΑΙ 0401 AJ' LNH 04-.·. 1023 TAli Hb 060 SZA ILA 04-· J /Α40 SZA ΓΙΑ /IF NU •» -ν -INK In I 040! 04'4 5244 IMF KACK6R 0404 042Ь 4544 ЖЧ 1 BKWF-ri 0405 04Jó 4406 МАЛ 0404 0427 1055 KtUINO. - TAO faTOFÏI ( Hf ( К Kt AK. 04 Í0 3136 DCA blüRl ОАО/ 04J1 4406 RI ΑΠ 0610 0432 З0.і5 DL A M int OAU 0411 lO-j-j Τ4Γ> -ir IKL 061 ' 04 І4 1207 IAD Ν /LUUK FUR 'U'UFR t ASF · 0435 7640 ΒίΛ Α 043Α ^•ν JH1 ΚΙϋΙΝΠ Û4Î/ 11 ΪΑ IAD SΙ ORI /FOUND' PRFViIH', /FI AD ANI· t Fil 0440 105/ IAD MNL /ГгіАК. 'NEU l INF' ОМ? 7<-40 0441 7Λ40 SZA CIA Ол 0 4.1. 044J ^2/ JNF KFUIMD ^4 ι 440/ 0441 4'*45 JNb I h KURD /YF-tf F IRUARD )А2 44t* 7 0444 4620 ВЛСКЬК.. JM5 1 LMl'-42 >Í_1 ООН /RtAD AND I UFI F It F 044.» 4-40 JH5 sK'9 ч,424 0002 044Α 4406 Μ Αίι •v..·" _4'> 0447 4406 R-AD 04 А 0000 04',0 4404 URITF 0411 1 40 M"1 "Ji.lO /•ΒΑΙΜ,Κ:· 04').? 4405 IMS I LOCK /READ =FN. /•ÎEAD ÏNTi-Rf-cROGRAM. RIAD ΟΑ',Ι 71Ϊ2 ИЛ Iñf CI Α (·ΓΙ ΚΓΚ /TNITtALlZf MAXf MN 04 tl F Ι Ν1F h 04^4 J12Ï IK А Г /AND л екмл CNF Ul 0005 04Jb /133 CLA ГАГ ЧТ1 RTfi ОЛ ÍS 045Ä J124 Г<ГЛ ГИ /MAX 0.*>»· 10'4 04 14 AUS 04І7 '332 CIA ЬП RTR \>S37 OOI 1 /SKIF A I Unk 04Λ0 3120 DCA S 0440 0005 04¿1 ?33^ CIA SU Rfk 0441 ОО Ю f (XT 04 Α2 3121 ПГА Stl /MIN 0.5*2 1024 044 · 440А RIAD /100 0463 312/, ILA III ИГА υ .АО/ 04Α4 1127 DCA V+l JMI I CHI I - 0000 04Α5 ЙГ A υ-íJ 0Л4' . 3130 /AVth 0 0000 04AÓ 064/ 3106 DCA J 0000 0447 4406 DATAIr JM', 1 CONTRI /MORL DATA » О/. 4 7 0470 1106 TAD J /LOC К ]N AMFI : ÏEK StrTINbS. 0471 4503 JHS 1 INDtXL /FIND FlUAIlNb AHM I Sb LUC MN. O 0472 31 10 DCA AJL UK1 ft 0473 1023 TAI NK /IF NK * AND KUN 1 MFSGÏ 0474 10' ' TAD RUN /SKIF SAM.. KFAD КЛГКО, 0453 4407 rtNItk 047*> 7740 '>MA nZA t LA 511 F i.F Ι Г 0476 4210 JM4 bKF? 0012 ui m иг /FRINÌ NR 0477 4407 FfNTER 0050 ο*-.οο 00*. INPUT /RIAD DATA 04' / 0000 0*01 ÔÙO'-j 5 /(S DIGÏ1S) 0/60 4404 0Λ4Ι Ί 0502 0000 F F XT 1/1 0462 »thsti miv OCOÎ 4404 ftêAD 10 2 7 044 î 4541 0Ь04 /041 Ι ΙΑ 06A4 440/ ОЪОЬ /001 I Al 04A' AIA ' 0504 7440 S7A ΠΑ /OVF Kl OAD * 0444 OOI 1 050/ Ы14 IMF .+5 0A4/ 0001 /SFNStl IWIY ОЫО 4407 F E Nif К /VF i> 04/0 A12C 0511 '05 > Fl FT L10000 /SF Ι *Ό000 0471 0012 0512 1СІ2 FA:: cioooo 0472 0030 0513 0000 FEXT 04/1 51 'О « 0* 14 4404 kl АГ' 04/4 4142 FUT Ъ OMS 704. 1 IA 06/*. 4044 Г* IV Fl Al I CilA /001 (Al 067* 0000 FFUI SF NS Il XT 0*117 7440 'JZA LLA /HATA ΝίΠΑΤΙ^' ' 06/7 4404 0520 54 Μ IMF , f4 0700 4 .4/ RFAD 05 η 4407 FFNIFR /YH,* Ч' ,ΑΓΕ. 0701 105J JMi> I CUNURT 05" 0010 NCCATt 0702 /Î44 DLA STORI 05^і 0000 FfcXT 0701 lOjj SIA I I l RA 0524 4404 ht AD 0704 /,.00 IAD SI livr 0525 4407 FFNltk О/О" 5311 SIA 0'. Ά 40'Ρ FDIV LI0000 0704 4404 UM' .+4 0527 3044 I HF Y Sf Hb 0707 ÏA23 URI ft OUJO 4510 FFUΓ I АЛ /AC Ι) -ΓΙΑГА* Ι Ν' /10000 0710 51 >0 MESOl 1 0531 11 'Α F AU» υ /J st+Al 1) 0711 /440 IMP .*.0 0532 4124 F F UT У 0712 0316 SZA 0713 4404 0533 5510 FbfcT I AJL /A 98 0/?5 44C/ FFMFfc 1104 A"11 I 07 Ji 5044 FUL <,fN 1101 34.15 FHFY tlOOO 0?^? 3141 1106 20 > JSZ S F I /< JF: 6044 FFUг SENS /lEhS bFhbtUOOO ЬЕМ J O;JÜ 1107 530b 0731 0000 ρεχ- 1110 6201 Jlw 00 07J? 2156 IbZ COUNT Uli 4716 JHS I Ar »DI /PREPARE FUR JHF .-A C733 '.325 412 7200 Γι A / AFODISAftílN 0714 1346 TAD N7 /к A-ÍRANG'· DATA э I FIAT (fcNTRF IS N LOCATION ¡ 0735 Ï156 OCA rOUNT 1ПЗ 01 FAD 1-512 0736 4406 RtAI lii4 7041 'ЧА 0737 2 56 .Ы 1 OUNT 1115 074 0740 5336 JHP .-2 1116 7440 HAXLOC 1 2 0741 7100 CLA TLL 1117 1JA4 ІЧ> ^Ч.І-І /YFSr PIIHF 0742 5650 JMF I LCCKIS U '0 1114 DLA Η /И HAXLIh * 0743 0012 C1000* 00.2 /1000 11П 1Ό7 DCA R 0744 3720 1/20 112 114 FAD H 074-, 0000 0000 1121 //10 Ь^А .A 0746 ///1 47r 7 1124 111/ J4 ÇhNGl /^АГСН IIR АРОРІЧАГІОН. 1125 1107 TAD К .-->НІЬ LEFT Η Fl Al ES 0747 0000 'ODt 0 126 4Ъ01 141 f INDEXL 07 i0 1074 TAO HAXLlir DCA AKI 0751 7104 \ LL RAL /.*H FAD К 07-.2 /041 CIA TAD H 07'JT 1106 TAD J /J-2*M JMb I INDFX 0754 7510 SPA / »-o ·* ΙΙΓΑ A Jl A<-\FMAXLOL-M-> 0715 7200 TLA /NO» SFURF H -1 JMI- XKNJ' 07Г;6 1074 TAC' HAXLQ« /YES. 11ORF J H 1/ .. гм . FI FMJO 07S7 7041 CIA 0/4/ Al OHI . FOD 0760 1105 IAD H 2 IIJ/ КЧЧІ>1 . IAD Ч O/'Sl /041 CIA /(H-512) OR (J M 512) /041 LIA 076_' /ЧОО Ϊ>ΊΛ / С ' 10/4 FAD HAXLOC 07A3 /200 (1A /NO. Sit Rf 11' 11 04 IAD Fill ГАИ PSI2 /vtS. b+DRE-tt (>R M 0764 not* 4101 JH^ I INDFXl 0765 3055 KCA S Г )Ч- Il 10 DCA AJI 0766 1055 TAIi STOKt /33 1 tl A S Fl lAC R 0767 /104 CCL RAL /2*bniRE 110/ l IAD К 0770 4 ,43 JMS Ι ΠΟΑ Г /001 I AC 0771 4407 fLMlCh 7041 ΓΙΑ 0/72 4100 FlUW PI 4Ь01 JMb I INDI XL 07/1 6123 Hifi Г /T 2*S~I]F!E/F I 1112 'AKI A U 02 1-М 07/4 0000 ILXr 440/ 077 ι 3/4/ JMf I 1 UÜ ι ilO Α112 «1000 Η UI Ι AK 1000 /746 M/FRO» 0032 /-^DM 0 0000 -10/ ι Ι ΧΓ 1001 7652 MFNt». 3 · 0160 /-.DM 1 ІЬ/ К 0002 HLC. 160 0116 / IBHtLOUER 1 AIE /333 IOO-· Π Л STI lAC КГ-ч DATA 1 END'. LUU TAF E НО/ /CONTfcOl OF ОАТЛ. 99 i JA J 112) /K*0 OR Ы>> SET S 0 1441 4407 FENTER 126 J Î121 Üít\ SU 1444 5047 FGET RES 1J64 11?** Οι-A St 2 1445 1047 FADD RES /CALCULATF 1JAT 440/ FfcNTtft 1446 1047 FAtr RfS /RESOLUTION. 1266 Jllb F Cl Τ ( 1447 6047 FFUT RES /kFS-3«RES І^б/ 0001 ЧПКГ 1450 6010 FPUT FIOta /FLOW-RES i^/0 61 >l HUT f 14S1 0000 FEXT FGtr S 1452 1105 TAD P51? bOht 1453 4543 JMS I FLOAT f/S 11 'J f Äfft Γ 1454 4407 FENTER 1 '/4 OOC ςοκκΓ 1455 3041 FMPY DFLF nui ι AKI 1456 6033 FPUT t-HIGH /FHIGH 51?*riFLF 0000 tt ΧΊ 1457 0000 FEXT 44// (HS 7 Ι Α' г /K-51. ' 1460 7344 STA CLL RAL S J (A tMF F DUI Ь /Nil. ΓΙΙΝΠΝΙΚ 1461 1024 TAI NI HCl 10'7 IAI· F SF Lik /F IRSI ЫЬГГкіІН 1462 7640 Ч7А ILA /Ν1-·2 » ПО.' 10 'A tAt N'.FÍTN 1463 5320 J« DIRCT noi /A'O SNA ΓΙ A 1464 4404 URITE /YFS L '04 JHP ΝΓΧΤ 146t 33/3 MEbü23 /PLOT ilO-ì tn ei h 1466 4404 WRITE /SAMPLF" AND НОЙ IH·, l INITL 1467 1504 MESIV /BACKGROUND ' I W7 hENTh 1470 4537 JMS I ANSWER 1110 H.E* t AKl 1471 1140 TAD ANbMk ΠΙ I ff-IIT [ AJI /АСКНЫРкЕ) A(K) 14 72 1060 TAD MINYFS 0000 Κ·ΧΙ 1473 7640 SZA CLA ПmИ. 447/ MS I l AS Г /К ^12 ' 1474 511? JMF DIRECT /NO-PLOT RATIO 1 Ï14 *Л06 (Hf HOOF /NO. CONÏINOt 147S 1056 TAO 1FFRST /YES 1110 lOAl IAH мша /YFÎ>» hFAD FRtVIOUS 1476 3531 DCA I »LKTP /SUH FKOM l IftFt UIA 4',-i¿ JHS I KHIAFI 1477 1061 ТАГ' ΗI N8 /READ SAMEI f 1J1/ 10A1 • Ali MINO 1500 4532 JMb I RDTAFE /FROM I-TAPE u'o i;i3 IA[i Г Ы MI 1501 4472 JMS I N0RH1 /NORMALI/E TfHlK IFBLK-fl Π 1 Î'ÎÎ N A I bl KU 1502 4466 JMS I SFFIT /Fl ОТ SCALES lï" no/ l'< А К 1503 4467 JMS I bFFLT /FLOT SAHF4.E И '3 44/A Ih', I INI It 1504 1061 TAD MIN8 1 l.»4 4407 FfNltl·. 