This page intentionally left blankOptoelectronic Sensors This page intentionally left blankOptoelectronicSensorsEdited by Didier DecosterJoseph HarariFirstpublishedinFrancein2002byHermesScience/Lavoisierentitled:Dtecteursoptolectroniques LAVOISIER, 2002First published in Great Britain and the United States in 2009 by ISTE Ltd and John Wiley & Sons, Inc. Apartfromanyfairdealingforthepurposesofresearchorprivatestudy,orcriticismorreview,as permitted under the Copyright, Designs and Patents Act 1988, this publicationmay only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiriesconcerningreproductionoutsidethesetermsshouldbesenttothepublishersatthe undermentioned address: ISTE Ltd John Wiley & Sons, Inc.27-37 St Georges Road 111 River Street London SW19 4EUHoboken, NJ 07030 UK USAwww.iste.co.uk www.wiley.com ISTE Ltd, 2009 TherightsofDidierDecosterandJosephHararitobeidentifiedastheauthorsofthisworkhavebeen asserted by them in accordance with the Copyright, Designs and Patents Act 1988. Library of Congress Cataloging-in-Publication Data Dtecteurs optolectroniques. English Optoelectronic sensors / edited by Didier Decoster, Joseph Harari. p. cm. Includes bibliographical references and index. ISBN 978-1-84821-078-3 1.Optical detectors. 2.Image sensors.I. Decoster, Didier, 1948- II. Harari, Joseph, 1961- III. Title.TK8360.O67D4813 2009 681'.25--dc22 2009011542 British Library Cataloguing-in-Publication Data A CIP record for this book is available from the British LibraryISBN: 978-1-84821-078-3 Printed and bound in Great Britain by CPI Antony Rowe, Chippenham and Eastbourne. Table of Contents Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiChapter 1. Introduction to Semiconductor Photodetectors. . . . . . 1 Franck OMNES1.1. Brief overview of semiconductor materials . . . . . . . . . . . . . 1 1.2. Photodetection with semiconductors: basic phenomena . . . . . 3 1.3. Semiconductor devices. . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.4. p-n junctions and p-i-n structures . . . . . . . . . . . . . . . . . . . 5 1.5. Avalanche effect in p-i-n structures . . . . . . . . . . . . . . . . . . 7 1.6. Schottky junction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.7. Metal-semiconductor-metal (MSM) structures . . . . . . . . . . . 10 1.8. Operational parameters of photodetectors . . . . . . . . . . . . . . 11 1.8.1. Response coefficient, gain and quantum efficiency . . . . . 11 1.8.2. Temporal response and bandwidth . . . . . . . . . . . . . . . . 12 1.8.3. Noise equivalent power . . . . . . . . . . . . . . . . . . . . . . . 13 1.8.4. Detectivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 Chapter 2. PIN Photodiodes for the Visible and Near-Infrared. . . 15 Baudoin DE CREMOUX2.1. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.2. Physical processes occurring in photodiodes . . . . . . . . . . . . 17 2.2.1. Electrostatics in PIN diodes: depleted region . . . . . . . . . 17 2.2.2. Mechanisms of electron-hole pair generation . . . . . . . . . 19 2.2.3. Transport mechanisms. . . . . . . . . . . . . . . . . . . . . . . . 23 2.3. Static characteristics of PIN photodiodes . . . . . . . . . . . . . . 25 2.3.1. I/V characteristics and definition of static parameters . . . . 25 2.3.2. External quantum efficiency . . . . . . . . . . . . . . . . . . . . 27 vi Optoelectronic Sensors 2.3.3. Dark current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.3.4. Breakdown voltage. . . . . . . . . . . . . . . . . . . . . . . . . . 31 2.3.5. Saturation current. . . . . . . . . . . . . . . . . . . . . . . . . . . 32 2.4. Dynamic characteristics of PIN photodiodes . . . . . . . . . . . . 34 2.4.1. Intrinsic limitations to the speed of response. . . . . . . . . . 34 2.4.2. Limitations due to the circuit . . . . . . . . . . . . . . . . . . . 37 2.4.3. Power-frequency compromise, Pf2 law . . . . . . . . . . . . 41 2.5. Semiconductor materials used in PIN photodiodesfor the visible and near-infrared . . . . . . . . . . . . . . . . . . . . . . . 42 2.5.1. Absorption of semiconductors in the range 400-1,800 nm . 42 2.5.2. From 400 to 900 nm: silicon and the GaAlAs/GaAs family 43 2.5.3. From 900 to 1,800 nm: germanium, GaInAsP/InP . . . . 46 2.6. New photodiode structures . . . . . . . . . . . . . . . . . . . . . . . 49 2.6.1. Beyond the limits of conventional PIN . . . . . . . . . . . . . 49 2.6.2. Photodiodes with collinear geometry . . . . . . . . . . . . . . 50 2.6.3. Waveguide photodiodes. . . . . . . . . . . . . . . . . . . . . . . 52 2.6.4. Traveling-wave photodiodes. . . . . . . . . . . . . . . . . . . . 53 2.6.5. Beyond PIN structures . . . . . . . . . . . . . . . . . . . . . . . 54 2.7. Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 Chapter 3. Avalanche Photodiodes . . . . . . . . . . . . . . . . . . . . . . 57 Grard RIPOCHE and Joseph HARARI3.1. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 3.2. History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 3.3. The avalanche effect . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 3.3.1. Ionization coefficients . . . . . . . . . . . . . . . . . . . . . . . . 61 3.3.2. Multiplication factors . . . . . . . . . . . . . . . . . . . . . . . . 62 3.3.3. Breakdown voltage. . . . . . . . . . . . . . . . . . . . . . . . . . 64 3.4. Properties of avalanche photodiodes . . . . . . . . . . . . . . . . . 66 3.4.1. Current-voltage characteristics and photomultiplication . . 66 3.4.2. Noise in avalanche photodiodes. . . . . . . . . . . . . . . . . . 68 3.4.3. Signal-to-noise ratio in avalanche photodiodes . . . . . . . . 71 3.4.4. Speed, response time and frequency responseof avalanche photodiodes . . . . . . . . . . . . . . . . . . . . . . . . . . 73 3.5. Technological considerations. . . . . . . . . . . . . . . . . . . . . . 76 3.5.1. Guard ring junctions . . . . . . . . . . . . . . . . . . . . . . . . . 77 3.5.2. Mesa structures. . . . . . . . . . . . . . . . . . . . . . . . . . . 78 3.5.3. Crystal defects and microplasmas . . . . . . . . . . . . . . . . 79 3.6. Silicon avalanche photodiodes . . . . . . . . . . . . . . . . . . . . . 80 3.6.1. Si N+P APDs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 3.6.2. Si N+PP+ APDs . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 3.6.3. Si N+PP+ APDs . . . . . . . . . . . . . . . . . . . . . . . . . . 84 Table of Contents vii 3.6.4. SiPt-Si N Schottky APDs. . . . . . . . . . . . . . . . . . . . . . 87 3.7. Avalanche photodiodes based on gallium arsenide . . . . . . . . 88 3.8. Germanium avalanche photodiodes . . . . . . . . . . . . . . . . . . 90 3.8.1. Ge APDs with N+P, N+NP and P+N structures for 1.3 m communication . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 3.8.2. Ge APDs with P+NN- structures for 1.55 mcommunication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 3.9. Avalanche photodiodes based on indium phosphate (InP). . . . 95 3.9.1. InGaAs/InP APDs for optical communicationsat 2.5 Gbit/s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 3.9.2. Fast InGaAs/InP APDs . . . . . . . . . . . . . . . . . . . . . . . 99 3.10. III-V low-noise avalanche photodiodes. . . . . . . . . . . . . . . 1003.10.1. III-V super-lattice or MQW APDs . . . . . . . . . . . . . . . 1013.10.2. Spin-orbit resonance APDs . . . . . . . . . . . . . . . . . . . . 1023.11. Prospects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1043.11.1. Si/InGaAs APDs . . . . . . . . . . . . . . . . . . . . . . . . . . 1043.11.2. Waveguide MQW APDs . . . . . . . . . . . . . . . . . . . . 1043.11.3. Low-noise APDs with a very thin multiplication region. . 105 3.12. Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1063.13. Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107Chapter 4. Phototransistors . . . . . . . . . . . . . . . . . . . . . . . . . . 111Carmen GONZALEZ and Antoine MARTY4.1. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1114.2. Phototransistors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1124.2.1. Phototransistors according to their fabrication materials . . 112 4.2.2 Phototransistors classified by structure. . . . . . . . . . . . . . 1144.3. The bipolar phototransistor: description and principlesof operation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1184.3.1. The phototransistor effect. . . . . . . . . . . . . . . . . . . . . . 1194.3.2. The response coefficient of a phototransistor . . . . . . . . . 1244.3.3. Static electrical and optical gains of the phototransistor. . . 125 4.3.4. Dynamic characteristics of phototransistors . . . . . . . . . . 1264.3.5. Noise in phototransistors . . . . . . . . . . . . . . . . . . . . . . 1384.4. Photodetector circuits based on phototransistors. . . . . . . . . . 1404.4.1. Amplification circuits . . . . . . . . . . . . . . . . . . . . . . . . 1404.4.2. Nonlinear circuits. . . . . . . . . . . . . . . . . . . . . . . . . . . 1414.5. Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1424.5.1. Galvanic isolation . . . . . . . . . . . . . . . . . . . . . . . . . . 1424.5.2. Phototransistors for optical telecommunications . . . . . . . 1454.6. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1504.7. Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151viii Optoelectronic Sensors Chapter 5. Metal-Semiconductor-Metal Photodiodes . . . . . . . . . 155Joseph HARARI and Vincent MAGNIN5.1. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1555.2. Operation and structure . . . . . . . . . . . . . . . . . . . . . . . . . 1565.2.1. Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1565.2.2. Materials used . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1615.3. Static and dynamic characteristics. . . . . . . . . . . . . . . . . . . 1655.3.1. Response coefficient . . . . . . . . . . . . . . . . . . . . . . . . . 1655.3.2. Dynamic behavior . . . . . . . . . . . . . . . . . . . . . . . . . . 1725.3.3. Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1755.4. Integration possibilities and conclusion . . . . . . . . . . . . . . . 1775.5. Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178Chapter 6. Ultraviolet Photodetectors. . . . . . . . . . . . . . . . . . . . 181Franck OMNES and Eva MONROY6.1. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1816.2. The UV-visible contrast . . . . . . . . . . . . . . . . . . . . . . . . . 1896.3. Si and SiC photodetectors for UV photodetection . . . . . . . . . 1906.3.1. UV photodiodes based on silicon. . . . . . . . . . . . . . . . . 1916.3.2. SiC-based UV photodetectors . . . . . . . . . . . . . . . . . . . 1946.4. UV detectors based on III-V nitrides . . . . . . . . . . . . . . . . . 1956.4.1. Photoconductors . . . . . . . . . . . . . . . . . . . . . . . . . . . 