Portland State University PDXScholar Dissertations and Theses Dissertations and Theses 5-1-1969 A method of measuring the electron energy losses in transmission through thin films John Patrick Stewart Portland State University Let us know how access to this document benefits you. Follow this and additional works at: https://pdxscholar.library.pdx.edu/open_access_etds Recommended Citation Stewart, John Patrick, "A method of measuring the electron energy losses in transmission through thin films" (1969). Dissertations and Theses. Paper 908. 10.15760/etd.908 This Thesis is brought to you for free and open access. It has been accepted for inclusion in Dissertations and Theses by an authorized administrator of PDXScholar. For more information, please contact pdxscholar@pdx.edu.
AN ABSTHAC' l OF 'fhe 'l'hesis OF John Patrick Stewart for the Naster of Science degree in Physics presented on June 24, 1968. TitIe: A l'1ethod of Measuring the Electron 파 lergy Losses in Transmission 맘 1rough Thin Films I 'lakoto Takeo 안 le energy distributionin 와 lelectron be 없 n transmitted by a thin aluminum filmwas studied by a retarding potential method in which the energy 없 lalysis could be made as a function of the polar angle and azimuth of scattering. 맏1e results indicated that the tr랴lsmitted be없n contained electrons which had lost essentially zero energy and groups of electronswhich had suffered losses of approχimately 15 ev and 25 ev, and possib1y75 eve In addition there appeared to be a continuous back암 round of energy losses over the range studied (from 0 to 80 ev). 만1e resolution of 합1e energy analyser was limited by the separation of the data points aridwas not adequate to observe the dependence of the 15 ev energy loss (plasma loss) on the polar angle of scattering.
This stuqy demonstrated the feasibilityof this methodof energy analysis as well as the short-comingsof the apparatus. Suggestions for future improvements are made.
A 꽤많 OD OF 꽤 ASURING 말 IE ELECTRON 뻐 ERGY LOSSES IN 돼 ANSMISSION THROUGH TI 표 N FI 파 15 by JOHN PA 돼 ICK ST 믿 IrlART A thesis su뻐 ni.ttedin partial fulfil뇨 nent requirements forthe degreeof of the MASTER OFSCIENCE 뇨 1 PHYSICS Portland State University 1969 PORYL 쐐騙 STATE U 햄 WE 챔 S!TY LIB 뻐 R
TO 맡 IE OFF ICE OF GRADUATE Sπm 꽤 s: 앞 le members of the Committee approve the thesis of John Patrick Stewart presented June 24, 1968. Gertrude F. Rempfer 않 udnian Makoto Take APPHOVED: Hay 23, 1969
파 따TABLE OF CONT 멜 NTS 腦APPENDICES AC Kl' JO짜..EnG페ENTS.... L 工 ST OF TABI펴S LIs'r OF li'igures CHAP 돼It I II INTRODUCTION 짧PERIMENTAL! 머빨lOD III EXPE1UMENTAL RESULTS AND DISCUSSION IV CONCLUSIONS A꾀D F UTURE WORK BIBLIαi 뻐PHY P V l 5 21 33 36 38
AC 뻐 OW1EDGMENTS I would like to thank the members of n 만 thesis committee, ProfessorsGertrude Rempfer, Makoto Takeo, and John Dash. I am especially grateful to Professor Rempfer for the m따 ~ hours she spent introducing me 七 eχperimen 七 al electron ptic$ and to experimental physics in general. F rofessor Takeo was extremely helpful in reading and discussing several theoretical papers relating to this thesis. Mr.Michael Mauck was also helpful in general discussions about the apparatus. Mr. Jack J 따 lacek, Head of the Science DivisionMachine Shop, andh 土 s assist 월 lt, 빠 't 페라 lk Bell, perfo~ed the machine work on the Apparatus. Mrs. Lorriane Ivlercer and 빠 s. Laura Luskof the Electron Microscope Group, Tektronix, Inc., prepared the specimens used. I would like to express ~ gratitude to n 띤 stepfather 없 ld mother, 빠 하 ld Mrs. Wayl 밟 ld ~rd, for the fin 웰 lciaj. aid given to my f 웰 nily and.me during this study. Finally, I would like to express my gratitude to ~ wife, 빠 s. J 없 lice Stewart, forthe technical assistance I received in preparing ~ thesis.
LIST OF TABLES '.L 1 Al1LE I Essential Dimensions PAGE 19
ιη샤list OF FIGURES E IGURE PAGE l 맘 le focusing of scatter ed r a:s-s in 七 he plane P. 6 2 X3.6 enlargement of the diffraction pattern of alwninwn taken v1ith a specimen to plate distance of 18.2 αn. 없ld a pr:ijnary be빠 voltage of 15 kv. 10 11 qj[schematic diagr없n of the analyser Electron-optical aspects of the analyser 그Scatterin당 pattern for aluminum taken at ~5 volts bias ζustrip pattem?l Pattern mask QU Schematic diagr월n of the 밍cper뇨nental. sy꽤em 나 Q/ Physical set-up in the electron-opt 土 cal bench EssentialDimensions. Calibration Curve: tr빼홉nission of the primary be월n by the 획1려 ~sing mesh as a function of the mesh biasvoltage 11n퍼디돼 l ny/ mκ26 12--17 Tr밟l없nssion. 바lrough the mesh 와1alyserof the electron beam scatteredby alumin빼 1 as a function of I빼sh bias voltage 27-- 32 AI Intersection of the pl없18 P by the conesof scattered rays from So and s. A2 Lack of registration of 하1e intersection points on the pi학18 P in the direction of the spec꾀nan points 40 41
v 그.!i'IGUH.E Bl B2 B3 01 표 ler 짧따 1alyser........... Equiliv 와 lt optical syst 앉 n.: Electron-optics of the mesh an 려 :y ser PAGE 니 때 Inclination of the electron pa합 1S to the axis of 합1e system 49 Ii 때띠
CF 파 PTER I INTRODUCTION 돼 1e stuqy of the,inelastic collisionswhich occur wh 앙 1 a beam of electronstraverses arnaterialprovides arne 하 lod for the investi 단 ation of the properties of matter. 말 1e energy losses which the electrons suffer dur 끄 19 scattering can be measured in the emerging be 리 n and give information about the electronicenerfr1 levels 끄 1. the material. 돼 pically a spectrum of energy losses for a material contains severalpeaks corresponding to discrete losse 윈 and a g 않 leral background indicating acontinuousi 없 1ge of ener 짧 losses. Many investigators have utilized 합 le energy loss me 하 lod in stu 때 ing the propertiesof various materi 려.s. Huch of 합1e energy loss data has be양1 assembled 최1 a review article by IvIarton, Leder, 따ld Mend1owitz 9 Two of thepossible mech 월 1.i 훨 ns which can be identified as causing electron energy losses in metals are, accor 뼈 ng to Farrell 6 : a) one-electron tr 웰 lsistions 짜 lere 웰 1 electron 뇨 1 the metal is raised in energy.trom a level 뇨 lone band to 웰뼈 occup 土 ed level in another band and b) excitation of plasma osci11ations, which are collective oscillations of 해 1e charge density in the electron sea or 해 1.8 metal. The 뇨 ltensity peaks in the energy
