Life time, Mechanisms for Relaxation
The excitons within the quantum dot that are optically generated require lift times that are
long enough for them to be collected at the anodes. The collection requires the excitons,
charge carriers, to interact outside of the initial confinement of the dot where bulk
properties begin to play an effect. Within the quantum dot the excitons have life time
that is highly dependant on the strength of the confinement, the stronger the confinement
the longer the life time. This long lifetime is characteristic of the excitons undergoing
radiative relaxation, in which it self-annihilates releasing a photon. This process has been
explained theoretically which included a size dependency on the exciton life time has
been confirmed with experiments [1].
Non-radiative relaxation mechanisms are much quicker and dominate bulk
semiconductors carrier life times, but these mechanisms are suppressed within quantum
dots due to the break in periodicity of the lattice. There are three main sources of nonradiative relaxation of excitons, phonon interaction, surface reflection, and non-uniform
confinement potentials. Phonon relaxation occurs with quantum dots through some of
the same mechanisms as they do for the bulk, but at decreased rate. This decreased rate
leads to a longer exciton life time which is the primary reason for the enhanced collection
efficiencies of quantum dots. The main methods of relaxation in bulk semiconductors are
the Frohlich interaction, deformation potential interactions, and the piezoelectric
interaction [2]. These are all present for quantum dots as well, but have much different
characteristics, and have been found to be highly dependant on the size of the quantum
dot
The Frohlich interaction occurs when longitudinal optical phonons generate temporary
dipoles in the lattice atoms that are at the same energy of the exciton. This energy
dependency, a small issue in bulk semiconductors, dominates the Frohlich interaction rate
within quantum dots. As a quantum dot has discrete energy levels, only certain phonon
energies can create the dipoles that will interact with the excitons. This leads to a phonon
bottleneck [3], where the number of excitons is higher then the number of phonons at the
correct energy. This bottlenecking is a predominant effect as it results in a decreased
probability of interaction because all of the phonons of the correct energy are being
absorbed faster then they are being generated. The piezoelectric interaction is the same
process, except where it is acoustic phonons.
The deformation potential interaction occurs when the charge carriers interact with the
discontinuity of the lattice caused by phonons. As the phones propagate through the
substrate they cause the lattice atoms to vibrate, if this vibrations are strong enough then
the atom can resembled a defect, which creates small shifts in the electron band structure.
Within the quantum dots this effect is suppressed due to the electron band structure has
spread out states, thus requiring phonons of certain energies to interact with the electrons
once again creating a phonon bottle neck.
Although the quantum dot confinement reduces the probability of undesirable relaxation,
it generates alternative mechanisms for relaxation. The two predominant relaxation
mechanisms are the surface interactions and non-uniformity quantum dots [1]. The
impact of the quantum dot within the lattice of the substrate can create dislocations along
the surface. This dislocations act as scattering points for the charge carriers moving out
of the quantum dot, figure 1. These dislocations create small electric fields caused by
dangling bonds, which can interact with the carriers. This effect can be reduced by the
material choice and manufacturing method by ensuring that the dislocations are
minimized. The manufacturing method also affects the shape of the dot, and can result in
inhomogeneous shapes that result in asymmetric confinement. These effects lead to
spatial varying confinement, in which the exciton density will favour the less confined
portions of the quantum dot relaxing non-radiatively [1]. These two effects can not be
eliminated but their impact can be reduced by choosing the correct materials for the
quantum dot and the substrate and by having a controlled manufacturing method.
Recent research has developed a method of reducing these surface effects by using
periodic self assembled quantum dots [6]. By generating layers of self-assembled
quantum dots with 5 nm layers of substrate between them results in self assembled
periodicity [7]. The quantum dots form into a square lattice within the plane and begin to
align in the vertical direction, thus resulting in a rectangular lattice. This ordering is
caused by the strain field induced within the substrate from the initial quantum dots. This
effect results in the vertical alignment. As the quantum dots are created the atoms
attempt to minimize energy, which results in the spreading out of nucleation sites,
resulting in the in-plane periodicity [8]. It was seen that after 10 layers of quantum dots
the strains from each layer add up with the in-plane periodicity resulting in the self
assembled rectangular.
