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Ptiyaica Wbrid Spt mb v
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Arraysof quantum dots promise improved
performancefor semiconductor lasersandhavethe
added advantage that theycanassem ble themselves
Quantum-dot lasers
KARLEBERL
bulk semiconductor material
SEMICONDUCTOR lasers
are key
components
in
many
of
the appliances that wetakefor granted in everyday life.
Fibre-optic communications and compact-disc players
are
perhaps the two best known examples. There is alsoa
world-wide research
and
development effort
to
improve
the performance of these devices by making them smaller,
brighter, more efficient
or
capable
of
lasing
at
new wave-
lengths. A new class
of
semicond uctor laser
- a
quantum-
dot laser that self assembles
-
is showing great promise
in
many
of
these areas.
Semicon ductor lasers emit light when
an
electron
in the
conduction band recombines with an empty electron
state
or
hole
in
the valence b and. The wavelength
of
the
lightisusually determined by thebandgap ofthe semi-
conductor
- the
energy difference between
the top of
the
valence band
and the
bottom
of the
conduction band.
Gallium indium phosphide,
for
example,
has a
band
gap
of about
1.9
eV, which leads
to the
emission
of
red light.
The band gap, whichisresponsibleformostofthe use-
ful properties
of
sem iconductors,
is due to the
quantum
nature of the electron waves as they travel throughthe
crystal. Quantum mechanics
forbids the electrons from
having energies inside
the
band gap.
In
a
bulk semiconductor,
such as silicon or gallium
arsenide,
an
electron
in the
conduction band behaves like
a free electron and can occupy
states with continuous values
of momentum and energy.
This picture changes dramat-
ically, however, when the
motion
of the
electron
is
restricted in one or more
dimensions (figure la
and
b .
Iftheelectrons are confinedin
a small enough region, their
energy levels will be quantized,
similar
to the
energy levels
in
an atom.
One way to
make
such
an
artificial atom
or
quantum dot
is to
surround
a small regionofsemiconduc-
tor with another semiconduc-
tor thathas alarger bandgap
(figure lc).
The
electrons
are
effectively confined
in the
region with
the
smaller band
gap as they seek to reduce
their energy.
Ina simplified modeltheconfinement potentialcan be
considered
as a
square well (figure Id .
In
this model
the
separationof the discrete energy levels depends inversely
on the size ofthequantumdot.Th e dot must be 10
nm or
smaller
for the
energy levels
of
the quan tum well
to be
separated
by
more than
the
thermal energy
at
room
tem-
perature. Such quantum dots contain only a few thousand
atoms
and
should
be
able
to
emit light
at
wavelengths
determine d by the energy levels
in
die do t, rather tha n
the
band-gap energy.
However, various processes conspiretostopasemicon-
ductor emitting light. Impurity atoms
can, for
example,
trap the charge carriers and prevent recombination.
Electrons
and
holes
can
also emit phonons
(i.e.
lattice
vibrations) rather than photon s when diey recombine. To
overcome these problems, the surface
of
the qu antum
dot
mustbe passivated :inother words,thesmall-band-gap
material must
be
completely embedded
in the
barrier
material without any crystal defects
and
impu rities.
Quantum dots are widely used for experiments that
semiconductor quantum dot
10
nm
band gap
light
emission
1 a) The periodic crystal potential in a piece of bulk
semiconductor material allows almost free motion for
electrons, which results in energetic bands separated by a
forbidden band gap. Within the conduction band, electrons
have continuous kinetic energy and momentum, o) The
situation is totally different for an electron confined in a very
small ~ 10 nm in diameter) semiconductor cluster and the energy spectrum becomes discrete like that for atoms.
c) A schematic illustration of a passivated quantum dot with the charge carriers purple) confined in the small-
band-gap material red), which is completely embedded in a large-band-gap material blue) without any crystal
defects and impurities present. The charge carriers are confined in all directions. The location of the electron is
indicated schematically and is similar to the orbitals in atoms, d) A model square-well confinement potential
showing the quantized energy states red lines).
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4 8 Physics World September 1997
elastic strain relaxation
wetting layer
2(a) Cluster formation during epitaxial growth of a semiconductor
material (red) on top of another se miconductor with a smaller (by a few
per cent) lattice constant (blue). For example, indium phosphide has a
4%
larger lattice constant than gallium indium phosphide, so InP forms
clusters as shown in figure 3. The cluster formation is energetically
favourable, because the lattice can elastically relax compressive strain
and thus reduce strain energy, (>) In an alternative growth mode the
epilayer is laterally com pressed to match the substrate lattice. This so
called "pseudomorphic growth" is observed for heterostructures that
have only a small lattice mismatch.
probe the fundamental quantum behaviour of semicon-
ductors. They also have many potential device appli-
cations. Th e most promising of these are single-electron
transistors (see Harmans in further reading) and quan-
tum-dot lasers. The latter offer the possibility of improved
device performance and increased flexibility to adjust the
laser wavelength.