2 loss spectrwn corresponding to interband transistions are generaj.ly not as sh 랴 " as those due to pia 하 na oscillations. Interband losses m~ rangedown to low energies, for ex 없 nple around.3 ev for gold. It should be possible to correlate the interb 없 1d losses with optical absorption bands wheredata are available. on the other hand, the collective oscillationloss pe 밟 is relatively sharp and larger than the smallest interbandiosses. loss is not expected to be correlated with 짧 optical absorption bnnd, but rather with a minimum cut-off frequency for transmission of electroma 힘 1etic radiation through 하 1e metal. F errell s 맘 lis view is that in every metal there will be at least one collective loss, of relatively large 양 lergy 와 ld int 앙 lsity, 하 ld none to several one-electron losses of generally smaller 잊 1ergy 와 1d intensity. Bohmand Pines l, 2,.3,11 have shown theoretically that collective oscillations above a certain critical wavelength corresponding to a max:1jnum value of the frequency can e 월 at 12 the electron sea. Watanabe.&.'- has shown 와 ld verified 밍 cper 꾀 nentally that 하 1e frequency of 하 1e oscillation increases with the scattering angle of the exci 七 ing electron. F r smallscatter 土 ng 웰 19les 융 the frequency c 웰 be expressed as: ω =, 싼 ).f. 4.".t/E 8 2 까 1 where E is 하 1e kinetic 빼 era or 뻐 e exciting electron, is 빠 e plasma frequen 따. tor zero angle, and..,. depends on the scattering m 하 terial. F r metals 폐 lich appr 월 mate the free electron model p 흩 (41rne 2 /m) 꿇, 웰 1d v' 톨 0.45. in
A number of different types of energy ana1ysers have been 3 used to obtain the ener 않 r loss specti'\ 끄 n of 하 1e scattered electron beam. Il'he most widely used. at present is a high resolution instrument devised by IvIollenstedt. It is based on the highoffajds chromatic aberration of an electrostatic lens and has a I esolution capabilityof less than one electron-volt forpr 뇨떠뀐 electrons of 20 kev. Comprehensive descriptions of this type of 10...._tl instrument have been given by 1 1ilyutin 와 ld Kab 없 lov... and Hahn... alon 당 lolith ex 따 nples of its application to 하 1e 양 ler 짧 analysis. of electron beams. Using this type of analyser, Watanabe...- 12 observed both collective and one-electron 양 1ergy losses and verified ex~ perimentally the properties of the collective oscillations for metals such as aluminumwhich appro: 입.mate 하 1e free electron model used by B 뼈 n 없 dp 土 nes. Another type of high resolution 7 instrument" described by Haberstroh', is based on a retarding potential me" 뻐 od 따 ld me 윌 aures the 웰 1ar: 앓 r loss 받 >ectrwn, integrated over small scattering angles. In most of 하 1e experimental studies the primary be 윌 n vol.. tage, defined~ 훨 1V 2 = evb, has been in the x anse from five to 따 kv. '!be energy losses do not depend on the pr:i.nw.xγ be없n voltage, but are characteristic of 합18 material 없ld are sometimes called eig 앙 1108 열 es. Multiple scattering" which is inherent in reflection studies and in transmission through 납 lick specimens, pr 뼈 Ices additional peaks in the spectrwn 웰.d increases 하 le diffuse background. 멜 lese complications are avoided if the specimen is 하 lin
enou당h so 합lat the intensity of the singly scattered component of the 빼lerging beam is largerelative t 뼈at of themultiply scattered component. 맘lin specimens areessential in studies of the losses asa function of scattering 와19le. The apparatus described 뇨1 하lis thesis was designed to measure 월le electron energyloss spectrum as a runc 七 ion of the scattering direction. 맡lG electx In be없n is an~sedin a pl하1e following the specimen and normal t 합le axis of the prijnary be떼. 밑le position of 하leelectrons in the analysing pi없ie is determined PY the direction of scattering. 말1e convergence of the pr뇨뻐꾀r be윌n is such that electrons scattered 피해e same azimuth through the s웰ne polar 앓19le by' different parts of the spec끄nan are focused 뇨1 the 없l려 :ys끄19 plane. 말1e energy analyser is or 합1e retarding pot밍ltial typei but differs from that of Haberstroh which analyses the energy loss spectrum integrated over scattering 없 Igle and az 끄 nuth. The measurement f the energy loss spectrwnwas carried throughfor a.l'wlli.nwn a.t room temperature wi 합 1 apr. 때벌 ry be 윌 n voltage or l'kv.
CHAPTER II EXPER 묘꽤 ~TAL.~ 머봐 iod A discussion of the electron optical aspects of 합le method used 뇨1 월lis study are facilitated by Figures 1 해U'ough4. As shown in Figure 1, electrons diverge from an essentially point source 없1d are redirected by a lens toward a focusin the pi따le, P. 빨1e image of the source, formed in the pi벌1e P, is demagnified 없ld is of 하1e order of 0.001" in diameter. 빠len a specimen is placed as shown in the path of 합1e be빼1, rays which are scattered in a given azimu뻐하trough the s없ne polar 와191e' e by different parts of 합18.spec뇨 nan are also rocused, to first order, in the pi윌1e P (see Appendix A). 맡1e energy loss analysis of the electron 뻐하n is c빼ried out in the pi없1e P where 합1e spectrwn'obta 뇨led as a function of position 뇨1 the. pattern can be correlated w 土 th the polar 없19le and 합18 az 뇨rxu.th of scattering. 'llle diffraction pattern of the spe때nen is focused 뇨1 this pi웰1e also. 밀1e contrast and sharpness of 해1e diffraotionpattern is anindication olthe predominance of 합1e single-collision components of the transm 土 tted be없n. Figure 2 is the diffraction pattern of the aluminum spec삐len used in thisexper:lment. 말le dotted circle surrounding 합1e center of 하18 pattern included the r웰198 or 월 \glee over 빼1ich the angular dependence of 합 'le energy losses was studied.
6 @U다떠서@φ쇠껴섭꺼이늙띠μ성mμm껴꺼띠Um때 뼈섭꺼이섭8일ω웹 세씨비뻐셉μ 디ψ업에U @ Qnm 역여여늘μ띠염 꺼μQ(U꺼껴여-터@되Um)이섭φ녀섭 μ껴다@ 떠m섭 μ껴um셔띠힘 ψuμ의 띠써β 0%\ \ \ \ l \ \ \\m 농띠띠성ωLHωηfdF때Un
7 (111) (200) ( 샅 20) (311) (331) (420) li'igure 2. X3.6 enlargement of the diffraction pattern of aluminum taken wi함1 aspec뇨 nen to plate dist와lce of 18.2 cm. and a prj~ be따n voltags of 15 1π.
