Emissione di luce in campo prossimo da atomi artificiali

Transcription

1 Università degli Studi di Messina Dipartimento di Fisica della Materia Italye Tecnologie Fisiche Avanzate Ecole Polytechnique Fédérale de Lausanne Switzerland Institute of Theoretical Physics Emissione di luce in campo prossimo da atomi artificiali O. Di Stefano, G. Pistone, S. Savasta, G. Martino, R. Girlanda, S. Portolan

2 Outline: Spatially resolved photoluminescence in semiconductor nanostructures (G. Pistone et al. APL 2004) Near-field light emission from dark-states excitonic occupations (G. Pistone et al. APL 2008) Time and spatially resolved photoluminescence in semiconductor macroatoms (G. Pistone et al. PSS(b) 2008) Conclusions

3 Microscopic quantum theory of spatially resolved photoluminescence in quantum wells A microscopic quantum theory of spatially resolved photoluminescence in quantum wells with interface fluctuations that includes light quantization, acoustic phonon scattering, and inhomogeneous sample-excitation and/or light-detection is presented. The theory can model low-temperature photoluminescence and photoluminescence excitation experiments performed in illumination, collection or illumination-collection mode or diffusion experiments where the spatial positions of excitation and collection are scanned independently. Numerically calculated two-dimensional images clarify the impact of the microscope setup on the obtained images and resolutions [1-4]. [1] G. Pistone et al., Appl. Phys. Lett. 84, 2971 (2004) [2] H. F. Hess et al., Science 264, 1740 (1994) [3] D. Gammon et al., Phys. Rev. Lett. 76, 3005 (1996); Science 273, 87 (1996) [4] Q. Wu et al., Phys. Rev. Lett. 83, 2652 (1999)

4 Theoretical background The positive frequency components of the operator describing the signal that can be detected by a general near-field setup can be expressed as [5]: Elastic background signal proportional to the input electric-field operator where P + (r) is the sample polarization density operator, A is a complex constant depending on the impedance of the material constituting the tip and E out (r) is the signal mode delivered by the tip. [5] J-J. Greffet and R. Carminati, Progress in Surface Science 56, 133 (1997)

5 ...theoretical background The polarization density operator can be expressed in terms of exciton operators as Confinement function Exciton wavefunction Exciton operator See e.g. Di Stefano et al. APL 2000 relative inplane eh coordinate centre of mass motion

6 ...theoretical background Photoluminescence can be defined as the incoherent part of the emitted light intensity. The PL that can be measured by a photodetector after the collection setup (broadband detection) is proportional to The steady-state spectrum of incoherent light emitted by the semiconductor quantum structure and detected by the SNOM setup can be expressed as: G. Pistone et al., Appl. Phys. Lett. 84, 2971 (2004)

7 The system Hamiltonian The Hamiltonian determining the dynamics of the semiconductor system is given by the three contributions Electronic Hamiltonian of the semiconductor system Interaction of the semiconductor with the light field Inelastic scattering due to the interaction of excitons with the phonon bath

8 The kinetic equation The kinetic equation for the diagonal terms of the exciton density matrix can be derived starting from the equations of motion Heisenberg for the exciton operators under the influence of : eventually inhomogeneous generation rate inward ph-scattering outward ph-scattering + radiative decay Rate for spontaneous emission proportional to the exciton oscillator strength

9 The Generation term and I PL The generation term depends on the spatial overlap between the illuminating beam and the exciton wavefunctions corresponding to exciton levels resonant with the input light: spatial overlap between the illuminating beam and the exciton wavefunctions Once the exciton densities have been derived, the PL spectrum can be readily obtained. Applying the quantum regression theorem, we obtain Overlap of the exciton wavefunctions with the signal mode supported

10 Spatially resolved photoluminescence in QWs with interface roughness The disorder potentials The effective disordered potentials V(r) are modelled as a zero mean, Gauss distributed and spatially correlated process defined by the property where denotes ensemble average random is the width of over the energy distribution, is configurations, the correlation length and characterizing the potential fluctuations. 100 nm (a) (b) ξ = 16 nm, v 0 = 2.0 mev and ξ = 7 nm, v 0 = 2.2 mev

11 Spatially resolved PL (collection mode) 4 K 40 K 4 K 40 K nm 100 nm K FWHM (nm) 110 Energy integrated spatially resolved photoluminescence when the samples have a temperature of T=4K and T=40K for different spatial resolutions (b) K FWHM (nm) 70 (a) Martino et al. J. Phys. Cond-Mat. (2006) For sample (a) the enhancement of spatial resolution up to 30 nm is crucial to map both the real-space distribution of eigenstates within quantum dots and the potential profile. Instead, for sample (b) is not possible to obtain information about the potential but it is still possible to map the exciton eigenfunctions.

