Combined effects of temperature and confinement on the Shannon entropy of two-dimensional hydrogenic impurity states in the GaAs semiconductor quantum well

Abstract

Understanding the quantum properties of two-dimensional (2-D) hydrogenic impurity states in the GaAs quantum well is essential for their applications in the semiconductor devices. Here, we report the combined effects of temperature and quantum confienment on the Shannon entropy of 2-D hydrogenic impurity states in the GaAs quantum well. First, by calculating the position and momentum space Shannon entropy (Sr and Sp), as well as the Shannon entropy sum (St), for the hydrogenic impurity states in the GaAs quantum well at room temperature, we show fascinating quantum confinement properties in the two conjugated spaces. Then, the effects of temperature on the Shannon entropy for different hydrogenic impurity states are examined and compared. Intriguingly, we discover that the Shannon entropy sum exhibits the property of translation invariance under the influence of temperature. Finally, with the radius of the quantum well fixed at a constant, we observe that the value of the Shannon entropy for a given quantum state is highly sensitive to the variations in temperature. While the size of circular quantum well is constrained by design parameters, such as the fabrication process and intended application, temperature adjustment emerges as a viable means to control the quantum properties of 2-D hydrogenic impurities in the quantum well. This research presents a pioneering method that employs temperature as a versatile tool for modulating the Shannon entropy of hydrogenic impurity states in the quantum well, and has potential applications in the field of semiconductor physics, material physics, chemical physics, etc.