8 말 le analyser consists of a fine metall 그.c mesh supported between 랴 ld electrical 파뇨 lsulated from two outer electrodes \l1hich, along wi 납 1 the structure supporting the mesh, have cylindrical symmetry. 맘 1e two outer electrodes are atground potential as is 하 1e spec 빼하 i, and the inner mesh electrode is negative 없 ld closeto cathode potential (see the schematic diagram infi 핸 re 3). An adjustable bias between the. mesh 따 ld cathode pot 잊 ltials is used to an~se the distribution 끄 1 앙 lergy of electrons in 七 he be 빼 1. 만 1e mesh acts like a sieve allowing electrons' above acerta.i1'l energy (depending on 합 1e passthrough while returning those of lowerenergy. bias) to Because of the field between 하1e negative mesh 없ld the grol끄lded end electrodes the potential 꾀하18 mesh op 양lings is less negative 해lan that of the mesh. 봐1erefore a negative b 土 as on the mesh is needed to cut-ofr transmission of 합1.8 be빼훨1tirely. The ch월1훌es 뇨i 土 ntensity of 합18 be빼1 tr없i홉nitted by the mesh as 합18 negative bias is reduced trom cut-otf gives the ener않r distribution in 하1e be힘n. Electron-optical efrects 피하18 an와 :yser due to the electric fields between. 빠1e eleotrodes and aro\ 파d 합1e apertures in 하10 end electrodes cause 빼1.e effeotive position and size of the mesh, referred t 합1e space outside 합1e an따 :yeer, to be differ빠 1t from :L'lis actual pos 土 tion 뭘1d size. 맡1e caloulations are worked out in Appendix B. 말1e result is that the mesh has a virtual magnifioation of 2/3, 웰ld its dist없lce frα1). 합1e aperture on 해1e s 土 de or 합18 referenoe space appears'to be increased
9 m 껴써핵φ성 μμom셔떠갱섭띠 Hφm늙서여섭랙ψ꾀껴L}ORdμ당얘껴 써Q꺼껴삐셉ω꾀이띠써씨빔뼈에헤{써m U y 띠 ω영oμμuω매씨성디떠(늘u{입l)y뻐애섭 {뼈빼껴협ψ성 되쩌빼U FψMV.띠껴 O 띠띠꺼끼m서꾀서씨μm의꺼언책
by the factor 4/3 (see Figure 4). 앙 1e plane P in Figure 1 in 10 which the scattering pattern is focused and in which the energy analysis is to be done should th 앉 1 be made to c 따 lcide wi 하 1 the virtual plane M rather than Me in Figure 4. Distancesr from. the axis in this pi 와 le 따 -emeasured in terms of 합 1e mesh constant of 11 which is 2/3 the size of 때 맘 19 polar 밟 19le of scattering, 8, corresponding to a distance r off~ a.xi s is given by: 8 ; taxi 8 = (r/sm) = n(2/3)c p... (4/3J6 where n is the number of mesh spacings frαmthe center 와ld c is 합 1C mesh constant. A further electron-optical aspec 七 of 하1e analyser is discussed 뇨1 App양1d다 c. 말lis involvesthe reduction 뇨1 the 없cial speed of 합1e electron as 하1e scattering angle is increaeed. Corresponding파, the part. of 하1e be빼 voltage associated with the 없와따 rection"definedby evz = (1/2) 빼 g, is rgduced as the scattering 와19le is increased.f r the chief rq of a diverging pencil, 하1e loss in 밍cia! be웹n voltage of an electron inside 하16 analys원 r is given by: Vz(loss) 톨 VB 92 ( 1... pi뼈 )2 In general the beam voltage depends on both 합 1e scattering 따 19le e and 하 1e angle ot convergence 4, which results 얼 1 a variation in axial be없11 voltage tor Do g1ven pencil. 안1e analysing mesh measures the ajζi.al energy 웰1d consequently records 따1. appnrant energy loss in 하1e ort-axis be웰n which must be talcen into account 뇨1 comp웰ing the transmission throu힘 1 the
11 t/) m 쉬썩넥μ r---m~m파핵 μmmk셔띠섭띠ω죄μμ mμuω(씨m여. 띠O에셔QO 섭 μμum π띠 셰씹센쐐때 ""-- "",,--- m.... - ~ F α. 댁mμ5껴μmQ여 {m의 μ되껴다ψφmm 여섭O쉬믿 찌꺼써mω앙 다 ψμ껴}껴μu 써떼 쇠m3 μ쇠껴 φm애니. r껴의 죄μ껴 *> 섭φωmm 띠섭 꺼껴 (애쇠 ω흰 li.핵φjh3prh@젠여 {m셜 μ쇠μ섭@@m이여디 껴껴 꺼띠OQ쇠이ψ-- l원n
l 십 mesh of be 퍼 ns scattered at different angles. Furthermore the variation in axial beam voltag 앙 in a given pencil sets a 1 피 it on the energy resolution. As the beam'passes through the mesh it isscattered by the electric fields around the mesh openings, which act as 와 1 array f tiny lenses scr 려 nbling,therays from the different openings. 맡 1e rays c 없 1 be unscrambled by using 않 lelectron lens following the analyser to reimage 합 1e plane of 해 1e mesh. 파 1 addition" this lens can be used to magnify the image. 앞 lis is desirable since the mesh spacing const뭘1ti돼 s 쩌v ei뀐 γ small (ωoι.002 깐I 녕 ) a.r I 파 out magnif1cι ation 합 1e 라 1 펴 alysiswouldbe inconvenien1 七 :i. 'lhe illumination in the mesh image as a function of position relates 하 1e current of theelectrons gett 뇨 19 through 합 1e.mesh with the corresponding 쩌 ngle of scattering. 파 i 하 1.6 e,χ:per 최 nentalarrang 양 nent" the rna 힘 1ifiedmesh 피 age, illuminated by the electronswhich the mesh transmits, can be observed on a fluoi ascent screen. The ma.gni첼ing lens.is ad.. justed so that the mesh is 압1 focus and 하1.e spec최nen lens 셉 adjusted 섭 o that the unscatteredr~spassing through the specimen arc focused in the plane of the mesh. 맑 1e mesh 꾀 nage is 합 len recorded on a photographic plate for stu~ in a d~nsitometer. Fi 따 lre 5 is a s wn.ple photograph ofthemagnified image as recorded on the plate. 만1.e original intention was to record a full pattern for each mesh bias setting on a separate plate and from these plates to deter.mine the energy distribution as a function of both az끄ml하1 and 없19le of scattering. However, the scatterin힘
13.썩서 겸g φ죄껴늙 μ성ω껴띠u.꺼성섭서 꾀겁mm띠섭 껴m 껴껴띠서ωμμφ껴섭φU섭μφ컵업.섭μ@껴꾀떠Aα써섭띠 이.씹월만{Nηl서이, ηl@ w) 여 +>.; h.-- 엽 u 서 7 띠,[ l '\.,( 잉N l N l 씨띠 man껴서rm, 검섭m춰m써법냄때벼대r셔O써섭 Rm껴껴쩌WQMW섭폐 셔φ껴쩌찌WU띠.m @ 섭빼꺼&
------ - - -- - - -------- - --,r- - ------ 一 pattern for 합le specimen used appeared to be az뇨nuthally symmetric and it was decided to record only a representative strip of the pattern. 말lis made i 七 possible to record patterns for a range of mesh bias settings on 하le s 없ne plate by advancing the plate behind a slit opening. 맡1e pat 七 ern strip was recorded 11 for a series of mesh bias settings 합 lroughthe bias voltage r 머 1ge, -35 to 460 volts, 따 ld back. Four plates were neededfor the series, which was recorded in sections: -35v to 0, 0 to ~O v, -+6Ov to 0, 없 1d 0 to - 35v. Figure 6 illustra' 七 es the appearance f the pattern strips for the range from zero bias to cut-off. 맘 le location of the center of the patternrelative to the strip is indicated in 합1e sketch. 맏1e plates were ex없nined to determine the variation in density with mesh bias at a givenposition in 해1e 뇨nage. Densitometer readings for a giγen mesh opening were taken for 합 1e series of bias 'settings 없 ld plotted as a function of bias volta 당 e. 만 le effective ima 칭 e density fora mesh opening was obtained by masking orf the surrounding pattern (see Figure 7) and measuring the average tr 와 lsmission of light throu 힘 1 the mesh hole image. 맡le effectivedensity is related to the current of electrons through the mesh openin 훌. A comparison of the density readings, corresponding to eχposures taken at 하 1e s 월 ne bias setting (each setting occurred twice in a series) served to checkon individual differences 피 1 the platesand on progressivechanges 뇨 1 be 없 n intensity, e.g., as rni 잠 ht be causedby the heat 土 ng ourrent falling orf in the 밍 nitt 끄 19 i1 빼 lent. 맡 'le analyser wa.s
1, ~1esh hole ima 앉 e 웅 \ < /" / \ / 기 / \\ 9 OO2 i 씻 - S> \ / \ / J \ /./... ~' \ / / ~' y \ v I /' / \ I / < > A/< \ /./" \ \ /./ I \\ // \ \ / \ / \// / /A / / / / / / / / \ // /\\\/ / / /I\\ < > / / \ / \ / < / \ / v / < / / \ / \ <, \ / \ / \ / / / / \ / \ / \ < / \ / \ / / Mask Figure,., Pattern mask.
