Quantum Dots in Photonic Structures

1. Lecture 7: Lowdimensionalstructures Quantum Dots in PhotonicStructures Wednesdays, 17.00, SDT Jan Suffczyński Projekt Fizyka Plus nr POKL.04.01.02-00-034/11 współfinansowany przez Unię Europejską ze środków Europejskiego Funduszu Społecznego w ramach Programu Operacyjnego Kapitał Ludzki

2. Plan for today Reminder 2. Doping and holes 3. Lowdimensionalstructures

3. Wigner-Seitz Cellconstruction Form connection to all neighbors and span a plane normal to the connecting line at half distance

4. Envelope part Periodic (unit cell) part Bloch waves Bloch’stheorem: Solutions of the Schrodingerequation Felix Bloch 1905, Zürich - 1983, Zürich for the wave in periodicpotential U(r) = U(r+R) are: Bloch function: modified slide from Rob Engelen

5. Nearlyfreeelectron model Origin of a band gap! Kittel

6. Isolated Atoms

7. Diatomic Molecule

8. Four Closely Spaced Atoms conduction band valence band

9. Band formation

10. Electronicenergybands allowed energybands

11. Brilluoinzones e (k): single parabola folded parabola

12. Electronvelocity and effective mass in the k-space

13. Electronvelocity and effective mass in the k-space Velocityis zero at the top and bottom of energy band.

14. Electronvelocity and effective mass in the k-space Velocityis zero at the top and bottom of energy band, the. Efective mass: m*>0 at the band bottom, m*<0at the band top,in the middle:m*→±∞(effective mass descriptionfailshere).

16. Doping of semiconductors

17. Holes • Consider an insulator (or semiconductor) with a few electrons excited from the valence band into the conduction band • Apply an electric field • Now electrons in the valence band have some energy statesinto which they can move • The movement is complicated since it involves ~ 1023 electrons

18. Holes • We can “replace” electrons at the top of the band which have “negative” mass (and travel in opposite to the “normal” direction) by positively charged particles with a positive mass, and consider all phenomena using such particles • Such particles are called Holes • Holes are usually heavier than electrons since they depict collective behavior of many electrons

19. Low-dimensionalstructures

20. Dimensionality Increase of the dimension in one direction Increase of the volume 1 2 21 2 22 2 2 23

21. B A B B A B A z z z Low-dimensionalstructures quantum dot quantum wire quantum well

22. V x=0 x=L Discrete States • Quantum confinement  discrete states • Energy levels from solutions to Schrodinger Equation • Schrodinger equation: • For 1D infinite potential well • If confinement in only 1D (x), in the other 2 directions  energy continuum

23. Quantum Wells Energy of the firstconfinedlevel Decrease of the levelenergywhenwidth of the Quantum Welldecreased W. Tsang, E. Schubert, APL’1986

24. Quantum Wells Energy of confinedlevels GaAs/AlGaAs Quantum Well R. Dingle, Festkorperprobleme’1975

25. In 3D… • For 3D infinite potential boxes • Simple treatment considered • Potential barrier is not an infinite box • Spherical confinement, harmonic oscillator (quadratic) potential • Only a single electron • Multi-particle treatment • Electrons and holes • Effective mass mismatch at boundary

26. Density of states

27. Quantum Dots

28. QD asanartificialatom

29. QD as anartificial atom

30. QD as anartificial atom- differences

31. QD size • Should be small enough to see quantum effect • kBTat 4.2 K ~0.36 meV--> for electron maximum dimension in 1D ~100-200 nm • Small sizelarger energy level separation (Energy levels must be sufficiently separated to remain distinguishable under broadening, e.g. thermal)

32. QD types and fabricationmethods • Goal: to engineer potential energy barriers to confine electrons in 3 dimensions • Basic types/methods • Colloidal chemistry • Electrostatic • Lithography • Epitaxy • Fluctuation • Self-organized • Patternedgrowth - „Defect” QDs

33. Colloidal Particles • Engineer reactions to precipitate quantum dots from solutions or a host material (e.g. polymer) • In some cases, need to “cap” the surface so the dot remains chemically stable (i.e. bond other molecules on the surface) • Can form “core-shell” structures • Typically group II-VI materials (e.g. CdS, CdSe) • Size variations ( “size dispersion”) Si nanocrystal, NREL CdSe core with ZnS shell QDs Red: bigger dots! Blue: smaller dots! Evident Technologies: http://www.evidenttech.com/products/core_shell_evidots/overview.php Sample papers: Steigerwald et al. Surface derivation and isolation of semiconductor cluster molecules. J. Am. Chem. Soc., 1988.

34. ElectrostaticallydefinedQDs • Only one type of particles (electronorholes) confined • --> (No spectroscopy)

35. LithographydefinedQDs QW • QW etching and overgrowth Etching Verma/NIST Overgrowth • Mismatch of bandgaps potential energy well • The advantage: QD shapingand positioning • The drawback: pooropticalsignal (dislocationsdue to the etching!)

36. LithographydefinedQDs V. B. Verma et al., Opt. Express’2011

37. Lithography • Etch pillars in quantum well heterostructures • Quantum well heterostructures give 1D confinement • Pillars provide confinement in the other 2 dimensions • Disadvantages: Slow, contamination, low density, defect formation A. Scherer and H.G. Craighead. Fabrication of small laterally patterned multiple quantum wells. Appl. Phys. Lett., Nov 1986.

38. FlucutationtypeQDs Flucutation of QW thickness Flucutation of QW composition

39. Epitaxy: Self-Organized Growth Self-organized QDs through epitaxial growth strains • Stranski-Krastanov growth mode (use MBE, MOCVD) • Islands formed on wetting layer due to lattice mismatch (size ~10snm) • Disadvantage: size and shape fluctuations, strain, • Control island initiation • Induce local strain, grow on dislocation, vary growth conditions, combine with patterning Lattice-mismatchinduced islandgrowth