Early days
Semiconductor lasers have developed rapidly since their
invention in
1962.
Th e first semicondu ctor laser consisted
ofagallium arsenide p -n junction that was forward biased
such that electron-hole recombination took place in the
depletion region between the positively doped (p) and
negatively doped (n) regions. Polished surfaces (called
facets) perpendicular to the junction were used to form
the reso nant cavity needed for laser action. The se facets
fill the role played by mirrors in conventional lasers.
The performance of the early semiconductor lasers was
greatly improved by sandwiching the gallium arsenide
(GaAs) active layer between aluminium gallium arsenide
(AlGaAs) layers in a hetero structure device. This
improved laser performance for two reasons. First, the
AlGaAs layers have a larger
band gap than the GaAs
layers, which helps to confine
the charge carriers in the
active layer. Second, AlGaAs
has a lower refractive index
than GaAs, which confines the
light within the active layer
and thus acts as a waveguide.
In 1970 this concept lead to
the continuous room-tem-
perature operation of GaAs/
AlGaAs heterostructure lasers.
A key figure-of-merit for a
semiconductor laser is the
current density needed for lasing to start. This figure
should be as low as possible and by 1975 threshold cur-
rent densities of about 50 0Acm
2
had been achieved with
active layers abou t 0.1 |0.m thick. The practical use of
semiconductor lasers in real applications such as fibre-
optic data transmission began around this time.
In 1974 Raymond Dingle ofBellLaboratories in the US
demonstrated quantum confinement of charge carriers for
the first time. And in 1979 Won -Tien Tsan g, also of Bell
Labs, built the first semiconductor laser based on quan-
tum confinement. The active region in Tsang's laser was
only about 0.01 um (10 nm) thick, so the charge carriers
(i.e. electrons and holes) were only free to move in just
two dimensions. The se qua ntum-w ell lasers had three
advantages over previous devices: considerably higher
light amplification or optical gain ; m uch lower thresho ld
current densities (less than 50A cm
2
) and significantly
improved tem perature stability. The se advantages are all
linked to the redu ced energy spread of occupied states for
electrons and holes in quantum-well devices compared
with bulk semiconductors.
The next step - from quantum-well lasers to quantum-
wire lasers - came in the late 1980s. In quantum-wire
lasers the charge carriers are free to move in only one
direction, which further increases optical gain, reduces
threshold current densities (to less than 10A
cm
2
),
and
improves temperature stability.
In 1986 Masahiro Asada of the Tokyo Institute of
Technology and co-workers, building on earlier work by
Yasuhito Arakawa from Tokyo University, predicted that
quantum-dot lasers - lasers in which the active region
contains a large number of equally sized quantum dots -
would have even better characteristics. A quantum dot
confines the motion of the electrons in all three of the
spatial directions.
The discrete energy spectrum of the quantum dots
prom ises highly efficient lasing at a distinct energy. Two
key requirements in any laser are a population inversion
(i.e. there should be more electrons in the excited state
than in the ground state) and that the optical gain is
greater than the losses. Lasers also rely on stimulated
emission: in this process a photon of a given frequency
causes another photon of the same frequency to be emit-
ted. In a laser diode, only those electrons in the conduc-
tion-band minimum that recombine with holes in the
valence-band maximum contribute to stimulated emis-
sion. Since the electronic states in a quantum dot are
squeezed into discrete transition energies, fewer charge
carriers will be needed to create a population inversion,
which should lead to lower threshold currents than found
in existing laser diodes.
Temperature stability should also be improved in quan-
tum-dot lasers. In a conventional semiconductor laser the
3 A cross-sectional transmission electron m icrograph of an InP cluster on GalnP. The cluster was formed
during epitaxial growth of nominally three atomic layers of InP. Since the islands are extremely small and
appear spontaneously during growth , they are called self-assembling quantum dots.
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PhytkaWo rid Septembar 1997 4 9
GaAs substrate
laser output
GalnP waveguide
^^
with one layer of InP
4 An optically pumped InP quantum-dot laser. The electron-hole pairs are excited by a ^ - i . * ^ ^ quantum d ots
focused stripe of green light incident from the left. The stimulated red -light emission (laser
output) originating from the dots is observed perpendicular to the excitation light. The experiment was performed at low temperature (8 K) under
continuous excitation , with the sample mounted in a cryostat. The layer of InP dots is in the middle of a GalnP film, wh ich is surrounded by AllnP
layers that have a smaller refractive index and thus keep the light close to the active layer.
spread of energy states usually causes the threshold cur-
rent to chang e significantly w ith tem perature. F or a q uan-
tum-dot laser, however, the discrete energy spectrum and
large separation between the energy levels almost elim-
inates any temperature d ependence.