1966.4.2. Schottky barrier photodiodes based on AlGaN . . . . . . . . 2026.4.3. MSM photodiodes . . . . . . . . . . . . . . . . . . . . . . . . . . 2096.4.4. p-n and p-i-n photodiodes . . . . . . . . . . . . . . . . . . . . . 2106.4.5. Phototransistors . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2146.5. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2166.6. Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218Chapter 7. Noise in Photodiodes and Photoreceiver Systems . . . . 223Robert ALABEDRA and Dominique RIGAUD7.1. Mathematical tools for noise . . . . . . . . . . . . . . . . . . . . . . 2247.1.1. Known signals with finite energy or power . . . . . . . . . . 2247.1.2. Random signals and background noise . . . . . . . . . . . . . 2267.2. Fundamental noise sources . . . . . . . . . . . . . . . . . . . . . . . 2277.2.1. Thermal noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2277.2.2. Shot noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2287.2.3. Multiplication noise . . . . . . . . . . . . . . . . . . . . . . . . . 2297.3. Excess noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2327.3.1. Generation-recombination noise . . . . . . . . . . . . . . . . . 2327.3.2. 1/f noise. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233Table of Contents ix 7.4. Analysis of noise electrical circuits . . . . . . . . . . . . . . . . . . 2357.4.1. Representation of noise in bipoles . . . . . . . . . . . . . . . . 2357.4.2. Representation of noise in quadripoles . . . . . . . . . . . . . 2377.5. Noise in photodetectors . . . . . . . . . . . . . . . . . . . . . . . . . 2397.5.1. Characteristic parameters . . . . . . . . . . . . . . . . . . . . . . 2407.5.2. PIN photodiodes . . . . . . . . . . . . . . . . . . . . . . . . . . . 2427.5.3. Avalanche photodiodes . . . . . . . . . . . . . . . . . . . . . . . 2447.6. Noise optimization of photodetectors. . . . . . . . . . . . . . . . . 2457.6.1. Formulation of the problem . . . . . . . . . . . . . . . . . . . . 2467.6.2. Concepts for photodetector-transistor matching. . . . . . . . 2517.7. Calculation of the noise of a photoreceiver . . . . . . . . . . . . . 2537.7.1. Basic equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2537.7.2. Models of transistor noise . . . . . . . . . . . . . . . . . . . . . 2557.7.3. Example calculation: a PIN-FET photoreceiver. . . . . . . . 2597.8. Comments and conclusions . . . . . . . . . . . . . . . . . . . . . . . 2667.9. Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268List of Authors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269Index. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271This page intentionally left blankPrefacePhotodetectionisfoundinalargenumberofprofessionaland mass-marketsystems.Therearenumerousapplicationsincluding: fiber-basedandfree-spaceopticaltelecommunications,galvanic isolation, solar cells, proximity detectors, etc. All of these applications arebasedonthesameprocess:thetransformationofopticalpower intoanelectricalsignal,withthissignalneedingtobeaslargeas possibleforanopticalfluxasweakaspossible.Wheninformation needstobetransmittedquickly,potentiallyatveryhighspeeds,the photodetectormustreactveryfast.Thesebasicconsiderationsimply thatacertainnumberofperformancerequirementsshouldbemetin ordertosatisfythedemandsoftheintendedapplication.Itisinthis contextthatvariousphotodetectingstructureshavebeenconceived: photoconductors,p-nandp-i-nphotodiodes,avalanchephotodiodes, phototransistors,Schottkyphotodiodes,MSM(metalsemiconductor-metal)photodetectors.Therangeofwavelengthsrelevanttothe applicationalsoplaysanimportantrole.Itisoftenthis,throughthe intermediary of the semiconductor bandgap, which dictates the nature of the material(s) used. Thisbookgatherstogetherthemostdetailedandsignificant contemporarythinkingonphotodetectionforwavelengthsfromthe near-infraredtotheultraviolet1.Itscontentnotonlygivesthereader 1.Theveryparticularnatureofphotodetectioninthemid-andfar-infraredrequires specific treatment and thus is not covered here. xii Optoelectronic Sensors thegroundingtodesignsimplephotodetectorswithspecified performancecharacteristics,butalsodiscussesthestateoftheartin photodetection.Chapter1beginswithanintroductionto photodetectionandthemostwell-knownphotodetectorstructures. Amongthese,somearemorecommonlyusedthanothers,oroffer more exciting possibilities. Because of this, each of Chapters 2 to 5 concentrates in great depth onaspecificphotodetectortype.Insequence,thereaderwillbeable to learn about: thePINphotodiodewhichisthephotodetectoronwhichthe majority of systems are based (Chapter 2); theavalanchephotodiode,whichisarefinementofthePIN photodiodeandwhich,underasufficientlyhighbiasvoltage,allows us to achieve a gain (Chapter 3); thephototransistor,whichisanothermeansofobtaininggainin photodetection (Chapter 4); theMSMphotodiodewhichiswellsuitedtomonolithic integrated circuits such as MMICs (Microwave Monolithic Integrated Circuits) (Chapter 5). Chapter6,however,isdifferent.Itisdedicatedtoultraviolet photodetectors. Given the significant role that this wavelength range is likelytotakeinthenearfuture,notablyforenvironmental applications,thissubjectdeservesaseparatechapter.Inthiscase,all typesofphotodetectorareconcerned,anditisthematerialwhichis thesourceofimprovement,notablywiththeappearanceofAlGaN materials with a very large bandgap. Finally, Chapter 7 is entirely dedicated to noise, as this concept is absolutely fundamental for the photodetection of low-intensity signals. Preface xiiiThechaptersofthisbookhaveallbeenwrittenbyspecialistsand we take this opportunity to thank them sincerely and warmly for their contributions. Didier DECOSTER and Joseph HARARIThis page intentionally left blankChapter 1 Introduction toSemiconductor Photodetectors1.1. Brief overview of semiconductor materials Asemiconductormaterialisacontinuouscrystallinemedium characterizedbyanenergybandstructurecorresponding,inthecase ofaninfinitecrystal,toacontinuumofstates(which,inpractice, meansthatthecharacteristicdimensionsofthecrystalare significantlylargerthanthelatticeparameterofthecrystalstructure; this applies as long as the crystal dimensions are typically larger than afewdozennanometers).Ingeneralterms,theenergystructureofa semiconductor consists of a valence band corresponding to molecular bonding states and a conduction band representing the molecular anti-bonding states. The energy range lying between the top of the valence band and the bottom of the conduction band is known as the forbidden band,ormorecommonlythebandgap.Anelectronsituatedinthe valence band is in a ground state and remains localized to a particular atominthecrystalstructure,whereasanelectronsituatedinthe conductionbandexistsinanexcitedstate,inaregimewhereit interactsveryweaklywiththecrystallinestructure.What Chapter written by Franck OMNES. 2 Optoelectronic Sensors differentiates semiconductors from insulators is essentially the size of thebandgap:werefertosemiconductorswherethebandgapofthe material is typically less than or equal to 6 eV, and to insulators when the bandgap is more than 6 eV: above this, the solar spectrum arriving ontheEarthssurfaceisunabletoproduceinter-bandtransitionsof electronssituatedinthevalencebandofthematerial.Semiconductor materialsaremostlydividedintotwolargeclasses:elemental semiconductors(groupIVoftheperiodictable):silicon,germanium, diamond,etc.andcompoundsemiconductors:IV-IV(SiC),III-V (GaAs, InP, InSb, GaN) and II-VI (CdTe, ZnSe, ZnS, etc.). Impurities canbeintroducedintothevolumeofthesemiconductormaterialand canmodifyitselectricalconductionproperties,sometimes considerably. An impurity is known as a donor when it easily releases afreeelectronintotheconductionband.Thecharacteristicenergy leveloftheimpurityisthereforeinthebandgap,slightlybelowthe conductionband.Forexample,inthecaseofcompound semiconductorsingroupIVoftheperiodictablesuchassilicon,the maindonorimpuritiesarethosewhich,beingfromgroupVofthe periodic table (arsenic, phosphorous, etc.), are substituted in place of a siliconatominthecrystalstructure:sincesiliconistetravalent,these atomsnaturallyformfourcovalentbondswiththesiliconatoms aroundthem,andalsoeasilygiveuptheirsurpluselectrontothe crystalstructure.Theseelectronsbecomefreetomove,subjecttoa weak activation energy provided by thermal agitation. In this case we referton-typedoping.Inthecaseofsilicon,agroupIIIelement incorporatedintothecrystalstructureofsiliconnaturallyformsthree covalentbondsaroundit,andthencompletesitsownouter-shell electronicstructurebycapturinganelectronfromitsfourthnearest-neighborsiliconatom,againsubjecttoaweakthermalactivation energy.Suchanimpurityisknownasanacceptor,anddopingwith acceptorsisknownasp-typedoping.Aholecarryingapositive elementarychargeandcorrespondingtoavacantenergystateinthe valence band is therefore left in the crystal structure of the silicon. In the case of III-V composites, the donors are mostly atoms from group IV(silicon)substitutedinplaceofgroupIIIelements,orgroupVI elements(S,Se,Te)substitutedinplaceofgroupVelements,and acceptors are group II (zinc, magnesium) substituted in place of group Introduction to Semiconductor Photodetectors 3 IIIelements.InthecaseofII-VIcomposites,themostcommonly-encountered donors belong to group VII (chlorine, etc.) substituted in placeofgroupVIelements,andacceptorsbelongtoeithergroupI (lithium,etc.)ortogroupV(nitrogen,arsenic,phosphorous,etc).In this last case, the group V element is substituted in place of a group VI elementinthesemiconductorcrystalstructure,whereasgroupI acceptorsaresubstitutedinplaceofgroupIIelements.Thechemical potential, or Fermi energy, of an intrinsic semiconductor (i.e. one free from n and p impurities) is found in the middle of the bandgap of the material.Whenamoderaten-typedopingisadded,theFermilevel rises from the middle of the bandgap towards the conduction band, by an increasing amount as the level of doping rises. When the level of n-typedopingbecomeslarge,theFermilevelcancrossthebottomof theconductionbandandbefoundinsidethisband(Motttransition). Thesemiconductorthenbehaveslikeametalandforthisreasonis called a semi-metal. In this case it is referred to as degenerate. In the caseofp-typedoping,thesemiconductorissaidtobedegenerate when the Fermi level is below the top of the valence band.1.2. Photodetection with semiconductors: basic phenomena Photodetection in semiconductors works on the general principle of thecreationofelectron-holepairsundertheactionoflight.Whena semiconductor material is illuminated by photons of an energy greater thanorequaltoitsbandgap,theabsorbedphotonspromoteelectrons