1S0S 4S1> JMS I RDIAFL /kfAl« BACKGROUND F (.F I AKI 1506 4472 JMS I NORHl /NORMALI7F F AM· 1 A H 150/ 446/ JMS I SFIIT /FIOT FHJl [ Ahi •ΆίΚ) AtKlfUINIK) 1510 10A1 TAD MINA /hFAIi КАПО SPECTRUM 1110 0000 FCX1 1511 4512 JMS I RDTAFE /( ROM I TAF L 1111 447/ JUS I LAM 1512 44/1 DIRECT-r JMb I MAXI1 /FIND MAXIMUM 131 » Μ2Ϊ JHI Al'I· /NO· I (INTTNIlt isn 51?! JMF DIRCT+1 /.Ol Ι Ι А 1ΑΓ 1514 0007 HNDRD. 0007 /100 IO Ά TAI· N'jFLIk /Nb» С IK 1 ? 1515 1100 1100 7A40 S/A I IA 1516 0000 0000 l НА S143 mi .+5 /NO 151/ 1601 F-tOTSli. PIOTS? 7144 m/ SIA 111 RAI /Yl Ь it-^o 447? IURLT. JMb I NORHl /IF N1-1. NDRHALI/fc 10.4 /NI ·* » 15^1 4404 Ukllt 1140 7A40 TAI· NI 1 141 S/A ΓΙΑ 15->2 173? MFbG28 /•FLOW S/АО /NO. CAI CUI ATI FREO. 1142 tOAÏ mt- l kAl ΙΟΙ 1523 4407 I ENTEk I 141 /YFSf «ΚΠΙ 1524 5030 FGET F l OU 4,11 TAC тын /ON t I Al I 1144 /144 JMS I UM Af f IS25 0012 OUTFUT I 141 1021 SIA ( LL ЬАІ 1526 0040 40 /PRINT FLOU 114A 7A40 TAD NP /Nb *» •» 1527 0000 FtXT I 147 S162 Li¿A (LA 1510 4404 WRITE 1 ГіО -.0 2 IMF NX! /NO 1531 1736 MFSC2? /•FHIGH· 1 1 il *4А1 I ,Z KUN 1532 440/ FfcNTth г VÍ' /344 JME 1 Wkbfc 1533 5033 FOfcT (HIGH 13Γ.ΐ 1022 STA ( U (sAl 15J4 001"» OUTPUT ІГ>4 »026 ICA KUN /RUN 2 1S35 0040 40 /PRINT FHIbH llliü Ί4Α2 IS' NbFCTK /I A .( SFtf ΓΚΙΙΜ ' 1536 OOOO FtXT 13ti6 %/Al jm 1 SAMF /NOfhi AH NEXT SAMPLE 1537 4404 URITE Ι Τ, 7 1412 JHI I NX I 1 /CALCUl Al- KAUO 1540 3652 MESG18 /•HAXIHUMÍIN *>:· 1404 RATIO 1 1541 4407 TENTER 1024 NX1 I*'i4'' 5016 , TAP N1 FGFT MAX 1 A2 1541 3314 FHF Y HNDRD Í lAl IAD ЯUN /kUN NI » 1544 0012 OUTFUT 1364 S/A I I A 1545 0010 30 /PRINT MAX HAS )HF NX 11 1546 0000 FEXT 1 IAA fS/ ι ' F( Tk /YFSf I AST SAMPLE 154/ 4546 JMS I PCRIF 1367 MF I SAHI /NO. rONUNllb 1 Î/O 1550 /201 CLA IAC ΊΑΙι BNk /YLS 1551 3022 PLOTS. DCA RUN 1371 IiLA I SfLTK /f SFCTR-HNK 1 137' TAI· I 51 LT h ISS" 4404 URITE /NEW FREO.LIMITS τ 13/3 Ι ΙΑ 105! 3715 МЕЬЬ?7 1554 453/ IMS I ANSUER 13/4 Γ·ΓΑ NSFCTR /МЬИСГН -PSFTTR 1375 1555 1140 FAD ANSWR 1 l'A ІЬ.7 kIJN ІЬоб 1060 TAD HINYES 1 (// >rt i Ы M.» /RFA» FIRST RAI M>· 11.7 7640 S7A CLA 1400 fΑΠ ΜΙΚΗ 1560 5717 JMF I PLOTS! /NO 140*. 'AD I Ы KIF 1G61 4404 WRITE /YES 1402 1533 DI A I PIKTF /Il hlK^IFBI K-8 1562 3732 MFSGSB /•FLOW 1401 2026 íbZ NSFCIk /LAST PACKÙR » 1563 4541 JMb I SICNV /INFUT 404 '461 JM I liCKGft /NO)CON tiNUL 1564 4543 JMS I FLOAT 140в TAP TFFkST 1565 440/ FENTER 140Λ ILA I DLKIf 1JA6 6030 FF UT FLOU 140/ 106 I TAL· Μ1ΝΘ 1567 0000 FEXT I I I kAI 1410 /104 1570 4404 UK I TE /•FHIGH' JHS I kUTAFF /RL AD SAHPbf AND («АГКГ.Р. 1411 4532 1571 3736 MESb29 CLA 141 1572 4541 JMS I SirNV /INPUT TLA К 1411 1571 4543 JMS I FLOAT 1414 ,MS I INIM 1574 440' FENTFR 14 IS STA CI» kAL IJ/ 6033 FFUT FHTGH 1416 TAD Nf 1576 0000 FEXT S7A HA 1577 4546 JMS I PI RLF mt FREO 1600 2022 IbZ RUN FFhTEk 1420 4407 1601 4404 PIÜTS2I WRITE /•NEU MAXIMUM *· FbEl I AKl /CALCUlATE RATTO 1602 3641 MESbl? FT IV I AJI /A(h)- F FIJI I AKl 1601 4537 JMS I ANSUER /A^Í/AtK+FbTORE) 1604 1140 TAD ANSWR 14*4 0000 Ff XT TA|i К 1605 1060 TAD MINYFS 142b 110/ /CALCULATE FREUUFNI Y 1606 "640 SZA ΓΙΑ 1426 4b4J JMb I FLOAT 1607 5222 JHF SH /NO M"·/ 4407 FENTbR 1610 4404 URITE /YES 1430 Î04I FMF Y DELF 1611 3652 HESG18 /•MAXIHUMUN Zìi' F F 111 f AJL 1431 АЫО /A 100 16-4 4L 1/ JH4 1 ANSUÍK /COHFLEX DATA, 16Jb 1140 TAI· ANSUW 2000 0000 MAIN· 0 Іб.1* 1060 IAH HINYtS 2001 /201 CLA IAC IA"1/ /640 S7n CLA 2002 3366 DCA DJ /SIART UITH DJ-1 lòSÙ 5?3Í JMF .+3 /NO. STAM FLOT 2003 Д275 TAD Ρ? JÄil 4473 JMS I SHTH1 /TES» SMOOTHC 2004 7041 CIA luíJ ?0¿2 IS7 RUN 200S 3367 DCA MINF /? INTERMEDIATE TRANS. ι* л 10?2 TAU KUN 2006 4304 PLOOP. JHS LO0P1 /SET UF FOR INT. TRANS. ІйИ 7650 SNA LIA 2007 33/0 DCA L /L=0 1*10 '>A46 mi I MGN 2010 1114 ΓΑΡ Η léJA 44AA JHS I SCfl Г /HOT SCALES 2011 7041 CIA 1¿Í^ 44A'i JHS I R&SNR /PLOT NR AND RES 2012 33/1 DCA HJNL /H PART,/INT. 1640 4467 JHS I SFU f /PLOT SFtCTRUn 2013 1370 LLOOP. TAD L ІЛ41 ',642 JHF I .Fl 2014 3106 DCA J /J=L IA4-* lí.t.1 UOIb 2015 1106 JLOOP. TAD J 1641 ìf?'' HNI.h. /0.01 2016 1114 TAD H 1Ó44 '4 16 241///6. 2017 3107 DCA к /k-'J'FH IA4', '^60*, 560· 20J0 4674 JMS I SETLOP /GET ADDRESSES 1A4A J JA i у\ш, Wf.IN 2021 4407 FENTFR «16 .4 2022 5513 FGET I ANFkl /FAST FOUKIlb IkANSFIlRM. 2023 3120 FHFY S lAZtA 0000 FFT. 0 2024 627A FFUT m lóbb 411.? JMS tl UHI /PtRMIJTE TU 1 ОНІІГХ 2025 5512 FGET I AkL lAlió 4 Α Α.' JMS Ι ,ΙΑΙΝΙ /I'O FFT 20-Ά 1115 FMfY Г Ιό',/ 4AA1 JHS Ι UNSI RI /UNSIRAHKLE 2027 127A F ADD M ΙΑΑΩ '^•.4 JHF I II 1 /EXIT 2030 4274 FFUT Dl /Р1*С*А(Ю*5*А(512+К> 1661 ' '00 UNbCF-l . UHSCKH 2011 5512 FGET I AkL 166.· '000 ИЛІЫІ . MAIN 2032 3120 FHPY Ъ /чимдшпнг Ш 1 INI· 1 LltATTNI» AM'RtSStS OF 2033 6301 FFUT El /ή( І).п<Ы >і> J).A(K), ANP AíM.'+h) 20 Î4 5513 H»ET I ANFM 1AA1 0000 st ног. 0 ¿035 3115 FHFY С JAA4 HO* ΓΛ1· 1 2036 2301 FSUP El lAA'f 4 10 S jn4 IMPtX '037 6301 FFUT El /El'C*A(512+K>-S*A 101 •ч л. 4120 ПОТ Ь MÏ4 V.li 1 (>( 1 1 ANI II J15A С. - FGH M _U' 2'» I 1 f .UI« 1 ANI M ?1 >' Ч '4 FMFY V -51^ ΑΛΙ FFUT 1 ANF II /A(J1 't 11 Л 60 1120 FADO Ч 2137 1347 F АН» F 5 / AC J1 't J) A(J12+M Л 61 4120 1 PUI Ь /i>=S*T+R4*V _140 3341 F MF Y IN ?1AJ 0000 FEXT 2141 4513 1 Hit I ANI KL /АСЫ 'tKl- 2164 2Ï70 ISl L /L=L+1 2342 5347 1 Ы I 1 . / <Л(М 4 l)l('»)*f M Л 64 7000 NOP 2143 ...11 ISIIH I ANFJl .445 *>740 JHF I StruPL /EXIT 2144 1141 1 Ml Y IN Л 66 0000 bJt 0 214 . Α511 F PUI I ANI Я /Λ(51't!) 