Typical quantum dot densities of ∼ 109QDs/cm2 lead to inter quantum dot distances of
∼ 300nm. Therefore in order to measure individual quantum dots a high spatial resolution is required. This resolution can be reached with a so-called confocal microscope. The following sections will discuss its working principle and the setup used for the experiments reported in this thesis.
Figure 4.1: Schematic representation of the confocal microscope setup. The objective fo-cusses the light from the excitation source on the sample. The PL is collected by the same objective. The pinhole blocks any light from the sample that is out of focus in any way.
4.2.1 Diffraction limit and confocal microscope
To achieve a sufficiently high resolution, diffraction limited optics is necessary. Let us assume that the quantum dot can be considered as a point light source. When illuminating an objective, the spherical waves from the quantum dot converge via the objective to the focal point. Due to the finite aperture of the objective, an Airy diffraction pattern is formed.
The radius of the central Airy disk of this pattern is given by [38]
rAiry= 0.61 λ
N A (4.1)
where N A is the numerical aperture of the objective and λ the wavelength of the emitted light. The numerical aperture is a measure for how much light can be collected by the objective; the larger the numerical aperture, the larger the imaginary cone that has its light focussed by the objective. When using the Rayleigh criterion, which assumes two points sources to be resolvable if they are separated by a distance of at least the radius of the central Airy disk, the resolution of the objective used in our setup can be determined to be
∼ 500nm [39]. A schematic representation of the confocal microscope is shown in figure 4.1.
The laser beam is focused onto the sample by the objective, after which the photolumi-nescence is collected by the same objective. Because of this, any light which is out of focus, both vertically and laterally will be blocked by the pinhole. This means that only PL-signal emitted by the part of the sample exactly in focus of the objective is left after the pinhole.
As the diffraction limit of ∼ 500nm is still larger than the average inter dot distance of
∼ 300nm, in general the excitation spot will illuminate more than one quantum dot. This is not an issue as the number of quantum dots will still be small, and due to the spectrally
Figure 4.2: Overview of the used micro-photoluminescence setup. The magnet is located in the outer chamber of the cryostat and is cooled using liquid helium. At the center of the magnet, inside the insert, the sample is placed on top of a piezo stack. This allows the sample to be positioned. On top of the microscope stick, the optical head is located. The paths of the excitation light (red) and the collection light (orange) are visible.
different properties of each quantum dot they can still be distinguished from one another.
Moreover, the sample studied in this thesis was found to have an unusually low quantum dot density. Because of this, the excitation spot always contained at most one quantum dot.
Now that the working principle of the confocal microscope has been explained, an overview of the used setup will be given. The setup is shown in figure 4.2 and consists of four main components; the cryostat containing the superconducting magnet, the optical head which is in essence our confocal microscope, the microscope stick which contains our sample and a monochromator which is able to detect and analyze the photoluminescence signal.
4.2.2 The cryostat and superconducting magnet
The cryostat consists out of four compartments. The outer layer is a vacuum shield con-taining super-isolation and is pumped down to typically 10−5mbar. This thermally isolates the inner chambers from the outside world. Next is the magnet bath, which contains a cooled superconducting magnet, capable of producing magnetic fields up to 10T . This bath is cooled with liquid helium to reach a temperature of 4K. The magnet bath is separated
from the inside of the system using another vacuum layer. This layer is typically filled with some contact gas, to cool down the sample as well as the magnet. Our microscope stick, which is a closed vacuum chamber containing the sample, is inserted into the inner chamber.
4.2.3 The microscope stick
The microscope stick is a metal tube, the length of which matches the cryostat in such a way that the sample is located at the center of the superconducting magnet. At the bottom of this metal tube, the sample is mounted on top of a piezostack consisting of three independent piezos, allowing us to translate the sample in any of the three directions with a precision of ∼ 10nm. Right above the sample (several millimeters) the objective is placed.
On top of the stick, outside of the chamber, the optical head is mounted (see next section).
After flushing with helium gas to prevent condensation while cooling, the stick is filled with
≈ 10mbar of gaseous helium, to ensure the sample is also cooled down to the liquid helium temperature, 4K.
4.2.4 The optical head
The optical head consists of three arms; an excitation arm, a collection arm and an imaging arm. The excitation source used is a laser diode emitting at 780nm. Through a fiber the laser light is coupled to a lens, which it is collimated by. The light passes through the first beam splitter, which reflects half towards the microscope objective and the other half to a power meter for monitoring purposes. The objective focusses the laser onto the sample and then collects the PL signal. As the objective is chromatic, its focal point depends heavily on the wavelength of the light. Therefore when aligning the optical head for the laser wavelength, the head will have to be slightly realigned when moving to the PL wavelength.
When the PL returns to the optical head, half of the signal is lost by the first beamsplitter.
The second beamsplitter reflects half the signal towards another lens, which images the signal on the CCD camera, again for monitoring purposes, while the other half is reflected towards the collection fiber. Before reaching the fiber, the laser wavelength is filtered out by a high pass filter and the signal is focussed onto the collection fiber via the third lens.
This fiber, which has a diameter of ∼ 5µm acts as the pinhole described in the previous section. From here, the light will be directed to the monochromator.
4.2.5 Monochromator
The monochromator is used to analyse the PL signal. The monochromator consists of three stages, each consecutive one allowing for a better resolving ability. In our experiments, only the first stage is used, which has a focal length of 750mm. The first stage has three different gratings which can be used with 750, 1100 and 1800grooves/mm. Using a mirror, the light from the fiber is directed towards a slit, which reduces the spot diameter to 5µ. As the original laser spot has the same size, this should get rid of any redundant light. The slit is placed in the focus of a curved mirror, which will collimate the light. The collimated light is then diffracted by the grating. Another curved mirror than refocusses the now dispersed light onto the exit slit. An extra mirror is used to direct the light to either an InGaAs detector or a Si CCD camera. As the detection efficiency and noise-signal ratio of the Si CCD camera is a lot better as opposed to the InGaAs detector, the Si detector will be used in this project. While scanning the sample in the search of quantum dots, the 750-grating
is used. When finally performing measurements on a quantum dot, this is switched to the 1800-grating, to achieve the highest possible resolution which in this case is 15µeV /pixel.