fromthevalencebandintoexcitedstatesintheconductionband, wheretheybehavelikefreeelectronsabletotravellongdistances acrossthecrystalstructureundertheinfluenceofanintrinsicor externally-appliedelectricfield.Inaddition,thepositively-charged holesleftinthevalencebandcontributetoelectricalconductionby movingfromoneatomicsitetoanotherundertheeffectsofthe electricfield.Inthiswaytheseparationofelectron-holepairs generatedbytheabsorptionoflightgivesrisetoaphotocurrent,whichrefersbydefinitiontothefractionofthephotogeneratedfree charge-carriers collected at the edges of the material by the electrodes ofthephotodetectingstructure,andwhoseintensityatagiven 4 Optoelectronic Sensors wavelength is an increasing function of the incident light intensity. On thislevelwecandistinguishbetweentwolargecategoriesof photodetectorsbasedonthenatureoftheelectricfield,whichcauses thechargeseparationofphotogeneratedelectron-holdpairs: photoconductors,whichconsistofasimplelayerofsemiconductor simply with two ohmic contacts, where the electric field leading to the collection of the charge-carriers is provided by applying a bias voltage betweenthecontactsateitherend,andphotovoltaicphotodetectors, whichusetheinternalelectricfieldofap-norSchottky(metal-semiconductor)junctiontoachievethechargeseparation.Thislast termcoversp-njunctionphotodetectors(photovoltaicstructures consistingofasimplep-njunction,andp-i-nphotodetectorswhich includeathinlayerofsemiconductormaterialbetweenthepandn regionwhichisnotdeliberatelydoped),aswellasallSchottky junctionphotodetectors(Schottkybarrierphotodiodesandmetal-semiconductor-metal (MSM) photodiodes). Wewillnowbrieflyintroducethemainphysicalconceptsatthe rootoftheoperationofthedifferentsemiconductorphotodetector families.Heretheemphasisisplacedonaphenomenological description of the working mechanisms of the devices in question; the correspondingformalismhasbeendeliberatelykepttoanabsolute minimum in the interests of clarity and concision.1.3. Semiconductor devices Photoconductorsrepresentthesimplestconceivabletypeof photodetector: they consist of a finite-length semiconductor layer with anohmiccontactateachend(Figure1.1).Afixedvoltageof magnitude VB is applied between the two end contacts, in such a way thatabiascurrentIBflowsthroughthesemiconductorlayer,simply followingOhmslaw.Theactiveopticalsurfaceisformedfromthe regionbetweenthetwocollectionelectrodes.Whenitisilluminated, thephotogeneratedchangesproducedundertheeffectoftheapplied electricfieldleadtoaphotocurrentIPHwhichisaddedtothebias current, effectively increasing the conductivity of the device.Introduction to Semiconductor Photodetectors 5 Figure 1.1. Diagram of a photoconducting device Themainpointofinterestinaphotoconductingdeviceisits increasedgain,theresponseofphotoconductorsbeingtypically several orders of magnitude greater than that of photovoltaic detectors foragivenmaterial.Ontheotherhand,itsotheroperational parameters(bandwidth,UV/visiblecontrast,infraredsensitivity)are generallybelowthatofothertypesofphotodetectors,whichoften greatly limits the scope of its potential applications (this is particularly thecaseforphotoconductorsbasedonIII-Vnitrides,aswewillsee later on).1.4. p-n junctions and p-i-n structures Inp-ndiodes,themetallurgicallinkageofaregionofap-type dopedsemiconductorandaregionofn-typedopingformsap-n junction,wherethejoiningoftheFermilevelsinequilibriummostly occursthroughaflowofchargebetweenthenandpregions.In equilibriumwethereforefindaregionwithnofreechargecarriers immediately around the junction, similar to a charged capacitor, where thereare,onthenside,positivelyionizeddonorsand,onthepside, negativelyionizedacceptors(thiszoneisknownasthespacecharge region(SCR),whereionizeddonorsandacceptorsprovidefixed charges).Thepresenceofchargeddonorsandacceptorsproducesan electricfieldinthatregionwhichcurvestheenergybandsand,in equilibrium,formsanenergybarrierbetweenthetworegions:the 6 Optoelectronic Sensors bottom of the conduction band and the top of the valence band on the n side are below the corresponding levels on the p side (Figure 1.2).Figure 1.2. Curvature of the energy bands and mechanisms ofphotocurrent generation in a p-n junction ThewidthoftheSCRisadecreasingfunctionofthelevelof dopinginthematerial,whiletheheightoftheenergybarrierisan increasingfunctionofit.Anelectron-holepairproducedinthisSCR (situation2inFigure1.2)isthereforeseparatedbytheeffectofthe internalelectricfieldofthejunction,andsodoesnotrecombine. These are the charge carriers which contribute to the photocurrent, to which we can add, to some extent, those generated at a distance from the junction less than or equal to the diffusion length (situations 1 and 3inFigure1.2).Thebandstructureofthejunctionimpliesthatthe photocurrentwillconsistofminoritychargecarriers.Forthisreason, thephotocurrentflowsintheoppositedirectiontothebiasonthe diode, where the forward direction is defined as the direction of flow of the majority charge carriers (from the n to the p region in the case of electrons, and vice versa for holes). Moreover, the application of an opposingexternalelectricfield(VpVn>VBI, its value is E =V d [2.3] These approximations will be used throughout the remainder of the chapter unless explicitly stated otherwise. PIN Photodiodes for the Visible and Near-Infrared 19 2.2.2. Mechanisms of electron-hole pair generation 2.2.2.1. Radiative generation and optical absorption Electronic transitions between permitted levels in the valence band (VB)andlevelsintheconductionband(CB)canoccurunderthe actionofphotonstransferringtheirenergytotheelectrons.Thus,a photon can be absorbed, creating an electron-hole pair. This process of radiative generation, shown schematically in Figure 2.3, is the inverse oftheprocessofrecombinationwhichgivesrisetostimulated emission of photons in laser diodes. Itfollowsfromthisthattheonlyphotonsabsorbedefficientlyare those whose energy hQ is greater than the width of the bandgap EG of the material under consideration: hQ _ EG = EC EV[2.4] Figure 2.3. Radiative generation Thematerialistransparenttophotonswithlowerenergies.The parameter EGisthusacriterioninthechoiceofmaterialswhen designingaphotodetector.Opticalabsorptionischaracterizedbythe coefficient of absorption D (cm1), according to the relationship: dFFdz = [2.5] 20 Optoelectronic Sensors where F(cm2s1)isthephotonfluxpropagatinginthezdirection. The level of radiative generation GR (cm3s1), the number of electron-hole pairs created per unit volume and time, is therefore: GR =DF [2.6] Itfollowsfromthesedefinitionsthatthelevelofradiative generation in a homogenous material, for a photon flux F0 falling on a surface at z=0, can be written: GR =DF0expDz( )[2.7] We see that 1/D (cm) gives an order of magnitude for the distance requiredtoabsorbtheradiation.Furthermore,theknowledgeof variationofDwithphotonenergy(orwiththeirwavelength)is essential for the choice of materials for use in a photodetector. Figure 2.16showsgraphsforthemainsemiconductorsusedinthespectral domain under consideration in this chapter. TheshapeofthesegraphsandthemagnitudeofDdependonthe directorindirectnatureofthebandstructureofthematerial.This natureisdefinedinFigure2.4whichrepresents,forthetwotypesof material, the variations in energy of the electrons, with the wavevector k describing their motion in the periodic crystal lattice. Figure 2.4. Direct bandgap on the left and indirect bandgap on the right PIN Photodiodes for the Visible and Near-Infrared 21 For materials with a direct bandgap (such as gallium arsenide) the mainminimumintheconductionbandisfoundatthesamevectorkasthemaximuminthevalenceband.Furthermore,radiative transitionsmustsimultaneouslyconservetheenergyandmomentum of the particles involved (the photon and electron). The momentum of theelectronismuchgreaterthanthatofthephoton,andasaresult radiativetransitionsareeffectivelyverticalandconnectwithahigh probability those states at the top of the VB and those at the bottom of the CB. The opposite is true for materials with an indirect bandgap (such as silicon),andradiativetransitionsrequiretheinvolvementofthethird particle,aphonon,toprovidethedifferenceinmomentumbetween theinitialandfinalstates.Thesetransitionsaremuchlessprobable and D grows much less quickly with the energy of the photons above EG.2.2.2.2. Non-radiative generation Aswellastheradiativeprocessestherearealsonon-radiative processesofgeneration-recombination.Thus,intheSRH(ShockleyReadHall)processshowninFigure2.5ingenerationmode,the required energy is borrowed from the thermal motion of the crystal lattice.Thisisoneofthecontributionstothedarkcurrentof photodetectors, a detrimental parasitic phenomenon. Figure 2.5. Non-radiative SRH generation 22 Optoelectronic Sensors The transition takes place in two parts, via a deep state of energy ET, which is close to the middle of the forbidden band and is the result of a crystal defect (impurity, vacancy, etc.). The rate GNR (cm3s1) of SRH generation-recombination can be written [SZE 81, p. 35]: GNR =VnVpQthNTni2np( )VnnniexpET EIkT(())

lllllVpp niexpET EIkT(())

