Construction of a data base for secondary electron emission by a novel approach based on Monte Carlo simulations

Transcription

1 Construction of a data base for secondary electron eission by a novel approach based on Monte Carlo siulations T Iyasu and R Shiizu Departent of Inforation Science Osaka Institute of Technology -79- Kitayaa Hirakata-shi Osaka Japan shiizu@isoitacjp (Received: April 8 6 ; Accepted: Septeber 5 6) A novel approach is proposed for a construction of data base for the secondary electron eission which is described by the equation de δ ( ) k ( αz) exp where k and α are the secondary eission coefficient and absorption coefficient respectively to be derived for the data base E is the priary energy of incident electrons and [ de ] the energy dissipation with respect to depth which is to be obtained fro Monte Carlo calculation This approach is based on the use of theoretical secondary electron yield δ ) to derive and by coparing with experiental secondary electron yield δ Usually is characterized by the two exp ) δ ) physical quantities the axiu of secondary yield δ and the priary energy which provides ie E δ δ These physical quantities δ and E have been believed to be independent of one δ ( E ) k α another The present study however has revealed that α and E are closely correlated enabling us to derive and by coparing δ ) with either experiental δ exp ( E) or a set of experiental values of δ and E A preliinary construction of a data base of kα for 5 aterials is presented ( ) Introduction The secondary electron yield δ the average nuber of secondary electrons per nuber of priary electrons is described by a siple equation [] de δ ( E ) k exp( z () ) α where [ de ] E is the energy dissipation with respect to depth of an incident electron of priary energy E α is the absorption coefficient which was used by Bruining in the theory of secondary electron eission [] and has been widely used in studies of secondary electron eission since then [3] to describe the probability of secondary electrons generated at the depth z to eerge fro the surface k is the secondary eission coefficient that describes the efficiency with which energy dissipated in a layer at the depth z is converted to generation of secondary electrons So k and α ay be regarded as such aterial constants such as the Richardson constant and the work function in therionic eission [4] recise knowledge of the set ( kα ) therefore allows a Monte Carlo siulation approach to describe the secondary electron eission with considerable quantitative accuracy for various boundary conditions of practical iportance for scanning electron icroscopy (SEM) in particular critical diension (CD)-SEM [5] The question ay arise as to why the absorption coefficient α has been used here even though the inelastic ean free path λ inel has been widely used in surface electron spectroscopies [6] eg Auger electron spectroscopy (AES) X-ray photoelectron spectroscopy (XS) etc The reason is that a secondary electron undergoing inelastic scattering processes still has the possibility to reain as a secondary electron because the energy spectru of the secondary electrons spreads over the energy region fro to ~5 ev [7] Furtherore those secondary electrons with higher energies often cause a collision cascade of secondary electrons leading to the generation of other secondary electrons with lower energies The concept of an absorption coefficient or its inverse α is therefore not as siple as the case of the inelastic ean free path which describes the attenuation of signal electrons where the decay of signal intensity is siply described by exp( s / λ with s inel ) being the path length Despite the fundaental iportance of understanding secondary electron eission only very few experiental Copyright (c) 6 by The Surface Analysis Society of Japan

