Temperature-dependent Photoluminescence of a GaAs Quantum Well and Sb2O3
Advisor: Dr. Mo
Internship Location: San Jose State University Science Building
Onsite Mentor: Christopher Smallwood, Associate Professor, San Jose State University
Photoluminescence (PL) spectroscopy is a powerful optical characterization technique that can determine properties of semiconductors. In this project, I will calibrate a temperature-dependent photoluminescence spectroscopy (temperature-dependent PL) setup by analyzing the PL spectra of a gallium arsenide (GaAs) quantum well. To do this, I will study quantum effects and use the software Igor Pro. Results on GaAs will be used to determine whether or not the instrument’s thermometers are correctly calibrated. Following the GaAs study, I will research an antimony trioxide sample with temperature-dependent PL to see if I can gain insights into whether the material can host quantum emitters, which are sources of single photons necessary for quantum computing technologies.
Project Blog
Post 1: Blog 1: Introduction
Hi everyone, welcome to my senior project blog! In this first post, I will be discussing some background behind the first part of my project, the temperature-dependent photoluminescence of a gallium arsenide quantum well. Perhaps you’re thinking, what do the terms “photoluminescence” and “quantum well” even mean? So, I will start by going over background information on semiconductors, photoluminescence spectroscopy, and quantum wells.
Semiconductors
You might know that semiconductors have properties between metals and insulators, but specifically, the difference between these types of solids can be seen in their band diagrams, which show the energies their electrons can have.
The conduction band consists of higher energies that allow electrons to conduct electricity while the valence band is their lower-energy non-excited states. Energies electrons cannot have between these two bands form the band gap. In conductors, the band gap is basically nonexistent, so electrons can easily go to the conduction band. In insulators, the band gap is large so electrons are unable to be excited to the conduction band. Semiconductors have a small band gap, so with some energy, electrons can be excited to the conduction band and the material can conduct.
Photoluminescence spectroscopy
Photoluminescence is the process in which a material absorbs light, exciting its electrons, and then emits light as its electrons return to their original states. Photoluminescence spectroscopy is an optical technique that shines a laser at a material and measures all the light reemitted, which can tell us information about the band diagram, as the peak wavelength reemitted is very much related to the band gap, and help us understand semiconductors better and implement them in novel technologies.
Quantum wells
Quantum wells are nanoscale 2D structures consisting of a thin layer of semiconductor between two layers of another semiconductor. The band gap of the outside material is larger than the middle material which causes quantum confinement of electrons in the middle layer. Because of this, radiative recombination, which is when light is emitted after an electron is excited, is more likely in quantum wells than bulk materials, allowing quantum wells to be more efficient and produce higher intensity in light-emitting devices.
Over the next few weeks, I will discuss my research process and how temperature affects photoluminescence. Thanks for reading and stay tuned!
Post 2: Blog 2: Setup
Welcome to my second blog! This week, I’ll be discussing the setup that we work with to collect data and some things we did to prepare it. This is what our optical table looks like at San Jose State University and I made a diagram for it.
We have a temperature-dependent photoluminescence (PL) spectroscopy and optical microscopy setup. For PL spectroscopy, the laser path is shown in blue, while the emitted light from the sample follows the red path to the spectrometer. For optical microscopy, we remove the mirror at the bottom right and use a white LED. The light travels along the green path to the sample, then reflects and follows the red path to a camera, allowing us to view the sample and ensure proper alignment.
The laser is a He-Cd continuous wave laser with a wavelength of 442 nm. The light passes through a Keplerian spatial mode filter and beam expander, which consist of two lenses with the second one having a longer focal length, and a pinhole in the middle to block side “noise” and produce a clean beam. The periscopes all consist of two mirrors which are at 45° angles to horizontal and change the height and direction of the light beam. Next, the beam hits a dichroic mirror, which reflects shorter wavelengths and allows longer wavelengths to pass through, so the light from the laser reflects. The scan lenses become important after the light reaches the sample and the sample emits light. The microscope objective and first two scan lenses form an infinity optical system, a diagram of which is shown in the picture below. The objective makes the light collimated, and then there is double the focal length between the first and second scan lenses so that we have collimated light going into the third. The third focuses the light into the spectrometer. By collimating the light, we can ensure minimal distortion when other elements are inserted in the beam path.
(Infinity Optical Systems. Nikon’s MicroscopyU. https://www.microscopyu.com/microscopy-basics/infinity-optical-systems.)
