# part iv: epitaxial semiconductor nanostructures properties of low-dimensional quantum confined...

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PART IV: EPITAXIAL SEMICONDUCTOR NANOSTRUCTURES Properties of low-dimensional quantum confined semiconductor nanostructures Fabrication techniques of low-dimensional semiconductor nanostructures Formation and properties of self-assembled QDs Growth of QWRs-QDs on patterned surfaces Mechanisms of self ordering in epitaxial growth Slide 2 Properties of low-dimensional quantum confined semiconductor nanostructures Slide 3 Effect of quantum confinement on energy spectrum Energy spectrum for electrons confined in 1, 2 or 3D with infinitely deep, rectangular potential wells with sizes t x, t y, t z : Slide 4 Electron DOS in low-D systems Lower D sharper DOS potential advantage for optical and electronic properties 3D - bulk 2D - QW 1D - QWR 0D - QD Slide 5 Sizes needed to observe QC At T = 0K electrons occupy all energy states up to E F, corresponding to de Broglie (Fermi) wavelength F = 2 / (3 2 n) 1/3, with n = electron density. Quantum confinement for t i F Metals: 1 electron / atom F 0.5nm Semiconductors: much higher, depends on doping: e.g., n~1X10 18 cm -3 F = 29nm, t i 10nm is sufficient Slide 6 Subband population in QC systems If more subbands are populated, motion along confinement direction results only ground state must be populated, i.e., E 12 > k B T For infinite square QW, this means For electrons in GaAs at T = 300K t x < 20nm For holes, more complicated relations and m h >m e smaller t x Equivalent sizes for other confinement dimensions Slide 7 Uniformity requirements in QC structures Size non-uniformity inhomogeneous broadening of DOS For wells, | E i | / E i = 2 t i / t i ; E i Optical properties of QDs RT PL intensity, energy and FWHM as a function of Intensity: maximum for ~ 2.3ML Energy: broad minimum for ~ 2.3- 2.7ML ( largest QDs) FWHM: minimum for ~ 2.6ML (30- 35meV) larger islands: better optical quality, higher homogeneity > 2.7ML: formation of dislocations: decreased intensity, energy shift, broader lines. (Chu et al., JAP85, 2355 (1999)) Previous experiment: higher homogeneity, slightly higher size for lower (first stages of QD formation) high influence of experimental conditions! Slide 27 Effect of growth temperature (MBE) Increasing T (480-530C) decreasing energy larger QDs Explanation: larger diffusion length there is a larger nucleation-free area around islands ( nucleation centers, adatom sinks) where adatoms can be collected by the island 550C: In desorption (smaller QDs), In-Ga intermixing higher energy Increasing T: stronger, narrower lines better material quality Ground state 1st subband separation (530C): ~ 70meV (Chu et al., JAP85, 2355 (1999)) Slide 28 Effect of V/III ratio (MBE) T=480, different As 4 flux: enhanced In diffusion for lower As 4 /In ratios Lower As 4 fluxes: increased QD quantum efficiency Lower As 4 fluxes: small redshift increased QD size ( larger diffusion length, coherent with T dependence) (Chu et al., JAP85, 2355 (1999)) Slide 29 Lithographic positioning of SA QDs Self-assembled Ge islands on Si(001) pre-patterned with oxide lines Increased uniformity in size and separation Possible mechanisms: Diffusion barrier on the stripe edge Reduced strain energy at the stripe edge T. I. Kamins and R. S. Williams, APL 71, 1201 (1997) Slide 30 Lithographic positioning of SA QDs Preferential formation of InAs QDs in shallow, sub- m-size GaAs holes defined by electron-beam (a) 1.4ML, b) 1.8ML InAs) Holes with (111)A and B faces, QDs formed on B faces (favorable nucleation sites for In atoms). S Kohmoto, MSEB 88, 292 (2002) Slide 31 Vertical stacking of QDs Coherent InAs islands separated by GaAs spacer layers exhibit self-organized growth along the growth direction. The island-induced evolving strain fields provide the driving force for self-assembly provided the spacer is not too thick Bright field TEM pictures taken along [011] azimuth of five sets of InAs islands separated by 36 ML GaAs spacer layers. Q. Xie et al., PRL 75, 2542 (1995) X-STM constant current topography image of two stacks of InAs QDs. D. M. Bruls et al., APL 82, 3758 (2003) Slide 32 Lithographic positioning of stacked QDs Twofold stacked InGaAs/GaAs QD layers grown on GaAs(001) substrates patterned with square arrays of shallow holes ((a)(-d): 100-200nm period). The second QD layer responds to the lateral strain-field interferences generated by the buried periodic QD array: vertically-aligned QDs or satellite QDs placed on strain energy minima. Base size and shape, and lateral orientation are predefined by the E str distribution on the underlying surface. H. Heidemeyer et al., PRL 91, 196103 (2003) Slide 33 Growth of QWRs and QDs on patterned surfaces Slide 34 Grating fabrication for QWRs Slide 35 MOCVD on V-grooved substrates Stable facets forming in the groove: sidewalls: {111}A ~ 5-10 off towards (100) top and bottom