Characteristics of a Photonic Bandgap Single Defect
Microcavity Electroluminescent Device
Abstract—A
microcavity surface-emitting coherent
electrolumi- nescent device
operating at room temperature under
pulsed cur- rent injection is described. The microcavity is formed by a single defect in the center
of a 2-D photonic crystal
consisting of a GaAs-
based heterostructure. The gain region
consists of two 70- Å com-
pressively strained In) 15 Ga) 85 As quantum wells, which exhibit a spontaneous emission peak at 940 nm. The maximum
measured output power from a single
device is 14.4 W. The near-field image of the output
resembles the calculated TE mode distribution in a single defect microcavity. The measured far-field
pattern indicates the predicted directionality of a microcavity light source. The light-
current characteristics of the device
exhibit a gradual
turn-on, or a soft threshold, typical of single-
or few-mode microcavity devices. Analysis of the characteristics with the carrier
and photon rate equations yields a spontaneous
emission factor 
0 06.
Index Terms—Defect mode,
microcavity, photonic bandgap,
sur- face emitting.
INTRODUCTION
IT IS NOW well known that spontaneous emission
is not an intrinsic atomic property.
It can be modified by tailoring the electromagnetic environment that the atom
can radiate into.
This was first realized by Purcell [1], who noted
that the spontaneous emission rate can be enhanced
for an atom placed inside
a cavity with one of its modes resonant with the transition under consid- eration, and by Kleppner [2], who discussed
the opposite case
of inhibited
spontaneous emission.
In bulk material, or in a large cavity, the photon density of states is a monotonic function and spontaneous emission occurs into
a large number of states, which occupy a spectral region much larger
than the spontaneous emission linewidth. In a con- ventional laser made of such materials, most of the spontaneous
emission is lost to free space as radiation modes
and only a small
fraction couples to the resonant mode of the cavity formed by the mirrors.
Therefore, significant stimulated emission output can only be obtained when the
input power crosses a threshold to overcome the free-space loss. In a
wavelength-sized micro- cavity [3]–[5], formed by 1-, 2-, or 3-D photon-mode
confine- ment, the photon-mode density develops singularities, just as in the case of carrier confinement. In
this case, a single spectrally distinct mode, determined by the microcavity
dimensions, can receive most or all of the spontaneous emission.
By applying Fermi’s golden rule, it
has been shown that the rate of spontaneous emission is enhanced
in such a microcavity,
due to the change in the mode density [4]. The spatial
profile of the spontaneous
emission in the cavity plane has also been cal-
culated, and it has been shown that the profile can become ver- tically collimated. This is easily
seen in a planar microcavity, with confinement in one direction, but has also
been theoreti- cally shown in a wavelength sized microcavity created
by lateral confinement and without high-reflectivity mirrors in the
direc- tion of the guided modes [6], [7].
The most appealing
technique to realize a true photonic microcavity is to use a dielectric
photonic crystal, realized with a periodic modulation of the dielectric
constant [8], [9]. As lightwave scatters within a material
with a periodic variation in the dielectric
constant, destructive interference of certain frequencies,
depending on geometry and index variation, produces a photonic bandgap (PBG)
[10]. Photons whose energies lie within the gap cannot propagate through the
structure. However, a point defect—a
missing period or phase slip—in the structure will locally trap photons and create
a microcavity [11]–[19]. All the photons
corresponding to the wavelength
of the defect, generated by recombination in the PBG crystal or otherwise, will
be funneled into the single resonant mode of the defect and this mode can
propagate in the crystal. Such a single-mode microcavity light-emitting diode,
with a spontaneous emission factor , can also be viewed as a thresholdless laser. However, there are important differences.