The spectrometer contains a diffraction grating, which works like a prism, so the light is split by wavelength, and the different pixels of the charge-coupled device (CCD) camera measure the intensity of each wavelength. The beam splitter allows half of the light to go through and half to reflect. In this case, it is there for optical microscopy with the LED.
In order to prepare the setup, one test we did was inserting a helium lamp in the beam path. As elements have known distinct spectral lines, we confirmed the spectrometer was working when we obtained the expected results.
We collected photoluminescence spectra at 3.8 K, 5 K, and, in increments of 5 K, up to 55 K for the gallium arsenide quantum well. Next week, I’ll be finishing up analysis of our first set of data. See you next time!
Post 3: Blog 3: Some more notes on setup + beginning data analysis
Hi everyone, welcome back! This week, I mostly worked on analyzing data. But first, I acquired some more information about our setup which I discussed last week.
Setup part 2
Here is a diagram again for reference.
I ended with talking about the infinity optical system, but I found out there’s more to it. The mirror in between the dichroic and a scan lens is motorized. This allows the light from the laser to reach all parts of the sample, which can be seen from this diagram I made, so we can take measurements over the whole area.
Data analysis
The software I am using is Igor Pro. Transferring the photoluminescence (PL) spectroscopy data for the GaAs quantum well from the CCD camera to Igor Pro, we can get something that looks like this, where the horizontal axis is wavelength because the light was split by the diffraction grating inside the spectrometer, and the vertical axis is vertical position.
From this, I took an average of 40 rows of pixels in the middle to produce the PL spectra which looked something like this (this is at 15K).
Now, the parameters we are interested in include the peak position and peak width, so we wanted a systematic way of extracting these values, which we can do by fitting a curve. My advisor first suggested Gaussian curves for each peak, but this produced a fit that was not great, not matching the peak or the shoulders.
I first tried adding a linear offset which was not effective enough.
Then my advisor suggested trying other functions like the Lorentzian which looked a lot better, and adding a linear offset looked even better. This makes sense because Gaussian lineshapes tend to better capture statistical variance whereas Lorentzian lineshapes tend to better capture resonance features, which also can explain why there appears to be slightly more Gaussian shape at lower temperatures.
Let me now explain how this works in Igor Pro and the problems I ran into. I created the function you can see in the bottom white rectangle and you have to make pretty good guesses for each of the parameters. Otherwise, it tells you there may be no dependence or it gives you negative or nonsensical values.
After I found the best fit function, I was about to implement it to all 12 temperatures we collected data at when it kept telling me there was no dependence. I tried different guesses and my other fits but nothing was working. I asked Luke, an undergrad at SJSU, and he identified that I did not choose the right Y Data here, which I thought was automatic before.
So after choosing the right data, I still made a lot of bad guesses but I got all the fits and was able to create these two graphs, where FWHM stands for full width at half maximum and I calculated to be equal to 2w for this function.
I still need to add error bars, which is where Google Sheets fails me, and it might be good to look at peak area vs. temperature, but we do see peak position increasing with temperature as expected, and it looks like only the width of one peak is affected by temperature.
Next week, I will continue with data analysis and try to read some textbooks to understand what is happening. Stay tuned!
Post 4: Blog 4: More plots + reading
Hi everyone, this week was kind of busy but I worked some more on plotting the data and tried to understand some theory.
Plots
I figured out how to add custom error bars in Excel. However, since the error is based on the standard deviation Igor Pro gives me for each coefficient of the PL spectra fits, they are mostly not visible. The graph with the most visible error bars is the one of peak width.
I also wanted to plot peak area against temperature. Since we decided that a Lorentzian function fits our data the best, all the peaks have the form of , and if we take the integral from negative infinity to positive infinity over x, we see that it evaluates to an arctan function and the area is just a multiplied by π. This is the graph we get. I am not sure how to interpret this yet.
For the graph of peak position I had, I converted from wavelength to energy using and 1 eV = 1.6*10^-19 J because electron volts seem to be the standard unit when working with these optical transitions and band gaps.
You might notice that compared to my last blog, in all these graphs a data point is gone, the 3.8 K one. This is because it was not following trends, and when I asked Luke if there was any setting changes, he told we he noticed that it was strange when collecting data and it may be because the laser was not warmed up, which makes sense because peak width and area seem to be lower than expected (this data is actually from 1/21 so I came after school and they had already started collecting data). We may redo that measurement. Also, my advisor told me the different peaks correspond to a light hole and a heavy hole transition, which I don’t really understand yet, so I am trying to read textbooks to understand related theory.
