Coherent X-ray Diffraction on Quantum Dots

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1 Coherent X-ray Diffraction on Quantum Dots Ivan Vartaniants HASYLAB, DESY, Hamburg, Germany Or Coming Back to Crystallography

2 Participants of the Project University of Illinois, Urbana-Champaign, IL, USA Prof. Ian Robinson G. Williams M. Pfeifer J. Onken M.Liang F. Pfeiffer, Swiss Light Source, PSI, Switzerland Zh. Zhong, MPI, Stuttgart Prof. Gunter Bauer, Inst. für Halbleiter-und Festkörperphysik, Austria H. Metzger, ESRF, France 2

3 CONTENTS 1. Introduction 2. Imaging of QD s with Coherent X-ray Beams 3. Experiment (Ge islands on Si 4. Reconstruction of QD s from GISAXS data 5. Problems & Future Direction 6. Conclusions 7. Coherent X-ray Diffraction Project at DESY 3

4 Motivations 1. Electronic and optical properties of nano-devices depend on the structure (shape and strain 2. Development of different scattering methods for imaging nano-structures is extremely important Imaging Can we compete with electron microscopy? 4

5 Coherent X-ray Diffraction or X-ray Lensless Microscopy CCD Partially Coherent X-rays sample CCD First approach: Focusing Optics 5

6 Focusing Optics KB mirrors mirrors sample 100(V 200(H mm Focal spot size 1.5(H 1.0(V µm Robinson et.al., (2003 Optics Express, 11, 2329 Coherent X-ray Diffraction pattern from Ag nanocrystals of size D=170 nm 6

7 Alternative Approach: Using Periodic Array of Quantum Dots Motivations: Using a periodic patterned array for bio-molecules imaging I. Vartanyants & I. Robinson, J. Synchrotr. Rad. (2003, 710, 409

8 Imaging of biomolecules with femtosecond X-ray pulses Explosion of T4 lysozyme induced by radiation damage R. Neutze, et al., Nature ( , 752 8

9 Imaging of Biomolecules with Femtosecond X-ray Pulses Simulated continuous scattering image of a single T4 lysozyme molecule under ideal conditions without sample movement or damage. R. Neutze, et al., Nature ( , 752 9

10 Imaging of Quantum Dots with Coherent Beams Source Sample CCD [ s ( r p ( ] p( r S( r r = z S(r shape of coherently illuminated area s z (r projection of shape of one island s(r,z Electron density of periodic array of QD s p ( r = δ ( r rn n Diffracted intensity: I 2 2 coh ( q = A coh ( q = s z ( hn S( q hn n 10 2

$2D array of QD s and it s diffraction$ $island Diffraction pattern of individual$

11 2D array of QD s and it s diffraction pattern 2D array of QD s Diffraction pattern of 2D array Image of individual island Diffraction pattern of individual island 11

12 Iterative phase retrieval algorithm s k (x FFT A k (q Real Space Constraints Reciprocal Space Constraints s' k (x FFT -1 A' k (q Real space constraints: finite support real, positive Reciprocal space constraint: A k ( q I exp ( q J.R. Fienup, Appl Opt. ( , R.P. Millane & W.J. Stroud, J. Opt. Soc. Am. (1997 A14, 568

$used for reconstruction Diffraction intensity of$ reconstructed image Reconstructed image

13 Reconstructed image of 2D array of QD s Support used for reconstruction Diffraction intensity of reconstructed image Reconstructed image Reconstructed image with superposition of twin images 13

14 Experiment 14

$025 Q 1.965 x Diffraction pattern around Ge (202 peak I.$

15 Experiment (Sector 34 APS 1.95 Qz AFM image of 2D ordered Ge islands with corresponding line scans Z. Zhong & G. Bauer Q x Diffraction pattern around Ge (202 peak I. Vartaniants et. al., PRB 71, (2005