In a microcavity, or defect, there is feedback of the dominant mode in all
directions. Also, unlike a laser, in which the output is a result of mode
competition and gain saturation, in a true microcavity there is only one mode
that is emitted. The resonant defect mode is highly localized around the defect
and can either propogate in the plane of the PBG crystal by tunneling, or leak out in the vertical direction. Lasing with optical pumping from a microcavity formed by a
single defect in the center of a disc-shaped photonic crystal
has been demonstrated [18], [19] and we have recently reported
room-temperature operation of a PBG microcavity surface emitting
electroluminescent device [20]. Photon confinement and the modal properties of
a PBG-based microcavity are quite
similar to those of a reflector-based microcavity. However, the former relies on multiple reflections from distributed scatterers, instead of the multiple
reflections from localized mirrors in the
latter, which selects only those modes having
in-phase multiple reflections
and rejects all other electromagnetic modes.
In this paper, we report the
characteristics of a GaAs-based single defect PBG electroluminescent device in
detail. The
Fig. 1. (a)
Device heterostructure grown by MOVPE on n GaAs substrate with two
70 ·A In Ga As–GaAs
quantum wells in a .\-cavity.
(b) Room-temperature PL spectra for an as-grown sample (dotted
line) and for the 2-D PBG crystal
without defect (solid line). Note that the suppression ratio is at least 20 dB for the PL intensity in the latter case.
single defect in a 2-D
photonic crystal, formed of semicon- ductor
heterostructures containing In Ga As–GaAs quantum wells, forms the microcavity.
In particular, the light- current ( - ) characteristics are very different from
conven- tional lasers, or even microcavity VCSELs. Data from the device also indicate that light
emission truly occurs from the microcavity formed by the defect and not from
the rest of the 2-D PBG. The device is, at best, a “few mode” LED. The concept
of a threshold current, therefore, cannot be strictly applied, and instead, we
see a gradual turn-on, exactly as described by Yokoyama [3]. However, for
simplicity, we will refer to the current at the turn-on point as a threshold,
even though the device may not operate as a laser. In fact, we have analyzed
this by the appropriate carrier and photon rate equa- tions and by taking into
account the substantial nonradiative recombination at the air holes. Excellent
agreement is obtained with
experimental data. In what follows, the device design is described in Section
II and device fabrication in Section III. The experimental results, together
with analysis of the data are described in Section IV, followed by a discussion in Section V. The important results are summarized in Section VI.
DESIGN OF PBG CRYSTAL AND MICROCAVITY
Epitaxial growth
and fabrication of the devices
have been described by us elsewhere [20], but is briefly reiterated for com-
Fig. 2. Calculated TE bandstructure and defect-mode levels
using plane wave expansion
techniques for a 2-D hexagonal PBG crystal geometry
with air-holes surrounded by a region with effective index of 1.8 (to
account for the index steps in the 2-direction of our finite 2-D slab) and (r/a) = 0.32. A
single-defect mode centered in the bandgap at a normalized frequency (a/.\) = 0.43 corresponding to a = 0.4 µm and .\ = 940 nm is shown.
pleteness. The device heterostructure, grown by
metal-organic vapor phase epitaxy
(MOVPE), is shown in Fig. 1(a). It consists
of an undoped cavity region of thickness
with two 70-Å
pseudomorphic In Ga As
quantum wells in the middle and
-type Al Ga As and contact layers
on the top. - and -type Al Ga As layers are inserted
for lateral wet-oxidation during
the processing of the device. Therefore, the heterostruc- ture is similar
to that of an oxide confined VCSEL [21], without the top distributed Bragg
reflector (DBR) mirror.
The reflectivity of the top surface is that provided
by the semiconductor-air interface.