lllll[2.8] with the following notation: VnandVpcapturecross-sectionsforelectronsandholesbythe deep state; vth, thermal velocityQth = 3k T m*( )( ); NT, density of deep states; ni, intrinsic electron density; n and p, electron and hole densities; EI, middle of the forbidden band; kT, Boltzmann factor. Inthedepletedregionofaphotodiodewehavenp = ni2.Ifwe furtherassumethatVn=Vp=VandET= EI,anddefineaneffective lifetime Weff:GNR = niQthNT2 = niWeff[2.9] We also know that: ni2= NCNVexpEGkT( )[2.10] where NCandNVaretheequivalentdensitiesofstatefortheCBand VB. We can draw the following conclusions from this: PIN Photodiodes for the Visible and Near-Infrared 23 GNR increases very rapidly as the ratio EG/kT decreases; GNR is not an intrinsic characteristic of the material, but depends for its purity on NT.Inanelectricallyneutralregionoftypep(n),wheretheelectron (hole)deficiencyrelativetothermodynamicequilibriumisGn(Gp),if wedefineWn(Wp)asthelifetimeoftheminorityelectrons(holes),it follows that: GNR =GnVQthNT=Gn Wn[2.11] SRH non-radiative generation is particularly active at the surface ofdevices,wherethedensityofdefectsisveryhigh.Itcanbe reducedbyapassivationtreatment;forsiliconthemosteffectiveis thedepositionofitsnaturaloxideSiO2,silica.Anotherprocessof non-radiativegenerationisshockionizationwhichoccursina semiconductormaterialunderastrongelectricfield.Itgrowswith EG and the breakdown field is of the order of EB = 105V/cm for the materialsconsidered.Thiseffectisonecauseofbreakdownin diodes,limitingthereverse-biasvoltagethatcanbeapplied.Itis exploitedasagainmechanismintheavalanchephotodiodeswhich aredescribedinChapter3,andwhosestructureisoptimizedwith this in mind. 2.2.3. Transport mechanisms Thechargecarriers,electronsandholesgeneratedbythe aforementionedprocesses,aretransportedinthedevicetothetwo electrical contacts that transfer it to the external circuit specifically, to the load resistance across the terminals, across which the electrical signal is measured. 24 Optoelectronic Sensors 2.2.3.1. Transport under electric field and resultant current In the depleted region of a photodiode (normally reverse-biased) an elevated electric field is present, and the electrons and holes are driven ataspeedwhichdependsontheintensityofthefield,asshownin Figure 2.6. Figure 2.6. Characteristics Qn(E) and Qp(E) in logarithmic coordinates ForelectricfieldssuchthatE 104 V/cm, the velocities are fairlyconstantandequaltoasaturationvelocityoftheorderof vs= 107cm/s.Betweenthesetworegions,andforcertainmaterials, theelectronvelocitypassesthroughamaximum(highmobility regime). PIN Photodiodes for the Visible and Near-Infrared 25 2.2.3.2.Transportalongtheconcentrationgradientanddiffusion currentIn the contiguous electrically neutral regions in the depleted region, electronsandholescanbetransportedintheabsenceofanelectric field under the effect of their concentration gradients. Their fluxes Fnand Fp can be written: Fn, p = Dn, p 0n, p0z[2.13] where Dn, p = Pn, pkT q cm2s( ) are the diffusion coefficients. Thevariousrecombinationprocessesarealsoactiveinthese regions,suchthattheelectronsandholesareonlyefficiently transportedoveradistanceknownasthediffusionlengthandgiven by: In, p = Dn, pWn, p[2.14] 2.3. Static characteristics of PIN photodiodes 2.3.1. I/V characteristics and definition of static parameters Figure2.7showsI/Vcurves,linkingthecurrentcrossinga photodiodetothevoltageacrossitsterminalsforthreeillumination conditions. From this we can extract the parameters commonly used to characterizephotodiodeoperation,whoserelationstothestructureof the device are described in the following sections. The photocurrent IPproducedby aphotodiodeisproportionaltotheilluminationacrossa largerangeofopticalpowerP.Thecoefficientofproportionalityis theresponsecoefficientR (A/W)(responsivity),nottobeconfused withthesensitivity,whichmeasurestheminimumopticalpower detectablebyanopticaldetector,andwhichdependsonthecircuit intowhichthephotodiodeisinsertedandthespecificationsofthe signal to be received.26 Optoelectronic Sensors Figure 2.7. I/V characteristics of a photodiode, inserted in the circuit shownand under several illumination conditions TheexternalquantumefficiencyKelinksthegeneratedelectron flux to the incident photon flux. Thus, we have: R =IpP=qhQ Ke[2.15] where q is the charge of an electron and hQ is the energy of a photon. ThedarkcurrentI0,discussedinsection2.3.3,iscausedbynon-radiative generation and/or the tunnel effect. ThesaturationcurrentIMisthephotocurrentabovewhichseveral mechanisms limit the linearity of the response: the intrinsic mechanism, due to the screening of the electric field inthedepletedregionbythespacechargethatisproducedbythe mobile charge carriers created by the illumination (see section 2.3.4); PIN Photodiodes for the Visible and Near-Infrared 27 thecircuit-dependentmechanism,causedbythevoltagedrop across the load resistance (see the circuit in Figure 2.7). Again,characterizedbythemultiplicationcoefficientMdefined by: 0 pIMI I=[2.16] canbeobtainedunderahighreverse-biasvoltageVAVinavalanche photodiodes (see Chapter 3). The breakdown voltage VB is the highest reverse-bias voltage the diode can support. For V=VB the dark current growsveryrapidlyandthepowerdissipatedinthediodecanleadto its destruction. 2.3.2. External quantum efficiency Theexternalquantumefficiencydefinedabovecanbethoughtof astheproductofaninternalquantumefficiencyKiandanoptical efficiencyKo,theratioofthephotonfluxenteringthedevicetothe fluxofphotonsincidentonitssurface.Thesetworatios,whichare bothdependentonthewavelength,areconsideredinthefollowing text.2.3.2.1. Optical efficiency Theopticalrefractiveindexnofthesemiconductorsunder considerationisintheregionof3,andasaresulttheincidentlight raysarerefractedandreflectedatitssurface.Atnormalincidence, usedasthereferencesituation,theFrenseltransmissioncoefficient determines the optical efficiency: Ko =4nn1( )2[2.17] which is of the order of 70% and depends little on the wavelength and theangleofincidence.Itispossibletoachieveopticalefficiencies close to 100% at a given wavelength O, by depositing an antireflection 28 Optoelectronic Sensors coatingonthesurface,forexampleofrefractiveindexnand thicknessO 4 n( ). The optical efficiency therefore depends on O and on the angle of incidence. 2.3.2.2. Internal quantum efficiency Theelectron-holepairscreatedbytheabsorptionofphotons entering the device may, or may not, give rise to a current flow in the externalcircuit,dependingonwheretheyaregeneratedinthe structure.Ifgenerationisinthedepletedregion,theelectronsand holesareseparatedbytheelectricfield,asshowninFigure2.1, leading to the passage of one electron for each absorbed photon: thus, theinternalquantumefficiencyis100%.Inthecaseofgenerationin theelectricallyneutralPandNregions,wheretheelectricfieldis weak,onlytheelectrons(orholes)generatedlessthanonediffusion lengthawayaretransportedintothedepletedregion,andtheinternal quantum efficiency is in most cases weak. Itisthereforedesirabletodesignaphotodiodeinsuchawaythat theradiationshouldbeentirelyabsorbedinthedepletedregion. Figure2.8showsamodelwhichprovidesagoodevaluationofthe internal quantum efficiency of a PIN photodiode, as a function of the nature of the material on whose surface the radiation falls. The curves 1 and 2 represent the profiles of the radiative generation rate GR across two structures. The structure for curve 1 is that of a homojunction PIN, whereallofthematerialsusedhavethesamewidthofbandgap, which is below the energy of the photons to be detected. The radiation is assumed to be incident from the p side, and part of the radiation is absorbedthere,wherethequantumefficiencyisnegligible.Another part is absorbed in the i region, and has a quantum efficiency of 100%. Finally, the contribution of the residual radiation entering the n region is also negligible. The quantum efficiency can therefore be written: Ki =expDdp( )1expDd( )

lll[2.18] where the definitions of dP and d can be found in Figure 2.8. PIN Photodiodes for the Visible and Near-Infrared 29 Depleted regionFigure 2.8. Optical generation rate across the structure of two PIN photodiodes: curve 1 shows a homojunction PIN photodiodes;curve 2 shows a heterojunction PIN photodiode Curve2correspondstoaPINphotodiode,withthecapitalP indicating that the material in the P region has a bandgap width greater thantheenergyofthephotonstobedetectedandwhichistherefore transparent to them. The same reasoning provides us with the quantum efficiency: Ki =1expDd( )[2.19] 2.3.3. Dark current The dark current is the sum of several contributions: non-radiative generatedcurrentsrequiringaninputofenergy(suchastheSRH process)andthetunnelingcurrent,whichdoesnotrequiresuchan input.ThesetwoprocessesarerepresentedinFigure2.9forasharp p+n homojunction. 30 Optoelectronic Sensors 2.3.3.1. Generation currents Accordingtoequation[2.9],thedarkcurrentcontributionof generation in the depleted region is: I0 = SdGNR = SdniWeff[2.20] Taking account of equation [2.11] of the fact that the shortage of electrons(holes)inthep(n)materialnearthedepletedregionis 2, ,i ADn p n N G =and the fact that the thickness of the p(n) material is Ln,p (see section 2.2.3.2) the generation contribution in the neutral p and n regions can be written: I0 = Sqni2LnNAWn LpNDWp( )[2.21] This is the traditional expression for the reverse current of a diode according to Shockley. Figure 2.9. Profile of the VB and the CB of a reverse-biased p+n junction.The generation process (shown here in the depleted region) requires aninput of energy; the tunnel process occurs at constant energy PIN Photodiodes for the Visible and Near-Infrared 31 Thus,weseefromequations[2.20]and[2.21]thatthegeneration current is primarily a function of ni and varies very rapidly with EG/kT.2.3.3.2. Tunneling current Usingthetunnelingeffectelectronscanalsobetransportedata constantenergyacrossthetriangularpotentialbarrierpresentatthe junction,aslongasitisnarrowenough.Acalculationofthecurrent gives the following expression [STI 82]: IT= S2m*q3EV4S3h2EG1 2expS 2m* EG3 24qhE(())

[2.22] where E=V/distheelectricfieldinthedepletedregion,whichis constant for a PIN diode. From equation [2.22] we determine that, for agivenmaterial,ITincreasesveryrapidlywiththevoltageVacross theterminalsofthediode,mostlyasaresultoftheincreaseinE.Additionally,ITincreaseswhenEGdecreases,suchthatthe contributionofthetunnelingcurrenttothedarkcurrentismost significant for photodiodes made of materials with a small bandgap. 2.3.4. Breakdown voltage 2.3.4.1. Zener breakdown via the tunneling effect Theveryrapidvariationofthetunnelingdarkcurrentwiththe reverse-biasvoltageisthefirstprocessofbreakdown.Thismainly appliestomaterialswithanarrowdepletedregionandasmall bandgap; the two parameters which reduce the width and the height of the potential barrier at the PI junction. The tunneling effect can be the dominantoneinthematerialsusedfordetectionofthelongest wavelengthsconsideredinthischapter(seesection2.5.3.2),ifthe doping level of the i zone is too high [TAK 80]. 