t. meier, b. pasenow, r. eichmann, t. stroucken, p...
TRANSCRIPT
![Page 1: T. Meier, B. Pasenow, R. Eichmann, T. Stroucken, P ...groups.uni-paderborn.de/wehrspohn/phocs/projekte/main/...T. Stroucken, P. Thomas, and S.W. Koch Department of Physics and Material](https://reader036.vdocuments.us/reader036/viewer/2022071500/611ecb5e28d5750599356c36/html5/thumbnails/1.jpg)
Semiconductor photonic-crystal structures: Optical spectra and carrier dynamics
T. Meier, B. Pasenow, R. Eichmann, T. Stroucken, P. Thomas, and S.W. Koch
Department of Physics and Material Sciences Center,Philipps-University Marburg, Germany
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Photonic crystals and semiconductorsPhotonic crystals
• 1D, 2D, 3D
• photonic bandstructure
• light propagation,nonlinearities, …
• interaction with atomicoptical resonances= level systems
Semiconductors and heterostructures
• bulk and quantum wells, wires, dots
• electronic bandstructure andconfinement
• Coulomb interaction important for optical properties (excitons, etc.)
• level systems not adequate,instead many-body theory required
quantum well
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Outline
Theoretical description of semiconductor optics
Influence of modified transverse fields
• consequences of inhibited spontaneous emission
• changes of exciton statistics and photoluminescence
Influence of modified longitudinal fields
• spatially inhomogeneous band gap, exciton binding energy,and carrier occupations
• wave packet dynamics
• lasing of spatially inhomogeneous structure
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-
--
Interband-Polarisation
k
E c
v
++
Lichtfeld
- - -
light field
Interband polarization
Electron-hole attraction⇒ hydrogenic series of
exciton resonancesbelow band gap
Photoexcited semiconductors
energy
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Theoretical description of semiconductor optics
many-particleinteraction
Vq
interband excitationk
E c
v
minimal Hamiltonian
single-particle states
Coulomb interaction introduces many-body problem⇒ Consistent approximations required: Hartree-Fock,
second Born, cluster expansion, ...
cv
.
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Equations of motion and light-matter interaction
• Maxwell equation
• semiclassical equations of motion for material excitations(density matrix): semiconductor Bloch equations
• material response described by
and similar equations for carrier occupations and
=Coulomb renormalization scattering
andcorrelations
phase space filling
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Theoretical description of semiconductor optics
• classical light field:
semiconductor Bloch equations + Maxwell’s equations
• quantized light field (required for consistent description of luminescence):
semiconductor luminescence equations= coupled dynamics of material and light-field modes
including photon-assisted density matrices
⇒ Consistent solution of coupled dynamics of light and material system
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Influence of transverse fields on semiconductor optics
Exciton resonance lies in a photonic band gap
Tra
nsm
issi
on Absorption
Energy
Model study of exciton formation after injection ofthermal electrons and holes in the bands:
Quantum wire in a photonic crystal.
Lowest exciton level lies inside photonic band gap (modeled by reduced recombination).
Solution of semiconductor luminescence equations.