regions: (100) + {311}A Different surface crystalline structure different diffusion & nucleation rates growth rate R depends on orientation R top, R bottom < R sidewall expansion at top, sharpening at bottom BUT: profile stabilizes at the bottom at the 10nm-level {111}A (100) {311}A sidewalls GaAs substrate Slide 36R {ijk} (100) expanding R (100) > R {ijk} (100) expanding R (100) > R {ijk} conformal gr"> Profile evolution during self-limiting growth R (100) > R {ijk} (100) expanding R (100) > R {ijk} (100) expanding R (100) > R {ijk} conformal growth R (100) > R {ijk} conformal growth layer A: t 100 > t 311 > t s expansion of (100) and {311}A facets layer B: t 100 = t 311 = t s stable facets, self-limiting growth layer A: t 100 > t 311 > t s expansion of (100) and {311}A facets layer B: t 100 = t 311 = t s stable facets, self-limiting growth G. Biasiol et al., APL 71, 1831 (1997). Slide 38 Optical Properties of GaAs-AlGaAs QWRs * hh and lh related transitions observed polarization anisotropy in e-lh/e-hh ratio * F. Vouilloz et al. ICPS 23, Berlin, 1996 PL FWHM of QWR ~ 6meV Photoluminescence Photoluminescence Excitation Slide 39 Mechanisms of self ordering in epitaxial growth Slide 40 Driving force for lateral epitaxy Chemical potential ( driving force for epitaxy supersaturation) : Lateral variations of lateral variations of growth rate Slide 41 Chemical potential growth rate Diffusion towards areas of lower Growth rate: increased at lower , decreased at higher Nernst-Einstein relation Continuity equation Slide 42 Example: sinusoidal chemical potential (x)= sin (x) j(x) - (x)= -cos(x) R(x) (x)= -sin(x) j j j j Slide 43 How self-ordering is established Need for an equilibrating action between non-uniform chemical potential (stress, shape, composition) and another factor that drives atoms away from chemical potential minima. As growth proceeds, this should bring to steady-state growth profile. Any change in growth parameters (materials, temperature, fluxes, growth rates...) should bring to a new steady-state profile, independent of the initial one. Slide 44 Stressed surface self-ordering of QDs 1. SK growth mode: adatom flux towards islands island coarsening 2. Strain energy (chemical potential) E s : Flux away from islands E s larger for larger islands dissolution rate larger as island size increases 3. 1 + 2: kinetic mechanism stabilizing the island size: slowing of the growth rate of large islands and increase of the adatom density away from them, thus enhancing nucleation of new islands (with small E s faster growth). 4. narrow island size distribution in the system (for f = 5 and 7.5%). 1D KMC model, A.L. Barabasi, APL 70, 2565 (1997) f = 7.5% ( ) 5 ( ) 2.5% ( ) 0% ( ) Slide 45 Pairing probability between 1st and 2nd layer of dots decreases with thicker spacers Model: atoms of 2nd InAs layer arrive on stressed region (I) of width 2l s ( strain-driven diffusion towards top of 1st islands) or unstressed region (II) of width l-2l s ( random island formation) l s increases as GaAs spacer is thinner Surface diffusion model pairing probability as a function spacer thickness, dependent on island size and density (measured), lattice mismatch and strain (calculated) and In diffusion length L D (fit parameter) Very good match with exp data for L D = 280nm (@ T=400C) Full calculations in Q. Xie et al., PRL 75, 2542 (1995) Vertical self-ordering of stacked QDs Slide 46 Surface chemical potential on a patterned, faceted substrate Diffusion towards the bottom Growth rate: increased at the bottom, decreased at the top tt ss bb Ozdemir and Zangwill, JVSTA 10, 684 (1992) lblb ltlt Slide 47 Mechanism of self-limiting growth CapillarityGrowth rate anisotropy = Self-limiting growth G. Biasiol and E. Kapon, PRL 81, 2962 (1998), G. Biasiol et al., PRB 65, 205306 (2002). Slide 48 Self-Limiting Growth: Al x Ga 1-x As AFM cross section of a V- groove Al x Ga 1-x As heterostructure VQW L s (Ga) > L s (Al) stronger Ga capillarity to the bottom Ga-rich Al x Ga 1-x As vertical quantum well L s (Ga) > L s (Al) stronger Ga capillarity to the bottom Ga-rich Al x Ga 1-x As vertical quantum well Nonuniform composition ordered phase increase of the entropy of mixing to be included in the model Nonuniform composition ordered phase increase of the entropy of mixing to be included in the model G. Biasiol and E. Kapon, PRL 81, 2962 (1998), G. Biasiol et al., PRB 65, 205306 (2002). Slide 49 Composition dependence of self-limiting bottom width Evidence for entropic contributions fixed by experiment fitted, L s G =17520nm Al X Ga 1-X As; T = 700C G. Biasiol and E. Kapon, PRL 81, 2962 (1998), G. Biasiol et al., PRB 65, 205306 (2002). Slide 50 Temperature dependence Arrhenius plots fit: E B G = 1.90.3eV fit: E B A = 2.30.2eV GaAs: Al X Ga 1-X As: G. Biasiol and E. Kapon, PRL 81, 2962 (1998), G. Biasiol et al., PRB 65, 205306 (2002). Slide 51 Evolution to self-limit

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