12 Near-field light emission from dark-states in a quantum dot We theoretically study the carrier capture and distribution among the available energy levels of a symmetric semiconductor quantum dot under continuous-wave excitation resonant with the barrier energy levels. At low temperature all the dot level-occupations but one, the second (dark) energy level, decrease monotonically with energy. The second energy level, displays a steady-state carrier density exceeding that of the lowest level more than a factor two. This non equilibrium effect does not origin from radiative recombination before relaxation to lower energy levels, but at the opposite, it is consequence of carrier trapping due to the symmetry-induced suppression of radiative recombination [1]. While the observation of such effect by means of far-field spectroscopy is prevented, scanning near-field optical microscopy can detect the evanescent waves generated by dark-states occupations. Numerically [1] U. Hohenester calculated et al., Phys. two-dimensional Rev. Lett. 95, (2005) images clarify the [2] G. Pistone et al., Appl. Phys. Lett. 84, 2971 (2004) impact [3] of H. F. the Hess microscope et al., Science 264, setup 1740 (1994) on the obtained images and [4] D. Gammon et al., Phys. Rev. Lett. 76, 3005 (1996); Science 273, 87 (1996) [5] O. Di Stefano et al., Appl. Phys. Lett. 77, 2804 (2000) resolutions [2-6].

13 The sample A natural QD or terrace nm Confinement potential for excitons, which is induced by local monolayer fluctuations in the thickness of a semiconductor quantum well. mev The simulation domain is a sample of (240 x 240) nm with a prototypical (b) interfacefluctuation confinement of rectangular shape with dimensions (60 x 90) nm, and monolayer fluctuations giving rise to a 6 mev effective confinement potential.

14 Spatially resolved PL (collection mode) FWHM = 40 nm T = 2 K Energy (mev) 4 K PL (a) ABS A Tip Position (nm) Excitonic wavefunctions min max min max Photoluminescence (PL) and absorption (A) images as a function of photon energy and beam position obtained after uniform illumination of the sample at the energy of the 1s exciton in absence of disorder and collecting locally the emitted light along the symmetry line of the sample, in the direction of the greater

15 Spatially resolved PL (collection mode) 0 0 T=2K FWHM 35nm T=10K 80nm out O Energy (mev) T=30K Energy (mev) 150nm Tip Position (nm) PL images as a function of photon energy and beam position obtained at three different temperatures, with a spatial resolution of FWHM = 40 nm Tip Position (nm) PL images as a function of photon energy and beam position obtained at three different spatial resolutions, at the

16 Level occupations C LS 1 populations (d) T = 2 K T = 30 K rgy (mev) Energy (mev) 16/26

17 ...introducing disorder Specific realization of the effective disordered potential used for PL calculations. Corr. Length = 8 nm Amplitude = 0.6 mev Arb. Units 50 nm (a) FWHM = 40 nm, T = 4 K PL (b) PL energyintegrated image obtained after uniform illumination of the sample PL spectra calculated centering the tip in the center of the dot (C) and in the position indicated by a circle in the first panel (RS) Arb. Units C RS PL PL Far field (c) (d) Energy (mev) Energy (mev) Far-field PL spectrum 17/26

18 Spatially and time resolved PL line scans for different temperatures in collection mode FWHM = 20 nm 4 K Increasing the temperature, we observe a tendency to a more uniform emission from the dot. It is due to the fact that the increase of nonradiative decay with temperature reduces the difference in the total decay rates between the two lowest energy states of the dot. Comparing the panels at different temperatures, we can see, passing from 2 to 6 K, a slightly lowering in the decay time of the dot emission. On the contrary, increasing further the temperature (panels c and d), determines an increase of the decay time. We find that the temperature behaviour of population decay times strongly differs from that of the excitonic polarization (related to the nondiagonal elements of the density matrix) which monotonically decrease with temperature. At low temperature only a few energy levels (actually the first two) get populated, when increasing temperature higher energy optically inactive or poorly active levels get populated reducing the overall decay due to radiative recombination. ulse time-width: FWHM = 1 ps Excitonic wavefunctions min max min max We also observe that the maximum emission intensity is not located at the dot center but is laterally shifted. This behaviour is consequence of the fact that the largest contribution to near-field emission at this high spatial resolution comes from the second energy level of the dot that has a p-like shape with a node at the center of the dot. This state, owing to cancellation effects in is dark under far field collection, but detecting emission from this state becomes possible in near-field.

19 Normalized time resolved PL intensity Normalized time resolved PL intensities obtained at four different temperatures. The tip is centered at the dot emission maximum (point A in the previous panel). FWHM = 20 nm. Normalized time resolved PL intensities (FWHM = 20 nm, T = 2K) performed fixing the tip at the three different points of the sample indicated by letters A, B, C in the panel in the previous slide.

