There is currently great interest in fabrication of structures that are two and three dimensional analogs of the conventional quantum well. We review here the physics behind the use of arrays of such lower dimensional structures in semiconductor laser active layers. Methods which are currently under investigation for producing such structures will be discussed

Hoenk, Michael E.

Kuech, Thomas F.

Lebens, John A.

Sercel, Peter C.

Tsai, Charles S.

Vahala, Kerry J.

Zarem, Hal A.

Caltech Authors - Main

I 7)(A . - . j ) yq/7Invited Paper LA C 5' t k( L ( ( '
L I 1 1f
QUANTUM WIRE AND QUANTUM DOT
SEMICONDUCTOR LASERS
Kerry J. Vahala, John A. Lebens, Charles S. Tsai, Thomas F. Kuech t
Peter C. Sercel, Michael E. Hoenk, and Hal Zarem
Department of Applied Physics
Mail Stop 128-95
California Institute of Technology
Pasadena, California 91125
ABSTRACT
There is currently great interest in fabrication of structures that are two and three
dimensional analogs of the conventional quantum well. We review here the physics behind
the use of arrays of such lower dimensional structures in semiconductor laser active layers.
Methods which are currently under investigation for producing such structures will be
discussed.
Quantum wires and quantum dots are two and three dimensional analogs of the con-
ventional quantum well (see Figure 1). A quantum dot, for example, would confine an
electron in three dimensions to a size comparable to the de Broglie wavelength of the
electron in the crystal. To be useful in a device, arrays of quantum wires and quantum
dots must be considered as illustrated in Fig. 1. In such arrays quantum dots and wires
composed of a low bandgap material would be imbedded in a higher bandgap host (e.g.,
GaAs dots in an AlGaAs host). A potentially important application of these structures
is to laser diodes.' In such devices, the conventional bulk active layer is replaced with an
array of quantum dots or quantum wires. As discussed below, these devices would have
many advantages over conventional devices.
The most important property of quantum wires and quantum dots as concerns their
application to laser diode active layers is their density of states functions. Idealized versions
of these functions are presented in Fig. 2 for bulk, conventional quantum well, quantum
wire, and quantum dot active layers. In reducing dimension it is apparent that these func-
tions take on more singular behavior. For the quantum dot, the behavior is analogous to
the density of states of an atomic system. This narrowing of the density of states function
carries over directly into the optical gain spectrum, which, for k-conserving transitions,
is proportional to the effective density of states of the electronic system and the Fermi
t IBM Thomas J. Watson Research Ctr., Yorktown Heights, N.Y.
120 / SPIE Vol. 1216 Nonlinear Opt/ca/Materials and Devices for Photon/c Switching (1990)
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iD-OW
L4:..
'uantum
Wire
(b)
2D-QW
, QuantumDot
3D-OW
Fig. 1. Schematic drawing of quantum wells, wires and dots showing the successive
dimensions of confinement . The lower part of the figure shows arrays of these structures
suitable for incorporation into the active layer of a semiconductor laser. The structures
are formed from low bandgap material imbedded in a higher bandgap host.
Density of States Functions
- -
Fig. 2. Density of states functions for zero-, one-, two-, and three-dimensional systems.
The dashed curve indicates approximately the optical gain which results when the medium
is inverted.
Potential
Barrier
(a) (C)
BULK
D3(E) D2(E)
D1(E)
0-WELL
rNI
Egap E
0-BOX
/
D0(E)
Egap E Egap E
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occupancy factor giving the strength of the inversion. The dashed curves appearing in Fig.
2 show typical gain spectra for each case. Gain spectrum narrowing is maximum for the
quantum dot. In fact, here the gain spectrum width is zero according to this highly sim—
plified model.(In a more realistic model phonon scattering broadens the transition leaving
a Lorentzian lineshape as has been illustrated in the figure.)
A laser based on a narrower gain spectrum has many First, it is clear
that lower threshold currents are possible since fewer carriers are wasted in regions of the
spectral space that are not contributing to lasing action. It is important to note that
there is also a significant reduction in the transparency excitation level of the gain medium
simply from the reduction of the active layer volume. The resulting reduction in threshold
has been exploited in ultra low threshold conventional quantum well semiconductor lasers
and can also be exploited in quantum wire and quantum dot semiconductor lasers.
Dynamic and spectral properties are also improved in these devices. Consider, for
example, the direct modulation speed of a diode laser as determined by the relaxation
oscillation corner frequency. The square of this corner frequency is easily shown to vary
linearly with the differential gain (i.e., the derivative of gain with respect to carrier density).
Differential gain will, roughly speaking, vary inversely with spectral width. Hence, reduced
dimension results in higher modulation speeds.1 Using similar arguments it is possible to
show that chirp reduction, phase noise reduction, and intensity noise reduction also can
result from the reduction of the active layer electronic system dimension.1 The application
of quantum well and quantum wire active layers to phase noise reduction and modulation
speed enhancement in laser diodes was first discussed in Reference 1 . All of the theoretical