32 Optoelectronic Sensors 2.3.4.2. Avalanche breakdown WecandefineacriticalelectricfieldEC,oftheorderof 2 x 105 V/cm for the lightly-doped materials considered in this chapter, wherethemultiplicationcoefficientbecomesinfiniteandleadsto breakdown. In the case of PIN photodiodes, which are not designed to takeadvantageofavalanchegain,breakdowncanariselocally,most often around the edge of the junction where the point effect increases theelectricfield.Thebreakdownvoltageisthereforeapproximated below by: VC = ECd [2.23] 2.3.5. Saturation current 2.3.5.1.Extrinsiclimitationbythevoltagedropacrossthe load resistance Inordertohavealinearresponse,thephotodiodemustremain reverse-biased(V>1,andalltheilluminationisabsorbedclosetothePijunction.Wefurther assume that the mobile electrons in the i region are transported with the saturation velocity vs, independent of the electric field. Figure2.10showsthedensityprofilesofthefixedandmobile chargesandtheelectricfieldprofileacrossthestructure.Giventhe hypothesessetoutinthissection,itfollowsthatthechargedensity duetoelectronsis,sJ U Q =whereJisthecurrentdensity,the electricfieldvariationinthedepletedregionisG E = Ud Handthe maximum current IM, obtained whenG E = EB, can be written: IM=CJQsEB[2.26] where CJ is the capacitance of the junction. Depleted regionDepleted regionFigure 2.10. Space charge density and electric field, for I=0 (dotted line) and for I=IM (solid line). For I=IM, the electric field varies from 0 to the breakdown field EB34 Optoelectronic Sensors Note that, for this value of current, the voltage across the terminals of the junction is V = EBd 2 =VB2 [2.27] We can easily show that, regardless of the components in the bias circuit,thepartofthecurverepresentingthevariationoftheelectric fieldinthedepletionregion(marked:)rotatesaroundafixedpoint as the photocurrent varies. Its position depends on the values of V0 and RL;Figure2.10providesanexamplewhere RL=0andthevoltage across the diode terminals is constant and equal to the bias voltage V0= VC/2.2.4. Dynamic characteristics of PIN photodiodes 2.4.1. Intrinsic limitations to the speed of response 2.4.1.1. Transit time in the depleted region Thetransittimeofphotocarriersinthedepletedregionisthefirst limit to the response time of the photodiode. Its analysis is carried out here with the same approximations as in section 2.2.1, which is a good representation of the properties of real PIN diodes. Figure 2.11 shows the electric charge profile in the depleted region at a time t after a brief impulse signal, of energy W0, which was applied to the photodiode at time0.Thepacketofgeneratedelectronsistransportedatspeedvsand takes time Wt=dvs to cross the depleted region. Depleted regionFigure 2.11. Density of mobile charges produced in the depleted region of a PIN photodiode in response to an optical impulse G (z, t) PIN Photodiodes for the Visible and Near-Infrared 35 Figure 2.12. Impulse and frequency response of aPIN photodiode limited by the transit time The solution of Maxwells equations for the case RL=0 shows that the current generated by the diode is the rectangular impulse shown in Figure 2.12, of duration Wt and of intensity: I0 = q hQ( )W0Wt[2.28] ThefrequencyresponsecanthenbeobtainedbyFourier transformingtheimpulseresponse.ThisisshowninFigure2.12and given by: I f( )= I0sinS f Wt( ) S f Wt[2.29] The 3 dB cutoff frequencyI f()I0 =1 2( )is: ft =0.44 Wt[2.30] Weseethatthisvariesas1/d.InthecasewhereDd Iph0),the limitationonthegainisimposedbythedarkcurrentandinthese conditions, which can occur with Ge APDs, we have: Mmax ~VBn Id0R[3.20] 3.4.2. Noise in avalanche photodiodes NoiseindetectorsisdiscussedinChapter7andwewilllimit ourselvesheretorevisitingthemainresultsfornoiseassociatedwith theoperationofAPDsintheavalancheregime.Intheabsenceof multiplication,theAPDbehaveslikeatraditionalphotodiodewhose noiseisessentiallyshotnoisecausedbythedarkcurrentId0andthe primaryphotocurrentIph0acrossthejunction,andwhosespectral density is: i2=2 q Id0 Iph0( )[3.21]WhentheAPDoperatesintheavalanchesystem,thecurrents across the junction undergo a multiplication M, and hence the spectral densityofthenoiseismultipliedbyM2.Therandomnatureofthe impactionizationprocessresultsinafluctuationinthegains associated with the different carriers, contributing to the appearance of Avalanche Photodiodes 69 extranoiselinkedtothemultiplication.Thespectraldensityofthe shot noise of the multiplied current can be written: i2=2 q Id0 Iph0( ) M2 F M( )[3.22]where F(M),theexcessnoisefactor,representsthecontributionof multiplicationtothenoise.ThevalueofF(M)dependsonthe characteristicsofthep-njunctionandonthenatureoftheprimary carriers.F(M)expressionsforthetwotypesofprimaryinjection, electronsandholes,havebeenderivedbyMcIntyre[INT66]under theassumptionofanavalancheregionwithaconstantelectricfield. These are expressed as a function of M and the ratio of the ionization coefficientsk=Ei/Di,whichisconsideredconstant.Instancesofa pureinjectionofelectronsorofholesareofparticularinterest.The excessnoisefactorforaprimaryinjectionofelectronscanbe expressed by the following: FnM( )= Mn1 1k( )Mn 1Mn(())

2

llllll[3.23]and for a primary injection of holes: FpM( )= Mp1 11k(())

Mp 1Mp(())

2

llllll[3.24]Where Mn,p>>1,theseequationscanbeexpressedinthe following simplified forms: FnM( )= kMn 2 1k( )[3.25] FpM( )=1kMp 2 11k(())

[3.26]and for very high values of multiplication: 70 Optoelectronic Sensors FnM( )kMnand FpM( )1kMp[3.27]Inthespecificcaseofionizationbyonlyonetypeofcarrier, electronsorholes,theexcessnoisefactortakesaminimumvalueof F(M)=2,independentofM.Attemptscanbemadetoapproachthis valuethroughmodificationoftheionizationenergyorbycareful designofthedevice.Thetypicalvariationofthenoisefactorasa function of M for different values of k is shown in Figure 3.3. Figure 3.3. Excess noise factor as a function ofdifferent values of k for a pure injection of holes In order to obtain low excess noise values, two conditions must be met: the multiplication must be triggered by the more ionizing carrier, andamaterialmustbeusedwhoseionizationcoefficientsarevery different. Among the normal semiconductors (Si, Ge, GaAs, InP, etc.), onlysiliconsatisfiesthesetworequirements.Furthermore, considerationoftheexcessnoisefactorallowsustoapproachhigh values of the ratiok = EiDi, with this parameter playing an important role in the optimization of APDs. Finally, in the literature, the excess noise factor F(M) is often written in the form: F M( )= Mx[3.28]Avalanche Photodiodes 71 which comes directly from the spectral density of the noise, expressed as:i2=2 q Iph0M2x[3.29] The exponent x, which depends on the value of the k ratio, allows us to compare the different devices. This can often be found in device specifications alongside the value of F(M) for a given M. For k = 1, the excess noise factor is F(M) =M for the two types of injection, and the exponent xthereforetakesthevaluex =1.Forlowvaluesofk,the multiplicationistriggeredbyelectrons,whereasforhighvaluesof k,the injection of holes is favored. 3.4.3. Signal-to-noise ratio in avalanche photodiodes Inwidebandapplications,thelimitingnoiseoftraditional photodiodescomesfromthethermalnoiseassociatedwiththeload resistanceRLor,morecommonly,fromthenoiseofthefirststageof theamplificationcircuitrequiredtomakeuseoftheelectricalsignal producedbythephotodiode.Forsomeapplicationtypes,theinternal gain of APDs allows us to improve the signal-to-noise ratio (SNR) of thedetector.Thisdetector,consistingoftheAPDandamplifier, includestwosourcesofnoiseoutsidethediode,independentofthe multiplication (the load resistance and the amplifying stage), given by the equation: iext2=4kBTeRL 'f [3.30]where Te is the equivalent temperature of the noise, and also includes sources of shot noise connected with the multiplication process: iM2= 2q Id0 Iph0( ) M2 F M( ) 'f [3.31] where 'fis the bandwidth of the system. The mean squared value of the photocurrent is given by: 72 Optoelectronic Sensors iph2=12m2 Iph02 M2[3.32] where m is the modulation index of the incident light signal. The SNR for a system with bandwidth 'ftherefore follows the relationship: SB =12m2 Iph02 M2( )2q Id0 Iph0( ) M2 F M( )4kBTeM2 RL

lllll 'f[3.33] which can be rearranged into the following form: SB =12m2 Iph02( )2q Id0 Iph0( ) F M( )4kBTeM2 RL

lllll 'f[3.34]demonstrating the advantage of APDs over PIN photodiodes, since for low values of F(M) the thermal noise contribution is divided by M2.Figure 3.4. Variation of the SNR as a function of the gain Mfor two semiconductors, silicon and germanium As the gain increases, the SNR grows and reaches a maximum for anoptimalgainvalueMopt,whichdependscloselyonthepointat Avalanche Photodiodes 73 which the multiplied shot noise and the thermal noise are equal, such that, in the case where Id0 Di/Ei, the gain-bandwidthproductisconstant.ThegainMvarieswithfrequency according to the following law: MZ()=M01 M02Z2W2

lll12[3.42]where M(Z)andM0arethevaluesofthegainasafunctionofthe frequencyf=Z/(2S)andforaconstantsignal.Thegain-bandwidth product is given by: MZ() 'f = Nbk W1( )1[3.43] anddependsonthematerialthroughkandthecharacteristicsofthe avalancheregionthroughW1=la/vsat,wherelaisthelengthofthe avalanche region. It follows that the product will be much larger if the ratio kofthecoefficientsofionizationisweakandiftheavalanche regionisnarrow.Ahighvalueofthegain-bandwidthproductis desirable as it allows a higher value of gain for a given frequency. 3.5. Technological considerationsAPDsworkbestwhentheyarebiasedwithavoltageclosetothe volume breakdown voltage in the active region. As a result there is a very intense electric field (~4-5 x 105 V/cm) present in the avalanche region,whichmustbeashomogenousaspossiblethroughoutthe active region. Any inhomogenity present in the SCR that can cause a local increase in the electric field will lead to a premature breakdown whichwilldegradetheAPDperformance.Theseinhomogenitiescan becausedbythestructureitself,asinatraditionalplanarjunction obtainedbylocalizeddiffusioninacirculargeometry,orlinkedto imperfectionsinthecrystalstructure.Regardlessoftheirorigin,they always need to be eliminated. Avalanche Photodiodes 77 In the first case, the use of junctions with a guard ring or the use of a mesastructureallowsthesuppressionofperipheralbreakdown,as longasageometryisusedwhichisfreefromangularpartsliableto cause point effects. The suppression of crystal defects depends closely ontheprogressoftechnology,particularlyinthefieldsof crystallogenesis and techniques of epitaxial growth and doping. Figure 3.5. Cross-section of a planar photodiode 3.5.1. Guard ring junctions Forajunctionconstructedusingplanartechnology(Figure3.5), theelectricalfieldinsidethedepletedregionishigherinthecurved regionaroundtheedgeofthediffusedareathanintheactiveregion, as can be seen by solving Poissons equation [HAR 91a]. Breakdown duetoedgeeffectsthereforeoccursforavoltagesufficientlybelow the breakdown voltage of the active region so that light falling on the central region is not amplified or barely amplified. On the other hand, iftheilluminatedregionextendsbeyondthediffusedarea,the increaseintheinjectedglobalphotocurrentduetothehighelectric field present in a very narrow annular region around the edge can give theillusionofaphotomultiplicationeffect.Regardless,sucha photodiode cannot operate as an APD. In order to suppress peripheral breakdown,twokindsofstructuresarecommonlyused,whichhave annular guard rings modifying the electric field distribution around the outer perimeter. In the first structure (see Figure 3.6a), the guard ring is formed by anannulardiffusedjunctionwhichisrelativelyweaklydoped,and quite deep in order to increase the radius of curvature and thus reduce theperipheralfield;theactiveregionisobtainedbyashallower 78 Optoelectronic Sensors diffusionatahigherconcentration,partiallyoverlappingtheguard ring. The breakdown voltage of the gradual junction of the guard ring is much larger than that of the active region, because for a given bias voltage, the extent of the SCR is larger in the former than in the latter. Figure 3.6. Cross-section of (a) an APD with a traditional guard ring and (b) a PPN+ APDIn the second structure (see Figure 3.6b), the guard ring and active regionjunctionsarecreatedbydiffusion orionimplantationwithina weakly-dopedsubstrateS.Then+Sguardringjunctionwhich surroundsthen+pjunctionoftheactiveregionismuchdeeperthan thelatter,buttheweakconcentrationinthesubstrateprecludes breakdown.ThisisthePSPN+structure.Whenthen+Sjunctionis notvery deep,orevensuperficial,theaddition ofa guardringofthe first type is necessary to avoid peripheral breakdown. This is referred to as a P+SPSN+ structure. 