Textbook reading
I am starting with Optical Properties of Solids by Mark Fox. Not everything I write here may be relevant but it is what I understood from my readings so far. To start, a hole is the absence of an electron created in the valence band after an electron is excited. Both holes and electrons can conduct electrical current. Another important concept is band structure. This is what it looks like for GaAs.
On the vertical axis is energy and on the horizontal axis is the wave vector which is related to momentum through the de Broglie wave equation. Band structures are usually shown in the reduced zone scheme (shown left) which maps the energy bands to one zone because crystals are periodic.
Heavy and light refer to the effective masses of the holes and are defined by the curvature of the bands, and electrons and holes behave like charged particles with different masses. Different materials have electrons and holes with different effective masses.
I will continue trying to understand the theory better over the next few weeks but it is slow because it is too advanced for me. Come back to see how it goes next week!
Citations
Fox, Mark. Optical Properties of Solids. New York, Oxford University Press, 2012.
“Band Structure and Carrier Concentration of Gallium Arsenide (GaAs).” Www.ioffe.ru, www.ioffe.ru/SVA/NSM/Semicond/GaAs/bandstr.html.
Post 5: Blog 5: Infinite potential well
Welcome back to me trying to understand physics! If we look at the band structure for GaAs again, if the transitions for the heavy hole and light hole are the direct ones (same wave vector) at 0 wave vector, it appears that we should be getting one peak equal to the band gap but we clearly have two peaks.
https://www.ioffe.ru/SVA/NSM/Semicond/GaAs/bandstr.html
This is where the quantum well comes in. As a reminder from my very first blog, a quantum well consists of a thin layer of a semiconductor in between layers of another semiconductor, kind of like a sandwich. In my case, we have GaAs in between AlGaAs. Since these have different properties, we get a band diagram that looks like this, where the “sandwich” is standing on its side.
https://en.wikipedia.org/wiki/Quantum_well#/media/File:MCM_GaAs_AlGaAs_structure.svg
In the conduction band, the AlGaAs are higher than the GaAs and the opposite is true for the valence band, but the electrons in the conduction band and holes that form in the valence band also have opposite charges. Now as an approximation we consider the infinite potential well model, making the energy difference infinite.
https://en.wikipedia.org/wiki/Particle_in_a_box#/media/File:Infinite_potential_well-en.svg
The time-independent Schrödinger equation can be written
where E_n are the possible energies, psi_n are the corresponding wave functions, hbar is the reduced Planck’s constant, m is mass, V is potential, and x is position. As some background, probability .
Since potential is 0 inside the well, we have
This has solutions of the form
Let us substitute in k
We have two boundary conditions because the wave function/probability has to be continuous and there is 0 probability outside the well:
From the first condition, we get B=-A. Now our wave functions are
From the second we get k=nπ/L. Since total probability is 1, solving with an integral gives us
The important result though is
Of course, this is a bit too simple since we do not have infinite potential, but this provides a basic reason why the different effective masses of the light hole and heavy hole give us different energy peaks.
(Note: I might have messed up some notation.)
Post 6: Blog 6: Quantum confinement continued
Hi everyone, welcome back! You might remember a couple of blogs ago I started reading parts of Optical Properties of Solids by Mark Fox. The most important chapter for me is probably Chapter 6: Quantum confinement. The infinite potential well (see last blog) is actually part of this chapter but it does things a bit differently and skips more steps.
The most famous quantum confinement effect is probably how the color of quantum dots changes with their size. However, clearly, this does not happen with regular, everyday objects which are of a much larger scale. Quantum size effects are important if the confinement energy is comparable to or greater than the thermal energy. If a particle is confined to , the Heisenberg uncertainty principle tells us that . Then, we have . Thermal energy is , so we must have . This is around 5 nm for an electron with effective mass of one tenth the mass of a free electron in a typical semiconductor at room temperature.
Quantum wells have 1D quantum confinement, quantum wires have 2D quantum confinement, and quantum dots have 3D quantum confinement. The book focuses on quantum wells in this chapter because we can separate the xy-plane and the z direction, allowing us to see the effects with simpler calculations.
A more accurate model than the infinite potential well of last week is the finite potential well. I have decided not to write out all the math for this, but the steps are pretty similar with a few more conditions. However, the wave function extends outside the well and we require it to exponentially decay there. Compared to this model, the infinite potential well predicts energies for electrons and holes that are too high.
Citations
Fox, Mark. Optical Properties of Solids. New York, Oxford University Press, 2012.