Making quantum dots
Th e exp erimental challenge is to make 10 nm semicon-
ductor structures in an efficient and reproducible way. A
large number of dots are needed and they must be equal
in size and optically active. However, conventional semi-
conductor-processing techniques that are based on litho-
graphy and etching face inherent problems such as
limited resolution and the introduction of surface defects
during production.
Over the past few years several research groups have
started working on the direct synthesis of various semi-
conductor nanostrucrures, including quantum dots, by
combining epitaxial growth tech-
niques, such as molecular beam
epitaxy or chemical vapour de-
position, with lithography. Con-
ventional lithographic techniques
are used to create a pattern on
the surface before the quantum-
dot material is deposited. Epi-
taxial growth on patterned
substrates leads to the formation
of sharp edges or V-grooves on
the surface. Quantum dots and
wires can then be formed in a
self-adjusting way.
A much simpler idea is based
on the islands that form when a
semiconductor is deposited on a
substrate that is made from a
material with a significantly
smaller lattice constant. This
process is known as the Stranski-
Krastanov growth mode, and
quantum dots that have dimen-
sions of only a few atomic dis-
tances across have been grown
this way (figure 2a . An import-
ant point is that the size of the
S S pectrum of the laser output (a) and photoluminescence
spectrum (b) from the InP quantum-dot laser shown In figure
4. The laser-output intensity19about a factor of 200 times
more intensive than the lower spectrum.
quantum structure is controlled within the epitaxial de-
position in a self-adjusting process. For the first few
atomic layers, the atoms arrange themselves in a planar
layer called the wetting layer. As epitaxial growth pro-
ceeds, the atoms tend to bunch up and form clusters.
Cluster formation is energetically favourable, because the
lattice can elastically relax the compressive strain and thus
reduce the strain energy within the islands.
In an alternative growth mode known as pseu dom or-
phic grow th , the epilayer is laterally compressed to ma tch
the substrate lattice (figure
2b .
The lateral strain is auto-
matically introduced as the growth proceeds.
To see how these techniques work, consider the growth
of indium phosphide (InP) on gallium indium phosphide
(GalnP). GagjInojP has the same lattice constant as
gallium arsenide, so it is possible to grow good quality
G aln P layers on gallium arsenide sub strates. Th e lattice
constant of InP is about 4% larger. However, with opti-
mized molecular-beam-epitaxy growth conditions, defect-
free clusters or dots form after
1.5 or more monolayers of InP
have been deposited. For exam-
ple,
after three nominal layers
have been deposited, clusters can
be seen on top of the wetting
layer. There are about 5 x l0
1 0
dots per square centimetre and
they nucleate preferentially at the
atomic step s that are always
present on a surface. The dots
have a truncated pyramid shape,
and are about 15 nm in diameter
and 3 nm high (figure 3). Sur-
prisingly, the dot size varies by
only about 10%, which is essen-
tial for making a quantum-dot
laser. After the InP dots have
been grown, a thick layer of
GalnP is deposited to passivate
the dots.
The dot size strongly depends
on the amount of deposited dot
material. And since the energy
levels in the dot depend on its
size, so does the wavelength of
light emitted by the dot. Bulk
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5 0 Ptiyttct Worid Septwntw S97
indium phosphide has a band gap
of 1.35 eV, which corresponds to a
wavelength of
1
[im.The growth of
two monolayers of InP on GalnP
produces dots with diameters of
abou t 12 nm , whereas for seven
monolayers the diameter is about
50 nm. The energy shift for 12 nm
dots is 1.85 eV, which corresponds
to red-light emission. The larger
50 nm dots have lower energy shifts
(1.65 eV) and emit in the infrared.
The pronounced increases in
energy are due to carrier confine-
ment and strain in the dots.
However, once more than seven
monolayers of InP have been
grown, various dislocations are
introduced and these reduce the
light output.
The size of the dots can also be
adjusted within a certain range by
changing the growth conditions.
For example, an extended interrup-
tion between the deposition of the
dot material and the growth of the capping layer leads to
larger dots with a lower dot density - smaller dots disap-
pear and larger dots grow higher during the interruption.