3.5.2. Mesa structuresIn mesa structures, the footprint of the active region of the APD is definedbychemicaletchingorbydryetchingfollowedbysurface reconstruction using a suitable chemical bath. This structure, shown in Figure 3.7, offers the sometimes deceptive advantage of simplicity. It allowsustoreducethecapacitanceofthedevice,whileeliminating theguardringjunction.However,theextensionoftheavalanche region at high electric fields outside the edges of the etched region can leadtomigrationofsusceptibleionspecies,causingagrowthinthe dark current which is often accompanied by instability of the diode. In order to avoid these drawbacks, different passivation techniques have Avalanche Photodiodes 79 beenusedwithmoderatesuccess,whichmakessuchastructure difficult to commercialize on account of its lack of reliability. Figure 3.7. Cross-section of a mesa APD 3.5.3. Crystal defects and microplasmas Crystaldefectssuchasdislocation,stackingfaults,metallic precipitation,etc.,presentinaPNjunctionintroducelocalizedor microplasmabreakdowns:isolatedregionsofafewm2wherehigh current densities cross, and which appear at well-defined bias voltages whichmayormaynotbeclosetothevolumebreakdownvoltage. Unlessthesemicroplasmasappearatavoltageveryclosetothe breakdownvoltage,theirpresencedecreasesAPDperformanceby limitingthephotomultiplicationfactortothatofthebreakdown voltageofthefirstmicroplasma.Athighervoltages,thenoiselinked toelectricaldischargestriggeredbytherandominjectionofcharge carriersinthemicroplasmaissosignificantthatitprecludesany interestintheuseofsuchdiodes.InthecaseofSiAPDs,inspection underamicroscopeallowsthemicroplasmastobevisualized, appearingintheformofbrightredspots.Intheabsenceof microplasmas,adiffuse,palelightuniformlyilluminatesthewhole active surface when the breakdown voltage is reached. Observation of the current induced in a scanning electron microscope also allows the detectionofinhomogenitiesintheelectricfield.Inaddition,the presence of microplasmas leads to vertical jumps of several A in the inverse characteristics Id(V), interspersed with resistive sections in the relationship,thusenablingtheelectricalsortingofAPDsthrough systematicmeasurementoftheId(V)characteristics viaprobes. Microplasmascanbeeliminatedusingsubstrateswithalowlevelof 80 Optoelectronic Sensors dislocationsandnon-aggressivefabricationtechniquestailoredtothe specificmaterialsused.Theconstructionofhigh-performance, reliabledeviceswithahighfabricationyielddependscloselyonthe quality of the base material and on the standard of technology used in each stage of the fabrication. 3.6. Silicon avalanche photodiodes Silicon, an indirect-bandgap semiconductor, with a bandgap energy Eg=1.1eVatambienttemperature,issensitivetolightinthe wavelength range of 0.41.1 m. The absorption length, considerably lessthan1matO=0.4m,variesbetween10and10minthe wavelengthrange0.80.9m,thefirsttransmissionwindowfor opticalfibers(attenuation~2dB/km),andismorethan200matO=1.06m,whichistheemissionwavelengthoftheNdlasersthat areverypopularinmilitaryapplications.Also,theionization coefficientsofelectronsandholesareverydifferent,withelectrons havingthehigherionizationenergy(Di>> Ei).Thesecharacteristics playanimportantroleinthedesignofdevicestargetedatdifferent applications, with the aim of achieving a weak excess noise factor and an acceptable compromise between sensitivity and response time.3.6.1. Si N+P APDs Si APDs with an abrupt-junction N+P structure are fabricated on a P substrate with a concentration around 1016cm3. As the width of the depleted region is between 2 and 3 m, these APDs are well-suited to thedetectionoflightsignalswithwavelengthsbelow0.7m(ruby lasersemitat0.63m).Commercializedin1966,theywereinitially developed for military applications such as laser telemetry at 1.06 m, takingadvantageofanatmospherictransmissionwindowallowing targeting at 2025 km with high precision (of the order of a meter). Avalanche Photodiodes 81 For the first APDs we will study, the guard ring and active region junctionsaremadebyadoublediffusionofphosphorimpurities, maskedusingalayerofsilicaobtainedbythermaloxidation;the fabricationconditionsforthedifferentstagesoftheconstruction procedurehavebeendevelopedtoensurehighperformanceinterms ofthedarkcurrentandphotomultiplication,alongwithahigh fabrication yield. The homogenity and reproducibility of phosphor ion implantationusedasapredepositiontechnologyhavegreatlyhelped theachievementofmicroplasma-freeAPDs.Additionally,thechoice ofsubstrateswithfairlyhighdislocationlevels(~3,000cm2),but whicharestableundervariousthermaltreatmentsathigh temperatures(T1,0001,200C),hasallowedtheattainmentof fabrication yields considerably higher than 50%, whereas they were at bestaround20%withthezerodislocationsubstratesadvocatedin the literature. These APDs, with a breakdown voltage VB~ 60 80 V, offer M(V)characteristicswhichvaryextremelyrapidlyasbreakdownis approached, with the exponent n in the Miller equation taking a value closeto4.AtshortwavelengthsabsorbedintheN+layer,the multiplication is initiated by holes. For O > 0.7 m, the multiplication ismostlyinitiatedbyelectronsandtakeshighervalues.Atthe operatingpoint,M~50to100,withthegradientdM/dVverylarge. ToavoidissueswithvariationsinM,theratioV/VBmustbekept constant.SincethebreakdownvoltageVBfollowsvariationsin temperature,somesystemofregulationisrequired.Theinvolvement ofaZenerdiodewithabreakdownvoltageclosetothatoftheAPD hasallowedthemultiplicationtoberegulatedwithinthetemperature range from 30C to +80C. Other regulation systems make use of the noise linked with multiplication. TheimpulseresponseofSiN+PAPDs(seeFigure3.8)is dominatedbythediffusiontimetDiffofthechargecarriersgenerated outsidethedepletedregion.Itconsistsofabriefrisetothesignal ( 'Ev or ofholeswhen'Ec< 'Ev.Forexample,inthecaseofthe InAlAs/InGaAspair,anelectronwhichundergoesatransitionina barrierregioncrossestheinterfaceandfallsintotheadjacentwell, gaininganenergy'Ec,oralternativelybenefitsfromanartificial reduction in its ionization energy, thus favoring ionization in the wells. Conversely,movementfromawelltoabarrierreducestheionizing poweroftheelectronwithinthebarrier.Thecrossingofnumerous barrier-wellinterfacesinsuccessiontranslatesintoanincreaseinthe multiplicationtriggeredbytheelectrons,equivalenttoanincreasein DI. On the other hand, the ionizing power of the holes traveling in the oppositedirectionislessfavored,andoverallthisresultsina reductionoftheeffectiveratioofionizationcoefficientsk =EI/DI,leadingtoareductionintheexcessnoisefactor.When'Ev> 'Ec,suchasinInP/InGaAs,itistheionizingpowerofholeswhichis favored,leadingtoareductionintheratioDI/EIforthisstructure. Pairsofmaterialswithveryasymmetricbandgapdiscontinuitiesare favored; thus, the combination of In0.52Al0.48As/In0.53Ga0.47As ('Ec = 0.55 eV, 'Ev= 0.2 eV) is more favorable than InP/In0.53Ga0.47As ('Ec= 0.22 eV, 'Ev= 0.38 eV). The number of barrier-well layers and the 102 Optoelectronic Sensors thicknessofthoselayersbothhaveasignificantinfluenceon performance. Uptonow,thebestperformanceshavebeenobtained[WAT97] foraplanarAPDwithanimplantedTiguardringwithaMQW multiplication layer of InAlGaAs/InAlAs (0.27 m, 13 repeats) and an absorptionregionofInGaAsP(1.3m,p =8u1015 cm3)separated by a thin doped layer of InP-P+ (0.04 m, p = 4 u 1017 cm3) in order toreducetheelectricfieldbetweenthetworegions.TheseAPDsare characterizedbyaweakdarkcurrentof0.36AatM =10,a bandwidthof15GHz,again-bandwidthproductof110GHz,a responsecoefficientof0.8A/Wat1.55m,anexcessnoisefactor F(M) ~ 3 atM = 10 and a high reliability. They are well fitted to the specifications of high-sensitivity 10 Gbit/s receivers. 3.10.2. Spin-orbit resonance APDs 3.10.2.1. GaAlSb/GaSb APDs The strong increase in the ionizing power of holes which is seen in Ga1xAlxSb/GaSb APDs with x ~ 0.05, sensitive at 1.3 and 1.55 m, is linked, according to the interpretation of Hildebrand et al. [HIL 81], to theionizationmechanismforholeswhichcausesthe valencebandto besplitintwoviaspin-orbitcoupling.Theresultisthat,aroundthis composition, the structure of the energy bands specific to this material hastheunusualpropertyofhavingabandgapenergyEgclosetothe difference in energy ' separating the maximum values for the valence band and the additional split band. If 'Ego1, through the resonance effect, the ratio of the ionization coefficients E/Do and the ionization energy of holes is equal to Eg.Subsequent construction of Ga1xAlxSb/GaSb APDs with x ~ 0.05 has madeitpossibletoobtaindeviceswithaweakexcessnoisefactor F(M)=3.8atM =10,correspondingtoavalueofk =EI/DI~5,but much lower than the value of 20 to 30 that has been anticipated, and a gain-bandwidth product of 90 GHz [KAT 90]. These performances are higherfortheseparametersthanthoseobtainedwithcomparable Avalanche Photodiodes 103 InGaAs/InP APDs; however, the inability to reduce and stabilize their darkcurrentortofabricateaplanarAPDhasledtothese investigations being abandoned. 3.10.2.2. HgCdTe avalanche photodiodes Research into ternary, mercury-rich alloys Hg1xCdxTe, which had alreadybeenexploredwiththeaimoffabricatingdetectorsfor military applications in the infrared windows at 3.5 m and 814 m, wasextendedatthestartofthe1980sforthedevelopmentof alternativestoGeAPDdetectorsforfiber-optictelecommunicationsat 1.3 m and 1.55 m. The alloys with cadmium-rich compositions (x~0.70.6)correspondingtothesetwotransmissionwindowsoffer the same electronic properties of spin-orbit coupling, which offers the opportunity to develop APDs with performances similar to Ga1xAlxSb.AmethodhasbeendevelopedforgrowingHg1xCdxTewafers withagivenstochiometriccomposition,allowingtheconstructionof p-typesubstrateswithdopinglevelsaround2u1016cm-3,40mmin diameter, with a high homogenity in terms of doping, and a low level of dislocations. The devices are constructed in a planar structure using traditional techniques of insulator deposition by cathode bombardment, andphotolithography.Then-typeguardringisobtainedbymercury diffusion.Theactiveregionjunctionismadebyionicimplantation (Al++,65keV,1014ionscm-2)followedbyredistributionannealing. The result is a PIN junction. Compositions with x close to 0.6 are the most suitable, because they cover both transmission windows and also give the highest values of the ratio EI/DI [ORS 87], with the best being thecompositionwithx =0.62,Eg=0.72eVandEI/DI=30. Encouraging initial results obtained in terms of dark current, response coefficientandexcessnoisefactorhavenotbeenconfirmedatthe predevelopment stage. 