“More 1D Problems.” Utk.edu, 2025, electron6.phys.utk.edu/phys250/modules/module%202/1d_problems.htm. Accessed 23 Apr. 2025.
Post 7: Blog 7: Unexpected events
Hi everyone, in this blog, I thought I would talk about 2 events that happened sequentially that I did not expect during the course of my project.
Cryostat
The cryostat stopped working. It failed to cool the chamber down and when we tried, the alarm would beep. Eventually, Andre, a master’s student at SJSU, took out the air filter and it was very dusty. He cleaned it and after that, the cryostat started working again. During the time it was not though (around a week), we did not collect any data.
Laser change
The group added a HeNe laser to the table, along with other optical components to direct the laser beam to the sample chamber. This is because the HeCd laser has a wavelength of 442 nm while the HeNe laser has a wavelength of 632.8 nm. Converting to energy, these are 2.87 eV and 1.96 eV, respectively. These are both higher than the band gap of GaAs and MoS2, which another group in the lab is studying. Exciting the electrons in the material with a laser with light with energy much higher than the band gap would cause the electrons to go very high in the band gap, and that extra energy would probably have to be lost in the form of heat, or the electrons might follow other unwanted pathways. Ultimately, the data produced might not be as nice. Of course, switching lasers meant realigning all the lenses and mirrors to focus the laser beam, which was time-consuming (and kind of annoying). The next step is to collect data using this laser, which I’ll discuss in a later blog. See you then!
Post 8: Blog 8: Laser power dependence
Welcome back! I started thinking about how I would complete my project goal of calibrating the cryostat. After talking to Dr. Smallwood again, I unfortunately came to the conclusion that I could not do this very well. However, he suggested that one possible source for the temperature displayed being inaccurate would be if the laser is heating up the sample and the thermometer not registering it, so to test this, we could collect a set of data with the laser hitting the sample at different brightness or power. So, we inserted a laser power meter and using a tunable neutral density filter in front of the laser, we can adjust how much of the laser we let through. After we adjust we take out the meter to collect photoluminescence and we repeat to collect a range of data for different laser powers. I extracted all the fits again (see blog 3 if you want to see more of this process, though it was more successful this time), and I saw that the peak positions did not change at all.
My other parameters changed which makes sense since greater laser power excites more electrons and we get more photoluminescence, and I kind of observed the decrease in intensity as I was taking the data. Ultimately, I think we can conclude that the laser does not contribute to any significant temperature increase unaccounted for. This experiment was done with the HeNe laser I talked about last blog, so we will do temperature-dependence with this one next to compare with our HeCd data. Stay tuned!
Post 9: Blog 9: Temperature dependence part 2
Welcome back! My teammates collected the temperature dependence with the HeNe laser when I was not there. I forgot to mention this last week, but I accidentally selected a different resolution on the spectrometer, meaning the range of wavelengths on the x-axis was smaller than when we got the data with the HeCd laser.
Because we don’t get much outside of the peaks, I thought it wouldn’t make much sense to apply a linear offset, and the slope I got was around 0.6 anyway. Before, it came from the AlGaAs peaks further to the left, but now I could not see the effects. I was in the middle of finding my fits when I noticed that this was not true for all the data.
So, I decided to start over and apply the Lorentzian with a linear offset fit to everything. After I found all the fits, I plotted the same data for peak position, peak width, and peak area.
I started comparing my results from the HeCd laser and the HeNe and trying to analyze my results, but I’ll leave that until my next blog. I also figured out how to combine my PL spectra and add a legend, so I’ll end this blog with some rainbow graphs for the HeCd, HeNe, and laser power in order (I did the colors manually!).
Post 10: Blog 10: Interpreting results
Hi everyone, welcome back! I kind of have been putting off interpreting my data because I wanted to learn more theory, but I have came to the conclusion that this is too hard for me and I probably need a couple more years of physics. So, I ended up relying on directly asking Dr. Smallwood and Luke (SJSU student) questions, though I tried to find what they said in papers, too. For the rest of this post, I’m going to put in data from using both the HeCd laser (fewer data points) and the HeNe laser (more data points) for peak position, width, and area, and then attempt to explain the trends.
Peak position
For this one, I also added a green line representing the band gap of bulk GaAs, graphing the equation from the Ioffe Institute, Eg=1.519-5.405·10-4·T2/(T+204) (eV). We can see an expected decrease in the band gap, which is very closely related to the peak position. Physically, this is because as temperature increases, atoms vibrate more, and the average interatomic distance increases. From this graph of the electronic bands in a material, we can see that the band gap decreases as the interatomic distance increases.
