Temperature-dependent variations in donor binding energy in a pillbox quantum dot

This study investigates the influence of temperature (T) and dot size (H) on the binding energy (E<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</inf>) of a shallow donor impurity in a GaAs/Ga<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1−x</inf>Al<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</inf>As pillbox, enclosed by Ga<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1−y</inf>Al<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">y</inf>As. Via the variational method (VM) within the effective mass approximation (EMA), the analysis accounts for temperature-dependent changes in the electron effective mass (EEM), dielectric constant (DC), and Conduction band shift. Subband energies are computed using the finite difference method, while E<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</inf> of impurity is determined via the VM. Results highlight that T strongly influences the E<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</inf>, particularly for smaller quantum dots, with additional dependencies on Aluminum concentration and dot radius. These findings associate with existing literature and donate to a deeper understanding of quantum dot comportment under varying temperature conditions. Additionally, our conclusions are consistent with existing literature and provide meaningful insights into the physical properties of quantum systems under these conditions.