2 data for α have been reported so far probably due to the laborious task to obtain the absorption coefficient in experient Seiler and Staerk [8] easured the decrease of secondary electron intensity by irradiating a Cu-specien surface with an electron bea which resulted in the growth of a hydrocarbon fil on the specien with increasing irradiation tie They estiated the inverse of absorption coefficient for the hydrocarbon as α (hydrocarbon) n fro the decay curve of the secondary electron intensity plotted as a function of the hydrocarbon fil thickness Bronshtein and Segal [9] have also reported a systeatic investigation of α by plotting δ as the ordinate and the backscattering coefficient η as the abscissa a so called δ η curve by depositing one aterial onto a substrate of another aterial Since the experients to obtain the absorption coefficient are laborious extensive work can hardly be expected even though up-to-date data on α has been attracting reviewed attention fro industry in particular plasa display panel (D) anufactures In contrast to α experiental easureents of δ exp ) have been reported continuously [] Hence if the absorption coefficient can be derived fro δ exp ) the absorption coefficients for aterials of practical interest can be deterined ore easily In this paper we propose a novel approach to derive the absorption coefficient α and then the secondary eission coefficient k fro coparisons of with theoretical δ ) values obtained fro Monte Carlo calculations The secondary eission yield is characterized by the two physical quantities the axiu secondary yield δ and corresponding priary energy E [] Verification of the approach and its application to 5 aterials as a preliinary construction of a data base of ( α k) are presented It is also noted that a siilar attept to describe the secondary electron yield as a function of E and atoic nuber Z for 44 eleents has been reported by Lin and Joy [] Monte Carlo calculation First a Monte Carlo calculation was perfored to obtain [ de ] The odel is based on the use of screened Rutherford forula and Bethe s stopping power equation as follows []: The elastic scattering process is described by dσ Ze d 4 Ω v y hλ v sin v and ω are ass velocity and polar scattering angle of an incident electron respectively is the Bohr radius 4 ω + y 3 Z λ 885a a () and Z the atoic nuber of the target ato Bethe s equation in the continuous slowing down approxiation with Joy s correction factor [] to describe inelastic scattering is 4 de πe E ρn AZ 66E ln A J 9 J 976Z + 588Z for Z 3 (3) J 5Z for Z where the ean ionization energy J in the original Bethe s equation was replaced by J [3] which allows us to extend the equation to the energy range below kev Z A ρ and N A are the atoic nuber atoic weight density and Avogadro nuber respectively Then [ de ] E was calculated for different priary energies under the boundary condition corresponding to the experient as seen in Fig δ ) is then calculated for different values of α to find the best fit value of the absorption coefficient α by coparing with the relevant experiental δ exp ) Note the coparison has revealed that these exists a very close correlation between α and E This suggests the possibility that one can find a best fit value α which provides [ E ] MC agreeing well with the experiental [ E ] exp It has long been believed that E and α are independent each other Actually it has turned out that they are closely correlated to each other Once the best fit values of absorption coefficient α is obtained one can then find a k value k which satisfies de δ k exp( z ) (4) α E The values of k and α thus obtained are listed in Table and copared with the experiental results α exp published so far [9] 3 Results and Discussion 3 Universal curve plot Baroody [4] proposed the universal plot δ ( ) δ versus E E curve for various where he presued de δ ( E ) k (5) exp( z) α δ is the axiu secondary yield to be obtained at priary energy E E ie δ δ ( E ) Aong the physical quantities k α δ and E the present work has revealed that there exists a very close correlation between α and E which have long been believed to be independent of each other This therefore enables α to be obtained fro by coparing theoretical E J J J + 85 E

3 de E ( ev n) n Fig Trajectories of incident electrons of kev in a Cu target The energy dissipation in-depth is also depicted Table Coparison of theoretical absorption coefficients (9) experiental values ( ) α ex Material α (n) α ex (n) k Be 7 7 Ag 4 t Bi δ exp ( ) with δ E values with experiental easureents or ore directly with the experiental E According to the experiental universal curve plot proposed by Baroody [4] theoretical universal curves were obtained fro Monte Carlo calculations for Be Ag t and Bi Results are depicted in Fig All of the δ δ versus E E curves for each eleent plotted for different values of α overlap each other foring alost a single curve In other words all the curve plotted for different α values depicted for each eleent in Fig are represented by a single curve in Fig 3 This strongly indicates that α is very closely correlated with E suggesting that α can be derived fro E by using [ de ] which is obtained fro Monte Carlo calculations E α The difference in the shapes of the curves for the four eleents in Fig 3 can be attributed to the Rutherford scattering forula not being a good approxiation to describe elastic scattering for heavier eleents in the low energy region below kev [5] A systeatic MC calculation based on the use of Mott scattering cross-sections has provided better agreeent aong the curves for different eleents including the above four eleents which are then represented by a single universal curve ore reasonably [6] Consequently the results shown in Fig indicate that the present approach describes δ exp ) sufficiently for the derivation of α and k fro the database of δ and E which has been published [7] so far for a nuber of aterials of practical use α 3 reliinary construction of data base for (k ) Since a set of δ and E has been reported [7] for nuber of aterials we have applied the present approach for these aterials to derive k and α The results are listed in Table in which up-to-date data for TiO are also presented It is found that α values are around n or less except for a few etals which are liable to being oxidized under the experiental conditions of insufficient high vacuu In fact this was the situation when these easureents were perfored Hence α values of these etals are probably not so accurate as those of the other aterials The α values in Table ay therefore lead to the coon feature that the α values are around n or less with ost between ~ and ~5 n though this finding calls

4 E E Secondary electron yield (au) Secondary electron yield (au) δ δ E t riary energy (ev) E Be α 3n α n α 9n α 7n α 5n riary energy (ev) α n α 8n α 6n α 4n α n Secondary electron yield (au) Secondary electron yield (au) δ riary energy (ev) δ E Ag α 6n α 4n α n α n α 8n α α Bi n n α 8n α 6n α 4n E riary energy (ev) Fig Theoretical δ ) obtained fro Eq4 for different values of absorption coefficient: (a)be (b)ag (c)t and (d)bi Fig3 Theoretical universal curve plot as a function of absorption coefficient for Be Ag t and Bi