16 GISAXS measurements α i > α c ; α f < α i α i < α c ; α f > α i 1.2 deg α f =α i α f 0.7 deg α f =α c 0.2 deg µm µm -1 Q y -160 µm µm -1 Q y 16

17 Ewald sphere construction Q z CCD 2π/d x k f 2π/s z 2π/N x d x k i Q x 17

1 µm 1 µm Q z Experimental Data (Log scale

18 Reconstruction of quantum dot shape GISAXS measurements (α i < α c 930 µm µm 1 µm Q z Experimental Data (Log scale 240 µm µm µm -1 Q y Reconstruction 18

19 Reconstruction of quantum dot shape GISAXS measurements (α i < α c Final support 0.43 µm Best real space image Comparable with resolution in electron microscopy Average size: 128(H 45(V nm Resolution: 20(H 5(V nm 19

-1-190 µm -1 0 Q y 190 µm -1-190 µm -1 Q y 190

20 Reconstruction of quantum dot shape GISAXS measurements (α i < α c 930 µm -1 Q z 240 µm µm -1 0 Q y 190 µm µm -1 Q y 190 µm -1 Experimental Data (Log scale Reconstruction 20

21 Questions Problems Future Directions 21

$Simulation of diffraction pattern Beam stop effects An array of quantum dots$

22 Simulation of diffraction pattern Beam stop effects An array of quantum dots used for simulation 786 px Simulated diffraction pattern R 0 Beam stop 444 px 22

23 Test Reconstructions for the Different Size of the Beam Stop R 0 =0 px R 0 =10 px R 0 =20 px R 0 =30 px R 0 =40 px R 0 =50 px 23

24 Anomalous Ge K-edge Energy E(keV In this way we hope to separate Ge and Si contributions 24

25 25 Simulations Using DWBA Theory + = island i dv e A r q q r q ( ( ( χ + = island i f dv e R A r q q r q ( ( ( ( χ α + = island i f i dv e R R A r q q r q ( ( ( ( ( χ α α + = island i i dv e R A r q q r q ( ( ( ( χ α M. Schmidbauer et al., Phys. Rev. B ( ,

26 Simulations Using DWBA Theory 60 nm q z (Å -1 α i =0.1 Ge 60 nm Si 120 nm q z (Å -1 α i =0.3 D. Grigoriev, HU Berlin q y (Å -1 26

27 Simulations Using DWBA Theory I(q= A 1 (q 2 I(q= A 1 (q+ A 4 (q 2 I(q= A 1 (q+ A 2 (q+ A 4 (q 2 I(q= A 1 (q+ A 2 (q+ A 3 (q+ A 4 (q 2 27

28 Conclusions and Outlook Periodic systems of quantum dots can be effectively imaged with coherent x-rays with nanometer resolution Coherent X-ray Diffraction on buried quantum dot systems Coherent X-ray Diffraction on a patterned biological samples (viruses, molecules and etc. 28

29 Coherent X-ray Diffraction Project at HASYLAB Andreas Schropp Christian Schroer Edgar Weckert

30 Experiment on ID-01 in ESRF Staff of ID-01: Hartmut Metzger Christian Mocuta, Peter Boesecke CCD Sample 100 µm 40 µm 4.2 m 18 cm 80 cm 30

$Diffraction Pattern$ px (120 µm -1 500 px

31 Diffraction Pattern 7 kev 700 px (120 µm px (85 µm -1 Simulation 31

32 Samples Electron Microscopy O. Kuparova, II Physikalishes Institut, Aachen First Results of Reconstruction 32

33 Thank you for your attention 33

Coherent x-ray diffraction from quantum dots

$Coherent x-ray diffraction from quantum dots$ Coherent x-ray diffraction from quantum dots I. A. Vartanyants, 1,2 I. K. Robinson, 2 J. D. Onken, 2 M. A. Pfeifer, 2 G. J. Williams, 2 F. Pfeiffer, 3 H. Metzger, 4 Z. Zhong, 5,6 and G. Bauer 6 1 HASYLAB,