Peak width
We generally see an upward trend, except for the FWHM of the heavy hole from the HeCd data, which appears not to change, so further investigations may be needed for that. The increase can be explained by phonon broadening. As temperature increases, there are more vibrations in the material, and phonons are particle representations of the vibrations. Phonons can interact with the electron-hole pairs that are created in photoluminescence, causing the peaks to widen.
Peak area
As temperature increases, the higher energy in the material opens up more nonradiative pathways, which is why there is a general decrease in intensity, which peak area represents. However, we see the light hole increases at the beginning. This is because the heavy hole pathway is a lower energy change, which makes it preferred, especially at lower temperatures. At higher temperatures, both pathways even out.
Conclusion
Most of these results can be explained, so I think our setup is ready for new projects. We have already replaced the GaAs quantum well with a Sb2O3 sample. We are trying to do Raman spectroscopy with the same setup up though we needed to change a few things. It is not working so far.
I finished my presentation, got advice for how to improve it, and gave a presentation to my research group at SJSU at our weekly group meeting. Next blog will be my last one, and I’ll write some concluding thoughts. See you then!
Citations
Chetvorno. Solid State Electronic Band Structure. 10 Mar. 2017, Wikimedia Commons, https://commons.wikimedia.org/wiki/File:Solid_state_electronic_band_structure.svg.
“Band Structure and Carrier Concentration of Gallium Arsenide (GaAs).” Www.ioffe.ru, www.ioffe.ru/SVA/NSM/Semicond/GaAs/bandstr.html.
Gammon, D., et al. “Phonon Broadening of Excitons in GaAs/AlxGa1−XAs Quantum Wells.” Physical Review B, vol. 51, no. 23, 15 June 1995, pp. 16785–16789, https://doi.org/10.1103/physrevb.51.16785.
Houng, M. P., et al. “Broadening Factor due to Electron–Phonon Collisions in Semiconductor Quantum Wells.” Journal of Applied Physics, vol. 77, no. 12, 15 June 1995, pp. 6338–6344, pubs.aip.org/aip/jap/article-abstract/77/12/6338/528048/Broadening-factor-due-to-electron-phonon, https://doi.org/10.1063/1.359104.
Jiang, Dapeng, et al. “Temperature Dependence of Photoluminescence from GaAs Single and Multiple Quantum‐Well Heterostructures Grown by Molecular‐Beam Epitaxy.” Journal of Applied Physics, vol. 64, no. 3, 1 Aug. 1988, pp. 1371–1377, https://doi.org/10.1063/1.341862.
Post 11: Blog 11: Reflection
As senior projects have concluded, I wanted to talk a bit about this journey. I became interested in this field in general because of the summer camp I attended before junior year. My instructor there helped me connect with Dr. Smallwood. I was pretty certain since last year that I wanted to pursue a senior project, since it would give me extra guidance from BISV, and I am really grateful that I did not have to find a new external advisor.
However, my T3 looked quite different from what I expected. Including Disneyland, I went on 5 trips for college visits and other things, and while on those trips, I wasn’t motivated to spend any time on my project. Also, as college decisions were coming out, I wasn’t as nervous as some others, but I was struggling to focus after decisions were released, as I discussed them with my friends. Finally, I definitely had some senioritis. Working with students at SJSU, I started on this project in January, which helped a little, but ultimately, I was not able to get to the part of my project involving Sb2O3.
What I completed in my project also turned out differently from expected. At the beginning, I thought I would learn the physics to be able to do calculations to compare with my results, but I realized that to understand a little of just a few pages of textbooks or papers, I needed to reread it many many times, and I had no idea how to do anything myself. Hopefully if I keep taking physics classes in college I will be able to understand more of the theory involved in this field in the future.
I want to end by thanking all of the people who worked with me and guided me through this project. Without them, it would have been impossible. First, Dr. Smallwood, for providing me with resources and patiently teaching me. I would also like to thank Dr. Mo for giving me advice throughout. They helped me prepare, in my opinion, the best presentation I have ever given, even though I stumbled a bit in the middle. Thank you to Dr. Noble for advising me for a couple of weeks. I’m also grateful to my teammates Ayane, Luke, and Andre for answering my questions and working with me. Lastly, Mr. Cunningham for running this whole program.
Thank you to everyone who came to my presentation or read my blogs. Hopefully you learned something. That’s all from me for now!