Instructions for the Experiment Excitonic States in Atomically Thin Semiconductors 1. Introduction Alongside with electrical measurements, optical measurements are an indispensable tool for the study of semiconductor materials, as they reveal many of the materials properties. In this experiment, photoluminescence and reflectance measurements are employed in order to study excitonic physics in WSe2 monolayers. This document describes the experimental setup in detail and explains how the experiments are to be performed. It will also give instructions on how to analyze the acquired data. 2. Experimental Setup A picture of the experimental setup is shown in illustration 1. The whole setup is built on top of an optical table. In the following sections, the different components of this setup are explained, following the path of the light in the setup. Illustration 1: Top view of the optical setup. The green, red and white lines represent the excitation path, the detection path and the path of the white light, respectively.
2.1 Laser Sources Several laser sources are available for the optical excitation of the sample. The lasers differ in photon energy (wavelength) and laser type (pulsed or continuous wave). Since in this experiment only time-integrated measurements are performed, a 660nm continuous wave diode laser (illustration 2a) is used, which excites the WSe2 monolayer at a photon energy higher than the material s optical band gap but lower than the B-exciton energy or its electronic band gap. 2.2 Excitation Path The laser light is guided to the cryostat using a set of mirrors, a beam splitter and a scanning mirror system. The properties of the exciting laser light can be modified via a combination of optical components in the excitation path: The intensity of the incident laser light can be adjusted using neutral density filters. A motorized filter wheel (illustration 2b) provides discrete transmission factors between 3 10-9 and 1. In this experiment transmission factors down to 1 10-3 are useful. The laser light can be spectrally cleaned using a suitable band pass filter. This avoids that low energy laser modes (or spontaneous recombination) are superimposed on the photoluminescence signal from the sample. Another filter wheel (illustration 2c) provides a set of band pass filters. For the 660nm diode laser, a band pass filter with a central wavelength of 660nm is available. In order to define the polarization of the laser light, a linear polarizer, a half-wave-plate and a quarter-wave-plate (illustration 2d) can be introduced into the excitation path. These three optical components are sufficient to change the polarization of an arbitrarily polarized input beam into any desired polarization. Illustration 2: a) laser source, b) neutral density filter wheel, c) band pass filter wheel, d) polarization optics Illustration 3: a) beam splitter, b) optical diode, c) scanning mirror, d) 4f-relay-lens-system After setting the beam properties, a beam splitter (illustration 3a) splits the exciting beam into two parts; one is used to excite the sample and the other one is used to measure the laser intensity using an optical diode (illustration 3b). A tiltable scanning mirror (illustration 3c) is used in combination with a 4f-relay-lens-system (illustration 3d) in order to scan the beam across the sample surface.
The 4f setup relocates the center of rotation the objective within the cryostat (illustration 4). from the scanning mirror into Illustration 4: Working principle of a 4f-relay-lens-setup. The scanning mirror can be tilted in order to deflect the beam. Two lenses with identical focal lengths relocate the center of rotation from the center of the scanning mirror into the center of the objective. 2.3 Cryostat A picture of the open cold-finger cryostat is shown in illustration 5. The sample is placed on the cold finger of the cryostat with the sample surface facing downwards. The temperature of the sample can be lowered to 11K using liquid Helium. The objective with a focal length of approximately 3mm is located within the cryostat. The sample can be moved using an x-y-z stepper stage. Two thermometers are continuously measuring the temperatures of the cold-finger and the sample. The cryostat provides electrical contacts to the sample. However, for this experiment, no electrical contacts to the sample are needed. 2.4 Detection Path Illustration 5: Open cryostat. The light emitted from the WSe2 monolayer is collected by the objective and then guided to the spectrometer. In the detection path different optical components can be used to analyze the emitted light before spectrally resolving it with the spectrometer: Similar to the definition of the polarization in the excitation path, a quarter-wave-plate, a half-wave-plate and a linear polarizer (illustration 6a) are sufficient in order to determine fully the polarization state of the emitted light.