104 Optoelectronic Sensors 3.11. Prospects Alargeproportionoftheworkinprogressisaimedatthe developmentofdevicesforhigh-bitratecommunications(20to40Gbit/s)thatarebothfastandlow-noise.Particularlysignificantis theworkonSi/InGaAsAPDs,waveguideMQWAPDsandlow noise APDs with a very thin multiplication region. 3.11.1. Si/InGaAs APDs TheseAPDs,combiningtheverylowexcessnoisefactorofSi APDswiththestrongabsorptionofInGaAs,shouldsimultaneously allowhighquantumefficiencyandahighbandwidth,ahighgain-bandwidthproductandalowlevelofnoise.Preliminaryresults obtainedforSi/InGaAsstructuresfabricatedusingthetechniqueof waferfusionareverypromising:bandwidthsof13GHzforgainsof 135,correspondingtoagain-bandwidthproductof315GHzhave beenmeasured.However,thedarkcurrentisraisedverycloseto breakdown and is unstable under a bias voltage [HAW 97]. Importantworkremainstobedonetodevelopenough understanding of wafer construction and the stages of APD fabrication in order to overcome the limitations linked to the large discrepancy in the lattice parameter between Si and InGaAs on the one hand and, on the other hand, also linked to the difficulties of passivation. 3.11.2. Waveguide MQW APDs Inordertoreducethemaximumtransittimeofchargecarriers withoutreducingthequantumefficiency,thelightsignalisinjected laterally, perpendicular to the electric field, in a vertical waveguide structure whose InGaAs core is very thin (~0.5 m). Avalanche Photodiodes 105 Since the MQW InAlAs/InGaAlAs or InAlAs/InGaAs multiplication region is also very thin, the transit time of charge carriers is very short andbandwidthsof25GHzhavebeenobtained.Thegain-bandwidth productismorethan5.Foradiodeoflength20m,theresponse coefficient at M = 1 is 0.9 A/W at 1.55 m for a fiber-diode coupling factor of 80% [COH 97]. 3.11.3. Low-noise APDs with a very thin multiplication region ThestudyofAPDswithaverythinmultiplicationregion(0.2to 0.5m)hasdemonstratedthepossibilityofmakingdeviceswitha lowexcessnoisefactoroutofmaterialssuchasInP,GaAs,InAlAs whose ionization coefficients are similar, even in the case of a primary injection by the least ionizing charge carriers. Under such conditions, McIntyresanalysisisnotrelevantbecausethedeadspace,the distancerequiredforachargecarriertoacquireenoughenergyto ionize,isnolongernegligiblecomparedtothethicknessofthe multiplicationregion.Consequently,theionizationprocessisless random, and as a result there is less noise. Excess noise factors comparable to those measured for multi quantum well APDs (F ~ 4 at M= 10) have been published for traditional [DRI 99] and waveguide [KIN 00] In0 53Ga0.47As/In0.52Al0.48As APDs with a high bandwidth (~20 to 30 GHz), whose multiplication region in the high-electric-fieldmonolithicInAlAsmaterialisseparatedfromthelow-fieldInGaAsabsorptionregionbyaverythinbutheavilydopedInP layer.Theprimaryinjectionofelectronsmakesthepresenceof quaternarytransitionlayersunnecessary.Thismakessuchstructures veryattractiveforhigh-bitrateapplicationsastheyaresimplerto fabricate.Additionally,arecordgain-bandwidthvalueof290GHzwas obtainedforInAlAs/InGaAsAPDswithaverticalstructure incorporatingaresonantcavitycenteredatO=1.55m,ahigh responsecoefficient(above0.8A/W)andaweakdarkcurrentfora thicknessof0.2mfortheInAlAsmultiplicationregion[LEN99]. However,theseAPDsrequireanexcellentunderstandingofepitaxial 106 Optoelectronic Sensors growthinordertoachievestackingofthemirrorlayersandthe activeregion,andaremuchmoredelicatetofabricatethanthe traditional structure in [DRI 99]. 3.12. Conclusion Initiallyrespondingtothedemandsofmilitaryapplications,the development of avalanche photodiodes has occurred in parallel to that ofopticalfibertelecommunications,withonenotbeingpossible withouttheother.Theresultisthatforeachgenerationoffibers correspondingtoaspectraltransmissionwindowofsilica,0.85m, 1.3 m and 1.55 m respectively, there is a specific APD associated, be it P+SPN+ Si APDs, Ge APDs, and then SAGM InGaAs/InP APDs, tailoredtotherelevantemitter.Theperfectionofhigh-performance APDshasbeenoneoftheimportantfactorsintheachievementof competitiveopticalcommunications.Anincreaseinthesensitivityof the photoreceiver, consisting of the APD combined with an associated amplifier, allows either a reduction in the power of the signal emitted inthefirstplaceorareductioninthenumberofrepeatersalongthe link.Inaddition,thehighlevelofreliabilityofSAGMInGaAs/InP APDshascontributedtotheexpansionofsubmarineopticalfiber linksoverthelastdecade,whichhasseentheinstallationofmany intercontinentallinksathigherandhigherbitrates(5to10Gbit/s) withshorterandshorterlatencies.TraditionalSAGMInGaAs/InP APDshavemet,andcontinuetomeet,theneedsofdesignersupto 5Gbit/sandeven10Gbit/s.However,theadventofopticallinksat bitrates of 20 or 40 Gbit/s and beyond leaves no question that there is nocurrentAPDstructurewhichisreallyapplicable,andfurther research is required. Avalanche Photodiodes 107 3.13. Bibliography [ALA74]ALABEDRA R.,MAILLE C.,LECOY G.,RIPOCHEG.,PhotodiodeSchottky SiPt-Si N avalanche, ESSDERC, 1974.[CHI 80] CHIN R., HOLONYAK N., STILLMAN G., TANG J., HESS K., Impact ionisation in multilayeredheterojunctionstructures,ElectronicsLetters,vol.16,no.12,p. 467, 1980.[COH97]COHEN-JONATHANC.,GIRAUDET L.,BONZO A.,PRASEUTH J.P., Waveguide AlInAs/GaAlInAsavalanchephotodiodewithagain-bandwidth product over 160 GHz, Electronics Letters, vol. 33, no. 17, p. 1492, 1997.[DRI 99] DRIES J., THOMSON K., FORREST S., In0,53Ga0,47As/In0,52Al0,48As separateabsorption,charge,andmultiplicationlayerlongwavelengthavalanche photodiode, Electronics Letters, vol. 35, no. 4, p. 334, 1999.[EMM67]EMMONSR.,Avalanchephotodiodefrequencyresponse,Journalof Applied Physics, vol. 38, no. 9, p. 3705, 1967.[HAR91a]HARARIJ.,Etudesthoriquesetexprimentalesdephotodiodes avalanche planaires GaInAs-InP, PhD Thesis, Lille Flandre Artois University of Science and Technology, 1991.[HAR 91b] HARARI J., DECOSTER D., VILCOT J-P., KRAMER B., OGUEY C., SALSAC P.,RIPOCHEG.,Numericalsimulationofavalanchephotodiodeswithguardring, IEEE Proceedings, vol. 138, no. 3, p. 211, 1991.[HAW 97] HAWKINS A., WU W., ABRAHAMP., STREUBEL K., BOWERS J., High gain-bandwidthproductsiliconheterointerfacephotodetector,AppliedPhysics Letters, vol. 70, no. 3, p. 303, 1997.[HIL81]HILDEBRAND O.,KUEBART W.,BENZ K.,PILKUHN M.,Ga1-xAlxSbavalanche photodiodes:resonantimpactionizationwithveryhighratioof ionization coefficients, IEEE Journal of Quantum Electronics, vol. 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This page intentionally left blankChapter 4Phototransistors4.1. Introduction Theeffectsoflightontransistorshavebeenstudiedsince transistorswerefirstcreated,withthemainmotivationforthis research being to produce a combination of photodetection and signal amplification in single device. The first work on phototransistors dates from1951whenShockleyetal.[SHO51]proposedtheuseofa bipolarn-p-norp-n-pstructureasaphototransistoroperatingwitha basecurrentgeneratedbyopticalmeans.Thefirstdemonstrationof thistypeofphotodetectorwasachievedtwoyearslaterwhenShive [SHI 53] described a Ge-based n-p-n phototransistor, operating in the spectral region of 1.2 m wavelength, with an optical gain of the order of100.Inthe1960s,itwasmostlybipolarSiphototransistors, operating in the near-infrared, which were developed. However, since theopticalabsorptioncoefficientofsiliconisweak(104cm1).Thesetwocharacteristicshave openedupthepossibilityofapplyingphototransistorsbasedonIII-V materialstothefieldofopticaltelecommunications.Heterojunction bipolartransistorsandfieldeffecttransistors,madewiththese materials,begantobestudiedasphototransistorsinthe1970s[ALF 73, BAA 77]. Insection4.2,wepresentasummaryofthedifferenttypesof phototransistorsbasedonthematerialsusedfortheirfabricationand asaresulttheirsensitivitytoopticalwavelengths.Wewillthen classifythemaccordingtotheirstructure.Insection4.3wedescribe the mechanisms of operation of a bipolar phototransistor and its main properties. Section 4.4 is dedicated to some examples of circuits based around bipolar phototransistors. Finally, in section 4.5, we review the main fields of application of this device. 4.2. PhototransistorsIn terms of photodetectors, phototransistors can be classed according to their fabrication material and, just like their transistor analogs, they can also be sorted according to structure into two categories: unipolar field effect devices and bipolar devices. This section reflects this dual classification. 4.2.1. Phototransistors according to their fabrication materials Thefirstphototransistorswerebasedonabipolarhomojunction silicontransistor.Inthisindirectbandgapmaterial,theenergyofthe bandgapis1.12eV.Asaresult,siliconisphotosensitiveto wavelengthsinthenear-infrared,0.60.8m.Later,startinginthe 1970s,technologicalprogressachievedwithIII-Vcompoundsand Phototransistors 113 theirternaryandquaternaryalloysenabledthedevelopmentof heterojunctiondevices:fieldeffecttransistorsandbipolartransistors. These materials have a direct band structure, and some of their ternary compounds have bandgap energies which match the spectral windows oflowestattenuationinopticalfibers:0.85, 1.3and 1.55 m.Thisis whytwovariantsbasedonIII-Vmaterialshavebeendeveloped:the GaAs variant (for O = 0.85 m) and more recently the InP variant (for O=1.3and1.55m).Heterojunctionphototransistorsbasedon AlGaAs/GaAsarephotosensitivetowavelengthsbetween0.8and 0.9 m, with the GaAs bandgap being 1.43 eV. This value of bandgap iscompatiblewiththespectralwindowofopticalfibersaround0.85 m, for which there is an attenuation of around 2 dB/km. The optical absorptioncoefficientofGaAsforthiswavelengthisrelativelyhigh: oftheorderof104cm-1.Thefirstopticalsystems,operatinginitially at0.85m,werelatertargetedat1.3and1.55mwherethe attenuation in optical fibers is 0.5 and 0.2 dB/km respectively. Thus, it is the ternary and quaternary alloys based on InP which are bestsuitedforphotodetectionatthesewavelengths.Inparticular,the ternaryalloyInxGa1xAswithx =0.53,whichmatchesthelattice spacing of InP, has a bandgap energy of 0.75 eV. This value of energy iscompatiblewithphotodetectionat1.3and1.55m.Theoptical absorptioncoefficientofInGaAsis1.16u104cm1forO=1.3m and 6.8 u 103 cm-1 for O = 1.55 m. The bandgap energy (Eg) and the applicablespectralrangeforthemainmaterialsusedin phototransistor fabrication are shown in Table 4.1. Table 4.1. Bandgap energy and applicable spectral range for variousmaterials used in the construction of phototransistors 114 Optoelectronic Sensors 4.2.2. Phototransistors classified by structure Homojunctionorheterojunctionbipolartransistors(photo-HBTs) andunipolarfieldeffecttransistors(photo-FETs)arethree-terminal devices.Whenilluminated,theopticalinputactsasanadditional terminalacrosswhichthedevicecanbecontrolledoptically.These devicescanbeintegratedintoMMICs(MonolithicMicrowave IntegratedCircuits)toachieveoptically-controlledamplificationor switching,orevenmoresophisticatedmicrowavefunctionssuchas opticallockingofoscillatorsandthemixingofopticalandelectrical signals [SEE 90]. 