Detecting Dark Matter via the Modeling of Plasma Frequencies of Ge Semiconductors using Fermi-Dirac Approximations through Variation of Temperature and Dopant Concentrations

By Omkar Arasaiah

Dark matter is the name given to the hypothetical form of exotic matter thought to comprise nearly 85% of the total matter of the universe, and about a quarter of the total mass-energy present. Dark matter is quite literally called “dark” since it does not interact with photons, the main constituent particle of electromagnetic radiation. Unfortunately for this exact reason, dark matter is impossible to detect through direct visual means, although this experiment aims to develop a novel method to detect these unknown particles through a phenomenon called the plasma frequency.

The plasma frequency is defined as the highest frequency in which a particle/wave can interact with a material. Similar to acoustic based resonance, the frequency of the input particle can resonate with the plasma frequency of the material and give off energy that we can detect. In order to detect these particles, a connection must be made between the particles being detected and the material detecting them firsthand. In conjunction with a property of semiconductors known as the Fermi-Dirac level, a specific particle can be detected given the proper constraints of the plasma frequency.

The Fermi-Dirac Level of a semiconductor is the point at which the number of electrons and acceptors (holes) equal each other and the intrinsic charge there is neutral. The novel approach to this phenomenon is linking it with the semiconductor’s plasma frequency and adjusting the properties of it to in turn adjust the plasma frequency, thus serving as a detector for a multitude of materials.

The goal of this experiment was to develop a program to calculate semiconductor properties by automatically varying conditions (temperature and dopant concentration) to find the Fermi-Dirac levels for the semiconductor. Then using the properties at that specific level, the program calculates the plasma oscillation frequency in which the material i.e. the semiconductor would electrically resonate with on the subatomic level. Given the frequency of the particles that we are looking for signs of, simply backtracking the program would present the exact temperature and dopant concentration necessary to create a semiconductor that would serve as a detector for the particles in question, in this case, dark matter particles.

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