Magnetic Properties of Doped Semiconductors in the Low Temperature Limit Kristopher Shuman Advisor: Dr. Adam C. Durst Department of Physics and Astronomy, Hofstra University, Hempstead, NY 11549 Overview Quantum computing is the future of cyber security and data encryption, and therefore quantum interactions are of utmost interest in the contemporary scientific community. Semiconductors, and particularly doped semiconductors, are of great interest to those who want to create a quantum computer, but the exact nature of the interactions for dopants isn’t fully understood. In our research, we sought to investigate the nature of acceptor-acceptor interactions in doped semiconductors by building off the foundation established by Bhatt and Lee in the 1980s. Bhatt and Lee studied donor-donor interactions and calculated the magnetic susceptibility of a “box” of randomly distributed spins as the temperature was gradually lowered. We expanded upon this research by studying three different models for acceptoracceptor interactions, with the third type being the most realistic model. Following a similar procedure to Bhatt and Lee, we developed a code in MATLAB that essentially creates a box of randomly distributed spins for a specific semiconductor and then calculates the magnetic susceptibility of the box as the temperature is iteratively lowered. This is done for all three interaction types for a selected number of initial spins, and then the data is graphed as a magnetic susceptibility versus temperature plot. It is of particular interest to compare the three types to each other to see how the different models behave in the low temperature limit. Our research offers three models for acceptor-acceptor interactions in doped semiconductors, and directly allows for the comparison of our magnetic susceptibility data to experimentally gathered data. In the event of such comparison, one could make judgements regarding the validity of our three models and theoretically pinpoint if one is an accurate description of reality. Thus, our work has a direct implication on the scientific community’s understanding of acceptor-acceptor interactions in doped semiconductors and may potentially influence the future of quantum computing depending on both experimental data and the way quantum computing develops.
Figure 3 https://phys.org/news/2020-08-google-largest-chemical-simulation-quantum.html
Implications Background Information A conductor is a type of material that permits the flow of electrons, whereas an insulator is a type of material that inhibits the flow of electrons. These electrons are the valence electrons of the constituent atoms from whichever material you are dealing with. In a semiconductor, the material has just enough energy at room temperature to allow for electrons to escape the atoms and flow. Therefore, a semiconductor may behave as a conductor at room temperature and as an insulator at lower temperatures.
Figure 1 Source: http://hyperphysics.phy-astr.gsu.edu/hbase/Solids/dope.html
Figure 2 Source: https://www.youtube.com/watch?v=cl7mutMHI0U&ab_channel=BhanudaySharma
Doping Semiconductors
Methods
We can modify the material properties of a semiconductor by adding physical impurities to it–which is called “doping” the semiconductor. When adding these impurities, you have the choice to either add donors, which contribute free electrons to the material, or acceptors, which create holes in the material. In Figure 1 we can see examples of both nand p- Type semiconductors, which are semiconductors doped with donors and acceptors, respectfully. On the left is a diagram of silicon doped with antimony, which is n- Type because antimony is a donor and contributes free electrons. On the right is a diagram of silicon doped with boron, which is p- Type because boron is an acceptor and creates a “hole”—which is the typical name for the absence of an electron.
To investigate the nature of acceptor-acceptor interactions in doped semiconductors, we developed a code in MATLAB that essentially creates a “box” of randomly distributed spins for a specified material. In Figure 2 one can see a representative diagram of the “box of spins” that our code creates; in this diagram, each red dot represents a single spin. We wanted to keep track of the interactions between all of these spins, and so we followed a similar procedure to that of Bhatt and Lee where we calculated the magnetic susceptibility at gradually decreasing temperatures. As we lowered the temperature, we would renormalize the high energy interactions and remove any interactions with energies that were either too high or too low. For an energy to be too high, it would have to have a value greater than the temperature as our process for lowering the temperature was based on setting our temperature at the strength of our strongest remaining interaction. We would calculate these magnetic susceptibility values at various temperatures for all three types for a set number of initial spins, and then graph this data as a magnetic susceptibility versus temperature plot.
Our research gathers data regarding the magnetic susceptibility of various semiconducting materials as a function of temperature. We have three models for the acceptor-acceptor interactions that take place in our “box of spins”, and this allows for comparison with experimentally gathered data for these same semiconducting materials. In the event of such comparison, the validity of our three models can be evaluated and one can deduce if any accurately matches up with reality. Therefore, our work will have a direct implication on the scientific community’s understanding of acceptor-acceptor interactions in doped semiconductors. Furthermore, there is the potential that our research will influence the development of quantum computers in the future depending on both experimental data and the way quantum computing develops. Currently, quantum computers are being developed globally with various quantum systems playing the role of a qubit. There is interest in quantum computing because it theoretically should be able to perform certain calculations much faster than regular computers due to the quantum mechanical properties of the qubits that allows multiple operations to be done at once. Our research with acceptoracceptor interactions will help push forward our general understanding of what’s physically happening in these semiconductors, and this may potentially open some doors in the development of quantum computers.
Literature Cited Bhatt, R. N., and P. A. Lee. “Scaling Studies of Highly Disordered Spin-½ Antiferromagnetic Systems.” Physical Review Letters, vol. 48, no. 5, 1982, pp. 344–347., doi:10.1103/physrevlett.48.344.