Electron Biprism in the Condenser System for CHIRALTEM Experiment

Transcription

1 Fakultät Mathematik und Naturwissenschaften, Institut für Strukturphysik Electron Biprism in the Condenser System for CHIRALTEM Experiment Petr Formánek, Bernd Einenkel, Hannes Lichte Speziallabor Triebenberg Zum Triebenberg 50 D Dresden Germany 1

2 Motivation phase shift k0 k + g 0 q q' direct (Lorentzians) detector interference (Kikuchi band) 2

3 Goals Illuminate specimen with two overlapping coherent electron waves => Interference fringes on a specimen Control the width of the interference area and the fringe spacing Target fringe spacing ~ 200 nm or ~ 0.1 nm Control phase shift between the two waves Phase shift ± p/2 fringe spacing 500 nm width of interference area 3

4 Electron Biprism - Principle of Operation Optical Biprism Electron Biprism 4

5 Biprism holder Controlling the fringe spacing and interference width Optimisation 5

6 Biprism holder Controlling the fringe spacing and interference width Optimisation 6

7 Holography vs. CHIRALTEM Setup C1 C1 Condenser C2 Condenser C2 biprism Objective MC OC OI specimen biprism Objective MC OC OI specimen DIF DIF Projector INT P1 Projector INT P1 P2 P2 7

8 Biprism Holders C2 Aperture holder Standard Triebenberg biprism holder Standard FEI biprism holder 8

9 New Biprism Holder Construction place for 2 apertures 4 mm 2 mm 9

10 New Birpism Holder Construction Technical Drawing M R R

11 Biprism holder Controlling the fringe spacing and interference width Optimisation fringe spacing 500 nm width of interference area 11

12 Electron Biprism - Control of Parameters P 1 P 2 crossover position Width of interference field W = 2bg 0 U bp 2r f (b+a)/a Fringe spacing S = l(a+b)/(2ag 0 U bp ) a Deflection angle g = g 0 U bp g g biprism b b intermediate image plane U bp biprism voltage l wavelength of electron waves g 0 = rad/v interference field 12

13 Optical System of CM200 Microscope Condenser Objective C1 C2 MC OC OI biprism specimen Problems Biprism inside the lens Coupling of condenser & objective Control of parameter a C1, C2 excitation Gun lens, extractor voltage Control of parameter b MC, OC excitation DIF Projector INT P1 a P2 b 13

14 Rotating the Coordinate System Condenser C1 C2 biprism biprism specimen Objective MC OC OI specimen DIF C1 C2 MC OC OI Projector INT P1 Condenser Objective P2 14

15 Thin Biprism Approximation biprism magnetic field electric field 5 mm 10 mm C2 15

16 Biprism in the C2 Lens - An Equivalent Model Program for plotting of beams in a Glaser-field lens Approximation of a thin biprism => Analytical calculation: Biprism in a lens is optically equivalent to biprism behind the lens <=> 16

17 Diffraction Mode Diffraction pattern of <001> silicon 5 nm -1 U bp = -190 V U bp = -140 V U bp = -90 V U bp = -40 V U bp = 0 V U bp = 60 V U bp = 110 V U bp = 160 V U bp = 210 V 17

18 Diffraction Mode distance of splitted reflections in diffraction plane [1/nm] Diffraction pattern of <001> silicon 5 nm -1 U bp = -190 V U bp = -140 V U bp = -90 V U bp = -40 V U bp = 0 V U bp = 60 V biprism voltage U bp [V] Deflection angle g ~ U bp In diffraction plane Dk = nm -1 /V U bp U bp = 110 V U bp = 160 V U bp = 210 V 18

19 Imaging Mode - Biprism Diagram Width of interference field W = A U bp -B Fringe spacing S = C/U bp B = 0: W = CA/S 1000 log W log S w W [nm] 100,, C2 = 0 %,, C2 = 30 %,, C2 = 70 %,, C2 = 100 % Open symbols: SuperTwin objective Filled symbols: Lorentz objective Lines: calculations in thin lens approximation S s [nm] 19

20 Biprism holder Controlling the fringe spacing and interference width Optimisation 20

21 Optical System of the Condenser (FEI CM200) Beam- -limiting aperture biprism C1 C2 MC OC OI f 1 f 2 f 3 f 4 f 4 specimen Imaging equation 1/f = 1/g + 1/b g 1 b 1 Magnification M = 1 - b/f Angular magnification b/g = 1 - g/f g 1 b 1 D 1 D 2 D 3 D 4 Free parameters Lens focal distances: f 1, f 2, f 3, f 4 Biprism voltage: U bp Position of the first crossover: g 1 Imaging conditions Fringe spacing of a certain value Certain number of fringes Parallel illumination of the specimen Maximum intensity at the specimen Certain minimal magnetic field at the specimen 21