The same happens for very slow deposition rates. Larger
clusters are energetically favourable because there is less
strain at the top of large dots. However, short-wavelength
lasers (e.g. those working in the visible) require small dots,
which can be made by keeping the growth interruption
short. This also reduces the range of dot sizes.
The ability of self assembly to make regular arrays of
extremely small quantum dots without the need for litho-
graphy and etching makes it a highly promising technique
for the fabrication of quantum-dot lasers.
Let there be light
To make a quantum-dot laser we need a dense array of
equal-sized dots within the active region, and a mirror at
each end ofthe region to form the laser
cavity.
The energy
of the radiation depe nds on the ba nd gap of the dot m ater-
ial and the strain, and inversely on the size of the dots.
Electrons an d holes can be created in the dot by optical or
electrical excitation (figure 4).
In 1995 my group at the Max Planck Institute in
Stuttgart in collaboration with Andreas H angleiter's group
at the University of Stuttgart observed room-temperature
lasing in the visible range from an optically excited indium
phosphide q uantum -dot laser. Th e electron-hole pairs
were formed by focusing green light onto the active layer,
and red laser emission was observed emerging from the
mirrors of the laser structure (figure 5). Th e threshold
current for lasing was comparable with that obtained for
GalnP/AlGalnP quantum wells in a similar set-up.
Also in 1995 Dieter Bimberg's group at the Technical
University in Berlin, in collaboration with researchers
from the A F Ioffe Physical Technical Institute in St
Petersburg, demonstrated room-temperature operation
of an electrically pumped quantum-dot laser. This
device contained a closely packed stack of indium
arsenide (InAs) quantum-dot layers and emitted in the
infrared. Bimberg and co-workers also achieved thresh-
old current densities comparable with quantum-well
lasers (below 20
A cm
2
)
at liquid-nitrogen temperatures
6 A cross-sectional transmission electron micrograph
from a sample with three stacked layers of InP dots.
Stacking individual do t layers helps to Increase the total
amount of active material within the waveguide of a
laser structure.
and with better temperature sta-
bility. However, they have not yet
been able to match the perform-
ance of quantum-well laser diodes
at room temperature.
Stacking layers of dots in the laser
structure increases the amount of
active material in devices (figure 6).
In 1995 James Harris and co-
workers at Stanford University in
California reported a significant
reduction in photoluminescence
linewidth from stacked InAs dot
layers. This reduction is thought to
be due to the more uniform distri-
bution of dot sizes caused by the
correlated nucleation of the dots:
atoms that arrive during the growth
of the upper layer tend to accumu-
late and form new dots just above
those in the underlying layer. This
correlation - which is caused by the
strain field around the embedded
dots - is observed if the separation
between the layers is not too large.
Recently Bimberg and co-workers and Hideaki Saito's
group at NEC in Tsukuba have built laser diodes with a
stack of ten layers of dots.
Self-assembled futures
Although the research is still at an early stage, experiments
have already shown that self-assembled quantum dots do
make good lasers. Th e next challenge is to ma tch and sur-
pass the performance of quantum-well lasers. This would
give quantum-dot lasers a chance to move into appli-
cations such as ultrafast optical data transfer. A key aspect
of this challenge will be to improve our control over the
size distribution of the dots produced in the self-assembly
process. But given the rapid progress m ade so far, experts
in the field are confident that there will be significant per-
formance improvements in the near future.
Further reading
1986 Gain and the
box lasers
IEEE J.
M Asada, Y Miyamoto and Y Suematsu
threshold of three-dimensional quantum
Quantum
Electron.
QE-22 1915
D Bimberget
al.
1997 InGaAs-GaAs quantum dot lasers IEEE
J.QuantumElectron.
3 1
K Eberl, P M Petroff and P Demeester 1995 Low-dimensional
structures prepared by epitaxial growth or regrowth on pat-
terned substrates
NATO ASI
Series
E:
Applied Science VbL
29 8
(Kluwer, Dordrecht)
K Harmans 1992 Next electron, please...Physics Wbrld March
pp5O-53
A M oritzet al 1996 Optical gain and lasing in self-assembling
InP/GalnP quantum dotsA pp Phys.Lett.69 212
P M Petroff and S P DenBaars 1994 MBE and MO CVD growth
and properties of self-assembling quantum dot arrays in HI-V
semiconductor structuresSuperlatticesan dMicrostructures 15 15
H Saito et al. 1996 Room-temperature lasing operation of a
quantum-dot vertical-cavity surface-emitting laser
App. Phys.
Lea.
69 3140
Karl Eberl is in the Max-Planck-lnstitut fur Festkorperfof
schung,
Heisenbergstr. 1, 70569 Stuttgart, Germany (email:
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