calibrated by recording the transmission of theprimazγ 16 monoenergetic be 없 n through the nlesh (without a specimen) and plottingthe density versus bias settings in 합 1e s 라 ne way. 맡 1e experiment was conducted in an electron-optical bench. 맡 Ie pressure was below 10-4 Torr. 앞 1e benchwas provided with V-ways to align 하1e optical components of the spectrometer, electricalfeedthroughs for supplying voltages, an electron source, 웰 ld a multiple photographic plate holder~ A glass top for viewing the experi피 lent was r양novablefor access to the syst양n. 돼1e I point source' of electrons was for.med by using a condenser lens to d양na않1ify the waist of the be밍n from the electron source. 맡1e 없1웬l1ar aperture c:(:' of 해1e be없n directed through the specimen was limited to about 0.007 radi없15 by a stopon the spe뻐nen lens. 봐1e magnifying lens also was stopped down to avoid undue spherical aberratiox 1. 맡iese 1양lses were of the three-electrode unipotential type with avariable focal power depending on the ratioof 합 1e lens voltage to the accelerating voltage. 와 18 pt 뀐 sioal syst 훨 n was arr 없 1ged s that the 웰 lode was at ground potential and the cathode negatively off ground. FiguI e 8 is a sch 훨 natic diagr 웰 n of the experimental system and Figure 9 is a photograph of. 하 18 setup 따 1 theelectron-opt10 라 benoh. The table in F 土 gure 10 gives the numerioal value of 하 1e essential dimensions.
ι?r성mμm Sm입여 서띠 꺼성Uh.O 뼈에때M싸m꺼찌m.g 꺼[φ서QU ωω되 F I I ---------- ------- 껴껴애m 꺼 m 다 'r케늄 4예 케섭 m b.o 잉여 m S 니 n배 H m m-되mω업 F 괴 rc a \N m s 꺼딩이 φ 섭 P예 φ cf.) 녀 늙서다여랙원섭 +ψ서띠껴다k m에껴때려ω찌um때씨쉐17 ----l - Il - ḻ - 띠껴η mk꺼f꺼띠mmhh폐
18.죄O섭@ρ,돼야1꺼껴 써 섭Q SUφ φφ.져껴엉에 씨성l씩φn버띠O께m R m띠mm섭u니mw섭 꺼띠띠힘,꺼lm며 셔φ성서 법m껴서씨서A버섭ωmμU떠껴섭φO띠φFμO섭서 디mmfHo m섭 꺼 gm.꺼서혜벼섭꺼엉서m,꺼되때0.꺼껴φ김mm성m죄d ιho섭0년껴μ ιn.낌m냐 Hmm섭@엉섭 UφUμ션r 띠섭 rh껴um. 띠-
19 딩 pecimen \ Analyser T.Jens "' r- \,- rl Point Source Specimen i 下 下 p F i 낌 ure 10. Schematic Dia 용 rwn of the essential dimensions. cuvv- - Table of dimensions.mb 따-b -l - d p s A A 2 Value 41 cm. 1.4 cm. 김.01 ern. 0.65 em. o.067cm. 0.381 em. Table I. Essential dimensions.
20 맡 1e alumin 피 n spec JJrlen, appro:j 머..mately 100 따 19stroms thick, was prepared by vacuum evaporation on 七 mica. It was subsequently floated off on water 와 1d mounted on a st 없 1dard electron-microscope grid for stu( 합 in the apparatus.
CHAPTER III EXP 꾀 R 끄따 ~T. 따 따 :SULTS AND DISCUSSION 맡1e exper 끄nental data are represented graphically in Figures 11 through 17. Each figure is a plot of effective image density as afunction of bias voltage from-35 volts to 460 volts. The density scale 따ld uni 七 are arbitrarily chosen so that the numerical value is zei at cut-off and one at zero bias. 안 16 density readings g 뻐 19 toward and coming from cut-off are shmvn as separate points, (tt> 없 ld vertical bars. «), at the ends of'the E igure 11 is the calibration curve for the mesh, taken without thespecimen. 맑lebe빼없19le e was zero. 밀 \8 density curve drops sharply to zeroas cut-oft (at -33 volts) is approached 웰ld indicates a resolution of one volt at 합1e toe. A sharper cut-otf could be obtained wi 하 1. a finer mesh in the 없 lalyser 따 1d finer steps in 합 1e bias adjus 월 nent. A slight spread in the axial be 웰 n voltage 월 ld consequently a slight 따 1 sharpness 뇨 \ cut-orr is caused by the oonvergence of the beam heading toward focus 피하 18 때 alys 파 19 plane. 만 1e angle of oonvergence, after the divergent effect of 합 1e aperture field of the an 혀 :yser is 뇨 lcluded" 土 s about 0.00,radians. 말 lis causes a spread in 훨 i 려. be 웰 n voltage tor 합 1e unscattered r~s of les 멸 합 lan one-half volt 빼 lich is below the present resol: 펴파 g power.