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J74A DIA Η Iti (A( h 11 /4 2/4/ 440/ SrALF4,. FENTFR /n/ Un 'it/t /M Г SI /I-. J/ЪО FOE Τ !> Il Л [AI J/'.L 0000 FtXT /101 MA OMINT /41-Г ORIENTAI IHN J'S 4A7/ IMS I XI ОКР I f INTIh '7r1 TI'ÎA ΜΑ .-Л H ( 1 f4*, . 'li4 /001 I AC nui (. /Γ 4ΐ J/ .*• 4403 FLOT /FLOΓ NARK FfXT J7',* 0000 0000 IAI· Ml TA J7*.7 4A '0 4AJ0 IIA >TOM /1 (ЫІІКІ > АИПМГЫО) >7A0 /JOO CLA 1 ПННК •7A1 11 ".* TAD ,-З П.І 1 L J/ÓJ J3«4 DÍA .tj F IIP V 4401 FLOT FtXI 0000 0000 Irtli HOWi 4A0'> 4A0A Λ Λ IIA /υ с ' 7200 LLA 1 ·7Α ІИІ . + J ТАР Г 4//О IAK I S1 OKI /rt'.. INIFRVAU LiSTdftf) ΡΓΛ A4LIY IHf ''t Al 1 1 TAD . Ь η N1 IK /NO DCA ASCIX ЮІ 1 ( ?7/3 4407 FÌNTE К F Hf Y I Ht L J//4 MJO F (iE Τ S /Ι .'»Γ 001 ' ÛUTFor /PLOT NUMBER 1 ''//А 001' Τ /f ( 4 TORE > NFXr ADIifiESS '/// M*»© F OE Τ S B JOOO 1 14 F API· Ι H MA и /H INTEKVAl 1001 АПО FFUT S MA 100. 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MESb32. 151/ /МО Λ h '4 •; Η.''Χ 2 4* J F t'A 6AJ2 1766 04 2Ь 0425 /DU LiA( KbR 0444 i-F Ν: 1001 кіч AA31 3767 1401 1401 /LA H M,R оол* Hl .Gl 146/ klUAFf 01 3> 3770 2411 2411 /U I.M.lN ÎÏ6Ï hl b.O ϊ ./0 1 37/1 1716 1716 /ON IHJN U46 nf Uli "Ί',Α , 377J 4001 4001 / A fMrh 04 >1 Η (>)1. 1ΑΙ ' 3774 Ib-'O 1520 /HF l KU» I' 0144 Ж' Ы1 162 Ι 3/74 1411 1411 /H '•IMF OLM ИЬ f.4 16- . kFUlNU 04 '/ 3775 242Ь 2425 /ru (f Ü 6614 3//6 0405 040·; /1"C 11 ι ιΛ »/ Ϊί f KHl. И *' 37/7 /200 7200 /: ЖЧ.І/ -Ν kkNul Il 1/ »4000 dl -.t. ΙH ie .2 ι Ni ' И .1 /ROUTINF TO FIJT FKOGKAtl1 OH 'Flft-HATA· TAFI HI ,Ι/ΐν lAAl 1 kNf. ^ Un» 4000 /^01 CIA IAC Ι AI Cl 0606 »I '.I ' Α'ΜΛ KUN OO · 4001 3247 I'Cn TFflAlj /F IE l l'-Q LHf 1 К ОАО/ m »020 31'.4 h4 1 400' 1207 TAP f440 /FIRST TAFT H.OLK ι 111 ι M OW Hf ,Г. Ч ЗІАО 4003 3261 t'CA ТІЫІч I IKh ' 04 '0 Ж »li'J 3 1/1 Í L ì 4004 1210 TAP MH 1 114 П\ tOOÏ Ж SI. M fft/4 ъл\ ж « < f 400Ь 4235 JMS Ufi π Tl· /WfvITt θ Βί OCKS Of 1 ІЧГгІ UJ6 rtl .O^D 3161 bAMF1 f 01/1 4006 /402 HL Τ -JWO 014/ Ж Sb Ά 11/I í' A -'411 400/ C440 P440· 440 I 0004 Ж SO»/ ï/t'j ΊΙ Al I 1 'A '0 4C10 /770 MR. //70 /-Θ r IN! Ol .4 Жb02Ü J/l' SC Al I '/01 TFFLAG 4047 /FíM Tit 1//' Ж S '9 3/36 sCAI F 4 -/4/ TPBLK-40AI Ih |· 17/í MfSfjl 1Ъ14 A j П1 4 JkirT·- 40*** t ·ύΟ 0/4 î Ж 41.10 3/43 SU AOO \ 1 »00> 00J2 f F •>< 11 1/·"1 S( F ..Ol ', '0 ( Ι ι '0 « Ό , r ltU f •OC A r F fJ12 ι//·; I biQ Ï115 • f f Ι Τ 101 1 Uri-A 04'.J Ы NS 0044 »К IAI 046/ • I II IX 1661 1» ι 16A4 M II Ol ('11 1 0041 .f 11 (F ( /A ΓΊ 1 1 '6/1 F IUI I M' 4 Hi L 1 . ' JLA ( 1 ur I ' U и|1<( 1 1 j 20 MUI '140 ItJkf-C 1 1 .1 > ΙΙΝΥι " OvoJ .HI /41 1 Hi »IAA 41'MB 00Λ1 HVl /40/ m С 1002 Ml ^O/A HNL 00./ )l . 464 MU hfl -07' 1 tub ОбО » HOVh t 10A IX( Olii/ hilft /SOI t 1 401 HUI 74 4 I'. MA/ m« MUY /4'. • M HI Λ 1 F ..Ь<, OOÖ' HS 1ok г J'.l? MT H' > /ι F .11 i' 1000 Nili /40'. >F »1 t T l'A I t I 107 *4_00 4 1^4 /041 CIA /TELÊTYFe INPUT SUWUJUTINt.. 415' /700 SNA LLA 4200 0000 KhBX» 0 4354 5/44 IMP Ι ΡΑΤΓΗ 4->01 6032 KCC 4157 2157 IS2 EXP 4202 6031 KSF 4340 7000 NOP 4203 5202 JHF .-1 4361 1140 TAP HORD 4204 6036 KRB 4362 7130 ''TL RAK 4205 5600 JMF I KKBX 4363 3140 PCA HORD 420* 0000 ANSI ι 0 4344 5744 JMf I FATCH 4207 4200 JHS KRUX /READ ANSUER /ERROR SUPROUTjNE. 4210 3140 DCA ANSUR 4365 0000 FUG χ * 0 4211 1140 TAD ANSUR 4344 4404 URiTF 4212 4405 TYFF 436 7 4373 ME 40 4213 4200 ANSi JMS KRBX 4370 1345 TAP BURI /HAL Г IvIlH I OCATION 1 4..Ч4 З" !? DCA RtTKN 4371 /402 HL Τ /IN ACCU 421& 1232 TAP REIRN /RETURN^ 4374 5745 JMF I BUIJI r 4JÍA 1233 TAI" MR TRW 4Î73 37C HCÍfir !?<>' / F 4217 7650 SNA CLA 43/4 -.-^з /KK 44 ·0 5230 J№ . + 10 /YES 4375 1722 17-" /OK 4J21 І^ДЗ TAD RETRN /NO 4 1/4 J/00 3700 4222 1234 ТЛИ MRU« /RUB OUT·» »4400 4223 7440 S7A ΓΙΑ /SUBROUTINF ГО FLOT ι(VSCI I СНЛКАІ TtKS. 4224 5"ЧЗ JHP ANS /NO 4400 0000 FLTASr,. 0 4225 1235 TAD PCKSL /YES 4401 0314 ANP MASK7/ 4226 4405 TYPE 4402 1334 TAP ASCII 4_27 '.-О? JMP ANbl+l /RFAP AGAIN 4403 3311 PCA ASC 4230 4546 INS I FLRLF 4404 1150 TAD ASriX 4231 5606 JMF I ANSI 4405 J->1"> DCA F5 42T' 0000 RETRNF 0 440A 1151 ТАР ASCIT 4233 7563 HRTAN. --•15 /-RETURN 440/ 3211 PCA +4 4234 7401 MKUB, 377 /-RUP-OUT 4410 7001 ΙΑΓ 423Ъ 0334 KCKSL. 334 /BACKSLASH 44И 4403 HOT /IHltGtK INPUT AND CONVERSION. 4412 0000 0 4230 0000 SICONVr 0 441 Ϊ 0000 0 4237 7300 CLA CLL 4414 7100 CLA CLL 4240 3305 DCA NOI D 4415 1715 ΓΑΡ Ι А5Г 4241 5263 JMF SINFUT /READ CHARACTER 4414 3315 PCA ASC 4242 3136 DCA STORI 4417 131*> FAD АЧГ 4'МЗ 1136 TAD SIDRI 4420 0310 AMP M5KNUM /NUMBFR UF 4244 1303 TAD H-»AO / 260 (ΙΕ.Ό·> ' 44 1 7106 CU κτι /STORARt UORV, 4245 7Ы0 SFA 442.. /004 RU 4244 52/0 IMF s rem /YtS 44 1 7041 CIA 4247 1304 IAD SIM271 /NO, 271 (IE.·?·) "» 4424 3317 DCA FLCNT 4250 //40 SMA SZA CLA 442''» 7040 Γ MA 4251 5270 JMF- SICTR1 /YES 44.A I 115 ΓΑΡ ASI 4252 1305 TAD HOLD /NO' DFCINAL DIGIT 442/ OTO AND MSKAPR /STORAITE ADDR. t 4233 7106 CLL RTL 4430 п-ч TAP CHAR 4244 1305 TAP HOLD 4431 3011 IÍA INIEXC 4255 7004 RAI 443' 1411 PL ASI 1.- TAI I INDfcXr 4256 3305 DCA HOLD /HOLP-HOLPÄIO 44 J Í 3322 PLA MATRIX 4257 1136 TAP STORI 4434 /344 STA ΓΙ 1 RAL /-•> 4260 030' AND SIMASK 443 3323 PCA MTRXN 4-·61 1305 TAD HOLD /ADD DIGIT 44 JA 132? TAP MATRIX 4262 3305 DCA HOLD 443/ /012 KTR 4->6 5 4031 SINPUT. KSF 4440 /012 RTR -, 4 44 5-Ά1 IMF -1 4441 /012 RTR 426% 6036 KF.D /READ 4442 0314 FLASI 21 ANP MASK/ 4266 6046 TLS /URITE 4441 33^4 ΡΓΑ MAIRX 4.'6 7 5242 JMF SrC0NU+4 4444 1324 TAD MATRX 42/0 7200 SICTRL. CIA 4445 0324 ANP MASb,X /МАГКІХ COLUMN 4271 1136 TAH STORI 444^ 7110 CU RAR 42/2 1233 TAP MRTRN /RETUtf* * 444/ 701 -> KIR 4273 7650 SNA ΓΙΑ 4450 3731 P^A I XCRPl 4-,74 S300 JMP +4 44'! tV*4 IAD ΜΑΓηΧ 4273 1235 TAP BCKSL /NO. RUB-OUT 445^ 03.Л ANP MASNY /МАГК.