Even the bottom DBR is not necessary, but was incorporated to achieve a high index step (reflectivity) in the bottom side and to ensure
leakage of light
from the top surface. The cavity was designed with a 2-D PBG encompassing the peak emission
wavelength at a normalized frequency of for the
TE modes. The calculated bandgap
for the TE modes and the defect mode are shown in Fig. 2. The calculations were done in the
frequency domain considering a 2-D geometry with an ef- fective index to take into account the index
steps in the vertical direction. The
calculations are based on the plane-wave expan- sion method and effective
medium theory [22]–[24]. While a unit cell was used in the perfect PBG, where
circular air holes are arranged
in a triangular lattice in a dielectric background with a dielectric constant
of 12.5 (inset of Fig. 2), a supercell
[24] must be used when
a defect is introduced into an other- wise perfect PBG, where the structure is approximated with the
discrete-translationally symmetric structure. Recalling that the electric field
is primarily parallel to the interface for TE
modes and perpendicular for TM modes, it is straightforward to under-
stand that a dielectric tensor, which is valid for any polariza- tion, can be
generated in terms of the effective medium theory.
In our case, the PBG center frequency ,
which corresponds to the quantum-well peak emission wavelength of
0.94 m. Values
of and 
and 0.13 m,
respectively, give the best experimental results, and we believe these
dimensions place the quantum well emission within the PBG of the 2-D crystal. Some amount of trial and error was involved since only
a quasi-3-D model was used.
Fig. 3. (a) Schematic of the electrically injected
photonic crystal surface-emitting light
emitter with single defect forming the microcavity.
(b)
SEM images of top view of a fabricated
device with top electrical ohmic contact surrounding the PBG with the single
defect magnified in the inset.
(c)
Cross-sectional SEM image of the 2-D PBG slab, with deep etching through the cavity down to the bottom DBR region.
DEVICE FABRICATION
Mesa-etched devices with p and n contacts were first fabri- cated by optical lithography, dry and wet etching, metallization, and polymide planarization. Lateral wet-oxidation [25] of the Al Ga As layers was used
here to funnel the charge car- riers
more efficiently into the center of the PBG region, which is next formed by e-beam lithography, pattern transfer, and deep dry etching techniques [26]. The window
inside the oxide ring is
measured to be m in diameter. A single
defect in the center defines the
-sized microcavity. The 0.8- m deep etch goes
through the entire cavity region and well into
the bottom DBR to ensure a good overlap with the optical
field. Dimensions of and m define the final PBG microcavity. A schematic of the complete device with -
and -type con- tact metallizations are shown in Fig. 3, together with scanning electron microscope (SEM) images of the PBG
and the defect. The active area aperture,
created by the single defect, is sur-
rounded by over 40 periods of PBG, having
an extent (radius)
of
20 m, which also coincides with the current
funneling aperture formed by wet oxidation of the Al Ga
As layers. Excel- lent diode
characteristics were measured for the device at var- ious stages. The reverse
leakage current increased from 40 pA to 1 nA after formation of the PBG crystal.
Room-temperature photoluminescence
(PL) measurements were also done on the as-grown heterostructures and on the
samples after etching of air holes to form the PBG. The measurements were made
with a 632-nm laser, 1-m scanning spectrometer, and a liquid-nitrogen cooled photomultiplier with lock-in amplification of the signal. The luminescence measured from the InGaAs quantum wells is
shown in Fig. 1(b). This output is predominantly transverse-electric (TE)
polarized due to the compressive strain in the InGaAs quantum wells. This is an advantage, since the PBG defect
mode is predominantly TE polarized. It may also be noted that the peak intensity (940 nm)
of the PL signal from the PBG region is at least
ten times lower than that from the as-grown
heterostructure. We also fabricated oxide-confined microcavity
VCSEL-like devices with the epitaxial heterostructures before etching the air
holes. No top DBR mirror was formed. These devices did not show lasing
behavior. These control experiments are crucial in eliminating other possible
sources of light emission that is subsequently observed in the devices
with the PBG crystal with single defect.