22 맏le "sag 당ing" of the potential across the mesh openings.accounts for the cut-off occurring at -33 voltsinstead of zero bias. Figures 12through 11 are image densityversus bias voltage plots for electrons tran밟nitted by the th뇨1 aluminum spe꾀nen at roomtemperature for scattering 와19les of 0.0024, 0.0035, 라ld 0.0055 radians. The two curves for each 와19u1ar setting are for twodifferent mesh openings on opposite sides f the center of the strip. 말1e insert is the densityplot from cut-off to zero bias with 없1 eχpanded vertical scale. All of the curves show a sharp cut-off at about -32 volts. This.is very close to thecut-off on the calibration curve at ~ =0 and correspondsto a group of electrons which have lost no appreciable energy. A' comp훨1.son of the curves for be없ns scattered at differ없 lt 없19les indicates a slight shift in the cut-off bias over the 따1힘파랴 r월1ge. 말1e shift of about one volt is consistentwith the shift to be expected because of 10홉 S 꾀1 "axial be밍n voltage, for beams 뇨lcl뇨led to the axis (seeappendix c),. lbe spread in 훨ial be윌n voltage due to the convergence f pencils inclined totheaxis sets a resolution 1화nit of about two volts at the largest scattering 월 19le for which measurements were taken. The spread in axial be 없 n voltage c 뻐 be reduced by the use of a smaller stop to decrease the 월 1 힘 llar aperture of the converging p 하 lcil. Ano 합 ler abrupt rise in the density as 하 1e b 土 as increases pos 土 tively from cut-orr occurs between -20 때 d -15 volts (in all of the curves eχcept 하 lat in Figure 14). This rise occurs at
23 about 15 voltsfrom cut-off 와ld c때 be accounted for by a group of electrons which have lost 15 ev of 앉lergy and which begin to be transmitted as the mesh potential becomes 15volts more positive than cut-off. 돼1e 15 ev loss is approximately equal to 바le 11.~.8 ev 1055 found by Wa 七 anabe and which he a 七 tributed to the excitation of a pia밟na or collective oscillation.. Over the range ofscattering 없19les used, thi s energy loss was expected to show a shiftof about one volt in the position of the toe as n function of scatterilig angle. However, the bia~ volta당 e steps were not fine enough (eχcept near cut-off) to accurately determine the location of 하1e toe of 합1e density rises. Itwas therefore not possible tover 土합하1e 없19uJ.ar dependence. Most of 하1e curves show a density rise occurringat a bias voltage be 七 ;ween -10 없ld -5 volts corresponding to 없1 energy loss of approximately 25ev. This is close t 합1e 23 ev loss which Watanabefound 없ld attributedto 때 interband tr밟lsistion related to thef얼 1e structure in the L absorption edge for x-rays. There 土 s also a slight indication of a density rise at +45 volts mesh bias corresponding to a loss of about 75 ev. 봐 18 75 ev loss is outside the range of losses studied bywat 짧 labe, however a loss of appi 0' 다.mately this amount has beenrelated.by Cauchois 4 to the fine structure 뇨 1 하 1e K absorption edge for x-r 뭘 ra. A continuous background distribution of electron 잊lergies is suggested by 빼1e gl빼 leral slope of 하1e specimen curves, which could be due to radiation losses which occur when 해 1e electron
is accelerated in collisions. 앞 1e general slope ~ be due in 21+ partalsoto small intensity interband losses which were not observed because of lack of resolution. 맙 1e data assl 밍 nbled by }1arton, Leder, and. 9 :Hend1ow:itz.7 include the losses observed in thisstudy along wi.th 빠 lers.not obseiπred here. 말 1e inserts on some of the figures show the separate image density curves for increasing 없 1d decreasing bias from cut-off to zero. π1e differences between 합 1e curves of increasing 없 1ddecreasing biasmay be due to differences in the plates used to I ecord thesesections of 합 1e series of bias voltage settings. It is also possible 하lat the be월n had changed during the run, but the method of choos끄19 七 he density sc~le for the curves would tend to minimize 하lis eflec 七. However, 뇨1 both curves the same energy groups appearj' as indicated by the position of 합1e steeper slopes, althou양 lnot with the s밍ne 히nplitude. In Figuresl2 없ld 13 where 따ly one curve appears the photo앙raphic data for one direotion of bias ch없1ge was impaired by fogg뇨19. 멸 1e density versus bias curves in Figures 12 and 18 are for scattering 뻐 gles of 0.0024 radians. Two separate mesh penings, Nos. 6 없 ld8, on opposite aides of c 웰 lter were measured to obtain these curves. In Figure 12 the energy losses are more noticeable than in Fi 힘 Ire 18 but have the s 뼈 e values. π1e differences between 하 18 curves may be due to di.tferences in the scattered beam in 하 18 two scatterin 원 azimuths which
would indicate 합 1at 'the scattering lias not azimuthally 25 s,ymmetric as supposed earlier. Figures 14 월 ld 15 arefor scattering angles ofo.0035 radians correspondingto mesh open피gs Nos.5 and 9. 빨1e curve in F 생ure 14 differs frαn all of the other spec뇨nen curves in that the energy losses appeared tobe shifted toward cut-of by about 5 volts. At present, 七 he expl따1ation for this is not kno\m. 말1e curves in Fi~ 끄 es 16 라1d 17 are for scattering angles of 0.0055 radi와1s and correspond to mesh openings Nos. 4 and 10. A당 ain, the energy losses 'appear tobe 합1e same but have different intensities. Again the only ex따라lation is th.a'~ the sca.ttering pattern was not azimuthally synunetric.
ε6(mμ서 )ωm띠껴,[ m m 쉬띠이l서 μ{m서 ωm띠μ kr터mm쇠l건f서띠당쉬 H 배m섭여꺼번띠μm. + @ mm며껴서 m띠 꺼꾀죄mω터φ μk 섭 쉬μU잉3L위떠m띠죄mm Rm섭 꺼mK서여섭띠m.김껴k꺼ρ터mψ(μkr셔떠딩뉘LR 얘@{아껴힘O섭 껴mm 꺼白lm섭여설 φ 섭O다 꺼협겁꺼매띠U 세네.씨씨려폐떼crt crt +' ;j p. ζ) cd r-f 섬 μ o (1) μ > rr. 예 口 L꺼일 lμ3u{uμ여능 둬 - P ( S~ 펴 un A.1'9 I 꽉 q..t 허 A'+lsuaa 口 r.
27 o \o o l( (m껴. )ψ삐띠껴서 띠띠.에띠 이 서o.;..:j' ( 그 π1.성띠μm. +파이.n @ \O. 섭댄섭껴섭UQ 쇠mm설 ru{m서 φm셔씨껴서 업여m(μknιH띠터꺼μA mm띠μ서 m m.꺼g쇠mω임힘 섭.쉬껴U섭섭μ여m m 티끽-김꺼티섭서여ι μ성@μφμ꾀띠um터mmρ섭 μ껴uφ서ωφ되ηfι써 ιrmmιn서여섭때죄mω입ω되껴죄뼈며 μ쇠니섭 꺼mm뉘Rm다떠쉽 웨씨며볍테CH 야껴 o ~ a 폼 게터 μ f1.l H > a. 口 kl써 :lμ섭u@l서띠늄 틴o n m, (] 셔 [) 이 mn (] m n n. 셔{] 짜 o r-i N (8 낀 un A.z 밍.z~ tq.z'8 )λ~lsuea π1
28 o.성여μm. +각이. @ π1 ( 띠껴l - )ωm띠껴터0 /서en. 섭뻐섭뉘겁ψQ 되mψFr rμ{m서 φ뼈여껴서 kr터띠m(μkk여엽쉬l 배 m뻐애μ서 rm @쉬 μ되mφ터일 섭 껴꾀U.섭앙일여m 띠티섭섭꺼턱섭셔찌 커ρ멘ωrHm껴껴여Um터띠φ 일섭 LR껴U@ φm쇠껴힘 μmm {서여섭때꾀mm터m엽죄뻐며 μ죄껴섭 꺼mm꺼터mg럽 웨씨빔볍폐π{여l μω F kk,μ5u를 μkl씩힘 l껴야{p성 H여률 틴. 口 m 띠에여c α H, ν*여,(μmn K 마 lsuaa []m n.