Х KOU 4276 4405 TYPE 44'_1 1/1- PCA I YCRD1 4277 5237 JMP SICONVH /REINITIALIZE 44I4 4713 JMS I FSIZtl /SIZE 4300 1305 TAP HOLD /YES 4455 173 TAD I XrRDl /OR'tNTft'iON 4301 5636 JHP I SICONV /EXIT 4454 1150 ΓΑΟ ASCIX 4302 0017 SIMASKf 17 4457 3270 DCA til 4303 7520 M 2 АО, -260 4460 1/32 TAD I YvKDl 4304 7/6/ SIM271. -И 444i 1151 ΓΑΡ ASwIY 4305 ОООО HOL!'. 0 444 32/1 I» A +/ /1-A ICH FOR fL.PNT. INTERPRETER. 4441 1124 TAD ΜΑΓΚΧ /ALL INniRECT COHMANBS TO FIELD DEFINED BY FCDF 4444 0327 ANP MSKFEN /FEH UF OR POUN' 4306 0000 FUFO» 0 4465 7440 SIA CIA 4307 7300 CLA CLL /SET FL DF-0 4446 /001 ІЛС 4310 1344 TAD UFO 446/ 4403 F l ОТ 4311 3321 ПСА INPIk+1 4470 0000 0 4312 5706 INF I FDFO 44/1 0000 0 4313 0000 FDFl t 0 44/2 1322 ТАР MATRIX 4314 7300 CIA CLL /SET FL.PF-1 44/J -'З'З 14/ MTKXN 4115 1345 TAD uri 4474 5242 IMF FLASC-· 4116 зз-ч OCA INDIR+1 44/ . 7300 CI A CU 4*17 57П JMF I FDFI 4476 231/ IS7 PLCNT 4320 0000 INDIRr 0 4477 Ь-'З· JMF FI ASCI 4321 0000 0 4500 4..04 rtfu 432? 1321 TAP 1 4501 1330 TAP NEXT /SET ЮК ΝΙΧΓ 4 1 'J 3332 DCA ST0RE1+1 450 3/11 DCA I XtRPl /IHARAÍ rtK 4*24 5720 JMP I INDIR 4J01 3/32 DCA I Y( RP1 432·» 0000 RESET, 0 4 .04 4733 IMS I « SlZtl 4326 7006 RTL /SETS DF=0 AF^ER 4'>0'> 1731 ТАР I XCRPl 4327 4201 CDF 0 /LOADING FAC. 4r06 1150 TAO ASCIX 4330 5725 JHF I RESET 4507 3150 PCA A<4 IX 4331 0000 ST0RE1. 0 4' 10 17 12 TAD I vCkDl 4332 0000 0 /SETS DF FOR FFUT 4511 1151 'AP ASriY 4333 -.731 JMF I STORE! 4·ϋ2 3151 ОГА ASCIY 4334 0000 NEXTlr 0 4513 5400 IMF I PLTA5C 433·» 7300 CLA CLL /SFT4 DF-O BEFORE 4514 007/ HASK//r 0077 4336 6201 CDF 0 /oeniNf. NFX- 4515 0000 A'>C, 0 4337 5734 JMF 1 NtXTl /INSTRUCTION 4516 7000 M^NUHr /000 4140 1344 DIR. TAP DFO /SET4 DF-0 FOR 447 0000 PUNT- 0 4341 3332 РГА STifiFltl /STORAGE 4520 C777 MSKADRf 0777 4Í42 '•-741 IMP I +1 4521 4721 CHAR, CHARAC 4341 6630 LOOFOl 45 J 2 0000 MATRIX, С 4144 4201 DF-O. Cut 0 45'3 0000 MTRXN, 0 4345 6211 PFl. CDF 10 45'>4 ооос MATRXr 0 4146 0000 PATCH» 0 /PATCH FOR DNPRM 4525 000/ MASKT. 0007 4347 1161 IAP LORD ΛΗΐίΚ FOR LARGEST 4' "•4 0030 HASKXr 0010 4350 7440 S7A CLA /NEGATIVE MANTISSA 4527 004С HARFEN, 0040 4351 •І744 JMF I FATCM 4510 СГС5 NEXT, 0005 43'2 1160 ΙΛΡ HOKD 4^31 4717 XCRIiw XCRIJ 4353 /МО SFA 4532 4 7.0 Y( RP1, TRI' 108 4 Л1 46 Π fîl/Fl. '.I/FI 4714 5704 4 tl4 45ÍJ AbCII» .+1 4715 0000 SIZES. 4Sïi 1000 1000 /0, 4/16 0000 SZECNT. 4·;ΪΑ 4001 4001 /IPA 471/ 0000 XCRD. 45J7 5005 5005 /2»» 4720 0000 YCRD. 4*". 40 4012 4012 /l.C 4/21 4040 CHARAC. 4040 4C.41 JOl* 301A /4»D 4722 0215 0215 4723 2532 2532 45 4 J! W.>1 1021 /b.fc 3042 2024 2024 /A.F 4724 3042 4^43 4725 3272 3272 4Ί44 6026 602* /7,G 0525 1014 /lOfH 4726 0525 4Ь45 Ï034 4727 3423 3423 444 ή Î037 1037 /11.1 4730 0363 0363 4·;4/ Л042 3042 /12.J 3231 t 4731 3231 45 )0 2045 104·; /13.N 4712 2000 2000 4V>1 20S0 20'0 /14.L 4731 7120 /120 4-,52 'O'iJ 20'Ρ /ij.n 1001 < 4714 1001 4Γ.53 •014 ?0 І4 /16. N 4735 04*5 0415 4,і,>4 60')6 бО- * /17,0 4736 '534 2534 4Г>,>«1 4064 3064 /20. Ρ 4737 0525 0525 4Ь,>А 606/ АО*/ /21.Q 4740 3431 3431 4%Ь7 4075 4075 /'»2.Ч 4/41 2000 2000 4"1Ó0 6101 *101 /21.5 4742 7C00 7000 4ίά1 407 .107 /24. Τ 4743 0535 0535 40А2 3111 31U /25.U 4/44 4323 4323 40*3 2114 2114 /26. W 4745 0535 0535 /27. U 4/46 4323 4323 4,64 1116 3116 7120 406Ь 2i-;i 2121 /30.X 4747 7120 4750 1001 1001 4'.А6 .121 Μ->3 /31.Y 0415 ?130 2130 /32.Ζ 4/Ы 0415 4Ь*7 470? 2534 2534 4./0 1000 1000 /33. 6232 /14f 4753 6232 4S/1 1000 1000 4754 3070 3070 1000 1000 4755 0543 0543 4'./3 1000 1000 /!'./36.." 4756 33/5 33/5 40/4 1000 1000 /17( 47Ъ7 10/0 30/0 45/5 1211 1211 /40tSFACt 4/60 5030 5030 4',/6 J '40 2240 /41.' 4/Al 6025 A025 4'>// 2J4J »242 /42.' 4762 5535 5535 4А00 1000 1000 /43. 4/63 4110 4110 4А01 1000 1000 /44.» 47А4 2011 2031 4A0J 62 J 2 A?! J /45. % 4/AS 3575 3575 4А(И JOOO 1000 /46. t 4/66 05/5 05/5 4А04 000 1000 /4/. 476/ 0253 0253 4А0'- '•"0 2220 /50. ( 4/70 30/0 30/0 4АОА 22-2 2222 /Mt) 4//1 4j00 4500 4AÖ/ 1000 1000 /521* 47/2 3070 3070 4А10 .1.4 . . .4 /53.+ 4//3 0513 0513 4AU ι 'гА 1 "А /54 t. 4//4 3530 3530 4А1 ' 1Ί27 12'7 /55.- 47/5 0532 0532 4A1J 12Ϊ0 1230 /56 t, 4/76 7530 /530 /5/./ 47/7 5001 5001 4614 12 51 1231 0415 4А1Ь btSJ 5132 /AO.O 5000 0415 5001 2534 2514 4А1А U37 313/ /6Ы 3120 414-· /62.2 5002 3120 4А1/ 4142 5001 10*4 1064 4Α"Ό A14A А146 /A3t3 3575 /64,4 5004 3575 4ή21 11·,4 1154 500*> 0525 0525 4AJJ >1 >/ MV7 /65,·. 500* 1433 3433 4Α·3 Α164 6164 /66 t 6 5007 2202 2202 4Ч?4 21/2 '1/2 /A/,7 =,010 5001 5001 4ώΛ /1/4 /1/4 //O.ö 5011 0415 0415 л-чн 6203 /71,9 4*-·* 5012 2534 2534 4 A J/ 2* 12 2212 //2.: 5011 3120 3120 4AJO '214 2234 /73., SOI 4 1061 1061 4AU 2 '44 2244 /74. 5015 3070 3070 4-Я J 22 *6 22 16 //5.- 5016 0525 0525 4А11 224Α '2 4 А /76. 5017 3433 3433 4АЭ4 1 ".0 •>2<і0 /77.-» 5020 2202 2202 4АІЬ 0000 bl£ílt 0 /SIZt OF f-HARAC 5021 6230 6230 4*16 1117 IAH XLbl« /HR AND 5022 4110 4110 4ΑΪ7 4104 (HS SI Л » /ORIbNTATIDN. 5023 •Ό31 2031 4*40 И17 DCA Х<КГ' 50*4 3223 3223 4A41 11 Ό Τ Ali YCM' 5025 1304 1304 502* 1525 1525 4А4* 4304 IH<Î «1171-» 3474 4A4Î 11 '0 P 5032 4001 4501 4А4А té ib JW- I SlZti 5033 1020 »020 464/ //00 ЬНЛ LI А 5034 3135 3135 46%0 S.'ÄO IM ,40 5035 4510 4510 46'. 1 1117 TAH XCkli 50 ÏA 3575 35/3 46..? /041 ΓΙΑ 503/ 4500 4500 46 >ï 131/ DCA ХСкР 5040 1320 1320 46-54 13 Ό TAD YCRD 5041 3575 3575 4AV. /041 CIA 5042 3545 1545 4A5* 3320 DCA YCRD S043 3070 3070 4A./ .635 JW J SI7F1 S044 4110 4110 4660 /040 CMA 5045 2031 2031 4661 tl ",4 TAD ORIENT 5046 3545 3545 4A6J /640 bZñ LLA 5047 0312 0312 4661 '•(274 mr .tti 5050 2233 2233 4664 1120 TAD YCRD 5051 4515 4t35 4ЛА% ms WA SIZE3 5052 0030 0030 4AAA 111/ TAD XCRD 5051 5001 5001 4667 7041 ( ΙΑ 5054 0415 0415 4670 1120 IiLA YCRf 5055 2534 2534 46/1 I US rAD SIZF3 5056 3120 3120 46/2 1317 14 A XCRD 5057 10S0 1050 JHP I 41711 50*0 5425 S425 4АЛ5 5635 2050 46/4 1117 1AD XCRD 50*1 2050 5062 30/0 3070 4А/Ь 3315 DCA bIZE.3 4415 46/* 1320 TAD YLKD 5063 4415 0064 2534 2534 467/ 7041 CIA 5065 3300 3300 4/00 331/ DLA XCRD 0066 3070 3070 4/01 1315 TAD 4ÌZLÌ 5067 441S 4415 4702 1320 HCA YCRD 50/0 2534 2534 4'0Л 5635 JHF I SI7F1 50/1 2313 2313 4/04 0000 SIZE2. 