![Page 9: T. Meier, B. Pasenow, R. Eichmann, T. Stroucken, P ...groups.uni-paderborn.de/wehrspohn/phocs/projekte/main/...T. Stroucken, P. Thomas, and S.W. Koch Department of Physics and Material](https://reader036.vdocuments.us/reader036/viewer/2022071500/611ecb5e28d5750599356c36/html5/thumbnails/9.jpg)
Exciton distribution in quantum wire
• T = 10 K, strong vs. weak recombination(free space) (1/100 due to photonic band-gap)
• strong depletion of q = 0 excitons in free space• overall shape NOT Bose-Einstein distribution• resulting influence on photoluminescence
Phys. Rev. Lett. 87, 176401 (2001)
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Influence of longitudinal fields on semiconductor optics
generalized Coulomb gauge generalized Poisson equation
generalized Coulomb potential VC
solution for piecewise constant ε(r)
J. Opt. Soc. Am. B 19, 2292 (2002)
⇒ near a periodically structured dielectricthe Coulomb potential varies periodically in space
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• 2D photonic crystal (air cylinderssurrounded by dielectric medium)
• cap layer• semiconductor quantum well
Model system
• ellipsoidal shape ofcylinder bottom
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• position-dependent band gap:biggest increase underneath center of the air cylinders
Corrections due to generalized Coulomb potential
• position-dependent electron-hole attraction: strongest underneathcenter of the air cylinders
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Spectrally selective excitation
-4 -2 0 2 40.0
0.2
0.4
0.6
Im χ
(arb
.uni
ts)
E-Egap
(EB)
phys. stat. sol. (b) 238, 439 (2003)
⇒ spatially-inhomogeneous carrier occupations excited by spectrally-narrow andspatially-homogeneous pulses
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Coherent wave packet dynamics
Spectrally selective excitation of quantum wire
-10 -5 0 5 10
15
10
5
0
position (a )
time
(ps)
position (a ) position (a ) -10 -5 0 5 10 -10 -5 0 5 10
B B B
⇒ spatially inhomogeneous carrier occupations evolve in timedue to wave packet dynamics
lowest intermediate highest exciton
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Incoherent processes: Dephasing and relaxation
Excitation at highest exciton. Carrier relaxation modeled by thermalization time T1. (T=50K)
coherent dynamics T1 = 4ps T1 = 2ps
⇒ in quasi equilibrium carriers accumulate in between the air cylinders
-10 -5 0 5 10
15
10
5
0
position (a )
time
(ps)
position (a ) position (a ) -10 -5 0 5 10 -10 -5 0 5 10
B B B
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Semiconductor lasers
⇒ gain spectra of semiconductorheterostructures, e.g., quantumwells, can be quantitativelydescribed using many-body theory
⇒ hybrid semiconductor photonic-crystals laser structures have been fabricated
Noda, et al., Science 293, 1123 (2001)
see, e.g., J. Optics B 3, 29 (2001)
• photonic crystal next to quantum well
• injection pumped laser structure
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Quasi-equilibrium carrier occupations
carrier ocupations for quantum wire close to photonic crystal at T=20K
electron distribution hole distribution
⇒ electrons and holes avoid positions underneath air cylinders
-10 -5 0 5 100.00
0.01
0.02
0.03
-10 -5 0 5 100.00
0.01
0.02
0.03
position (aB)
n = 0.06 0.12 0.18 0.24
position (aB)
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Influence of spatial inhomogeneity on absorption/gain spectra
bare quantum wire quantum wire close to photonic crystal
⇒ characteristic changes of lineshapeand gain at slightly lower total density due to spatially-inhomogeneous carrier occupations
quasi-equilibrium absorption for different carrier densities at T=20K
-6 -4 -2 0
0
30
60
90
120
-6 -4 -2 0
0
30
60
90
120
Im χ
(arb
. uni
ts)
E-Egap
(EB)
n = 0 n = 0.10 n
0
n = 0.20 n0
n = 0.23 n0
n = 0.24 n0
E-Egap
(EB)
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Spatially-resolved absorption/gain spectra
underneath air cylinder (low density) in between air cylinders (high density)
⇒ due to the space-dependent densitysome regions are absorbingwhereas others show gain
-6 -4 -2 0
-2
0
2
4
6
-6 -4 -2 0
-2
0
2
4
6
E-Egap
(EB)
n=0 0.04 n
0
0.08 n0
0.12 n0
Im χ
(ar
b. u
nits
)
E-Egap
(EB)
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Summary
Due to inhibited spontaneous emission a photonic band gap strongly influences material properties
• exciton formation and statistics, and photoluminescence
Coulomb interaction is altered near a photonic crystal
• spatially-varying band gap and exciton binding energy
• wave packet dynamics
• spatially-inhomogeneous quasi-equilibrium carrier occupations
• lasing of spatially-inhomogeneous structure
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Acknowledgments
Schwerpunktprogramm “Photonische Kristalle”
Heisenberg fellowship (TM)
cpu-time on parallelsupercomputer
Interdisciplinary Research Center Optodynamics