This periodicity was shown to greatly reduce the surface scattering due to the quantum
dots, thus improving the overall quantum efficiency [6]. The periodicity reduces the
scattering by generating an intrinsic electrical field around the quantum dots reducing the
probability of surface scattering. This effect is energy dependant and has been measured
to be increase the quantum efficiency of the lower energetic photons. This is because the
surface scattering can be modeled as a small perturbation in the conduction band, which
would effect the lower energetic carriers most.
Overall, these effects allow for the excitons to have a long life time (50-200 fs) [4],
giving them adequate time to relax through the reverse-auger effect causing charge
multiplication. The reverse-auger effect is when a high energy exciton relaxes by
exciting another exciton [ibid]. It is commonly discussed as two electron collision where
the higher energy electron ionizes the low energy electron. Because the electronic band
structure of the quantum dot excitons is closely spaced the reverse auger effect is
accented.
There is currently a debate on whether or not the reverse auger effect is the primary
mechanism for charge multiplication within quantum dots. Experiments have shown that
the multiplication occurs near instantaneous (order of ps), would is too fast to be
explained by the reverse Auger effect [5]. They explain the instantaneous carrier
multiplication as the result of a quantum effect such that the photon interacts with the
electron cloud wave function causing an excited wave function that has electrons in the
superposition of both multi-exciton and single exciton states. This is possible because an
excited single exciton in a high energy state has close to the same energy of multiple
excitons at lower levels, thus allowing for mixing states. This would result in the peak
theoretical efficiency of quantum dots to be limited by the mixing ratio of these two
states. This mixing ratio is difficult to measure as it is appears to be highly responsive to
materials and the confinement potential. It is also hard to theoretically predict because of
the probability of generating greater then two excitons.
[1] Theory of the quantum confinement effect on excitons in quantum dots of indirectgap materials, Takagahara, Takeda, Physical Review B V46 N 23, 1992
[2] Influence
of electron–phonon interaction on the
optical properties of III nitride semiconductors
X B Zhang, T Taliercio, S Kolliakos and P Lefebvre
J. Phys.: Condens. Matter 13 (2001) 7053–7074
[3] Breaking the Phonon Bottleneck for Holes in Semiconductor Quantum Dots
Ryan R. Cooney, Samuel L. Sewall, Kevin E. H. Anderson, Eva A. Dias, and Patanjali Kambhampati
PRL 98, 177403 (2007) PHYSICAL REVIEW LETTERS week ending
27 APRIL 2007
[4] Auger Effect in Semiconductors Author(s): A. R. Beattie and P. T. Landsberg Source:
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, Vol.
249, No. 1256 (Jan. 1, 1959), pp. 16-29
High-efficiency carrier multiplication
through direct photogeneration of
multi-excitons via virtual single-exciton
states
[5]
RICHARD D. SCHALLER1, VLADIMIR M. AGRANOVICH2,3 AND
VICTOR I. KLIMOV1*
nature physics VOL 1 DECEMBER 2005 www.nature.com/naturephysics
[6] Enhanced quantum efficiency of solar cells with self-
assembled Ge dots
stacked in multilayer structure
Arnold Alguno,a) Noritaka Usami, Toru Ujihara, Kozo Fujiwara, Gen Sazaki,
and Kazuo Nakajima
Institute for Materials Research
APPLIED PHYSICS LETTERS VOLUME 83, NUMBER 6 11 AUGUST 2003
[7] Lateral and vertical ordering in multilayered self-organized
InGaAs
quantum dots studied by high resolution x-ray diffraction
A. A. Darhuber, V. Holy,a) J. Stangl, and G. Bauer
Institut fu¨r Halbleiterphysik, Johannes Kepler Universita¨t, A-4040 Linz, Austria
A. Krost, F. Heinrichsdorff, M. Grundmann, and D. Bimberg
Institut fu¨r Festko¨rperphysik, TU-Berlin, D-10623 Berlin, Germany
V. M. Ustinov and P. S. Kop’ev
A. F. Ioffe Physical-Technical Institute, 194021 Saint Petersburg, Russia
A. O. Kosogov and P. Werner
Appl. Phys. Lett., Vol. 70, No. 8, 24 February 1997
[8] Lateral ordering of quantum dots by periodic subsurface
stressors
A. E. Romanov,a) P. M. Petroff, and J. S. Speckb
APPLIED PHYSICS LETTERS VOLUME 74, NUMBER 16 19 APRIL 1999