20 Spatially and time resolved PL intensity Illuminating the sample at the barrier energy, we notice a rapid decay of the emission and then an increase of the PL spectrum due to the radiative state; we also observe that at this low resolution the two lobes from the dark state disappears, as expected. FWHM = 150 nm, T = 2K

21 Conclusions We have investigated the spatially and time resolved PL emission of a naturally occurring symmetric quantum dot induced by monolayer fluctuations in the thickness of a semiconductor quantum well, showing the impact of the reduced dark-states relaxation on the distribution of electron-hole pairs among the available energy levels after a far-field continuous wave excitation. The obtained numerical results show that the carrier recombination dynamics is significantly affected by thermal populations in optically inactive or poorly active exciton states in agreement with recent experimental results. The calculated near-field luminescence properties of these states depend critically on tip position, temperature and spatial resolution and clearly indicate the potentiality of near-field PL for addressing general questions regarding

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23 International Conferences: G. Pistone, S. Savasta, O. Di Stefano, G. Martino, R. Girlanda, and S. Portolan, Near-field light emission from dark-states in semiconductor quantum dots oral presentation at HCIS 15-15th International Conference on Nonequilibrium Carrier Dynamics in Semiconductors Tokyo, Japan - July 23-27, 2007 G. Pistone, S. Savasta, O. Di Stefano, G. Martino, R. Girlanda, and S. Portolan, Near-field control of the light emission properties of a symmetric semiconductor quantum dot OECS th International Conference on the Optics of Excitons in Confined Systems Messina, Patti Italy, September 10-13, 2007 G. Pistone, S. Savasta, O. Di Stefano, R. Girlanda, and S. Portolan, Time and spatially resolved photoluminescence of quantum structures with interfacial roughness: a theoretical description OECS th International Conference on the Optics of Excitons in Confined Systems Messina, Patti Italy, September 10-13, /26

24 Publications: G. Pistone, S. Savasta, O. Di Stefano, and R. Girlanda, Spatially resolved spectra in semiconductor quantum structures: Spatially averaged spectra compared to far-field spectra, Phys. Rev. B 67, (2003) G. Pistone, O. Di Stefano, S. Savasta, and R. Girlanda, Is the spatially averaged spectrum equal to the global spectrum?, Phys. Stat. Sol. (c) 0, 1425 (2003) O. Di Stefano, S. Savasta, G. Pistone, G. Martino, and R. Girlanda, Optical mapping of amplitude and phase of excitonic wave functions in a quantum dot system, Phys. Rev. B 68, (2003) O. Di Stefano, S. Savasta, G. Martino, G. Pistone and R. Girlanda, Towards perfect nanoscale microscopy, Conference Proceedings Vol. 84, Progress in Condensed Matter Physics, G. Mondio and L. Silipigni (Eds.), SIF, Bologna, 2003 G. Pistone, S. Savasta, O. Di Stefano, and R. Girlanda, Spatially resolved photoluminescence in semiconductor nanostructures: A theoretical description, Phys. Stat. Sol. (c) 1, 560 (2004) G. Pistone, S. Savasta, O. Di Stefano, and R. Girlanda, Microscopic theory of spatially resolved photoluminescence in quantum structures, Semicond. Sci. 24/26 Technol. 19, S327 (2004)

25 G. Pistone, S. Savasta, O. Di Stefano, and R. Girlanda, Microscopic quantum theory of spatially resolved photoluminescence in semiconductor quantum structures, Appl. Phys. Lett. 84, 2971 (2004) G. Pistone, S. Savasta, O. Di Stefano, and R. Girlanda, Quantum theory of spatially resolved photoluminescence in semiconductor quantum wells, CP772, Physics of Semiconductors: 27 th International Conference on the Physics of Semiconductors, edited by José Menèndez and Chris G. Van de Walle, American Institute of Physics, 2005 S. Savasta, G. Martino, G. Pistone, O. Di Stefano, and R. Girlanda, Microscopic theory of spatially resolved photoluminescence in disordered nanostructures, Atti dell Accademia Peloritana dei Pericolanti, Classe di Scienze Fisiche, Matematiche e Naturali, Vol. LXXXIII, DOI: /C1A ( ), Adunanza del 16 maggio 2005 A. Piccolo and G. Pistone, Estimation of heat transfer coefficients in oscillating flows: The thermoacoustic case, Int. J. Heat Mass Transfer 49, 1631 (2006) G. Martino, G. Pistone, S. Savasta, O. Di Stefano, and R. Girlanda, Spatially resolved photoluminescence in quantum wells with interface roughness: a theoretical description, J. Phys.: Condens. Matter 18, 2367 (2006) A. Piccolo and G. Pistone, Computation of the time-averaged temperature fields and energy fluxes in a thermally isolated thermoacoustic stack at low acoustic Mach numbers, Int. J. Thermal Sciences 46, 235 (2007) 25/26

26 G. Pistone, S. Savasta, O. Di Stefano, G. Martino, R. Girlanda, and S. Portolan, Near-field light emission from dark-states in semiconductor quantum dots, Phys. Stat. Sol. (c), 5, 382 (2008) G. Pistone, S. Savasta, O. Di Stefano, G. Martino, R. Girlanda, and S. Portolan, Near-field control of the light emission properties of a symmetric semiconductor quantum dot, to appear on Phys. Stat. Sol. (c) (2008) G. Pistone, S. Savasta, O. Di Stefano, R. Girlanda, and S. Portolan, Time and spatially resolved photoluminescence of quantum structures with interfacial roughness: a theoretical description, to appear on Phys. Stat. Sol. (b) (2008) G. Pistone, S. Savasta, O. Di Stefano, G. Martino, R. Girlanda, and S. Portolan, Near-field light emission from dark-states excitonic occupations, to appear on Appl. Phys. Lett. (2008) 26/26