0 5072 6332 *332 4/0- 1315 DCA 4I/L3 50 73 3120 3120 4/0* 1153 Г AD 41 Zt. /SIZE 5074 1001 1001 4/07 /041 CIA 4/10 1316 DCA S/FrNT 4711 115 TAD SI7E.1 4712 2116 ISZ SZECNT 4/U MU Mt 2 109 ΊΟ /-ι 6502 6502 /4 5253 '261 l'>/ ELAb2 /NOT FOUND •УО/6 32/0 3275 5 '54 4515 IM1; I PUb ЪО// 3070 3070 52ГЛ 4206 jM5 ITKURV /Rb AD AÜAIN 5100 4110 4110 /5 5256 4406 REM· MOI 2031 2031 5257 4217 JMS fOkURCi "5102 3223 3223 52A0 4406 Ktrtli 5103 0305 0305 '.'Al 3116 OCA STOhl •под 3575 3575 526 J ,"'34 JMF СОМУІ *» 3105 7425 7425 /6 .i26J 0000 HAG?, 0 ΉΟΑ 1504 1504 5.64 0000 01 ui Τ» 0 5107 0110 ОНО 526 л 0000 IBM. 0 5110 2031 2031 > 'AA 5301 IKMTBI•• . + 13 -7111 3223 3223 526/ 7/47 //47 /IBM 9 ill2 1302 1302 5 '70 ///0 7//0 / θ ЫІЗ 4535 4535 5271 /7/1 /'/I 5114 1050 1050 // 5272 7/J2 //52 /-/ ó/ 5115 5302 S302 / 5273 //..3 //53 / 5 5116 0110 ОНО ,274 7//4 ///4 / 4 5117 2031 2031 3275 //55 7/55 /-3 5120 3223 3223 .,276 /77A 77/6 3121 1104 1304 -.27/ Т/П //77 //- 1 > 5122 1525 1525 -,300 /746 //46 / 0 512J Î423 3423 5(01 //64 MINIO- /7AA 5124 4110 4110 /9 /'OBROUTINE 1С TYFf IR ÍLCT ASLII 5125 "OSI 2031 /1HARALTtRb. -.126 3425 3425 5302 0000 1YFFU 0 5127 1504 1504 jJ03 1136 DLi ^lUkl 5130 0312 0312 *• '04 52 f AD lYf-t-L Γ /· FE OR FLO" Μ31 2233 2233 «=10- 7640 57A ^LA G1J2 70/0 7070 /SPACE *Л06 3315 14"= . F/ /FLOT 5133 3555 3555 /X 5Î07 ЛЗА TAD ЬГ.КІ /TYFE Ы34 0504 0504 5110 6041 ТЬК bU-í 1415 1415 5111 5310 JMF .-1 &tlA 6131 6131 531.' 6046 \УЯ 5137 3020 3020 5311 /300 CLA CL L Ы40 2161 2161 JIM 5/02 JMF Ι ΤΥΓΕ1 5141 6011 6011 5115 1134 TAD ЬТОМ 5142 1423 1425 /( 5UA 4/20 JM5 I FLOTSC S143 5021 5021 51 7 5/02 JMF I TYFri 5144 2415 2415 /) •-T10 4400 FU U4i .• r L ГАЧГ 5145 4232 4J32 /+ /bJBKOUTlNF ГП TYDF ПЧ r-^JT TFXT. Ъ146 6024 6C24 •=321 0000 TYFXf 0 &14/ 5021 5021 51 '2 /100 ' ή Γι ι sito 4232 4232 /» 5121 1721 TAD I TYPX /GFT FOINTFR Í.151 6020 6020 /- 51-14 333/ OCA TYFNF /AND SAWË IT _iJ ALL Y зпг 3575 3575 /. 5125 2321 ISZ ΓΥΡΧ 5153 6020 4020 // 5126 173/ TAD Ι ΓΥΙΝΓ ПЛ Γ ι Ff Г HAND Ы54 6424 64-4 /: •)Í2/ /012 fvTR /CHARALItR. 5155 J021 5021 .110 /012 R1R '-.156 64 -Ά 6424 /» 5311 /01 *» R!R 5ІІ/ 4131 4131 ,132 4340 JM5 lYfY /LÜNVLfíT AND TYPF •-,ΙΑΟ 7303 7303 /= 1133 1/17 TAD 1 TYFNT ΚΚ,ΗΙ HAND CHAR. 5161 6521 6521 .,134 '33/ is/ m NT /F »INT. 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TAH txi /ггит-б /066 23/0 IS/ TFSI * 6707 47/7 JMS I STCRL2 /06/ 1 1/0 ТЛИ !(ЬГ! 6710 3657 ГСА I Mit'K /070 1171 DCA ГЕЫ4 6711 ¿257 ISL ADDR 7071 '371 f S/ USI« 6/13 1160 TAD HORK 1371 ГАИ ІІЫ4 ¿713 34Ь7 Г"ГА I ADI* /0/,· /071 31/2 Γ« ή It S Ib 6714 2257 1Ы ADDR /0/4 •l/"» IS/ ΓΙ S Γ' 671Ь 1161 ТАГ lORD 70/5 /»40 LIA CMA 'SUBIR.1 KHI .IH Γ 6716 J657 ОСА I APliR 70/6 1166 IAD AMOUNT /CUUNI KIF ASI 6717 5201 JMF FFWT+l '0/7 3304 МЛ »H [f 13 /INSU IILllON 6720 4741 TL SU. JMS I OFMINS /FSUB-Z 100 l//t TAD l TISI« /LOU ORIKR 6721 4//1 FLAP, JHS I ALCJN /FIAD 1 FIRST 'ΙΟΙ 7421 MOI 6722 5201 JMF FFNI+1 /ALIGN tXtONENTS /102 1//0 I AI I HSU /ΗΙΙ,Η ИМИ f 6723 4772 JHS I UNORM /lot 7415 ASR 6724 1173 TAD OVtRl /TRIFLfc (KtCtb- /104 ΟΟν,Ο SHIFU. - 0 6723 11/4 TAD 0VER2 /ION ADDITION /IO' Π04 PI A SHtFM /MCI IRPIR 6726 3174 ОГА UWtRJ /bINLF BITS ARE /1С6 /VU MOA /І4\\ HR Al (ι ΝΜΙΝΊ ) 6727 7004 RAL /SHIFTED RIGHT. /107 1313 DLA Ul|t 1,0 /Ι ΓΙ; ORI Ι Κ 6730 1172 TAD AC IL /110 IJAA IAD AMOUNT /(ΑΙ II Κ Al IÜNMI N1 6731 1161 TAD LORD /UI 1312 ТАГ' MINI' 6732 1161 DPA LORD /MO Л A 6731 7004 KAI /il-· 7113 ^З-і/ JMF ItSStïi /It Sb IHAN t I SHU I' 6734 U/l ÎAD АГ1Н /114 33-4 MA .tl /AHOUNl t ' »HII IS. 67« 1160 TAD HtJRD /11Ί 1//1 IAD ( IFS14 /1 OU ORDÌ К 6736 3160 DCA HORD /116 /4't MOI 6737 4770 NOKF. JMS I NORM /NORMALIZE /И/ 1/70 ΓΑΡ I ІГМЗ /Hit H ORPI h. 6740 5201 JHP FPNT+1 /1 Ό /41/ Lbk 6741 7412 0PH1NS.. MIWJS2 /14 0000 >HIFI2. 0 6/42 1254 fXIT- TAD JUHP /OF CODE-0 /122 7701 MOA UÀ 6/4J 0261 AMD MASK3 /ARE BITS 8-11-0 /і-^з "1//2 DI A TF Τ, /(CI КПОЫ 6744 7450 БЧА 7124 I 104 ΓΑΡ HIFI) 6745 5600 JMP I FPNT /VES=FEXT 71 Гі 3//0 DIA ι rtSlï 6746 1360 TAD AC0N6 /COOKUP ON TABLl /124 111! TAD UU lili 6747 32^5 DCA JUMF2 /12/ J//1 DIA 'E , 4 6/50 1655 TAD I JJ1P2 71JC *->o DONb r 7 ALibN 6751 3245 ОГА JUtF 2 /IJl 5." Ό IMI [ Al RN 6Г=І? 1200 TAD tPNT •ΊΙ-» 7/ΑΪ Μ N ''i. •i *7Sî Ч "іб DCA G 12 /I J J 0000 0 / 1 URMIKt Uh I LH 4754 4655 JMS I JUMF? /CALL AS 4ÜB4JUfINt nu-(.о. /1 14 1170 'Ail t Χ. / Iti PU I 6755 t?56 TAH (.02 /KLSrORfc F.F. 7115 /041 (MA A( 6756 3200 DCA FFNT /FOINTLR /136 U*>7 TAU tXF 6757 5201 IMF FPNTtl /1!7 7004 RAL 6760 7544 ЛССЫб. TADLE6-1 7140 7200 Ι ΙΑ /L NK UN il FXl F <Г 6761 /201 FLMY- LLA IAC /F MPY-3 7141 ГІ731 IMP Г ПИТЫ' б/А-1 1170 TAD EXl /142 И/О ЖІі.О» Dt A К' Tl П ANT HC At CWf t 1157 TAD EXF /ADD EXPONENTS 6743 /л4 \ 1//0 •ìli /1 Aht.t >r CUE . IN tl 3157 ι n-sri 6764 БСА txr '144 115/ IK A 1 XF /1 Al 6765 4767 JMS I MULT /MUL ГIFLY 714«; 21/0 IS/ Π SM 6744 Ь201 JMF FFNT+1 7146 1 "0 ΓΑΡ 1 ΓΙ ' M 6/67 7221 MJLT. DMULT 714/ 440 PC Λ HOMI 6770 7600 NOKH> DNOKM b /l 0 * >e\ 1*/ fFSM 67/1 7020 ALGNr Al IG« /It,! 1//0 IAH 1 rt s I 1 6772 7564 UNORHr IHJNORM 7l'i2 1141 DI A 1 UM< 6/73 4334 NLXT2» NEXT1 Πί »б-'О IMI 1 At ION 67/4 4340 DIM* DIR /1-54 U/O NÜHtht . I4P t XI /МАНИ И A 0 6775 4320 INDIR1. INDIR /1V> It */ DIA \ XI 6776 4325 RFSETl» fit4FT /1^6 j 130 JMF PONI 6777 4331 ST0ftF2. ЬТОКЕІ '1-./ /240 1 E SS li, г I 1 A 1 MA /SUBIR. 1 І-чІЧ .HU Γ «7000 7160 1366 TAH AMI IINT /LOHNT 1 ПК 1 .