DEVICE CHARACTERISTICS
The - and spectral
characteristics of the PBG microcavity devices were measured in the pulsed mode
(1- s width with 1% duty cycle) with probe contacts. The output was measured in
a direction normal to the surface. It may be remembered that the dominant mode
in the defect region can propagate laterally, or leak out vertically. The DBR
mirror at the bottom helps in surface emission from the top. A turn-on, or soft
threshold-like behavior in the injection current is consistently observed in
the L-I characteristics (Fig. 4). We have observed a similar threshold-like
behavior in 1.55- m oxide-confined microcavity electroluminescent devices [27].
The maximum output power is 14.4 W [Fig. 4(b)]. Care was taken to ensure that
the measured power lies within the operating spectral and sensitivity regimes
of the Ge detector, especially at low output powers. The measured spectral
outputs at different injection currents, below and above the turn-on, or
threshold, are shown in Fig. 5. The spectra at low injection currents, below
the turn-on, are also characterized by several distinct peaks, rather than a
broad output. From a lineshape analysis of the main peak at 931 nm (above
threshold), we derive a linewidth of 8 ,
which leads to a quality factor of
1164. This is, of course, different from the cold cavity , which we believe is
lower in value. Our spectral data are also very noisy due to low output power, in addition to multimode behavior,
thereby making the measurement of the linewidth less accurate. We estimate the 
value to be 200, and
the values of 300–500 for similar
devices have been reported [18]. It may be noted that the vertical cavity is very low ( 12 in
our case) since there is no DBR on the top surface. The peak output wavelength
corresponds to a normalized frequency of 0.43, which is within
Fig. 4. L-J characteristics of the single-defect PBG device at 300
K in pulsed mode showing: (a) “soft” threshold
current of 300 µA
and (b) maximum power output
of 14.4 µW.
Fig. 5. Measured
spectral outputs for the device at different biasing currents. The peak
emission for the injection current
of 5 mA is at 931 nm with a linewidth
of ,-- 8 Å.
the bandgap of the photonic crystal incorporated in our
device. While the PL emission peaks at 940 nm at 300 K, the output emission
center wavelength is 931 nm. We believe the shift is
Fig.
6. (a) Calculated electric field energy distribution (TE) in a horizontal (7:-y plane)
slice of the middle of the single-defect PBG crystal showing two degenerate modes localized in the single defect. (b) Measured near-field image of the device
output superimposed on the 2-D air-hole photonic
crystal pattern.
mainly due to the process induced PBG position and
defect level shift [28].
The field distribution
and the localized defect mode in and around the defect in the photonic crystal
were also calculated by the technique described in Section II. The computations
re- veal that most of the energy of the defect
mode leaks in the ver- tical direction, rather than
being guided in the plane ( - ) of the
photonic crystal. The modes are predominantly TE, with a small contribution from unguided transverse magnetic
(TM) modes. Fig. 6(a) shows the calculated dominant
TE modes in the
middle of the cavity for and dipole, respectively, which have a
symmetrical distribution and extend radially through the first few periods
of the air holes in the photonic
crystal. The distribu- tion is that of a pair of
degenerate dipole modes, which may be
present in the measured output
spectrum of Fig. 5. We have also
measured the near-field image [Fig.
6(b)] of the light output
with a Spiricon Laser
Beam Diagnostics system
for an injection cur- rent of 2.2 mA, which is above threshold. The imaging was done
at a distance of 4 mm from the surface of the device through an objective lens.
It is evident that the modes spread out from the defect (microcavity) region during its propagation along the
vertical direction. The nonuniformity in the mode profile is pos-
sibly due to light scattering in the air holes and diffraction at the
surface [29]. Nonetheless, it is important to note that the 4- m
Fig. 7. Measured polarization characteristics of the
device (at ..\ == g31 nm) for an injection current of 4
mA. It is evident that the output does not display a single definite polarization.
lateral extent of the
near field image is much smaller than the oxide window diameter of 40 m and
further helps to exclude
the possibility that the entire 2-D-PBG crystal
beyond the defect
microcavity contributes to the observed output. Ideally,
there should be a rapid decay of the electromagnetic fields inside the PBG lattice. In our case, the fact
that the measured near-field image extends out to five lattice
periods implies a spreading out of some sort, and the image may not
exactly map the real field distribution pattern inside the cavity.