4.2.2.1. Unipolar field effect transistors Unipolarfieldeffecttransistors(FETs),basedonIII-Vmaterials, onlycreateasingletypeofchargecarrier.Outofthefamilyoffield effecttransistors,mostresearchhasbeenfocusedonheterojunction phototransistorswhichareSchottkygatetransistorsmadewithGaAs (MESFETs, Metal-SemiconductorFieldEffectTransistors)andhigh electron mobility transistors (HEMT). This popularity is mostly due to thepossibilitiesofusingthephototransistoreffectinMMICs (Monolithic Microwave Integrated Circuits). Figure4.1showsthecross-sectionofanilluminatedMESFET device (photo-MESFET). Two distinct phenomena occur in the photo-MESFET during illumination by light: a photoconductor effect which istheresultoftheincreaseinconductivityduetothecreationof photocarriers,andaphotovoltaiceffectwhichoccursclosetothe gate/channelandchannel/substratejunctions.Severalinvestigations [GAU 85, MAD 92] have shown not only that the photovoltaic effect dominates the photoresponse of the device, but also that this effect is thecauseofthemediocredynamicperformanceofphoto-MOSFETs. Physically,wecanexplainthisdegradationbythepoorcoupling between the incident light and the gate junction (poor overlap between theopticalabsorptionregionandtheregionwithan electricfield).A largeproportionofthephotocarriersenduptrappedinlowfield regions (e.g. the barrier), thus distorting the static characteristics of the device.Phototransistors 115 Compared to a photo-MESFET without illumination, an important reductioninperformancehasbeenobservedforthetransition frequencyfTandthemaximumfrequencyofoscillationfMAXwhen illuminated[SIM86].Thebestdynamicperformanceobtainedunder illuminationisforabandwidthlessthan100MHz[BAR97]. Dynamicopticalperformancesareverypoorcomparedtothose obtained electrically. Figure 4.1. Structure of a GaAs MESFET under illumination. The channel is ann-type semiconducting region sandwiched between a semi-insulating substrate and the space charge region (depletion region) of the reverse-biased Schottky junction MESFET-basedphototransistorshaveshownthemselvestobea poorapproachfordevelopingphotodetectorsinthemicrowaveand millimeterrange.OtherdevicesintheFETfamily,notablyHEMT, suffer from the same limitation [ROM 96] 4.2.2.2. Bipolar phototransistors Analternativetothephoto-MOSFETisthesilicon-based homojunctionbipolarphototransistorortheheterojunctionbipolar phototransistor (based on GaAs or InP). In the bipolar phototransistor, thereisanoverlapbetweentheregionoflightabsorptionandthe high-electric-field depletion region. This overlap is as good as in PIN photodiodes. As will be shown in section 4.3, the frequency response to a modulated optical signal is directly related to its purely electrical properties.Tomakethebestuseoftheperformanceofatransistor, differentilluminationapproacheshavebeenconsidered,suchas 116 Optoelectronic Sensors vertical illumination through the front or rear face, lateral illumination, or even the use of a waveguide. 4.2.2.2.1. Traditional surface illumination Thefirstphototransistorsweresurface-illuminated,whichisthe traditionalsituation,particularlyforsiliconphototransistors.This verticalilluminationallowseasycouplingbetweentheopticalfiber andthephototransistor,makingtheintegrationofthedeviceeasier. Several solutions have been proposed: in the case of an opening in the metalliccontactoftheemitter,theincidentlightfluxcrossesthe emitter without being absorbed, and the electron-hole pairs are created in the active (or intrinsic) base-collector region of the photo-HBT, that is,theregionwhichisjustbelowtheemitter.Ifabasecontactis removed, as shown in Figure 4.2a, the optical flux directly illuminates thebaseandthecollectorintheextrinsicregionofthe phototransistor. 4.2.2.2.2. Rear-face illumination Theaimofrear-faceilluminationofatransistoristhecreationof photocarriersintheactiveregionofthetransistor(seeFigure4.2b) withoutmodifyingtheemittercontact.ThetraditionalHBTstructure is used with a substrate which does not absorb the incident light. The absorptionoflighttakesplaceinthecollectorandthebase. Furthermore,theresponsecoefficientisimprovedbecausethe metallic contact of the emitter acts as a mirror. Phototransistors 117 Figure 4.2. Cross-section of a HBT phototransistor with(a) front-face illumination and (b) rear-face illumination 4.2.2.2.3. Lateral illumination Lateral illumination (parallel to the layers) offers another approach fortheinjectionoflightintoatransistor.Itisinspiredbythe technologicalprocessesdevelopedforphotodiodes.Thistypeof illuminationrequiresafaceveryverticaltothebase-collectorisland, inordertoobtainthebestpossibleinjectionefficiency.Inlaterally-illuminated phototransistors, the photons and charge carries no longer propagateinthesamedirection,asisthecaseofverticallyilluminated photo-HBTs.Theaimoflateralilluminationistosimultaneously improvetheconversionofopticalpowerintoelectricalpower (quantumefficiency)andthespeedperformance(highoperating frequencies) of the device. 4.2.2.2.4. Lateral illumination with an integrated waveguide However,lateralilluminationdoesposesignificantdifficultiesin termsofachievingagoodopticalcouplingbetweenthefiberandthe device. This is why one trick involves the fabrication of a waveguide integratedintothestructureofthedevice,asshowninFigure4.3. With this approach, the matching of the mode leaving the optical fiber to the propagation mode inside the device is made easier [FRE 96]. In the best cases, an improvement to the injection efficiency is observed which rises from 50% to 90%, with an improved frequency response. 118 Optoelectronic Sensors 4.3.Thebipolarphototransistor:descriptionandprinciplesof operationThebipolarphototransistorisatransistordesignedsuchthatthe signalcurrentwhichfeedsthebaseterminalismostlyprovidedby photoelectriceffects.Thissignalisthenamplifiedbythetransistor effectofthedevice.Firstwerevisittheprincipleofoperationofa bipolarn-p-nphototransistor,whichconsistsoftwodistinctp-n junctions, as shown in Figure 4.4. Then, we shall discuss the parameters characterizingthephototransistor:theresponsecoefficient,thestatic and dynamic gains, the response time, the conversion gain and the noise. Across-sectionofann-p-ntypebipolarphototransistor,usingmesa technology, is shown in Figure 4.4, along with its bias circuit. Figure 4.3. Cross-section of an integrated waveguidephototransistor under illumination Figure 4.4. Schematic diagram of an n-p-n phototransistor, along with its bias circuit in common-emitter configuration. The shaded regions are free from mobile charges. The base, collector and sub-collector parts can be thought of as a PIN photodiode Phototransistors 119 4.3.1. The phototransistor effect InFigure4.4,then-p-nphototransistorisbiasedinthecommon-emitterconfiguration,withvoltagesVBE>0andVCE>0.Itdiffers fromtraditionalbipolarstructures,havingarelativelylargesidearea of the base-collector junction; this is called the optical window and is whatbecomesilluminated.Thispartofthedeviceiseffectivelya photodiode,connectedbetweenthecollectorandbasecontactsofthe active transistor. When illuminated, electron-hole pairs are created by thephotoelectriceffect,inthebaseandinthespacechargeregion (SCR)associatedwiththebase-collectorjunction(weassumeforthe sakeofsimplicitythatnoabsorptiontakesplaceinthesub-collector andthatthecollectorisentirelyfreeofmobilecharges).A photocurrent I,knownastheprimaryphotocurrent,isestablished betweenthebaseandcollectorregions;itistransportedbyminority electrons from the base which diffuse towards the collector, and by the carriers generated in the SCR, which are separated and moved by the electricfield.TheflowofthisphotocurrentIgeneratesavoltage acrossthebase-emitterandbase-collectorjunctionssuchthatthe transistorfindsitselfinitsnormaloperatingsystem(VBE>0and VCE> 0). Theholesattractedbythebasewillthereforefindthemselves blocked by the emitter-base junction. This excess of holes will cause a reductionintheemitter-basepotentialbarrier,whichresultsinan injectionofelectronsfromtheemitterintothebase,fromwherethe majoritywilldiffuseuntiltheyareatthelevelofthecollector.Thus, thisisthetraditionalbehaviorofabipolartransistor.The amplificationofthephotocurrentisapurelyelectricalphenomenon due to the transistor effect. 4.3.1.1. The main currents in the phototransistor Inthenormaloperatingsystem,thephototransistorcanbe characterized in terms of the following currents (see Figure 4.5): Firstly,theemitterinjectselectronsintothebaseregion.These, minoritycarriersinthisregion,diffuseperpendiculartothejunction layoutand,ifthebaseisthinenoughthatrecombinationcanbe 120 Optoelectronic Sensors ignored, they reach the depletion region of the base-collector junction, wherethehighelectricfieldpresentinthisregionclearsthemout towardsthecollectorregion.Theflowofthesechargecarriersgives the contribution Ine, which is shown in Figure 4.5. Conversely, a current Ipe of holes, majority carriers in the base, is injected from the base towards the emitter. Generation-recombinationphenomenamostlyoccuratthelevel of the emitter-base junction, Ireb, and in the base, Irb. Ireb comes from therecombinationofelectronsintheSCRoftheemitter-base junction. Irbiscausedbytherecombinationofelectronswithholes, majority carriers, in the base. Illumination produces the primary photocurrent I. Mostly created in the SCR of the base-collector junction, I originates from a current ofelectronswhichmigratedirectlytowardthecollectorcontact,and from a current of holes which accumulate at the level of the base. Thus,balancingthedif