χ 7000 0 0000 ACMINSr /ROUTINE TO PER- 7161 33-4 l<( A ЬНК Г > /IN IRIH IHM. 7001 7300 CLL CLA /FORM TRIFIE /162 IAH 1 ТІЫІі /(IVI Kl LOU 0VER2 /PRFCISION ι//-* 7002 1174 TAD '163 7421 MOI 7003 7041 CMA IAC /NEGATION OF /164 1//1 IAH 1 І1ЬТ4 /1 OU ORPI К 3174 7004 ICA CVLR2 /FLOATING AC /ΙΑ'"» .520 IMI SHIF1 * l 7005 1161 TAH LORD 7\66 000 ^ AlüUN Г > 0 7004 7040 CMA /1A/ //JO ΓΙ ЬЛ ». 7007 7430 ьгі /1/0 0000 It ·>Ι 1. О !<) 7010 7101 CLL :AC /1/1 OOOO ΓΙ'»14, 0 7011 DfA LORD 3161 0000 Tl' Г,τ 0 7012 1160 TAD HORD /!/-/1/>1 Oil/ ÎACU IXF 7013 7040 CMA /1/4 ООН І^Ь'. Í XI txi 7014 /430 SZL /1/5 COOO EX.M. 0 / lifMY SUPMUIUNF 7015 7101 CLL, JAC 71/6 *>//*i IMF FXII4 7016 3160 DCA HORD * /200 7017 (MF I Al MINS 5600 /200 0000 PIVI» 0 /SH(F I 1 Al RICHI /SUEiR.ïO Al lüN 7020 0000 ALIhN* 0 /•01 /100 (ΙΑ MI 7021 1160 TAD HORD /BINARY FOIN Г', / •0'' 1160 TAP MURI 7022 7640 SZA CLA /FOR ADD 'jlJUR. /»03 /MO SFA .t4 7024 522/ JMP / »04 /1 '0 HI IMI /024 r 1161 TAD 1 OKD /MANribSA-O* / »0 . 7010 RAR 7025 7650 SNA CLA /»Об 1160 DCA HOR Ρ 7024 53Ь4 JMf NOHERE /YES / »0/ UA1 ΓΑΡ l ОКР IAH 7027 1171 АГ1Н /OPERANDO» /•no /010 RAK CLA /030 7640 SZA / 11 1161 DIA l ORI' 7031 52 Ï5 JMF .+4 /212 1 1/4 'AP OVt R > 7012 1172 TAD AC1L /41 7010 KAR 70 ІТ /650 bNA CLA 7 4 11/4 Po A (IVI-R2 /034 5620 JMf I Al IG4 /ROTH ZERO-EXIT /2 5 7.00 (1 1 7035 U/O TAD EXl / ' A 1SZ FXF 7034 /041 ГМА 1AC 7 >i/ /00!·>0/ ΝΠ /0J7 1157 TAD FXP /2 0 -.600 •Ml l DIV /040 74oO SNA /EX NTS tlüALT /22 0000 DMULT» 0 lOIIPLÉ tl.li . MUI Ι 7041 5330 JMF DONE /YFS 7 ' '2 /100 ΓΙ л ι 1 /'AUF FMHi IRIILF 7042 /•510 bfA 72 '1 4 110 JMS Κ,Ν /FRI 1 ISIUN. /043 /041 < HA IAC 7044 IJ64 UCA AMOUNT 114 /411 Τ?/7 bul F · 3/// /4 IJ COCÍ f (NI '-- F 0 /NIGAft Ji-LiA4Ii <>>0) 741.3 7300 ( LA LLl /IKIPLF «-KLiIblJN ;.«/ 'i>t Jl/4 ІСЛ riVfR. 7414 .*/Τ 'AD OVERI F4II 7J1J 1140 ι «IM» 7415 7041 CHA 1AL 7-ЧІ fié KIn . M /41¿ 11/3 PCA OOEfil /-M4 II/ * ГАП ЛС lu /417 χ172 TAD AC1L /••it. /4 4* MUI MUY /420 7040 СПА /JÍA OOOO 0 74 Л 7430 SZL ΪΓ30 ГИЛ ΛΜ/ и '422 7101 CLL IAC / '40 /',01 пол 423 3172 DCA AflL I л» 1 /•Ml U/4 ουικ" /424 1J71 TAD АПН /·4-> f 1/4 Ι« ή и<л к > 7425 7040 CHA /?4Í /004 ΚΑΙ 74Jé 7410 4ZL ГАИ /-'44 1 MO и 74?/ 7101 CI 1 IAC t 40 (<ΓΛ /'4Ü и /4 iO ÏI/t Г'СА AC IH /MA ТЛИ AC IH ll/l /4.31 SAI.' JMF- 1 ЧІМНБг /M/ ï •!. ' 14 л . + ( /unum У ККІСІППЧ DlVltit MU 1 lìhb /4І·» 0000 IiUMiIOi . 0 /IF-ERANDS N(IRMALT7£D 1 li Щ1Y 7433 ¿133 ПСА I'Vl· I U /C ^ V A(>. 0 /4Í4 11/J Ι ΑΠ ΑΓΙί /SHIf Г DIVIDIR IhFI гсл KU ι /4J' /104 LIL ΚΑΙ /1 DIT 10 115 /j/l .764 С JHI- I MINORH '75' //10 .РА LI A ?Ъ72 ruwi /200 ΚΛΚ1, /1A M _ MV RdllM.tl 4/600 '757 1171 TAD Fl AM 7600 0000 DNOhHf 0 /SUB*. TO NORMALIZF /760 3177 DCA FLАО 7601 7320 ΓΙΑ (Il (HL /FLOATING AC /761 5AA5 JHF I SURÜCT 760? 1160 TAI» HORD /762 0000 ITERI. 0 7603 7710 SPA CIA /IS HANTISSA NFO. 7763 0000 0 7604 4772 JH', I NEG /YLS /764 0000 0 7605 /0 1 INK IF NIb 7430 bZL 7/AS 0000 ЬОКТ, 0 7606 7040 CHA //AA 0000 0 7607 ТА DCA SirNl /767 0000 0 7610 1160 ТАГ HORD 77/0 3015 Ч0( ONI > .1015 /611 /640 Ь7А Π А /Ib HANTISSA 0 /771 0000 FL AOl. 0 7612 /NO. *І22Ь JMF I OF 7/72 7000 NtC ACM TN:. 761 î 1161 TAD LUKD /AB'.Ol иГЬ MAI Ut Ih Fll HAIIMd F( ) 7614 7510 SFA 7771 0000 ABS, 0 7615 Ь226 JHP t ΟΓ+1 /NO. //74 tlAO TAD HURD 7616 /'iHIFT ICFT l? PUS, Ï1A0 ОГА HOR0 77?·Ί 7/10 SfA (LA 7617 1174 ГАК 0VFR2 /7/A 4//' JHo I Ntb /620 31А1 DCA CURD '7/3 »HF [ AD , 76 Л 3174 DCA OVER > //// 762? 1-Ά3 TAD FOltfUN 762-ï 11-7 TAD FKF 7624 31&7 К A EXF 7625 1161 LOF, TAC l ОЫ· /626 74"Ч HOI /627 И АО TAD ИІЛЛ /630 /411 NHI 7611 ?Ле,0 SNA 76J2 1157 DCA t-XF /MAN'"'tÌf.A-0 76JJ 3160 DCA 40k[ι /6Ï4 7441 SCA /6FT STEF 1 OLMFR. 76 IS 7450 SNA 76 Ï6 5-,<і'> fflP EX 'I /NO. '.MIFTINC. •»A3 7 7041 1 HA InL 7640 1157 TAD EXF 7641 1157 DCA EXF /A4 2 7441 SCA /А4Ч 1- .4 TAD ONF 7644 3251 ССЛ bHIfT /645 11/4 TAD OVFR-1 7646 /421 H01 7A4/ 1161 TAD 1 OKI' /650 741 ΐ ЪНІ /Λ51 0000 SHIFT, 0 /NUMI*1 ь Ή SHIFTS 1 76;>> 3161 ]>ΓΑ 1 Ohi' 7A .3 /501 HOA /6Ь4 3174 ПСА 0VFK2 7655 2262 f-XITl, IS¿ S IGNI 7656 4/72 ІНЬ I NLG 7AS7 4661 JHS I t M M /АЛО 5А00 JHF 1 DN0R1 7AÄ1 434А ""АТСНЬ• FATCH 76А2 0000 SICNlr 0 76А1 77А4 tΟϋΚΓΝ· 14 7664 7777 ONC, t 7665 0000 SORDOГ. 0 /FL LAT.SQUARE KÛOl 7666 3371 DCA FIA( l /TAktb ROOI OF ADS> /66/ UAO TAD HOM« /VAI UI 76/0 7700 SHA LIA /6/1 52/4 JHF .*( /А?'' «,ϊη JH4 I Nfü /NllMPtR I'. NEGATIVL /6/J ?17l IS/ FlAül 76/4 440/ FLNTLK /6/5 6365 \\\ì\ snRf /А/А 0000 FEXT /Ni urtlNS HETHOD. 767/ 1157 IAD FXF /NIJHbth 7700 7100 CIL /- - *AN 7701 /510 SFA / AN 7702 7020 CML· /- -Ah-fl 7703 7010 «AR 7704 7430 ^ZL //HAK E FIRST AFfPOX. 7705 7001 TAC /706 3362 DCA IILfvl 7707 1370 TAD SnCONl /1015 7710 1361 DCA Utbl + l //11 3364 DCA ІГ(М*2 7712 13ΑΑ TAD SORTtl 7713 7Α40 bZA CIA 7714 5325 JHF ( κ U 7715 1367 TAD SOM+2 7716 7640 SZA CLA 7717 Ы 5 JHF CI CU 7/20 315/ ItCA EXP /NtlMftkR 0 //?! S66S JHF I SOROÍH 7/22 440/ FvOOTGO, FFHTEk 772 Ï 6362 'FUT ITERI 7?-'4 JOO0 FEXT 7725 4407 Г uU. •"LNTER 772А 5Ϊ65 -ЗРГ SRRI 7727 4J62 FM υ irtk 7730 ΠΑ? ••ADD ITtRl 7731 0000 FEXT 7732 7240 TLA ΓΜΑ 7733 11S7 TAO EXF /734 ili? DCA tXF 7735 11 •/ TAD tXt* 773А 7041 1 HA IAC 7737 1J62 TAD ITERI 7740 7640 »ZA CIA /EXFONTS EOUAL' 7741 5322 JHF ROOTGO /NO 774? 1160 TAD HOM» /AkL HIGH ORDER 7743 /041 CHA IAC /HANTISSAS KIUAL 7744 1363 TAD ITFM + 1 7745 7640 SZA CLA 7746 5 Г»-» JHF kOfllGO /NO 7747 1161 TAD LORИ 7750 7041 ( HA IA( 7751 13Δ4 FAD ITERIF2 /DO LOW 04DER 7752 7500 SHA /iA4!]SSAS АІіЯЕЕ /753 7041 СНА ΙΛΓ /JITrilN 1 DiT' 7754 /001 IAC 116 4i^7 S.НПО! ІЛИІ f rix NOR MI 714/ SJORÍ Ι 4 UI FIXR Û14J NIO ( 1.5 STOM-2 6/// HX1 A '00 ONE /MA STURI 01 in ЛЬ П7\ HAD A72I Of-MINS A/41 S7ECNT 4/1A nCMIN ό·>67 FLAG 0177 mur 63./ TABI f 6666 ACMINS 7000 Fl AGTF 0114 ОКІЬМГ 0154 TABLFA 7345 ACONi А/60 FI AGI /7/1 ou roc Ó14T TAÜl 71/3 nCJH 0171 flrtbr 5'A J OUTGO /m TAG2 71/4 ACIL 0172 FIDV 7310 ou π-υ ί 001^ TEMFX 63A4 ADUA ЬЬЬ? FIGI ΑΔ7/ ου TX 6321 TEN A171 A-ON 6771 FLINT» 5A00 OVEKl 01/1 TENTh AlAA Al IGN 70*Ό ПИТ A/Al OVFR? 0174 TtST · 716/ ΑΠΟΙΙΝΓ 71ΑΑ FIDA 65S0 F AG'NO AAA4 ГГЬГЗ /I/O ANS 4.