29(띠껴서 )ω띠때껴서 이 m.꺼띠이.[ O 서l N o π1...=:t.성여rhm. +mmoo- α. 섭m디꺼다띠Q 되띠ωR 쇠m버 mm여껴셔 kr티@@(μ늙μ띠터 꺼μ이 mm띠껴서 krm 띠꺼 {되mm티μ 딩 꺼껴O섭섭힘여m 띠티에서섭꺼터며셔띠knn{ 성ωLHω껴껴서씨Um터벼ωρ섭 μμoωj φ@ {껴힘 HωmK서여섭여검m日ω엽죄m며 μ겹다 꺼m띠꺼딩띠섭떠럽 펴네씨빔볍폐Q띠서LHω r 힘힘 lnfpu쉽oμ LR휘 P며U성L 띠-툴 틴.0 口됨 n이 m m n. 서 J l [ 카 (8 낀 un A.1. 낌 1'+ 원 I 씬 A'+T 8ua a π1
30 u 3 ~I m (U一n.(μ-+mmcn--(μ 대o :.:1" (") π1 (m껴서 )ω떠띠껴서o섣m띠꺼m 이 샤셔c u. 섭찌섭뉘섭ψQ {mm설 FU{m서 ωm여껴서 - 임mψ {ki셔떠입쉬lhr배 ωm여껴. m m.써p쇠mu 섭힘 섭 꺼껴Q잉며μ띠m m 딩셔서섭꺼딩셔셔서띠 aρ성u HU껴껴여Um터mmp섭 μμuωhm@죄이fk μωmh서여섭여죄mm딩m쇠꾀죄벼5 설껴딩O껴띠띠써딩m섭띠겁 씨네에때밟에떠π빼어서LHω r L위힘 l껴야μug μ-w일μ 껴섭U성r셔며농 틴.0 口 o o mn ( s 샤 un κ..t 잃 ':):J: q..t'b )A 꽉십 uaa nm n
31 ("1(m껴서 )φ얘여μ m여꺼띠n-- l [ 이 G m, C) 仁 튼 t.성여 Hmo n.( +mmn.c @. 섭m딩껴섭φQ 되mU}깐..:t 씌m서 mm떠껴서 r ι5mm { 커rH떠딩껴μ@m띠껴서 m m꺼p쇠m밍션k 섭 쉬낌U 섭섭힘여m여협억디꺼터섭서여L꺼ρ성ωLHφ껴껴여Um섭5mωρ섭 μμum ωφ쇠껴일 μmm늙셔띠섭여되mω터ω집되뼈며 μ쉽섭o꺼mm쉬티m섭여립 폐-왜없세에(에서써서μm.0 口 ιrk l껴섭u터 μ μ힘,μau성 H여놓 FFmN n m o - n x, 0 F 케 (8 깎 un 1\.%'9 설 lq.% '9 )A ':l- ls 때 a CVl
32(m괴 )@@얘니 m 띠.껴m 이(](μ니 u -파(v).성여LH이.( +mm. @ o 케. 다m섭 꺼다mQ 되띠miL 씌m서 mm삐껴서 틸mωριnμ떠터뉘LR 버 mm여껴서 이 m에ρ되mω터k 섭 꺼껴U섭섭ι뻐애m 띠섣셜섭 꺼업섭서떠 np성mrhm껴껴서ωum터띠mρ섭 LR껴Um서Um [{ fk μmm늙셔얘섭여쇠mm딩@쇠껴되압 μ되껴되 꺼mm쉬터miμ띠럼 세낌셉볍떠어서μφ 口0 ι썩k 껴야닝P릅 μ L휘일 FiμU성ιH띠능 HmN1(녕on m. p. 셔 압l 셔 (s 따 1fR xag.iqiqj 딩 ) 쐐 lsu 딩 Q A'
CHAPTER IV CONCLUSIONS AND FUTURE WORK 싼 1e energy distribution in an electron beam, 다 학 lsmitted by a thin a1wninwn film, which serv,ed as a test specimen, was studied by a retarding potential method in which the energy analysis could be made as a function of the polar angle and azimuth of scattering. 빨1e pr꾀뻐 "y energy was 15 kev. The results showed thatthe transmit 七 ed beam contained electrons which had lost essentially zero energy aj.ong with groups of electronswhich hadsuf ered losses of about 15 ev 웰 1d 25 ev, and possibly 75 ev. In addition there appeared to be a continuous backgroundof electron energy losses over ther와1ge studied (trom 0 to 30ev). 맡1e 15 ev loss has been attributed to the eχcitation of plasma or collective oscillations of the electrons in the spec 뻐 lan l 없 ld 하 1e 2.5 웰 1d 7.5 ev losses have been attributed to interb웰ld tr와lsitions. 돼1e continuous background could be due to x adiat 土 on losses, 따1d uni esolvedsmal1 intensity interband losses. It was not possibleto observe the dependenceof the plasma loss on the 웰 191e of scattering because of lack of resolut 土 on in the mesh bias settings. This stuqy demonstrated the feasib 土 lity of thismethod of en 원 rgy analysis of electronbe 없 ns as well as the shortcomin 당 s of the apparatus 없ld measurements.
맘Ie resolution of the energy analysis could be improved considerably by finer settings in the bias voltage. However, 3 뇨 taking 하 ld working up the data would.be very time consuming if the photographicmethod described in this thesis were used. It would seem better to use a differentmethod of recording the image obtained; e.g., a fluorescent screen 라 ld aphotomultiplier tube could be used to measure the illwnination a' 七 a given position in the pattern as the bias voltage is varied continuously through its range. If, in addition, the bias voltage and photonmltiplier outputs were used to run 않 lxy-plotter, data recording would be greatly facilitated. Another improvement in resolution would result from using a finer mesh in the 웰 lalyser. Meshes of 20001ines per inch 랴 e available commercially, whereas the mesh used in this experiment was 500 lines per inch. 맡 1e axialbe 하 nvoltage loss due to angle of scattering can be avoided by arranging 하1e spec뇨nen lens between the specimen and the 와lalyser in such a w~thatthe pencils of scattered rays have their axes normal tothe 없lalyaing mesh inside the analyser. In thi앙 arrangement the individual pencils of scattered rays converge, as before, toward a focus inthe pi따18 1-1, at a diat따lce 4 6/3 beyond A. However, the spec끄nen is positioned so that its 꾀뻐 ge is projected at a distance 4s beyond A. 빨 lechief r~s of the scattered p 훨 lcils head toward the ax.i.al point of the image and on entering the 없 lalyser are dlver 딩 ad by the aperture lensinto a par 따.lel be 웰 n normal to the 웰 laly 잉 ing mesh.