It may also be noted
that the quantum-well emission shown in Fig. 1(b) overlaps
with the bottom of the air band at the point,
and this emission can, therefore, couple with
the air- band-guided modes propagating in the direction. The near- field image indicates increased leakage in the direction. However, it cannot be confirmed
whether only the dipole de- fect mode or a combination of defect and air-band modes are
observed.
Finally, we have also measured the far-field radiation
pattern in devices with and without PBG crystal formation. The linewidth
(full-width at half-maximum) of the pattern is 30 , in contrast to 90 for larger oxide-confined
light-emitting diodes, confirming that the observed light output originates
from the single-defect microcavity.
The enhancement in spontaneous emission due to the mi- crocavity
effect (Purcell factor) was estimated [30], [31] from the measured
cavity 
and a calculated effective modal volume . An enhancement by a factor of 15 is derived based on the
calculated effective modal volume.
The measured polarization
characteristics of the device at an
injection current of 4 mA is shown in Fig. 7. Although a pref- erential polarization direction can be easily identified, output is clearly not
in one definite polarization state, which is in agree- ment with data reported
from a similar defect mode laser with optical pumping [18]. We attribute the polarization behavior to
the fact that the emission peak output consists of at least a pair of degenerate modes. By lowering
the cavity symmetry
[19],
CONCLUSION
We report the characteristics of an electrically injected micro- cavity
light emitter in which the mode-confining volume is de- fined by a single defect in a semiconductor-based PBG crystal. The bandgap of the photonic
crystal is designed to contain the radiative emission from In Ga As–GaAs
quantum wells, which form the gain medium
Fig.
9. (a) Schematic of a possible single defect PBG defect mode emitter array. (b) Calculated field distribution in the array. Note that the defect
spacing for such an array can be as small as 4 µm, since theoretical calculations show that seven
periods of air holes surrounding the single defect
is enough to achieve
more than 2-dB suppression of unwanted modes.
Realization of the device reported
here involves careful pro- cessing and low damage etching with a high aspect
ratio. If the thickness of the PBG region is reduced, the TE field is less con-
fined in the microcavity. The - characteristics of the device exhibit a “soft” threshold, or turn-on, behavior, as expected from true microcavity light emitters. The
light output results from all or most of the spontaneous emission being
funneled into a few microcavity modes. From analysis of the data with appro-
priate carrier and photon rate equations, a value of
is derived. It is
important to realize that the device need not have DBR mirrors; even the bottom
mirror in our heterostruc- ture is not required. The lithography and etch dimensions will be much larger
and the tolerances much better for 1.55- m emit- ters, using InP-based
materials, which inherently have smaller surface recombination.
Surface-emitting light emitters at this wavelength are technologically important for optical communi- cations. In spite of a relatively large value of , the output power is
low. This is due to the small microcavity volume.
However, a closely spaced array,
as schematically shown in Fig. 9, will have much higher—and at the same time collimated—power outputs. Such an array can also be designed to be
multi-wavelength by simply varying the PBG crystal dimension [34], [35], which
would be useful for dense WDM (DWDM) lightwave commu- nication systems.
REFERENCES
[1]
E. M.
Purcell, “Spontaneous emission probabilities at radio frequen- cies,” Phys. Rev., vol. 69, p. 681, 1946.
D. Kleppner,
“Inhibited spontaneous emission,” Phys. Rev. Lett., vol. 47, pp. 233–236, 1981.
[2]
H. Yokoyama, “Physics and device applications
of optical microcavi- ties,” Science,
vol. 256, pp. 66–70, 1992.