ПЗ Fi ОАГ 0141 1 -ULH 434A TFS14 /t/l ANSUER 01J7 FL OF A342 РАГСЧІ /661 TEST3 7172 ANSUR 0140 FIO! TP AOOC FTRLF 014A TKM1-». 5362 ANSI 4^0A FLFT Л70Л FI ή*.·"1 TkM37 53A0 ASC 4M3 FL5U A 7 JO FIQT АТ14 TM 00 5361 ASCII 4Ь34 FMP* 3000 PI ASCI 44 12 TR21S 53A1 ASCIX OlbO •NEG 65A1 H ASC2 4442 Tk237 53A4 ASLIY 0151 FNOR 7000 F IFF 6166 TK77 5357 ASR 74ÍS РЭкМ 0167 F l FF 650.· TFBLK 4061 BACK Ó2/S FORMAT 01AA ILCNT 4M/ TFCNT 4154 BCKSL A? Vi FORUKD 5217 I LU H 6'Î14 TFFIAG 4047 HCKUKD ^"»O* FOUR 6ПА PI DR 6515 TUUFI 6517 BtXF ¿Ul F 01 IR TN 7('A3 PI DU бЫ"* TYFf 4405 SFhSr A134 1- ОНИ Ν А0Ч7 ri ОТ 4403 TYFFl 5302 fiKURD 0144 FPA( t 01A2 PIOTA S4*,0 TYFNT 513/ BLKTP Olli I INT AAOO Fl Ol DU 5334 TYFFLF 01 '-2 M ΟΓίν 41?", FHJT 6000 PI OTDX 556/ τγ^x 5321 Β10ΓΚΝ 41*;* FRURD 014S F l OTDY 53/0 TYPY 5340 BUFI ER ó í/О FS1N A400 FlOTMV 55/? UNORH 6/72 BUFST éJSA FbUB 2000 PLÜTNft bWl URITE 4404 BUG Otis FXAD 61 IJ PIOTNX 3565 VRITTF 4015 BUGI 4 IA'. /411 GOOF PLOTNY 55Л6 MRTAFF 0111 (HAR 4S?t 601 OÍAS FLOTFN 5564 yRTTF 4041 ГНАКАС 47'>1 G0-> AA56 FlOTSL 5320 «RTTf1 40/4 СНГ Ali' HOLD 4J0-. FLOTTI 5S43 X 6525 HORD 01 АО CHX AJ« 1 FlOTT? *·-,50 XCRD 4717 с β Γ CLCU 77?5 HTFMP .6л1 PLOTTJ 5 3 XCRD1 4531 CQNV S230 ІВЧ "¡ÍA'J PLOTWT 5Ί7 1 XSQR 6530 CONVRT 0147 IBMTBL 52A6 PLGTX '•400 XXX 6317 CChW -i'JA IN 630 j PLO 11 54^7 YCRD 4770 (OS 0004 INDEX OOIO FL0T2 34/5 YCRD1 4532 COUNÌ 015A INDFXC ООН FLCT3 3516 1 , CKIF SÌA ) INDIR 43' 0 FL0r4 5543 TU 477"! INDIR1 А775 PLPD 6524 C13 A56.' INI.RCT 666-1 PL PL Α521 tl44 S77Ï INF U Γ 001 ι PLPR A-îtl C«! 3770 ITFf 1 77 .', Fi_PU Α504 C2S5 5771 JUMF АА54 PL4F 6501 C2A0 Al'l JUMF-2 ΔΑΪ>5 FuTAbC 4400 Г27 SAIA RFFF' 72 ΙΑ PLUH 6422 C3 A544 RRBX 4200 FLUL 6SJ1 C5 A541 K7 А153 Ρ UR 6S13 Г7 АЫА LFb41b 7107 PNTR 6547 C9 A'14 LF 5J74 POINT 6162 D 7.'IO l OOF 01 AAJO PRNT1 6251 DFCONV SAI/ LOF 76 -«ï. P4I2F1 4533 DCLR A311 LOhli 0161 OUOL 01/6 DFO 4144 Lbü 741/ RARI 75/2 OFl 434S ITFHF 565' RrtR3 7S44 DGFT ^77A MASKX 4526 MiA 661' DIG ¿330 МАЧКТ 45.", RBS 6631 DIGIT 5.>64 MASM 6130 RDTAPE 0132 DIR 4140 ЛАЬК2 61-·7 RDTF 4117 DIRI 6774 HASRi 6661 RFAD 440Α DIVIDE 7330 HASKb 666 > RE AD TP 411S DIVTWO ¿152 HASK/ Α6Δ3 READI 5200 DIVI 7200 HASK77 4514 REMAIN 5654 DI VP 734A MATRIX 45 J? REbET 4325 , DNULT 72. l MATRX 4S24 RFSETt 6776 DNORH 7A00 mno 4044 REST 7352 DONE 7110 MESh 4373 RET 62 ΙΑ DÜBDIV 7412 MINS 7154 RETN ¿025 DUBLAD 36/1 MING2 7Î53 RETN2 7400 DUMOKH 7-544 Η INIIe;.' 7412 RETRN 423? DVFLG 73 li MINUS? 6133 RFO 6634 DVI 7407 1IN10 530 L RODΓΟΟ 7722 0V1 4177 MIN15 /112 RA 6225 DV2 7430 MIN6 6344 SAsiE ΑΑΑΟ DVI 7455 MQA 7501 SCA 7441 DV4 747A MOL 7421 S-OUNT Α3Α5 DVS 7501 4QLMUY 7425 SOM 7151 DVA 7513 MRTRN 42Ï1 33M1 5723 DV7 7^*4 HkUB 4214 SHIFT /Α.1 fKKQR 73€:.5 МЫ >N •"f 70 A iHIh Г2 71 ·1 FhlOKl »401 Иt^^AD^ 4 .>! 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NORF A/17 S, í lARF 4 /0 FG07 A114 NOkrt Л//') srjk 'Μ ι 117 SUMMARY This thesis deals with the investigation of the temperature- and mag netic field-dependence of the photoconductivity spectra of shallow donors and acceptors present in high purity germanium. These spectra lie in the difficult region of the far infrared. To enter this region a Michelson inter ferometer has been constructed capable to cover the wave number range of 5-350 cm . This instrument, the relevant detector system (bolometer cooled with liquid helium) and the experimental arrangement for photoconductivity measurements are described in Chapter II. This latter system allows measure ments at controlled temperatures between 1 and 15 K. In the progress of these investigations it was discovered that a sub stantial deviation from the real spectrum may be caused by radiation which is reflected back into the interferometer due to reflection on the sample. In Chapter III, which starts with the elementary theory of Fourier spectros copy on which our experimental method is based, the theoretical and experi mental investigation of this reflection-effect is discussed. In Chapter IV the application of the interferometer to the study of the photoconductivity in ultra-pure germanium is treated. Using the technique of photo-thermal ionization spectroscopy the impurities, which are present in extremely low concentrations of 10 -10 atoms/cm , are analyzed. The binding energies of the electron/hole of the donor/acceptor impurities were determined very accurately from the temperature dependence of the peak-in tensity in the hydrogen-like excitation spectra. The complete temperature dependence of the photo-thermal conductivity signal was thoroughly investi gated, both theoretically and experimentally. From measurements in a magnetic field, the linear and quadratic Zeeman- terms were determined for all lines of the boron acceptor excitation spectrum. The relevant values for these levels are compared with the available values from the literature. Some of the lines showing up in a magnetic field could be identified as states associated with light-hole Landau levels. The computer programs developed for the processing of the measured in- terferogram data and executing the Fourier transform to get the frequency spectrum are collected in an Appendix. These programs are suitable for a PDP-12 (or, with slight modifications, for a PDP-8) laboratory computer. 