3, A smaller angle of converg 앙 lce of 하 le pencils of r~s focused in the analysing plane would reduce 하 le spread in a:χial beam volta원e resultingfrom this cause. 맡le angle can be decreased qy the useof a smaller stop on the specimen lens rby 없1 increase in distance between 七 he specimen and the 따 lalysing plane. It would be interesting to apply this method, with impx ov앙nents of resolution, to o 바ler specimens. It would be especially.interesting to stu~ a case where the scattering pattern isnot rotationally symmetric.
BIBLIOGRAPHY 1. Bolun, D. 따 ld Pines" D. uacollective Description of Electron Interactions: I. Ma 양 letic Interactions." Physical Re 찌 ewj 82: 625-634. 1951. 2. Bohm" D. 밟ld Pines" D. 패. Collective Description of Electron Interactions: II. Collective vs Individua1 Particle Aspects of 하le Interaotions. 1I Physical ReviewJ 86: 338-353. 1952. 3. Bolun" D. a.ndpines" D. "ACollective Description of Electron Interactions: III. Coulomb Interactions in a Degenerate Gas. 1 Physical Review, 92: 609 625. 1953. 4. Cauchois".P.Y. "Etude compare I s 삐 Spectra K d'absorjjtion de 1 Aluin:i.nium Me tallique. ~gtac~sta~lographie, 5: 351-356. 1952 5. Davisson, C. J. 월 ld Calbick" C. J... 꾀 ectron Lenses." Physical Review, 42: 580. 1932 6. Ferrell" R. A. 밸 1 힘 llar Dependence of 해 1e Characteristic 표 le ;rgy Lossof.El~ctr6nsPassing 멜 1rough 봐 lin Foils.n Phys 섭 al Review, 101:,54-563. 1956. 7. Haberstroh" G. r Untersuchung der char와해er 土 stischen 파lerg:L e깨rerluste 따Lt Hilfe dergegenfeldme하 lode." Zeitschritt fur Physik. Bd. 11퍼 s 20,3. 19.$6. 8. H 허 1n, E. "Zur 봐 180riedes elecktrostatischen Geschwindigkeitsf 土 lters. 1I Jenaer J 앓 lrbuch, 1961/[I.,325. 9. Marton"L." Lede:r" L., and Mendlo 폐해 "H. "Characteristic 표 lergy Losses ot Electrons in Solida." Adv 없 'lces in Electronics, 7: 18.3-238. 19,5.
10. Mi.lyutin, V. I. and Kabanov, A. N. "An Electrostatic Electron-Velocity Ana 그 :yser. n Adv 따 lees in Physical SciencesJ LXI: 588-62μ.1957 ( 표 없 lslated rrom Uspe 빠 1i Fizicheski. 파 1 Nauk). 37 11. Pines, D. ita Collective Description of Electron Interactions: IV. Electron Interaction in Netals. 1I Physical Review, 92: 626-636. 1953 12. Watanabe, H. "Experimental Evidence for the Collective Nature of thecharacteristic ~ner잃r Loss of Electrons in Solids-Studies on 합1e Dispersion Relation or Plasma F reφl잊ley. 1I Journal of 합le l'hysieal Society or Jap없1, 11: 11~-11V; 1956;
APP 휠 NDICES
APPENDIX A FOCUSING OF SCAT 많 RED RA 쪼 S In Figure A1 rays scattered. by two different specimen points, So 때 d ~Iinto cones of the same angle e are shown. 만 1e axes of these cones are incl 뇨 led to each other at an an 렘 e 야따 ld intersect at e 뇨 1 the pi 없 le P. The cone of rays from So hasits axis normal to P 따 ld intersects P in a circle of radius z tan 8. 앞 1e azimuth ofthe scattered r~ corresponds t 합 1e 하 19le ~ in 합 1e pi 웰 le. 봐 1e r~s from 5 1 intersect P in an ellipse. 만 1e p 파 lts of intersec 납 on do not c 뻐 lcide pe:rfectly with those frαn So e 土합 ler 뇨 1 'dist 없 1ce from 0 or in azimuth in theplane. 만 1e lack of reg 土 stl ation of the 뇨 ltersection points is greatest in the direct 土 onof the separation of the 'spe 빠 nan points. 빨 1e r 혐 rs corresponding to this diraction are 따 'awn 土 nf 土뱀 re A2. These r~s from 31 intersect P r at 6 max and "n 다 n. From the law of sines: r m 필 I g 뇨 19 - z sect( - sin(90o.9.'" - or r m훌x": z sin e eec c:( cos(9 -+t'c ) Also from the law of sines: rm;i.n - z sec oc. - z eec c( sm e - sin(906- e+«)~ cos(e-κ ), 웹-g룹-M 4
lρ.서띠성섭여 m딩 μkmk@rh 성mμω껴껴여Umk mm다 um꾀껴료n배잉여서gu집힘o섭 닙U@mAψ니섭서 셰헤l셉미씨세때Q 예 r-l tf) \\\ \\\ l* 섭m터꺼UφQ m
41 섭ψc 꺼υψ 얘mω{ {껴μog 꺼껴Uφ μ 성ω져껴잉 π써섭 μuωnμψ껴딩 φ쇠꾀k g.꺼껴써씨μ껴m mψμfh φ o 업.~ r 녁업 Q H ω f 피예 싫 Is N CJ) F 에 Cf.) J..:I ~
42 01 r ndn 톨 빨 le rays from S... intersect Pat: o -e 따없z l- r= z t 랴 lq e s-- %-& 4 -) The ej 뿌 ressions f'or 괜 ax' Ij 빠 n' and r differ only in seoond and higher order terms in 용 and.~.' For of. = 0.001 radians 와 ld Q 0.006 radians(the largest value of' g was O.OO55radi 와 15), 윌 ld z 톨 P 4- (4/3)5 2.88 em, r~_... can be evaluated: max I rnaχ.:: z$(1-e 2 /3!) (1+ d,.2/2!) (1 +(e+4)2/2,1) 를 r(i _6XIO 6... 2$::0.0-6 0+. 85X10-6) =r(1... 10. 4 ). The lack of' registration, for riiiax and r r_~_ and r is less 하 1 따 1 that for min At a distance of,fifj'meshspacings (0.002") for the largest e used 웰 1d for a mesh op 훨과 ng or 0.001" 합 1e fractional γariation of' r over the mesh opening is: 0.001 11 =1/9, (γ 했 0.002" which is much 1 랴 'ger than 합 18 lack of registration' (10-4 parts ofr) of r maχ on r. TheretoI e 합 1e ellipse 따 ld circle 土 ntersection curves C 따 1 be considered tobe in registration. 말 1e azimuths of 합 1e intersection pointsalsoagree to first order and c 웰 1 be consider 당 d to be in registration.