[3]
H. Benisty,
J. Gerard, R. Hondre, J. Rarity, and C. Weisbuch,
Eds., Con- fined Photon Systems:
Fundamentals and Applications: Springer, 1999.
[4]
T. Baba, “Photonic crystals and microdisk cavities based
on GaInAsP-InP system,” IEEE J. Select. Topics Quantum Electron., vol. 3, pp.
808–830, 1997.
[5]
I.
Vurgaftman and J. Singh, “Spatial and spectral characteristics of spontaneous
emission from semiconductor quantum wells in micro- scopic cylindrical
cavities,” Appl. Phys. Lett., vol.
67, pp. 3865–3867, 1995.
[6]
E. F. Schubert and N. E. J. Hunt,
“Enhancement of spontaneous emis- sion in microcavities,” in Vertical-Cavity Surface-Emitting Lasers: De- sign, Fabrication, Characterization,
and Applications, C. Wilmsen, H. Temkin, and L. A. Coldren, Eds. Cambridge,
U.K.: Cambridge Univ. Press, 1999,
pp. 68–107.
[7]
E. Yablonovitch, “Inhabited spontaneous emission
in solid-state physics and electronics,” Phys. Rev.
Lett., vol. 58, pp. 2059–2062, 1987.
[8]
, “Photonic band-gap structures,” J. Opt. Soc. Amer. B, vol. 10, pp. 283–295, 1993.
[9]
J. D.
Joannopoulos, R. D. Meade, and J. N. Winn, Photonic
Crys- tals. Princeton, NJ: Princeton
Univ. Press, 1995.
[10] P. Villeneuve,
S. Fan, and J. D. Joannopoulos, “Microcavities in photonic crystals: Mode symmetry, tunability, and coupling efficiency,” Phys. Rev. B, vol. 54,
pp. 7837–7842, 1996.
[11]
S. Lin, V. Hietala, S. Lyo, and A. Zaslavsky, “Photonic band gap quantum well and
quantum box structures: A high-Q resonant cavity,” Appl. Phys. Lett., vol. 68, pp.
3233–3235, 1996.
[12] D. Labilloy et al.,
“High-finesse disk microcavity based on a circular Bragg reflector,” Appl. Phys. Lett., vol. 73, pp.
1314–1316, 1998.
[13] A. Shaw et al.,
“Lasing properties of disk microcavity based on a circular
Bragg reflector,” Appl. Phys. Lett.,
vol. 75, pp. 3051–3053, 1999.
[14] A. Mekis, M. Meier, A. Dodabalapur, R. E. Slusher, and J. D.
Joannopoulos, “Lasing mechanism in two-dimensional photonic
crystal lasers,” App. Phys. A,
vol. 69, pp. 111–114, 1999.
[15]
M. Imada et al., “Coherent two-dimensional lasing
action in surface- emitting laser with triangular-lattice photonic crystal
structure,” Appl. Phys. Lett., vol.
75, pp. 316–318, 1999.
[16]
K. Inoue, M.
Sasada, J. Kawamata, K. Sakoda, and J. Haus, “A two-dimensional photonic
crystal laser,” Jpn. J. App. Phys., vol. 38, pp. L157–L159, 1999.
[17] O. Painter et al.,
“Two-dimensional photonic band-gap defect mode laser,” Science, vol. 284, pp. 1819–1821,
1999.
[18]
J. Hwang et al., “Room-temperature triangular-lattice two-dimensional photonic bandgap lasers operating at 1.54 µm,” Appl. Phys. Lett., vol. 76, pp.
2982–2984, 2000.
[19]
W. D. Zhou, J. Sabarinathan, B. Kochman, E. Berg, O.
Qasaimeh, S. Pang, and P. Bhattacharya,
“Electrically injected single-defect photonic
bandgap surface-emitting laser at room temperature,” Electron. Lett., vol. 36, pp. 1541–1542, 2000.
