Thermodynamic properties of two electrons quantum dot with harmonic interaction

We present a theoretical study of the effect of the Harmonic e-e interaction on the thermodynamic properties of one dimensional parabolic quantum dot. The energy spectrum for two electrons is obtained by solving the Schrödinger wave-equation analytically. These energy levels are employed to calculate the mean energy, heat capacity Helmholtz free energy and entropy of the quantum dot system using canonical ensemble approach. It is noted that for small values of temperature the mean energy increases slowly with temperature, but with further increase in temperature the mean energy becomes independent of interaction strength and it increases more rapidly. However the mean energy increasing monotonically with increasing confinement strength and this increase becomes linear in the weak confinement region. As a function of electro's separation it is found that initially the mean energy decreases with increasing the separation and the effect of temperature change is negligible but after a certain distance beyond which the effect of the change in temperature is noticeable on the mean energy and it displays an asymptotic behavior. As a function of confinement length. The mean energy is found to decrease with increasing confinement strength, but with further increase in confinement length the confinement effect on the mean energy becomes intangible when the dot size lo is as larger than 12 nm. It is observed that for small values of temperature heat capacity increases very rapidly and then tends to saturate with a value of 2kB as temperature increases. It is also shown that the effect of interaction strength on both heat capacity and mean energy is tangible at low temperature like T=10K an 20 K, and the effect becomes negligible at sufficiently high temperature values like T=30 and 40 K. The variation of entropy with interaction strength shows interesting behavior, it is noted that, in the low interaction strength region, entropy remains constant with interaction strength, while it begins to increase rapidly as the interaction strength increases where the effect of interaction potential becomes more and more pronounced. Also, to ensure the stability and confinement of the QD system F-T curves are drawn. It is shown that the greater the strength of interaction, the more stable the system will be. It is also shown that our approach has limitations in the applicability regarding to the quantum number Nmax and the separation of electrons inside a QD.