predictions concerning conventional quantum well active layers have since that time been
verified.
The fabrication of quantum wires and quantum dots poses many challenging problems.
At the present time there are two general approaches being taken. Historically first are
a variety of techniques in which a quantum well which has been grown on a substrate
is modified for lateral confinement on a nanometer scale. In all of these techniques a
nanometer scale pattern is first generated on the sample using lithographic methods such
as electron or ion beam lithography. The techniques then diverge in terms of how this
pattern is transferred to the quantum well resulting in a quantum wire or a quantum dot.
One simple example of this could be referred to as the "cookie cutter" approach. In it the
lateral confinement is produced by actually etching away unmasked regions of the quantum
well sample.2'3 Although extremely small structures are possible with this approach, the
resulting structures suffer from free surface induced nonradiative recombination. Recent
efforts in this direction are addressing the issue of surface passivation either by chemical
treatment or by actual regrowth on the etched structures. A more sophisticated pattern
transfer technique that does not leave behind free surfaces is based on disordering of the
quantum well either by ion implantation4 or by diffusion.5 These techniques have produced
convincng results and are illustrated by the example in Fig. 3. Here again a mask is
patterned onto the surface of a semiconductor, containing in this case a shallow quantum
well. The mask is patterned using electron beam lithography and subsequently arrays of
silicon lines are deposited in a liftoff process. The silicon then serves as a mask in a shallow
zinc diffusion into the quantum well. The diffusion of zinc is known to abruptly disorder a
122 / SPIE Vol. 1216 Nonlinear Optical Materials and Devices for Photon/c Switching (1990)
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A12Ga8AsQuantum
Well
Al3 Ga7 As
Fig. 3. A schematic drawing of diffusion induced disordering of a shallow quantum well to
produce quantum wires. A narrow stripe of silicon is produced by electron beam lithog-
raphy and subsequent liftoff on the surface of a sample containing a shallow quantum
well. The silicon stripe serves as a mask for a zinc diffusion which selectively disorders the
quantum well.
Fig. 4. Secondary electron and cathodoluminescence images of several arrays of wires and
an isolated wire. The left half shows the silicon mask as a conventional SEM micrograph.
The width of the silicon stripes in the arrays varies from 3700A (upper left array) to 1600A(lower right array). The right half shows the spectrally resolved cathodoluminescence
image of the same region at a wavelength of 780 nm. The sample temperature is 77K.
SPIE Vol. 1216 Nonlinear Optical Materials and Devices for Photon/c Switching (1990) / 123
20Mm
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quantum well. By timing the diffusion correctly, wire-like regions of low bandgap quantum
well material are left behind. Fig. 4 shows a scanning electron micrograph of several silicon
arrays with elements of various widths.
Also shown in the figure is a cathodoluminescence (CL) micrograph of this same region
of the sample. Cathodoluminescence is an alternative means of imaging with a scanning
electron microscope. Rather than collecting secondary electrons, CL uses light that is
emitted by the recombining electron-hole pairs that have been excited by the electron
beam.6 The collected CL emission in this micrograph is spectrally resolved using a grating
monochrometer before detection. The wavelength selected is slightly blue shifted from
the original quantum well emission peak. The CL image indicates that the quantum well
has been successfully disordered in the unmasked regions of the sample. The inability
to actually resolve the lines is a consequence of CL's limited spatial resolution which is
determined by carrier diffusion.
Before discussing the second category of fabrication approaches, it is interesting to
consider again the application of these structures to semiconductor laser active layers. In
addition to the considerations mentioned earlier, we will now include an additional non-
ideality that plays a central role in determining the ultimate performance of a quantum
wire or quantum dot semiconductor laser. This is fabricational inhomogeneity. Consider,
for example, arrays of quantum dots. The confinement energy depends strongly in these
structures on the size of the dot. This, in turn, implies that the gain spectrum for an
array of quantum dots experiences fabricational induced inhomogeneous broadening. Such
broadening tends to counteract the beneficial effects of quantum confinement. The in-
teresting question is therefore: what fabricational tolerance is required if a quantum dot
active layer is to outperform a conventional active layer? This question is addressed in Fig.
5 where maximum attainable gain (in both inverse spatial and temporal units) has been
plotted for various densities of GaAs quantum dots versus a fabricational RMS variance
in dot diameter.7 There are actually two sizes of dots considered in the plot. Large dots
having a radius of 100A and small dots having a radius of 50A. Consider the case of small
quantum dots with a packing density i = 1.25 x 1017cm3. To attain a maximum optical
gain of 120 cm1 (a number typical of bulk GaAs material under high excitation) all dots
must be filled with two electrons and two holes (i.e., the equivalent carrier density will be
2.50 x 1017cm3) and a fabrication tolerance of 20A must be maintained. This is well over
