One of the major barriers in studying the optical
properties of semiconductor QDs is to isolate the spectral features
of a single QD out of a large inhomogeneous ensemble. This barrier
has been overcome by either using near field probes or micron scale
apertures to reduce the number of QD under observation. Although near-field
techniques provide very high spatial resolution, their poor collection
efficiency and technological complexity severely limit overall effectiveness
and flexibility to combine with other existing optical spectroscopic
techniques. In far-field optics based techniques, micron scale apertures
have been successfully utilized to the study the spectroscopic properties
an individual QD in low density SAQD's and naturally formed QD system.
However, for a high density QD ensemble, an aperture of 1 micron in
diameter can only reduced the number of probed QD's to ~ a hundred.
The spectra collected through the aperture usually composed of a group
of atomically sharp spectral lines. It is essential to further isolate
the spectral feature of a single QD out of that jungle of peaks.
Spectroscopic Imaging

We accomplished this task by exploiting the fact that the position
of the diffraction limited image of a point light source can be determined
with nanometer scale much below the diffraction limit. We used conventional
low temperature microphoto-luminescence (µPL) imaging system
with Ti:Sapphire laser beam incident at the 30º inclined to the
sample surface. The images of QD's collected by the imaging optics
overlapped each other in the real space. However, since each quantum
dot usuallyemits at different wavelengths, we can dispersed their
PL peak images without distorting their spatial positions along the
axis perpendicular to the spectral axis by using imaging spectrograph.
Liquid nitrogen cooled charged coupled device detector (CCD) mounted
at the exit plane of the spectrograph can collect spectral images
containing both spatial and spectral information. Spatial mis-alignment
of PL peak in the magnified spectral image shown in Fig(b) (peak #1-#4)
clearly demonstrated this fact. The exact spatial origin of these
peaks can be determined by fitting their intensity distribution along
the lines parallel to x-axis with the point-spread function as shown
in Fig.(c). In this way, we can determine the position of the PL peak
with precision of ±0.1 pixel (±40nm). This method is
most effective in locating spectrally isolated PL peak.
2 Dimensional Mapping of QDs at Nano-meter
Scale.

Two Dimensional Mapping of QDs under an aperture with 2 mm diameter
is achieved by scanning the real space image of the aperture across
the slit of the imaging spectrograph with 200nm steps. A spectral
image like the one shown in the previous figure was taken at each
scanned position. Two dimensional map was reconstructed from the spectra
taken at each position. Fitting the intensity in x and y direction
gives the center position of the QDs within the aperture. Center position
and size of the ellipses in the right figure correspond to the position
of the QDs and uncertainty in position given by fitting process.
Cross Sectional NanoPL.


Cross-sectional nano-PL is yet another scheme to perform single QD
spectroscopy. As the name suggests, we perform the PL measurements
on the cleaved edge of MBE grown sample. The sample can be arranged
in two geometries. Each has its own advantages. In the first case
we aligned the sample so that the QD layer is perpendicular to the
spectrograph slit as shown in the top schematic. By narrowing the
spectrograph slit, one can limit the observation region down to a
few hundred nanometers (slit size divided by the magnification). This
significantly reduced the effective probing volume as the other lateral
dimension is automatically confined by the sample structure and the
probing depth along the z-direction is limited by the adsorption length
(<1 micron). The spatial location of QDs along one dimension can
be further separated by scanning either the sample or the focusing
lens mounted in front of the imaging spectrograph as the one shown
in the top figure. This scheme of cross-sectional nano-PL can be adopted
with other types of detectors such as linear array or single element
detectors. Alternatively, when CCD is available, one can orient the
QD layer along the slit of imaging spectrograph as shown in the bottom
schematic and to use one of the dimensions of the CCD array to determine
the spatial location of the QD in the same manner as the top-view
nano-PL [bottom figure]. In either geometry of cross-sectional PL,
one eliminates the need to use micron/submicron apertures to reduce
the effective probing volume. By using this new method, we studied
the quantum confined Stark effect in single stacked and vertically
coupled double stacked SAQDs. The results are submitted to be published
in APL.