5 for ore systeatic investigation to obtain ore reliable data for E and δ with odern surface analytical instruents before construction of the data base of k and α Since easureents of δ and E with odern surface analytical instruents should be easier than in the early days of secondary electron eission studies the construction of a data base of k and α is now becoing attainable As an exaple of this proposal experiental results for Ti and TiO have recently been obtained by the authors [7] under the sae experiental conditions The results clearly indicate that the α value for TiO is larger than that for Ti This supports the idea [3] that the escape depths of the secondary electrons in insulators and seiconductors are longer than those for etals because the interaction with conduction electrons is uch saller 4 Suary The present paper reports a basic study of the secondary electron yield described by de δ ( E ) k exp( z) (6) α We proposed a novel approach to derive two physical quantities of practical iportance ie the secondary electron absorption coefficient α and the secondary eission coefficient k The results are suarized as follows: () A study of Eq 5 led to the finding that an intrinsic correlation does exist between α and E () Based on this finding we proposed a novel approach to derive the absorption coefficient α and the secondary eission coefficient k fro a database of δ and E by using the energy dissipation with depth [ de ] which is obtained fro Monte Carlo calculations (3) Once a data set ( α and k ) for a specific aterial of practical interest is provided by the present approach one can extend the quantitative calculation of secondary electron eission under different experiental conditions of practical use eg different priary energies E and angles of incidence θ of priary electron bea by using δ de ( E θ ) k exp( z α ) θ [ ] θ E (7) where de can easily be obtained fro Monte Carlo E calculation with sufficient accuracy An application of Eq (6) for critical diension (CD) SEM has been under exaination to find the best choice of E and θ for eliinating the charging up effect and the result will be published shortly Table Theoretical absorption coefficient and k values obtained fro Eq4 after δ and are deterined by coparison with E experiental data fro references () and (7) Inverse of Absorption coefficient α (n) k Experient () δ E (ev) Be 7 5 Mg Al Si 4 5 Ti Fe Co 6 Ni Cu 3 6 Ga Ge Zr Ag Cd Sn Sb Ba W t Au Hg b Bi Th 3 8 δ E (ev) α - (n) k TiO Fro reference (7)

6 Acknowledgeents One of the authors(rs) gratefully acknowledges enjoying the cooperation of Dr Yoshihara for international standardization over 5 years starting fro joining the VAMAS- TWA-Surface Cheical Analysis in 985 and then establishent of ISO-TC/(Surface Cheical Analysis) in 99 in which Dr Yoshihara has been leader of the Japanese delegation and later Chairan The authors wish fro the botto of their hearts that Dr Yoshihara will enjoy continuous success in his new career in industry References [] O Hachengerg and W Brauer Adv Electronics and Electron hysics 43 (959) [] H Bruining hysics and Application of Secondary Electron Eission ergaon ress London 954 [3] A J Dekker in Solid State hysics vol 6 F Seitz and D Turnbull Eds Acadeic ress New York 959 p5 [4] A J Dekker Solid State hysics rentice Hall Inc 957 chap7 [5] U Dersch A Korn C Engelann C G Frase W Haessler-Grohne H Bosse F Letzkus J Butschke Metrology Inspection and rocess Control for Microlithography XIX ed R M Silver SIE Bellingha WA 5 p63 [6] S Tanua C J owell and D R enn Surf Interface Anal 7 9 (99) [7] H Seiler Z Angew hys 49 (967) [8] H Seiler and M Staerk Z hys (965) [9] I M Bronshtein and R B Segal Sov hys Doklady 384 (958) [] CRC Handbook of Cheistry and hysics CRC ress Boca Raton Florida published every two years) [] Y Lin and D Joy Surf Interface Anal (5) [] Use of Monte Carlo Calculations in Electron robe Microanalysis and Scanning Electron Microscopy Eds K F J Heinrich D E Newbury and H Yakowitz NBS Special ublication 46 NBS Gaithersburg 975 [3] D C Joy and S Luo Scanning 76 (989) [4] E M Baroody hys Rev (95) [5] A Jablonski F Salvat and C J owell J hys Che Ref Data (4) [6] Z J Ding and X D Tang J Appl hys () [7] T Iyasu M Inoue H Yoshikawa and R Shiizu Surf Interface Anal 38 (6) in press