APPENDIX B ELECTRON-OPTIC. 따 I ASPECTS OF 밸 IE ANALYSER 맡1e eφrl.valent optical system for the 없18그 :yser is 합1e S와neon both sides 하ld is 합1erefore worked out for one side on과 (see Figure Bl). 많e effect of the electricfield in the 따laJ.yser c때 be thought 'of as thesum'of 하1e separate effects f 七 ;wofields: Auniform field between the positive end electrode A at potential VA 없id the negative mesh electrod~ Ho at potential V M, 따ld a field associated with theaperture in the endelectrode. 맘1e local fields associated wi 七 h the small penings in the mesh are takenintoaccount separately_ 만1e 때 e 해 ure fie 펴 was sho 때 by Davisson and Calbic 원七 () be" to.first order" a 합 lin electron lens 'or focal leng 하 u f:= 4 V B r~ V7~z1-2'-=- C) -V7.)z)1 VB is the be 없 n voltage of the electron at 합 1e potential of the apertured electrode andis equal tova _ Va where Vc i 홉 the cathode potential. (~V/clz)2 and (~V/lz)l are the potential gradients which would 0: 쉴 at on 월 1e.two sides or 하 1e electrode in the absence of the aperture and have values of: (JV 써 Z)l =0 웰 ld (~Vl'z)2 - ( VA - VH ) s
싹핵- -MW@φμ셜* 뜯 - ---- m 꺼mj 힘- - ------. r딩 Udm 늙m F 띠 { 서딩 껴 α N mμμ m잉 ω서 jσ, U 따. 려.kCα,@V i o :> t..~-----~- m 껴싸팩~ 검 -- 채 - & 랩 t 픽 쇠농 - L 띠애
111e aperture field acts like a diverging lens of focallength: * 톨4(VA - Va) s l i -(VA - VM) Since Vlo.~ ~ v. M-- va r =. -4s 45 말le un:i.form fieldbetween the electrodes causes the electrons to travel on parabolic paths wi합1 verticesat No appx 0:> 다 matel.y. These paths when referred to 납lepot양ltial.of the end electrode c뻐 be replaced by 합leir t랴1gents justinside the aperture lens. 맘1e distance between the end elec다 ode andthe mesh as indicated by 하1e 七와1gents is 2s, 七 Mice the actual distance. F igure Bl c휠1 therefore be replaced by the op 七 ical counte만 )art, Fi힘끄 e B2, in which 합ler~s inside the 없lal~ser are straight. The rnesh 꽤 is the s웰ne size as ~~. Parabolic paths whichhave their vertices at a poin 七뇨l Mo 납lerefore have i따tial tangents which focus at..~ 때, a dist없1c e s. beyond Mo. Since electrons entering. the analyser are a.f'fected by the diverging action of the aperture field, a pencil for which the t때gents inside 하le 웰la과ser are to be focused at! 렐, must be directed from outside 하 1e analyser toward a focus atm(s 홉 e Fi 맴 re B.3). 만 1e position of Mrelative to 하 1e aperture lens is given by: r therefore (l!am)..,. (l/f) (l/' 때없 ) (l/am) + (1/- 때 ) 톨 (1/2s), AN =(4/3)8. The magnification of Mis given by: m=~ 따빼 213;
46 μ@mk꺼m섭m@ 되원임 moj께껴α,섭 kpo@셔떠m 띠 찌빅에비때에베띠 u) n -μmm늙서여섭얘φ쉴φ받쉬m껴야켜 이 늙여jHm되껴힘 --c 꺼m-딩mμunω셔여에서껴μ꺼 μψ 늙셔며잉여U껴써df디서k h셔써μ서여n껴u댁 1,..
47 'lbus t' 1, 하 le 꾀뼈 go of H_ referred to thespace outside the o analyser, is 2/3 the size or 예와 1d islocated wi 하 1 뇨 1 하 1e an 와 :yserat adistance (4/3)s f'romthe aperture lens. 맡 1e 패밍 llar aperture d:. of 하 1e pencil of r 했 s converging 설 1 납 1e space ou 七 sidethe 려 1a1ys~r to a focus at 11 is a.lso affected by the action of the aperturelens. 맡 1e diverging of.fect of this lens reduces 합 16 따 i 힘 llar aperture t tj.. = (2/3) c as c 와 1 be seen from Figure B3.
APPENDIX C E UR'I1IER ASPECTSOF 많 m 뼈 ALYSER 말 1e 와 l aj.yse :r measures 해 1e energy associatedwith the axiaj. velocity of theelectron8. 말 1e axial beam voltage, def뇨led by 캘nv~ 를 ev", depends on the angle which the electron z z pa 합 1 makes 'With the z-axis. In the space, outside theanalyser the chief ra:y (the electron path) -along'the axis.of the imaging cone',makes 웹때 gle 용튿 ~ /p withthe aj 다 s. The aperture 1 없 18 of 하 1e analyser increases 합 1e 따 19le to e, as shown 뇨 lf1gure 01, given-by: which c 와 lbe expre 홉 sedas: 용 1..9+ 戰 I, g =9(1+p/4s) where p. pqand -' f -4s., 말 1e be 웰 n voltage' just 'inside the an 따 ser is g 土 ~enby: 2..., 2., 2 IV... =ev.. - ev.tot. = 훨 nv- = 혈 nv:+ 혈 W B - _. A - - 0 '!hen the loss 끄 1 웰며. 봐. beam voltage due to 합 1e inclination of the rq is given 며 V z (loss) =,V B '--V z 1/2( 뼈 )vg and remains constant as 하 18 electron approachesthe retarding mesh.; S 뇨 lce v_is constant 파 1S 土 de 합 1e an 따뺀 ere 파 1 terms of 딩, r the axial he 빼 1 volta 훌 e loss-tor 해 e chief' ray is:
49 V 누.--- m지껴꺼wq섭 1셔껴Uω,... φ 4 껴 m다ω 씌U꺼n서떠U 디 mm 꺼 여Qφ<{ 껴 멀m껴m늙mφ 썩껴힘 힘 잉 뉘꺼여섭께셔O섭뉘띠껴씩여ψ쇠껴 μ내꺼페없배떠p 예 ω다 um다꺼뻐여를껴일 m껴씩펙섭φr% 께U @ Qm
vz(loss) 률 1/2(m/e)(v sinq,)2 50 or in terms of G: - VB si112 용 1\ =VB ~ 21 _ "... 2 Vz(loss) =vber-( l~ p/4s)ι In the penoil ofrays convergin 당 to M'~the angle to the o z.. 밍 ds varies in rna 힘 litude.from 용 ;...tt' to Q +~ for 9 7~1 or from zero to e κ for 9 1 쓰 (( 봐 l~ oorresponding range in 킬 dal be 월 n voltage loss is: f T g, > 44 ax1d for.q 스 0:... 1) _, 2,~, 21 V z (lo:3s) =V B I(e of t:( )C. _(Q -0.. )CoI = 4VB9 11 - = VB(9... '" )2 F 짧쩍 n 싫웹 g 없 'ATE 뱀짧 6 생 ERS!TY LIBRARY