[20]
J. L.
Jewell, J. P. Harbison, A. Scherer, Y. H. Lee, and L. T. Florez, “Vertical-cavity surface-emitting lasers: Design,
growth, fabrication, characterization,” IEEE
J. Quantum Electron., vol. 27, pp. 1332–1346, 1991.
[21]
R. D. Meade, A. M. Rappe, K. D. Brommer, J. D. Joannopoulos, and O.
L.
Alerhand, “Accurate theoretical analysis of photonic band-gap mate- rials,” Phys. Rev. B, vol. 48, pp. 8434–8437,
1993.
[22]
T. Sondergaard, “Spontaneous emission in two-dimensional
photonic crystal microcavities,” IEEE J. Quantum Electron., vol. 36, pp. 450–457,
2000.
[1]
O. Painter,
J. Vuckovic, and A. Scherer, “Defect modes of a two-di- mensional photonic
crystal in optically thin dielectric slab,”
J. Opt. Soc. Amer. B, vol. 16, pp. 275–285, 1999.
[2]
J. M. Dallesasse, N. Holonyak
Jr., S. R. Sugg, T. A. Richard, and
N. El-Zein, “Hydrolyzation
oxidation of Al Ga As-AlAs-GaAs quantum well heterostructures and superlattices,” Appl. Phys.
Lett., vol. 57, pp.
2844–2846, 1990.
[3]
E. Berg and S. W. Pang, “Cl plasma passivation of etch induced
damage in GaAs and InGaAs with an inductively coupled plasma source,”
J. Vac. Sci. Tech. B, vol. 17, pp. 2745–2749, 1999.
[4]
W. D. Zhou, P. Bhattacharya,
and O. Qasaimeh, “InP-based cylindrical microcavity light emitting diodes,”
IEEE J. Quantum Electron., vol. 37, pp. 48–54,
Jan. 2001.
[5]
A. Chutinan
and S. Noda, “Effects of structural fluctuations on the pho- tonic bandgap during fabrication of a photonic
crystal: a study of a pho-
tonic crystal with a finite
number of periods,”
J. Opt. Soc. Amer. B,
vol. 16, pp. 1398–1402, 1999.
[6]
D. Ochoa
et al., “Diffraction of cylindrical Bragg
reflectors surrounding an
in-plane semiconductor microcavity,” Phys.
Rev. B, vol. 61, pp. 4806–4812, 2000.
[7]
R. Coccioli,
M. Boroditsky, K. W. Kim, Y. Rahmat-Samii, and E. Yablonovitch,
“Smallest possible electromagnetic mode
volume in a dielectric cavity,”
in IEE Proc. Optoelectron., vol. 145,
1998, pp. 391–397.
[8]
M.
Boroditsky et al., “Spontaneous
emission extraction and Purcell en-
hancement from thin-film
2-D photonic crystals,” J. Lightwave Technol.,
vol. 17, pp. 2096–2112, 1999.
[9]
C. H. Henry, R. A. Logan, and
F. R. Merritt, “The effect of
surface recombination on current in Al Ga As heterojunctions,” J. Appl.
Phys., vol. 49, pp. 3530–3542, 1978.
[10]
G. Bjork and
Y. Yamamoto, “Analysis of
semiconductor microcavity lasers using rate equations,” IEEE J. Quantum Electron., vol. 27, pp. 2386–2396, 1991.
[11]
R. Lee, O. Painter,
B. Kitzke, A. Scherer, and A. Yariv, “Emission prop- erties of a defect cavity in a two-dimensional photonic
bandgap crystal slab,” J. Opt. Soc. Amer. B, vol. 17, pp. 629–633, 2000.
[12]
O. Painter, A. Husain,
A. Scherer, P. T. Lee, I. Kim, J. D. O’Brien, and P.
D. Dapkus,
“Lithographic tuning of a two-dimensional photonic crystal
laser array,” IEEE Photon.
Technol. Lett., vol. 12, pp. 1126–1128, 2000.