The laser light is spectrally filtered using a long-pass filter in front of the spectrometer (illustration 6b). In this experiment a long-pass filter with an edge position at 700nm is used, which reflects the laser light but transmits the photoluminescence signal. Note that for reflectance measurements, this filter needs to be removed. For reflectance measurements, a spatial filtering of the signal is required. For this purpose a confocal setup including two lenses and a pinhole can be inserted in the detection path (illustration 6c). Finally, the emitted light is focused on the entry slit of the spectrometer (illustration 6d) and dispersed on a CCD. Illustration 6: a) polarization optics, b) 700nm long-pass filter, c) confocal filtering, d) spectrometer entrance slit 2.5 Imaging In order to find the position of interest on the sample, the sample surface can be imaged. For this purpose the sample can be illuminated with white light and the reflected light can be imaged on a CCD camera. A pellicle beam splitter on a flip mount allows for easy on- and off-switching of the imaging path. 3. Software Most components of the experimental setup can be controlled remotely from a computer. In some cases (alignment of optical components, finding a point of interest on the sample), it is convenient to use the instrument software provided by the instrument manufacturers. However, in the real measurements, where many instruments need to be synchronized, a Python-based data acquisition framework called QCoDeS will be used. Almost all instruments in this setup can be integrated with QCoDeS. In the next sections, the software used throughout the whole experiment is explained. 3.1 Attocube Daisy The Attocube Daisy software is used to control the x-y-z stepper stage within the cryostat. The xand y-axes are used to laterally move over the sample, whereas the z-axis is used to move the sample into the focus of the objective. In the software each axis is represented by another tab. For the movement of the axes, a voltage and a frequency need to be set. At a sample temperature of 11K, the voltages should be set to 55V. The frequencies need to be set according to the desired axis speed.
3.2 Andor Camera The Andor Camera software (illustration 7) is used for the imaging of the sample. After starting the software, the parameters for the image acquisition need to be set: 1. Acquisition Setup Acquisition Setup Camera The exposure time should be set to a reasonable value. Too low exposure time leads to noisy images, whereas too high exposure time leads to a saturation of the CCD, which can result in damage. 2. Acquisition Setup Acquisition Image Orientation The image should be flipped both horizontally and vertically in order to achieve a unrotated image of the sample. 3. Hardware Shutter Control The internal shutter should be set to permanently open. After setting up all acquisition parameters, the sample can be imaged by clicking on the small video symbol (red circle in illustration 7). Illustration 7: Screenshot of the Andor Camera software. In order to reduce the amount of stray light, the Andor camera software provides the option to remove a background image from the acquired image. This mode can be enabled by 1. Acquisition Setup Data Type: Select Counts (BG corrected) 2. Acquisition Take Background: Take a background image at a plane spot of the sample. 3.3 Andor Spectrometer The Andor Spectrometer software (illustration 8) is used in order to measure the spectrum of the light that enters the spectrometer. After starting the software, the parameters for the spectrum acquisition need to be set: 1. Select a suitable grating (red box in illustration 8). The grating determines the spectral resolution, as well as the covered spectral range. For photoluminescence measurements, a
grating with 600 lines per mm is recommended. For reflectance measurements, a grating with 299 lines per mm is recommended. 2. Set the shutter to auto (blue box in illustration 8). 3. Close the slit (green box in illustration 8) in order to minimize the amount of stray light in the spectrum. For a well-aligned setup, a slit width of 100um is recommended. 4. Set the central wavelength of the grating (orange box in illustration 8). The central wavelength depends on the spectrum that one wants to measure. 5. Set a suitable exposure time (purple box in illustration 8). A suitable exposure time should minimize the signal-to-noise ratio while keeping but keep the experiments short. After setting the parameters, the spectrum acquisition can be started (yellow circle in illustration 8). Illustration 8: Screenshot of the Andor Spectrometer software. 3.4 QCoDeS QCoDeS is a Python-based data acquisition framework that allows for easy integration of multiple instruments involved in a measurement. As an example, a measurement of the excitation power dependency of a spectrum requires control over at least three instruments: 1. The neutral density filter wheel sets the intensity of the exciting laser light. 2. The optical diode at the transmission side of the beam splitter measures the laser intensity. 3. The spectrometer acquires the spectrum of the light emitted from the sample. QCoDeS can be controlled from Jupyter notebooks. In this experiment predefined Jupyter notebooks are provided to the students. These notebooks include the Python codes for the
measurements in this experiment, as well as detailed instructions on how to perform these measurements. 4. Measurement Instructions 4.1 Aligning the setup After the optical setup is taken over by a new person, one should check the proper alignment of the setup. This includes the following steps. 1. Make sure you are wearing laser safety goggles suitable for the laser used. 2. Make sure the laser beam is aligned with the cage system of the optical setup. Pinholes within the cage system can be closed and used as a reference for the cage center. Two mirrors are sufficient to fully align the beam with any of the cages. 3. Make sure the laser enters the objective centrally. For this purpose, one can move the sample slightly away from the focus point and observe the Airy pattern on the camera. If it does not look symmetric, the mirror underneath the cryostat can be used to correct the beam path. 4. The emitted light needs to be focused well onto the entry slit of the spectrometer. For this purpose, the focusing lens in front of the spectrometer is placed on an x-y-stage. This stage should be used to maximize the counts on the spectrometer with the slit being closed to a reasonable value. 4.2. Finding the WSe2 monolayer The WSe2 monolayer has a size on the order of 10um and is placed on a 5mm SiO2 chip. The chip is equipped with metal markers (illustration 9), which allow for the localization of the monolayer using the x- and y-axes of the stepper stage in the cryostat. On the day of the experiment, the students will receive micrographs of the freshly prepared sample together with all the necessary information on its location on the chip. 4.3 Photoluminescence Map A photoluminescence map of the WSe2 monolayer is Illustration 9: Chip layout. acquired. For this purpose, the monolayer is scanned using the tiltable scanning mirror. After each step of the scanning mirror, a spectrum is acquired with the spectrometer. This measurement can be run from the Jupyter notebook photoluminescence_map.ipynb. The hyperspectral dataset can be analyzed using the Py2DSpectroscopy software (https://github.com/svenbo90/py2dspectroscopy/). A detailed description and a video tutorial can be found on the github page. The highest quality position on the sample (lowest emission linewidth) can be found using Py2DSpectroscopy. All further experiments should be performed at this position.