an order of magnitude better than the bulk material which would only attain these values
at carrier densities on the order of 5 x 1018cm3.
There are two important points to be made here. First, the above estimate is good
news for approaches based on nanolithographic patterning, because although a 20A tol-
erance on an array of 200A diameter dots exceeds the current state-of-the-art in beam
patterning and pattern transfer, it is well within an order of magnitude of what is cur-
rently attainable. Second, in considering the figure, it is clear that what is truly needed
is a fabrication technology capable of monolayer tolerences, i.e., the equivalent of MBE or
MOCVD in the lateral directions.
124 / SPIE Vol. 1216 Nonlinear Optical Materials and Devices for Photon/c Switching (1990)
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12000
1200
y-
'0 I
ci
U) 4rrt (_)Q_ i:u%— z
0
2
FABRICATION TOLERANCE
Fig. 5. Maximum possible optical gain versus fabrication tolerance(given as the rms
roughness of dot diameter) for arrays of quantum dots of various dot densities(ijL,iis).
Large quantum dots (density ) will have an average diameter of 200A and small quantum
dots (density its) have an average diameter of iOOA. The cross hatched region is beyond
the geometrical packing limit of the quantum boxes.
Although such a technology does not yet exist, the second category of techniques are
clearly moving in this direction. These are techniques that seek to extend the fabricational
control offered by MBE and MOCVD in the z-direction into the x and y-directions. In this
way the quantum wires or dots can be formed in the growth process. Examples of these
techniques are vicinal growth to produce vertical superlattices8 , quantum well thickness
control through growth on patterned substrates9 , and very recently compositional control
through growth on patterned substrates.1° Fig. 6 illustrates the latter of these. The top of
Fig. 6 shows a schematic drawing of a substrate patterned by chemically etching a groove.
MBE growth of A1GaAs epilayers on such a substrate proceeds along various directions.
Surprisingly, under appropriate growth conditions, it has been demonstrated that the
(111) growth directions segregate into a quasi periodic structure having a period between
50— 70A.1° On the average the composition is uniform, but the microscopic ordering along
SPIE Vol. 1216 Nonlinear Optical Materials and Devices for Photonic Switching (1990) / 125
1
0.01
lÀ 2A 5A bA 20A 50A bOA
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ca.
a
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Fig. 7. SEM micrograph of selectively grown GaAs dots showing faceted nature of growth.
SPIE Vol. 1216 Nonlinear Optical Materials and Devices for Photon/c Switching (1990) / 127
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the (111) growth directions produces an abrupt lateral change in the effective bandgap
energy. This is apparent in Fig. 6 where CL micrographs of groove crossections are shown
at two different wavelengths.
A new technique which we are currently pursuing is the use of selective epitaxy to grow
quantum dot and quantum wire structures.It is related to the above techniques in that
the dot structure is formed during growth. It is also related to beam patterning methods
descibed earlier since the positions at which the dots or lines are grown is patterned prior
to growth. Selective epitaxy refers to a lateral spatially controlled growth of an epitaxial
material within openings of a mask material residing on the substrate during growth. The
masking material we use is a dielectric layer of Si 3N 4. Recent optimization of growth
conditions and selection of growth precursors have produced the high quality growth of
GaAs in openings down to the micron scale11 . By using electron beam lithography to
generate the openings we have successfully grown structures with diameters less than
700A. Fig. 7 shows an SEM micrograph of .25jm GaAs dots grown by this method. These
photos illustrate the facetted nature of the growth.By performing a subsequent growth of
A1GaAs these GaAs structures can be completely imbedded in a higher bandgap material.
We have recently achieved such growth and have seen luminescence from GaAs dots less
than ioooA in diameter.
In conclusion, the optical properties of arrays of quantum dots and quantum wires have
been discussed with emphasis on their application to semiconductor lasers. In addition, a
number of approaches to fabrication of these structures have been discussed. Fabrication
approaches currently under investigation divide into two broad categories: fabrication
based on beam patterning and in-situ fabrication approaches. Extremely good control of
fabrication tolerance is essential if quantum wires and quantum dots are to be be useful in
semiconductor lasers. With continued refinements in existing fabrication techniques useful
quantum wire and quantum dot semiconductor lasers should be possible. To fully tap the
performance advantages of these structures, however, will probably require an entirely new
fabrication technology.
The authors would like to acknowledge the support of the Office of Naval Research and
the Strategic Defense Initiative Organization/Innovative Science and Technology. One of
us (PS) would like to acknowledge the support of a graduate National Science Foundation
fellowship.
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Quantum wire and quantum dot semiconductor lasers

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Quantum wire and quantum dot semiconductor lasers

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