22 Condition for the Fringe Spacing Beam- -limiting aperture biprism C1 C2 MC OC OI specimen f 1 f 2 f 3 f 4 f 4 g 1 b 1 g 2 b 2 a b a b D 1 D 2 D 3 S = l a+ b ag U 2 0 bp b + D b Db s= S Ł f3 f4 f3f4 ł f3db f3f4( D3 + b 4) b= D2 - fb 3 4+ ( D3+ b 4) f4- f3f4-db Dgf ( D1+ g1) ff 1 2 a =- f( D + g) + f g + f f -Dg

23 Condition for the Number of Fringes Beam- -limiting aperture biprism C1 C2 MC OC OI specimen f 1 f 2 f 3 f 4 f 4 NS = W N number of fringes a b g 1 b 1 g 2 b D 1 D 2 D 3 Nl( a+ b) = 4abg U - 4 g U r ( a+ b) bp 0 bp f f3db f3f4( D3 + b 4) b= D2 - fb 3 4+ ( D3+ b 4) f4- f3f4-db Dgf ( D1+ g1) ff 1 2 a =- f( D + g) + f g + f f -Dg

24 Condition for the Parallel Illumination Beam- -limiting aperture biprism C1 C2 MC OC OI specimen f 1 f 2 f 3 f 4 f 4 g 4 = f 4 g 1 b 1 g 2 b 2 g 3 b 3 g 4 D 1 D 2 D 3 ( D - f ) f D - f - f a = D 2 a =- - Dgf ( D1+ g1) ff 1 2 f( D + g) + f g + f f -Dg

25 Condition for the Intensity at the Specimen Beam- -limiting aperture biprism C1 C2 MC OC OI specimen f 1 f 2 f 3 f 4 f 4 g 4 => minimum g 1 g 4 g 1 b 1 g 2 b 2 g 3 b 3 g 4 D 1 D 2 D 3 g g D f g D + a = g Ł f1 łł f2 f2 f1- g1łł f3 ł - Dgf ( D1+ g1) ff 1 2 a =- f( D + g) + f g + f f -Dg

26 Summary of All Conditions s 0 a+ b b + D b Db = l Ł ag 0Ubp f3 f4 f3f4 ł Desired fringe spacing s 0 Nl( a+ b) = 4abg U - 4 g U r ( a+ b) Desired number of fringes N bp 0 bp f ( D - f ) f D - f - f a = D 2 Parallel illumination g g D f g D + a fi min Ł f1 łł f2 f2 f1- g1łł f3 ł Maximum intensity f < f Limit of the magnetic field 4 4,lim a =- - Dgf ( D1+ g1) ff 1 2 f( D + g) + f g + f f -Dg b = D - 2 f3db f3f4( D3 + b 4) fb + ( D + b ) f - f f -Db

27 Possible W-S values: Brute Force Method area for CHIRALTEM w [nm] ,, C2 = 0 %,, C2 = 30 %,, C2 = 70 %,, C2 = 100 % Open symbols: SuperTwin objective Filled symbols: Lorentz objective Lines: calculations in thin lens approximation forbidden area s [nm] 27

28 Possible W-S values: Brute Force Method Standard objective lens (SuperTwin) area for CHIRALTEM w [nm] ,, C2 = 0 %,, C2 = 30 %,, C2 = 70 %,, C2 = 100 % Open symbols: SuperTwin objective Filled symbols: Lorentz objective Lines: calculations in thin lens approximation forbidden area s [nm] 28

29 Possible W-S values: Brute Force Method Lorentz objective lens area for CHIRALTEM w [nm] ,, C2 = 0 %,, C2 = 30 %,, C2 = 70 %,, C2 = 100 % Open symbols: SuperTwin objective Filled symbols: Lorentz objective Lines: calculations in thin lens approximation forbidden area s [nm] 29

30 Summary Desired fringe spacing of 200 nm reached with objective lens switched off 30

31 Outlook Optimise hardware to increase intensity Croissant-shape contrast aperture in rotatable holder 10 mm Grid-shape SA aperture 10 mm 31

32 32

33 Acknowledgement Dr. Peter Tiemeijer, FEI Company, for providing information necessary to progress the project 33