4.4 Power Dependence Measurement A power dependence measurement of the WSe2 monolayer photoluminescence can be performed using the automatic neutral density filter wheel. The measurement can be run from the Jupyter notebook power_dependence.ipynb. The acquired dataset can be analyzed using the Py2DSpectroscopy software. From this measurement a suitable excitation power for further measurements can be obtained. A good excitation power gives narrow linewidth emission but keeps the measurement duration short. 4.5 Polarization Dependence Measurement For the polarization dependence measurement, the polarization optics need to be inserted in the excitation and detection paths of the optical table. On each side, a linear polarizer, a half-wave-plate and a quarter-wave-plate are needed (illustration 10). Illustration 10: Polarization optics in the excitation and detection paths. The polarization optics in the excitation path are used to set the polarization of the exciting laser light. The students will be provided a calibration sheet (i.e. the rotation offsets) of the polarization optics on the day of the experiment. The sample should be excited using R-, L-, H- and V-polarized laser light. For each excitation polarization R-, L-, H- and V-polarized light should be detected. In total, 16 spectra need to be acquired. This measurement can be run from the Jupyter notebook polarization_dependence.ipynb. 4.6 Reflectance Measurement In the reflectance measurement, the reflection of white light from the WSe 2 surface is measured. This reflection is then compared to the reflection from the SiO 2 surface in order to obtain the reflectance of the sample. In contrast to the photoluminescence emission, the reflected white light needs to be filtered spatially. For this purpose a confocal setup including two lenses and a pinhole is inserted in the detection path. The pinhole position is then aligned by maximizing the laser counts on the spectrometer. The laser source can now be turned off (or blocked) and the white light source is turned on. The semi-transparent pellicle needs to flipped such that it reflects the white light towards the sample. The reflection from about five points on the WSe2 monolayer should be measured. In order to obtain identical illumination conditions for the reflection measurements on WSe 2 and SiO2 the Attocube stage is now used to move the probe area away from the WSe 2 monolayer. Then, the light is measured at the same positions as on the WSe2 monolayer. This measurement can be run from the Jupyter notebook reflectance.ipynb.
5. Data Analysis The acquired data should be used to gain insight into excitonic physics in a WSe2 monolayer. 5.1 Identification of Excitonic Complexes The students are asked to identify as many excitonic complexes as possible and specify their optical properties. From the acquired photoluminescence map the students should make a list of all observed emission energies. Please note that the emission energy of a single excitonic line may vary by a few mev across the sample due to mechanical strain. From the power dependence measurements, the students should extract the integrated intensity of an excitonic line as a function of laser intensity. Plotting these intensities on a log-log plot will let the students fit a linear function to the plotted data. The slopes of these fits reveal information on the nature of each excitonic line. Biexcitonic complexes tend to have slopes larger than 1 whereas excitons and trions show slopes smaller than 1. From the polarization dependence measurements, the students should specify which of the excitonic lines show circular dichroism and valley coherence. This will give further insight into the nature of each excitonic line. 5.2 Determination of the Optical and Electronic Band Gap The students are asked to estimate the binding energy of the lowest energy excitonic state. The optical band gap can be determined by measuring the emission energy of the neutral exciton. Since this value varies across the sample (due to strain) a spatially averaged value with standard deviation should be reported. The exciton binding energy can be approximately obtained from the spacing between the two lowest states of the neutral exciton. For this purpose, the reflectance data has to be analyzed. The normalized reflectance can be calculated as Δ R= R monolayer R substrate R substrate The oscillator strength of the first excited state of the neutral exciton is weak compared to its ground state. Therefore, plotting the derivative of ΔR can make this state more visible. Smoothing the data for example with the Savitzky-Golay algorithm may further improve the visibility of this state. For two-dimensional semiconductors it is expected that Eb 2 Δ E 1,2. With this approximation, the students can make an estimate for the electronic band gap of the material.