119 SAMENVATTING Dit proefschrift behandelt het onderzoek naar de temteratuur- en mag- neetveld-afhankelijkheid van de fotogeleidings spektra van ondiep liggende donors en acceptors die aanwezig zijn in ultra-zuiver germanium. Deze spektra liggen in het moeilijke gebied van het verre infrarood. Om door te dringen in dit gebied werd een Michelson interferometer gekonstrueerd die een be reik heeft van golfgetallen tussen 5 en 350 cm . Dit instrument, het bij behorende detektor systeem (bolometer, gekoeld met vloeibaar helium) en de experimentele opstelling voor foto-geleidings metingen worden beschreven in Hoofdstuk II. Dit laatstgenoemde systeem maakt metingen mogelijk bij een gekontroleerde temperatuur tussen 1 en 15 K. In de loop van het onderzoek werd ontdekt dat een aanzienlijke afwijking van het werkelijke spektrum kan worden veroorzaakt door straling die ten gevolge van reflektie op het sample wordt teruggekaatst in de interferometer. In Hoofdstuk III, dat begint met de elementaire theorie over Fourier Spek troskopie waarop onze experimentele methode is gebaseerd, wordt het theo retische en experimentele onderzoek van dit reflektie-effekt besproken. In Hoofdstuk IV wordt de toepassing van de interferometer bij het bestuderen van de foto-geleiding in ultra-zuiver germanium behandeld. De onzuiverheden, die aanwezig zijn in extreem lage concentraties van 10 -10 3 atomen/cm , worden geanalyseerd door gebruikmaking van de techniek van foto- thermische ionisatie Spektroskopie. De bindings-energieën van het elektron/ gat van de donor/acceptor onzuiverheden werden zeer nauwkeurig bepaald uit de temperatuur-afhankelijkheid van de intensiteit van de pieken in de water- stof-achtige excitatie spektra. De volledige temperatuur-afhankelijkheid van het foto-thermische geleidings-signaal werd grondig onderzocht, theore tisch zowel als experimenteel. Uit metingen in een magneetveld werden de lineaire en kwadratische Zeeman-termen bepaald voor alle lijnen van het excitatie spektrum van de borium acceptor. De desbetreffende waarden voor deze niveau's worden ver geleken met de beschikbare waarden uit de literatuur. Enige van de lijnen die ontstaan in een magneetveld konden worden geïdentificeerd als toestanden die verbonden zijn met Landau niveau's van lichte gaten. De computer programma's die werden ontwikkeld voor het verwerken van de gemeten interferogram data en het uitvoeren van de Fourier transformatie om 121 het frekwentie spektrum te verkrijgen zijn verzameld in een Appendix. Deze programma's zijn geschikt voor een PDP-12 (of, met geringe wijzigingen, voor een PDP-8) laboratorium computer. 122 CURRICULUM VITAE H.W.H.M. Jongbloets Geboren : 22 december 1943, Nijmegen 1950 - 1956 : Lagere school, Nijmegen 1956 - 1961 : Dominicus College, Nijmegen; HBS-b 1961 - 1963 : Technische Hogeschool, Eindhoven Elektrotechniek 1964 - 1965 : Militaire dienst 1965 - 1972 : Katholieke Universiteit, Nijmegen Natuurkunde studie, in april 1972 afgesloten met het doctoraal examen Experimentele Natuurkunde, hoofdvak Vaste Stoffysica 1972 - 1978 : Promotie-onderzoek Experimentele Vaste Stoffysica, als F.O.M, medewerker bij de afdeling Experimentele Natuurkunde 4, Faculteit der Wiskunde en Natuurweten schappen, Katholieke Universiteit Nijmegen, groepsleider: Prof.Dr. P. Wyder april-okt. : In dienst van de vakgroep Vaste Stoffysica van de afdeling 1979 der Technische Natuurkunde van de Т.Н.-Eindhoven voor een tijdelijk onderzoek gestationeerd in Nijmegen, groepsleider: Prof.Dr. M.J. Steenland 123 STELLINGEN I De extrinsieke geleiding van halfgeleiders wordt in het algemeen bepaald door de absolute waarde van het verschil van de donor- en acceptor- koncentraties Onder bepaalde omstandigheden echter dragen donors en acceptors afzonderlijk bij tot de geleiding II Bij de bestudering van de bandenstructuur van materialen als Cd-As- Ρ via optische effecten kan de nauwkeurigheid van de analyse sterk worden vergroot door naast reflectie en transmissie-metingen de absorptie te bepalen via de kalorische methode M.J. Gelten, A. van Liesnout, C. van Es and F.A.P. Blom, J. Phys. С П, 227 (1978) III Anders dan bij metalen kunnen bij halfmetalen veranderingen in de effectieve massa van de electronen als gevolg van de electron-fonon interaktie niet worden verwaarloosd bij fonon-spektroskopie met behulp van de puntkontakt methode A.G.M. Jansen, F.M. Mueller and P. Wyder, Science 199, 1027 (1978) IV Door een ongunstige verhouding tussen golflengte en bundel-diameter treden bij verre infrarood apparatuur vaak diffractie-problemen op, die vermeden kunnen worden door bundels met een gaussische intensiteits-verdeling te gebruiken Een dergelijke intensiteits-verdeling zou kunnen worden verkregen door toepassing van metaal-maas filters met een kontinu verlopende stnp-breedte D.H. Магігп and J. Lesurf, Infrared Physics 18, 405 (1978) ν De optische eigenschappen van bepaalde materialen kunnen worden bestudeerd door de spiegels van een Fabry-Perot interferometer met de¿e materialen te bedekken De werking van de interferometer kan worden geoptimaliseerd via de bedekkingsgraad L-.G o.M. de kort3 Iroefs^hpbft, rfzjmegen ±979 VI Smith en Loewenstein geven een uitdrukking voor de efficiency van een beamsplitter, waarbij ook de absorptie in rekening wordt gebracht Deze formule geeft echter alleen betrouwbare resultaten indien rekening wordt gehouden met de mvalshoek-afhankelijkheid van de absorptie term D.R. Smtth and ö.t7. Loewenstebn, Apv . Ovt. 14, ?^?Ъ {19?$) VII Het is mogelijk verre infrarood straling te detecteren via de gelijkncht- ende werking van een puntkontakt tussen normale metalen bij lage temperatuur VIII Indien camera's in een lichte kleur zouden worden uitgevoerd ι ρ ν het gebruikelijke zwart, zou de opwarming ten gevolge van geabsorbeerde zonne straling en daardoor de kans op afwijkingen in de film veel geringe^ zijn IX Daar er geen direct veroand Destaai tussen heL orandbLuf-vtrutuik en -Je lawaai-produktie van de verschillende auto-modellen, zal de inning van de heffing geluidshinder wegverkeer via een prijsverhoging voor de brand stoffen wel een stimulans zijn om te kiezen voor zuinige, maar niet voor geluidsarme auto's H.W H M Jongbloets Nijmegen, 13 maart 1980